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Experimental studies of the delamination mechanisms in impacted fiber-reinforced composite plates

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Title:
Experimental studies of the delamination mechanisms in impacted fiber-reinforced composite plates
Creator:
Takeda, Nobuo, 1952-
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Language:
English
Physical Description:
xiv, 184 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Composite materials ( jstor )
Crack propagation ( jstor )
Delamination ( jstor )
Fracture mechanics ( jstor )
Impact damage ( jstor )
Kinetic energy ( jstor )
Laminates ( jstor )
Specimens ( jstor )
Velocity ( jstor )
Wave propagation ( jstor )
Dissertations, Academic -- Engineering Sciences -- UF
Engineering Sciences thesis Ph. D
Fibrous composites -- Mathematical models ( lcsh )
Plates (Engineering) -- Mathematical models ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1980.
Bibliography:
Bibliography: leaves 175-183.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Nobuo Takeda.

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EXPERIMENTAL STUDIES OF THE DELAMINATION MECHANISMS
IN IMPACTED FIBER-REINFORCED COMPOSITE PLATES










BY

NOBUO TAKEDA


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY










UNIVERSITY OF FLORIDA


1980




































To my parents,

Wasaburo and Aiko Takeda















ACKNOWLEDGEMENTS

The present investigation was part of a three-year effort, under

Army contract DAAG29-79-G-0007 to study fracture mechanisms in centrally impacted composite laminates, and the assistance and financial support of U.S. Army Research Office, Durham, North Carolina, and the program monitor, Dr. Y. Horie, are gratefully acknowledged.

The author's graduate study at the University of Florida was supported financially by the Japan Society for the Promotion of Science, and the support by JSPS and the program monitor, Ms. Audrey Harney, International Institute of Education-Atlanta, is appreciated.

The author sincerely appreciates the efforts of his supervisory committee chairman, Dr. Robert L. Sierakowski and co-chairman, Dr. Lawrence E. Malvern, whose assistance went far beyond that required by their position. For their constant encouragement and advice, and for their guidance and teaching, the author is greatly indebted.

Special appreciation is extended to Dr. Ulrich H. Kurzweg, Dr. Chang-Tsan Sun, and Dr. Ellsworth D. Whitney, for their assistance, support, and for serving on the supervisory committee.

The author would like to gratefully acknowledge the continuous support and encouragement of Dr. Kozo Kawata, the author's adviser at the University of Tokyo, who provided the opportunity to study in U.S. on leave from the University of Tokyo.

The author thanks the department technical staff for their help in carrying out experiments and the department office staff for their kind assistance with administrative problems and clerical support.

iii








Finally, special thanks are directed to the author's friends both in the U.S. and in Japan who understood and supported what the author wanted to do.















TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS .......... ......................... iii

LIST OF TABLES ........... .......................... vii

LIST OF FIGURES ........... ......................... viii

ABSTRACT ............. ............................ xii

CHAPTER 1 INTRODUCTION .......... .................... 1

1.1 Motivation of the Research .... ............... . 1
1.2 Impact Problems of Continuous Fiber-Reinforced
Composite Materials (FRCM) ....... ................ 2
1.3 A Historical Review of Prior Research on Impact
Problems of FRCM .......... .................... 3
1.4 Localized Impact Problems of Composite Laminates . ... 8
1.4.1 Localized Impact Damage Experiments ..... . . . 8
1.4.2 Solution of Simplified Wave Propagation
Problems Based on Continuum Mechanics Models 11
1.4.3 Hertzian Contact Approaches to Impact Problems 14
1.5 Experimental Studies on Fracture Mechanisms of
Impacted Composite Laminates at the University of
Florida ......... ........................ 15
1.6 Composition of the Dissertation ... ............ 20

CHAPTER 2 LAMINATED PLATE SPECIMEN FABRICATION .. ........ .. 22

CHAPTER 3 EXPERIMENTAL IMPACTOR/PLATE CONFIGURATION
INTERACTION STUDIES ..... ................ 30

3.1 Introduction ........ ...................... . 30
3.2 Experimental Procedure ...... ................. . 30
3.3 Studies on Impactor Nose Shapes and Length Effects . . . 31
3.3.1 Purpose of the Studies ... ............. . 31
3.3.2 Fracture Patterns ...... ............... .. 37
3.3.3 Delamination ...... .................. 43
3.3.4 Transverse Cracks ...... ............... . 49
3.3.5 Contact Time Measurement ... ............ 57
3.4 Studies on Ply Orientation Effects ... ........... . 60

CHAPTER 4 MICROSCOPIC OBSERVATIONS OF CROSS SECTIONS OF
IMPACTED COMPOSITE LAMINATES ... ............ . 64

4.1 Introduction ........ ..................... . 64
4.2 Sample Preparation ....... ................... . 65
4.3 Results and Discussion ...... ................. . 69








TABLE OF CONTENTS (Continued)


Page


EXPERIMENTAL WAVE PROPAGATION STUDIES OF IMPACTED
COMPOSITE LAMINATES USING STRAIN GAGES . ....... . 83

Introduction ........ ...................... 83
Experimental Procedure and Consideration .. ........ . 84
Documentation Tests for Characterizing Embedded Gages . 86 Strain-Gage Results and Discussion ... ........... . 88
5.4.1 Surface-Gage Results for [(0�)5/(900)5/(0.)5]
Laminates ........ ................... 88
5.4.2 Surface- and Embedded-Gage Results for [(00)5/
(900)6/(00)51 Laminates ..... ............. .109
5.4.3 Surface-Gage Results for [(30�)5/(-30�)5/(30�)5]
Laminates ........ .................... 115

EXPERIMENTAL CRACK PROPAGATION STUDIES OF IMPACTED
COMPOSITE LAMINATES ...... ................. .121


6.1 Introduction ....................
6.2 Delamination Crack Propagation Studies Using a HighSpeed Camera ....................
6.2.1 Experimental Procedure ..... .............
6.2.2 Results and Discussion ..... ............
6.3 Measurement of Generator Strip Formation Velocities .
6.3.1 Experimental Procedure ..... .............
6.3.2 Results and Discussion ..... .............


CHAPTER 7


SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS FOR FUTURE WORK ........ ....................


7.1 Summary and Conclusions ....... .................
7.2 Recommendations for Future Work ..... .............


* . 121

* . 122
* . 122 . . 123
* . 150
* . 150
* . 150


* 159

* 159 165


APPENDIX A APPENDIX B


CALCULATION OF THE THEORETICAL WAVE PROPAGATION VELOCITIES IN IMPACTED LAMINATES .... .......... .168


CALCULATION OF THE RATIO OF PEAK STRAINS ALONG X AND Y AXES ......... ....................


LIST OF REFERENCES .......................


173 175


BIOGRAPHICAL SKETCH .......... ........................ .184


CHAPTER 5


5.1 5.2 5.3 5.4








CHAPTER 6


Q














LIST OF TABLES


Table Page

2.1 Details of processing materials and instruments for laminated plate specimen fabrication .... ............ ... 27

3.1 Impactors used in this study ...... ................ ...36

4.1 Supplies used in the sample preparation for SEM observation .......... ........................ ... 67

5.1 Average modulus and critical stress acr measured in the four types of specimens and the corresponding calculated
values .......... ........................... ....88

5.2 Peak strains and strain rates measured from gages along the x-axis and y-axis for Gage layout (c) ....... . 101

5.3 Wave propagation velocities, and peak strains and strain rates measured from gages along the y-axis for
Gage layout (e) ......... ...................... . 109

6.1 Generator strip formation velocities .... ............ . 151

A.1 Static properties of Scotchply 1002 matrix and E-glass fibers at room temperature ...... ................. ...171














LIST OF FIGURES


Figure Page

1.1 A generator strip and two delamination areas in a plate with three five-layer laminas ...... ................ ...19

1.2 Schematic of three sequential delaminations .. ......... ...19

1.3 Total delamination area versus impactor kinetic energy for plates with five three-layer laminas and plates
with three five-layer laminas ...... ................ ...19

2.1 Baron Model BAC-24 autoclave ................ 23

2.2 Layup system for prepreg tapes ..... ............... ...24

2.3 The sequence of fabrication of composite laminate specimens . 25 3.1 Schematic of gas gun assembly and related equipments . ... 32 3.2 A gas gun and its control valves ..... ............. ...33

3.3 The velocity measuring system ........ ................ 33

3.4 A target plate clamped by a metal frame specimen holder . . . 34 3.5 Specimen holder assembly installed inside a protective box . 34 3.6 Schematic of impactor contact time measurement . ....... ...35

3.7 Photographs of [(0) 5/(90*)5/(0O)5] laminates impacted by various types of impactors .. ....... .............. ..38

3.8 Schematic of fracture patterns and deformations of laminates impacted by two different types of impactors .. ........ .42

3.9 Total delamination area versus initial impactor kinetic energy for [(0) 5/(900)5/(00)5] laminates ... .......... . 44

3.10 Mean transverse crack distance v.s. impactor velocity for
[(0) /(90) 5/(0) 51 laminates impacted by various types of
impact ors . . . . . . . . . . . . . . . . . . . . . . . 53

3.11 Typical oscilloscope records for contact time measurement . 58 3.12 Contact time versus impactor velocity .... ............ . 59

3.13 Total delamination area versus impactor kinetic energy for
angle-ply laminates ......... .................... ...60


viii








LIST OF FIGURES (Continued)


Figure


3.14 Schematic of delamination pattern in [(+6)5/(-e)5/(+6)5]
angle-ply laminates ........ ......................

4.1 Joel JSM-35C scanning electron microscope ... ...........

4.2 Typical fracture patterns of a [(0�)5/(90�)5/(0�)5] laminate
impacted by 2.54 cm blunt-ended steel projectile at a velocity of 75.1 m/sec (246.5 ft/sec) ..... ...............

4.3 Schematics of several cross sections of the laminate shown
in Fig. 4.2 .......... ..........................

4.4 An undamaged interface of a [(0�)3/(90�)3/(0�)3/(90�)3/(0�)3] laminate . . . . . . . . . . . . . . . . . . . . . . . . . .

4.5 Typical SEM pictures of cross sections of a [(00)5/(90�)5/
(00)5] laminate impacted by a 2.54 cm blunt-ended steel
projectile at 75.1 m/sec ..................
4.6 Tensile and shear stresses developed in the transverse
lamina . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.1 Recording setup for strain-gage experiments ... .........

5.2 Tensile test coupons tested in documentation tests for
characterizing embedded gages ...... ............... .

5.3 Surface-gage layout for [(0)5/(90�)5/(0*)5] fiberglass/
epoxy laminates ......... ........................
5.4 Strain-gage outputs from surface gages with Gage layout (a)

in Fig. 5.3 .......... .....................

5.5 Schematic of the impacted plate response ..........

5.6 Strain-gage outputs from surface gages with Gage layout (b)
in Fig. 5.3 .......... ..........................

5.7 Strain-gage outputs from front surface gages with Gage layout (b) in Fig. 5.3 ...................

5.8 Strain-gage outputs from front surface gages with Gage layout (c) in Fig. 5.3 ...................

5.9 Strain-gage outputs from surface gages with Gage layout (d) in Fig. 5.3 .......... ..........................

5.10 Strain-gage outputs from front surface gages with Gage
layout (e) in Fig. 5.3 ..................

5.11 Surface- and embedded-gage layout for [(0�)5/(900)6/(00)51
fiberglass/epoxy laminates .................

ix


100 101


105 108 ill


Page








LIST OF FIGURES (Continued)


Figure Page

5.12 Strain-gage outputs from surface- and embedded-gages with
Gage layout (a) in Fig. 5.11 ...... ................ ...112

5.13 Strain-gage outputs from surface- and embedded-gages with
Gage layout (b) in Fig. 5.11, and the contact time record . 114

5.14 Surface-gage layout for [(30)�5/(-30O)5/(30')5] fiberglass/
epoxy laminates ........... ....................... 116

5.15 Strain-gage outputs from surface gages with Gage layout (a)
in Fig. 5.14 .......... ........................ .117

5.16 Strain-gage outputs from surface gages with Gage layout (b)
in Fig. 5.14 .......... ........................ .119

6.1 Setup of a Nova Model 16-3 16 mm high-speed camera ...... .123

6.2 The overall experimental setup for measuring delamination crack propagation velocities using a high-speed camera . . . 124

6.3 Sequence of delamination crack propagation in a [(0�) / (90�)5/(0*)5] laminate impacted by a 2.54 cm blunt-enaed
impactor at 74.5 m/sec (244.4 ft/sec) .... ............ .125

6.4 Sequence of delamination crack propagation in a [(0�) / (9Q0)5/(Q0)5] laminate impacted by a 2.54 cm blunt-enaed
impactor at 83.2 m/sec (273.0 ft/sec) .... ............ .128

6.5 Sequence of delamination crack propagation in a [(0) 5/ (90*)5/(00)51 laminate impacted by a 2.54 cm hemispherical
impactor at 75.5 m/sec (247.6 ft/sec) .... ............ .131

6.6 Sequence of delamination crack propagation in a [(00) / (90�)5/(0')5] laminate impacted by a 5.08 cm blunt-ended
impactor at 58.8 m/sec (192.8 ft/sec) .... ............ .136

6.7 The resultant fracture appearance of impacted [(0�)5/(900)5/
(0o)5] laminates in Figs. 6.3-6.6 ..... ............. ..142

6.8 Distance of the propagating delamination crack tip from the plate center as a function of time AT after the first frame
where delamination appears, calculated from photographic data
in Figs. 6.3-6.6 ......... ...................... .146

6.9 Delamination crack propagation velocities in impacted [(0*)5/(90)�5/(0)5] laminates, calculated from photographic
data in Figs. 6.3-6.6 ........ .................... .147

6.10 Modified velocity gage arrangement .... ............. ..152








LIST OF FIGURES (Continued)


Figure Page

6.11 Voltage-time records for measurement of generator strip
formation velocities ............................. .153

6.12 Distance of the propagating generator strip tip from the
plate center as a function of time AT after the first
stripe is broken ......... ...................... .157















Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy EXPERIMENTAL STUDIES OF THE DELAMINATION MECHANISMS
IN IMPACTED FIBER-REINFORCED COMPOSITE PLATES

By

Nobuo Takeda

August, 1980


Chairman: Robert L. Sierakowski Co-Chairman: Lawrence E. Malvern
Major Department: Engineering Sciences

Experimental studies of the fracture mechanisms in centrally impacted fiber-reinforced composite laminated plates have been systematically conducted. Semitransparent specimens were fabricated from fiberglass/epoxy prepreg tapes with an autoclave. A cross-ply arrangement with 3 laminas each containing 5 unidirectional layers was studied unless otherwise stated. Macroscopic observations of impacted laminates, which revealed the impactor/laminate configuration interactions, have been supplemented by microscopic observations of cross sections of impacted laminates with a scanning electron microscope. Dynamic strains induced by impact of

2.54 cm blunt-ended impactors on laminates were measured using both surface and embedded gages with several different gage layouts. High-speed photos for semitransparent impacted laminates were taken from the back of the laminates illuminated from the front side. A Nova high-speed camera recorded rapid delamination crack propagations at speeds up to 40,000 frames/sec.








According to macroscopic observations, the impactor energy was more dissipated within the front lamina and damage was more widely spread there with blunt noses than with hemispherical noses. Sequential delamination mechanisms were identified for all types of impactors tested. The larger impactors have a 30 percent higher apparent delamination surface energy than the smaller ones. So-called transverse cracks in the fiber direction of each lamina showed an almost evenly distributed crack spacing. The mean crack spacing decreased as the impactor velocity increased. According to contact time measurements, both single and multiple contacts were possible. The heavier and/or faster impactors had longer contact times.

Microphotos revealed such details as that the transverse cracks obtained travel perpendicular to lamina interfaces where there is no delamination, while they travel oblique to interfaces where accompanied by delamination.

Strain-gage records showed that the predominant wave was a flexural one for the tested velocity range, 30-40 m/sec. The largest amplitude of the flexural wave had on the average a measured velocity at 3.81 cm from the plate center of 290 m/sec and 225 m/sec in the 00 and 90� direction, respectively, with a decrease in velocity with distance from the impact point. Measured in-plane and flexural wave velocities agreed well with the calculated values obtained from known material elastic constants.

High-speed photos revealed that: The delamination crack in the

90o000 direction at the first[second] interface propagated initially at 300-400[400-500] m/sec which decreased to 200-300[270-400] m/sec during the period of observation, and decelerated to stop at about 1001300] microseconds. This latter velocity agreed well with the largestamplitude flexural wave velocity measured by the strain gages. This xiii









appears to be further documentation that delamination is caused by the flexural wave. Some transverse cracks were found to propagate while' the delamination cracks propagated in several recorded photos. This is further evidence that transverse cracks and delamination cracks occur almost simultaneously, along with oblique transverse cracks and sudden jumps in strain-gage signal records. Transverse cracks are considered to be caused by membrane tensile waves due to a large deflection of the plate.

A velocity gage consisting of a silver conductive paint was modified to measure velocities of the generator strip development. This generator strip formation velocity was found to be higher than the measured delamination crack propagation velocity. This fact is consistent with the assumption that the generator strip generates delamination cracks.















CHAPTER 1

INTRODUCTION

1.1 Motivation of the Research

In recent years, fiber-reinforced composite materials (FRCM) have attracted considerable attention for practical use because of their high strength-to-weight and/or stiffness-to-weight ratios when compared with conventional monolithic materials [1]. This is particularly true in the aerospace area where advanced developments and usage of component parts made with FRCM are continuously being made. Other commercial usage such as in the sporting goods area for fishing rods, golf clubs, and tennis rackets has also been evident. Most recent usage has begun in the automotive sector of the economy where products made with sheet molding compounds (SMC), that is, chopped fibrous type composite materials have appeared. Our interest here is focused on continuous fiber composites. Therefore, FRCM will hereafter define continuous fiber-reinforced composite materials unless otherwise specified.

Despite the known advantages of high static strength, high stiffness, and low weight of FRCM, knowledge of the impact resistance of such materials is rather scarce. As a specific example of the importance of this problem, FRCM used in turbine blades in jet engines may be damaged during take-off and flight by ingestion of stones, ice balls, birds, and other foreign objects [2]. This foreign object impact damage (FOD) problem has attracted much attention recently. Another example is the delamination failure of relatively thick laminates in actual large-size fiberglass-reinforced plastic boats exposed to impacts produced by ocean








waves and often susceptible to delamination. The seriousness of these problems has accentuated the need for a better understanding of the impact damage tolerance of such FRCM [3].

1.2 Impact Problems of Continuous Fiber-Reinforced Composite Materials

(FRCM)

Impact problems differ from static problems in several ways [4]. One is the necessity for considering stress wave propagation in the material. In static problems the deformation energy can be distributed throughout the structure, but in impact problems the volume of energy storage is limited by the speed of the wave propagation. For short time impact loads, even a small amount of energy in a small volume can result in stresses which can fracture the material. A second important consideration is the strain rate the material is subjected to. It is known that both the fibers and matrices of FRCD have different strength properties under high strain rates from those under lower strain rates (5].

Composite materials have as inherent properties anisotropies and inhomogeneities, which need special attention for the design of an impact resistant structure. In composite materials the degree of anisotropy can be varied so that the designer can change the directional distribution of stress waves in an impact zone and avoid serious failure. For example, inhomogeneity introduces certain material discontinuities which produce dispersive effects as the stress pulse propagates within the medium.

When compared with observed damage in conventional materials, the damage or failure of composite materials has different characteristics. Various failure mechanisms have been observed, such as fiber pull-out, debonding between fibers and matrix, plastic deformation of the matrix,








delamination, breakage of fibers, and so on [6,7]. This variety of failure mechanisms causes many difficulties in programming experiments and establishing meaningful analyses.


1.3 A Historical Review of Prior Research on Impact Problems of FRCM

Initial analytical studies dealing with the dynamic properties of composite materials have been based upon some type of continuum model to describe the composite material response. Some experiments have also been conducted to evaluate these proposed modeling theories. A review of many of these have been noted by Peck [8] and Hegemier [9] and include: (1) effective modulus theories [10,11], (2) effective stiffness theories [12], (3) mixture theories [13,14], (4) theories of micromorphic continua [15), (5) modified dislocation theories [16], (6) viscoelastic analogies [17], and (7) continuum theories with a microstructure based upon asymptotic expansions [9,14,18]. Due to mathematical complexity these theories have in general been restricted to problems of harmonic wave propagation in infinite or semi-infinite media, or to problems with planar motions. As a consequence of these complexities, structural analysts have continued to study structural (plate and shell) configurations using theories based upon the traditional assumptions. These approaches are reviewed in Sections 1.4 and 1.5.

The impact testing of composite materials encompasses a variety of loads and specimen conditions. Many impact test methods have been developed for evaluating materials toughness or resistance to fracture [4,19].

The most common and classical Charpy and Izod tests use relatively small beam-like specimens (less than 3 in. long) under a transverse point force at low impact velocities (less than 5 m/sec) and give a qualitative energy to fracture.








For example, Chamis et al. [20] performed miniature-Izod impact

tests on unidirectional fiber composites of glass, graphite, boron, and Kevlar fibers in an epoxy resin matrix, with the fibers either parallel or transverse to the cantilever longitudinal axis. Three prevalent failure modes were observed for longitudinal fiber arrangements. These were cleavage, cleavage with fiber pull-out, and cleavage combined with partial delamination due to interlaminar shear failure. The transverse failure mode was cleavage. The fracture surface included matrix fracture, fiber debonding, and some fiber splitting.

Novak and DeCrescente [21] have performed Charpy impact tests for unidirectional graphite, boron, and glass fibers embedded in a resin matrix and tested in the fiber direction. The impact strength of the glass fiber composites was found to be significantly higher than that of either the boron or the graphite composites. They found that the tensile stress-strain characteristics of the fibers are of primary importance in determining the level of composite impact resistance and that toughness of the resin does not appear to be an important factor.

Toland [22] has used an instrumented Charpy testing machine to record the stress and strain in the specimen during impact, and cited the importance of differentiating between the energy absorbed elastically and that absorbed during the failure process. He also reported the dependence on specimen thickness of maximum load, initial energy, and total energy absorbed.

Adams and Perry [23] also used an instrumented Charpy machine in conjunction with a scanning electron microscope (SEM) for studying the resulting fracture surfaces.

Beaumont et al. [24] in running instrumented Charpy tests have established the terminology associated with the energy to the peak load as the








initial energy, the energy absorbed after the peak load as the propagation energy, and the ratio of propagation energy to initiation energy as the "Ductility Index." They proposed to use this parameter in conjunction with the maximum impact stress and total impact energy for characterizing impact behavior.

Adams [25] summarized and discussed Charpy test results of composite materials. He categorized the contributors and their data into general classifications with representative experimental results being included to emphasize the conclusions presented. The topics he discussed included the use of scanning electron microscopes, advantages of hybrid composites, layup patterns, notch insensitivity, specimen thickness, impact velocity, and "Ductility Index."

Limitations to the aforementioned test methods lie in their inability to provide meaningful data on the material properties [4, 19]. The measured value of impact energy is not a material property but influenced by the size and geometry of the specimen and test arrangement. In other words, such test data cannot be used directly when designing a real composite structure.

A second method that has been used to study impact strength of FRCM is the drop test method. Rotem and Lifshitz [26] measured longitudinal tensile strengths of unidirectional FRC4 over a wide range of strain rates
-1)
(5< <30 sec ). Stress and strain were measured with strain gages bonded to a load cell and to the specimen. The recorded dynamic tensile strength values of FRCM with loading times of the order of a few milliseconds were more than twice that noted from static test data.

As a combination of the previous two methods, Broutman and Rotem [27] used the drop weight impact test for studying beam specimens of various unidirectional and cross-ply glass fiber laminates. They showed that the








orientation of the lamination planes with respect to the impact load is important and determines the failure mode as well as the impact energy. Lifshitz [28] used the same technique to measure tensile strength of angle-ply FRCM.

A third method which also used the drop weight was developed by Kimpara and Takehana [29]. A special impulsive inertia loading test device was used in order to measure the interlaminar strengths in separate failure modes (interlaminar shear and tension) for various constant stress rates (5 to 45 GNm-2/sec). In this case, the maximum observed interlaminar shear and tensile strengths were taken as the fracture criteria.

A fourth dynamic test method is the flyer plate technique which produces almost unidirectional strain in the specimen by impacting a flyer plate against a specimen. The pulses generated are of extremely short duration (0.12-0.22 psec) and the impact velocities are high (up to 2400 m/sec). When the compressive wave front encounters the free back surface of the composite specimen, it is reflected as a tensile wave which may cause spalling of the specimen at some distance away from the back surface.

Schuster and Reed [30] used this method to study internal damage and failure mechanisms of aluminum alloy laminates reinforced with boron filaments. Reed and Schuster [31] ran additional tests to note the filament fracture inside the composite specimen tested with momentum traps to suppress spall and measured the post-impact tensile strength of the materials tested. The literature on spall fracture in composites using one dimensional shock waves has been reviewed by Peck [8].

In the last three methods, the stress and/or strain state can be considered unidirectional and the strength (maximum stress) of each








fracture mode can be measured in contrast with the Charpy and Izod tests which result in highly localized impact which causes a very complex stress state and difficulties in ability to measure the fracture energies.

An alternate test method used for studying dynamic effects in composites is by impacting FRCM specimens with various projectiles which are fired from air guns over an extended velocity range (up to 500 m/sec). In contrast to the previous flyer plate technique, impact takes place over a small area in this type of impact test. Another significant difference between these test methods is the length of pulse generated during the impact event. The flyer plate technique produces extremely short pulses which are rapidly dispersed by the relatively large diameter fibers generally considered. The localized impact technique, however, produces pulses of much longer duration (longer than 100 Psec) and less affected by the relatively small diameter fibers embedded in the matrix. This localized impact technique leads to a complicated stress state. However, the merit of this test technique is the ability to stimulate such actual impact problems as the previously described FOD problems of turbine blades. The main research discussed herein deals with such localized impact problems of composite laminates, and this technique is reviewed in the following section.

As discussed earlier, scale effects are of importance in impact

tests if test data are to be extrapolated and applied to larger structures. For example, if a plate is part of a large structure fewer reflections might be obtained than in a small test specimen. Moon [4] recommended the nondimensional parameter

VT
L

where T is the contact time, V is a wave speed, and L is a representative








length. It was suggested that this parameter should be matched in addition to other variables in order to compare different experimental data.


1.4 Localized Impact Problems of Composite Laminates

The localized impact problems of beams and plates of homogeneous and isotropic elastic materials have been studied quite extensively and summarized by Goldsmith [32] and Backman and Goldsmith [33]. An equivalent study of similar problems for structures of composite materials has only recently been the center of considerable research activity. Generally composite material problems have been studied from three different points of view.

1. Localized impact damage experiments.

2. Solution of simplified wave propagation problems

based on continuum mechanics models.

3. Hertzian contact approaches to impact problems.


1.4.1 Localized Impact Damage Experiments

Some of the early experimental studies dealing with the impact

resistance and penetration characteristics of FRCM were run on locally impacted composite plates. Gupta and Davids [34] have studied the penetration resistance of fiberglass cloth/polyester plates of varying thickness and density. They found a linear relation between the energy loss in penetration and the thickness, a linear relation between the impact energy and the thickness of plates required to just stop the projectile, and a relation between the density and the stopping thickness. They found that the weight efficiency of fiberglass cloth is greater than that of steel.

Morris and Smith [35] observed noticeable internal damage in fiberglass laminated plates tested at very low impact energy levels without








noting any apparent surface damage. They also measured the residual tensile and four-point bending strengths of impacted specimens. The resultant internal damage, delamination or debonding and/or fiber breakage was found to reduce strength significantly particularly in bending.

Some further investigation on the impact resistance of fiberglass/ epoxy plates reinforced with wire sheet were conducted by Wrzesien [36]. The wire reinforcement gave a significant improvement in composite impact resistance and better damage containment. It was noted that plates with apparently good penetration resistance were heavily delaminated indicating that a considerable amount of impact energy was absorbed by the delamination.

Askins and Schwartz 137] reported that a two-stage failure mode consisting of extensive delamination followed by tensile loading of individual laminas increased energy absorption in composite backup panels for ceramic armor. They conjectured that the tensile loading stage was the major energy absorbing mechanisms in their tests but that extensive delamination was needed to prevent "plugging" of the panel and to permit more of the panel to participate in the impact event and contribute to energy dissipation. Test results indicated that for such applications fibers should have low density, high tensile strength, high stiffness, and low interfacial bond strength.

The effects of preload and of ply layups for graphite/epoxy and boron/epoxy laminated plates on composite penetration characteristics, particularly the residual strength and the threshold strength, have been examined by Francis et al. [38] and Olster and Roy [39]. Francis et al. used a biaxial preloading which produced a variety of failure patterns for transverse impacts. Olster and Roy showed that the residual strength








and the threshold strength correlate directly with the fracture toughness of the laminates. They also measured the propagation velocities of cracks which initiated from projectile holes and found the cracks traveled at approximately 55 percent of the shear wave velocity for each of the materials tested.

Some residual strength studies of advanced composites have been made [4U-42]. Avery and Porter [40] compared the residual strength and damage size for metals as well as for boron/epoxy and graphite/epoxy composites. Suarez and Whiteside [41] also compared the residual and impact fracture strengths of boron/epoxy composites with metals. Husman et al. [42] studied the residual strength of boron, graphite, and glass/epoxy laminates and discussed an analogy between damage inflicted by a single-point hard particle impact and damage by inserting a flaw of known dimensions in a static tensile coupon.

Preston and Cook [43] observed the damage of graphite/epoxy cantilever panels caused by impacting spherical projectiles of gelatin, ice, and steel. Steel projectiles were found to have the lowest damage threshold. A hertzian analysis showed small steel projectiles were most likely to cause delamination and penetration damage.

Kawata and Takeda [44] conducted foreign projectile impact experiments on glass roving cloth/polyester laminated plates consisting of three laminas. They found that below the perforation speed, the dominant energy absorbing fracture mechanisms were delamination between laminas and debonding occurring between fibers and matrix. It was also shown that the total damaged area and the initial kinetic energy have a linear relation.

Gorham [45] used high-speed photography to examine and explain some

features of the fracture behavior of fibrous and laminated composite plates.








The semitransparency of the materials selected for testing enabled internal failure to be examined photographically. Both commercial and model composite systems were loaded at very high rates of strain by highspeed water impact as well as hard body impact. In particular, lamina model experiments suggested the initiation of shear along a lamina interface by waves which produced frontal delamination in the laminates.

Impact tests on full-scale laminated turbine blades have also been carried out by the engine manufacturers [46-48]. Impactors used for these studies include gravel, ice, steel, gelatin, and real birds.

Experimental studies on failure mechanisms of impacted composite laminated plates [49-56] have been conducted intensively at the Department of Engineering Sciences, University of Florida, for several years. These studies are the basis of the present research and are reviewed separately in Section 1.5.


1.4.2 Solution of Simplified Wave Propagation Problems Based on
Continuum Mechanics Models

Theoretical analyses of wave propagation in transversely impacted composite laminates have been discussed by many investigators [57-67] with only a few experimental investigations having been reported [60, 68].

A laminated plate theory developed by Yang et al. [57], which includes both thickness shear deformation and rotary inertia, was investigated by Whitney and Pagano [58], who solved several boundary value problems.

Using a similar laminated plate theory, Chow [59] derived the dynamic equations for orthotropic laminated plates. The propagation of flexural waves and the transient response of a rectangular plate to a normal impact were investigated. The effect of transverse shear on the amplitude of the deflection was evaluated in this dynamic study of anisotropic composites.






12

Chou and Rodini [60] have demonstrated the accuracy of the laminated plate theory in transient wave propagation problems, comparing experimental measurements with theoretical calculations. The experimental program consisted of impacting the edge of a specimen plate with a striker plate. Each specimen was subjected to two separate impact loadings; an in-plane impact and a so-called shear-bending impact. The analytical phase consisted of solving the Whitney and Pagano equations by the method of characteristics.

Sun and Lai [61] later demonstrated the adequacy of the lamination theory, comparing the more exact orthotropic elastic solution with the lamination theory solution, using the fast Fourier transform (FFT) technique.

A series of analytical investigations on transient wave propagation have also been reported by Moon [62-66]. Moon [62] investigated the shape of wave fronts of an infinite laminated plate subjected to both transverse and central impact loads. The mathematical model used for the plate element analyzed was based on the effective modulus theory for composites [4] and Mindlin's theory for plates in which the displacement is expanded in the thickness variable by using Legendre polynomials. The velocity and wave surface were described as functions of the layup angles for the graphite/epoxy plates examined.

In following papers, Moon [63,643 studies the one-dimensional stress and displacement distribution induced in the same model by impact line forces, using the fast Fourier transform (FFT) technique. Moon [64,65] also gave a two-dimensional analysis which results in five two-dimensional stress waves. Three of the waves are flexural and two involve in-plane extensional strains. Results obtained using this analysis indicate that the points of maximum stress travel along the fiber directions. It was








shown that for � 15 deg. angle-ply layups lower flexural stresses are generated than for 0, �30, and �45 deg. cases.

In a recent paper, Kim and Moon [66] modeled a multilayer composite plate as a number of identical anisotropic layers with Mindlin's theory then applied to each layer in order to obtain a set of differencedifferential equations of motion using the interlaminar stresses and displacements as explicit variables. Propagation of waves through the plate thickness was also examined in a simple way. This problem was also then extended to examining the effect of introducing damping layers between two elastic layers.

Kubo and Nelson [67] presented an analytical study of the twodimensional (plane-strain) response of an elastic laminated plate, using a finite element/normal mode technique. The physical behavior of the plate was represented along the in-plane length of the plate in the form of a Fourier series, and its behavior in the thickness direction modeled by a sufficiently large number of generalized coordinates to capture quantitatively the propagation and dispersion of stress waves due to a surface impact. This technique produced both high frequency and low frequency information for both long and short wavelengths with respect to the plate thickness.

Experimental investigations were conducted by Daniel and Liber [68] to understand the wave propagation characteristics, transient strains and residual properties of unidirectional and angle-ply boron/epoxy and graphite/epoxy laminates impacted with silicon rubber projectiles at velocities up to 250 m/sec. Strain signals recorded using surface and embedded strain gages were monitored and analyzed to determine the wave types occurring, wave propagation velocities, peak strains, strain rates, and attenuation characteristics. The predominant wave form was determined








to be a flexural one propagating at different velocities in different in-plane directions within the impacted plate.


1.4.3 Hertzian Contact Approaches to Impact Problems

In the wave propagation studies described in the preceding section, impulsive forces introduced in the laminates were assumed to be known. However, in reality, the loading is the result of an impact generated between the projected object and the plate and should be evaluated. The classical Hertzian contact theory of impact has long been applied to this localized impact problem to evaluate the contact force, the dynamic response of the plate, and the energy transfer.

Extension of the Hertzian contact theory of impact to anisotropic

half-space bodies has been made by Willis [69] and Chen [70]. The contact region was shown by Willis to be elliptic, deviating slightly from that of a circle.

A simple model for estimating the contact time for isotropic spheres impacting composites was suggested by Moon [64], which assumes as a premise a circular contact area. He then found that dependence of contact time T and peak pressure P on the impact velocity V was of the form,



1/5 2/5
T = l/V . , P =V


Greszczuk [71] and Greszczuk and Chao [72], also used a Hertzian contact theory to study the dynamic response to impact by spherical impactors, of both semi-infinite composite laminates and finite laminated plates. Three major steps were used to formulate a solution, these being: (1) the time-dependent surface pressure distribution under the impactor, (2) the time-dependent internal stresses in the target caused by the surface pressure, and (3) failure modes in the target caused by the internal stresses.








To verify predictions of failure modes, ball-drop tests were conducted on circular laminated plates [72] incorporating different fiber-resin combinations, fiber layups, and stacking sequences. The visible damage used in the analysis consisted of observed transverse cracks on the back face of the impacted plates.

As mentioned earlier, Preston and Cook [43] also analyzed the simple Hertzian contact problem for cantilever laminates. An interesting aspect of this analysis was that multiple impacts were predicted due to the combination of vibratory modes and the local elastic deformation occurring.

A more rigorous solution for the response analysis of laminates was presented by Sun and Chattopadhyay [73]. They used a method proposed by Timoshenko to derive a nonlinear integral equation to obtain the contact force and the resultant dynamic response of the simply supported laminated plate subjected to the central impact of a mass under initial stress. The plate equations developed by Whitney and Pagano [58], which include transverse shear deformation, were used as the governing equations. The energy transferred from the mass to the plate was obtained using this analysis.

Sun [74] developed a higher order beam finite element in conjunction with the hertzian contact law to determine the total energy which is imparted from the projectile to the beam and the damage energy which causes local damage in the laminated beam subject to impact of hard projectiles. Linear elastic analysis was used up to the maximum contact force point with subsequent unloading assumed as in rigid plasticity. 1.5 Experimental Studies on Fracture Mechanisms of Impacted Composite

Laminates at the University of Florida

Coordinated experimental and analytical studies on penetration mechanics of composite laminated plates have been done extensively at the








University of Florida and serve as the main background of information for this research study.

Ross and Sierakowski [49J have reported results on the influence of composite constituents, and geometrical arrangement of fibers on the penetration resistance of impacted plates. A comparison of data based upon an areal density merit rating system has shown a favorable energy absorption potential for fiberglass composites. One series of plates tested in their experiments were fabricated using fiberglass roving continuous filaments impregnated with an epoxy matrix and laid up in 0o-90 ply configurations. This series of tests examined the effect of varying the number of fiber layers in each unidirectional lamina, while keeping a constant total number of 15 layers in each plate. It has been anticipated that an alternating cross-ply arrangement, with one layer in each lamina, would offer greater resistance to perforation than any other arrangement. However, it was shown that a plate with five three-layer laminas or one with three five-layer laminas showed slightly better perforation resistance to normal impacts using blunt-ended impactors.

Close examination of some of the perforated and partly penetrated

plates led to the description of a sequential delamination mechanism [50], which appears to account for the good performance characterizing the penetration resistance of plates consisting of multilayer laminas. The delamination areas were clearly evident in the semitransparent fiberglass/ epoxy plates when a bright light was placed behind the plates as shown in the typical photograph of Fig. 1.1, which shows two delamination areas in a plate consisting of three five-layer laminas.

Figure 1.2 is a schematic diagram of the damage observed for three delaminated areas, marked A1, A2, A3. In impacts by a blunt-ended cylinder of diameter D on plates with such multilayer laminas at moderate








speeds, a shear cut-out is first noted. This circular plug does not necessarily extend all the way through the first lamina, and the sequential delamination is begun when a strip of width D in the first lamina (parallel to the fibers) is pushed forward by the penetrator. This "generator strip" loads transversely the second lamina and initiates a separation between the first two laminas. The generator strip from the first lamina is bounded by two through-the-thickness shear cracks, marked AA and BB in Fig. 1.2. This generator strip lengthens and the delamination area A enlarges until the available energy is insufficient to continue the propagation of the delamination. A new generator strip may be formed in the second lamina (perpendicular to the first one in the 0o-90 layup plates), which initiates a second delamination area A2 between the second and third laminas, and the process is then repeated with each subsequent delamination covering a larger area than the one before it. In very high-speed impacts plugging may extend all the way through the plate with almost no delamination visible, although the hole enlarges so that the last laminas perforated show more tensile breaking and less of a well-defined shear cut-off.

The dependence of these failure mechanisms on such parameters as

fiber type, ply orientation, and matrix-fiber interaction was investigated by Ross, Cristescu, and Sierakowski [51] using diagnostic tests such as pull-out tests and low-velocity repeated impact tests. The ductile-fiber steel/epoxy systems tested did not display the sequential delamination process but instead exhibited an almost symmetrical damage area without significant delamination.

A further series of tests on 0-90 fiberglass/epoxy plates was then undertaken to examine in more detail the mode of progressive failure and the effects of sequential layup arrangement on the development of the generator strip and the sequential delamination mechanism [52]. In








particular, the effect of the number of layers in the first and second lamina on the initiation mechanism was discussed.

Analysis of these controlled and ordered lamina tests [53] revealed a linear dependence of the total delamination area obtained on the initial kinetic energy of the impactor at speeds below the critical speed for perforation. As shown in Fig. 1.3, the straight line was fitted to the data for plates with five three-layer laminas. The equation of this line was shown to be


K = 3.5 + 0.315A for K>3.5J (1.1)


where K is the kinetic energy measured in joules and A is the delamination

2
area in cm . The apparent fracture surface energy was constant at 1580

2 2
J/m (or 0.158 J/cm , half of the coefficient of 0.315 in Eq. (1.1) since two surfaces are formed). The data for plates with three five-layer laminas were also plotted in Fig. 1.3 for comparison and found to agree well with the same straight line except for data run at higher speeds. These high-speed data correspond to cases where the delaminated areas have extended to the clamped boundaries.

Fiberglass plates of the same type as those centrally impacted in early studies, along with fiberglass cloth plates, were subjected to blast loading using a fuel air explosive device [54]. A delamination mechanism again appears to be the dominant failure mechanism for these plates, for blast loads below the edge failure load. Delamination begins at the plate edges and progresses toward the center of the plate with the total delamination area appearing to be proportional to the amount of plate deflection and the intensity of the applied blast pressure.

Some calculations on the elastic response to a simulated impact

loading applied as a pyramid shaped pressure distribution over a square
























































"E

20C 100


0 100 150
KINETIC ENERGY (Joules)


19








Fig. 1.1 A generator strip and two
delamination areas in a
plate with three fivelayer laminas.
















Fig. 1.2 Schematic of three sequential delaminations. The first generator strip is
bounded by AA and BB.
















Fig. 1.3 Total delamination area
versus impactor kinetic energy for plates with
five three-layer laminas
(circle and triangle points and fitted line) and plates
with three five-layer
laminas (square points).








area at the center of the localized impacted plates, were made using a DEPROP (Dynamic Elastic-Plastic Response of Plates) computer code for comparison with experimental data with some success [55]. Attempts were also made to calculate the location of the maximum shear stress, using simple elastic analyses for cylindrical bending of the laminated plates with orthotropic laminas having unequal moduli in tension and compression.

In addition, a summary of the above experimental and analytical studies has been reported by Malvern et al. [56].


1.6 Composition of the Dissertation

This dissertation is primarily concerned with the experimental studies on the failure mechanisms in centrally impacted composite laminates.

In Chapter 1, a historical review has been provided and organized

in order to clarify the localized impact problems of composite laminates of principal interest in this investigation. Specifically, previous experimental studies conducted at the University of Florida, which provide fundamental information on plate failure mechanisms, have been summarized.

In Chapter 2, prepreg fabrication procedures of composite laminate specimens have been described. The specimens have been fabricated from fiberglass/epoxy tapes using an autoclave to control the pressure and the temperature during the specimen forming and curing times.

In Chapter 3, experimental studies on failure mechanisms of centrally impacted composite laminates have been conducted systematically in order to investigate the effects on the fracture mechanisms of several parameters, such as impactor nose shape, impactor length (mass), impactor kinetic energy, and ply orientation of the fabricated prepreg








laminates. The overall fracture patterns, delamination, transverse cracks, and the contact time have been investigated intensively.

In Chapter 4, microscopic observations of cross sections of impacted composite laminates have been obtained using a scanning electron microscope. The photomicrographs have confirmed macroscopic observations and given added details which could not be obtained otherwise, particularly as to the interaction of the planar delamination and transverse cracks.

In Chapter 5, the details of the time history of the elastic waves before delamination have been measured using surface and embedded gages. These gages have been placed on and within the specimens in order to study what waves predominate and to relate'the wave behavior to the fracture mechanisms involved.

In Chapter 6, the delamination crack propagation velocities as measured by a high-speed camera have been discussed. The dynamics of the impactor and its interaction with the laminate have also been described from the optical data obtained. The velocities of the generator strip development have also been measured using a newly-devised velocity gage. These velocities are important parameters required to further understand the complex fracture behavior of the composite materials being investigated.

Finally, in Chapter 7, a summary of the overall study and concluding remarks have been made.














CHAPTER 2

LAMINATED PLATE SPECIMEN FABRICATION

All the composite laminated plate specimens used in this study were fabricated from fiberglass/epoxy prepreg tapes* using an autoclave (Fig. 2.1) to control the pressure and the temperature during the specimen fabrication. Twelve inch by twelve inch plates were prepared in the autoclave and cut into desired specimen sizes after fabrication. Many attempts were made to establish the best plate fabrication method for producing the standard 12" by 12" sized layup system as shown in Fig. 2.2. The established sequence of fabrication for the plates is shown in Fig.

2.3 and the fabrication methodology described below.

Upon receipt from the manufacturer, prepreg tapes were refrigerated and stored until use. Subsequently, for fabrication the tape was removed from the refrigerator and warmed up to room temperature before layup to prevent moisture from condensing within the specimens. A fabrication tool and specimen sizing dam were cleaned with acetone with the surface within the dam border coated with a release agent (Fig. 2.3(a)). A layer of teflon-coated vent cloth was then put on the fabrication tool to eliminate bonding of laminates to the tool surface (Fig. 2.3(b)). Prepreg tapes were cut into the required 12" by 12" size. A sharp paper cutter was used to cut ply layups with care taken so as not to disorient fibers and not to soil the plies. Clean plastic gloves were found to be




*The details of the underlined processing materials and instruments used in this thesis investigation and referred to in this chapter are given in Table 2.1.


















































Fig. 2.1 Baron Model BAC-24 autoclave.









BAG SEALING COMPOUND '---NYLON VACUUM BAG


RRIER FILM (MYLAR, 2 MILS) ,ALUMINUM CAUL PLATE


-GLASS CLOTH BLEEDER


f'7 TEFLON COATED VENT CLOTH


Fig. 2.2 Layup system for prepreg tapes.






















(a) (b)


(c) (d)


(e) (ff)


Fig. 2.3 The sequence of fabrication of composite laminate
specimens. See the text for details.





















(g) (h)


Fig. 2.3 - Continued









Table 2.1


Details of processing materials and instruments for laminated plate specimen fabrication


Processing Materials Description Manufacturer or Instruments


Fiberglass/Epoxy "Scotchply" Type 3M Company, Prepreg Tape 1003, 12" or 18" Minneapolis, Wide, B Stage of Minn. Curing, Resin Content 36% by Weight

Autoclave Baron Model BAC-24 Baron Blakeslee, Electrically Heated Santa Fe Springs, Autoclave, Calif. Max. Pres. 110 psig Max. Temp. 6500 F
Working Diameter 2 ft. Working Length 4 ft.

Fabrication Tool Aluminum Plate 17"xl7"xl/2"

Dam Aluminum Plate 14"xl"xl/8"
12"xl"xl/8"

Release Agent Ram Mold Release 225 Ram Chemicals, Gardena, Calif.

Teflon Coated TX 1040, Teflon, Pallflex ProdVent Cloth Coated Glass Fabric, ucts Corp., Porous, 0.002" thick Putnam, Conn.

Bleeder Ply Commercial Grade 120 Style Glass Cloth

Metal Caul Aluminum Plate Plate 12"x12"xl/4"

Barrier Film "Mylar" Film, 2 mils E. I. Dupont Co.
14"x14" Wilmington, Del.

Breather Ply Commercial Grade 120 Style Glass Cloth

Bag Sealing S. M. 5126 Schnee-Morehead Compound 3/8"x3/16" Corp., Irving, Texas

Vacuum Bag Nylon Film, 8 mils, 17"x17"








a requirement in order to properly handle the prepreg tapes. Each cut tape or ply was then laid up following the required stacking sequence (Fig. 2.3(c)) and pressed against the tool with a rubber roller to remove trapped air. A paper liner used to protect prepreg tapes from foreign matter was removed prior to each ply layup. After finishing the ply stacking sequence, the laminate was covered with two teflon vent cloths in order to prevent bonding the laminate to bleeder ply material. The glass bleeder ply was then placed in the system so as to absorb excess resin from the laminate (Fig. 2.3 (d)). Only one bleeder sheet was used in the fabrications described herein. Placed on top of the bleeder ply sheet was a metal caul plate, which is a perforated aluminum plate coated with release agent and used to smooth the laminate top surface (Fig. 2.3(e)). The total laminate assembly inside the dam was then covered with a barrier film (Fig. 2.3(f)) to prevent excess resin from overflowing the dam. After addition of several more breather ply materials, a bag sealing compound was placed along the periphery of the tool plate (Fig. 2.3(g)), and the entire assembly covered with a vacuum bag. The entire system was then sealed between the vacuum bag and the tool (Fig. 2.3(h)). This bagged layup was then connected to a vacuum pump installed in the autoclave using a vacuum bag adapter with a copper tubing and fitting (Fig. 2.3(i)).

The autoclave curing cycle consisted of the following procedure.

1. Place the vacuum pump in operation at up to 29.5 inches Hg

vacuum.

2. Check for bag leaks.

3. Raise the autoclave pressure to 40 psi.

4. Set the vacuum control switch to the "Auto" position in order

to operate at 27 inches Hg vacuum.








5. Heat the autoclave directly to 3200 F using a temperature

climb rate of 100 (�20) F per minute.

6. Keep the specimen at the above temperature and pressure for

1 hour.

7. Release the autoclave pressure and the vacuum.

8. Hold the temperature at 2800 F for 16 hours.

9. Cool to below 1500 F before the bagged layup is removed.

The fiber content of fabricated laminated plates was estimated to be about 70-72 percent by weight. A trial and error procedure was used to obtain fabricated plates with a suitable interlaminar strength for testing and satisfactory transparency so that delamination might be detected using a high-speed camera with light sources placed behind the plates. Plates consisting of more than 72 percent by weight of fibers were found to be deficient in possessing satisfactory transparency.















CHAPTER 3

EXPERIMENTAL IMPACTOR/PLATE CONFIGURATION INTERACTION STUDIES


3.1 Introduction

As reviewed in Chapter 1, experimental studies on failure mechanisms of impacted composite laminated plates [49-56] have been conducted systematically at the University of Florida, and have demonstrated the existence of a generator strip followed by a sequential delamination mechanism. Several parameters, such as fabrication methods, layup sequence, and filament selection have been changed during these studies in order to investigate the effects of these parameters on the failure mechanisms.

Since a considerable number of parameters can be varied, it was decided to concentrate on a single composite material system [glass/ epoxy] for the current experimental studies and to use Scotchply 1003 prepreg tapes exclusively as explained in Chapter 2. All test specimens used for the impactor/plate interaction studies described in this chapter were 15.24 cm (6 in.) square laminates. Parameters varied were impactor length (mass), nose shape, and kinetic energy as discussed in Section

3.3 and ply orientation in Section 3.4. The experimental procedure has been briefly described in Section 3.2.


3.2 Experimental Procedure

The impact tests in this study were performed using a gas gun assembly shown schematically in Fig. 3.1. The development of this equipment has been previously described in Ref. [75]. The gas gun used and its control








valves have been shown in Fig. 3.2. The impactor velocity was varied by changes in chamber pressure of the gas gun.

The impact velocities were measured by use of photocells in conjunction with light beams passing through the barrel of the gas gun (Fig. 3.1). As the impactor cuts the light beams a fixed distance apart, the output of the photocells measuring the light intensity is monitored on an oscilloscope. An independent check of the impactor velocity was made using a digital counter, which gave the measured time in microseconds. The velocity measuring system is shown in Fig. 3.3.

The sides of the target plates were clamped to steel frame specimen holders, which were held fixed relative to the ground as shown in Fig. 3.4. The effective test length of the sides of the square plates was thus reduced to 13.97 cm (5 1/2 in). This specimen holder assembly was placed at a distance of 12 cm from the end of the barrel to ensure normal impact and installed inside a protective box (Fig. 3.5).

The contact time of the impactor on the plates was measured in several tests using an apparatus as shown in Fig. 3.6. The impactor closed a gap between two brass tabs cemented to the front surface of the plate and connected to an electric circuit. The closing and opening of the circuit were recorded as steps on a digital oscilloscope trace, which provided a measure of the contact time in microseconds. An independent check on the contact time was made using a digital counter, which also gave the measured time in microseconds.


3.3 Studies on Impactor Nose Shapes and Length Effects

3.3.1 Purpose of the Studies

The [(0*)5/(900)5/(00)5 ply orientation was used mainly as the

laminate structure for this phase of the study unless otherwise mentioned.















IMPACTOR


E�J-


TEST PLATE


Fig. 3.1 Schematic of gas gun assembly and related equipments.






































Fig. 3.2 A gas gun and its control valves.


Fig. 3.3 The velocity measuring system.




































Fig. 3.4 A target plate clamped by a metal frame specimen holder.


Fig. 3.5 Specimen holder assembly installed inside a protective
box.


NPOMPqr-, PPw- q

























DIGITAL
COU14TER





DIGITAL

OSCILLOSCOPE
, 9v











LAMINATED PLATE BRASS TAB STEEL IMPACTOR


Fig. 3.6 Schematic of impactor contact time measurement.








The introduction of a graduated change in impactor nose shape from blunt-ended to truncated hemispherical and then hemispherical was used in order to examine the influence of impactor edge effects on generator strip formation, subsequent observed plate delamination, and overall fracture patterns including transverse cracks in each lamina.

Variations in impactor length (2.54 cm, 5.08 cm) and mass were made for both the blunt-ended and hemispherical impactors in order to determine whether the total delaminated area was linearly related to impactor kinetic energy for all cases studied and if so, whether the slope of the delaminated area versus impactor kinetic energy curve remained constant for changing length (mass). The threshold impactor energy required to initiate the delamination mechanism was also investigated.

Variations in impactor length and mass were expected to lead to

variations in impactor contact time on the target plates. Therefore, a study was made to see whether the impactor contact time produced an influence on the delamination area versus kinetic energy curve.

Impactors used in this study were 9.525 mm (3/8 in) in diameter and have been summarized in Table 3.1. A velocity scan was performed, testing a fixed impactor type at increasing impactor velocity well below the plate perforation velocity. The velocity range chosen was from 30 m/sec to 80 m/sec for the 2.54 cm impactors and from 30 m/sec to 60 m/sec for the 5.08 cm impactors.


Table 3.1 Impactors used in this study

(A) Blunt-Ended (B) Truncated (C) Hemispherical Hemispherical




2.54 cm (1 in.) 14.175 g 13.275 g 13.275 g 5.08 cm (2 in.) 28.35 g 27.45 g








3.3.2 Fracture Patterns

Composite laminates impacted by the various kinds of impactors were illuminated from the back side of the plates. Several are shown in Fig. 3.7. From careful examination of these photos, the following remarks on the fracture patterns obtained here are made.

It has been recognized that impacted composite laminates may fail

with several different failure mechanisms occurring separately or in some combinations such as: shear cut-out of a plug; fiber debonding, stretching, breaking, and/or pull-out; delamination; and matrix failure. Among them, the generator strip and sequential delamination mechanism mentioned in Chapter 1 appear to be dominant in most of the cases treated. In addition, evenly distributed fine transverse cracks parallel to the fibers were observed in each lamina of the impacted plates. This is a detail which had gone unnoticed in previously reported investigations under the impact loading conditions. The plates tested in these previous experiments were found upon careful re-examination to have transverse cracks in each lamina. Detailed discussions on the delamination cracks and transverse cracks found are given in Sections 3.3.3 and 3.3.4.

Nose shape was found to have a marked effect on the overall delamination/fracture pattern and the observed permanent deformations on the front and back surfaces of the tested laminates. A typical schematic of the fracture patterns and deformations found in these tests has been shown in Fig. 3.8. A hemispherical nosed impactor produces a more local crushing of the first lamina right under the nose of the impactor with a less developed generator strip indicated than a blunt-nosed impactor produces. For the hemispherical nose, a single line crack occurs in the back face of the plate directly ahead of the center of the impactor and produces a large permanent deflection. This crack exists along the crest







































Front Back

(a) 2.54 cm (1 in.), BLUNT-ENDED, 74.46 m/sec (244.3 ft/sec)

Fig. 3.7 Photographs of [(0)5/(900)5/(00)5] laminates impacted by various types
of impactors.










































Front Back

(b) 2.54 cm (1 in.), BLUNT-ENDED, 80.83 m/sec (265.2 ft/sec) Fig. 3.7 - continued.








































Front Back

(c) 2.54 cm (1 in.), TRUNCATED HEMISPHERICAL, 73.61 m/sec (241.5 ft/sec) Fig. 3.7 - continued.








































Front Back

(d) 2.54 cm (1 in.), HEMISPHERICAL, 78.21 m/sec (256.6 ft/sec) Fig. 3.7 - continued.








BACKSIDE VIEW

,LINE CRACK LARGE DEFLECTION DELAMINATION AT THE IST INTERFACE


PREDICTED DEFORMATION


HEMISPHERICAL NOSE


BLUNT NOSE


Fig. 3.8 Schematic of fracture patterns and deformations of
laminates impacted by two different types of impactors.


LINE
CRACK








of a ridge of material pushed forward at these subperforation speeds. This contrasts with the observed strip of width approximately twice the impactor diameter produced by blunt-nosed impactors in the back face of the plate specimen tested. As described in the following sections, the ratio of the front and back delamination areas is lower for hemispherical impactors when compared with blunt-ended impactors at the impactor velocity ranges where clear generator strips are developed in laminates impacted by blunt-ended impactors. The mean transverse crack distance developed in the impacted plates studied has been found to be smaller at the back face than at the front face with hemispherical impactors, while the reverse has been found with bluntended impactors.

In summary, damage is more localized and impact energy is less dissipated at the front lamina (as indicated both by smaller front delamination area and by more widely spaced transverse cracks at the front face) with hemispherical impactors than with blunt-ended impactors.


3.3.3 Delamination

The total delamination area in cm2 has been plotted versus initial kinetic energy of the impactor in joules in Fig. 3.9 for various kinds of impactor nose shapes and masses as listed in Table 3.1. All tests have been run at velocities below the velocity required for complete plate perforation.

It is observed that the nose shape of the impactor appears to be

insignificant in the amount of delaminated area obtained for a given impact velocity so long as damage does not extend to the plate boundaries. At higher impact velocities, that is, higher impactor kinetic energies, the delaminated area has extended to.the clamped boundaries because the blunt-ended impactor produces greater overall delamination.

















cm (1")
cm (1") cm (1") cm (2"), cm (2")


BLUNT-ENDED 0 TRUNCATED HEMISPHERICAL HEMISPHERICAL BLUNT-ENDED HEMISPHERICAL
0






0 /

o /

/0
730/


40


50


KINETIC ENERGY (Joules)

Fig. 3.9 Total delamination area versus initial impactor kinetic
energy for [(0*)5/(900)5/(00)5] laminates.


150-


140

130

120

110


2.54 2.54 2.54 5.08 5.08


100I


90


80


60 50

40 30


20


10 20








The mass and length of the impactor have some effects on the apparent fracture surface energy. For both the 2.54 cm and 5.08 cm impactors, the total delaminated area has been found to be linearly related to impactor kinetic energy. The straight line plots shown were fitted by least squares to the data for each impactor length and shown to be of the following form:


K = 0.8 + 0.750A (2.54 cm impactor)
(3.1)
K = 1.0 + 0.975A (5.08 cm impactor)

2
In the above equations, the area A is given in cm and the kinetic energy K in joules. These equations are valid between 10 joules and 40 joules, excluding the very large areas between 32 joules and 40 joules above the dashed line in Fig. 3.9. An absolute measure of the threshold impactor kinetic energy required to initiate delamination appears to be somewhat unreliable because of its relatively small magnitude. The apparent delamination fracture surface energy has been found to be constant at about


y = 0.375 J/cm2 (2.54 cm impactor)
2 (3.2)
y = 0.488 J/cm2 (5.08 cm impactor)


The above values are one half the coefficients of A as used in Eq. (3.1), since two surfaces are formed in the delamination process. These values are found to be higher than the 0.158 J/cm2 as obtained for glass/epoxy laminates fabricated by filament winding and matrix impregnation [53] and also the value 0.155 J/cm2 found for glass roving cloth/polyester laminates formed from three laminas using a hot press [44]. This result appears to occur due to the fabrication procedure used for forming the test laminates. Specifically, the prepreg tapes use an autoclave in the








forming process and have stronger interfaces than the filament-wound laminates based on the y values even if both types of laminates show similar delamination patterns.

The apparent delamination fracture surface energy obtained is an order of magnitude higher than the fracture surface energies obtained in static tests on pure epoxy double cantilever beam specimens [76] and on aluminum-epoxy combined mode adhesive joint specimens [77]. There appear to be at least four factors contributing to this difference in fracture surface energies.

The first factor is the crack velocity. Several investigators have reported higher values for the fracture surface energy in dynamic crack propagation than in static tests. Dynamic values approximately 100 percent higher than comparable static values for constant-velocity cracks have been measured in Homalite-100 plates [78]. The fracture surface energy of PMMA as a function of crack velocity has been reported by several investigators [79-81]. The dynamic values were found to be as much as an order of magnitude higher than static data before crack branching occurred. These results agree qualitatively with analytical data given by other investigators [82, 83].

A second factor is the actual fracture mode occurring, which may be related with the crack velocity. Cottrell [82, 84] noticed an increase in fracture surface energy and surface roughness with increase in the crack velocity. This is caused by the redistribution of stress ahead of the crack tip at higher velocities, which eventually changes the fracture mode. The adhesive fracture surface energy showed a definite increasing trend as the loading changes from a so-called mode I to mode II to mode III failure [a5], which was accompanied by increasing fracture surface roughness [86]. Therefore, fracture surface energies are rather dependent








on fracture modes. In the experiments reported here, a combination of interlaminar shear stress and the crack-opening loading caused by the generator strip are considered as the generators of the stress field around the delamination crack. This result may be quite different from the stress field as produced in the double cantilever beam specimens.

The third factor considered is the adhesive fracture energy which should be distinguished from the cohesive fracture energy. That is, delamination proceeds along the interface between a fiber layer and the matrix or in the matrix close to the interface, which may give different fracture surface energies from those of the bulk pure epoxy material. Some data reported on static double cantilever beam tests on the cleavage occurring at the interface between E-glass fabric/epoxy laminates have shown fracture surface energies at least double those reported for unfilled epoxy specimens [87].

The fourth factor is the surface treatment of specimens to be bonded, which is interrelated to the previous discussion. Effects of the surface treatment on fracture surface energies are known to be significant [87, 88]. In our experiments, no special fiber surface treatments have been introduced. However, the surface condition may be different from that used in double cantilever beam specimens in Ref. [76]. It is not known whether fracture surface energies are increased or decreased by this fourth factor in our experiments.

The effect of the impactor mass and length on the apparent delamination fracture surface energy y may be explained qualitatively using Goldsmith's theory [32] on transverse impact of a mass on a beam and a theoretical-experimental investigation conducted by McQuillen et al. [89] based on Goldsmith's theory, even though experimental conditions may be different from those in the current studies. The impact event generates








the full spectrum of vibration modes in the plate specimen, but it is only the first few modes which usually have a significant influence on the specimen response. For large impact masses the response is mainly in the first mode. However, for smaller masses the second and the third mode influences become appreciable. According to McQuillen et al. [89] for the beam, a unit of energy in a higher mode causes more strain than the same unit in a lower mode. Hence small impact masses provide larger strains and larger damage in the plate than large masses with the same kinetic energy. This appears to be the reason for the larger y value occurring for small masses when compared to the large masses.

Up to now, only the total delamination area has been discussed.

This area is the sum of the delamination area in the first lamina interface (A1) and that in the second lamina interface (A2). The ratio of A to A2 seems to change with nose shape, even though the total delaminated area for any given nose shape and length of impactor impinging upon a plate at a fixed velocity remains constant. At impactor velocities where a clear generator strip can be found in laminates impacted by bluntended impactors, the average ratio A1/A2 is 0.34. This ratio is 0.29 for truncated hemispherical impactors and 0.25 for hemispherical impactors. This result is also related to the differences in fracture patterns occurring for blunt-ended and hemispherical impactors as pointed out in Section

3.3.2.

The sequential details of the delamination crack propagation event are not clearly known, but it appears to involve mainly a flexural wave as discussed and shown in Chapter 5. The delamination cracks may be caused by the interlaminar transverse shear stress associated with the flexural wave, assisted by the crack-opening loading initiated by the generator strip.








3.3.4 Transverse Cracks

Observable transverse cracks in the 00 direction have been noted on the front and back laminas in the 00 fiber direction of the impacted plates, as shown in Fig. 3.7. Similar transverse cracks in the middle 900 lamina can also be found along the fiber direction when the plates are illuminated by a strong light placed behind them. These cracks form in a direction parallel to the fiber reinforcement in each lamina and show an almost evenly distributed crack spacing. Some transverse cracks extend the full length of the specimen in the fiber direction, while others are combinations of several cracks which look like full-length cracks.

Similar types of transverse cracks with evenly distributed crack spacing in cross-ply laminates have been observed in different static loading conditions by some investigators and discussed to some extent. A survey of previous studies on transverse cracks is given below.

In static tensile tests of cross-ply laminates, one interesting characteristic is a sudden change in the slope or so-called knee of the stress-strain curve which does not exist for unidirectional laminates. This knee has been verified to be associated with the failure of the 90* plies, i.e., transverse cracking [90, 91]. A similar phenomenon known as weepage is often found in unlined internally pressurized filament-wound pipes. The onset of weepage is connected with the formation of transverse cracks in the pipe [92, 93].

A further discussion of microscopical observations of transverse cracks has been given recently in [93-95], and will be reviewed in Section 4.1.

The strain concentration effects associated with the relatively

stiff fibers have been considered as the principal cause of the observed








transverse cracking. Kies [96] has examined the strain concentration around a fiber in the matrix, which arises from the different elastic properties of fiber and resin. Since the resin has a lower modulus than the fiber, the resin must sustain most of the transverse strain and the strain close to the resin-fiber interface may be large enough to cause failure. Kies has calculated that this strain magnification increases as the fibers approach one another and this factor becomes twenty for typical close-packed fibers and resin. Shultz [97] has modified and extended the work of Kies to include biaxial tensile and shear strains, and the effect of Poisson's ratio. Herrmann and Pister [98] have also calculated the strain concentration factors for systems under biaxial strains using numerical techniques to solve the plane strain elasticity problem.

An alternative theoretical approach to transverse cracking has been reported by Puck and Schneider [99]. They have developed realistic failure criteria based upon the microstresses of the fibers, the matrix, and the constituent interfaces and shown that the transverse tensile strength is possibly related to an adhesive failure of the glass-resin interface and is also strongly affected by stress concentrations due to voids and nests of the accumulated coupling agent.

Recently, several authors have investigated in detail these characteristic transverse cracks in uniaxial tensile tests of cross-ply laminates and defined the factors controlling this evenly distributed crack spacing [100, 101]. Garrett and Bailey [100] have found the spacing of transverse cracks to be dependent on the thickness of the transverse ply and the applied stress. Generally the higher the applied stress and the smaller the transverse ply thickness are, the smaller is the average crack spacing. A theoretical prediction on the spacing of transverse cracks and the








stress-strain curve was made based on a modified shear lag analysis which was used to determine the normal stresses in the longitudinal direction after cracks occurred in the tranverse ply. The stress is transferred from the longitudinal plies to transverse plies by shear stresses and the normal stress in the transverse ply builds up over a short distance and approaches the prefracture level. The general trend of experimental data was explained by this theory. Stevens and Lupton [101] have made similar investigations.

Under similar experimental conditions, some efforts have been made to increase the threshold strain of transverse cracking. Stevens and Lupton [102] have used a resin that undergoes yielding and cold-drawing under stress and that relieves the stress concentrations between fibers. Garrett and Bailey [103] have investigated the effect of a variation of the resin failure strain, by using rubbery resin systems, to increase the threshold strain. Parvizi et al. [104] have shown experimentally that crack constraint does occur at small transverse-ply thickness.

The above discussion on transverse cracking relates mainly to static tensile tests and cannot be applied directly to the locally impacted laminates studied here. However, some information can be inferred from these results on transverse cracking to those obtained for the impacted laminates.

In order to do this, the crack spacing on the front and back face of each lamina of each specimen was measured and the arithmetic mean was then calculated. The mean transverse crack distance (MTCD) as a function of impactor velocity was obtained and is shown in Fig. 3.10 for five impactor types. The two marks for each specimen correspond to the MTCD on the front and back laminas, respectively. For blunt-ended impactors (Fig. 3.10(a)), an upper point corresponds to a MTCD on a back lamina and a








lower point to a MTCD on a front lamina. That is, the MTCD has been found to be smaller at the front lamina of a plate than at the back, for blunt-ended impactors and for a given impactor velocity. For hemispherical and truncated hemispherical impactors (Fig. 3.10(b) and (c)), the reverse has been found. This is an interesting indication of nose shape effects that the impact energy is more widely dissipated at the front lamina with blunt-ended impactors than with hemispherical ones, as pointed out in Section 3.3.2.

The threshold impactor velocity for the development of the transverse cracks appears to be independent of impactor type and to be about 23 m/sec (75.5 ft/sec). Above this threshold velocity, the MTCD decreases sharply as the impactor velocity increases. The curves are eventually flattened out at higher velocities and the MTCD appears to reach its minimum value, approximately 3 mm for the [(0*)5/(900)5/(00)5] specimen. This is similar to the MTCD versus applied stress curve in static tensile tests of cross-ply laminates reported by Garrett and Bailey [100]. Although different nose shapes can result in a difference in the MTCD on the front and back surfaces, this does not lead to any differences in other observed characteristics of the curve.

Long (5.08 cm) impactors produce a larger MTCD than short (2.54 cm) ones at the lower velocities but the impactor length (mass) has little effect at the higher velocities.

The front and back surfaces of impacted plates of [(0*)/90*)7/001, [(00)3/(900)3/(00)3/(900)3/(0O)3] laminate configurations also show the same uniform transverse crack development as for the [(0*)5/(900)5/(00)5] ones. Some MTCD data for each impacted plate type have also been shown in Fig. 3.10(a). The MTCD decreases in the aforementioned order, while the threshold impact velocity for the transverse crack development increases in the above order.












Q 100 290(ft/sec)


0
oo oL






[(0)3/(900)1/(O)3/(90)./(O)31- -'--[(o/90�)7/O]-J W0 2.54cm(lin.) IMPACTOR 0 x


0 5.08cm(2in) IMPACTOR


VELOCITY


(a) Blunt-ended impactors. Paired points:
back face, lower for front.


Fig. 3.10


75(m/sec)


upper for


Mean transverse crack distance v.s. impactor velocity for [(00)5/(90�)5/(00)5] laminates impacted by various types of impactors.













I00


:~: Z.~


O 2.54cm(lin.) IMPACTOR U 5.08cm(2in.) IMPACTOR


25 50 75(m/sec)
VELOCITY

(b) hemispherical nose impactors. Paired points: lower for
back face, upper for front.


Fig. 3.10 - continued.


W7


E
E
w
0 5
z





CO,







Z2


2OO(ftysac)












100 200 (ft/sec)


SII


A
A


2550 75 (m/sec)

VELOCITY

(c) Truncated hemispherical nose impactors (2.54 cm).
Paired points: lower for back face, upper for front.


Fig. 3.10 - continued.








In the present experiments, the laminate specimen is believed to experience large deflections even if it is still elastic up to the point of plate delamination. This deflection magnitude can become comparable to or larger than the plate thickness so that membrane effects may have to be considered. The well-known von Kgrman theory for the large deflections of plates is described in Fung's text [105]. It makes use of Green's finite strain as follows.

Consider a Lagrangian material description and a fixed righthanded rectangular Cartesian frame of reference to be used, with the x, y plane coinciding with the middle surface of the plate in its initial, unloaded state, and the z-axis normal to this plane. Let the components of the displacements of points lying on the middle surface be denoted by u(x,y), v(x,y), w(x,y). In the Lagrangian description, the Green's strain tensor, referred to the initial configuration, is used, whose components are


E au z '2w (_.w.2
Exx = x - 2 11 + 1/
x
(3.3)

E av z2w +i/2 (w 2
yy ay a 2 /2y)
y


The first term in Eq. (3.3) can be small compared with other terms. The second term is the contribution of bending which also exists in the small deflection theory. The third term is particular to the large deflection theory and appears to be comparable to the second term. This term contributes a tensile component to the strain and causes tranvserse cracking in transverse laminas. A theoretical explanation developed by Garrett and Bailey [100] from static tensile test data, that is, a modified shear lag analysis, can be applied to explain this transverse cracking in crossply laminates, with some changes to account for wave propagation effects.








But the development of this theoretical approach needs further research in the future.


3.3.5 Contact Time Measurement

Typical oscilloscope records of the contact time measurements have been shown in Fig. 3.11. The records obtained indicate that both a single contact and multiple contacts are possible. Multiple contacts have been predicted for impact tests of cantilever graphite/epoxy laminates by Preston and Cook [43]. The combination of vibration modes excited by the impact event and the local deformation appears to produce this multiple contact phenomenon. Multiple contacts were especially noticeable for blunt-ended and shorter (2.54 cm) impactors. However, only the first contact period, appears to be important in transferring energy from the impactor to the laminate, and is taken as the contact time.

The contact time versus the impactor velocity has been shown in Fig. 3.12 for five impactor types. As shown, the contact time for all impactor types increases with increase in velocity. The contact time of the longer and heavier impactors is approximately four times as great as that of the shorter and lighter ones for a given velocity range, that is,


about 200 - 400 psec for the 2.54 cm impactors, about 1000 - 1200 psec for the 5.08 cm impactors.


For 2.54 cm impactors, blunt noses give longer apparent contact times than either the hemispherical or truncated hemispherical nose shapes. This is partly due to the inherent difficulty in impacting the projectiles exactly at the center of the plate. Thus, the actual contact does not necessarily result in the direct closing of the electric circuit for all nose shape impactors, particularly the hemispherical type.








802 1054


IMPACTOR TYPE AND VELOCITY

2.54 cm, BLUNT-ENDED 61.73 m/sec






2.54 cm, BLUNT-ENDED 69.45 m/sec


6 234


2.54 cm, HEMISPHERICAL 43.03 m/sec


6 304


850 1074


6 990


2.54 cm, HEMISPHERICAL 61.88 m/sec






5.08 cm, BLUNT-ENDED 30.49 m/sec


1186


5.08 cm, HEMISPHERICAL 59.10 m/sec


Typical oscilloscope records for contact time measurement. Time in microseconds.


Fig. 3.11


6 304



















































50
VELOCITY


400300

Z
0

200



I00




0





Fig. 3.12


(The same


Contact time versus impactor velocity. symbols are used as in Fig. 3.9.)







Hence, real contact times should be a little longer than those in Fig. 3.12 for rounded types of noses. In summary, it may be said that the nose shape difference does not affect the contact time.


3.4 Studies on Ply Orientation Effects

Some angle-ply laminate specimens have been fabricated and impacted with 2.54 cm blunt-ended impactors. Fifteen-ply symmetric laminates with ply orientation [(15O)5/(-15�)5/(15*)5] and [(30')5/(-300)5/(300)5] were chosen for the tests and the total delamination area as a function of the impactor kinetic energy has been shown in Fig. 3.13. The apparent delamination fracture surface energy y is very low compared with y for the


0







z .'- 50010





z V




Zo




0


/





0/


/0
/o


10 20
KINETIC ENERGY(Joules)


I


1
3(


<0 I00 z
(n





Wo


or
< 0 0-.



0

0~Ln
0-


Fig. 3.13 Total delamination area versus impactor kinetic energy
for angle-ply laminates.


PUI%^








[(00)5/(900)5/(00)5] cross-ply laminates. This may be due to the specimen fabrication for the angle-ply laminates in that weak interfaces may exist between laminas. The threshold energy for the development of delamination is higher for the angle-ply laminates than for the cross-ply laminates. Fracture mechanisms other than the delamination may be the principal energy absorbing criteria for such systems. For example, fiber stretching and breaking may play a significant role. These results are considered important but an insufficient number of tests have been conducted to warrant any definitive quantitative statements. Therefore, only a qualitative effect of ply orientation on the fracture patterns has been discussed in the following commentary.

Delamination patterns have been obtained in angle-ply laminates

similar to those found in cross-ply laminates with some differences in the actual shape of delamination noted. The same generator stripsequential delamination mechanism appears to exist and to be applicable to the angle-ply laminates. The first stage of the process consists of the formation of a generator strip in the first +e lamina, bounded by two through-the-thickness shear cracks, marked AA' and BB' in Fig.

3.14. This generator strip is pushed forward by the impactor and loads transversely the second -e lamina. In the second lamina, the generator strip loading is mainly supported by bending of a strip in the secondlamina fiber direction, bounded by CC' and DD'. This is because of bending stiffness of the strip bounded by CC' and DD' is larger than that of any other arbitrary strip bounded by any XX' and YY' passing through A and A'. As the generator strip loads the second lamina which supports the bending loading, delamination between the first two laminas is initiated along the lines AA' and BB'. This delamination spreads to the second-lamina fiber direction, that is, at an angle












A DELAMINATION CRACK PROPAGATES IN THE 2ND LAMINA FIBER DIRECTION


A DELAMINATION CRACK PROPAGATES IN THE 3RD LAMINA FIBER DIRECTION





Fig. 3.14 Schematic of delamination pattern in [(+e)5/(-6)5/(+6)5]
angle-ply laminates.





63

-20 to the generator strip, until the available energy is insufficient to continue the delamination process. A new generator strip can be formed in the second lamina at an angle -20 to the first generator strip and thus initiate delamination between the second and third laminas. The associated delamination with this generator strip propagates in the third-lamina fiber direction. The process may be then repeated with subsequent delamination covering a larger area than the one before it if there are enough independent angle-ply laminas in the laminate.














CHAPTER 4

MICROSCOPIC OBSERVATIONS OF CROSS SECTIONS
OF IMPACTED COMPOSITE LAMINATES

4.1 Introduction

As mentioned earlier, failure mechanisms in FRCM have not been extensively investigated experimentally to establish well-defined failure theories. Particularly, understanding of failure mechanisms in impacted FRCM specimens is needed in order to make full use of these materials. Macroscopic observations of locally impacted composite laminates have been discussed in the previous chapter. These results have shown existence of a sequential transverse crack-delamination mechanism. It appears desirable to make microscopic observations on the initiation and propagation of the observed transverse cracks and delamination cracks in order to confirm the results of the macroscopic observations and to investigate the interrelation between the above kinds of failure patterns in more detail.

Sample preparations and microscopic examinations of cross sections of FRCM specimens after loading have been reported on by some researchers in order to study stress-cycled failure [106], uniaxial compression failure [107], effects of voids on filament-wound (FW) structures [108], creep failure [109], weepage of pressurized FW pipes [93], and uniaxial tension failure [94, 95]. These examinations were carried out using optical microscopes (transmitted or reflected light) and/or electron microscopes.

Continuing improvements of the sample preparation methods for cutting and polishing the cross sections of FRCM specimens have recently 64








been made using special care to eliminate any damage produced during cutting and polishing of the samples, as reported in Refs. [106-109, 93]. The latest methods utilize coolants and room-temperature curing resins in the initial cutting and mounting of the samples. This has been done in an apparent effort to reduce or eliminate any thermallyrelated residual stress from being introduced into the sample.

Microscopic observations of cross sections of impacted composite laminates have not previously been conducted insofar as the author knows. However, cross sections of laminates damaged by static loading or fatigue loading which show similar damage appearance have been studied [107, 93-95]. In simple compression, creep, and fatigue tests, Broutman [1073 indicated that crack initiation occurred at the resinglass interface and traveled along the path of least resistance, that is the interface, to separate individual fibers and the matrix, resulting eventually in delamination between layers of filaments. Jones and Hull [931 examined pressurized FW pipes and described a weepage type failure mechanism, which included the debonding of individual fibers first followed by development of transverse cracks, and finally the occurrence of delamination resulting in a continuous crack path for weepage. Based upon uniaxial tension and cyclic loading tests of laminates, Reifsnider et al. [94] conjectured that delamination interacted with, and was quite possibly nucleated by, transverse cracking in transverse plies. The development of delamination from the ends of the transverse crack was typical of their observations. Reifsnider and Talug [95] then postulated a simple model, which could be used as a predictive method to account for this delamination development.


4.2 Sample Preparation

Based upon previous reports and our trials and errors to reduce damage during the preparation, the following sample preparation








procedure was used. For information purposes, the equipment and supplies used in this sample preparation have been listed in Table 4.1.

(1) Sectioning. Representative areas were first cut oversized from the impacted laminate using a band saw and then cut into the desired dimensions using a low-speed saw with a diamond wafering blade and with a water spray as a coolant. This sectioning procedure leaves the sample surface slightly scratched, but prevents excessive local heating.

(2) Mounting. Sectioned samples were mounted in "Caulk Nuweld," a room-temperature curing resin primarily used for denture repair, in order to avoid heating the samples.

(3) Grinding. The section was then ground on wet silicone carbide abrasive papers of successively finer grit sizes 180, 240, 320, 400, and 600 using a grinding wheel. The section was lightly pressed against each paper on the moderate-speed rotating wheel for 1 minute. Samples were washed with water between paper changes and after the final grind.

(4) Rough polishing. Six micron diamond polishing compound was then used on a cotton polishing cloth attached to a polishing wheel, with lapping oil for introducing a uniform distribution of the polishing compound over the polishing cloth and for cooling the sample. Moderate pressure was then applied to a high-speed wheel for approximately 2 minutes. This procedure allows for some features in the section such as transverse cracks and delamination cracks to be clearly visible with the naked eye.

(5) Fine Polishing. After the section was washed thoroughly, 1

micron diamond polishing compound was applied to a synthetic rayon cloth with lapping oil. Good resolution and contrast was obtained between fibers, resin, and cracks. Cross sections of fibers were polished without breakage.














Table 4.1


Supplies used in the sample preparation for SEM observation.


(1) Sectioning
"ISOMET" Low Speed Saw
Diamond Wafering Blade (Low Concentration) 4"xO.012"

(2) Mounting (a)
"CAULK NUWELD" Denture Repair Resin

(3) Grinding
"ECOMET" III Polisher/Grinder, 8"
"CARBIIET" Silicon Carbide Abrasive Paper Disc


(4) Rough Polishing
"ECOMET" III
"METADI" Diamond Polishing Compound, 6 micron
"IIETCLOTH" Polishing Cloth (a cotton cloth with
practically no nap)
"AUTOMET" Lapping Oil

(5) Fine Polishing
"ECOMET" III
"METADI" Diamond Polishing Compound, 1 micron
"MICROCLOTH" Polishing Cloth (a synthetic rayon cloth in which fibers are bonded to a woven cotton backing)
"AUTOMET"

(a): Manufactured by the L. D. Caulk Co., Milford, Del.
All other supplies are manufactured by Buehler Ltd.,
Evanston, Ill.





68

After the section was polished, carbon particles were vacuum-deposited on it in order to increase its thermal conductivity. Then the section was viewed in a scanning electron microscope (SEM). The SEM used in this study was a Joel JSM-35C (Joel LTD., Tokyo, Japan) as shown in Fig. 4.1.


Fig. 4.1 Joel JSM-35C scanning electron microscope








4.3 Results and Discussion

A [(00)5/(900)5/(00)5] laminate impacted by 2.54 cm (1 in.) bluntended steel projectile at a velocity of 75.1 m/sec (246.5 ft/sec) was selected as a typical sample for the SEM observations. Fracture patterns for this impacted laminate have been shown in Fig. 4.2 Note that a generator strip, transverse cracks, and delamination cracks are fully developed and recognizable for the sample selected for study. Several cross sections of this specimen have been cut along the straight lines as shown in Fig. 4.2(b). The schematic of each cross section has been shown in Fig. 4.3 where points A-G in Fig. 4.3 correspond to those in Fig. 4.2(b). A cross section from a virgin laminate is shown in Fig. 4.4 for comparison with the impacted specimen and found to remain undamaged after sectioning, grinding, and polishing as described in the previous section.

Typical SEM photographs of the cross sections of the impacted specimen have been shown in Fig. 4.5 where brief explanations have been included along with the photomicrographs. Note that the numbers in Fig. 4.3 correspond for consistency to the photo numbers in Fig. 4.5.

Based upon the SEM observations, the following general remarks can be made. The letters and numbers in the text correspond to those indicated in Figs. 4.3 and 4.5.

In general, transverse cracks are perpendicular to lamina interfaces in regions where there is no delamination. For example, see 202, 207, 306, 401, and 403. However, transverse cracks grow oblique to lamina interfaces where they are accompanied by a delamination crack. For example, see 201, 203, 207, 000, 501, and 602. The perpendicular transverse cracks appear to be formed as a result of both the in-plane tensile wave development and shear lag as developed between the 0* and 900 layers


































S '

























(a) Front

Fig. 4.2 Typical fracture patterns of a [(00-/(900)5/(00)5]
laminate impacted by 2.54 cm blunt-ended steel projectile at a velocity of 75.1 m/sec (246.5 ft/sec).









TRANSVERSE CRACKS


A DELAMINATION CRACK AT THE 2ND INTERFACE


A DELAMINATION CRACK AT THE IST INTERFACE
(b) Front, schematic


Fig. 4.2 - continued


















A B


back
H A


front


305, ,, 306,307







303

501




I K


1-1203





F 204 C







L --209 F

404.405- 403




P 0401


_,601

IL . ... Ktkt A(


E602
E


Fig. 4.3 Schematics of several cross sections of the laminate shown in Fig. 4.2.
(Points A-G in Fig. 4.3 correspond to those in Fig. 4.2(b)).



























Fig. 4.4 An undamaged interface of a [(00)3/(900)3/(0) R/(900) 3/(00)3]
laminate. (Note a resin-rich region in a 90 lamina corresponds to the boundary of two 900 prepreg tapes.)

























201: A DC at the second inter- 202: A lone and straight
face deflects into an TC.
oblique TC in the third
lamina. The DC travels just
inside the third lamina.


Fig. 4.5 Typical SEM pictures of cross sections of a [(0*)5/(900)5/(00)5]
laminate impacted by a 2.54 cm blunt-ended steel projectile at 75.1 m/sec. (Note that the numbers in Fig. 4.3 correspond to
the picture numbers in this figure. DC and TC mean a delamination crack and a transverse crack.)








203: A DC at the first interface deflects into an
oblique TC in the second
lamina, while a DC at the
first interface travels outward from the impact
region.


204: Connection of a DC and a
TC.


206: A DC associated with an oblique TC, which travels
through a portion with fiber
bunching.


205: A DC with two branches,
one at the second interface and the other just inside the third lamina.


207: An oblique TC associated
with a DC and a straight
TC without a DC.


Fig. 4.5 - continued.























208: Irregular TCs at the generator 209: A large magnification of
strip. 208.


000: An oblique TC near a DC. A TC
travels through a fiber-bunching region.


301: A DC with two branches,
one at the first interface and the other just inside the first lamina, connected to an oblique
TC.


302: A connection between a DC and a
TC.


Fig. 4.5 - continued.























303: A TC traveling through a 304: A DC just inside the
portion with fiber bunch- first lamina.
ing in the first lamina.


305: A large magnification
of an undamaged interface.


306: A lone TC with two
branches near the second
interface.


307: A large magnification of 401: Two perpendicular TCs
306. ahead of main DC.


Fig. 4.5 - continued.























402: A DC initiated at the tip 403: A lone TC with two
of a TC in the first lamina. branches near the interface in the third lamina.
















404: A TC with two branches 405: A large magnification of
traveling through a fiber- 404.
bunching region.






501: A DC at the first interface deflects into an oblique TC in the second ' ~ lamina, while the same TC is connected by a DC passing just inside the third lamina.


Fig. 4.5 - continued.























601: An oblique TC connecting 602: Connection of a DC and a
two DCs. The tips of the TC. The TC travels
DCs can be identified. through a portion of fiber
One DC at the first inter- bunching.
face stops at the TC.

Fig. 4.5 - continued.


as explained in Section 3.3.4, which introduce substantial tensile strains in the transverse laminas. The oblique transverse cracks accompanied by a delamination crack are considered to be due to a combination of the aforementioned tensile wave-shear lag and the interlaminar shear caused by the flexural waves. This is supported by the following observation. The angle at which each transverse crack deflects into interfaces should be noted. JH, FC, IK, and EG show that the transverse cracks in the second lamina deflect toward the impact point near the first lamina but away from the impact point near the third lamina. This is explained by the tensile and shear strains developed in the transverse lamina as shown in Fig. 4.6. Delamination cracking thus appears to interact with the observed transverse cracks.

As mentioned in Section 3.3.4, a cause of transverse cracks in impacted laminates is considered to be the strain concentration effects between transverse fibers which are much stiffer than the resin. Since the strain concentration factor increases as the interfiber spacing





80


















7











Fig. 4.6 Tensile and shear stresses developed in the transverse
lamina.



decreases [96], more transverse cracks should be found in regions of high fiber density than in resin-rich regions. Another cause of transverse cracking can be attributed to the adhesive failure of the glass-resin interface as discussed by Puck and Schneider [99]. In the present observations, transverse cracks appear to propagate in the regions of high fiber density, in other words, fiber bunching, and to avoid the large pockets of resin, where the fiber density is locally low. See, for example, 206, 207, 209, 000, 303, 403, 405, and 602.

Both transverse and delamination cracks appear to propagate near or at the fiber-resin interface. It is very difficult to tell whether those cracks are caused by adhesive fracture of the fiber-resin interface or cohesive fracture of the resin. Both cases have been identified








in the present experiments. For example, see 205, 206, 209, and 602.

Delamination cracks do not necessarily propagate along the lamina interface. Photos 201, 205, 301, 302, 304, and 501 show some examples where delamination cracks travel just inside laminas.

Some longitudinal cracks within laminas can also be found under the impact region as shown in JH and LF. Recall that the normally incident compressive wave is reflected at the back surface of the plate and returns as a tensile wave. This reflected wave may aid in initiating these observed longitudinal cracks within laminas. A generator strip crack has also been shown in LF. The irregularity of such cracks just under the impact region can be observed in 208 and 209.

A secondary shaded region in the delaminated area shown in Fig. 4.2(a) corresponds to the region(s) inside the dotted lines in the schematic of Fig. 4.2(b). For these regions, there appears to be no delamination crack at the second interface, according to NL or 305, while there is a delamination crack opening at the corresponding first interface.

Photos 401 and 402 show a transverse crack in the first lamina which began to form a delamination crack at the tip of the transverse crack. This crack is located well ahead of the main delamination cracks. Transverse crack growth due to the tensile wave-shear lag appears very rapid even though it may be temporarily arrested by resin pockets or other irregularities. Growth is eventually stopped when the transverse crack arrives near the lamina interface. Interlaminar resin layers temporarily arrest cracks until the flexural-wave-induced interlaminar shear stress at the crack tip exceeds the resin failure strength, and a delamination crack forms at the tip of the transverse crack. The transverse cracking








and the delamination cracking may occur almost at the same time and interact with each other. Photos 401 and 402 document this stage of failure. The delamination crack described above next appears to connect to a main delamination crack traveling from the impacted region. This appears to be the principal sequence in the failure process in the impacted laminates tested here.

Photos of sections of the impacted specimen confirm a fracture appearance as observed from the polished surfaces by visual observation of the sectioned specimen. For example, photo 602 illustrates two different delamination cracks stopped in different terminal positions.

The use of an SEM to inspect cross sections of impacted specimens has provided considerable information on the failure/fracture details of the tested specimens which could not otherwise be obtained by inspection by simple macroscopic observations. The use of this instrumentation for the quantitative analysis of dynamic impact studies appears to provide a powerful tool for documenting the sequence of events required to establish a suitable analytical model for interpretation of these tests.














CHAPTER 5

EXPERIMENTAL WAVE PROPAGATION STUDIES OF
IMPACTED COMPOSITE LAMINATES USING STRAIN GAGES

5.1 Introduction

In previous investigations, the fracture characterization has been described only after the laminate was damaged due to impact. The details of the high-velocity transient behavior of impacted laminates, such as the time history of the elastic waves before delamination, the generator strip formation, and the delamination crack propagation are necessary information which must be obtained for the impact event and have as yet not been established. The first of these problems is examined in this chapter and the last two problems in the next chapter.

Several experimental questions are required to be answered on wave travel in impacted plates. Among these are what kinds of waves are involved and which one is the dominating the transient phenomena occurring in the present studies. These results are directly related to the fracture behavior involved, which is the main concern of this total investigation program.

Recently, Daniel and Liber [68] have conducted elastic wave propagation studies on boron/epoxy and graphite/epoxy laminates impacted by silicone rubber projectiles, using both surface and embedded strain gages. These records have verified that the predominant wave is a flexural one propagating at different velocities in different directions for specimens with ply orientation of [(00)16] or [(0)2/�45]2S' Muldary [110], however, has reported some impacts on glass/epoxy plates where membrane-type deformation is predominant. The impacted plates in 83








his tests had a large [impactor velocity/plate bending stiffness] value and were flexible enough to deflect comparable to the plate thickness, so that membrane effects were important. The impacted plates in the present strain gage experiments as well as in Daniel and Liber's [68] had a smaller [impactor velocity/plate bending stiffness] value, and membrane effects were insignificant compared with flexural wave effects.


5.2 Experimental Procedure and Consideration

The strains induced by impact on fiberglass epoxy laminates with different ply orientations were measured by means of surface and embedded gages, and the characteristics of these strains, that is, types of waves, wave amplitudes, and strain rates were studied.

The embedded gages were Micro-Measurements WK-06-062AP-350 (MicroMeasurements, Raleigh, N.C.) fully encapsulated single gages with polyimide encapsulated ribbon copper leadwires and were self-temperaturecompensated. The lead wires were short (2 cm), and extension copper wires and small terminals were used for extension to the bridge circuit. The 16-ply laminates with [(0�)5/(900)6/(00)5] ply orientation were used for the embedded gage tests. The gages were embedded at the geometric mid-plane of the plate, that is, between the eighth and ninth plies of the laminate. The whole assembly was then cured using a vacuum bag in the autoclave following the same procedure as developed for specimens without embedded gages. The local thickness increase due to insertion of the embedded gages could not be detected by a micrometer.

The surface strain gages used in these studies were Micro-Measurements general purpose EA-06-062AQ-350 or EA-06-O31CF-120 type with ribbon copper leadwires and were bonded at the desired positions on the front and back surfaces after curing. Active gage length of each type of gage was 62 mils or 31 mils, respectively. The use of two strain gage outputs








with different gage lengths at the same relative position of a plate indicated that the gage lengths selected do not affect the recorded results. The 15-ply laminates with [(0*)5/(90�)5/(00)5] and [(300)5/ (-30-)5/(300)5] ply orientations were also used with surface gage tests and without embedded gages.

Different kinds of gage layouts were used to study the strains at different positions for each type of laminate, and gage layouts with results obtained for each case are given in Section 5.4.

The strain gages were connected to potentiometers in bridge circuits and, after suitable amplification, the transient signals were recorded on two 2-channel digital oscilloscopes (Explorer III Digital Oscilloscope, Nicolet Instrument Corporation, Madison, Wis.). The recording setup for the strain gage experiments is shown in Fig. 5.1.



















Fig. 5.1 Recording setup for strain-gage experiments


The 15 cm square specimens were then impacted with steel impactors following the same experimental procedure as mentioned in Section 3.2. The impactor contact measuring system described in Section 3.2 was used for triggering both oscilloscopes. It was confirmed that both oscilloscopes were triggered at the same time within an error bound of �0.5 microsecond.








It has been noticed that the impactor velocity is an important factor to measure the transient strains in cross-ply and angle-ply laminates. Transverse cracks occur even if the velocity is lower than the threshold velocity where a delamination crack is first observed. If a transverse crack crosses a gage, it reads a larger strain value than values at neighboring regions. This local strain increase should be carefully noted. Therefore, the laminates have been impacted at lower velocities where the density of transverse cracks is low and transient strains are insignificantly affected by the appearance of these cracks. Since the impactor velocities for this strain measurement are restricted to be lower than those in Chapter 3, the results in this chapter cannot be applied directly on a one-to-one basis with those established in Chapter 3. However, it is believed that the information on the flexural waves measured in the present investigation can be applied at higher impactor velocities where delamination is the main failure mechanism, even if little information on transverse cracking is available.

Related to the above problem is the fact that the bonded surface gages may have some strengthening surface effects. In fact, transverse cracks are likely to avoid the instrumented region having the surface gages. However, it appears that in the current experiments the overall strain levels are little affected by the stiffening effect of the bonded strain gages.


5.3 Documentation Tests for Characterizing Embedded Gages

It is a well-known fact that the integrity of a laminate may be

lost when poor bonding exists around embedded gages and that the embedded gages may cause some irregularity in the structure around them. To further document this statement, tensile tests were conducted in order to




Full Text

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EXPERIMENTAL STUDIES OF THE DELAMINATION MECHANISMS IN IMPACTED FIBER-REINFORCED COMPOSITE PLATES BY NOBUO TAKEDA A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIRE14ENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA

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To my parents Wasaburo and Aiko Takeda

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ACKNOWLEDGEMENTS The present investigation was part of a three-year effort, under Army contract DAAG29-79-G-0007 to study fracture mechanisms in centrally impacted composite laminates, and the assistance and financial support of U.S. Army Research Office, Durham, North Carolina, and the program monitor. Dr. Y. Horie, are gratefully acknowledged. The author's graduate study at the University of Florida was supported financially by the Japan Society for the Promotion of Science, and the support by JSPS and the program monitor, Ms. Audrey Harney, International Institute of Education-Atlanta , is appreciated. The author sincerely appreciates the efforts of his supervisory committee chairman. Dr. Robert L. Sierakowski and co-chairman. Dr. Lawrence E. Malvern, whose assistance went far beyond that required by their position. For their constant encouragement and advice, and for their guidance and teaching, the author is greatly indebted. Special appreciation is extended to Dr. Ulrich H. Kurzweg, Dr. Chang-Tsan Sun, and Dr. Ellsworth D. Whitney, for their assistance, support, and for serving on the supervisory committee. The author would like to gratefully acknowledge the continuous support and encouragement of Dr. Kozo Kawata, the author's adviser at the University of Tokyo, who provided the opportunity to study in U.S. on leave from the University of Tokyo. The author thanks the department technical staff for their help in carrying out experiments and the department office staff for their kind assistance with administrative problems and clerical support. iii

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Finally, special thanks are directed to the author's friends both in the U.S. and in Japan who understood and supported what the author wanted to do. iv

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TABLE OF CONTENTS Page ACKNOWLEDGEMENTS ill LIST OF TABLES vii LIST OF FIGURES viii ABSTRACT xii CHAPTER 1 INTRODUCTION 1 1.1 Motivation of the Research 1 1.2 Impact Problems of Continuous Fiber-Reinforced Composite Materials (FRCM) 2 1.3 A Historical Review of Prior Research on Impact Problems of FRCM 3 1.4 Localized Impact Problems of Composite Laminates .... 8 1.4.1 Localized Impact Damage Experiments 8 1.4.2 Solution of Simplified Wave Propagation Problems Based on Continuum Mechanics Models . . 11 1.4.3 Hertzian Contact Approaches to Impact Problems . 14 1.5 Experimental Studies on Fracture Mechanisms of Impacted Composite Laminates at the University of Florida 15 1.6 Composition of the Dissertation 20 CHAPTER 2 LAMINATED PLATE SPECIMEN FABRICATION 22 CHAPTER 3 EXPERIMENTAL IMP ACTOR/ PLATE CONFIGURATION INTERACTION STUDIES 30 3.1 Introduction 30 3.2 Experimental Procedure 30 3.3 Studies on Impactor Nose Shapes and Length Effects ... 31 3.3.1 Purpose of the Studies 31 3.3.2 Fracture Patterns 37 3.3.3 Delamination 43 3.3.4 Transverse Cracks 49 3.3.5 Contact Time Measurement 57 3.4 Studies on Ply Orientation Effects 60 CHAPTER 4 MICROSCOPIC OBSERVATIONS OF CROSS SECTIONS OF IMPACTED COMPOSITE LAMINATES 64 4.1 Introduction 64 4.2 Sample Preparation 65 4.3 Results and Discussion 69 V

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TABLE OF CONTENTS (Continued) Page CHAPTER 5 EXPERIMENTAL WAVE PROPAGATION STUDIES OF IMPACTED COMPOSITE LAMINATES USING STRAIN GAGES 83 5.1 Introduction 83 5.2 Experimental Procedure and Consideration 84 5.3 Documentation Tests for Characterizing Embedded Gages . . 86 5.4 Strain-Gage Results and Discussion 88 5.4.1 Surface-Gage Results for [ (O®)^/ (90°)5/(0°)5] Laminates 88 5.4.2 Surfaceand Embedded-Gage Results for [(0°)5/ (90°)5/(0®)5] Laminates 109 5.4.3 Surface-Gage Results for [ (30°)5/(-30°)5/(30°)5] Laminates 115 CHAPTER 6 EXPERIMENTAL CRACK PROPAGATION STUDIES OF IMPACTED COMPOSITE LAMINATES 121 6.1 Introduction 121 6.2 Delamination Crack Propagation Studies Using a HighSpeed Camera 122 6.2.1 Experimental Procedure 122 6.2.2 Results and Discussion 123 6.3 Measurement of Generator Strip Formation Velocities . . . 150 6.3.1 Experimental Procedure 150 6.3.2 Results and Discussion 150 CHAPTER 7 SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS FOR FUTURE WORK 159 7.1 Summary and Conclusions 159 7.2 Recommendations for Future Work 165 APPENDIX A CALCULATION OF THE THEORETICAL WAVE PROPAGATION VELOCITIES IN IMPACTED LAMINATES 168 APPENDIX B CALCULATION OF THE RATIO OF PEAK STRAINS ALONG X AND Y AXES 173 LIST OF REFERENCES 175 BIOGRAPHICAL SKETCH 184 vi

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LIST OF TABLES Table Page 2.1 Details of processing materials and instruments for laminated plate specimen fabrication 27 3.1 Impactors used in this study 36 4.1 Supplies used in the sample preparation for SEM observation 67 5.1 Average modulus and critical stress measured in the four types of specimens and the corresponding calculated values 88 5.2 Peak strains and strain rates measured from gages along the x-axis and y-axis for Gage layout (c) 101 5.3 Wave propagation velocities, and peak strains and strain rates measured from gages along the y-axis for Gage layout (e) 109 6.1 Generator strip formation velocities 151 A.l Static properties of Scotchply 1002 matrix and E-glass fibers at room temperature 171 vii

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LIST OF FIGURES Figure Page 1.1 A generator strip and two delamination areas in a plate with three five-layer laminas 19 1.2 Schematic of three sequential delaminations 19 1.3 Total delamination area versus impactor kinetic energy for plates with five three-layer laminas and plates with three five-layer laminas 19 2.1 Baron Model BAC-24 autoclave 23 2.2 Layup system for prepreg tapes 24 2.3 The sequence of fabrication of composite laminate specimens . 25 3.1 Schematic of gas gun assembly and related equipments .... 32 3.2 A gas gun and its control valves 33 3.3 The velocity measuring system 33 3.4 A target plate clamped by a metal frame specimen holder ... 34 3.5 Specimen holder assembly installed inside a protective box . 34 3.6 Schematic of impactor contact time measurement 35 3.7 Photographs of [ (0°) (90°) (0° ) ^] laminates impacted by various types of impactors 38 3.8 Schematic of fracture patterns and deformations of laminates impacted by two different types of impactors 42 3.9 Total delamination area versus initial impactor kinetic energy for [ (0°) (90°) (0°) laminates 44 3.10 Mean transverse crack distance v.s. impactor velocity for [(0°)^/(90°)^/(0°)^] laminates impacted by various types of impactors 33 3.11 Typical oscilloscope records for contact time measurement . . 58 3.12 Contact time versus impactor velocity 59 3.13 Total delamination area versus impactor kinetic energy for angle-ply laminates 60 viii

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LIST OF FIGURES (Continued) Figure Page 3.14 Schematic of delamination pattern in [ (+6)^/ (-0)^/ (+0)^] angle-ply laminates 61 4.1 Joel JSM-35C scanning electron microscope 68 4.2 Typical fracture patterns of a [ (0°)^/ (90°)5/ (0°)5] laminate impacted by 2.54 cm blunt-ended steel projectile at a velocity of 75.1 m/sec (246.5 ft/sec) 70 4.3 Schematics of several cross sections of the laminate shown in Fig. 4.2 73 4.4 An undamaged interface of a [ (0°)3/ (90°)3/ (0°)3/ (90°)3/ (0°)3] laminate 74 4.5 Typical SEM pictures of cross sections of a [ (O®)^/ (90°)5/ (0°)5] laminate impacted by a 2.54 cm blunt-ended steel projectile at 75.1 m/ sec 74 4.6 Tensile and shear stresses developed in the transverse lamina 80 5.1 Recording setup for strain-gage experiments 85 5.2 Tensile test coupons tested in documentation tests for characterizing embedded gages 87 5.3 Surface-gage layout for [ (0°)5/ (90°)5/ (0°)5] fiberglass/ epoxy laminates 89 5.4 Strain-gage outputs from surface gages with Gage layout (a) in Fig. 5.3 ... 90 5.5 Schematic of the impacted plate response . 93 5.6 Strain-gage outputs from surface gages with Gage layout (b) in Fig. 5.3 96 5.7 Strain-gage outputs from front surface gages with Gage layout (b) in Fig. 5.3 100 5.8 Strain-gage outputs from front surface gages with Gage layout (c) in Fig. 5.3 101 5.9 Strain-gage outputs from surface gages with Gage layout (d) in Fig. 5.3 105 5.10 Strain-gage outputs from front surface gages with Gage layout (e) in Fig. 5.3 108 5.11 Surfaceand embedded-gage layout for [ (0°)^/ (90°)^/ (0°)^] f iberglass/epoxy laminates Ill ix

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LIST OF FIGURES (Continued) Figure Page 5.12 5.13 5.14 5.15 5.16 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 Strain-gage outputs from surfaceand embedded-gages with Gage layout (a) in Fig. 5.11 112 Strain-gage outputs from surfaceand embedded-gages with Gage layout (b) in Fig. 5.11, and the contact time record . . 114 Surface-gage layout for [ (30) (-30°)^/ (30°)^] fiberglass/ epoxy laminates 116 Strain-gage outputs from surface gages with Gage layout (a) in Fig. 5.14 117 Strain-gage outputs from surface gages with Gage layout (b) in Fig. 5.14 119 Setup of a Nova Model 16-3 16 mm high-speed camera 123 The overall experimental setup for measuring delamination crack propagation velocities using a high-speed camera . . . 124 Sequence of delamination crack propagation in a [(0°)_/ (90°)5/ (0°)5] laminate impacted by a 2.54 cm blunt-ended impactor at 74.5 m/sec (244.4 ft/sec) 125 Sequence of delamination crack propagation in a [(0°)^/ (90°)3/(0‘’)5] laminate impacted by a 2.54 cm blunt-ended impactor at 83.2 m/sec (273.0 ft/sec) 128 Sequence of delamination crack propagation in a [(0°)^/ (90°)3/(0°)5] laminate impacted by a 2.54 cm hemispherical impactor at 75.5 m/sec (247.6 ft/sec) 131 Sequence of delamination crack propagation in a [(O®)-/ (90°)3/ (0°)5] laminate impacted by a 5.08 cm blunt-ended impactor at 58.8 m/sec (192.8 ft/sec) 136 The resultant fracture appearance of impacted [ (0°) (90°) r/ (O®)^] laminates in Figs. 6 . 3-6 . 6 142 Distance of the propagating delamination crack tip from the plate center as a function of time AT after the first frame where delamination appears, calculated from photographic data in Figs. 6 . 3-6 . 6 146 Delamination crack propagation velocities in impacted [ ( 0 °) 5 / (90) ” 5 / ( 0 °) 5 j laminates, calculated from photographic data in Figs. 6 . 3-6 . 6 147 Modified velocity gage arrangement 152 X

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LIST OF FIGURES (Continued) Figure Page 6.11 Voltage-time records for measurement of generator strip formation velocities 153 6.12 Distance of the propagating generator strip tip from the plate center as a function of time AT after the first stripe is broken 157 xi

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Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy EXPERIMENTAL STUDIES OF THE DELAMINATION MECHANISMS IN IMPACTED FIBER-REINFORCED COMPOSITE PLATES By Nohuo Takeda August, 1980 Chairman: Robert L. Sierakowski Co-Chairman: Lawrence E. Malvern Major Department: Engineering Sciences Experimental studies of the fracture mechanisms in centrally impacted fiber-reinforced composite laminated plates have been systematically conducted. Semitransparent specimens were fabricated from fiberglass/epoxy prepreg tapes with an autoclave. A cross-ply arrangement with 3 laminas each containing 5 unidirectional layers was studied unless otherwise stated. Macroscopic observations of impacted laminates, which revealed the impactor/ laminate configuration interactions, have been supplemented by microscopic observations of cross sections of impacted laminates with a scanning electron microscope. Dynamic strains induced by impact of 2,54 cm blunt-ended impactors on laminates were measured using both surface and embedded gages with several different gage layouts. High-speed photos for semitransparent impacted laminates were taken from the back of the laminates illuminated from the front side. A Nova high-speed camera recorded rapid delamination crack propagations at speeds up to 40,000 frames/sec. xii

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According to macroscopic observations, the impactor energy was more dissipated within the front lamina and damage was more widely spread there with blunt noses than with hemispherical noses. Sequential delamination mechanisms were identified for all types of impactors tested. The larger impactors have a 30 percent higher apparent delamination surface energy than the smaller ones. So-called transverse cracks in the fiber direction of each lamina showed an almost evenly distributed crack spacing. The mean crack spacing decreased as the impactor velocity increased. According to contact time measurements, both single and multiple contacts were possible. The heavier and/or faster impactors had longer contact times . Microphotos revealed such details as that the transverse cracks obtained travel perpendicular to lamina interfaces where there is no delamination, while they travel oblique to interfaces where accompanied by delamination. Strain-gage records showed that the predominant wave was a flexural one for the tested velocity range, 30-40 m/sec. The largest amplitude of the flexural wave had on the average a measured velocity at 3.81 cm from the plate center of 290 m/sec and 225 m/sec in the 0° and 90° direction, respectively, with a decrease in velocity with distance from the impact point. Measured in-plane and flexural wave velocities agreed v/ell with the calculated values obtained from known material elastic constants . High-speed photos revealed that: The delamination crack in the 90° [0°] direction at the f irst[second] interface propagated initially at 300-400[400-500] m/sec which decreased to 200-300[270-400] m/sec during the period of observation, and decelerated to stop at about 100 [300] microseconds. This latter velocity agreed well with the largestamplitude flexural wave velocity measured by the strain gages. This xiii

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appears to be further documentation that delamination is caused by the flexural wave. Some transverse cracks were found to propagate while the delamination cracks propagated in several recorded photos. This is further evidence that transverse cracks and delamination cracks occur almost simultaneously, along with oblique transverse cracks and sudden jumps in strain-gage signal records. Transverse cracks are considered to be caused by membrane tensile waves due to a large deflection of the plate . A velocity gage consisting of a silver conductive paint was modified to measure velocities of the generator strip development. This generator strip formation velocity was found to be higher than the measured delamination crack propagation velocity. This fact is consistent with the assumption that the generator strip generates delamination cracks. xiv

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CHAPTER 1 INTRODUCTION 1.1 Motivation of the Research In recent years, fiber-reinforced composite materials (FRCM) have attracted considerable attention for practical use because of their high strength-to-weight and/or stif fness-to-weight ratios when compared with conventional monolithic materials [1]. This is particularly true in the aerospace area where advanced developments and usage of component parts made with FRCM are continuously being made. Other commercial usage such as in the sporting goods area for fishing rods, golf clubs, and tennis rackets has also been evident. Most recent usage has begun in the automotive sector of the economy where products made with sheet molding compounds (SMC), that is, chopped fibrous type composite materials have appeared. Our interest here is focused on continuous fiber composites. Therefore, FRCM will hereafter define continuous fiber-reinforced composite materials unless otherwise specified. Despite the known advantages of high static strength, high stiffness, and low weight of FRCM, knowledge of the impact resistance of such materials is rather scarce. As a specific example of the importance of this problem, FRCM used in turbine blades in jet engines may be damaged during take-off and flight by ingestion of stones, ice balls, birds, and other foreign objects [2]. This foreign object impact damage (FOD) problem has attracted much attention recently. Another example is the delamination failure of relatively thick laminates in actual large-size fiberglass-reinforced plastic boats exposed to impacts produced by ocean 1

PAGE 16

2 waves and often susceptible to delamination. The seriousness of these problems has accentuated the need for a better understanding of the impact damage tolerance of such FROM [3] . 1.2 Impact Problems of Continuous Fiber-Reinforced Composite Materials (FRCM) Impact problems differ from static problems in several ways [4]. One is the necessity for considering stress wave propagation in the material. In static problems the deformation energy can be distributed throughout the structure, but in impact problems the volume of energy storage is limited by the speed of the wave propagation. For short time impact loads, even a small amount of energy in a small volume can result in stresses which can fracture the material. A second important consideration is the strain rate the material is subjected to. It is known that both the fibers and matrices of FRCM have different strength properties under high strain rates from those under lower strain rates [ 5 ]. Composite materials have as inherent properties anisotropies and inhomogeneities, which need special attention for the design of an impact resistant structure. In composite materials the degree of anisotropy can be varied so that the designer can change the directional distribution of stress waves in an impact zone and avoid serious failure. For example, inhomogeneity introduces certain material discontinuities which produce dispersive effects as the stress pulse propagates within the medium. When compared with observed damage in conventional materials, the damage or failure of composite materials has different characteristics. Various failure mechanisms have been observed, such as fiber pull-out, debondlng between fibers and matrix, plastic deformation of the matrix.

PAGE 17

3 delamination, breakage of fibers, and so on [6,7]. This variety of failure mechanisms causes many difficulties in programming experiments and establishing meaningful analyses. 1.3 A Historical Review of Prior Research on Impact Problems of FRCM Initial analytical studies dealing with the dynamic properties of composite materials have been based upon some type of continuum model to describe the composite material response. Some experiments have also been conducted to evaluate these proposed modeling theories. A review of many of these have been noted by Peck [8] and Hegemier [9] and include: (1) effective modulus theories [10,11], (2) effective stiffness theories [12], (3) mixture theories [13,14], (4) theories of micromorphlc continue [15], (5) modified dislocation theories [16], (6) viscoelastic analogies [17], and (7) continuum theories with a microstructure based upon asymptotic expansions [9,14,18]. Due to mathematical complexity these theories have in general been restricted to problems of harmonic wave propagation in infinite or semi-infinite media, or to problems with planar motions. As a consequence of these complexities, structural analysts have continued to study structural (plate and shell) configurations using theories based upon the traditional assumptions. These approaches are reviewed in Sections 1.4 and 1.5. The impact testing of composite materials encompasses a variety of loads and specimen conditions. Many impact test methods have been developed for evaluating materials toughness or resistance to fracture [4,19]. The most common and classical Charpy and Izod tests use relatively small beam-like specimens (less than 3 in. long) under a transverse point force at low Impact velocities (less than 5 m/sec) and give a qualitative energy to fracture.

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For example, Chamis et al. [20] performed miniature-Izod impact tests on unidirectional fiber composites of glass, graphite, boron, and Kevlar fibers in an epoxy resin matrix, with the fibers either parallel or transverse to the cantilever longitudinal axis. Three prevalent failure modes were observed for longitudinal fiber arrangements. These were cleavage, cleavage with fiber pull-out, and cleavage combined with partial delamination due to interlaminar shear failure. The transverse failure mode was cleavage. The fracture surface included matrix fracture, fiber debonding, and some fiber splitting. Novak and DeCrescente [21] have performed Charpy impact tests for unidirectional graphite, boron, and glass fibers embedded in a resin matrix and tested in the fiber direction. The Impact strength of the glass fiber composites was found to be significantly higher than that of either the boron or the graphite composites. They found that the tensile stress-strain characteristics of the fibers are of primary importance in determining the level of composite impact resistance and that toughness of the resin does not appear to be an important factor. Toland [22] has used an instrumented Charpy testing machine to record the stress and strain in the specimen during impact, and cited the importance of differentiating between the energy absorbed elastically and that absorbed during the failure process. He also reported the dependence on specimen thickness of maximum load, initial energy, and total energy absorbed. Adams and Perry [23] also used an instrumented Charpy machine in conjunction with a scanning electron microscope (SEM) for studying the resulting fracture surfaces. Beaumont et al. [24] in running instrumented Charpy tests have established the terminology associated with the energy to the peak load as the

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5 initial energy, the energy absorbed after the peak load as the propagation energy, and the ratio of propagation energy to initiation energy as the "Ductility Index." They proposed to use this parameter in conjunction with the maximum impact stress and total impact energy for characterizing impact behavior. Adams [25] summarized and discussed Charpy test results of composite materials. He categorized the contributors and their data into general classifications with representative experimental results being included to emphasize the conclusions presented. The topics he discussed included the use of scanning electron microscopes, advantages of hybrid composites, layup patterns, notch insensitivity, specimen thickness, impact velocity, and "Ductility Index." Limitations to the aforementioned test methods lie in their inability to provide meaningful data on the material properties [4, 19]. The measured value of impact energy is not a material property but influenced by the size and geometry of the specimen and test arrangement. In other words, such test data cannot be used directly when designing a real composite structure. A second method that has been used to study impact strength of FRCM is the drop test method. Rotem and Lifshitz [26] measured longitudinal tensile strengths of unidirectional FRCM over a wide range of strain rates • -1 (5
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6 orientation of the lamination planes with respect to the impact load is important and determines the failure mode as well as the impact energy. Lifshitz [28] used the same technique to measure tensile strength of angle-ply FROM. A third method which also used the drop weight was developed by Kimpara and Takehana [29]. A special impulsive inertia loading test device was used in order to measure the interlaminar strengths in separate failure modes (interlaminar shear and tension) for various con-2 stant stress rates (5 to 45 GNm /sec). In this case, the maximum observed interlaminar shear and tensile strengths were taken as the fracture criteria. A fourth dynamic test method is the flyer plate technique which produces almost unidirectional strain in the specimen by impacting a flyer plate against a specimen. The pulses generated are of extremely short duration (0.12-0.22 ysec) and the impact velocities are high (up to 2400 m/sec). When the compressive wave front encounters the free back surface of the composite specimen, it is reflected as a tensile wave which may cause spalling of the specimen at some distance away from the back surface. Schuster and Reed [30] used this method to study internal damage and failure mechanisms of aluminum alloy laminates reinforced with boron filaments. Reed and Schuster [31] ran additional tests to note the filament fracture inside the composite specimen tested with momentum traps to suppress spall and measured the post-impact tensile strength of the materials tested. The literature on spall fracture in composites using one dimensional shock waves has been reviewed by Peck [8]. In the last three methods, the stress and/or strain state can be considered unidirectional and the strength (maximum stress) of each

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7 fracture mode can be measured in contrast with the Charpy and Izod tests which result in highly localized impact which causes a very complex stress state and difficulties in ability to measure the fracture energies. An alternate test method used for studying dynamic effects in composites is by impacting FRCM specimens with various projectiles which are fired from air guns over an extended velocity range (up to 500 m/sec) . In contrast to the previous flyer plate technique, impact takes place over a small area in this type of impact test. Another significant difference between these test methods is the length of pulse generated during the impact event. The flyer plate technique produces extremely short pulses which are rapidly dispersed by the relatively large diameter fibers generally considered. The localized impact technique, however, produces pulses of much longer duration (longer than 100 psec) and less affected by the relatively small diameter fibers embedded in the matrix. This localized impact technique leads to a complicated stress state. However, the merit of this test technique is the ability to stimulate such actual impact problems as the previously described FOB problems of turbine blades. The main research discussed herein deals with such localized impact problems of composite laminates, and this technique is reviewed in the following section. As discussed earlier, scale effects are of importance in impact tests if test data are to be extrapolated and applied to larger structures. For example, if a plate is part of a large structure fewer reflections might be obtained than in a small test specimen. Moon [4] recommended the nondimensional parameter VT L where T is the contact time, V is a wave speed, and L is a representative

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8 length. It was suggested that this parameter should be matched in addition to other variables in order to compare different experimental data. 1.4 Localized Impact Problems of Composite Laminates The localized impact problems of beams and plates of homogeneous and isotropic elastic materials have been studied quite extensively and summarized by Goldsmith [32] and Backman and Goldsmith [33]. An equivalent study of similar problems for structures of composite materials has only recently been the center of considerable research activity. Generally composite material problems have been studied from three different points of view. 1. Localized impact damage experiments. 2. Solution of simplified wave propagation problems based on continuum mechanics models. 3. Hertzian contact approaches to impact problems. 1.4.1 Localized Impact Damage Experiments Some of the early experimental studies dealing with the impact resistance and penetration characteristics of FRCM were run on locally impacted composite plates. Gupta and Davids [34] have studied the penetration resistance of fiberglass cloth/polyester plates of varying thickness and density. They found a linear relation between the energy loss in penetration and the thickness, a linear relation between the impact energy and the thickness of plates required to just stop the projectile, and a relation between the density and the stopping thickness. They found that the weight efficiency of fiberglass cloth is greater than that of steel. Morris and Smith [35] observed noticeable internal damage in fiberglass laminated plates tested at very low impact energy levels without

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9 noting any apparent surface damage. They also measured the residual tensile and four-point bending strengths of impacted specimens. The resultant internal damage, delamination or debonding and/or fiber breakage was found to reduce strength significantly particularly in bending. Some further investigation on the impact resistance of fiberglass/ epoxy plates reinforced with wire sheet were conducted by Wrzesien [36]. The wire reinforcement gave a significant improvement in composite impact resistance and better damage containment. It was noted that plates with apparently good penetration resistance were heavily delaminated indicating that a considerable amount of impact energy was absorbed by the delamination. Askins and Schwartz [37] reported that a two-stage failure mode consisting of extensive delamination followed by tensile loading of individual laminas increased energy absorption in composite backup panels for ceramic armor. They conjectured that the tensile loading stage was the major energy absorbing mechanisms in their tests but that extensive delamination was needed to prevent "plugging" of the panel and to permit more of the panel to participate in the impact event and contribute to energy dissipation. Test results indicated that for such applications fibers should have low density, high tensile strength, high stiffness, and low interfacial bond strength. The effects of preload and of ply layups for graphlte/epoxy and boron/epoxy laminated plates on composite penetration characteristics, particularly the residual strength and the threshold strength, have been examined by Francis et al. [38] and Olster and Roy [39]. Francis et al. used a biaxial preloading which produced a variety of failure patterns for transverse impacts. Olster and Roy showed that the residual strength

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10 and the threshold strength correlate directly with the fracture toughness of the laminates. They also measured the propagation velocities of cracks which initiated from projectile holes and found the cracks traveled at approximately 55 percent of the shear wave velocity for each of the materials tested. Some residual strength studies of advanced composites have been made [40-42]. Avery and Porter [40] compared the residual strength and damage size for metals as well as for boron/ epoxy and graphite/epoxy composites. Suarez and Whiteside [41] also compared the residual and impact fracture strengths of boron/epoxy composites with metals. Husman et al. [42] studied the residual strength of boron, graphite, and glass/epoxy laminates and discussed an analogy between damage inflicted by a single-point hard particle impact and damage by inserting a flaw of known dimensions in a static tensile coupon. Preston and Cook [43] observed the damage of graphite/epoxy cantilever panels caused by impacting spherical projectiles of gelatin, ice, and steel. Steel projectiles were found to have the lowest damage threshold. A Jtiertzian analysis showed small steel projectiles were most likely to cause delamination and penetration damage. Kawata and Takeda [44] conducted foreign projectile impact experiments on glass roving cloth/polyester laminated plates consisting of three laminas. They found that below the perforation speed, the dominant energy absorbing fracture mechanisms were delamination between laminas and debonding occurring between fibers and matrix. It was also shown that the total damaged area and the initial kinetic energy have a linear relation. Gorham [45] used high-speed photography to examine and explain some features of the fracture behavior of fibrous and laminated composite plates.

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11 The semitransparency of the materials selected for testing enabled internal failure to be examined photographically. Both commercial and model composite systems were loaded at very high rates of strain by highspeed water impact as well as hard body impact. In particular, lamina model experiments suggested the initiation of shear along a lamina interface by waves which produced frontal delamination in the laminates. Impact tests on full-scale laminated turbine blades have also been carried out by the engine manufacturers [46-48] . Impactors used for these studies include gravel, ice, steel, gelatin, and real birds. Experimental studies on failure mechanisms of impacted composite laminated plates [49-56] have been conducted intensively at the Department of Engineering Sciences, University of Florida, for several years. These studies are the basis of the present research and are reviewed separately in Section 1.5. 1.4.2 Solution of Simplified Wave Propagation Problems Based on Continuum Mechanics Models Theoretical analyses of wave propagation in transversely impacted composite laminates have been discussed by many investigators [57-67] with only a few experimental Investigations having been reported [60, 68]. A laminated plate theory developed by Yang et al. [57], which includes both thickness shear deformation and rotary inertia, was investigated by Whitney and Pagano [58], who solved several boundary value problems. Using a similar laminated plate theory, Chow [59] derived the dynamic equations for orthotropic laminated plates. The propagation of flexural waves and the transient response of a rectangular plate to a normal impact were investigated. The effect of transverse shear on the amplitude of the deflection was evaluated in this dynamic study of anisotropic composites.

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12 Chou and Rodini [60] have demonstrated the accuracy of the laminated plate theory in transient wave propagation problems, comparing experimental measurements with theoretical calculations. The experimental program consisted of impacting the edge of a specimen plate with a striker plate. Each specimen was subjected to two separate impact loadings; an in-plane Impact and a so-called shear-bending impact. The analytical phase consisted of solving the Whitney and Pagano equations by the method of characteristics. Sun and Lai [61] later demonstrated the adequacy of the lamination theory, comparing the more exact orthotropic elastic solution with the lamination theory solution, using the fast Fourier transform (FFT) technique. A series of analytical investigations on transient wave propagation have also been reported by Moon [62-66]. Moon [62] investigated the shape of wave fronts of an infinite laminated plate subjected to both transverse and central impact loads. The mathematical model used for the plate element analyzed was based on the effective modulus theory for composites [4] and Mindlin's theory for plates in which the displacement is expanded in the thickness variable by using Legendre polynomials. The velocity and wave surface were described as functions of the layup angles for the graphite/epoxy plates examined. In following papers. Moon [63,64] studies the one-dimensional stress and displacement distribution induced in the same model by impact line forces, using the fast Fourier transform (FFT) technique. Moon [64,65] also gave a two-dimensional analysis which results in five two-dimensional stress waves. Three of the waves are flexural and two involve in-plane extensional strains. Results obtained using this analysis indicate that the points of maximum stress travel along the fiber directions. It was

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13 shown that for ± 15 deg. angle-ply layups lower flexural stresses are generated than for 0, ±30, and ±45 deg. cases. In a recent paper, Kim and Moon [66] modeled a multilayer composite plate as a number of identical anisotropic layers with Mindlln's theory then applied to each layer in order to obtain a set of differencedifferential equations of motion using the interlaminar stresses and displacements as explicit variables. Propagation of waves through the plate thickness was also examined in a simple way. This problem was also then extended to examining the effect of introducing damping layers between two elastic layers. Kubo and Nelson [67] presented an analytical study of the twodimensional (plane-strain) response of an elastic laminated plate, using a finite element /normal mode technique. The physical behavior of the plate was represented along the in-plane length of the plate in the form of a Fourier series, and its behavior in the thickness direction modeled by a sufficiently large number of generalized coordinates to capture quantitatively the propagation and dispersion of stress waves due to a surface impact. This technique produced both high frequency and low frequency information for both long and short wavelengths with respect to the plate thickness. Experimental investigations were conducted by Daniel and Liber [68] to understand the wave propagation characteristics, transient strains and residual properties of unidirectional and angle-ply boron/epoxy and graphite/epoxy laminates impacted with silicon rubber projectiles at velocities up to 250 m/sec. Strain signals recorded using surface and embedded strain gages were monitored and analyzed to determine the wave types occurring, wave propagation velocities, peak strains, strain rates, and attenuation characteristics. The predominant wave form was determined

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14 to be a flexural one propagating at different velocities in different in-plane directions within the impacted plate. 1.4.3 Hertzian Contact Approaches to Impact Problems In the wave propagation studies described in the preceding section, impulsive forces introduced in the laminates were assumed to be known. However, in reality, the loading is the result of an impact generated between the projected object and the plate and should be evaluated. The classical Hertzian contact theory of impact has long been applied to this localized impact problem to evaluate the contact force, the dynamic response of the plate, and the energy transfer. Extension of the Hertzian contact theory of impact to anisotropic half-space bodies has been made by Willis [69] and Chen [70]. The contact region was shown by Willis to be elliptic, deviating slightly from that of a circle. A simple model for estimating the contact time for isotropic spheres impacting composites was suggested by Moon [64], which assumes as a premise a circular contact area. He then found that dependence of contact time T and peak pressure on the impact velocity V was of the form. T Greszczuk [71] and Greszczuk and Chao [72], also used a Hertzian contact theory to study the dynamic response to impact by spherical impactors, of both semi-infinite composite laminates and finite laminated plates. Three major steps were used to formulate a solution, these being: (1) the time-dependent surface pressure distribution under the impactor, (2) the time-dependent internal stresses in the target caused by the surface pressure, and (3) failure modes in the target caused by the internal stresses.

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15 To verify predictions of failure modes, ball-drop tests were conducted on circular laminated plates [72] incorporating different fiber-resin combinations, fiber layups, and stacking sequences. The visible damage used in the analysis consisted of observed transverse cracks on the back face of the impacted plates. As mentioned earlier, Preston and Cook [43] also analyzed the simple Hertzian contact problem for cantilever laminates. An interesting aspect of this analysis was that multiple impacts were predicted due to the combination of vibratory modes and the local elastic deformation occurring. A more rigorous solution for the response analysis of laminates was presented by Sun and Chattopadhyay [73]. They used a method proposed by Timoshenko to derive a nonlinear integral equation to obtain the contact force and the resultant dynamic response of the simply supported laminated plate subjected to the central impact of a mass under initial stress. The plate equations developed by Whitney and Pagano [58], which include transverse shear deformation, were used as the governing equations. The energy transferred from the mass to the plate was obtained using this analysis. Sun [74] developed a higher order beam finite element in conjunction with the Hertzian contact law to determine the total energy which is imparted from the projectile to the beam and the damage energy which causes local damage in the laminated beam subject to impact of hard projectiles. Linear elastic analysis was used up to the maximum contact force point with subsequent unloading assumed as in rigid plasticity. 1.5 Experimental Studies on Fracture Mechanisms of Impacted Composite Laminates at the University of Florida Coordinated experimental and analytical studies on penetration mechanics of composite laminated plates have been done extensively at the

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16 University of Florida and serve as the main background of information for this research study. Ross and Sierakowski [49] have reported results on the influence of composite constituents, and geometrical arrangement of fibers on the penetration resistance of impacted plates. A comparison of data based upon an areal density merit rating system has shown a favorable energy absorption potential for fiberglass composites. One series of plates tested in their experiments were fabricated using fiberglass roving continuous filaments impregnated with an epoxy matrix and laid up in 0°-90° ply configurations. This series of tests examined the effect of varying the number of fiber layers in each unidirectional lamina, while keeping a constant total number of 15 layers in each plate. It has been anticipated that an alternating cross-ply arrangement, with one layer in each lamina, would offer greater resistance to perforation than any other arrangement. However, it was shown that a plate with five three-layer laminas or one with three five-layer laminas showed slightly better perforation resistance to normal impacts using blunt-ended impactors. Close examination of some of the perforated and partly penetrated plates led to the description of a sequential delamination mechanism [50] , which appears to account for the good performance characterizing the penetration resistance of plates consisting of multilayer laminas. The delamination areas were clearly evident in the semitransparent fiberglass/ epoxy plates when a bright light was placed behind the plates as shown in the typical photograph of Fig. 1.1, which shows two delamination areas in a plate consisting of three five-layer laminas. Figure 1.2 is a schematic diagram of the damage observed for three delaminated areas, marked A 2 , A^. In impacts by a blunt-ended cylinder of diameter D on plates with such multilayer laminas at moderate

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17 speeds, a shear cut-out is first noted. This circular plug does not necessarily extend all the way through the first lamina, and the sequential delamination is begun when a strip of width D in the first lamina (parallel to the fibers) is pushed forward by the penetrator. This "generator strip" loads transversely the second lamina and initiates a separation between the first two laminas. The generator strip from the first lamina is bounded by two through-the-thickness shear cracks, marked AA and BB in Fig. 1.2. This generator strip lengthens and the delamination area A^ enlarges until the available energy is insufficient to continue the propagation of the delamination. A new generator strip may be formed in the second lamina (perpendicular to the first one in the 0°-90° layup plates) , which initiates a second delamination area A 2 between the second and third laminas, and the process is then repeated with each subsequent delamination covering a larger area than the one before it. In very high-speed impacts plugging may extend all the way through the plate with almost no delamination visible, although the hole enlarges so that the last laminas perforated show more tensile breaking and less of a well-defined shear cut-off. The dependence of these failure mechanisms on such parameters as fiber type, ply orientation, and matrix-fiber interaction was investigated by Ross, Cristescu, and Sierakowski [51] using diagnostic tests such as pull-out tests and low-velocity repeated impact tests. The ductile-fiber steel/epoxy systems tested did not display the sequential delamination process but instead exhibited an almost symmetrical damage area without significant delamination. A further series of tests on 0°-90° fiberglass/epoxy plates was then undertaken to examine in more detail the mode of progressive failure and the effects of sequential layup arrangement on the development of the generator strip and the sequential delamination mechanism [52]. In

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18 particular, the effect of the number of layers in the first and second lamina on the initiation mechanism was discussed. Analysis of these controlled and ordered lamina tests [53] revealed a linear dependence of the total delamination area obtained on the initial kinetic energy of the impactor at speeds below the critical speed for perforation. As shown in Fig. 1.3, the straight line was fitted to the data for plates with five three-layer laminas. The equation of this line was shown to be K = 3.5 + 0.315A for K>3.5J (1.1) where K is the kinetic energy measured in joules and A is the delamination 2 area in cm . The apparent fracture surface energy was constant at 1580 2 2 J/m (or 0.158 J/cm , half of the coefficient of 0.315 in Eq. (1.1) since two surfaces are formed) . The data for plates with three five-layer laminas were also plotted in Fig. 1.3 for comparison and found to agree well with the same straight line except for data run at higher speeds. These high-speed data correspond to cases where the delaminated areas have extended to the clamped boundaries. Fiberglass plates of the same type as those centrally Impacted in early studies, along with fiberglass cloth plates, were subjected to blast loading using a fuel air explosive device [54]. A delamination mechanism again appears to be the dominant failure mechanism for these plates, for blast loads below the edge failure load. Delamination begins at the plate edges and progresses toward the center of the plate with the total delamination area appearing to be proportional to the amount of plate deflection and the intensity of the applied blast pressure. Some calculations on the elastic response to a simulated impact loading applied as a pyramid shaped pressure distribution over a square

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19 Fig. 1.1 A generator strip and two delamination areas in a plate with three fivelayer laminas . Schematic of three sequential delaminations. The first generator strip is bounded by AA and BB. 1.3 Total delamination area versus impactor kinetic energy for plates with five three-layer laminas (circle and triangle points and fitted line) and plates with three five-layer laminas (square points) .

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20 area at the center of the localized impacted plates, were made using a DEPROP (Dynamic Elastic-Plastic Response of Plates) computer code for comparison with experimental data with some success [55]. Attempts were also made to calculate the location of the maximum shear stress, using simple elastic analyses for cylindrical bending of the laminated plates with orthotropic laminas having unequal moduli in tension and compression. In addition, a summary of the above experimental and analytical studies has been reported by Malvern et al. [56]. 1.6 Composition of the Dissertation This dissertation is primarily concerned with the experimental studies on the failure mechanisms in centrally impacted composite laminates . In Chapter 1, a historical review has been provided and organized in order to clarify the localized impact problems of composite laminates of principal interest in this investigation. Specifically, previous experimental studies conducted at the University of Florida, which provide fundamental information on plate failure mechanisms, have been summarized. In Chapter 2, prepreg fabrication procedures of composite laminate specimens have been described. The specimens have been fabricated from f Iberglass/epoxy tapes using an autoclave to control the pressure and the temperature during the specimen forming and curing times. In Chapter 3, experimental studies on failure mechanisms of centrally impacted composite laminates have been conducted systematically in order to investigate the effects on the fracture mechanisms of several parameters, such as Impactor nose shape, impactor length (mass), impactor kinetic energy, and ply orientation of the fabricated prepreg

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21 laminates. The overall fracture patterns, delamination, transverse cracks, and the contact time have been investigated intensively. In Chapter 4, microscopic observations of cross sections of impacted composite laminates have been obtained using a scanning electron microscope. The photomicrographs have confirmed macroscopic observations and given added details which could not be obtained otherwise, particularly as to the interaction of the planar delamination and transverse cracks. In Chapter 5, the details of the time history of the elastic waves before delamination have been measured using surface and embedded gages. These gages have been placed on and within the specimens in order to study what waves predominate and to relate the wave behavior to the fracture mechanisms involved. In Chapter 6, the delamination crack propagation velocities as measured by a high-speed camera have been discussed. The dynamics of the impactor and its interaction with the laminate have also been described from the optical data obtained. The velocities of the generator strip development have also been measured using a newly-devised velocity gage. These velocities are important parameters required to further understand the complex fracture behavior of the composite materials being investigated. Finally, in Chapter 7, a summary of the overall study and concluding remarks have been made.

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CHAPTER 2 LAMINATED PLATE SPECIMEN FABRICATION All the composite laminated plate specimens used in this study were fabricated from fiberglass/epoxy prepreg tapes* using an autoclave (Fig. 2.1) to control the pressure and the temperature during the specimen fabrication. Twelve inch by twelve inch plates were prepared in the autoclave and cut into desired specimen sizes after fabrication. Many attempts were made to establish the best plate fabrication method for producing the standard 12" by 12" sized layup system as shown in Fig. 2.2. The established sequence of fabrication for the plates is shown in Fig. 2.3 and the fabrication methodology described below. Upon receipt from the manufacturer, prepreg tapes were refrigerated and stored until use. Subsequently, for fabrication the tape was removed from the refrigerator and warmed up to room temperature before layup to prevent moisture from condensing within the specimens. A fabrication tool and specimen sizing dam were cleaned with acetone with the surface within the dam border coated with a release agent (Fig. 2.3(a)). A layer of teflon-coated vent cloth was then put on the fabrication tool to eliminate bonding of laminates to the tool surface (Fig. 2.3(b)). Prepreg tapes were cut into the required 12" by 12" size. A sharp paper cutter was used to cut ply layups with care taken so as not to disorient fibers and not to soil the plies. Clean plastic gloves were found to be *The details of the underlined processing materials and instruments used in this thesis investigation and referred to in this chapter are given in Table 2.1. 22

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23 Fig. 2.1 Baron Model BAC-24 autoclave.

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BAG SEALING COMPOUND 24 Fig. 2.2 Layup system for prepreg tapes.

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25 Fig. 2.3 The sequence of fabrication of composite laminate specimens. See the text for details.

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26 Fig. 2.3 Continued

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27 Table 2.1 Details of processing materials and instruments for laminated plate specimen fabrication Processing Materials or Instruments Description Manufacturer Fiberglass/Epoxy Prepreg Tape "Scotchply" Type 1003, 12" or 18" Wide, B Stage of Curing, Resin Content 36% by Weight 3M Company, Minneapolis, Minn. Autoclave Baron Model BAC-24 Electrically Heated Autoclave, Max. Pres. 110 psig Max. Temp. 650° F Working Diameter 2 ft. Working Length 4 ft. Baron Blakeslee, Santa Fe Springs, Calif. Fabrication Tool Aluminum Plate 17"xl7"xl/2" Dam Aluminum Plate 14"xl"xl/8" 12"xl"xl/8" Release Agent Ram Mold Release 225 Ram Chemicals, Gardena, Calif. Teflon Coated Vent Cloth TX 1040, Teflon, Coated Glass Fabric, Porous, 0.002" thick Pallflex Products Corp. , Putnam, Conn. Bleeder Ply Commercial Grade 120 Style Glass Cloth Metal Caul Plate Aluminum Plate 12"xl2"xl/4" Barrier Film "Mylar" Film, 2 mils 14"xl4" E. I. Dupont Co. Wilmington, Del. Breather Ply Commercial Grade 120 Style Glass Cloth Bag Sealing Compound S. M. 5126 3/8"x3/16" Schnee-Morehead Corp., Irving, Texas Vacuum Bag Nylon Film, 8 mils, 17"xl7"

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28 a requirement in order to properly handle the prepreg tapes. Each cut tape or ply was then laid up following the required stacking sequence (Fig. 2.3(c)) and pressed against the tool with a rubber roller to remove trapped air. A paper liner used to protect prepreg tapes from foreign matter was removed prior to each ply layup. After finishing the ply stacking sequence, the laminate was covered with two teflon vent cloths in order to prevent bonding the laminate to bleeder ply material. The glass bleeder ply was then placed in the system so as to absorb excess resin from the laminate (Fig. 2.3 (d)). Only one bleeder sheet was used in the fabrications described herein. Placed on top of the bleeder ply sheet was a metal caul plate , which is a perforated aluminum plate coated with release agent and used to smooth the laminate top surface (Fig. 2.3(e)). The total laminate assembly inside the dam was then covered with a barrier film (Fig. 2.3(f)) to prevent excess resin from overflowing the dam. After addition of several more breather ply materials, a bag sealing compound was placed along the periphery of the tool plate (Fig. 2.3(g)), and the entire assembly covered with ^ vacuum bag . The entire system was then sealed between the vacuum bag and the tool (Fig. 2.3(h)). This bagged layup was then connected to a vacuum pump installed in the autoclave using a vacuum bag adapter with a copper tubing and fitting (Fig. 2.3(i)). The autoclave curing cycle consisted of the following procedure. 1. Place the vacuum pump in operation at up to 29.5 inches Hg vacuum. 2. Check for bag leaks. 3. Raise the autoclave pressure to 40 psi. Set the vacuum control switch to the "Auto" position in order to operate at 27 inches Hg vacuum. 4.

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29 5. Heat the autoclave directly to 320° F using a temperature climb rate of 10° (±2°) F per minute. 6. Keep the specimen at the above temperature and pressure for 1 hour. 7. Release the autoclave pressure and the vacuum. 8. Hold the temperature at 280° F for 16 hours. 9. Cool to below 150° F before the bagged layup is removed. The fiber content of fabricated laminated plates was estimated to be about 70-72 percent by weight. A trial and error procedure was used to obtain fabricated plates with a suitable interlaminar strength for testing and satisfactory transparency so that delamination might be detected using a high-speed camera with light sources placed behind the plates. Plates consisting of more than 72 percent by weight of fibers were found to be deficient in possessing satisfactory transparency.

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CHAPTER 3 EXPERIMENTAL IMPACTOR/ PLATE CONFIGURATION INTERACTION STUDIES 3.1 Introduction As reviewed in Chapter 1, experimental studies on failure mechanisms of impacted composite laminated plates [49-56] have been conducted systematically at the University of Florida, and have demonstrated the existence of a generator strip followed by a sequential delamination mechanism. Several parameters, such as fabrication methods, layup sequence, and filament selection have been changed during these studies in order to investigate the effects of these parameters on the failure mechanisms. Since a considerable number of parameters can be varied, it was decided to concentrate on a single composite material system [glass/ epoxy] for the current experimental studies and to use Scotchply 1003 prepreg tapes exclusively as explained in Chapter 2. All test specimens used for the impactor/plate interaction studies described in this chapter were 15.24 cm (6 in.) square laminates. Parameters varied were impactor length (mass), nose shape, and kinetic energy as discussed in Section 3.3 and ply orientation in Section 3.4. The experimental procedure has been briefly described in Section 3.2. 3.2 Experimental Procedure The impact tests in this study were performed using a gas gun assembly shown schematically in Fig. 3.1. The development of this equipment has been previously described in Ref. [75]. The gas gun used and its control 30

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31 valves have been shown in Fig. 3.2. The impactor velocity was varied by changes in chamber pressure of the gas gun. The impact velocities were measured by use of photocells in conjunction with light beams passing through the barrel of the gas gun (Fig. 3.1). As the impactor cuts the light beams a fixed distance apart, the output of the photocells measuring the light intensity is monitored on an oscilloscope. An independent check of the impactor velocity was made using a digital counter, which gave the measured time in microseconds. The velocity measuring system is shown in Fig. 3.3. The sides of the target plates were clamped to steel frame specimen holders, which were held fixed relative to the ground as shown in Fig. 3.4. The effective test length of the sides of the square plates was thus reduced to 13.97 cm (5 1/2 in). This specimen holder assembly was placed at a distance of 12 cm from the end of the barrel to ensure normal impact and installed inside a protective box (Fig. 3.5). The contact time of the impactor on the plates was measured in several tests using an apparatus as shown in Fig. 3.6. The impactor closed a gap between two brass tabs cemented to the front surface of the plate and connected to an electric circuit. The closing and opening of the circuit were recorded as steps on a digital oscilloscope trace, which provided a measure of the contact time in microseconds. An independent check on the contact time was made using a digital counter, which also gave the measured time in microseconds. 3.3 Studies on Impactor Nose Shapes and Length Effects 3.3.1 Purpose of the Studies The [ (0°)^/ (90°)^/ (0°)^] ply orientation was used mainly as the laminate structure for this phase of the study unless otherwise mentioned.

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SYSTEM BLEED 32 a: Q. c ai e a. •H 3 u* (U Ti Q) XJ CO «H 0) TJ c CO rH 'a 0) w o O •H cO a Q) O w 00 •H gas gun as

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Fig. 3.2 A gas gun and its control valves. Fig. 3.3 The velocity measuring system.

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34 Fig. 3.4 A target plate clamped by a metal frame specimen holder. Fig. 3.5 Specimen holder assembly installed inside a protective box.

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35 LAMINATED PLATE BRASS TAB STEEL IMPACTOR FiS" 3.6 Schematic of impactor contact time measurement.

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36 The introduction of a graduated change in impactor nose shape from blunt-ended to truncated hemispherical and then hemispherical was used in order to examine the influence of impactor edge effects on generator strip formation, subsequent observed plate delamination, and overall fracture patterns including transverse cracks in each lamina. Variations in impactor length (2.54 cm, 5.08 cm) and mass were made for both the blunt-ended and hemispherical impactors in order to determine whether the total delaminated area was linearly related to impactor kinetic energy for all cases studied and if so, whether the slope of the delaminated area versus impactor kinetic energy curve remained constant for changing length (mass) . The threshold impactor energy required to initiate the delamination mechanism was also investigated. Variations in impactor length and mass were expected to lead to variations in impactor contact time on the target plates. Therefore, a study was made to see whether the impactor contact time produced an influence on the delamination area versus kinetic energy curve. Impactors used in this study were 9.525 mm (3/8 in) in diameter and have been summarized in Table 3.1. A velocity scan was performed, testing a fixed impactor type at increasing impactor velocity well below the plate perforation velocity. The velocity range chosen was from 30 m/sec to 80 m/sec for the 2.54 cm impactors and from 30 m/sec to 60 m/sec for the 5.08 cm impactors. Table 3.1 Impactors used in this study (A) Blunt-Ended (B) Truncated Hemispherical (C) Hemispherical ! c_ n v! 2.54 cm (I in.) 14.175 g 13.275 g 13.275 g 5.08 cm (2 in.) 28.35 g — 27.45 g

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37 3.3.2 Fracture Patterns Composite laminates impacted by the various kinds of impactors were illuminated from the back side of the plates. Several are shown in Fig. 3.7. From careful examination of these photos, the following remarks on the fracture patterns obtained here are made. It has been recognized that impacted composite laminates may fail with several different failure mechanisms occurring separately or in some combinations such as: shear cut-out of a plug; fiber debonding, stretching, breaking, and/or pull-out; delamination; and matrix failure. Among them, the generator strip and sequential delamination mechanism mentioned in Chapter 1 appear to be dominant in most of the cases treated. In addition, evenly distributed fine transverse cracks parallel to the fibers were observed in each lamina of the impacted plates. This is a detail which had gone unnoticed in previously reported investigations under the impact loading conditions. The plates tested in these previous experiments were found upon careful re-examination to have transverse cracks in each lamina. Detailed discussions on the delamination cracks and transverse cracks found are given in Sections 3.3.3 and 3.3.4. Nose shape was found to have a marked effect on the overall delamination/fracture pattern and the observed permanent deformations on the front and back surfaces of the tested laminates. A typical schematic of the fracture patterns and deformations found in these tests has been shown in Fig. 3.8. A hemispherical nosed impactor produces a more local crushing of the first lamina right under the nose of the impactor with a less developed generator strip indicated than a blunt-nosed impactor produces. For the hemispherical nose, a single line crack occurs in the back face of the plate directly ahead of the center of the impactor and produces a large permanent deflection. This crack exists along the crest

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TajjTT. 38 CO 0) a o CO CO > 3 * >* T3 ( 1 ) U O Cd cu e CO 0) cd c •H m /— N o O O O o\ s_x » O c O •H s— «’ t iH w* M-l O • B CO u CO o a 4J lO cd o • u cd CiO a o 6 /-N u ‘H Cd o s— / 4m Pm O CO ti •iH

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39 BLUNT-ENDED, 80.83 m/sec (265.2 ft/sec)

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40 TRUNCATED HEMISPHERICAL, 73.61 m/sec (241.5 ft/sec)

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41 HEMISPHERICAL, 78.21 m/sec (256.6 ft/sec)

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42 BACKSIDE VIEW LINE CRACK LARGE DEFLECTION DELAMINATION AT THE 1ST INTERFACE DELAMINATION AT THE 2ND INTERFACE SHARP CORNER LINE CRACK PREDICTED DEFORMATION HEMISPHERICAL NOSE BLUNT NOSE Fig. 3.8 Schematic of fracture patterns and deformations of laminates impacted by two different types of impactors.

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43 of a ridge of material pushed forward at these subperforation speeds. This contrasts with the observed strip of width approximately twice the impactor diameter produced by blunt-nosed impactors in the back face of the plate specimen tested. As described in the following sections, the ratio of the front and back delamination areas is lower for hemispherical impactors when compared with blunt-ended impactors at the impactor velocity ranges where clear generator strips are developed in laminates impacted by blunt-ended impactors. The mean transverse crack distance developed in the impacted plates studied has been found to be smaller at the back face than at the front face with hemispherical impactors, while the reverse has been found with bluntended impactors. In summary, damage is more localized and impact energy is less dissipated at the front lamina (as indicated both by smaller front delamination area and by more widely spaced transverse cracks at the front face) with hemispherical impactors than with blunt-ended impactors. 3.3.3 Delamination 2 The total delamination area in cm has been plotted versus initial kinetic energy of the impactor in joules in Fig. 3.9 for various kinds of impactor nose shapes and masses as listed in Table 3.1. All tests have been run at velocities below the velocity required for complete plate perforation. It is observed that the nose shape of the impactor appears to be insignificant in the amount of delaminated area obtained for a given impact velocity so long as damage does not extend to the plate boundaries. At higher impact velocities, that is, higher impactor kinetic energies, the delaminated area has extended to. the clamped boundaries because the blunt-ended Impactor produces greater overall delamination.

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AREA (cm*) 44 Fig, 3.9 Total delamination area versus initial impactor kinetic energy for [ (0°)^/ (90°)^/ laminates.

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45 The mass and length of the impactor have some effects on the apparent fracture surface energy. For both the 2.54 cm and 5.08 cm impactors, the total delaminated area has been found to be linearly related to impactor kinetic energy. The straight line plots shown were fitted by least squares to the data for each impactor length and shown to be of the following form: K 0.8 + 0.750A (2.54 cm impactor) K = 1.0 + 0.975A (5.08 cm impactor) (3.1) 2 In the above equations, the area A is given in cm and the kinetic energy K in joules. These equations are valid between 10 joules and 40 joules, excluding the very large areas between 32 joules and 40 joules above the dashed line in Fig. 3.9. An absolute measure of the threshold impactor kinetic energy required to initiate delamination appears to be somewhat unreliable because of its relatively small magnitude. The apparent delamination fracture surface energy has been found to be constant at about 2 y = 0.375 J/cm (2.54 cm impactor) 2 (3.2) Y 0.488 J/cm (5.08 cm impactor) The above values are one half the coefficients of A as used in Eq. (3.1), since two surfaces are formed in the delamination process. These values are found to be higher than the 0.158 J/cm as obtained for glass/epoxy laminates fabricated by filament winding and matrix impregnation [53] and also the value 0.155 J/cm found for glass roving cloth/polyester laminates formed from three laminas using a hot press [44]. This result appears to occur due to the fabrication procedure used for forming the test laminates. Specifically, the prepreg tapes use an autoclave in the

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46 forming process and have stronger interfaces than the filament-wound laminates based on the y values even if both types of laminates show similar delamination patterns. The apparent delamination fracture surface energy obtained is an order of magnitude higher than the fracture surface energies obtained in static tests on pure epoxy double cantilever beam specimens [76] and on aluminum-epoxy combined mode adhesive joint specimens [77], There appear to be at least four factors contributing to this difference in fracture surface energies. The first factor is the crack velocity. Several investigators have reported higher values for the fracture surface energy in dynamic crack propagation than in static tests. Dynamic values approximately 100 percent higher than comparable static values for constant— velocity cracks have been measured in Homalite-100 plates [78]. The fracture surface energy of PMMA as a function of crack velocity has been reported by several investigators [79-81]. The dynamic values were found to be as much as an order of magnitude higher than static data before crack branching occurred. These results agree qualitatively with analytical data given by other investigators [82, 83], A second factor is the actual fracture mode occurring, which may be related with the crack velocity. Cottrell [82, 84] noticed an Increase in fracture surface energy and surface roughness with increase in the crack velocity. This is caused by the redistribution of stress ahead of the crack tip at higher velocities, which eventually changes the fracture mode. The adhesive fracture surface energy showed a definite increasing trend as the loading changes from a so-called mode I to mode II to mode [35] , which was accompanied by increasing fracture surface roughness [86]. Therefore, fracture surface energies are rather dependent

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47 on fracture modes. In the experiments reported here, a combination of interlaminar shear stress and the crack-opening loading caused by the generator strip are considered as the generators of the stress field around the delamination crack. This result may be quite different from the stress field as produced in the double cantilever beam specimens. The third factor considered is the adhesive fracture energy which should be distinguished from the cohesive fracture energy. That is, delamination proceeds along the interface between a fiber layer and the iii^trix or in the matrix close to the interface, which may give different fracture surface energies from those of the bulk pure epoxy material. Some data reported on static double cantilever beam tests on the cleavage occurring at the interface between E— glass fabric/epoxy laminates have shown fracture surface energies at least double those reported for unfilled epoxy specimens [87] . The fourth factor is the surface treatment of specimens to be bonded, which is interrelated to the previous discussion. Effects of the surface treatment on fracture surface energies are known to be significant [87, 88] . In our experiments, no special fiber surface treatments have been introduced. However, the surface condition may be different from that used in double cantilever beam specimens in Ref. [76]. It is not known whether fracture surface energies are increased or decreased by this fourth factor in our experiments. The effect of the impactor mass and length on the apparent delamina— tion fracture surface energy y may be explained qualitatively using Goldsmith's theory [32] on transverse impact of a mass on a beam and a theoretical-experimental investigation conducted by McQuillen et al. [89] based on Goldsmith's theory, even though experimental conditions may be from those in the current studies. The impact event generates

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48 the full spectrum of vibration modes in the plate specimen, but it is only the first few modes which usually have a significant influence on the specimen response. For large impact masses the response is mainly in the first mode. However, for smaller masses the second and the third mode influences become appreciable. According to McQuillen et al. [89] for the beam, a unit of energy in a higher mode causes more strain than the same unit in a lower mode. Hence small impact masses provide larger strains and larger damage in the plate than large masses with the same kinetic energy. This appears to be the reason for the larger Y value occurring for small masses when compared to the large masses. Up to now, only the total delamination area has been discussed. This area is the sum of the delamination area in the first lamina interface (Aj^) and that in the second lamina interface (A 2 ) . The ratio of to A^ seems to change with nose shape, even though the total delaminated area for any given nose shape and length of Impactor impinging upon a plate at a fixed velocity remains constant. At impactor velocities where a clear generator strip can be found in laminates impacted by bluntended impactors, the average ratio A^/A 2 is 0.34. This ratio is 0.29 for truncated hemispherical impactors and 0.25 for hemispherical impactors. This result is also related to the differences in fracture patterns occurring for blunt-ended and hemispherical impactors as pointed out in Section 3.3.2. The sequential details of the delamination crack propagation event are not clearly known, but it appears to involve mainly a flexural wave as discussed and shown in Chapter 5. The delamination cracks may be caused by the interlaminar transverse shear stress associated with the flexural wave, assisted by the crack-opening loading initiated by the generator strip.

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49 3.3.4 Transverse Cracks Observable transverse cracks in the 0° direction have been noted on the front and back laminas in the 0® fiber direction of the impacted plates, as shown in Fig. 3.7. Similar transverse cracks in the middle 90° lamina can also be found along the fiber direction when the plates are illuminated by a strong light placed behind them. These cracks form in a direction parallel to the fiber reinforcement in each lamina and show an almost evenly distributed crack spacing. Some transverse cracks extend the full length of the specimen in the fiber direction, while others are combinations of several cracks which look like full-length cracks. Similar types of transverse cracks with evenly distributed crack spacing in cross-ply laminates have been observed in different static loading conditions by some investigators and discussed to some extent. A survey of previous studies on transverse cracks is given below. In static tensile tests of cross-ply laminates, one interesting characteristic is a sudden change in the slope or so-called knee of the stress-strain curve which does not exist for unidirectional laminates. This knee has been verified to be associated with the failure of the 90° plies, i.e., transverse cracking [90, 91]. A similar phenomenon known as weepage is often found in unlined Internally pressurized filament-wound pipes. The onset of weepage is connected with the formation of transverse cracks in the pipe [92, 93]. A further discussion of microscopical observations of transverse cracks has been given recently in [93-95], and will be reviewed in Section 4.1. The strain concentration effects associated with the relatively stiff fibers have been considered as the principal cause of the observed

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50 transverse cracking. Kies [96] has examined the strain concentration around a fiber in the matrix, which arises from the different elastic properties of fiber and resin. Since the resin has a lower modulus than the fiber, the resin must sustain most of the transverse strain and the strain close to the resin-fiber interface may be large enough to cause failure. Kies has calculated that this strain magnification increases as the fibers approach one another and this factor becomes twenty for typical close-packed fibers and resin. Shultz [97] has modified and extended the work of Kies to include biaxial tensile and shear strains, and the effect of Poisson's ratio. Herrmann and Pister [98] have also calculated the strain concentration factors for systems under biaxial strains using numerical techniques to solve the plane strain elasticity problem. An alternative theoretical approach to transverse cracking has been reported by Puck and Schneider [99]. They have developed realistic failure criteria based upon the microstresses of the fibers, the matrix, and the constituent interfaces and shown that the transverse tensile strength is possibly related to an adhesive failure of the glass-resin interface and is also strongly affected by stress concentrations due to voids and nests of the accumulated coupling agent. Recently, several authors have investigated in detail these character istic transverse cracks in uniaxial tensile tests of cross-ply laminates and defined the factors controlling this evenly distributed crack spacing [100, 101] . Garrett and Bailey [100] have found the spacing of transverse cracks to be dependent on the thickness of the transverse ply and the applied stress. Generally the higher the applied stress and the smaller the transverse ply thickness are, the smaller is the average crack spacing A theoretical prediction on the spacing of transverse cracks and the

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51 stress strain curve was made based on a modified shear lag analysis which was used to determine the normal stresses in the longitudinal direction after cracks occurred in the tranverse ply. The stress is transferred from the longitudinal plies to transverse plies by shear stresses and the normal stress in the transverse ply builds up over a short distance and approaches the prefracture level. The general trend of experimental data was explained by this theory. Stevens and Lupton [101] have made similar investigations. Under similar experimental conditions, some efforts have been made to increase the threshold strain of transverse cracking. Stevens and Lupton [102] have used a resin that undergoes yielding and cold-drawing under stress and that relieves the stress concentrations between fibers. Garrett and Bailey [103] have investigated the effect of a variation of the resin failure strain, by using rubbery resin systems, to increase the threshold strain. Parvizi et al. [104] have shown experimentally that crack constraint does occur at small transverse-ply thickness. The above discussion on transverse cracking relates mainly to static tensile tests and cannot be applied directly to the locally impacted laminates studied here. However, some information can be inferred from these results on transverse cracking to those obtained for the impacted laminates. In order to do this, the crack spacing on the front and back face of each lamina of each specimen was measured and the arithmetic mean was then calculated. The mean transverse crack distance (MTCD) as a function of impactor velocity was obtained and is shown in Fig. 3.10 for five impactor types. The two marks for each specimen correspond to the MTCD on the front and back laminas, respectively. For blunt-ended impactors (Fig. 3.10(a)), an upper point corresponds to a MTCD on a back lamina and a

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52 lower point to a MTCD on a front lamina. That is, the MTCD has been found to be smaller at the front lamina of a plate than at the back, for blunt-ended impactors and for a given impactor velocity. For hemispherical and truncated hemispherical impactors (Fig. 3.10(b) and (c)), the reverse has been found. This is an interesting indication of nose shape effects that the impact energy is more widely dissipated at the front lamina with blunt-ended impactors than with hemispherical ones, as pointed out in Section 3.3.2. The threshold impactor velocity for the development of the transverse cracks appears to be independent of impactor type and to be about 23 m/sec (75.5 ft/sec). Above this threshold velocity, the MTCD decreases sharply as the impactor velocity increases. The curves are eventually flattened out at higher velocities and the MTCD appears to reach its minimum value, approximately 3 mm for the [ (0°)^/(90°)^/ (0°)^] specimen. This is similar to the MTCD versus applied stress curve in static tensile tests of cross-ply laminates reported by Garrett and Bailey [100]. Although different nose shapes can result in a difference in the MTCD on the front and back surfaces, this does not lead to any differences in other observed characteristics of the curve. Long (5.08 cm) impactors produce a larger MTCD than short (2.54 cm) ones at the lower velocities but the impactor length (mass) has little effect at the higher velocities. The front and back surfaces of impacted plates of [ (0°)/90°)^/0®] , [ (0 ) 3 / (90°)^/ (0°)2/(90°)2/(0°)2] laminate configurations also show the same uniform transverse crack development as for the [ (0°)^/ (90°)^/ (0°)^] ones. Some MTCD data for each impacted plate type have also been shown in Fig. 3.10(a). The MTCD decreases in the aforementioned order, while the threshold impact velocity for the transverse crack development increases in the above order.

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MEAN TRANSVERSE CRACK DISTANCE (mm) 53 8^ 100 290 (ft /sec) I 4 ^ or i • : ? 6 cp o ? o 0 •6 I [( 0 ®/ 90 °) 7 / 0 »]O 2.54cm ( linj IMPACTOR O x • 5.08cm(2in.) IMPACTOR 25 50 VELOCITY 75(m/sec) (a) Blunt-ended impactors. Paired points: upper for back face, lower for front. Fig. 3.10 Mean transverse crack distance v.s. impactor velocity for [ (0°)^/ (90°)^/(0°)^] laminates Impacted by various types of impactors.

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MEAN TRANSVERSE CRACK DISTANCE (mm) 54 8r 100 “ 1 — 200(ft/sec) I 539 111 h I d 2r 2.54cm(lin.) IMPACTOR 5.08cm(2in.)IMPACT0R 25 50 VELOCITY 75(m/sec) (b) Hemispherical nose impactors. back face, upper for front. Paired points: lower for Fig. 3.10 continued.

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MEAN TRANSVERSE CRACK DISTANCE (mm) 55 100 200 (ft/sec) 5A A 3f25 50 VELOCITY 75 (m/sec) (c) Truncated hemispherical nose impactors (2.54 cm). Paired points; lower for back face, upper for front. Fig. 3.10 continued.

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56 In the present experiments, the laminate specimen is believed to experience large deflections even if it is still elastic up to the point of plate delamination. This deflection magnitude can become comparable to or larger than the plate thickness so that membrane effects may have to be considered. The well-known von Karman theory for the large deflections of plates is described in Fung's text [105]. It makes use of Green's finite strain as follows. Consider a Lagrangian material description and a fixed righthanded rectangular Cartesian frame of reference to be used, with the y plane coinciding with the middle surface of the plate in its initial, unloaded state, and the z-axis normal to this plane. Let the components of the displacements of points lying on the middle surface be denoted by u(x,y), v(x,y), w(x,y). In the Lagrangian description, the Green's strain tensor, referred to the initial configuration, is used, whose components are E XX 9u 3x + l/2(— E yy 9v 9y + 1 / 2 (| 2)2 (3.3) The first term in Eq. (3.3) can be small compared with other terms. The second term is the contribution of bending which also exists in the small deflection theory. The third term is particular to the large deflection theory and appears to be comparable to the second term. This term contributes a tensile component to the strain and causes tranvserse cracking in transverse laminas. A theoretical explanation developed by Garrett and Bailey [100] from static tensile test data, that is, a modified shear lag analysis, can be applied to explain this transverse cracking in crossply laminates, with some changes to account for wave propagation effects.

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57 But the development of this theoretical approach needs further research in the future. 3.3.5 Contact Time Measurement Typical oscilloscope records of the contact time measurements have been shown in Fig. 3.11. The records obtained indicate that both a single contact and multiple contacts are possible. Multiple contacts have been predicted for impact tests of cantilever graphite/epoxy laminates by Preston and Cook [43]. The combination of vibration modes excited by the impact event and the local deformation appears to produce this multiple contact phenomenon. Multiple contacts were especially noticeable for blunt-ended and shorter (2.54 cm) impactors. However, only the first contact period, appears to be important in transferring energy from the impactor to the laminate, and is taken as the contact time. The contact time versus the impactor velocity has been shown in Fig. 3.12 for five impactor types. As shown, the contact time for all impactor types increases with increase in velocity. The contact time of the longer and heavier impactors is approximately four times as great as that of the shorter and lighter ones for a given velocity range, that is, about 200 400 psec for the 2.54 cm impactors, about 1000 1200 psec for the 5.08 cm impactors. For 2.54 cm impactors, blunt noses give longer apparent contact times than either the hemispherical or truncated hemispherical nose shapes. This is partly due to the inherent difficulty in impacting the projectiles exactly at the center of the plate. Thus, the actual contact does not necessarily result in the direct closing of the electric circuit for all nose shape impactors, particularly the hemispherical type.

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6 304 802 1054 58 IMPACTOR TYPE AND VELOCITY 2.54 cm, BLUNT-ENDED 61.73 m/sec 830 1054 2.54 cm, BLUNT-ENDED 69.45 m/sec 6 234 2.54 cm, HEMISPHERICAL 43.03 m/sec 6 304 850 1074 2.54 cm, HEMISPHERICAL 61.88 m/sec 990 1186 \ 5.08 cm, BLUNT-ENDED 30.49 m/sec 5.08 cm, HEMISPHERICAL 59.10 m/sec Fig. 3.11 Typical oscilloscope records for contact time measurement. Time in microseconds.

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CONTACT TIME(psec) Fig. 3.12 Contact time versus impactor velocity. (The same symbols are used as in Fig. 3.9.)

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Hence, real contact times should be a little longer than those in Fig. 3.12 for rounded types of noses. In sununary, it may be said that the nose shape difference does not affect the contact time. 3.4 Studies on Ply Orientation Effects Some angle-ply laminate specimens have been fabricated and impacted with 2.54 cm blunt-ended impactors. Fifteen-ply symmetric laminates with ply orientation [ (IS^)^/ (-15°)3/ (15“)3] and [ (30°)3/(-30°)3/(30“)3] were chosen for the tests and the total delamination area as a function of the impactor kinetic energy has been shown in Fig. 3.13. The apparent delamination fracture surface energy y is very low compared with y for the Fig. 3.13 Total delamination area versus impactor kinetic energy for angle-ply laminates.

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61 [ (0°)^/(90°)^/(0°)^] cross-ply laminates. This may be due to the specimen fabrication for the angle-ply laminates in that weak interfaces may exist between laminas. The threshold energy for the development of delamination is higher for the angle-ply laminates than for the. cross-ply laminates. Fracture mechanisms other than the delamination may be the principal energy absorbing criteria for such systems. For example, fiber stretching and breaking may play a significant role. These results are considered important but an insufficient number of tests have been conducted to warrant any definitive quantitative statements. Therefore, only a qualitative effect of ply orientation on the fracture patterns has been discussed in the following commentary. Delamination patterns have been obtained in angle-ply laminates ®itiilar to those found in cross— ply laminates with some differences in the actual shape of delamination noted. The same generator stripsequential delamination mechanism appears to exist and to be applicable to the angle-ply laminates. The first stage of the process consists of the formation of a generator strip in the first +6 lamina, bounded by two through-thethickness shear cracks, marked AA' and BB' in Fig. 3.14. This generator strip is pushed forward by the impactor and loads transversely the second -9 lamina. In the second lamina, the generator strip loading is mainly supported by bending of a strip in the secondlamina fiber direction, bounded by CC' and DD' . This is because of bending stiffness of the strip bounded by CC and DD' is larger than that of any other arbitrary strip bounded by any XX' and YY' passing through A and A' . As the generator strip loads the second lamina which supports the bending loading, delamination between the first two laminas is initiated along the lines AA' and BB' . This delamination spreads to the second-lamina fiber direction, that is, at an angle

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62 Y A DE LAM I NAT! ON CRACK PROPAGATES IN THE 3RD LAMINA FIBER DIRECTION Fig, 3.14 Schematic of delamination pattern in [(+0)r-/(-0) /(+0) ] angle-ply laminates. -5 5 5

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63 -20 to the generator strip, until the available energy is insufficient to continue the delamination process. A new generator strip can be formed in the second lamina at an angle -29 to the first generator strip and thus initiate delamination between the second and third laminas. The associated delamination with this generator strip propagates in the third-lamina fiber direction. The process may be then repeated with subsequent delamination covering a larger area than the one before it if there are enough independent angle-ply laminas in the laminate.

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CHAPTER 4 MICROSCOPIC OBSERVATIONS OF CROSS SECTIONS OF IMPACTED COMPOSITE LAMINATES 4.1 Introduction As mentioned earlier, failure mechanisms in FROM have not been extensively investigated experimentally to establish well-defined failure theories. Particularly, understanding of failure mechanisms in impacted FROM specimens is needed in order to make full use of these materials. Macroscopic observations of locally impacted composite laminates have been discussed in the previous chapter. These results have shown existence of a sequential transverse crack-delamination mechanism. It appears desirable to make microscopic observations on the initiation and propagation of the observed transverse cracks and delamination cracks in order to confirm the results of the macroscopic observations and to investigate the interrelation between the above kinds of failure patterns in more detail. Sample preparations and microscopic examinations of cross sections of FRCM specimens after loading have been reported on by some researchers in order to study stress-cycled failure [106], uniaxial compression failure [107], effects of voids on filament-wound (FW) structures [108], creep failure [109], weepage of pressurized FW pipes [93], and uniaxial tension failure [94, 95]. These examinations were carried out using optical microscopes (transmitted or reflected light) and/or electron microscopes . Continuing improvements of the sample preparation methods for cutting and polishing the cross sections of FRCM specimens have recently 64

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65 been made using special care to eliminate any damage produced during cutting and polishing of the samples, as reported in Refs. [106-109, 93] . The latest methods utilize coolants and room— temperature curing resins in the initial cutting and mounting of the samples. This has been done in an apparent effort to reduce or eliminate any thermallyrelated residual stress from being introduced into the sample. Microscopic observations of cross sections of impacted composite laminates have not previously been conducted insofar as the author knows. However, cross sections of laminates damaged by static loading or fatigue loading which show similar damage appearance have been studied [107, 93-95]. In simple compression, creep, and fatigue tests, Broutman [107] indicated that crack initiation occurred at the resinglass interface and traveled along the path of least resistance, that is the interface, to separate individual fibers and the matrix, resulting eventually in delamination between layers of filaments. Jones and Hull [93] examined pressurized FW pipes and described a weepage type failure mechanism, which included the debonding of individual fibers first followed by development of transverse cracks, and finally the occurrence of delamination resulting in a continuous crack path for weepage. Based upon uniaxial tension and cyclic loading tests of laminates, Reif snider et al. [94] conjectured that delamination interacted with, and was quite possibly nucleated by, transverse cracking in transverse plies. The development of delamination from the ends of the transverse crack was typical of their observations. Reif snider and Talug [95] then postulated a simple model, which could be used as a predictive method to account for this delamination development. 4.2 Sample Preparation Based upon previous reports and our trials and errors to reduce damage during the preparation, the following sample preparation

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66 procedure was used. For information purposes, the equipment and supplies used in this sample preparation have been listed in Table 4.1. Secti oning . Representative areas were first cut oversized from the impacted laminate using a band saw and then cut into the desired dimensions using a low-speed saw with a diamond watering blade and with a water spray as a coolant. This sectioning procedure leaves the sample surface slightly scratched, but prevents excessive local heating. (2) Mounting . Sectioned samples were mounted in "Caulk Nuweld," a room-temperature curing resin primarily used for denture repair, in order to avoid heating the samples. _(_3) — Grinding . The section was then ground on wet silicone carbide abrasive papers of successively finer grit sizes 180, 240, 320, 400, and 600 using a grinding wheel. The section was lightly pressed against each paper on the moderate-speed rotating wheel for 1 minute. Samples were washed with water between paper changes and after the final grind. _(40 — Rough polishing . Six micron diamond polishing compound was then used on a cotton polishing cloth attached to a polishing wheel, with lapping oil for introducing a uniform distribution of the polishing compound over the polishing cloth and for cooling the sample. Moderate pressure was then applied to a high-speed wheel for approximately 2 minutes. This procedure allows for some features in the section such as transverse cracks and delamination cracks to be clearly visible with the naked eye . — Fine P olishing . After the section was washed thoroughly, 1 micron diamond polishing compound was applied to a synthetic rayon cloth with lapping oil. Good resolution and contrast was obtained between fibers, resin, and cracks. Cross sections of fibers were polished without breakage.

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67 Table 4.1 Supplies used in the sample preparation for SEM observation. (1) Sectioning "ISOMET" Low Speed Saw Diamond Wafering Blade (Low Concentration) 4"x0.012" (2) Mounting "CAULK NUWELD" Denture Repair Resin (3) Grinding "ECOMET"_III Polisher /Grinder, 8" "CARBIMET" Silicon Carbide Abrasive Paper Disc (4) Rough Polishing "ECOMET" III "METADI" Diamond Polishing Compound, 6 micron MbTCLOTK" Polishing Cloth (a cotton cloth with practically no nap) "AUTOMET" Lapping Oil (5) Fine Polishing "ECOMET" III METADI" Diamond Polishing Compound, 1 micron MICROCLOTH" Polishing Cloth (a synthetic rayon cloth in which fibers are bonded to a woven cotton backing) "AUTOMET" (a): Manufactured by the L. D. Caulk Co., Milford, Del. All other supplies are manufactured by Buehler Ltd., Evanston, 111.

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68 the section was polished, carbon particles were vacuum-deposited on it in order to increase its thermal conductivity. Then the section was viewed in a scanning electron microscope (SEM) . The SEM used in this study was a Joel JSM-35C (Joel LTD., Tokyo, Japan) as shown in Fig. 4.1. Fig. 4.1 Joel JSM-35C scanning electron microscope

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69 4.3 Results and Discussion A [ (0“)3/ (90°)^/(0°)^] laminate impacted by 2.54 cm (1 in.) bluntended steel projectile at a velocity of 75.1 m/sec (246.5 ft/sec) was selected as a typical sample for the SEM observations. Fracture patterns for this impacted laminate have been shown in Fig. 4.2 Note that a generator strip, transverse cracks, and delamination cracks are fully developed and recognizable for the sample selected for study. Several cross sections of this specimen have been cut along the straight lines as shown in Fig. 4.2(b). The schematic of each cross section has been shown in Fig. 4.3 where points A— G in Fig. 4.3 correspond to those in Fig. 4.2(b). A cross section from a virgin laminate is shown in 4.4 for comparison with the impacted specimen and found to remain undamaged after sectioning, grinding, and polishing as described in the previous section. Typical SEM photographs of the cross sections of the impacted specimen have been shown in Fig. 4.5 where brief explanations have been included along with the photomicrographs. Note that the numbers in Fig. 4.3 correspond for consistency to the photo numbers in Fig. 4.5. Based upon the SEM observations, the following general remarks can be made. The letters and numbers in the text correspond to those indicated in Figs. 4.3 and 4.5. In general, transverse cracks are perpendicular to lamina Interfaces in regions where there is no delamination. For example, see 202, 207, 306, 401, and 403. However, transverse cracks grow oblique to lamina interfaces where they are accompanied by a delamination crack. For example, see 201, 203, 207, 000, 501, and 602. The perpendicular transverse cracks appear to be formed as a result of both the in-plane tensile wave development and shear lag as developed between the 0“ and 90° layers

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70 (a) Front Fig. 4.2 Typical fracture patterns of a I (0® _/ (90®) ./ (0°) ] laminate impacted by 2.54 cm blunt-ended steel projectile at a velocity of 75.1 m/sec (246.5 ft/sec).

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71 TRANSVERSE CRACKS A DELAMINATION CRACK (b) Front, schematic Fig, 4.2 continued

PAGE 86

72 (c) Back Fig. 4.2 continued

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73 — -i Fig. 4.3 Schematics of several cross sections of the laminate shown in Fig. 4.2. (Points A-G in Fig. 4.3 correspond to those in Fig. 4.2(b)).

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74 Fig. 4.4 An undamaged interface of a [(0°)„/(90°) /(0°) /(90°) /(0°) ] laminate. (Note a resin-rich region in a 90° lamina cor^ responds to the boundary of two 90° prepreg tapes.) oblique TC in the third lamina. The DC travels just inside the third lamina. Fig. 4.5 Typical SEM pictures of cross sections of a [(0°) /(90°) /(0°) 1 laminate Impacted by a 2.54 cm blunt-ended steel projectile at^ 75.1 m/sec. (Note that the numbers in Fig, 4.3 correspond to the picture numbers in this figure. DC and TC mean a delamination crack and a transverse crack.)

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75 203: A DC at the first interface deflects into an oblique TC in the second lamina, while a DC at the first interface travels outward from the impact region. 204: Connection of a DC and a TC. 206: A DC associated with an oblique TC, which travels through a portion with fiber bunching. 205: A DC with two branches, one at the second interface and the other just inside the third lamina. 207 : An oblique TC associated with a DC and a straight TC without a DC. Fig. 4.5 continued.

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76 208: Irregular TCs at the generator strip. 209: A large magnification of 208. 000: An oblique TC near a DC. A TC travels through a fiber-bunching region. 4 « |; : T;:• Ii.y\ . > . ). . • ^ , 1 i > j '' . r I-'-, '1 i f' , ' 0301,100.0U UFMSE., 301: A DC with two branches, one at the first interface and the other just inside the first lamina, connected to an oblique TC. 302: A connection between a DC and a TC. Fig. 4.5 continued.

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77 303: A TC traveling through a portion with fiber bunching in the first lamina. 305: A large magnification of an undamaged interface. 307: A large magnification of 306. 25KU X390 304: A DC just inside the first lamina. 401: Two perpendicular TCs ahead of main DC. 306: A lone TC with two branches near the second interface. Fig. 4.5 continued.

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78 402: A DC initiated at the tip of a TC in the first lamina. 403: A lone TC with two branches near the interface in the third lamina. 404: A TC with two branches traveling through a fiberbunching region. 405: A large magnification of 404. 501: A DC at the first interface deflects into an oblique TC in the second lamina, while the same TC is connected by a DC passing just inside the third lamina . Fig. 4.5 continued.

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79 601: An oblique TC connecting two DCs. The tips of the DCs can be identified. One DC at the first interface stops at the TC. Fig. 4.5 continued. 602: Connection of a DC and a TC. The TC travels through a portion of fiber bunching . as explained in Section 3.3.4, which introduce substantial tensile strains in the transverse laminas. The oblique transverse cracks accompanied by a delamination crack are considered to be due to a combination of the aforementioned tensile wave-shear lag and the interlaminar shear caused by the flexural waves. This is supported by the following observation. The angle at which each transverse crack deflects into interfaces should be noted. JH, FC, IK, and EG show that the transverse cracks in the second lamina deflect toward the impact point near the first lamina but away from the impact point near the third lamina. This is explained by the tensile and shear strains developed in the transverse lamina as shown in Fig. 4.6. Delamination cracking thus appears to interact with the observed transverse cracks. As mentioned in Section 3.3.4, a cause of transverse cracks in impacted laminates is considered to be the strain concentration effects between transverse fibers which are much stiffer than the resin. Since the strain concentration factor increases as the interfiber spacing

PAGE 94

80 r -f . . < 5 + 1 T . Fi§* 4.6 Tsnsile and shnar stressss developed in the transverse lamina . decreases [96], more transverse cracks should be found in regions of high fiber density than in resin— rich regions. Another cause of transverse cracking can be attributed to the adhesive failure of the glass-resin interface as discussed by Puck and Schneider [99]. In the present observations, transverse cracks appear to propagate in the regions of high fiber density, in other words, fiber bunching, and to avoid the large pockets of resin, where the fiber density is locally low. See, for example, 206, 207, 209, 000, 303, 403, 405, and 602. Both transverse and delamination cracks appear to propagate near or at the fiber-resin interface. It is very difficult to tell whether those cracks are caused by adhesive fracture of the fiber-resin interface or cohesive fracture of the resin. Both cases have been identified

PAGE 95

81 in the present experiments. For example, see 205, 206, 209, and 602. Delamination cracks do not necessarily propagate along the lamina interface. Photos 201, 205, 301, 302, 304, and 501 show some examples where delamination cracks travel just inside laminas. Some longitudinal cracks within laminas can also be found under the impact region as shown in JH and LF. Recall that the normally incident compressive wave is reflected at the back surface of the plate and returns as a tensile wave. This reflected wave may aid in initiating these observed longitudinal cracks within laminas. A generator strip crack has also been shown in LF. The irregularity of such cracks just under the impact region can be observed in 208 and 209. A secondary shaded region in the delaminated area shown in Fig. 4.2(a) corresponds to the region(s) inside the dotted lines in the schematic of Fig. 4.2(b). For these regions, there appears to be no delamination crack at the second interface, according to NL or 305, while there is a delamination crack opening at the corresponding first interface. Photos 401 and 402 show a transverse crack in the first lamina which began to form a delamination crack at the tip of the transverse crack. This crack is located well ahead of the main delamination cracks. Transverse crack growth due to the tensile wave— shear lag appears very rapid even though it may be temporarily arrested by resin pockets or other irregularities. Growth is eventually stopped when the transverse crack arrives near the lamina interface. Interlaminar resin layers temporarily arrest cracks until the flexural— wave— induced interlaminar shear stress at the crack tip exceeds the resin failure strength, and a delamination crack forms at the tip of the transverse crack. The transverse cracking

PAGE 96

82 and the delamination cracking may occur almost at the same time and interact with each other. Photos 401 and 402 document this stage of failure. The delamination crack described above next appears to connect to a main delamination crack traveling from the impacted region. This appears to be the principal sequence in the failure process in the impacted laminates tested here. Photos of sections of the impacted specimen confirm a fracture appearance as observed from the polished surfaces by visual observation of the sectioned specimen. For example, photo 602 illustrates two different delamination cracks stopped in different terminal positions. The use of an SEM to inspect cross sections of impacted specimens has provided considerable information on the failure/fracture details of the tested specimens which could not otherwise be obtained by inspection by simple macroscopic observations. The use of this instrumentation for the quantitative analysis of dynamic impact studies appears to provide a powerful tool for documenting the sequence of events required to establish a suitable analytical model for interpretation of these tests.

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CHAPTER 5 EXPERIMENTAL WAVE PROPAGATION STUDIES OF IMPACTED COMPOSITE LAMINATES USING STRAIN GAGES 5.1 Introduction In previous investigations, the fracture characterization has been described only after the laminate was damaged due to impact. The details of the high-velocity transient behavior of impacted laminates, such as the time history of the elastic waves before delamination, the generator strip formation, and the delamination crack propagation are necessary information which must be obtained for the impact event and have as yet not been established. The first of these problems is examined in this chapter and the last two problems in the next chapter. Several experimental questions are required to be answered on wave travel in impacted plates. Among these are what kinds of waves are involved and which one is the dominating the transient phenomena occurring in the present studies. These results are directly related to the fracture behavior involved, which is the main concern of this total investigation program. Recently, Daniel and Liber [68] have conducted elastic wave propagation studies on boron/epoxy and graphite/epoxy laminates impacted by silicone rubber projectiles, using both surface and embedded strain gages. These records have verified that the predominant wave is a flexural one propagating at different velocities in different directions for specimens with ply orientation of [(0°) ,] or [(0°) /±45°] . xo z. Muldary [110], however, has reported some impacts on glass/epoxy plates where membrane-type deformation is predominant. The impacted plates in 83

PAGE 98

84 his tests had a large [impactor velocity/plate bending stiffness] value and were flexible enough to deflect comparable to the plate thickness, so that membrane effects were important. The impacted plates in the present strain gage experiments as well as in Daniel and Liber's [68] had a smaller [impactor velocity/plate bending stiffness] value, and membrane effects were insignificant compared with flexural wave effects. 5.2 Experimental Procedure and Consideration The strains induced by impact on fiberglass epoxy laminates with different ply orientations were measured by means of surface and embedded gages, and the characteristics of these strains, that is, types of waves, wave amplitudes, and strain rates were studied. The embedded gages were Micro-Measurements WK-06-062AP-350 (MicroMeasurements, Raleigh, N.C.) fully encapsulated single gages with polyimide encapsulated ribbon copper leadwires and were self-temperaturecompensated. The lead wires were short (2 cm), and extension copper wires and small terminals were used for extension to the bridge circuit. The 16-ply laminates with [ (0°)^/ (90°)^/ (0°)^] ply orientation were used for the embedded gage tests. The gages were embedded at the geometric mid-plane of the plate, that is, between the eighth and ninth plies of the laminate. The whole assembly was then cured using a vacuum bag in the autoclave following the same procedure as developed for specimens without embedded gages. The local thickness Increase due to insertion of the embedded gages could not be detected by a micrometer. The surface strain gages used in these studies were Micro-Measurements general purpose EA-06-062AQ-350 or EA-06-031CF-120 type with ribbon copper leadwires and were bonded at the desired positions on the front and back surfaces after curing. Active gage length of each type of gage was 62 mils or 31 mils, respectively. The use of two strain gage outputs

PAGE 99

with different gage lengths at the same relative position of a plate indicated that the gage lengths selected do not affect the recorded results. The 15-ply laminates with [ (0°)^/ (90°)^/ (0°)^] and [(30°)^/ (-30°)^/(30°)^j ply orientations were also used with surface gage tests and without embedded gages. Different kinds of gage layouts were used to study the strains at positions for each type of laminate, and gage layouts with results obtained for each case are given in Section 5.4. The strain gages were connected to potentiometers in bridge circuits and, after suitable amplification, the transient signals were recorded on two 2-channel digital oscilloscopes (Explorer III Digital Oscilloscope, Nicolet Instrument Corporation, Madison, Wis.). The recording setup for the strain gage experiments is shown in Fig. 5.1. FiS* 5.1 Recording setup for strain-gage experiments The 15 cm square specimens were then impacted with steel impactors following the same experimental procedure as mentioned in Section 3.2. The impactor contact measuring system described in Section 3.2 was used for triggering both oscilloscopes. It was confirmed that both oscilloscopes were triggered at the same time within an error bound of ±0.5 microsecond.

PAGE 100

86 It has been noticed that the impactor velocity is an important factor to measure the transient strains in cross-ply and angle-ply laminates. Transverse cracks occur even if the velocity is lower than the threshold velocity where a delamination crack is first observed. If a transverse crack crosses a gage, it reads a larger strain value than values at neighboring regions. This local strain increase should be carefully noted. Therefore, the laminates have been impacted at lower velocities where the density of transverse cracks is low and transient strains are insignificantly affected by the appearance of these cracks. Since the impactor velocities for this strain measurement are restricted to be lower than those in Chapter 3, the results in this chapter cannot be applied directly on a one-to-one basis with those established in Chapter 3. However, it is believed that the information on the flexural waves measured in the present investigation can be applied at higher impactor velocities where delamination is the main failure mechanism, even if little information on transverse cracking is available. Related to the above problem is the fact that the bonded surface gages may have some strengthening surface effects. In fact, transverse cracks are likely to avoid the instrumented region having the surface gages. However, it appears that in the current experiments the overall strain levels are little affected by the stiffening effect of the bonded strain gages. 5.3 Documentation Tests for Characterizing Embedded Gages It is a well-known fact that the integrity of a laminate may be lost when poor bonding exists around embedded gages and that the embedded gages may cause some irregularity in the structure around them. To further document this statement, tensile tests were conducted in order to

PAGE 101

87 establish that embedded gages did not ruin the integrity of the specimen and did not reduce the modulus and the strength of the specimen. Four tensile test coupons 15 cm long and 2.5 cm wide (Fig. 5.2), two with embedded gages in the longitudinal direction (Specimens A and C) and two without embedded gages (Specimens B and D) were cut from the same Fig. 5.2 Tensile test coupons tested in documentation tests for characterizing enbedded gages. fabricated laminate. Surface gages were then placed at the same position where an embedded gage had been placed on both the front and back surfaces of each coupon. Each coupon was then loaded up to the critical stress where the first transverse crack was visible using a TiniusOlsen 10,000-lb capacity testing machine. For Specimens A and C, strain readings of the three gages on each specimen (two on the surfaces and one embedded) were found to be in agreement within ±5 percent. The average modulus and measured in the four specimens have been listed in Table 5.1. Data for Specimens A and C with embedded gages agree with those for Specimens B and D without embedded gages within ±7 percent. The corresponding calculated modulus and based on the manufacturer's data on unidirectional 0° and 90° specimens have also been shown in Table

PAGE 102

88 5.1. These data also agree well with the average experimental values obtained herein. It is therefore concluded that embedded gages did not produce any adverse effects on the reported modulus and critical stress of the specimens as tested. Table 5.1 Average modulus and critical stress measured in the four types of specimens and the corresponding calculated values. Specimen Modulus , GPa (lO^psi) O , MPa (lO^psi) cr Measured Calculated Measured Calculated A 39.5(5.73) 41.0(5.94) 18.5(2.68) 19.8(2.87) B 39.9(5.79) 19.0(2.76) C 66.2(9.60) 61.8(8.96) 30.0(4.35) 29.9(4.33) D 62.5(9.06) 31.1(4.51) 5.4 Strain-Gage Results and Discussion 5.4.1 Surface-Gage Results for [ (0°)^/ (90°)^/ (0°)^] Laminates Laminates with [ (0°)^/ (90°)^/ (0°)^] ply orientation were then instrumented with strain gages on the front and back surfaces according to several different gage layouts as shown in Fig. 5.3. These specimens were then impacted using 2.54 cm blunt-ended impactors at 30-40 m/sec (90-120 ft/sec). Representative strain-gage outputs and a summary of the results obtained are given in the following remarks. Gage layout (a) : Figure 5.4 shows typical strain-gage outputs along the x-axls (fiber direction of the front and back surfaces) from four single strain gages located at the front and back surfaces of the plates and spaced at a distance of 2.54 cm (1 in.) apart. The traces of the

PAGE 103

89 liJ UJ Ql< (S)-Z UJ = QS I <
PAGE 104

90 CJ O o lO CM 'dU1 ti •H Strain-gage outputs from surface gages with Gage layout (a) in Fig. 5.3. Impactor velocity = 37.3 m/sec (122.5 ft/sec).

PAGE 105

126.5(3681) 91 < O continued.

PAGE 106

92 front and back surface gages are seen to be almost symmetric in shape at the same station (Gages IF and IB, or 2F and 2B) which implies that a flexural wave appears as the predominant wave system. The recorded transient strain behavior at 2.54 cm from the plate center (Gages IF and IB) can be characterized as follows. First, a very small in-plane tensile wave arrives at the gages of interest on both the front and back surfaces at 8.5 and 9.0 microseconds, respectively. Next, on the front [back] surface, a tensile[compressive] component of an oncoming transverse flexural wave arrives at Gages IF [IB] peaking at 18 [19] microseconds, followed by a large compressive [ tensile] component of the transverse flexural wave peaking at 30 [41. 5] microseconds at 2859 [-3133] microstrains. This difference of peak strains may be due to transverse cracks under gages and persists in the remainder of Gage records IF and IB. This latter flexural wave component may be the most important factor related to the resultant delamination fracture observed for the laminates. The transient strain at 5.08 cm from the plate center shows a slightly different behavioral pattern. That is, a small compressive [tensile] component of the transverse flexural wave first arrives at the gage on the front [back] surface, i.e.. Gages 2F[2B], before any other components do. These experimental observations and characteristics of the transient strain behavior agree reasonably well with the analytical calculation presented by Sierakowski et al. [55] using a large deflection laminated plate theory. The behavior of the flexural wave can be explained as shown in Fig. 5.5, where the front [back] surface experiences tension [compression] first followed by compression[tension] next. Therefore, the complicated strain-time history as recorded is due to a combination of factors which include the initial in-plane and

PAGE 107

93 flexural traveling waves as well as the waves reflected at the clamped boundaries. However, since the faster traveling waves have a much Fig. 5.5 Schematic of the impacted plate response. smaller strain amplitude than the slower traveling waves, the boundary conditions should provide relatively little Influence on the experimentally recorded data. According to Fig. 5.4, one should notice that the bending strains are larger for gages at 5.08 cm from the plate center (Gages 2F and 2B) than for those at 2.54 cm (Gages IF and IB), at corresponding peaks of the transverse flexural wave traveling past each gage. A very low-amplitude in-plane tensile wave is a longitudinal wave along the x-axis, that is, along the fibers of the front surface, and can be called a "precursor" wave. The average precursor wave propagation velocity measured from four tests is: ^xxL ~ ^"05 X 10^ m/sec (1.33 x 10^ ft/sec) (5.1)

PAGE 108

The corresponding theoretical value obtained using the known elastic constants of the material is: 94 ^xxL ~ '^•09 X 10^ m/sec (1.34 x lo"^ ft/sec) (5.2) Calculation of the theoretical wave propagation velocities has been summarized in Appendix A. The measured and calculated values appear to agree very well. The recording system which measures strains every 0.5 microsecond is also capable of giving an accurate longitudinal wave propagation velocity and avoids the discrepancy as obtained between the measured and calculated values reported on by Daniel and Liber [68]. The leading flexural wave velocity was measured by using the expanded scale on the Nicolet oscilloscope. The leading edge of the flexural wave was identified as the point where the front and back gage records diverged. The average flexural wave propagation velocity measured in this way from five tests conducted here is: The corresponding theoretical value associated with transverse-shear deformations is: The discrepancy between the measured and calculated values appears to be due partly to the approximations used to calculate the shear modulus G as described in Appendix A. The largest amplitude of strain caused by the flexural wave propagates at a lower velocity and this propagation of strain is considered to be the primary cause for the delamination failure associated with transverse cracks of the laminate. The average velocity of the CxxF “ 1-34 X 10^ m/sec (4.40 x 10^ ft/sec) (5.3) CxxF “ 1.52 X 10^ m/sec (4.98 x 10^ ft/sec) (5.4)

PAGE 109

largest-amplitude propagation measured from five tests conducted here is : 95 *"xxFP m/sec (951 ft/sec) (5.5) For example, the largest amplitude from Gages IB and 2B in Fig. 5.4 occurred at 30.0 microseconds and 126.5 microseconds, respectively. Gage layout (b) : Figure 5.6 shows the strain-gage outputs along the y-axis (fiber direction of the middle lamina) from four single gages located at the front and back surfaces and spaced at 2.54 cm (1 in.) apart. The transverse flexural wave is also shown to predominate in this case as well because of the near sjrmmetric traces observed on the front and back surface gages. It should be noted that the front surface gage at 5.08 cm front the plate center (Gage 4F) was broken after about 170 microseconds after impact. This was caused by a transverse crack that developed and passed just beneath the gage proper. The sum of strains of the two opposite-surface gages, 3F + 3B, which means double the in-plane component of the wave, has also been shown. The amplitude of this in-plane component is noted to be small compared with that of the bending component. Some sudden jumps in the 3F + 3B record, for example, at 170.5 microseconds, which are considered to correspond to transverse crackings can however be found while a flexural wave propagates. These 4F and 3F + 3B records are further documentation that transverse cracking occurs while a flexural wave propagates, possibly while delamination occurs. This result would appear to be most important in that it may be the first established evidence of delamination-transverse cracking interaction.

PAGE 110

96

PAGE 111

175.0(6998) 97 continued

PAGE 112

98 I vD lO 00 •H O continued

PAGE 113

99 Data from another test have been shown in Fig. 5.7 only for front surface gages 2.54 cm apart and without any transverse cracks crossing the gages. The characteristics of the transient strains described for the xaxis gages in Gage layout (a) are also applicable to those for the y-axis gages in this layout. That is, for the front [back] surface gage located at 2.54 cm from the plate center, a very small in-plane tension is first observed followed by a flexural tensile [compressive] wave of intermediate amplitude and then a large amplitude flexural compressive [tensile] wave. For the front [back] surface gage at 5.08 cm from the plate center, a small amplitude flexural compressive [ tensile] wave arrives before any other flexural wave components do. The amplitude of the in-plane tensile precursor wave has been found to be slightly higher for the y-axis gages than for the x-axis gages. The average in-plane tensile wave propagation velocity measured from three tests was found to be: CyyL = 3.17 X 10^ m/sec (1.04 x 10^ ft/sec) (5.6) The corresponding computed theoretical value was: CyyL = 3.27 X 10^ m/sec (1.07 x 10^ ft/sec) (5.7) The agreement between the measured and calculated values for C ^ is yyL noted to be very good. Also, the average transverse flexural wave propagation velocity measured from four tests was found to be: Cyyp = 1.14 X 10^ m/sec (4.07 x 10^ ft/sec) (5.8) The corresponding computed theoretical value was:

PAGE 114

56 . 0 ( 2512 ) 100 CsJ O 05 Fig. 5.7 Strain-gage outputs from front surface gages with Gage layout (b) in Fig. 5.3. Impactor velocity = 31.8 m/sec (104.3 ft/sec).

PAGE 115

101 Cyyp = 1.38 X 10^ m/sec (4.50 x 10^ ft/sec) (5.9) The discrepancy between the measured and calculated values for C „ can yyF be explained in part to the approximations used to calculate the shear modulus as discussed in Appendix A. The average velocity of the largest-amplitude propagation measured from four tests was found as, CyyFp = 225 m/sec (739 ft/sec) (5.10) Gage layout (c) ; For this gage layout, a comparison of the wave propagation properties along the xand y-axis can be made from a single test specimen. Figure 5.8 shows strain-gage outputs along both the x-axis and y-axis from four gages located at the front surface and spaced at 2.54 cm (1 in.) apart. The wave characteristics and propagation velocities described for the Gage layouts (a) and (b) hold also for this case. Peak strains and strain rates measured at all four gages have been summarized in Table 5.2. Table 5.2 Peak strains and strain rates measured from gages along the x-axis and y-axis for Gage layout (c) . Distance from the Plate Center 2.54 cm (1 in.) 5.08 cm (2 in.) ^xx peak -3770 pe -4284 PE • ^xx peak -156 e/sec -82.6 e/sec ^yy peak -7115 ye -5909 pe • ^yy peak -314 e/sec -90.4 e/sec

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259.0(2920) 102 O Fig. 5.8 Strain-gage outputs from front surface gages with Gage layout (c) in Fig. 5.3. Impactor velocity = 32.3 m/sec (105.9 ft/sec).

PAGE 117

422 , 0 ( 3441 ) 103 continued.

PAGE 118

104 Values for the gages located along the y-axis are noticeably higher than those for gages along the x-axis. Daniel and Liber [68] have reported that such differences in peak strains along different axes can be explained in part by the assumption and use of an isotropic energy propagation. A modification of their analysis has been applied to the present problem and included in Appendix B. This simple analysis gives: e , yy . _ 2.03 (calculated) (5.11) XX peak The measured values are: yy peak ^xx peak 1.89 (2.54 cm from the plate center, measured) (5.12) = 1.38 (5.08 cm from the plate center, measured) For gages near the plate center, the calculated and measured values agree relatively well. The discrepancy for gages far from the plate center can be attributed to the different attenuation characteristics in different directions, transverse cracking effects, boundary effects, and assumptions made in the analysis. Gage layout (d) : Figure 5.9 shows the strains obtained from gages located at 3.81 cm (1.5 in.) from the plate center in several different directions. The predominant wave in the 45° direction with respect to the Xand y-axis, appears to be a flexural one. (See Gage records 7F and 7B) . With regard to the wave propagation velocities, it can be concluded that :

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118.0(1182) 105 Strain-gage outputs from surface gages with Gage layout (d) in Fig. 5.3. Impactor velocity = 31.5 m/ sec (103.4 ft/sec).

PAGE 120

" 49.0 ( 6553 ) 106 continued

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107 ^45L “ ^yyL r 2 r ^45F ^yyF r > r 45FP ^yyFP (5.13) The first two relations can be deduced from similarity measurement principles of the elastic constants in the 45° and y directions. The last relation has been developed in Appendix A. The peak strains as found in each gage are given as, ^xx peak -4904 ye ^yy peak -8439 ye (5.14) ^45 peak -7239 ye, 6553 ye The ratio of the peak strains along y and x axis is: yy peak _ ^ -j 2 (measured) (5.15) XX peak and agrees rather well to the calculated value of 2.03. Gage layout (e) : Figure 5.10 shows strain-gage outputs from four front surface gages spaced at 1.27 cm (0.5 in.) apart along the y-axis. The wave propagation velocities, and C^^pp, have been summarized in Table 5.3. This data shows a significant change in velocity with distance for the observed waves. The averages of the secondand the third-column values gives the wave propagation velocities at 3.81 cm from the plate center, which are: CyyL = 3.03 X 10^ m/sec (1.16 x 10^ ft/sec) (5.16) Cyyp = 1.00 X 10^ m/sec (3.30 x 10^ ft/sec) (5.17) CyyFp = 240 m/sec (788 ft/sec) (5.18)

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34.5(2660) 108 Fig. 5.10 Strain-gage outputs from front surface gages with Gage layout (e) in Fig. 5.3. Impactor velocity = 32.5 m/sec (106.5 ft/sec).

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109 Table 5.3 Wave propagation velocities, and peak strains and strain rates measured from gages along the y-axis for Gage layout (e) • Gage No. 9F lOF IIF 12F Distance from the cm 1.27 2.54 3.81 5.08 Plate Genter (in.) (0.5) (1) (1.5) (2) 3 10 m/ sec 5.06 4.24 2.82 SyL. (10^ ft/sec) (1.66) (1.39) (0.926) 3 10 m/sec 1.34 1.10 0.908 SyF, (10^ ft/sec) (4.39) (3.62) (2.98) m/ sec 332 249 231 SyFP, (ft/sec) (1055) (817) (758) e , ue yy peak, ^ -10433 -7623 -9261 -9947 £ , £/ sec yy peak. -812 -242 -167 -137 Equations (5.16)-(5.18) correspond to Eqs. (5.6), (5.8), (5.10), respectively, which were measured for Gage layout (b) . A reasonable agreement between both sets of measured data is evident. The peak strains and strain rates have also been summarized in Table 5.3. These data show a high peak strain at Gage 9F which is near the impact region, a relatively low peak strain at Gage lOF, and increasing peak strains at Gages IIF and 12F in this order. The high peak strains in the vicinity of Gage 9F can be attributed to its proximity to the impact event. 5.4.2 Surfaceand Embedded-Gage Results for [ (0°)^/ (90°)^/ (0°)^] Laminates Laminates with [ (0°)^/ (90°)^/ (0°)^] ply orientation were fabricated adding one 90 ply in the middle lamina to the previous specimens in

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110 order to enable gages to be embedded in the middle of the laminates. The gage layouts have been shown in Fig. 5.11. Each laminate has been instrumented with a front surface, a back surface, and an embedded gage at 3.81 cm (1.5 in.) from the plate center. All specimens were impacted using 2.54 cm blunt-ended impactors. Gage layout (a) ; Figure 5.12 shows the strain-time records from gages located along the x-axis. The near symmetry of recorded strains on the front and back surfaces of the tested specimens shows that the flexural wave appears to be predominant. This fact can be documented by summing and subtracting respectively the front and back surface strains, and noticing that the sum (IF + IB), that is, an in-plane component of the strain is very small compared with the algebraic difference (IF IB), that is, a flexural (or bending) component of the strain. The sum of opposite-surface strains is similar to the strain recorded from the embedded gage (IM) placed in the middle of the laminate. This indicates that the in-plane component of the strain is almost uniform across the laminate thickness. Although the IF + IB and IM records contain some noise due to the low amplitude of recorded strain, the general trend noted above can be clearly observed from these records. Gage layout (b) : Figure 5.13 shows the strain-time records obtained from gages located along the y-axis. The same discussion as described for Gage layout (a) holds true for this layout. The principal difference between data occurs in that the surface strains are much higher than before, and that, because of these high strains, a transverse crack has occurred close to the front surface gage affecting the front surface strain. This result has produced a disturbance in the symmetry of the two surface— gage records. Another test showed that this symmetry was maintained without the appearance of any noticeable transverse crack effects.

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0-DEGREE LAMINA 111 >> 3 pq 43 B " 3 33 to m O 3 3 3 3 CO •H I 00 •H plane embedded gages.

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76.5(1776) 112 O Fig. 5.12 Strain-gage outputs from surf aceand embedded-gages with Gage layout (a) in Fig. 5.11. Impactor velocity = 24.4 m/sec (80.0 ft/sec).

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29.5(-l77) '293.0(-297) 113 Fig. 5.12 continued.

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412.0 ( 4767 ) 114 Fig. 5.13 Strain-gage outputs from surfaceand embedded-gages with Gage layout (b) in Fig. 5.11, and the contact time record. Impactor velocity = 24.5 m/sec (80.3 ft/sec).

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115 5.4.3 Surface-Gage Results for [ (30°)^/ (-30°)^/ (30°)^] Laminates Surface strains in different directions were also measured in [(30°^/ (-30°)^/ (30°)^] angle-ply laminates, impacted by 2.54 cm blunt-ended impactors. The gage layouts used for these tests have been shown in Fig. 5.14. Gage layout (a) : Figure 5.15 shows strain-time records from four gages placed parallel and normal to the fibers on the plate surfaces. The strain recorded from Gage 2F appears to be affected by a transverse crack which developed just beneath the gage. Gage layout (b) : Figure 5.16 shows once again the recorded strains ( history from four gages located along the xand y-axes on both the front and back surfaces of the plate specimens. The general wave form and wave characteristics as described in Section 5.4.1 hold also for these angleply specimens. The important point to be noted is that the wave-propagation velocities and the strain amplitudes are different in different directions. It can be concluded from these data that, the wave-propagation velocities vary as. 30 XX yy 120 for strain amplitudes ordered as. e 30 < e < e XX yy < ^120 ’ where the subscripts 30, 120, xx, yy, denote Gages 1-4, respectively.

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30-DEGREE LAMINA 116 CO 0) d u CO C d B cO cd i—H § >> X d a •H cu d) (U 1 u CO cO CO CO CO rH d 00 o u •H o CO rn d •rl 0) »4-l e •H f— » o m 0 • O CO cn a; Vw' 00 cO looo s O 0) o G cn CO 1 u d irjco s o O o CO cO rO 1—4 u d o CO M-l 4J 4J d d o o v-l >> m CO r— 1 G 4J
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117 N O O) hFig. 5.15 Strain-gage outputs from surface gages with Gage layout (a) in Fig. 5.14. Impactor velocity = 29.3 m/sec (96.0 ft/sec).

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531.5(5001) 118 Fig. 5.15 continued.

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91 . 0 ( 4040 ) 119 Fig. 5.16 Strain-gage outputs from surface gages with Gage layout (b) in Fig. 5^14. Impactor velocity = 28.7 m/sec (94.2 ft/sec).

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113.0 ( 7222 ) 1 ^ 148.0 120 Fig. 5.16 continued

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CHAPTER 6 EXPERIl'ENTAL CRACK PROPAGATION STUDIES OF IMPACTED COMPOSITE LAMINATES 6.1 Introduction As pointed out in Section 3.3.3, knowledge of the crack velocity is an important factor in determining the dynamic behavior of materials. Indeed, the dynamic fracture surface energy has been observed to increase as the crack velocity increases [78-84]. In particular. Refs. [79-81] include the dynamic fracture surface energy of PMMA as a function of crack velocity. An overall summary of dynamic crack propagation theories for homogeneous brittle solids has been reported by Erdogan [111] and a number of studies on this subject have appeared in the literature in recent years, as listed in Ref. [111]. In the current investigation, the dynamic fracture surface energy, which was defined as the delamination surface energy, was measured and has been discussed in Section 3.3.3. The delamination crack propagation velocity, however, has thus far been unknown. In the present studies, the delamination crack propagation velocity has been measured using a high-speed camera and correlated with the dynamic delamination surface energy described in Section 6.2. Other aspects of the impact dynamics of both the Impactor and the laminate have also been discussed. In addition to the delamination velocity, another important velocity to be measured in the present studies is that related to the generator strip formation. This velocity has been measured using a velocity gage technique which has been newly devised for this purpose and discussed in Section 6.3. 121

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122 6,2 Delamination Crack PropaRation Studies Using a High-Speed Camera 6.2.1 Experimental Procedure In order to characterize the impact dynamics of the impactor and the laminate, and to measure the delamination crack propagation velocities inside the laminate, a Nova Model 16—3 16 mm high-speed camera (Photo-kinetics, Inc., Poughkeepsie, N.Y.) was used. This camera consists of a continuously moving film strip, and employs a rotating prism as an optical compensator and shutter. The camera speed range is from 10 to 10,000 frames/sec with the standard 16 mm prism. For applications requiring more than 10,000 frames/sec, various prism assemblies are available. A one quarter frame prism was used in the present study to obtain photographic data at speeds up to 40,000 frames/sec. The resultant photos are thus one quarter in height, that is, 4 mm high, and 16 mm wide with projection on a standard 16 mm projector as four frames. An accessory 400 foot magazine was attached to the basic camera body in order to accommodate a 400 foot Kodak 4-X Reversal FILM 7277 film (Eastman Kodak Company, Rochester, N.Y.). The film used can be processed by normal commercial procedures and expanded in order to obtain larger photo reproductions. The setup of the camera assembly, including a camera body, a 400 foot magazine with a 400 foot film installed, and a power supply, has been shown in Fig. 6.1. The specimens tested were impacted with different types of steel impactor s following the same experimental procedures as described in Section 3.2, with the exception that the specimen holder assembly was placed at a distance of 40 cm from the end of the gun barrel in order to provide enough room for illuminating the specimen from the front side. The specimen assembly was then Installed inside a protective box with Plexiglas windows as shown in Fig. 6.2. The high-speed camera

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123 ,L Fig. 6.1 Setup of a Nova Model 16-3 16 mm high-speed camera. was then placed right behind the protective box so as to obtain the desired photographic details through the Plexiglas windows. Two strong collimated light sources illuminated the plate specimen through the Plexiglas side windows and were placed at 45° with respect to the impactor trajectory. 6.2.2 Results and Discussion Figures 6. 3-6. 6 show typical high-speed photos taken for [(0°)^/ (90 )^/ (0 )^] laminates impacted by blunt-ended and/or hemispherical impactors with different impactor kinetic energies. The impactor velocity and length (mass) have been changed in each case. Because these prints were made from a positive film, light and dark areas are reversed. Thus shadows and delaminations appear as light regions. Figure 6.3 shows typical high-speed photos taken for a laminate impacted by a 2.54 cm blunt-ended impactor at 74.5 m/sec (244.4 ft/sec).

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124 Fig. 6.2 The overall experimental setup for measuring delamination crack propagation velocities using a high-speed camera.

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125 Shadows of the impactor can be found. The shadows are coining towards the center of the target laminate. I 5 cm Fig. 6.3 Sequence of delamination crack propagation in a [ (0°)5/ (90°)5/ (0°)5] laminate impacted by a 2.54 cm blunt-ended impactor at 74.5 m/sec (244.4 ft/sec). 27.1 ysec/frame.

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126 6. The impactor velocity can be calculated from the propagation velocity of the impactor shadows. 8. The impactor hits the target laminate. 9. Delamination cracks begin to propagate. Fig. 6.3 continued.

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127 11. Both delamination cracks at the first and second interfaces propagate simultaneously. 12 . 13. The delamination crack at the first interface stops. 15. The delamination crack at the second interface stops. 14. Fig. 6.3 continued

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128 Fig. 6.4 Sequence of delamination crack propagation in a [ (0°)5/ (90°)^/ (O'’)^] laminate impacted by a 2.54 cm blunt-ended impactor at 83.2 m/sec (273.0 ft/sec). 25.0 ysec/frame.

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129 Delamination cracks begin to pro pagate. Delamination cracks at the first and second interfaces propagate simultaneously . 14. Delamination patterns become irregular. The spall strip of width approximately twice the impactor diameter begins to form. Some transverse cracks can be found to pro15. pagate. Fig. 6.4 continued.

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130 19. 20 . 21 . 22 . 23. 24. 25. The contact between the impactor and the laminate should end around this time. 26. Fig. 6.4 continued

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131 1. Shadows of the impactor appear. 2 . 3. 5. 6 . I 5 cm H 7. 8 . 9. The impactor hits the target plate and delamination begins to form. Fig. 6.5 Sequence of delamination crack propagation in a [ (0°)5/ (90°)^/ (0°)^] laminate impacted by a 2.54 cm hemispherical impactor at 75.5 m/sec (247.6 ft/sec). 30.1 psec/frame.

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132 Delamination cracks at the first and second interfaces propagate simultaneously. A single line crack at the center and a spall strip begins to form. The delamination crack at the first interface stops. 13. Some transverse cracks can be found clearly. 14. 15. The delamination crack at the second interface stops. 16. 17. 18. Fig. 6.5 continued.

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133 Fig. 6.5 continued

PAGE 148

134 Fig. 6,5 continued

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135 55. The shadows of the rebounding impactor can be found (Photos 47-63) . 56. Fig. 6.5 continued.

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136 Fig. 6.6 Sequence of delamination crack propagation in a [ (0°)5/ (90®)^/ (0°)^] laminate impacted by a 5.08 cm blunt-ended impactor at 58.8 m/sec (192.8 ft/sec). 27.1 psec/frame.

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11 . 13 . The impactor hits the target plate. Delamination cracks begin to propagate. Fig. 6.6 continued.

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138 19. 20 . 21. The delamination crack at the first interface stops. 22 . 23. 24. The delamination crack at the second interface stops. 25. 26. 27. Fig. 6.6 continued

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139 Fig 6.6 continued

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140 Fig. 6.6 continued

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141 The resultant fracture obtained after Impact has been documented in Fig. 6.7(a). In Figure 6.3, the first several photos include a shadow effect associated with the oncoming impactor as illuminated from behind by the collimated light sources. These shadows first appear at the edges of the plate and then coalesce towards the center of the target plate. The impactor velocity can be estimated from the velocity of these shadows. This estimated impactor velocity has agreed well with the impactor velocity as measured by the photocells in the gas gun system. The initial contact between the impactor and the plate appears to begin in Photo 8 and a delamination crack starts to form. Both delamination cracks at the first and second interfaces appear to propagate simultaneously (Photos 9-12) . The delamination crack at the first interface appears to stop first (Photo 13) before the other delamination crack at the second interface stops (Photo 15 or after). In this test, delamination lasts almost 150 microseconds, which is approximately half of the impactor contact time. Figure 6.4 shows additional high-speed photos obtained for a laminate impacted by a 2.54 cm blunt-ended impactor at 83.2 m/sec (273.0 ft/sec). The resultant fracture appearance after impact is shown in Fig. 6.7(b). For this test, more delamination can be found in Fig. 6.7(b) than in Fig. 6.7(a) due to the difference in impactor velocity. The shadows of the oncoming impactor before the initial contact can be seen in Photos 1-9 in Fig. 6.4. Both delamination cracks at the first and second interfaces propagate simultaneously (Photos 10-15) . It is not clear when delamination cracks stop in these photos. It is noted, however, that in Photo 14 a resultant spall strip of width approximately twice the impactor diameter begins to form. Some transverse cracks can also be found to form and propagate in Photos 14 and 15, while the

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142 (a) Fig. 6.3, 2.54 cm BLUNT-ENDED, 74.5 m/sec. (b) Fig. 6.4, 2.54 cm BLUNT-ENDED, 83.2 m/sec. Fig. 6.7 The resultant fracture appearance of impacted [ (0°)^/ (90°)^/ (0°)^] laminates in Figs. 6. 3-6. 6.

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(c) Fig. 6.5, 2.54 cm HEMISPHERICAL, 75 (d) Fig. 6.6, 5.08 cm BLUNT-ENDED, 58.8 .5 m/sec. m/ sec . Fig. 6.7 continued.

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delamination cracks propagate. This appears to be further documentation of the sequence of events described in Chapters 4 and 5 that transverse cracking occurs while delamination occurs. Figure 6.5 shows additional high-speed photos for a laminate impacted by a 2.54 cm hemispherical impactor at 75.5 m/sec (247.6 ft/sec). Again, the resultant fracture appearance after impact has been shown in Fig. 6.7(c). The impactor kinetic energy in this test is almost the same as that in the test shown in Fig. 6.3. Only the nose shape as a controlled parameter has been changed. Again and as before, the shadows of the oncoming impactor can be observed in the recorded Photos 1-8. The two delamination cracks at the first and second interfaces again appear to propagate simultaneously as shown in Photos 9-12. The first crack appears to stop in Photo 12, while the second stops in Photo 15 or immediately thereafter. A single line crack directly ahead of the center of the impactor, which is a characteristic fracture pattern for hemispherical impactors, can be found to propagate in Photos 11-13, along with the formation of the spall strip and the formation of the transverse cracks. The contact between the impactor and the laminate should end around in Photo 22 according to the contact measurement in Section 3.3.5. In photos 47-63, the shadows of the rebounding impactor can also be seen. Figure 6.6 shows high-speed phcftos for a laminate impacted by a 5.08 cm blunt-ended impactor at 58.8 m/sec (192.8 ft/sec). The resultant fracture appearance after impact has been shown in Fig. 6.7(d). The impactor kinetic energy in this test is almost the same as that in the test shown in Fig. 6.4. The shadows of the oncoming impactor can be found in Photos 1-17. The resultant delamination cracks at the first and the second interfaces again appear to propagate simultaneously in

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145 Photos 18-21. The first crack stops in Photo 21, while the second stops in Photo 24 or immediately thereafter. In Photos 53 and 54, it is noted that the impactor appears to lose contact with the target plate. This can be documented by the observed shadows occurring at the center of the plate. These latter photos correspond to about 1,000 microseconds after the initial contact, which is similar to the contact time measured for 5.08 cm impactors using the contact measuring system described in Section 3.3.5. From the data obtained in Figs. 6. 3-6. 6, delamination crack propagation velocities can be calculated as follows. Using the photographic data directly as in Figs. 6. 3-6. 6, the distance of the propagating delamination crack tip from the plate center can be plotted as a function of the time AT after the first frame where delamination appears, as shown in Fig. 6.8. Then, delamination crack propagation velocity can be plotted as a function of the distance of the propagating crack tip from the plate center for four tests as shown in Fig. 6.9, using data obtained in Fig. 6.8. The velocities in Fig. 6.9 were calculated by a two-point formula, which may exaggerate the variation in velocity in Fig. 6.8. Due to lack of data obtained, the effects of some parameters, such as, impactor velocity, length (mass), and nose shape, cannot be quantified. However, in general, it appears that delamination crack propagation velocities are little affected by these parameters as noted, according to Fig. 6.9. For all tests there exists an initial high crack propagation velocity followed by a decrease in velocity and finally by crack arrest. Note that a similar decrease in flexural velocities in Table 5.3 calculated from strain-gage data occurs. The delamination crack in the 90° direction at the first interface propagates somewhat slower and stops earlier than that in the 0° direction at the second

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146 h< O o (/> O in 1 C2 CO rH Q) CO CO T3 o U CO Q) (U XJ CO rH C U a O CO u O a) *H 0a 0) a U CO (— 1 CO rH c o CU 0 rH •H rH o 4J O CO 42 u 12 1— ^ •H B B T3 o CO •H rH rH 4-1 0) o CO a •H (U • 0) v£> 42 • a :5 vO CO 1 u cO CJ 4J u 2 CO CO M-l rH •H 2 Q CO CJ 00 • \o 60 •H CO U-l u HD C CO u c O •H 4J O 0) •H O o> (U CO a C! o *H XJ CO fl •H a CO 1— i a) TJ CO T3 u o o IOVaO 3H1 dO 30NV1SIQ (a)-(d) correspond to Figs. 6. 3-6. 6, respectively.

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147 DISTANCE FROM THE PLATE CENTER(mm) (a) Fig. 6.3, 2.54 cm BLUNT-ENDED, 74.5 m/sec. DISTANCE FROM THE PLATE CENTER(mm) (b) Fig. 6.4, 2.54 cm BLUNT-ENDED, 83.2 m/sec. Fig. 6.9 Delamination crack propagation velocities in impacted [ ( 0 °) 5 / (90°)5/ ( 0 °) 5 ] laminates, calculated from photographic data in Figs. 6. 3-6. 6. Solid [hollow] circles denote a delamination crack in the 90° [0°] direction at the first [second] interface. Records (a) -(d) in this figure correspond to records (a) -(d) in Fig. 6.8, respectively.

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VELOCITY(m/sec) o VELOCITY (m/sec) 148 DISTANCE FROM THE PLATE CENTER(mm) Fig. 6.5, 2.54 cm HEMISPHERICAL, 75.5 m/sec DISTANCE FROM THE PLATE CENTER(mm) (d) Fig. 6.6, 5.08 cm BLUNT-ENDED, 58.8 m/sec Fig. 6.9 continued.

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149 interface. The first-interface delamination propagates initially at about 300—400 m/ sec which decreases to 200—300 m/sec during the period of observation, and decelerates to stop at about 100 microseconds. On the other hand, the second-interface delamination propagates initially at about 400-500 m/sec which decreases to 270-400 m/sec during the period of observation, and decelerates to stop at about 300 microseconds. It was mentioned in Chapter 5 that the largest-amplitude flexural wave might be the most important factor related to the delamination fracture observed in impacted laminates. According to Fig. 6.9, the delamination crack propagation velocity in the 0° direction at the second interface measured at 3.81 cm from the plate center is approximately 300 m/sec, which is similar to 290 m/sec, the largest-amplitude flexural wave propagation velocity measured by strain gages at the same position (see Ed. (5.5)). Differences in the measured values can be due to the assumption that delamination can occur at lower strains before the peak strain arrives. This can also be attributed to the difference in the impactor velocities in both tests. The above discussion appears as further documentation that delamination is caused by the flexural wave produced by impact. As further documentation of the order of magnitude of the surface energy, Paxton and Lucas [80] measured the crack extension force G as a function of the crack velocity V for PMMA specimens under fixed boundary conditions and provided: G s 0.23 J/cm^ at V = 300 m/sec (6.1) In the present test. G = 2y = 0.75 J/cm^ at V s 300 m/sec ( 6 . 2 )

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150 for a 2.54 cm impactor. Equation (6.2) is higher than Eq. (6.1), but both are of the same order of magnitude. 6.3 Measurement of Generator Strip Formation Velocities 6.3.1 Experimental Procedure Generator strip formation is generally considered to be the key fracture mechanism associated with the delamination of the laminate. To establish bounds on the rate at which the generator strip propagates, a newly-devised velocity gage technique has been used for measuring purposes. As shown in Fig. 6.10, this gage sensor consists of a silver conductive paint (GC Electronics, Rockford, 111.) deposited normal to the predicted generator strip path and spaced at regular intervals on the front face of the plate such that each stripe is broken as the generator strip propagates. The length of each conductive stripe should be short so that each stripe is not broken by the transverse cracks occurring. Brass tabs have been bonded to the plate in order to connect the conductive stripes to an electric circuit. As each stripe is broken, a step appears in a voltage-time record on two 2-channel digital oscilloscopes. The impactor contact measuring system described in Section 3.2 has been used for triggering the oscilloscopes. 6.3.2 Results and Discussion Typical voltage-time records obtained from the digital oscilloscopes have been shown in Fig. 6.11 for laminates impacted by blunt-ended impactors with different impactor velocities and impactor masses. Distance of the propagating generator strip tip as a function of the time AT after the first stripe is broken can be plotted as shown in Fig. 6.12, using the data in Fig. 6.11. The generator strip formation velocities calculated from these measured data are summarized in Table 6.1.

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151 Table 6.1 Generator strip formation velocities. Test Impactor Impactor Generator Strip Formation Velocity Length, Velocity at a Distance L from the Plate cm m/ sec Center, m/sec (ft/sec) (in.) (ft/sec) L=18mm L=28mm L=38mm (a) 2.54 70.3 625 370 435 (1) (230.5) (2051) (1214) (1427) (b) 2.54 75.9 588 476 417 (1) (248.9) (1929) (1562) (1368) (c) 2.54 81.1 667 588 513 (1) (266.0) (2188) (1929) (1683) (d) 5.08 52.9 667 571 400 (2) (173.7) (2188) (1873) (1312) The decrease in velocities with distance from the plate center is noted. The generator strip propagates initially at about 600-700 m/sec, which decreases to about 400-500 m/sec during the period of observation. This generator strip formation velocity, V , appears to increase with gs increase in impact velocity for the 2,54 cm impactor except for Test (b) . The shear wave velocity of the epoxy resin, = J G/p is Vg = 1.06 X 10^ m/sec (3.48 x 10^ ft/sec) (6.3) based on the values of G and p given in Appendix A. Therefore at 18 mm from the plate center, V is of the order of 60 percent of V of the epoxy itself. The velocity might be closer to V^, if it were measured closer to the impactor. Only one test has been conducted for 5.08 cm impactors. More tests are necessary to make meaningful and conclusive remarks. However, the same order of magnitude for V would appear to be observed.

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152 TO EACH DIGITAL OSCILLOSCOPE INPUT Fig. 6.10 Modified velocity gage arrangement. (1 = 13 mm, d = 10 mm)

PAGE 167

VOLTAGE I 92.0 jjsec(43mm) 153

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92. 0 >jsec(43mm) 154 a Q) w 'e ON • LO 4J cO Pi o H a C P4 S M Q « • Q T3 Z (1) W 3 1 C H •H Z 4J z c 4 o pq o e 1 o iH ~d" 1— 1 in • • vO CN to Xi pz-(

PAGE 169

71. 5jjsec(43mm) 155

PAGE 170

76 . 0 jLisec( 43 mm) 156 T) 01 3 fi •H U c O U ti •H

PAGE 171

157 a. ol iO (ujuj)H 31N3D HlVld 3H1 WOHd dll dIdlS d01Vd3N39 3H1 dO 3DNV1SIQ U (U OJ CO o -n u — s 4J Cd Cd H s-/ 60 <1 CO o cx 0) u o IS u u TO CU d «4-l o 0> o cx IS CO 4J c d) o M M-l •H O 4J O a a 0) ts o 3 /-N c U-i -d cd N-> 4^ cd 1 CO /— S *H CO Cd Q Cd cs I— I vO W) •H

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158 In general, the generator strip formation velocity appears to be higher than and indeed almost twice as high as, the delamination crack propagation velocity described in Section 6.2. The generator strip appears to form within 100 microseconds after the initial contact and this fact appears to be consistent with the assumption that the generator strip generates the follow-on delamination cracks.

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CHAPTER 7 SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS FOR FUTURE WORK 7.1 Summary and Conclusions Experimental studies on the delamination failure mechanisms in partially penetrated composite laminated plates have been conducted. A summary of results obtained is described in the following paragraphs. In Chapter 1, both analytical and experimental work on impact problems of fiber-reinforced composite materials (FRCM) has been reviewed, with emphasis on the impact test methods used for FRCM. Among the cited problems, localized impact problems of composite laminates have been surveyed from three different points of view: (1) Localized impact damage experiments, (2) Solution of simplified wave propagation problems based on continuum mechanics models, (3) Hertzian contact approaches to impact problems. In addition, the previous experimental studies on fracture mechanisms of impacted composite laminates at the University of Florida have been summarized. In Chapter 2, the fabrication methods of composite laminated plates from fiberglass/epoxy prepreg tapes have been described. The fabrication method suitable for producing plates with desired strength and semitransparency has been established after trial and error using an autoclave to control the fabrication pressure and temperature. In Chapter 3, systematic experimental studies on the sequential delamination fracture mechanisms of centrally impacted composite laminates have been extended using a fiberglass/epoxy laminate mainly with [ (0°)^/ (90°)^/ (0°)^] ply orientations. Several parameters, such as 159

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160 impactor nose shape, impactor length (mass), impactor kinetic energy, and ply orientation have been varied in order to investigate the effects of these parameters on the fracture behaviors of the tested laminate. The important results obtained are: (1) A hemispherical nose produces more local crushing of the first lamina under the impactor and a less developed generator strip than does a blunt nose. The damage is thus more localized and the impact energy is less dissipated at the front lamina with hemispherical noses than with blunt noses. (2) Sequential delamination mechanisms have been identified for all types of impactors. The slope of the impactor kinetic energy versus the delaminated area, that is, the apparent fracture surface energy appears to be affected by the impactor length (mass), but not by the nose shape. Use of larger impactors results in a 30 percent higher surface energy than with corresponding smaller impactors. (3) So-called transverse cracks have been noted in the fiber direction of each lamina and show an almost evenly distributed crack spacing. The mean crack spacing decreases as the impactor velocity increases. These transverse cracks may be caused by membrane tensile stresses due to large deflections of the impacted plate, while delamination cracks may be caused by transverse shear associated with generated flexural waves. (4) Impactor contact time measurements indicate that both single and multiple contacts are possible. The heavier and/or faster impactors have longer contact times than the lighter and/or slower ones.

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161 (5) Angle-ply laminates have shown delamination patterns similar to those for cross-ply laminates with some differences in the actual shape of the delamination. In Chapter 4, microscopic observations of the cross sections of impacted [ (0°)^/ (90°)^/ (0)^] composite laminates have been made using a scanning electron microscope (SEM) . The sample preparation methods for cutting and polishing the cross sections have been established using special care to eliminate any damage introduced during the preparation. The microphotos obtained have confirmed macroscopic observations such as the initiation and propagation of the transverse cracks and delamination cracks and given some details which cannot be obtained macroscopically. The transverse cracks are perpendicular to lamina interfaces in regions where there is no delamination, while the transverse cracks grow oblique to lamina interfaces where they are accompanied by a delamination crack. Delamination cracking thus appears to interact with the observed transverse cracks. In Chapter 5, the dynamic strains induced by central impact of 2.54 cm blunt-ended impactors of fiberglass/epoxy laminates have been measured by means of surface and embedded gages with several different gage layouts, and the characteristics of these strains, that is, wave types, wave amplitudes, and strain rates have been studied. The predominant wave has been found to be a flexural one for the tested velocity range (30-40 m/ sec) . The recorded strains for front and back surface gages at 2.54 cm from the plate center for [ (0°) (90°) (0° )^] lamintes can be characterized as follows. First a very small in-plane tensile wave arrives at both surface gages. On the front[back] surface, a tensile [compressive] component of an oncoming flexural wave arrives followed by a large compressive [ tensile] component of the flexural wave.

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162 The largest-amplitude within the flexural wave may be the most important factor related to the resultant delamination fracture observed for the laminates. The largest-amplitude has an average measured velocity at 3.81 cm from the plate center of: 290 m/sec, in the 0° direction 225 m/sec, in the 90° direction The bending strains were larger for gages at 5.08 cm from the plate center than for those at 2.54 cm, but there was a significant decrease in velocity with distance for the observed waves. In general, measured in-plane and flexural wave velocities agreed well with the corresponding values calculated from the known material elastic constants. Embedded gages, which have been proved to work properly, recorded small strains and documented that the flexural wave was predominant in the present experiments. In addition, surface strains have been measured for [ (30°)^/ (-30°)^/ (30°)^] angle-ply laminates. These data revealed the directional dependence of wave velocities and strain amplitudes. In Chapter 6, high-speed photos for semitransparent [ (0°)^/(90°)^/ (0°)^] laminates impacted by different types of impactors and thus different kinetic energies have been taken. A Nova high-speed camera was used to record the rapid delamination crack propagations occurring with camera speeds of up to 40,000 frames/ sec used. These photos have revealed some important features in the impact event as summarized in the following remarks: (1) Both delamination cracks at the first and second interfaces start and propagate almost simultaneously, but the first crack stops before the second does.

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163 (2) It appears that delamination crack propagation velocities are little affected by impactor velocity, length (mass), and nose shape. (3) According to calculations based on high-speed photos, the delamination crack occurring in the 90° direction at the first interface propagates initially at about 300-400 m/sec which decreases to 200-300 m/sec during the period of observation, and decelerates to stop at about 100 microseconds, while the delamination crack generated in the 0° direction at the second interface propagates initially at about 400500 m/sec which decreases to 270-400 m/sec during the period of observation, and decelerates to stop at about 300 microseconds. This latter velocity agrees well with the largestamplitude flexural wave propagation velocity measured by strain gages. This is considered to be further documentation that delamination is caused by the flexural wave. (4) Transverse cracks have been found to propagate while the delamination cracks propagate in several of the photos obtained. This is further evidence that transverse cracks and delamination cracks occur almost simultaneously. (5) In sequential photos of the impact event taken with the longer (5.08 cm) impactors, a contact time of around 1,000 microseconds has been found. However, the delamination event was found to last for almost the same time as for the shorter impactors. A velocity gage technique using a silver conductive paint has been adapted to measure velocities of the generator strip development, which were initially about 600-700 m/sec and which decreased to 400-500 m/sec

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164 during the period of observation. The generator strip formation velocity has been found to be higher than and indeed almost twice as high as, the measured delamination crack propagation velocity. This strip appears to form within 100 microseconds after the initial contact and appears to be consistent with the assumption that the generator strip itself initiates delamination cracks. Based upon the studies conducted thus far, the following concluding remarks can be made. For blunt-ended cylinders impacting against [(0°)^/ (90°)^/ (0®)^] plates at subperforation velocities, delamination occurs in the following sequence of events. Impact on the plate is considered to generate a transverse flexural wave and in-plane tensile wave due to large deflections of the plate. First the impactor cuts shear cracks through the thickness of the first 0° lamina and bounds a generator strip cut from the first lamina. The strip so formed pushes forward on the second lamina and initiates delamination between the first two laminas. Then a second generator strip in the 90° lamina can form and initiate a delamination between the last two laminas. The generator strip itself develops faster than the delamination cracks according to measurement of its velocity (Section 6.3). This is followed immediately by delamination cracks occurring almost simultaneously at the first and second interfaces according to high-speed photos (Section 6.2). Delamination cracks are apparently caused mainly by an impact-generated flexural wave (Chapter 5 and Section 6.2). On the other hand, an impact-generated in-plane tensile wave travels at almost the same velocity as the flexural wave and generates so-called transverse cracks in the fiber direction of each of three laminas. Oblique transverse cracks associated with delamination have also been observed in SEM photos (Chapter 4). Strain-gage records with several sudden jumps in predominant

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165 flexural-wave records (Chapter 5), and high-speed photos (Section 6.2) as well as oblique transverse cracks support that this in-plane tensile wave travels almost simultaneously with the flexural wave. Thus delamination cracks and transverse cracks interact with each other. For round-ended types of impactors, no clear generator strip can be found. However, with this one notable exception it is believed that the same sequence of fracture events then occurs. The whole delamination event appears to be completed within approximately half a contact time. 7 . 2 Recommendations for Future Work Some important impact problems of composite laminates have been solved in this dissertation. However, there are many problems left to be solved and some are identified herein for future work. Composite material systems other than fiberglass/epoxy, such as graphite/epoxy , boron/epoxy. Kevlar/epoxy , and their hybrids should be used for similar experiments as conducted in this study. These materials should then be graded in terms of their impact resistance and compared with data obtained in the present experimental program. To record delamination events in non-transparent laminates, plates may be fabricated with conducting paths to be broken by the propagating delaminations. The time sequence of the various delaminations can be established in this way, although there may exist experimental difficulties associated with the fabrication of such laminates. In the present test program, the ability to record transient data simultaneously has been limited by the number of channels available in the oscilloscopes used. A multichannel recording facility is necessary to monitor the multiple surface and embedded strain gages in order to follow the induced flexural and shear waves by means of the implanted and bonded sensors. Such a multichannel data-recording system has been

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166 assembled experimentally at the Department of Engineering Sciences of the University of Florida [112] . The system uses an existing digital magnetic tape data handling equipment, an analog-to-digital converter to process the data into a form for computerized data analysis, and a microprocessor system with digital memory to store processed data. The latter system can be used with a computer plotting facility to display the signals graphically. Moire fringe observations of the back surface deflections of impacted laminates can be a useful experimental tool to give a full field representation of the deflections occurring and to provide further evidence as to the causes of the delamination and transverse cracks observed from strain-gage records and high-speed photos. This technique has previously been used successfully for air blast loaded plates [113]. For practical application purposes, the residual strength of the impacted laminates should be measured by some testing procedure such as static tests. The same specimen holder as used for the impact tests can be used in static plate bending tests in which the square plate is loaded centrally by a cylindrical ram previously used as an impactor. Static cylindrical bending tests on beam type specimens are also possible. A strip cut from the impacted laminate can be supported on two edges and loaded centrally by a wedge with a rounded edge. The loads required to produce detectable delamination would be recorded as well as the force-deflection curves to rupture. Any additional delamination introduced could be detected by the test operator or by measuring acoustic stress pulses generated by delamination during the test. For comparison purposes similar static bending tests would be performed on undamaged plates. To assess the extent to which the strength degradation is accounted for by delamination, some plates could be fabricated with built-in

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167 delamination of the size and shape of some of the delaminations produced by the impacts. This could be accomplished by cutting very thin sheets of Teflon into the appropriate delamination shapes and inserting them into the prepreg tapes prior to fabrication. These plates would then be tested in static bending using a procedure similar to the one described in the last paragraph. To obtain additional quantitative information on the stresses and strains in the elastic flexural wave and estimates of the threshold levels of shear stress for interlaminar shear failure, a computer elastic analysis using a laminated plate theory to accommodate multilaminar plate configurations could also be developed. One such attempt has been made [55] using a DEPROP computer code, but added improvements are necessary to facilitate such an analysis. Another area of study requiring attention is a possible description of a simplified model for predicting the propagating delamination crack in terms of fracture mechanics methods. The possibility of incorporating such a model in an analysis such as the DEPROP code could then be examined. Kim and Moon [66] have attempted to study just such effects, that is of interlaminar cracks in composite laminates in response to impact loads, and formulated the governing equations. As pointed out in Section 1.4.3, the impact dynamics of the Impactor and the dynamic response of the laminate interact with each other and Hertzian contact approaches to this problem have been found to be successful predictors in some cases. This analytical technique should be further extended to investigate the possibility for multiple contacts. The questions to be solved are under what conditions multiple contacts can occur and how much of the impactor energy can be transferred during each contact time.

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APPENDIX A CALCULATION OF THE THEORETICAL WAVE PROPAGATION VELOCITIES IN HIPACTED LAMINATES The equations which relate the elastic moduli and the phase velocities of the waves in an orthotropic elastic solid have been summarized by Tauchert and Guzelsu [112]. Daniel and Liber [68] have applied these equations to the wave propagation in laminates impacted by projectiles. A similar calculation can be made for laminate specimens of the type used in these studies as follows. For an orthotropic elastic material, the stress-strain relations in coordinates aligned with the principal material directions (x, y and z axes) expressed in terms of the classical engineering constants (and engineering shear strains) are given by: £ 1 _ Vyx Vzx 0 0 0 a X E E E X X y z £ Vxy 1 Vzy 0 0 0 a y E X E y E z y £ Vxz Vyz 1 0 0 0 a z E E E 2 X y z 0 0 0 1 0 0 T yz G yz 1 yz Y 0 0 0 0 0 T zx G ZX zx Y 0 0 0 0 0 1 X xy G xy xy The phase velocities can be obtained in terms of these elastic constants and have been reported on in Refs. [68, 112]. 168

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169 In the case of thin plates with the z-axis normal to the plate and the wave length much longer than the plate thickness, the wave propagation velocities along the two in-plane principal material directions can be written as: C xxL / p(l V V ) J xy yx (A2) /Za ] P(1 V (A3) where p is the density of the material. The primary flexural wave propagation velocities associated with transverse-shear deformations can be similarly expressed as: *"xxF (A4) (A5) In the 45° direction with respect to the xand y-axes, the flexural wave associated with particle motion in the z direction travels with a velocity of: C 45F Ig +G I zx yz i (A6) The values of the elastic constants appearing in Eqs. (A2)-(A6) are thus needed in order to obtain the wave velocities. Some of the elastic constants for unidirectional Scotchply 1003 or 1002 plates were provided by the 3M Company [113] and Parhizgar [114]. These values are:

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170 G V V 12 12 21 = 40.0 GPa (5.8 x 10^ = 8.27 GPa (1.2 x 10^ = 4.14 GPa (0.6 x 10^ = 0.26 = 0.05 psi) psi) psi) (A7) where 1, 2 and 3 denote directions along the fibers, normal to the fibers in the plane, and normal to the plate, respectively. Assuming transverse isotrophy, it can be shown that. E3 ^13 S2’ ^13 ^12’ ^31 ^21 (A8) Thus the only elastic constant left to be determined is G^^. Christensen [115] has obtained an analytical representation for G^^ in terms of the properties of both the fibers and matrix, and the volvune fraction of fibers, using a composite cylinders model. G„„ = G [1 + 23 m -] : (K + Vn G )v m m 3mm (A9) G^ G 2(K + 4, G ) f m m m^ In the above equation, K and v represent the bulk modulus and the volume fraction, respectively, while the subscripts m and f refer to the matrix and fibers. Static properties of the epoxy matrix and E-glass fibers for Scotchply 1002 were given by Gibson and Plunkett [116] and have been summarized in Table A.l. Using this data, values for G^^ and the density

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171 Table A.l. Static properties of Scotchply 1002 matrix and E-glass fibers at room temperature. Epoxy E-glass Young's Modulus, GPa (10^ psi) 3.79(0.55) 72.4(10.5) Shear Modulus, GPa (10^ psi) 1.38(0.2) 30.3(4.4) Bulk Modulus, GPa (10^ psi) 4.48(0.65) 40.0(5.8) Poisson's Ratio 0.36 0.2 Specific Gravity 1.23 2.54 Nominal Volume Fraction in Composite* 0.53 0.45 *approximately 2 percent voids. of the composite have been obtained as, 0^3 =3.03 GPa (0.44 x 10^ psi) (AlO) p = p^v^ + p^v^ = 1.795 X 10^ kg/m^ (3.483 lb • sec^/ft'^) (All) The elastic constants of the laminate appearing in Eqs. (A2)-(A6) can be then found with the use of Eqs. (A7), (A8), and (AlO). E X E y G xy G zx G yz V xy 2Ei + E^ E^ + 2E^ 3 ^12 ^^13 ^23 G^3 + 2G23 ^^12 ^^21 29.4 GPa 18.8 GPa 4.14 GPa 3.77 GPa 3.40 GPa 0.19 (4.27 x 10^ psi) (2.73 X 10^ psi) (0.6 X 10^ psi) (0.55 X 10^ psi) (0.49 X 10^ psi) V yx V12 + 2V 21 (A12) 3 3 0.12

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Substituting the values in Eqs. (All) and (A12) into Eqs. (A2)-(A6), one obtains 172 *^xxL ~ ^*09 X lO^ra/sec (1.34 x 10^ ft/sec) CyyL = 3.27 X lO^m/sec (1.07 x 10^ ft/sec) ^xxF ~ 1-52 X lO^m/sec (4.98 x 10^ ft/sec) Cyyp = 1.38 X lO^m/sec (4.50 x 10^ ft/sec) = 1.41 X lO^m/sec (4.64 x 10^ ft/sec) (A13)

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APPENDIX B CALCULATION OF THE RATIO OF PEAK STRAINS ALONG X AND Y AXES Only bending strains of the plate are considered in this discussion, neglecting the mid-plane strains. The x and y directions are principal o w axes of bending, so that M and K = ^ are zero. Moreover, the xy xy 9x9y ’ experiments indicate that at points of the x-axis [y-axis] , the surface strains satisfy £ « £ [e « £ ] , so that K « K [k « K 1 . Hence, yy XX XX yy y x x y ’ at points on the axes, the strain energy per unit area U is assumed to be given by the following expressions, where the subscripts on U denote not components but the axes on which the expressions for U are valid U X M K X X along the x-axis U y M K y y along the y-axis (Bl) On the axes, for [ (0°)^/ (90°)^/ (0°)^] laminates concerned, it is assumed that M = D K , X XX x’ M = D K y yy y where D XX 1 2 (1 -V V + " 2 I xy yx D yy 12(1 V V xy yx' y[E^ + 26E2] (B2) (B3) 173

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174 and 3h is the thickness of the plate. Also the surface strain magnitudes on the axes are £ = hK , XX 2 xx’ £ = hK yy 2 yy (B4) Substituting Eqs. (B2) and (B4) into Eq. (Bl) , we obtain o D „ „ D „ U = 2 ^ 2.^ 2 X 9 ^ XX ’ ^y 9 ^yy (B5) Daniel and Liber [68] compared peak strains in the two directions by assuming isotropic propagation of energy. If Peak U = Peak U at the same distance from the impact point (not X y necessarily at the same time) , then 2 2 PeaK. D £ = Peak D £ XX XX yy yy (B6) and the peak strain ratio would be ^yy peak ^xx peak P"l ^ ^2 \ \ + 26E2 2.03 (B7) where elastic constants in Appendix A were used. Daniel and Liber [68] commented that this was only a rough approximation and that unequal stress biaxiality in the two directions and nonuniform distribution of the energy would tend to reduce the ratio. The calculation is also entirely based on elastic wave propagation and takes no account of damage such as transverse cracks and delamination that may have occurred.

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LIST OF REFERENCES [1] Jones, R. M. , Mechanics of Composite Materials , Scripta Book Company, Washington, D.C., 1974. [2] Sun, C. T. and Sierakowski, R. L., "Recent Advances in Developing FOD Resistant Composite Materials," Shock and Vibration Digest, Vol. 4, No. 2, 1975, pp. 1-8. [3] Foreign Object Impact Damage to Composites , ASTM STP 568, 1975. [4] Moon, F. C., "A Critical Survey of Wave Propagation and Impact in Composite Materials," NASA CR-121226, May, 1973. [5] Sierakowski, R. L., Nevill, G. E., Ross, C. A., and Jones, E. R. , "Experimental Studies of the Dynamic Deformation and Fracture of Filament Reinforced Composites," AIAA/ASME 11th Structures, Structural Dynamics, and Materials Conf., Denver, Colorado, April 22-24, 1970. [6] Phillips, D. C. , and Tetelman, A. S., "The Fracture Toughness of Fiber Composites," Composites, Vol. 3, No. 9, 1972, pp. 216-223. [7] Kanninen, M. F. , Rybicki, E. F., and Brinson, H. F., "A Critical Look at Current Applications of Fracture Mechanics to the Failure of Fiber-Reinforced Composites," Composites, Vol. 8, No. 1, 1977, pp. 17-22. [8] Peck, J. C., "Stress-Wave Propagation and Fracture in Composites," Dynamics of Composite Materials , Lee, E. H. , ed., ASME, 1972, pp. 8-34. [9] Hegemier, G. A., "On a Theory of Interacting Continua for Wave Propagation in Composites," ibid., pp. 70-121. [10] Postma, G. W. , "Wave Propagation in a Stratified Medium," Geophysics, Vol. 20, 1955, pp. 780-806. [11] White, J. E., and Angona, F. A., "Elastic Wave Velocities in Laminated Media," J. Acous. Soc. America, Vol. 27, 1955, pp. 311-317. [12] Sun, C. T., Achenbach, J. D. , and Herrmann, G., "Continuum Theory for a Laminated Medium," J. Appl. Mech. , Vol. 35, Trans. ASME, Vol. 90, Series E, 1968, pp. 467-475. [13] Bedford, A., and Stern, M. , "Toward a Diffusing Continuum Theory of Composite Materials," J. Appl. Mech., Vol. 38, Trans. ASME, Vol. 93, Series E, 1971, pp. 8-14. 175

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176 [14] Hegemier, G. A., and Nayfeh, A. H. , "A Continuum Theory for Wave Propagation in Laminated Composites — Case 1: Propagation Normal to the Laminates," J. Appl. Mech. Vol. 40, Trans. ASME, Vol. 95, Series E, 1973, pp. 503-510. [15] Eringen, A. C., "Balance Laws of Micromorphic Mechanics," Int. J. Engr. Sci., Vol. 8, 1970, pp. 819-828. [16] Ben-Amoz, M. , "A Continuum Approach to the Theory of Elastic Waves in Heterogeneous Materials," ibid., Vol. 6, 1968, pp. 209-218. [17] Barker, L. M. , "A Model for Stress Wave Propagation in Composite Materials," J. Composite Materials, Vol. 5, 1971, pp. 140-162. [18] Ben-Amoz, M. , "Propagation of Finite-Amplitude Waves in Unidirectionally Reinforced Composites," J. Appl. Phys., Vol. 24, 1971, pp. 5422-5429. [19] Lifshitz, J. M. , "Time-Dependent Fracture of Fibrous Composites," Composite Materials , Vol. 5, Broutman, L. J., and Krock, R. H. , eds. , Academic Press, New York, 1974, pp. 249-311. [20] Chamis, C. C., Hanson, M. P., and Serafini, T. T., "Impact Resistance of Unidirectional Fiber Composites," Composite Materials , Testing and Design (2nd Conf. ), ASTM STP 497, 1972, pp. 324-349. [21] Novak, R. C., and DeCrescente, M. A., "Impact Behavior of Unidirectional Resin Matrix Composites Tested in the Fiber Direction," Composite Materials; Testing and Design (2nd Conf.) , ASTM STP 497, 1972, pp. 311-323. [22] Toland, R. H. , "Failure Modes in Impact-Loaded Composite Materials," Failure Modes in Composites Symposium, Spring Meeting, AIME, Boston, Mass., May 8-11, 1972. [23] Adams, D. F., and Perry, J. L., "Instrumented Charpy Impact Tests of Several Unidirectional Composite Materials," Fibre Science and Technology, Vol. 8, 1975, pp. 275-302. [24] Beaumont, P. W. R. , Rieward, P. G., and Zweben, C. , "Methods for Improving the Impact Resistance of Composite Materials," Foreign Object Impact Damage to Composites , ASTM STP 568, 1975, pp. 134158. [25] Adams, D. F., "Impact Response of Pol 3 rmer-Matrix Composite Materials," Composite Materials: Testing and Design (4th Conf.) , ASTM STP 617, 1977, pp. 409-426. [26] Rotem, A., and Lifshitz, J. M. , "Longitudinal Strength of Unidirectional Fibrous Composite Under High Rate of Loading," 26th Annual Technical Conf., Soc. Plast., Ind., Reinforced Plastics/ Composites Division, 1971. [27] Broutman, L. J., and Rotem, A. "Impact Strength and Toughness of Fiber Composite Materials," Foreign Object Impact Damage to Composites , ASTM STP 568, 1975, pp. 114-133.

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177 [28] Lifshitz, J. M. , "Impact Strength of Angle Ply Fiber Reinforced Materials," J. Composite Materials, Vol. 10, 1976, pp. 92-101. [29] Kimpara, I., and Takehana, M. , "Static and Dynamic Interlaminar Strength of Glass Reinforced Plastics Thick Laminates," Proc. Reinforced Plastic Congress, Brighton, England, Nov. 8-11, 1976, pp. 183-191. [30] Schuster, D. M. , and Reed, R. P., "Fracture Behavior of Shock Loaded Boron-Aluminum Composite Materials," J. Composite Materials, Vol. 3, 1969, pp. 562-576. [31] Reed, R. P., and Schuster, D. M. , "Filament Fracture and PostImpact Strength of Boron-Aluminum Composites," J. Composite Materials, Vol. 4, 1970, pp. 514-525. [32] Goldsmith, W. , Impact , Edward Arnold Ltd., London, 1960. [33] Backman, M. E., and Goldsmith, W. , "The Mechanics of Penetration of Projectiles into Targets," Int. J. Engr. Sci., Vol. 16, 1978, pp. 1-99. [34] Gupta, B. P., and Davids, N. , "Penetration Experiments with Fiberglass-Reinforced Plastics," Experimental Mechanics, Vol. 6, 1969, pp. 445-450. [35] Morris, A. W. H. , and Smith, R. S., "Some Aspects of the Evaluation of the Impact Behaviour of Low Temperature Fibre Composites," Fibre Science and Technology, Vol. 3, 1971, pp. 219-242. [36] Wrzesien, A., "Improving the Impact Resistance of Glass-Fibre Composites," Composites, Vol. 4, 1973, pp. 157-161. [37] Askins, D. R. , and Schwartz, H. S., "Mechanical Behavior of Reinforced Backing Materials for Composite Armor," AFML-TR-283, Wright-Patterson AFB, Ohio, Feb., 1972. [38] Francis, P. H. , Nagy, A., Pennick, H. G. , and Calvit, H. H. , "Ballistic Penetration Effects on Biaxially Loaded Graphite/Epoxy Composite Panels," BRL Contract Report, No. 148, April, 1974. [39] Olster, E. F., and Roy, P. A., "Tolerance of Advanced Composites to Ballistic Damage," Composite Materials; Testing and Design (3rd Conf.) , ASTM STP 546, 1974, pp. 583-603. [40] Avery, J. M. , and Porter, T. R. , "Comparisons of the Ballistic Impact Response of Metals and Composites for Military Aircraft Applications," Foreign Object Impact Damage to Composites , ASTM STP 568, 1975, pp. 3-29. [41] Suarez, J. A., and Whiteside, J. B., "Comparison of Residual Strength of Composite and Metal Structures After Ballistic Damage," ibid., pp. 72-91. [42] Husman, G. E. , Whitney, J. M. , and Halpin, J. C., "Residual Strength Characterization of Laminated Composites Subjected to Impact Loading," ibid., pp. 92-113.

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178 [43] Preston, J. L., Jr., and Cook, T. S., "Impact Response of GraphiteEpoxy Flat Laminates Using Projectiles That Simulate Aircraft Engine Encounters," ibid., pp. 49-71. [44] Kawata, K. , and Takeda, N., "Fracture Mechanisms of Laminates Composite Plates Impacted by Projectiles," Trans. Japan Soc. Composite Materials, Vol. 5, 1979, pp. 21-25. (in Japanese). [45] Gorham, D. A., "High Speed Photographic Study of Failure Processes in Composite Materials," Private Communication, Cavendish Laboratory, University of Cambridge. [46] Graff, J., Stoltze, L., and Varholak, E. M., "Impact Resistance of Spar-Shell Composite Fan Blades," NASA CR-134521, July, 1973. [47] Friedrich, L. A., and Preston, J. L., Jr., "Impact Resistance of Fiber Composite Blades Used in Aircraft Turbine Engines," NASA CR-134502, May, 1973. [48] Premont, E. J., and Stubenrauch, K. R. , "Impact Resistance of Composite Fan Blades," NASA CR-134515, May, 1973. [49] Ross, C. A., and Sierakowski, R. L., "Studies on the Impact Resistance of Composite Plates," Composites, Vol. 4, 1973, pp. 157-161. [50] Critescu, N., Malvern, L. E. , and Sierakowski, R. L., "Failure Mechanisms in Composite Plates Impacted by Blunt-Ended Penetrators," Foreign Object Impact Damage to Composites , ASTM STP 568, 1975, pp. 159-172. [51] Ross, C. A., Cristescu, N., and Sierakowski, R. L., "Experimental Studies of Failure Mechanisms in Composite Plates," Fibre Science and Technology, Vol. 9, 1976, pp. 177-188. [52] Ross, C. A., and Sierakowski, R. L., "Delamination Studies of Impacted Composite Plates," Shock and Vibration Bulletin 46 Part 3, 1976, pp. 173-182. [53] Sierakowski, R. L., Malvern, L. E., and Ross, C. A., "Dynamic Failure Modes in Impacted Composite Plates," Failure Modes in Composite III , Chiao, T. T., ed. , AIME, 1976, pp. 73-88. [54] Sierakowski, R. L., Malvern, L. E. , Ross, C. A., and Strickland, W. S., "Failure of Composite Plates Subjected to Dynamic Loads," Proc. of Army Symp. on Solid Mechanics, 1976, pp. 9-25. [55] Sierakowski, R. L., Ross, C. A., Malvern, L. E., and Cristescu, N., "Studies on the Penetration Mechanics of Composite Plates," Final Report DAAG-29-76-G-0085 to U.S. Army Research Office, University of Florida, Gainesville, Florida, 1976. [56] Malvern, L. E., Sierakowski, R. L., Ross, C. A., and Cristescu, N. "Impact Failure Mechanisms in Fiber-Reinforced Composite Plates," Proc. of lUTAM Symp. on High Velocity Deformation of Solids, Kawata, K. , and Shioiri, J. , eds., Tokyo, Japan, August 24-27, 1977.

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179 [57] Yang, P. C., Norris, C. H. , and Stavsky, Y., "Elastic Wave Propagation in Heterogeneous Plates," Int. J. Solids and Structures, Vol. 2, 1966, pp. 665-684. [58] Whitney, J. M. , and Pagano, N. J., "Shear Deformation in Heterogeneous Anisotropic Plates," J. Appl. Mech. , Vol. 37, Trans. ASME, Vol. 92, Series E, 1970, pp. 1031-1036. [59] Chow, T. S., "On the Propagation of Flexural Waves in an Orthotropic Laminates Plate and Its Response to an Impulsive Load," J. Composite Materials, Vol. 5, 1971, pp. 306-319. [60] Chou, P. C., and Rodini, B., Jr., "Laminated Composites under Impact Loading," Proc. Int. Conf. Composite Materials, Vol. 2, The Metallurgical Soc. of AIME, 1975, pp. 1106-1121. [61] Sun, C. T., and Lai, R. Y. S., "Exact and Approximate Analyses of Transient Wave Propagation in an Anisotropic Plate," AIAA J., Vol. 12, No. 10, 1974, pp. 1415-1417. [62] Moon, F. C., "Wave Surfaces Due to Impact on Anisotropic Plates," J. Composite Materials, Vol. 6, 1972, pp. 62-79. [63] Moon, F. C., "One-Dimensional Transient Waves in Anisotropic Plates," J. Appl. Mech., Vol. 40, Trans. ASME, Vol. 95, Series E, 1973, pp. 485-490. [64] Moon, F. C., "Theoretical Analysis of Impact in Composite Plates," NASA CR-121110, 1973. [65] Moon, F. C., "Stress Wave Calculations in Composite Plates Using the Fast Fourier Transform," Computers and Structures, Vol. 3, 1973, pp. 1195-1204. [66] Kim,B. S., and Moon, F. C. , "Impact on Multilayered Composite Plates," NASA CR-135247, April, 1977. [67] Kubo, J. T., and Nelson, R. B., "Analysis of Impact Stresses in Composite Plates," Foreign Object Impact Damage to Composites , ASTM STP 568, 1975, pp. 228-244. [68] Daniel, I. M. , and Liber, T., "Wave Propagation in Fiber Composite Laminates," NASA CR-135086, July, 1976. [69] Willis, J. R. , "Hertzian Contact of Anisotropic Bodies," J. Mech. and Phys. of Solids, Vol. 14, 1966, pp. 163-176. [70] Chen, W. T., "Stresses in Some Anisotropic Materials Due to Indentation and Sliding," Int. J. Solids and Structures, Vol. 5, 1969, pp. 191-214. [71] Greszczuk, L. B., "Response of Isotropic and Composite Materials to Particle Impact," Foreign Object Impact Damage to Composites , ASTM STP 568, 1975, pp. 183-211.

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180 [72] Greszczuk, L. B. , and Chao, H., "Impact Damage in GraphiteFiber-Reinforced Composites," Composite Materials: Testing and Design (4th Conf.) , ASTM STP 617, 1977, pp. 389-408. [73] Sun, C. T. and Chattopadhyay , S., "Dynamic Response of Anisotropic Laminates Plates Under Initial Stress to Impact of a Mass," J. Appl. Mech. , Vol. 42, Trans. ASME, Vol. 97, Series E, 1975, pp. 693-698. [74] Sun, C. T., "An Analytical Method of Evaluation of Impact Damage Energy of Laminated Composites," Composite Materials; Testing and Design (4th Conf.) , ASTM STP 617, 1977, pp. 427-440. [75] Sierakowski, R. L., Nevill, G. E., Jr., Ross, C. A., and Jones, E. R., "Studies on Ballistic Impact of Composite Materials," AFATL-TR-69-99 , Air Force Armament Laboratory, Eglin AFB, Fla., 1969. [76] Bascom, W. D. , Jones, R. L. , and Timmons, C. 0., "Mixed-Mode Fracture of Structural Adhesive," Adhesion Science and Technology , Vol. 9B, Leer, L. H. , ed. , Plenum Press, New York, 1975, p. 501. [77] Bascom, E. D., Timmons, C. 0., and Jones, R. L. , "Apparent Interfacial Failure in Mixed-Mode Adhesive Fracture," J. Materials Science, Vol. 10, 1975, pp. 1037-1048. [78] Bradley, W. B., and Kobayashi, A. S., "An Investigation of Propagating Cracks by Dynamic Photoelasticity," Experimental Mechanics, Vol. 7, 1970, pp. 106-113. [79] Broutman, L. J., and Kobayashi, T. , "Dynamic Crack Propagation Studies in Polymers," Dynamic Crack Propagation , Sih, G. C. , ed., Noordhoff, Leyden, 1973, pp. 215-225. [80] Paxson, T. L., and Lucas, R. A., "An Experimental Investigation of the Velocity Characteristics of a Fixed Boundary Fracture Model," ibid., pp. 415-426. [81] Doll, W. , "Application of an Energy Balance and an Energy Method to Dynamic Crack Propagation," Int. J. Fracture, Vol. 12, 1976, pp. 595-605. [82] Cottrell, B., "On the Nature of Moving Cracks," J. Appl. Mech., Vol. 31, Trans. ASME, Vol. 86, Series E, 1964, pp. 12-16. [83] Sih, G. C., "Dynamic Aspects of Crack Propagation," Inelastic Behavior of Solids , Kanninen, M. et al. eds., McGraw-Hill, New York, 1970, pp. 607-639. [84] Cottrell, B., "Velocity Effects in Fracture Propagation," Appl. Matls. Res., Vol. 4, 1965, pp. 227-232. [85] Anderson, G. P., DeVries, K. L. , and Williams, M. L. , "Mixed Mode Stress Field Effects in Adhesive Fracture," Int. J. Fracture, Vol. 10, 1974, pp. 565-583.

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181 [86] Anderson, G. P., DeVries, K. L., and Williams, M. L., "The Influence of Loading Direction upon the Character of Adhesive Debonding," J. Colloid and Interface Sci., Vol. 47, 1974, pp. 600-609. [87] Yeung, P., and Broutman, L. J., "The Effect of Glass-Resin Interface Strength on the Impact Strength of Fiber Reinforced Plastics," Polymer Engr. and Sci., Vol. 18, 1978, pp. 62-72. [88] Gledhill, R. A., and Kinloch, A. J. , "Crack Growth in Epoxy Resin Adhesives," J. Materials Science, Vol. 10, 1975, pp. 1261-1263. [89] McQuillen, E. J., Gause, L. W. , and Llorens, R. E., "Low Velocity Transverse Normal Impact of Graphite Epoxy Composite Laminates," J. Composite Materials, Vol. 10, 1976, pp. 79-91. [90] Broutman, L. J., "Fiber-Reinforced Plastics," Modern Composite Materials , Broutman, L. J., and Krock, H. , eds., Addison-Wesley, New York, 1967, Chapter 13, pp. 337-411. [91] Hahn, H. T. , and Tsai, S. W. , "On the Behavior of Composite Laminates After Initial Failures," J. Composite Materials, Vol. 8, 1974, pp. 288-305. [92] Bax, J., "Deformation Behavior and Failure of Glassf ibre-Reinf orced Resin Material," Plast. Polymers, Vol. 38, 1970, pp. 27-30. [93] Jones, M. L. C., and Hull, D. , "Microscopy of Failure Mechanisms in Filament-Wound Pipe," J. Materials Science, Vol. 14, 1979, pp. 165-174. [94] Reifsnider, K. L., Kenneke, E. G. , and Stinchcomb, W. W. , "Delamination in Quasi-Isotropic Graphite-Epoxy Laminates , "Composite Materials; Testing and Design (4th Conf.) , ASTM STP 617, 1977, pp. 93-115. [95] Reifsnider, K. L., and Talug, A., "Characteristic Damage States in Composite Laminates," Research Workshop on Mechanics of Composite Materials, Duke Univ. , N. C., October 17-18, 1978, pp. 130-161. [96] Kies, J. A., "Maximum Strains in the Resin of Fiberglass Composites," U. S. Naval Research Laboratory Report No. 5752, 1962. [97] Schultz, J. C., "Maximum Stresses and Strains in the Resin of a Filament-Wound Structure," 18th Annual Conf., Soc. Plast. Ind., Reinforced Plastics Division, Sec. 7-D, 1963. [98] Herrmann, L. R. , and Pister, K. S., "Composite Properties of Filament-Resin System," ASTM Paper 62-WA-239, 1963. [99] Puck, A., and Schneider, W. , "On Failure Mechanisms and Failure Criteria of Filament-Wound Glass-Fibre/Resin Composites," Plast. Polymers, Vol. 37, 1969, pp. 33-44.

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182 [100] Garrett, K. W. , and Bailey, J. E. , "Multiple Transverse Fracture in 90° Cross-Ply Laminates of a Glass Fibre-Reinforced Polyester," J. Materials Science, Vol. 12, 1977, pp. 157-168. [101] Stevens, G. T., and Lupton, A. W. , "Some Factors Controlling Transverse Cracking in Cross-Plied Composites," ibid., Vol. 12, 1977, pp. 1706-1708. [102] Stevens, G. T., and Lupton, A. W. , "Transverse Cracking in Cross-Plied Composites," ibid., Vol. 11, 1976, pp. 568-570. [103] Garrett, K. W. , and Bailey, J. E., "The Effect of Resin Failure Strain on the Tensile Properties of Glass FibreReinforced Cross-Ply Laminates," ibid. , Vol. 12, 1977, pp. 2189-2194. [104] Parvizi, A., Garrett, K. W. , and Bailey, J. E., "Constrained Cracking in Glass Fibre-Reinforced Epoxy Cross-Ply Laminates," ibid., Vol. 13, 1978, pp. 195-201. [105] Fung, Y. C., Foundations of Solid Mechanics , Prentice-Hall, Inc., Englewood Cliffs, N. J. , 1965, pp. 463-470. [106] Throckmorton, P. E., Hickman, H. M. , and Browne, M. F., "Origin of Stress Failure in Glass Reinforced Plastics," Modern Plastics, Vol. 41, No. 3, 1963, pp. 140, 142, 145, 148, 150. [107] Broutman, L. J., "Failure Mechanisms for Filament Reinforced Plastics," Modern Plastics, Vol. 42, No. 8, 1965, pp. 143-5, 148, 150, 214, 216. [108] Paul, J. T., Jr., and Thomson, J. B., "The Importance of Voids in the Filament-Wound Structure," 20th Annual Conf., Soc. Plast. Ind., Reinforced Plastics Division, Sec. 12-C, 1965. [109] Diggwa, A. D. S., and Norman, R. H. , "Mechanism of Creep in GRP," Plast. Polymers, Vol. 40, 1972, pp. 263-276. [110] Muldary, P. F., "Dynamics of Elastic Plates," M.S. Thesis, University of Minnesota, 1975. [111] Erdogan, F., "Crack-Propagation Theories," Fracture-An Advanced Treatise , Liebowitz, H. , ed. , Vol. 2, Academic Press, New York, 1968, pp. 497-590. [112] "Development of a Multichannel Data-Recording System" unpublished. Department of Engineering Sciences, Univ. of Florida. [113] "Moire Fringe Observation of Back Surface Deflections of Impacted Laminates," unpublished experimental results at Department of Engineering Sciences, Univ. of Florida. [114] Tauchert, T. R. , and Guzelsu, A. N., "An Experimental Study of Dispersion of Stress Waves in a Fiber-Reinforced Composite," J. Appl. Mech. , Vol. 39, Trans. ASME, Vol, 94, Series E, 1972, pp. 98-102.

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183 [115] 3M Company, Technical Data Sheets for Scotchply Type 1002 and 1003 Prepreg Tapes. [116] Parhizgar, S., "Fracture Mechanics of Unidirectional Composite Materials," Ph.D. Dissertation, Iowa State Univ. 1979. [117] Christensen, R.M. , Mechanics of Composite Materials . John Wiley and Sons, New York, 1979, p. 89. [118] Gibson, R. F., and Plunkett, R. , "Dynamic Mechanical Behavior of Fiber-Reinforced Composites: Measurement and Analysis," J. Composite Materials, Vol. 10, 1976, pp. 325-341.

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BIOGRAPHICAL SKETCH Nobuo Takeda was born on April 5, 1952, in Tokyo, Japan. In March 1971, he was graduated from the Upper Secondary School of the Tokyo University of Education, and in April 1971, he was admitted to Science I course. College of General Education, the University of Tokyo, In March 1975, he received the degree of Bachelor of Engineering with a major in aeronautics from the University of Tokyo. In April 1975, he enrolled in the Graduate School of the University of Tokyo. He received the degree of Master of Engineering in March 1977, with a thesis titled "Adhesive Fracture Mechanics." He continued his work toward the degree of Doctor of Engineering until August 1978, when he was nominated by the Japan Society for the Promotion of Science as a 1978-1980 all expense award grantee for graduate study in the United States. He enrolled in the Graduate School of the University of Florida for two years on leave of absence from the University of Tokyo. After he received the degree of Doctor of Philosophy in Florida in August 1980, he returned home to pursue the degree of Doctor of Engineering in Tokyo. 184

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Robert L. Sierakowski, Chairman Professor of Engineering Sciences I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Lawrence E. Malvern, Co-Chairman Professor of Engineering Sciences I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Ulrich H. Kurzweg Professor of Engineering Sciences I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Ca 1 7 Chang-Tsajri ISun Prof essorVjjf Engineering Sciences

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Ellsworth D. Whitney Professor of Materials Engineering This dissertation was submitted to the Graduate Faculty of the College of Engineering and to the Graduate Council, and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. August, 1980 Dean, College of Engineering Dean, Graduate School