Title: Process induced residual stresses and dimensional distortions in advanced laminated composites
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Title: Process induced residual stresses and dimensional distortions in advanced laminated composites
Physical Description: Book
Language: English
Creator: Niu, Xiaokai, 1967-
Publisher: State University System of Florida
Place of Publication: <Florida>
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Publication Date: 1999
Copyright Date: 1999
 Subjects
Subject: Aerospace Engineering, Mechanics, and Engineering Science thesis, Ph. D   ( lcsh )
Dissertations, Academic -- Aerospace Engineering, Mechanics, and Engineering Science -- UF   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )
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Summary: ABSTRACT: Process induced residual stresses can degrade the performance of composite structures by consuming a significant portion of the strength in certain plies. Cracking due to overload of these plies can then lead to degradation by environmental effects. A technique called cure referencing method (CRM) has been developed for determining the residual stresses in flat laminated composites. In this technique a diffraction grating used for moiré interferometry is transferred onto a composite laminate from a master autoclave tool during the curing process. This transfer takes place at the cure temperature where the matrix solidifies from the liquid state. After cure and upon cooling, the deformation of the composite is recorded with moiré interferometry using the tool grating as the reference. The deformation of the composite is then a function of the thermal contraction due to the temperature difference from the cure temperature to room temperature and the deformation caused by chemical shrinkage. These measurements are first conducted on a unidirectional lamina. Using a specially designed oven, the thermal contraction component of the deformation is separated from the overall deformation. For flat multidirectional symmetrical laminates, the residual stresses in each layer and the in-plane dimensional distortions of the laminate are then calculated from the unidirectional information, constitutive equations, equilibrium equations, and compatibility conditions. Several assumptions, which are similar to those used in laminate theory, are also adopted.
Summary: ABSTRACT (cont.): An independent method called shadow moiré is used to validate CRM. The shadow moiré method is used to measure the curvature of asymmetrical laminates while the lamination theory is used to calculate the curvature from lamina strain information measured with CRM. Good agreement validates the CRM. In addition, process induced strains on multi-directional composites were measured with the CRM. The validation of CRM and the methodology of predicting the residual stresses and dimensional distortions were achieved by comparing the measured residual strains with those determined through prediction using only the unidirectional material. The unique long term testing ability of the CRM is also demonstrated in this work. Initial investigation is conducted on the dimensional distortion of unidirectional curved composites. The out-of-plane chemical shrinkage is determined to be one order of magnitude higher than that of the in-plane in the transverse fiber direction that was measured using CRM.
Summary: KEYWORDS: composite, residual stress, dimensional distortion, autoclave process, moiré interferometry, cure referencing method
Thesis: Thesis (Ph. D.)--University of Florida, 1999.
Bibliography: Includes bibliographical references (p. 144-148).
System Details: System requirements: World Wide Web browser and PDF reader.
System Details: Mode of access: World Wide Web.
Statement of Responsibility: by Xiaokai Niu.
General Note: Title from first page of PDF file.
General Note: Document formatted into pages; contains xi, 149 p.; also contains graphics.
General Note: Vita.
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Bibliographic ID: UF00100729
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: oclc - 45265446
alephbibnum - 002484130
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PROCESS INDUCED RESIDUAL STRESSES AND DIMENSIONAL DISTORTIONS
IN ADVANCED LAMINATED COMPOSITES














By

XIAOKAI NIU


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

UNIVERSITY OF FLORIDA


1999



























Dedicated to

my parents
Fuwen Niu
and
Linfen Yang
for their encouragement and support in every aspect.















ACKNOWLEDGMENTS

I would like to thank my advisor Dr. Peter Ifju for his support, advice and

friendship. I am grateful to Dr. Bhavani Sankar, Dr. David Jenkins, Dr. David

Bloomquist, and Dr. Loc Vu-quoc for their help in my research and classes. I would like

to thank Mr. Ron Brown for his friendship and his help in the machine shop. I want to

give my gratitude to Shao-Chun Liu, Brian Kilday, John Avery, Scott Ettinger, Ali

Abdel-hadi, Leishan Chen, Brian Wallace, and Jongyoon OK for their help and

friendship. They together made the graduate study at UF an enjoyable experience.

Finally, I would like to especially thank my wife Qun Wang for her patience and love,

my sister Xiaofeng Niu, my brother in law Xiaoming Xing and my nephew Chenxi Xing

for their encouragement and support.















TABLE OF CONTENTS

page

A C K N O W L E D G M E N T S ..................................................................................................iii

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

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

A B S T R A C T ........................................................................................................ .......... x

CHAPTERS

1 IN T R O D U C T IO N .......................................................... ....... ......... .............. 1

B background ........................................................................ ............... ...... . ................. 1
Process Induced Residual Stresses in Advanced Composite Laminates.................. 2
Process Induced Dimensional Distortion in Advanced Composite
C om ponents .............................................................................. ........................ 4
O objective of R research ..... .. .................................. ........................... .............. 5

2 LITER A TU RE R EV IEW .. .................................................................... .............. 6

Process Induced Strain Measurements and Residual Stress Evaluation................... 6
D destructive M ethods .... ... ....................................... ....................... . . .......... 6
H ole-drilling m ethod ...................................... .. ...................... .............. 6
C cutting m ethod ............... .................. ........................................... 7
Ply sectioning m ethod ..................................... .. ........... ............ .. .......... 8
F irst ply failure m ethod ..................................... ....................... ............. 9
N on-destructive M ethods...................................... ........................ .............. 10
W arpage ......................................................................................................... 10
Im bedded strain gage ..................................... .. ............... .. .. .............. ..... 11
X -ray diffraction ............................................ ............ . .. ....... .... ......... .. 12
Evaluation of Process Induced Dimension Distortion......................................... 12
Variation Fiber Volume Fraction or Orientation........................................... 13
O ut-of-plane C ontraction Effect...................................................... .............. 14

3 CURE REFERENCING M ETHOD ....................................................... .............. 16

In tro d u ctio n .............................................................................................................. .. 1 6
C om posite M manufacturing .............................................................. .............. 17









Process Induced Contraction (Strain) by Curing Referencing Method.................. 21
M oire Interferom etry ........................................... ................. .. .. .... .. .......... 2 1
High Temperature Diffraction Grating Replication....................................... 22
Autoclave Processing......................... .. ..................... .... ............... ..... 30
High Precision M oire Interferometer Tuning .................................. .............. 31
Process Induced Strain M easurem ent.............................................. .............. 34
Process Induced Strains on [016] Unidirectional Lamina of AS4/3501-6............... 39

4 RESIDUAL STRESSES IN LAMINATED COMPOSITES .............................. 48

M material Property M easurem ent on A S4/3501-6....................................................... 48
T ensile Properties ............... .................. ........................................... 48
Shear Properties ............................................................ .. .................... ......... .. 50
Prediction of the Process Induced Residual Stresses........................................... 53
Process Induced Residual Stresses in [02/90212s Balanced Cross Ply
L am inate .............. ......... .... ...................... ...... ....... ...... ........... . . 54
Process Induced Residual Stresses in the [03/9012s Unbalanced Cross Ply
Lam inate .................................. ................................ ..... .. .... .............. 61
Process Induced Residual Stresses in [02/45212s Angle Ply Laminate.............. 65

5 VALIDATION OF CURE REFERENCING METHOD..................................... 71

Validation of CRM Using Unsymmetric Laminated Composites............................. 73
Predicting Curvature w ith CLT ............................................... ...................... 73
Measuring Curvature Using the Shadow Moire Method............................... 77
R e su lts................... ... .. ........................ ........................................... . .. 7 9
Validation of the CRM Using Symmetric Laminates............................................. 80
Prediction of Process Induced In-Plane Dimensional Distortions.................... 80
[02/90212s lam inate of A S4/3501-6 ................................................. 81
[03/90]2s lam inate of A S4/3501-6.............................................. .............. 82
[02/45212s lam inate of A S4/3501-6 ............................................ .............. 83
Measurement of Process Induced In-Plane Dimensional Distortions .............. 83
Specimen manufacture ..................... ........................ 83
Process induced strain measurement on the laminates ............................. 84
R e su lts .............................................................................................................. . .. 9 6
Chem ical Shrinkage Validation...... ............ ............ .................... 101
Experim mental A approach ................................... ........................ .............. 101
R e su lts................ ...................................................................................... . .. 1 0 4
Conclusion and Recommendation ...... ......... ........ .................... 105

6 INVESTIGATION ON LONG TERM EFFECTS ............................................... 108

In tro d u ctio n .............................................................................................................. 1 0 8
Therm al H history E effect ....................... ...................... .... .............. 109
Specimens and Deformation Measurement...... ...................................... 109
R results and D discussion .................................... ........................ .............. 109
M o istu re E effect ........................................................................................................ 1 15









Sw selling M easurem ent .................................... ........................ .............. 115
R results and D discussion .................................... ........................ .............. 117
C onclu sion ............................................................................... ....................... 119

7 PROCESS INDUCED DIMENSIONAL DISTORTION ON CURVED
LAMINATED COMPOSITES...... ........................... .................... 121

Introduction .............................................................................................................. 12 1
Existing Model and Distortion Prediction..................................... 122
Distortion Measurement on Curved Composites...... .................. ................. 125
Sem i-Cylindrical Com ponent ...... ......... .. .......... .................... 125
Specim en m anufacture...... ............. .............. .................... 125
Process induced radius change ....... ... ...................... 127
R ight A ngle B racket .. ............................................................... ......... ..... 130
Specimen manufacture..................... .............. 130
Process induced enclosed angle change...... .... .................................. 130
D discussion ...... ........ .... ................................. ... .. .. ... .... .................. 132
Full Field Investigation of Thermal Distortion on the Angle Composite
B ra c k et ............................................................................... ............... .................... 1 3 2
Diffraction Grating Replication for Moire Interferometry ............................ 132
E closed A ngle C hange................................... ...................... .. .......... ..... 134
Through Thickness CTE M easurement...... .... ..................................... 138
Through Thickness Chemical Shrinkage...... .... ................................... 140
C conclusion and D discussion .................................... ........................ .............. 142

LIST OF REFEREN CE S ..... ................................................................. .............. 144

BIOGRAPH ICAL SKETCH ................................................................. .............. 149















LIST OF TABLES


Table page

3.1 Process induced strain on [016] of A S4/3501-6...................................... .............. 41
3.2 C TE of A S4/3501-6 [016] lam inate .................................................. .................... 45
3.3 Process induced strain comparison before and after the heating/cooling (H/C)
cycles and bone-dried. ............................................ ......... .. .. ...... ........ ........... 47
4.1 Material properties of the AS4/3501-6 unidirectional lamina. ................................. 50
4.2 Predicted residual stresses in the AS4/3501-6 [02/90212s laminate at 20C ............ 59
4.3 Strength of AS4/3501-6 unidirectional lamina ...................................... .............. 59
4.4 Predicted residual stresses in the AS4/3501-6 [03/9012S laminate at 20C ............. 64
4.5 Predicted residual stresses in the AS4/3501-6 [02/45212s laminate at 20C ............ 69
5.1 Curvature of the AS4/3501-6 [04/90412 laminate ................................... .............. 80
5.2 Process induced strains of the AS4/3501-6 [02/90212S laminated composites ......... 94
5.3 Process induced strains of the AS4/3501-6 [03/9012S laminated composite ............ 95
5.4 Process induced strains of the AS4/3501-6 [02/45212S laminated composite ........... 95
5.5 Chemical shrinkage of the AS4/3501-6 unidirectional lamina............................. 105
6.1 Predicted residual stresses in the AS4/3501-6 laminates after experiencing
thermal loading ........... . ...... . . ........ ...................... 110
6.2 Predicted strains in AS4/3501-6 laminates after experiencing thermal loading
based on No.2 [016] unidirectional specimen measurements.................................. 111
6.3 Total strains in AS4/3501-6 laminates after experiencing thermal loading.......... 112
6.4 Moisture effects on the AS4/3501-6 [016] unidirectional composites................... 114
6.5 Predicted residual stresses in the AS4/3501-6 laminates after being exposed
to m moisture. ................................................................................................ .. ........... 116
6.6 Moisture effects on the AS4/3501-6 [02/90212s laminated composites ................. 118
6.7 Moisture effects on the AS4/3501-6 [03/90]2s laminated composites................... 118
6.8 Moisture effects on the AS4/3501-6 [02/45212s laminated composites ................. 119
7.1 Process induced radius change of semi-cylindrical components of the
A S4/3501-6 [016] unidirectional com posite......................................... .............. 129
7.2 Process induced angle change of right angle brackets of the
A S4/3501-6 [016] unidirectional com posite......................................... .............. 131
7.3 Thermal induced angle change of right angle bracket of the AS4/3501-6
[016] unidirectional com posite .............................................................................. 136
7.4 Through thickness CTE of the angular brackets of the AS4/3501-6 [016] lamina... 139
7.5 Comparison of chemical shrinkage in transverse fiber direction of the
AS4/3501-6 [016] composite specimens with different shapes............................. 141















LIST OF FIGURES


Figure page

3.1 Autoclave oven .................................... .................... ... ..... ... .............. 18
3.2 Vacuum bagging of composite autoclave processing. ....................................... 19
3.3 Curing profile of Thermoset AS4/3501-6. ..................................................... 19
3.4 Schematic of four-beam moire interferometry..................................... .............. 22
3.5 Schematic of the diffraction grating duplication technique. .............................. 24
3.6 High temperature diffraction grating making device. ........................................ 28
3.7 Teflon device for making thin diffraction grating film ...................................... 29
3.8 Autoclave vacuum bag lay-up for CRM .............................................. .............. 30
3.9 Four-beam interferom etry setup ........................................................... .............. 32
3.10 Imperfection of the collimated laser beams. ................. .............. 33
3.11 Imperfection of the perpendicularity of the cross grating lines. ........................... 35
3.12 Therm al C ham ber .................. ..................................... ...... ...... ...... ......... ..... 37
3.13 Room temperature fringe patterns of AS4/3501-6 [016] laminate......................... 40
3.14 Fringe patterns of AS4/3501-6 [016] laminate at various temperatures. ................ 43
3.15 Strain/temperature plot of [016] laminate of AS4/3501-6................................... 44
4.1 Stress/strain plot of AS4/3501-6 tensile specimen............................... .............. 49
4.2 Shear loading fixture. .................................................. .. .. ... ........ ............. 51
4.3 Shear stress/shear strain plot of the AS4/3501-6 0 shear specimen .................... 52
4.4 Lamina under residual stresses in the [02/90212s laminated composite ................. 55
4.5 The compatibility relations of the [02/90212s laminate ....................................... 56
4.6 Residual stress/temperature plot of the AS4/3501-6 [02/90212s laminate.............. 61
4.7 The compatibility relations of the [03/90]2s laminate........................... .............. 62
4.8 Residual stress/temperature plot of the AS4/3501-6 [03/90]2s laminate............... 65
4.9 The compatibility relations of the AS4/3501-6 [02/45212s laminate...................... 67
4.10 Residual stress/temperature plot of the AS4/3501-6 [02/45212s laminate.............. 70
5.1 Unsymmetric laminated composite panel before and after cure............................. 72
5.2 The coordinate system of the [02/902]s laminated composite ............................ 72
5.3 Schematic of the shadow moire experiment ...................................... ................ 76
5.4 Shadow moire fringe pattern of the AS4/3501-6 [04/90412 (3"x8") laminate. ......... 77
5.5 Moire fringe patterns of the AS4/3501-6 [02/90212s laminate at room
tem p eratu re .......................................................................... .......... .... ............... . 8 5
5.6 Moire fringe patterns of the AS4/3501-6 [03/90]2s and [02/45212s laminates at
room tem perature. ........................................ ........ ...... ...... .......... ..... ......... .. 86
5.7 Moire fringe patterns of the AS4/3501-6 [02/90212s laminate at various
tem perature..................... .............. .......... .............. ... . .. .............. 88
5.8 Moire fringe patterns of AS4/3501-6 [03/90]2s laminate at various temperature..... 89









5.9 Moire fringe patterns of the AS4/3501-6 [02/45212s laminate at various
tem p eratu re................................ ............... .............. ..... ... .... ................... . 90
5.10 Process induced strain/temperature plot of the AS4/3501-6 [02/90212S laminates. .. 91
5.11 Process induced strain/temperature plot of the AS4/3501-6 [03/9012S laminates..... 92
5.12 Process induced strain/temperature plot of the AS4/3501-6 [02/45212S laminates... 93
5.13 Predicted and measured process induced strains of the AS4/3501-6
[02/90212S lam inmates at various tem peratures ............................... ...................... 97
5.14 Predicted and measured process induced strains of the AS4/3501-6 [03/9012S
lam inmates at various tem peratures. ........................................................ .............. 98
5.15 Predicted and measured process induced strains of the AS4/3501-6
[02/45212S lam inmates at various tem peratures ....................................... .............. 99
5.16 Shadow moire fringe pattern for determining chemical shrinkage ..................... 103
5.17 Out-of-plane deflection/position plot ....... ....... .................... 103
6.1 Moisture effects on the [016] unidirectional lamina. .................... ...... ........... 115
7.1 Curved composite laminate before and after curing process. ............................. 122
7.2 Vacuum bag lay-ups for manufacturing the semi-cylindrical composite
co m p o n en ts................................................................ ............................................ 12 6
7.3 Schematic of the equipment setup for measuring the out-of-plane deflection
of semi-cylindrical composite components....... ... .................................... 128
7.4 M oire fringe patterns of the right angle bracket................................ ............... 135
7.5 Geometric relations of deformed and undeformed thickness of angular bracket. 137
















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

PROCESS INDUCED RESIDUAL STRESSES AND DIMENSIONAL DISTORTIONS
IN ADVANCED LAMINATED COMPOSITES

By

Xiaokai Niu

August, 1999


Chairman: Dr. Peter G. Ifju
Major Department: Aerospace Engineering, Mechanics, and Engineering Science

Process induced residual stresses can degrade the performance of composite

structures by consuming a significant portion of the strength in certain plies. Cracking

due to overload of these plies can then lead to degradation by environmental effects. A

technique called cure referencing method (CRM) has been developed for determining the

residual stresses in flat laminated composites. In this technique a diffraction grating used

for moire interferometry is transferred onto a composite laminate from a master autoclave

tool during the curing process. This transfer takes place at the cure temperature where

the matrix solidifies from the liquid state. After cure and upon cooling, the deformation

of the composite is recorded with moire interferometry using the tool grating as the

reference. The deformation of the composite is then a function of the thermal contraction

due to the temperature difference from the cure temperature to room temperature and the

deformation caused by chemical shrinkage. These measurements are first conducted on a









unidirectional lamina. Using a specially designed oven, the thermal contraction

component of the deformation is separated from the overall deformation. For flat

multidirectional symmetrical laminates, the residual stresses in each layer and the in-

plane dimensional distortions of the laminate are then calculated from the unidirectional

information, constitutive equations, equilibrium equations, and compatibility conditions.

Several assumptions, which are similar to those used in laminate theory, are also adopted.

An independent method called shadow moire is used to validate CRM. The shadow

moire method is used to measure the curvature of asymmetrical laminates while the

lamination theory is used to calculate the curvature from lamina strain information

measured with CRM. Good agreement validates the CRM. In addition, process induced

strains on multi-directional composites were measured with the CRM. The validation of

CRM and the methodology of predicting the residual stresses and dimensional distortions

were achieved by comparing the measured residual strains with those determined through

prediction using only the unidirectional material. The unique long term testing ability of

the CRM is also demonstrated in this work. Initial investigation is conducted on the

dimensional distortion of unidirectional curved composites. The out-of-plane chemical

shrinkage is determined to be one order of magnitude higher than that of the in-plane in

the transverse fiber direction that was measured using CRM.
















CHAPTER 1
INTRODUCTION


Background


Advanced composite materials (ACMs) were originally developed to meet the

extreme mechanical, electrical and environmental requirements of aircraft, aerospace and

military applications. Distinguished from conventional metallic materials like aluminum

and steel, ACMs provide high specific strength, high specific stiffness, better fatigue

characteristics and less thermal expansion. Another superior characteristic of ACMs is

the tailorability of their material properties. The desired material properties can be

achieved by selecting different fiber/matrix systems and aligning different fiber

orientations. This unique ability expands the possibilities of engineering design. Often

ACMs are the only candidate materials to implement new design concepts.

ACMs have been used extensively in military aircraft like the B-2, F-22, V-22

and stealth equipment. Commercial aircraft are also recently using an increasing amount

of ACMs. Fifteen percent of the Airbus is ACM and 13% of the Boeing 777 will be

ACM. Using ACMs on aircraft can reduce cost as well. Integrated ACM structures use

fewer parts, joints, and fasteners. In helicopter manufacture, the total number of parts has

been reduced by more than a factor of 5, resulting in a 90% reduction in the number of

fasteners. Other military applications include ballistic vests, ballistic helmets,

lightweight and portable composite bridges, and so on.









Another important recent application of ACMs is sports equipment. The high

strength, high stiffness-to-weight ratio, and the tailorability of ACMs (especially carbon

fiber reinforced composites) have revolutionized sports equipment such as tennis

racquets, golf clubs, and archery equipment. With the introduction of ACMs to the tennis

racquet manufacturing industry, designers can now freely design lightweight, strong, and

durable tennis racquets, varying the stiffness to meet various playing styles. This could

not be done with conventional laminated wood or metallic materials. The number of

ACM components produced in the United States has increased continuously in this

decade. The estimated value will reach 20 billion dollars in the year 2000. That is 10

times the total in 1989.

Compared with conventional metallic materials, ACMs are not only newer but

also more difficult to characterize. Because ACMs consist of more than one constituent

(fiber and matrix material), they typically behave orthotropically. The large databases

and theories that have been accumulated in the past to study traditional metals cannot be

directly adapted to ACMs. A large amount of research is still required. The objective of

this work is to add to the knowledge base of ACMs by characterizing the process induced

residual stress and deformation of ACM parts.

Process Induced Residual Stresses in Advanced Composite Laminates


Fiber reinforced polymeric composites are the most popular form of ACM. This

type of ACM is usually divided into two categories: thermosetting and thermoplastic,

based upon the thermal behavior of the matrix material. Processing of polymeric ACMs

usually involves heating the resin, wetting fibers, and curing at high temperature. The


1 Source: Office of Technology Assessment, U.S. Congress









development of "prepreg" material was a major breakthrough in composite

manufacturing technology. Prepreg is a form of tape that has continuous fibers pre-

coated, or pre-impregnated, with polymer resin. The tape is preprocessed and the

polymer resin is partially cured (B-stage). To fabricate parts using prepreg, it is no

longer necessary to worry about mixing the resin to the right ratio. Fabrication of

structures with prepreg tape only requires lay-up of the tapes at the required fiber

orientations and stacking sequences on a mold, and then curing the lay-up under elevated

temperature and pressure.

The study of residual stresses is divided into two scales, micro-mechanical scale

and macro-mechanical scale (or fiber scale or ply scale). A flat unidirectional composite

laminate (all prepreg layers have the same fiber orientation) made from unidirectional

prepreg tape gradually undergoes polymerization at the curing temperature. As this

happens, the polymer resin becomes bonded to the fibers. The matrix material undergoes

a volumetric change (known as chemical shrinkage) during the polymerization process

while the fiber remains volumetrically stable at the curing temperature. This mismatch

causes residual stresses between the resin and fibers. Since the fiber and polymeric resin

have different CTEs (coefficient of thermal expansion), the resin tends to shrink more

than the fiber when the laminate is cooled to room temperature. This causes additional

residual stresses to be added between the cured polymeric resin and the fibers. The

residual stress between the fiber and polymeric resin is referred to in the micromechanics

study of fiber/resin interface or interphase.

For non-unidirectional laminates, there is an additional source of residual stresses.

For each lamina (individual layer of a laminate), the overall deformation caused by









chemical shrinkage along the fiber direction is smaller than that along the transverse fiber

direction. The same is true for the deformation caused by cooling the laminate from the

curing temperature to room temperature. If there were no restrictions, each lamina would

have the same final contraction after the curing process. The laminae, however, are

oriented in different directions in the laminate. Free contraction is then restricted.

Constraint between the laminae causes residual stresses on the ply scale. This ply scale

residual stress will be the major focus in this study.

In the composite laminate, residual stresses will prestress the lamina and will

affect the predicted overall strength. Residual stresses can also cause microcracks in the

matrix material. Microcracks allow the fibers to be exposed to environmental

degradation without any protection. Chemical attack may occur at the fiber or the

fiber/matrix interface thus degrading the composite.

Process Induced Dimensional Distortion in Advanced Composite Components


Observations of composite parts have shown that the final parts often are not the

same as the mold shape after the prepreg lay-up has fully cured. In other words, the final

composite structure may be different from the one that was originally designed. There is

a well-known phenomenon called "spring-in", spring-forward" or "spring-back" in

composite manufacturing. This occurs when a composite shell component is

manufactured in an angular mold. After cooling from the curing temperature to room

temperature, it is released from the mold. The resulting angular shaped parts have an

angle that is smaller than the mold angle, even for unidirectional panels. This angle

change is also a function of the service temperature. Orthotropy of the lamina is the main

factor leading to dimensional distortion. Because of fiber reinforcement, the material









properties of a unidirectional lamina are dominated by the fiber properties along the fiber

direction and dominated by the matrix material along the transverse fiber direction. Fiber

and matrix material properties usually differ greatly.

Objective of Research


The process induced residual stresses and dimensional distortions in composites

have the same origin. Both are the results of chemical shrinkage and the volumetric

change caused by temperature change. Characterization of these effects is very important

for achieving good composite structural design and fabrication of high quality composite

components. The work shown here will focus on developing the experimental

methodology for characterizing the effects of chemical shrinkage and temperature

dependent volumetric changes that occur during composite processing. Since the

unidirectional lamina is the basic constituent of any multidirectional laminate, the

residual stresses in laminated composites with any stacking sequence will be predicted

analytically using experimental measurements from the unidirectional lamina. The

experimental methodology will also be validated using an independent method.

Experimental investigation will be conducted on curved laminated composites. Process

induced chemical shrinkage and thermal deformation measured using a newly developed

method will be used as the basis for studying the process induced distortion in curved

composites. Moire interferometry, a full field displacement technique, will also be used

to gather data on the "Spring in" phenomenon.
















CHAPTER 2
LITERATURE REVIEW


Process Induced Strain Measurements and Residual Stress Evaluation


There have been considerable efforts put forth to evaluate residual stresses in

composites. There are a number of existing methods for characterizing residual stresses.

Each method has its unique advantages when used in certain situations. Together, they

supply a useful means of understanding residual stress. However, all of them suffer from

one or more disadvantages, and each has its own limitations. In general, these methods

can be divided into two categories, destructive and non-destructive.

Destructive Methods

The methods that fall into this category usually involve removing some material

from the test coupons. In most cases, the specimen is permanently damaged and cannot

be re-used.

Hole-drilling method

The hole drilling method is the most widely accepted and practical technique for

measuring residual stress in isotropic materials like metal structures. By introducing a

hole into a residually stressed body, all of the stresses perpendicular to the hole surface

are relaxed and become zero. The relaxed stresses change the strain fields around the

hole. The strain fields in the area surrounding the hole can be correlated to the stresses

released. This principle was first proposed by Mathar [35]. The most widely used hole









drilling method involves drilling a tiny blind hole and using a strain gage rosette to

measure the relieved strains [36]. The analytical solution of the residual stresses was

obtained based on the solution of through-hole stress relief under certain assumptions.

Considerable effort has been devoted to implementing this technique on

orthotropic materials [3,31,47,51]. The solution for correlating the residual stresses and

relieved strains are much more complicated than that of isotropic materials. When

applied to laminated composites, the problem is very cumbersome. Many assumptions

were made to simplify the derivation of the solution. Complicated numerical or

experimental techniques are also needed to calibrate the coefficients needed in the

solution. It is also difficult to achieve precise measurement of relieved strains around the

hole because of the highly orthotropic properties of the laminated composite. Even high

sensitivity moire interferometry cannot accurately resolve the relieved strain field along

the fiber direction [38].

Cutting method

Cutting methods use the same principle as the hole-drilling method. By notching

the composite, a free edge is introduced. The residual stress is released along the free

edge and a corresponding strain field will result. A full field optical technique called

moire interferometry was incorporated in conjunction with cutting to measure the

released strain field in the area surrounding the notch by Lee [32,33]. He and his

colleagues put a diffraction grating on the trimmed edge of a laminated composite panel.

A deep notch was cut perpendicularly to the grating surface into the laminate. A strain

field change was recorded and the strain data was entered into a computer. With the help

of a commercial FEM code, the released residual stresses were obtained.









In Lee's work, he obtained a full field displacement contour map by using high

sensitivity interferometric technique. He also avoided dealing with approximate

analytical solutions for correlating the released residual strains and released residual

stresses by using FEM. However, there is still doubt about his measurements. He

trimmed an edge of the composite before applying the diffraction grating. As a result,

some of the residual stresses perpendicular to that surface were released and a very

complicated stress field was introduced underneath the surface. The residual stress field

below the trimmed surface is different from the original residual stress field. Doubt was

raised about the measurement because what he measured was the released strain field

resulting from this stress field. In order to eliminate or compensate for these errors,

further investigation needs to be conducted.

Sunderland et al. proposed a technique called successive grooving [53]. A groove

was cut into the specimen incrementally through the composite thickness. Released

strain was recorded with a strain gage placed on the opposite of the grooving surface.

The residual stress was calculated using a numerically derived 2-D model for each cut

layer. This technique does not have the problem described above.

Ply sectioning method

Joh et al. proposed a method to measure the residual stress in thick composite

laminates [24]. By sectioning between layers, the lamina was freed from the adjacent

layer's constraint. The released deformation was recorded with full field moire

interferometry. The residual stresses were then calculated from the measured strains.

Caution was taken to minimize the problems encountered in the cutting method

mentioned above. Since the free edge can induce a complicated stress field before the









sectioning process, a thin strip specimen coupon was cut from the edge of the laminated

composite to achieve a plane stress state. Moire interferometry helped to ensure the

sensitivity and accuracy of the measurement.

Sectioning was conducted by machining away the outside layers of the composite

to generate an unbalanced composite laminate [6,34]. The sectioning disturbed the

equilibrium of the internal residual stresses of the flat composite. As a result, the

unbalanced laminates become warped. The residual stresses were calculated by laminate

theory using the warpage measurements as inputs.

Manson et al. introduced a method called process simulated laminate (PSL) [34].

A thin release film is placed between certain layers inside the laminated composite before

processing. The sectioning was avoided after the manufacturing process by simply

cutting the composite. However, there were several key assumptions used for PSL.

Manson et al. assumed that the release film was perfectly bonded to the adjacent layers of

the composite in order to transfer the stress through the layers. The accuracy of this

assumption still remains in question.

Most of the destructive methods that involve machining typically use some sort of

water or oil based coolant to reduce the stresses due to machining or to avoid the

hazardous dusts. The composite absorbs moisture or oil when they are exposed to these

coolants. The swelling effect will cause errors in the residual strain measurements.

First ply failure method

The maximum stress failure criterion has been used to calculate residual stresses

[15,27]. Hahn and Kim used a cross-ply laminate. They recorded load and strains while

loading the specimen to failure. The stress at which the first ply failure occurred was









calculated using an elastic assumption. The calculated stresses at the failed ply were

compared with the strength of the unidirectional laminate of the same material. The

difference is equal to the residual stress. Effort also was put into considering the visco-

elastic effect on this method [25].

Non-destructive Methods

Non-destructive methods are always preferred to destructive methods. The reason

is obvious. No one wants to destroy the structure when you are conducting tests on it,

especially for in-situ measurements. Additionally, non-destructive methods are good for

long term tests on the same structure.

Warpage

For asymmetric laminated composites, the process-induced stresses are not

balanced internally. The composite warps to reach a new internal residual stress balance.

The curvature of the warped composite can be related to the residual stresses with

analytical solutions. Numerous studies have been performed using this method

[10,12,19,22,23,26,27,34,58]. Classical laminate theory (CLT) is normally used to

calculate the residual stresses from the curvature.

The warpage method is very useful and easy to implement for characterizing the

residual stresses at both room temperature and at elevated temperatures. However,

because the residual stresses cause the warpage on the asymmetric laminated composites

and cause an unexpected shape of the final product, composites with asymmetrical

stacking sequences are not practical. The applications of asymmetric laminates are

mainly in academic research.









Warpage was also used to determine the residual stress due to chemical shrinkage

[10,11]. Daniel made a composite laminate directly on a previously cured laminate with

identical lay-ups and processed the composite in the autoclave. Only the chemical

shrinkage caused warpage after processing because the thermal contraction was canceled

due to the identical CTE of the new laminate and the existing panel. The curvature was

measured and the shrinkage was calculated using classical laminate theory. An

assumption was made that the additional curing of the existing half of the panel does not

alter the material properties. Daniel's method was practical even though chemical

shrinkage and thermal contraction are not conducted on the same specimen.

Imbedded strain gage

There are two types of strain gages that have been used for this purpose:

traditional electrical-resistance strain gages and fiber optic strain gages [5,7,8,9,56].

Daniel was the first researcher to measure residual stress using traditional strain

gages by imbedding the gage directly into the composite laminate between the lamina

layers [7,9,8]. High temperature strain gages were selected for this technique. Because

the carbon fiber itself is conductive, polyimide strips were used to insulate the strain

gages from the carbon fiber. In order to separate the strain gage output due to specimen

deformation (residual strain) and the output due to the change in resistance and gage

factor with temperature, Daniel also instrumented strain gages on dummy specimens

made of a material with a known CTE (coefficient of thermal expansion).

Thermocouples were also placed on both the composite specimen and dummy specimen.

The output of both the strain gages and thermocouples were recorded throughout the

curing cycle. The residual stresses were calculated from the residual strain









measurements. The main drawback of this technique is that a foreign object was

introduced inside the composite. This alters the material properties in that region.

Therefore, the measured thermal strain differs from the actual strain. The use of the

insulation material actually created a void within the composite. Voids change the

material properties around that area, and can also cause delamination of the composite.

Recently, fiber optic strain gages have been used for measuring residual strains.

The fiber optic was imbedded in the laminate just as the fibers in the composite. It has

the potential to be the preferred device used for in-situ and long-term measurements.

However, there is the same concern as with imbedded resistance strain gages. The gages

can locally alter the material properties because the diameter of the fiber optic is about

one order of magnitude larger than the diameter of the fibers used in the composite.

X-ray diffraction

The X-ray diffraction technique was originally used for metals. It has been

recently implemented in residual strain measurement [13,44]. Metallic particles were

first mixed into the composite matrix materials. The size of the particles used is usually

the same order of magnitude of the diameter of the fiber. The measurement was then

conducted on the particles. The measurement results were correlated to the stresses

applied to the particles to calculate the residual stresses. Whenever foreign objects are

inserted, a question about how the foreign objects will affect the material properties arises

(changes the CTE).

Evaluation of Process Induced Dimension Distortion


Residual stresses can cause warpage on asymmetric laminated composites. For

this reason, this type of laminate has almost never been used in practice. Process induced









distortion, however, can happen on symmetric laminates. A typical example is the

phenomenon known as "spring-in" or "spring-forward" or "spring-back" [19,42,64]. In

the past, an iterative method was used to shape the mold to compensate for process

induced distortion [49]. This trial and error tooling process requires a tremendous

amount of effort. Therefore, the cost was very high. In addition, the mold is useless if

the process profile changes or the material composition changes. There are many

parameters that can cause distortion during processing. All of them are induced by

chemical shrinkage or thermal contraction applied to orthortropic materials. These

factors can be divided into two categories: variation of fiber volume fraction or

orientation through thickness, and out-of-plane contraction during processing.

Variation Fiber Volume Fraction or Orientation

Distortion of symmetric laminate parts after processing was considered to be the

result of CTE mismatch of the mold and composite material or part/tool sticking [42].

Since the CTE of the tool is generally lower than that of the composite material, the side

adjacent to the tool will be stretched and cause permanent deformation during cooling.

According to this explanation, a concave shape was expected on a flat composite panel.

Contrary to this explanation, the observation showed that the flat thin unidirectional parts

always experience a convex up curvature away from the flat tool. Another explanation

was that the curing temperature had variations through the laminate thickness. However,

this explanation could not answer why the curvature decreased when the laminate

thickness was increased. Recently, an explanation about the process induced distortion

was proposed by Radford [45]. He noted that the fiber volume gradient is one of the

reasons for this type of distortion. The resin rich side induced more shrinkage than the









fiber rich side. In other words, "fiber volume asymmetry" caused the warpage of flat

unidirectional laminated composites. With a metallographic technique, the fiber volume

fraction was obtained through the thickness of the specimen. It was found that there was

a resin rich layer on the composite surface closest to the autoclave tool and a resin poor

layer on the opposite surface. This was explained by the fact that the top bleed method

removed more resin from the lamina near the bleeder cloth, while the surface tension

between the tooling and the resin yielded a resin-rich zone at the bottom. Yang observed

the same phenomenon in woven graphite/epoxy composites [63]. He developed a

method to predict the curvature of an otherwise flat composite based on the measured

volume fraction gradient. However, the distortion caused by volume fraction gradient

was less when the composite was thicker. Tseng considered another possible cause of

distortion in his numerical simulation model [55]. Fiber orientation through the part

thickness could potentially vary. This is common during the compression molding

process.

Out-of-plane Contraction Effect

During manufacturing of composite parts with complex geometry, larger

distortions than that of flat parts were observed. The distortion was worse, especially

among the parts containing angular portions. Some researchers [16,37,40,41,46,48,52]

surmised that this type of distortion was based in geometry and the main factor was the

difference between the in-plane and out-of-plane contraction. The enclosed angle change

of an anisotropic semi-cylindrical shell was predicted using either elastic analysis [41] or

simple geometrical analysis [46]. Both analyses produced a similar solution. The

analyses predict that the enclosed angle change is independent of shell thickness and






15


radius of the tool. Radford's experiments showed that the thermal effect induced angle

change of a right angle bracket was independent of the specimen thickness. He also

calculated the through thickness CTE using the analytical solution for the angle change

and measured angle change. The CTE was found to be close to the data supplied by the

manufacture. Huang [17,18] used Radford's model with the manufacturer's supplied

CTEs and chemical shrinkage data to predict the distortion of the angular composite

tools. He claimed that the prediction matched the experimental results well.
















CHAPTER 3
CURE REFERENCING METHOD


Introduction


From the literature review, there is no method that can directly reveal residual

stress measurements. Residual stresses are always calculated from the strain

measurements associated with residual stresses. Additionally, the preferred method for

measuring the process-induced strain (stress) would be a non-destructive method. A

method that allows direct measurement on the composite parts would be optimal. It was

shown that there is no existing method allowed for measuring the chemical shrinkage of

composites on the composite parts directly. There are only two papers [10,61] found that

addressed this subject. Daniel's method [10] was practical even though chemical

shrinkage and thermal contraction are not conducted on the same specimen. White's

method [61] was crude compared with Daniel's. It was not precise because the

measurements were not made in the actual manufacturing environment such as inside the

vacuum bag or under the hot press.

A technique called cure referencing was developed here at the University of

Florida. This technique incorporates a full field optical method called moire

interferometry. A diffraction grating is attached to the composite during the curing cycle.

It is nondestructive, and appropriate for long term measurements. Using cure

referencing, the process induced contraction due to chemical shrinkage and thermal









contraction can be separately measured with one specimen. This technique can be

implemented on either flat sample specimens for prediction purpose or on the flat part of

an actual structural part for real-time measurement.

The experiments in this study were conducted on a thermosetting composite

called AS4/3501-6 graphite/epoxy. This material system was chosen because it is one of

the most characterized. In order to explain this technique thoroughly, the commonly used

composite processing method is first described.

Composite Manufacturing


Laminated composites are most commonly processed in an autoclave oven

(Figure 3.1). The autoclave is a pressure oven that has vacuum line hook-ups inside the

chamber. In general, the autoclave process involves the following steps:

1. Prepreg lay up: place and shape the prepreg on the composite mold (tool)

according to the designed stacking sequence.

2. Vacuum bagging: lay up the vacuum bagging material on the prepreg and seal

the vacuum bag.

3. Composite processing: place the vacuum bag inside the autoclave with the

vacuum line connected to the bag. Operate the autoclave to cure the

composite according to the specified temperature, pressure and vacuum

profile.

Figure 3.2 shows the typical prepreg vacuum bag lay-up with the flat tool. The

tool surface and prepreg lay-ups were separated with non-porous release film or other

release agents. This ensures easy release of the composite from the tool after processing

as well as keeping the composite resin from adhering to the tool surface and requiring









laborious cleaning afterwards. The porous release film placed on top of the prepreg also

has dual functions. It is used to allow liquid resin to escape during processing and to

ensure easy separation of the bleeder cloth from the composite afterwards. The bleeder

cloth is made of absorbing material. It absorbs excess resin in the prepreg lay-up to keep

the composite in the proper fiber volume fraction range. The function of the breather

cloth is to ensure good air ventilation inside the bag so that the vacuum can reach every

corner of the vacuum bag. The non-porous release film is also placed between the

breather and bleeder cloth to prevent resin from being sucked into the breather cloth. A

saturated breather cloth could clog the air path inside the vacuum bag and cause air to be

sealed inside the bag. Uneven vacuum is one of most common causes of defects in

composite parts during manufacturing. The vacuum bag is sealed with pressure sensitive

tape and is connected to the vacuum line inside the autoclave. The prepreg is then ready

for processing.


Figure 3.1 Autoclave oven.










Porous release film Breather c
Bleeder cloth I


Vacuum bag Vacuum line


Autoclave tool


I Non-porous release film
Prepreg


Figure 3.2 Vacuum bagging of composite autoclave processing.


-- Temperature

- Pressure


KPa


176.7 C(350 F)@6h

Heating/cooling rate=2.8C(5 F)/min

107.2 oC End@79.4 C(175
S(225 F)@lh \

690KPa(100Psi), Release the pressure @end
------------------1
I I
I I
S103KPa(15Psi)
s:01


'I I I' I I I I I I I I


- 2000
1500

OF)
- 1000


500


0 1 2 3 4 5 6 7 8 9 10
Vacuum: Apply full vacuum (29 in Hg) from beginning. Release vacuum
when pressure reaches 207kPa(30Psi) after first pressure dwell.


Figure 3.3 Curing profile of the thermoset AS4/3501-6.


200 -r o


60-


120 -


80 -


40


0


Hour









Figure 3.3 shows the typical curing profiles used in composite autoclave

processing. A standard temperature curing cycle includes two steps. The temperature is

increased from room temperature to the first dwell temperature at a certain rate. The

temperature is held constant for a certain period-one hour in the figure shown. The

purpose of the first step is to allow gases including entrapped air, water, or volatile gases

to escape from the matrix material as well as to facilitate compaction of the part by

allowing the matrix to flow. The purpose of the second step is to allow polymerization to

take place. It is at this temperature that the material properties of the composite are

developed, as well as the chemical shrinkage that causes residual stress in the laminate

and distortion of the composite component. Vacuum and pressure are applied to the

composite lay-up during the process. Vacuum is used during the first dwell period to

facilitate degassing. Pressure is used to consolidate the part and ensure fiber-matrix

interaction as well as to achieve better heat conductivity.

As mentioned above, the chemical shrinkage due to composite matrix material

polymerization is developed at the second dwell temperature period. It is one part of the

process-induced contraction. The other part is developed when the composite is cooled

from the second dwell temperature period to room temperature.

In order to fully understand the process induced residual stresses in the laminates

and process induced dimensional distortion, it is very important to characterize the

process induced contraction of the composite. A technique called the cure referencing

method (CRM) was developed to fulfill that purpose. In this technique, a diffraction

grating is attached to the composite during the autoclave process. The strain caused by

chemical shrinkage and thermal contraction is measured at room temperature with moire









interferometry by referencing the undeformed state of the composite at the process

temperature to the master tool grating.

Process Induced Contraction (Strain) by Curing Referencing Method


Moire Interferometry

Moire interferometry is a full field, laser based optical technique [43]. A contour

map of the in-plane displacement field can be obtained using this technique. Moire

interferometry has very high sensitivity. The sensitivity of the system used in this work

is 0.4171pm. In order to implement this technique, a diffraction grating is replicated onto

the specimen. Then, the moire interferometer is tuned with the reference grating in order

to null the displacement field for recording the displacement field of the deformed

specimen. The reference grating can be either the grating on the undeformed specimen or

the master grating used to replicate the specimen grating. The most important

characteristic of moire interferometry is that the final specimen deformation can always

be accurately recorded no matter how complicated the loading history is, as long as the

reference grating was kept. In other words, the deformation can be measured at any time

by tuning the moire interferometer with the reference grating. This is one of the most

important reasons why moire interferometry was chosen in this study.

A four-beam moire interferometer and cross-lined phase type diffraction gratings

with a frequency of 1200 1/mm were used in this work. Figure 3.4 illustrates the

schematic of four-beam moire interferometry. The three governing equations (Eq. (3.1),

(3.2), and (3.3)) for determining the strains from fringe patterns are illustrated, where f

(2400 line/mm) is the frequency of the reference grating. Nx and Ny are the fringe

order in the x (U) and y (V) displacement fields respectively.












Input laser light


Fringes

.. )_Camera /
Sens /








Figure 3.4 Schematic of four-beam moire interferometry.



dU 1(aNx
Ex = (3.1)
S dx f ax

9V 1 (Ny
Ey = d f 7 y (3.2)


dU 9V 1 (aNx +Ny
S= -+- -+ y (3.3)
S y dx f ay a+x

High Temperature Diffraction Grating Replication

In order to capture all of the contractions (chemical shrinkage and thermal

contraction caused by cooling from the cure temperature to room temperature) that occur

during processing, a diffraction grating must be attached to the composite during









processing. Since the diffraction grating experiences the same processing profile as

curing of the composite, the chemical shrinkage is locked into the grating at the cure

temperature. When the composite is cooled down to room temperature at the end of the

process, the diffraction grating will have recorded the thermal deformation because it is

attached to the composite.

Since the autoclave composite process involves high temperature and high

pressure, attaching a grating is inherently more difficult compared to grating replication

at room temperature. The initial intent was to replicate a diffraction grating onto the

composite with the excess epoxy from the prepreg during processing. The resulting

specimen grating turned out to have very poor diffraction efficiency. Normally the

master grating was damaged because of the hardness of the fibers and the high pressure

applied to the grating. Attempts were also performed using silicone rubber as the

specimen grating material. No high quality grating was obtained. Numerous early failed

grating replication efforts showed that using procedures similar to general room

temperature grating replication were not feasible. After many failures, a detailed

procedure featuring an intermediate fully cured grating film transferring technique was

developed. An ultra low expansion glass called Astrositall was chosen as the master tool

grating. Because the CTE of Astrositall material is around 0.3x10-7 mm/mm/C,

Dimensional change of the tool caused by temperature fluctuation during the processing

is negligible. This reduces the experimental errors and eases the latter residual stress

calculation. The tool master grating is used as the reference grating to tune the

interferometer. The master grating can then be replaced with the specimen and the














Make a silicone rubber
grating mold

High

Replicate the intermediate
grating using high temp. epoxy


Vacuum deposit
aluminum onto the intermediate
grating

High

Replicate a grating onto
the autoclave tool
using high temp. epoxy


SSilicone rubber
grating



npgt Silicone rubber

Intermediate grating
(high temp. epoxy)


Intermediate grating
(high temp. epoxy)

Aluminum deposition


(high temp. epoxy
on Astrosital)


Sd Aluminum deposition
V a c u u m d e p o s i t A t c a
aluminum onto the autoclave
tool grating Autoclave tool


High temp. Teflon covered flat
glass plate.
Cast a thin film onto .
the autoclave tool grating Autoclave tool
using high temp. epoxy


High temp.
high press. Composite prepreg
Transfer the epoxy film
onto the composite panel
during cure in the autoclave Autoclave tool


Figure 3.5 Schematic of the diffraction grating duplication technique.









absolute deformation of the specimen can be determined. Figure 3.5 illustrates the step-

by-step procedure of the diffraction grating attachment technique. The diffraction

gratings used in this work were phase type crossed line with a nominal frequency of 1200

lines/mm. The same grating substrates were used to eliminate frequency change during

the high temperature replication.

1. A grating was replicated at room temperature onto Astrositall glass

(3"x4.5"x0.5") using silicone rubber (GE RTV 615) from an original

photoresist master grating. The two parts of the silicone adhesive were mixed

in a glass test tube for 2 minutes. In order to get rid of the air bubbles

entrapped in the mixture, the test tube was placed into a centrifuge for 20

minutes.

2. From the silicone rubber grating, a new grating (called the intermediate

grating) was replicated onto another Astrosital glass (3"x4.5"x0.5") using a

high temperature epoxy (Shell Epon 862 with curing agent W). The ratio of

the Epon 862 and W was 100 to 26.4 by weight. They were mixed thoroughly

in a glass tube. The mixture was then heated in an oven for 5 minutes to

reduce its viscosity and finally centrifuged for 5 minutes to remove air

bubbles. Initially, both the silicone rubber grating and the substrate for the

intermediate grating were heated to 1300C. After centrifuging the epoxy

mixture, the silicone rubber grating and intermediate grating substrate were

then removed from the oven. A pool of epoxy was poured onto the silicone

rubber grating. The intermediate grating substrate was then lowered onto the

pool of epoxy. In order to achieve high quality grating replication at elevated









temperature, a special tool (Figure 3.6) was developed to minimize the contact

of the operator's hands with the hot glass. The two sandwiched pieces of

glass were then placed back into the oven to cure at 1300C for 10 hours. Once

the epoxy had cured, the two gratings were separated using a fixture similar to

the one described in Post et al. [43].

3. Two thin layers of aluminum were vacuum-deposited onto the intermediate

grating. A dilute Kodak Photo Flo solution was applied between the two

deposition steps to act as a parting agent to aid in separation of the top layer of

aluminum. The Photo Flo was applied twice using a dragging method [43].

4. The intermediate grating was then used to replicate a grating onto the

Astrositall autoclave tool. This grating was made using 3501-6 epoxy. It was

cured at a temperature of 130C for 10 hours with a 2-hour post cure at

1770C. Additionally, since the 3501-6 is in the glassy state at room

temperature, it was heated in a vacuum oven to 1770C for 15 minutes before

replication. This allowed the gases to escape from the epoxy.

5. Aluminum was then deposited onto the surface of the grating to facilitate

separation in subsequent steps. The orientation of the tool grating lines was

determined using a device similar to the grating alignment device shown in

Post et al. [43]. A straight line was marked on the tool to indicate the

direction of the tool grating lines. This line was later used as the guideline for

aligning the fiber direction of the composite with the tool grating lines.

6. A thin film of 3501-6 called the intermediate grating film was then cast onto

the aluminized grating of the autoclave tool. A Teflon film 0.025 mm (0.001









inch) covered device (Figure 3.7) was used to replicate the epoxy grating film.

Before replication, the epoxy was heated to 1770C in a vacuum oven to lower

the viscosity and remove entrapped air bubbles. A small amount of the heated

epoxy was pooled on the preheated tool (1770C). The Teflon was tensioned

on the flat glass surface after preheating at 1770C. This was done to eliminate

wrinkles in the Teflon sheet in order to cast a uniform thin epoxy layer. The

Teflon device was lowered into the pool and the epoxy was squeezed into a

thin film. Because all the procedure involved hot components, a simple guide

tool (Figure 3.7) was designed to assure a high quality film. During the use,

the Teflon device was put on top of the guide tool and gradually lowered into

the epoxy pool. No air bubbles were entrapped. The epoxy was cured at

1770C for 10 hours. Then, the Teflon device was disassembled and the Teflon

was peeled off the fully cured grating film using a sharp angle. The film

thickness was approximately 0.025mm (0.001 inch). The thickness of the

grating film can be controlled by varying the amount of weight on the Teflon

device.

7. The composite prepreg was then layed-up on top of the grating film of the

autoclave tool. The intermediate grating film was transferred to the composite

panel in the autoclave according to the procedures described in the next

section. As the panel begins to cure, the epoxy from the prepreg adheres to

the flat side of the thin film. Once the panel was separated from the tool, the

grating side of the film became the surface of the panel. Since the cast layer

was thin compared to the thickness of the panel (around 1.905 mm or 0.075")








and was made of the same material as the prepreg epoxy, it is assumed that the

measurement of the deformation was not significantly altered by the presence

of the grating. Because of its minimal thickness, the grating did not

significantly reinforce the surface of the specimen.

The tool grating and the intermediate grating film were intentionally made larger

than 51mm (2 inches). This ensured a large grating area on the composite. A larger

grating area means a longer gage length, reducing measurement error.


Intermediate grating


I. ..... ... ..................... ..2 ". ..


... ..... ...


T.. : ..":..: ":ii::.......


Rotatinu lifter


Stopper


/


- Tool uratinu


Figure 3.6 High temperature diffraction grating making device.


















Stretching screws


Tool grating


Figure 3.7 Teflon device for making thin diffraction grating film.












Porous release film Breather cloth
Bleeder cloth Vacuum bag


..~ .. .. ...


Norn-porous release film
Pre-preg



Pre-preg


3501-6 Epoxy grating film
Evaporated aluminum films
3501-6 Epoxy grating

Astrositall autoclave tool


Figure 3.8 Autoclave vacuum bag lay-up for CRM.



Autoclave Processing

Upon the completion of casting the intermediate grating film, the tool surface was

covered with a non-porous release film. A 38.1mm (1.5") diameter hole was cut into the

release film. The hole allowed the intermediate grating film to be exposed to the

composite prepreg. The non-porous release film used here is about 0.076mm (0.003")

thick. This is about the total thickness of the tool grating and the intermediate grating

film. This minimized the indentation caused by the uneven surface of the tool and

grating area.









This study was conducted on thermoset composite AS4/3501-6 graphite/epoxy

that was manufactured by Hexel Corporation. The prepreg tape with 36% resin content

in weight and 145 area weight was used to fabricate the composite laminates. All the

specimens were made using the prepreg from the same lot to maintain consistency of the

material properties. The prepreg was first laid up on a flat surface with the desired

configuration. The lay-up was then put onto the tool grating with the surface fiber

direction aligned with that of the tool grating lines. Figure 3.8 illustrates the vacuum bag

lay-up for CRM. The lay-up is accordance with the recommendation of the

manufacturer. Inside the vacuum bag, Airweave N10 (Airtech Co.) was used as the

bleeder and breather. In order to control the consistency of the fiber volume fraction of

the composite, the bleeder cloth was cut to the same size as the prepreg lay-up. Figure 2

illustrates the manufacturer suggested curing profile of the AS4/3501-6 composite. The

maximum temperature is 1770C and maximum pressure is 690 KPa (100 Psi). At the end

of the second 6-hour temperature dwell period, the autoclave was cooled to 79.4C

(1750F) at 2.80C (50F) per minute. After the pressure was released from the autoclave

chamber, the specimen was released from the autoclave tool.

High Precision Moire Interferometer Tuning

Figure 3.9 is a photograph of the moire interferometer set-up used in this study.

The four-beam system incorporates a 10 milliwatt Helium Neon laser (632 nm

wavelength) and a 108 mm (4.25 inch) diameter parabolic mirror. The working distance

is about 76.2 mm (3 inch). The field of view is 38.1 mm (1.5 inch) in diameter. The

laser light is coupled into a single mode fiber optic and is guided through the fiber optic

































Figure 3.9 Four-beam interferometry setup.


to a fiber optic positioner. With this system, a virtual grating with 2400 lines/mm

frequency can be obtained. The frequency of the virtual grating is twice that of the

specimen grating.

The key to tuning the interferometer is to tune the virtual frequency to 2400

lines/mm on both the horizontal (U) and vertical (V) field. This was achieved by tuning

the second order diffraction dot from the master tool grating back to the fiber optics tip

for all the adjustable mirrors. Fine adjustment was made by tuning the U and V field

mirrors individually until a null field was obtained in both fields. Caution was also taken

to avoid the situation shown in Figure 3.10. In Figure 3.10, the interferometer tuned with

the master tool grating at position B could cause errors if the specimen was put back to









AB C
I I I



g ^/ ~(a)
.... Diverging
lam, a Beams


I -\


AB C






I I




ABC /


(b)
Converging
Beams









(c)
Collimated
Beams


Figure 3.10 Imperfection of the collimated laser beams.









the A or C position. The reason is the imperfection in the collimated laser beam. The

error could be serious when the measurement is conducted along the fiber direction of the

unidirectional laminate. Since the residual strain along the fiber direction for the

unidirectional composite laminate is usually very small (around 3 fringes per inch), one

fringe inaccuracy in the interferometer will cause a 30% error in the measurement. Final

tuning was done by adjusting the fiber optic positioner and mirrors iteratively until

changes in the tool grating position did not disturb the null field.

Process Induced Strain Measurement

A "cross hair" was lightly scratched onto the composite specimen grating surface

using a needle with the "hairs" in the fiber direction and the cross fiber direction on the

top lamina. That "cross hair" was also coincident with the grating line direction. The

gage length was also marked using a compass with the center of the "cross hair" as the

origin. The gage length in diameter was set to 25.4 mm (1 in.). The gage marks are used

to provide a scale for fringe analysis.

In this study, the interferometer was tuned with the autoclave tool grating, which

was the mirror image of the specimen grating at the undeformed state. Therefore, the

specimen was always rotated 900 with respect to the autoclave tool grating when it was

put in front of the tuned interferometer to replace the tool grating. This procedure can

eliminate the rotation caused by the imperfect perpendicularity of the horizontal and

vertical grating line of the autoclave tool grating. The imperfection was found in most of

the master gratings. Figure 3.11 illustrates the null fields of a master grating and the

fringe patterns after the grating was rotated 900. Since the rotation only appeared in
















Null fields


U field


V field


After 900 rotation


V field


Figure 3.11 Imperfection of the perpendicularity of the cross grating lines.


U field









one field, it will be counted as shear strain during the analysis according to Eq. (3.3).

The grating used in Figure 3.11 contributes an excessive 591x10-6 mm/mm shear strain

error if no caution was taken. By putting the specimen grating 900 with respect to the

autoclave tool grating, substantial error would have been introduced if the grating

frequencies along the two axes were not identical. The difference (1 line per inch) is

usually small and negligible in most situations. However, it can cause 30% errors in the

deformation measurement along the fiber direction of the unidirectional lamina because

the deformation is about 3 fringes per inch in that direction. Therefore all the tool

gratings were checked after a 900 rotation. The frequency difference was compensated

for by tuning the fringes along the x direction in the U field and along the y direction in

the V field back to null. Tuning was achieved by adjusting the angle of the mirrors that

control the frequency of the virtual grating.

In general, the laminate was labeled and gage marks were scratched onto the

composite grating soon after the composite was cooled to the room temperature. The

interferometer was tuned with the autoclave tool grating. The interferometer was tuned

again after the tool grating was rotated 900. The tool grating was then replaced with the

composite grating for the measurement. The fringe patterns of both the U and V field

were photographed using Kodak Tmax 400 35mm film. Enlarged prints were made from

the negatives for later analysis. The actual process induced strains were then calculated

using Eq. (3.4).

1 measure tool
E2 2 measure + tool (3.4)
12 E12 measure 0










1 1E measure
Where E2 is the actual strain matrix and E2 measure is the matrix of measured
12 [12 measure


Tool
strains. Et ot is the deformation of the autoclave tool when it was cooled down from
0

curing temperature to room temperature. The thermal chamber (Figure 3.12) was used to

determine the tool deformation at the curing temperature of 176.7' (350F). The

procedure was the same as that used to determine the thermal deformation on the

composite panels described in the latter paragraph. The autoclave tool was determined to

be an isotropic material.


Figure 3.12 Thermal Chamber.









In order to minimize moisture absorption, the laminate was kept in a sealed

desiccator when not being used for experimental operations. All room temperature

measurements were performed within 6 hours after the specimens had been

manufactured.

After the room temperature measurements, the composite was put into the thermal

chamber (Fig. 10). The thermal chamber was manufactured with a window in the front

where the composite can be observed using the interferometer. The process-induced

contraction was measured with respect to temperature. The components of contraction

caused by chemical shrinkage and caused by thermal contraction were separated. This

operation began by tuning the interferometer to the null field using the composite grating.

This is equivalent to adding tensile carrier fringes to compensate for contraction induced

during the curing process. By doing this, the reference is set to zero at room temperature.

The nature of this tuning is to increase the virtual frequency by the percentage of the

strain value. Error will be induced. Because the strain along the transverse fiber

direction of the unidirectional composite has the highest value (around 0.5%), the largest

error possible caused by the added carrier of extension and carrier of contraction in this

study was estimated with Eq. (3.5):


error = -- X100% (3.5)


Where e' is the measured strain and e is the actual strain. They were calculated using

Eq. (3.2):

1 0 N
f(1+ 0.5%) [y









1 D NA


Therefore,

error = 0.50%

This error was considered small and negligible.

All of the measurements conducted at elevated temperature are in terms of

relative deformation with respect to the deformation at room temperature. The absolute

deformation at elevated temperature was determined by adding the difference of the

measured value at room temperature from that at elevated temperature to the actual strain

at room temperature. Photos of the fringe patterns were taken at regular temperature

intervals during heating and cooling. At each increment, the temperature was held for at

least 20 minutes to insure thermal equilibrium before the moire fringe patterns were

recorded. The time used for photographing was about 1 minute. After the fringe patterns

were analyzed, the strain-temperature relation was plotted.

Process Induced Strains on [01] Unidirectional Lamina of AS4/3501-6


Measurements were first conducted on a unidirectional laminated (to simulate a lamina):

[016]. Four specimens were made in separate autoclave runs. Figure 3.13 illustrates the

fringe patterns of two unidirectional laminates at room temperature. They were recorded

within 4 hours after the specimen was manufactured. A high quality fringe pattern

implied a high quality specimen grating. All of the specimen gratings produced using the

procedures describe above remained high quality even after experiencing the 8-hour high

temperature and high pressure curing process. The fringe patterns were then analyzed.

The results are illustrated in Table 3.1. The measurements from the four specimens


























Run 1


U field or Nx


V field or Ny


Figure 3.13 Room temperature fringe patterns of AS4/3501-6 [016] laminate.


...... ..... -
.... ................ ..












Table 3.1 Process induced strain on the [016] laminate of AS4/3501-6.

Measured Strain Actual Strain Actual Strain


fringe/inch fringe/inch x 106 mm/mm


Lunl 1 Lunl 2 Luni 1 U 2 ul1 Lunl 2


Run 1 -3.6 -282.0 -5.5 -283.9 -90.2 -4657.2


Run 2 -3.4 -290.0 -5.3 -291.9 -86.9 -4788.4


Run 3 -3.1 -290.0 -5.0 -291.9 -82.0 -4788.4


Run 4 -2.2 -286.0 -4.1 -287.9 -67.3 -4722.8


Average -3.1 -287.0 -5.0 -288.9 -81.6 -4739.2


Cv -20.1% -1.3%


Thermal -3.6 -228.8 -58.5 -3753.4


(% of Total) (71.7%) (79.2%)


Chemical -1.4 -60.1 -23.1 -985.8


(% of Total) (28.3%) (20.8%)









are very consistent. The C, (coefficient of variation) is -1.3% and 20.0% in the

transverse fiber direction and the fiber direction respectively. The C, appears very large

in the fiber direction. The maximum variation of the strain in the fiber direction,

however, is only 23pe. The process induced strain is much greater along the transverse

fiber direction than along the fiber direction. This is because the matrix dominates the

material properties along the transverse fiber direction while the fiber dominates the

material properties along the fiber direction. All four specimens were heated and cooled

two times. Figure 3.14 illustrates the fringe patterns of the unidirectional lamina at

various temperatures. Figure 3.15 illustrates the strain/temperature plot of the [016]

specimens with two heating/cooling cycles. The transverse fiber direction showed much

larger thermal deformation than the fiber direction. It is also observed that the

contractions are not zero at the curing temperature (176.70C). The residual contraction at

the curing temperature is the chemical shrinkage component. The AS4/3501-6 showed

linear thermal expansion/contraction during heating and cooling. The linear CTE

(Thermal Expansion Coefficient) of AS4/3501-6 was determined using linear regression

with the data from 200C to 1200C. The results for AS4/3501-6 are listed in Table 3.2.

Consistent results were obtained from the four specimens at every heating and cooling

cycle. The maximum Cv, which is 5.2%, of the 4 specimens in the transverse fiber

direction occurred at the second heating cycles. The C, of the average CTE of the 4

specimens is 3.7%. The C, in the fiber direction is as high as 33.0%. This is because the

strain changes were small (less than 10 pe/C) when the temperature was changing






43


Heating 1 @ 153C


1 @ 173C


U field or Nx + Carrier


Cooling 2 @ 61C












V field or Ny + Carrier


Figure 3.14 Fringe patterns of the AS4/3501-6 [016] laminate at various temperatures.






44







0.001

0 [ Is I' I I" I Inil
0 50 100 150 200
-0.001
Cooling 1
= -0.002 Heating 2
-0 0 Heating 1 Cooling 2
w -0.003

-0.004
-- run2-x
-0.005 run2-

-0.006
C


0.001



0 50 100 150 200
-0.001

-0.002 u- runl-x
-0- runl-y
-0.003 run2-x

-0.004 -- run2-y
-*- run3-x
-0.005 -- run3-y
--run4-x
-0.006 -a- run4-y


Figure 3.15 Strain/temperature plot of the [016] laminate of AS4/3501-6.






45


during the experiment and small measurement errors could cause large variation. The

process induced strain component caused by chemical shrinkage was determined using

Eq. (3.6).


urn chemical 1 urn 1 uIn 1
un chemical 2 urn 2 un 2 AT
um chemical 12] un; a12 un; 12


(3.6)


Table 3.2 CTE of the AS4/3501-6 [016] laminate.





x 10-6 in/in/C x 10-6 in/in/C


Heating 1 Cooling 1 Heating 2 Cooling 2 Average Average


Run 1 24.32 25.71 25.54 25.62 25.30 0.44


Run 2 24.42 27.12 26.65 25.84 26.03 0.49


Run 3 23.72 24.27 23.86 24.09 23.98 0.35


Run 4 23.35 24.88 24.08 25.04 24.39 0.21


Average 23.95 25.50 25.03 25.14 24.91 0.37


Cv 2.1% 4.8% 5.2% 2.9% 3.7% 33.0%










tum chemical 1
Where Eun| chemical 2 | is the matrix of chemical shrinkage induced during the curing

[um chemical 12


un; 1
process. Em 2 [ is the total process induced strain matrix of unidirectional lamina





calculated using Eq. (3.4). aum 2 is linear CTE (Thermal Expansion Coefficient)

umn 12

matrix of the unidirectional lamina. In this study, the CTE of the first heating cycle was

used. ATis the temperature difference between the curing temperature and the

temperature of the Lab where the experiment was conducted. It is equal to 156.7C

(176.70C-200C) in this study. The strain components due to chemical shrinkage were

shown in Table 3.1. Chemical shrinkage was determined to contribute 28.3% to the total

process induced strain along the fiber direction and 20.8% along the transverse fiber

direction. In the transverse fiber direction, the chemical shrinkage is only 0.1%. It is

very small compared to the chemical shrinkage of the neat resin that is around 5%. This

distinguishes one unique characteristic of the CRM that the measured chemical shrinkage

already included the information of creep effects of the composite. In other words, only

the chemical shrinkage that could contribute to residual stresses in the multidirectional

composites was measured.

In Figure 3.15, the deformation along the transverse fiber direction during the first

cooling did not follow the path of the first heating. After the initial heating cycle,

however, the second heating and cooling followed the same path of the first cooling.









There was a substantial difference in residual strain after the heating/cooling cycles. The

reason for this is still not fully understood. Moisture effect between the autoclave run

and the heating/cooling test was eliminated as a possibility. This was determined by

checking the deformation again after the specimens were dried for 12 hours at 1100C.

This was done using the interferometer that was tuned with the autoclave tool grating.

Table 3.1 illustrates the comparison of the measurement shortly after the autoclave run

and after being dried. A large discrepancy was observed.




Table 3.3 Process induced strain comparison before and after the heating/cooling (H/C)
cycles and bone-dried specimens.


Processed induced strain (x 10-6 in/in)


Before

H/C


After

H/C


Run 1 -90.2 -95.1 -4.9 -4657.2 -5789.0 -1131.8


Run 2 -86.9 -100.1 -13.2 -4788.4 -6133.5 -1345.1


Run 3 -82.0 -80.4 1.6 -4788.4 -5444.6 -656.2


Run 4 -67.3 -80.4 -13.1 -4722.8 -5477.4 -754.6


Before

H/C


Diff.


After

H/C


Diff.
















CHAPTER 4
RESIDUAL STRESSES IN LAMINATED COMPOSITES


Material Property Measurement on AS4/3501-6


Tensile Properties

Material properties such as E1, E2, V12, and G12 of lamina are essential for

predicting the residual stresses in composite laminates. The objective of the tensile test

was to determine the in-plane Young's modulus along the fiber direction (Ei) and

transverse fiber direction (E2) along with the Poisson's ratio (v12). One 305mm x 152mm

(12"x6") [016] AS4/3501-6 unidirectional panel and one [9016] panel of the same size

were manufactured following the same procedure described in the previous chapter. The

panels were trimmed by 38mm (1.5") along the longer edges using a diamond embedded

saw blade. Specimens were cut into 305mm x 25.4mm sections (12"xl"), two for each

panel. Rectangular aluminum tabs were bonded to the specimen ends using high strength

epoxy (Epoxy 907 Adhesive System, Miller-Stephenson). The tab dimensions were

38.1mm x 25.4mm x 3.2mm (1.5" x 1" x 1/8"). Four strain gages (CEA-06-250UN-350,

Measurement Group) were used on each of the specimens with 0 and 90 degree front and

back configuration. The averages of the front and back strain gage outputs were used as

the longitudinal and transverse strain. Each strain gage was connected to the strain gage

circuit as a quarter bridge during the experiment. Five volts were used as the
































-0.001 -0.0005 0 0.0005 0.001 0.0015
Strain

I-25-----------------

900 specimen
20


15


10

o 90 Trans
5 90 Long




-0.0005 0 0.0005 0.001 0.0015 0.002 0.0025

Strain


Figure 4.1 Stress/strain plot of AS4/3501-6 tensile specimen.












Table 4.1 Material properties of the AS4/3501-6 unidirectional lamina.

E1 (GPa) E2 (GPa) v12 G12 (GPa)


Specimen 1 147.79 10.38 0.330 6.68


Specimen 2 147.86 10.39 0.321 6.59


Average 147.83 10.39 0.325 6.64


excitation voltage. This voltage was determined experimentally. Starting from 2 V, the

excitation voltage was increased incrementally at 0.5 V intervals up to the highest voltage

possible without output voltage drift. In this study, the optimal voltage was determined

to be 5 V. The specimens were tested on a screw driven testing machine with 1.27

mm/minute (0.05 inch/minute) cross head speed. Each specimen was tested for 3 times

to get an average in order to minimize error induced by specimen misalignment. Figure

4.1 illustrates the stress-strain curves of one of the specimens. The tensile properties

measured are listed in Table 4.1.

Shear Properties

Two [016] shear specimens were made to determine the in-plane shear modulus

G12. The size of the specimen was 76.2 mm x 11.43 mm x 19.05 mm (3"x0.45"x0.075").

Two [9016] specimens of the same dimensions were also prepared to be used in

















Figure 4.2 Shear loading fixture.


Spcie



Siev e









verifying the results. A new shear testing fixture was designed for this experiment. This

fixture is illustrated in Figure 4.2. The fixture is self-aligned and self-centered regardless

of the specimen thickness. It minimized the specimen twist during loading. Because the

specimen was clamped around the entire thickness of the specimen rather than point

loaded, premature failure around the contact area, which often occurs with other loading

fixtures [1,20], was avoid. In addition, the fixture is easier to load and align. A special

strain gage called the shear gage (N2A-06-C032A-500, Measurement Group) was used to

record strain during loading. Unlike the traditional 450 strain gage rosette, the




25 -
0 degree shear specimen

20 -









A Average
5o Front gage
/ #a o Back gage

0 'I I I
0 0.001 0.002 0.003 0.004
Strain


Figure 4.3 Shear stress/shear strain plot of the AS4/3501-6 00 shear specimen.









shear gage integrates shear strain along the entire test section. Therefore, it gives a more

accurate average shear strain value. The shear gage has already been successfully applied

to various composite materials [21,20]. Additionally, the shear gage has been shown to

be insensitive to normal strain by both analytical and experimental proof [20,39]. Two

shear gages were applied to each of the specimens-one on each side. The average of the

front and back shear gages was used as the shear strain. This configuration eliminates the

effect of specimen twist. The shear gage includes 450 filaments and was connected in a

half bridge configuration. In such a circuit, the gages are self temperature-compensated.

The excitation was chosen to be 5 V. Figure 4.3 illustrates the shear stress/shear strain

response of one of the 00 specimens. The shear modulus is shown in Table 4.1. The

experiments were also conducted on 900 specimens. Because the 900 specimen always

failed prematurely in the early load level, errors result from a lack of data points for the

analysis. In this study, the 900 specimens were used only to check the 00 specimen

results. The variations in shear modulus obtained using the 900 specimens was found to

be less than 5% from that using the 00 specimens.

Prediction of the Process Induced Residual Stresses


A methodology is proposed to predict the process induced residual stresses in

each layer of flat multidirectional laminated composites of any stacking sequence using

the information measured from the unidirectional lamina. Prediction was applied to three

representative laminates of AS4/3501-6. They were [02/902]2S [03/90]2s, [02/452]2S

laminates.









During the composite manufacturing process, each layer in a multidirectional

panel intends to deform as a unidirectional lamina. Each layer, however, is constrained

by its adjacent layers. The mutual constraints cause residual stresses. In order to predict

the residual stresses, the following assumptions were made in addition to the assumptions

used in CLT (classical laminate theory) [54,62]:

1. The interlaminar shear stresses are negligible from the curing temperature to

room temperature.

2. During curing, the interlaminar shear stresses are negligible after the chemical

shrinkage starts to take effect on composite laminates.

According to these assumptions, each layer inside the multidirectional laminate was

considered as a separate unidirectional lamina under simple loading conditions. The

loads applied only include in-plane tensile/compressive and in-plane shear stresses.

These stresses deform each lamina from the free contracted dimension to the dimension

of the multidirectional laminate. The dimension of the free contracted lamina was

considered the same as that of the [016] unidirectional panel. The dimensional change of

[016] unidirectional panel, which is the process induced strain, was measured using CRM.

The relations between process induced residual stresses in the laminate and process

induced strain of unidirectional lamina were developed by using Constitute, equilibrium

and compatibility relations. The residual stresses were solved from the relations.

Process Induced Residual Stresses in [0,/90J2s Balanced Cross Ply Laminate

Because both the fiber and transverse fiber directions of the [02/902]2s laminate

aligned with the principle axis, there was no shear coupling between the layers. Using

the assumption described above, each layer of the [02/902,2s was considered under





















Cross 90-x Gcross_90_y







Gcross_90_y cross 90 x


Figure 4.4 Lamina under residual stresses in the [02/902]2s laminated composite.



only tensile and compressive residual stresses. Figure 4.4 illustrates the residual stresses

in adjacent 00 and 900 layers. Since the residual stresses had to be balanced in the x and

y directions, the equilibrium relations can be obtained:

cross 0 x cross 90 x
8- cross 0 +8- cross 90 0 (4.1)
0 0


cross 0 x cross 90 x
Where across 0_y and cross 90 y are the residual stress matrices in the 00 and 900
0 0


layers respectively. The shear stresses equal 0 since the laminate had only 00 and 900

layers. The number 8 indicates the number of layers in each direction. Figure 4.5 is the

illustration of the compatibility relations of the lamina under free contraction and










Prepreg [0'on.]- [016] [9016]
I --I T















l lll lloss.90rllesx cross_0resx.









Figure 4.5 The compatibility relations of the [02/902]2s laminate.


the lamina under residual stress. The strains instead of length changes were directly used

for determining compatibility relations because of all the strains were based on the same

original dimensions. The relation along the x-axis is summarized in Eq.(4.2).
--- --- -- --- i'























um 2 rum 1 cross _res 0 re _y cross _90_ resy (4.2)

Where un, 1 and Eun 2 are equivalent to the process induced strains of [016i

unidirectional lamina, which were measured using the CRM. The number 1 and 2

represent the two principle directions, fiber and transverse fiber directions, respectively.









The Ecross 0 res x and E cross 90 res xare the residual strains in 00 and 900 layers respectively,

which were caused by the residual stresses in the x-direction when the lamina was

deformed from the free contracted shape to the shape of the laminate. The relation along

the y-axis was determined to be the same as that along the x-axis (Eq. (4.3), (4.4), and

(4.5)) because of the 00 and 900 symmetrical lay-up.

Eurn 1 -urn 2 _1 cross 0 res y y cross _90 _res y (4.3)

cross 0 res x =cross 90 res y (4.4)

.cross 0 res y =cross 90 res x (4.5)

Where cross 0 res_y and Ecross 90res_ y are the residual strains caused by the residual

stresses in the y direction in 00 and 900 layers respectively. Equation (4.6) is the matrix

form of the compatibility relations summarized from Eq. (4.2) and (4.5).

um 1 um 1 cross 0 res x cross 0 res x
[T29 = ,_-[ ..E E.*E (4.6)
[2]90 uni 2 uni 2 cross _0_res_y 2 90 cross _0 _resy
0 0 0 0

Where [T2 ]90 is the transformation matrix. It is determined by substitute 0 with the

lamina angle 900 in Eq. (4.7).

cos2 o sin2 0 cos0sin 0
[T2 [ = sin20 cos2 -cos in 0 (4.7)
-2cos0sinO 2cos0sin0 cos2 0 sin2 0

The stress/strain relations in the x direction and the y direction are showed in Eq.

(4.8) and (4.9) respectively.









[across 0-y cross 0 resy

0 0


I cross 90 x
Scross_90 y
0


90 res x .cross 0 res x
90 r[y cross_0 res _y
0 0


(4.9)


Where [QO is the transformed stiffness matrix. It was determined using Eq.(4.10),

(4.11), and (4.12).


O I =T, [Q]. 1T210

cos2 sin 20 2cos0sinO
[Ti] = sin20 cos2o -2cos0sinO
-cos0sinO cos0sinO cos2 0- sin2 0


Q11Q
[]= Q12
0


0
0 =
Q66


E1
1- 12V21

-V12V21
0


v12E2
1 -12v21
E2
1 -12v21
0


(4.10)


(4.11)


(4.12)


In Eq.(4.10), and (4.11), the 0 represents the angle of the lamina of the laminate that is

studied. The [Q] matrix is the stiffness matrix of the lamina. It is a function of the

material properties such as El, E2, V12, G12.

Combining the equilibrium relation (Eq. (4.1)), compatibility relations (Eq. (4.6)),

and constitutive relations (Eq. (4.8) and Eq. (4.9)), a total of 8 equations were established.

In these equations, only the 4 residual stress components and 4 strains that are caused by

residual stresses are unknowns. A program was written in Mathcad (Mathcad 7.0,

Mathsoft, Inc.) in order to solve the residual stresses in the AS4/3501-6 [02/90212S


(4.8)













Table 4.2 Predicted residual stresses in the AS4/3501-6 [02/90212s laminate at 200C.


ax (MPa) y, (MPa) TCxy (MPa)


00 900 00 900 00 900


Total -46.01 46.01 46.01 -46.01 0 0


(% of strength) (3.9%) (95.3%) (95.3%) (3.9%)


Thermal -36.50 36.50 36.50 -36.50 0 0


(% of Total) (79.3%) (79.3%) (79.3%) (79.3%)


Chemical -9.51 9.51 9.51 -9.51 0 0


(% of Total) (20.7%) (20.7%) (20.7%) (20.7%)





Table 4.3 Strength of AS4/3501-6 unidirectional lamina.

SL (MPa) SL(- (MPa) ST() (MPa) ST(- (MPa) SLT (MPa)


1448 -1172 48.3 -248 62.1









laminate from the 8 equations. The results are illustrated in Table 4.2. The total process

induced stresses were calculated using the total process induced strains as input while the

residual stresses caused by thermal and chemical shrinkage were calculated using the

thermal and chemical component of the strains respectively. By prediction, chemical

shrinkage contributed 20.7% of the total residual stresses in the [02/90,]2s laminate. The

strengths of the AS4/3501-6 unidirectional lamina, which were found in the literature, are

listed in Table 4.3. The comparison of the predicted residual stresses with the strength

values showed that the residual stresses in the transverse fiber direction of both the 00 and

900 specimen reached 95.3% of their transverse tensile strength while they only

consumed 3.9% of the strength along the fiber direction. Residual stresses along fiber

and transverse fiber direction at various temperatures are plotted in Figure 4.6. The

calculation of the residual stresses was the same as mentioned before except the process

[rum 1 T
induced strain Ieun, 2 T at elevated temperatures were used. It is calculated using Eq.
[um 12 TT

(4.13).



un 2- Ti 2 -n am- 2 "(T1- 20 C) (4.13)
ruin 12 T1 u 12 am 2 I

Where TI is the temperature that the residual stresses were calculated. In this analysis,

the room temperature material properties were used. It was a reasonable approximation

when the temperature was below the glass transition temperature Tg for the thermoset

matrix composite [14,50]. In this study, the Tg of AS4/3501-6 was estimated to be






61



60


40


20




0 50 100 150 200

-20


-40- (--*- .cross 0 x
0 cross _0_y

-60
C



Figure 4.6 Residual stress/temperature plot of the AS4/3501-6 [02/90212s laminate.




higher than 1400C (from Figure 3.15 and [4]). Better approximation could be achieved if

the elevated temperature material properties were available. The magnitude of the

residual stresses decreased as the temperature increased. There was a no-reversible part

of the residual stresses since the residual stresses were not zero at the curing temperature.

It was caused by chemical shrinkage.

Process Induced Residual Stresses in the [0r/9012s Unbalanced Cross Ply Laminate

The residual stresses in [0/901]2s laminate were similar to those in the [02/90212s

laminate. Each layer of the laminate still needed to satisfy the equilibrium (Eq. (4.14)),

compatibility (Eq. (4.15)) and constitutive equations (Eq. (4.17), (4.18)).








unbalanced _0 [x unbalanced 90 x
12. l unbalanced0 _y + +4. unbalanced 90 y -=0
0 0


(4.14)


unbalancedx 0 x unbalanced 90 x
Where unbalanced 0 y and unbalanced 90 y are the residual stress matrix of 00 and 900
0 0

layers respectively. They are unknowns. The coefficients in front of the matrix represent

the layer number of 00 and 900 lamina in the [03/9012S laminate.


Prepreg
r-'1


[03/9012s


H


[016]


I-......


[9016


Fi:.. ,


Figure 4.7 The compatibility relations of the [03/9012s laminate.










lunz 1 um 1 unbalanced 0 res~x unbalanced 90 res x
90 2 2 unbalanced 0 rey unbalanced 90 res (4.15)
0 0 0 0


Unbalanced 0 res x Junbalanced 90 res x
Where unbalanced 0 _res_y and Eunbalanced 90_res_y are the strain matrices of 00 and 900
0 0

layers caused by residual stresses. They are unknowns also. Their relation was

illustrated in Eq. (4.16).

Unbalanced 90 res x [unbalanced 0 res x
_unbalanced _90 resy 02 90 unbalanced 0 res 4y 16)
0 0


1tunbalanced 0 x unbalanced 0 res x
S unbalanced s0 y w unbalanced 0 resy (4. 17)
0 0


Unbalanced 90 x unbalanced 90 res x
(unbalanced _90_y k6 90 Cunbalanced 90 _resy (4.18)
0 0

The compatibility relations are also illustrated in Figure 4.7. Process induced residual

stresses in the AS4/3501-6 [03/9O]2s laminate were solved from the governing equations

(Eq. (4.14), (4.15), (4.17), and (4.18)) using a Mathcad program. The predicted results

are listed in Table 4.4. The residual stress along the transverse fiber direction of the 00

layer reached 90.7% of its tensile strength while the residual stress consumed 80.5% of

its tensile strength along the transverse direction of the 900 layers. The residual stress

along the fiber direction of the 00 and 900 layer consumed 1.3% and 10.0% of their

compressive strength respectively. By prediction, chemical shrinkage contributed











Table 4.4 Predicted residual stresses in the AS4/3501-6 [03/90]2s laminate at 200C.


a, (MPa) ay (MPa) Txy (MPa)


00 900 00 900 00 900


Total -14.60 43.81 38.86 -116.58 0 0


(% of strength) (1.3%) (90.7%) (80.5%) (10.0%)


Thermal -11.58 34.75 30.83 -92.48 0 0


(% of Total) (79.3%) (79.3%) (79.3%) (79.3%)


Chemical -3.02 9.06 8.03 -24.10 0 0


(% of Total) (20.7%) (20.7%) (20.7%) (20.7%)


20.7% of the residual stress along every direction of each layer. Following the same

analysis described in previous section, the residual stresses in AS4/3501-6 [03/90]2S

laminate at various temperatures were also calculated. The results were plotted with

respect to temperature in Figure 4.8. Residual stresses were noticed existed in this type

of laminate at the curing temperature.














60

40

20

0 2--
( A--- 5-- --------* 100 150 2(0
-20

-40

-60

-80
-80 Gunbalanced 0 x
-100 6 unbalanced_ Oy
-2 unbalanced 90 x
-120 unbalanced 90_y

-140
OC



Figure 4.8 Residual stress/temperature plot of the AS4/3501-6 [03/9012s laminate.





Process Induced Residual Stresses in [02/45212 Angle Ply Laminate


Different from the [02/90212s, [03/9012s laminates, the [02/45212s laminate has the 450

angle layers. Residual shear stresses are induced as a result of this lay-up. Even so, each

layer still has to satisfy the equilibrium, compatibility and constitutive equations. The

form of these equations is more complicated than the cross ply type lay-ups. Care has to

be taken to consider the in-plane shear effects. The following are the governing

equations:










Equilibrium relations:


[angle _0_x "angle_45_x
8.1 aangle_0_y +8.- angle 45_y (4.19)
Tangle_0_xy [angle _45 _xy


[angle _0_x angle _45_x
Where | angle_ 0 y and 'angle 45 _y are the process induced residual stress matrices in

[angle_0_xy angle_45_xy


the 00 and 450 layers respectively. The coefficients of the matrices represent the number

of layers in the corresponding orientation.

Constitutive relations:


angle _0 _x angle _0 _res_ x
10angle _0 _y J5 angle _0 _res y (4.20)
angle 0 _xy Yangle _0 _res _xy


angle_45_x angle _45 _res_x
angle _45_y 5 angle _45 res y (4.21)
Tangle _45 _xy angle _45 _res _xy


angle 0 _res_x angle _45 _res_x
Where E angle_0 res_y and E angle 45_res y are the strain matrices caused by residual

Yangle _0 res _xy [angle 45 res xy


stresses in the matrix of the 00 and 450 layers respectively. They are also unknowns.

Superposition principle was employed to conduct the analysis to determine the

compatibility relations. The relation between the shear strains was studied separately.

Figure 4.9 illustrates the compatibility relations of the [02/45212s laminate. They are also

summarized in Eq. (4.22).









Normal Strain Relations


---------------------/AJ .....







_45_sx a 0~/ __xL P I__
Clgle_45 Yes x/ & gleO0esx uni


I 0 --


I


Prepreg
l--|
I I
L-a



[O/45j]s











[4516

Kc/


Sha -- ~ %angle _45resxy aiglex_uni_12


Shear Strain Relations


Figure 4.9 The compatibility relations of the AS4/3501-6 [02/45212s laminate.


1










Compatibility relations:


anglexunz _1 um _1 angle_ _res_x angle_45_res_x
Angle_ y _un 2 um 2 angle 0 res_ y angle _45 _res (4.22)
Yangle xy um _12 unum 12 [Yangle 0 resxy Yangle _45 _res_xy


anglexun._1
Where angle _yun_ 2 represents the process induced strains in the x-y coordinate

Y angle _xy um 12

system of the unidirectional lamina when its fiber direction is aligned to 450 off the x-

axis. This matrix was calculated using the transformation matrix and the process induced

strain measurement on [016] by CRM (Eq. (4.23)).


anglexun_1 umn 1
Angle y _un 2 E2n45 2 (4.23)
Angle _xyum_12

The equilibrium relations (Eq. (4.19)), the constitutive relations (Eq. (4.20) and

(4.21)) and compatibility relations (Eq. (4.22)) established 12 independent equations.

The 12 unknowns, which include 6 residual stresses and 6 strains that were caused by

residual stresses, were then solved using a program written in Mathcad. The calculated

residual stresses are listed in Table 4.5. The chemical shrinkage caused 20.7% of the

total residual stress in each direction of every layer while the thermal contraction

contributed the rest of the 79.3%. The percentages were the same as those in [02/90212S,

and [03/9012S. These numbers were close to the thermal and chemical composition of the

process induced strains along the transverse fiber direction of [016] lamina. The reason

was that the analysis described above is a linear analysis based on the process induced

strains on [016] and for the unidirectional lamina, the strain along transverse









Table 4.5 Predicted residual stresses in the AS4/3501-6 [02/45212s laminate at 200C.


ax (MPa) y, (MPa) TC, (MPa)


00 450 00 450 00 450


Total -18.05 18.05 18.05 -18.05 18.05 -18.05


(% of strength) (1.5%) (1.5%*) (37.4%) (37.4%*) (29.1%) (29.1%*)


Thermal -14.32 14.32 14.32 -14.32 14.32 -14.32


(% of Total) (79.3%) (79.3%) (79.3%) (79.3%) (79.3%) (79.3%)


Chemical -3.73 3.73 3.73 -3.73 3.73 -3.73


(% of Total) (20.7%) (20.7%) (20.7%) (20.7%) (20.7%) (20.7%)

*: The percentage of the strength was calculated at principle direction respectively.


direction is much bigger than that along the fiber direction. In the 00 layers, the residual

stresses consumed 37.4% of its tensile strength along the transverse direction while only

1.5% of the compressive strength was reached along the fiber direction. In the 450 layers,

the residual stresses were transformed to its principle axis (fiber direction) using Eq.

(4.24).


(angle 45 _x1 -angle_45_x
('angle _45 _y _2 45 angle_45_
angle_45 _y 12 angle_45_ y


(4.24)







70


[ angle_45 _x _1l
Where ange 45 _y_ 2 is the matrix of the residual stresses along the principle axis in the
a[ngle_45 _xy_12


450 layers. The results were found to be the same as the residual stresses in the 00 layers.

The corresponding percentages of strength that the residual stresses consumed were then

calculated also. Figure 4.10 illustrated the relations of the residual stress and temperature

of the [02/902]2s laminate. The residual stresses were calculated using the same method

described in previous sections. It was also observed that the residual stresses was not

zero at the curing temperature for this type of laminate.



20





10
20 i--------------------------------------







0 50 10050 200



-10
-' tangle_0_x
l ~angle_0_y
^angle_0_xy
-20


Figure 4.10 Residual stress/temperature plot of the AS4/3501-6 [02/45212S laminate.















CHAPTER 5
VALIDATION OF CURE REFERENCING METHOD

In the previous chapters, a technique called the Cure Referencing Method (CRM)

was described. This technique was used to measure the process induced strains on [016]

unidirectional lamina of AS4/3501-6 composite material. The thermal and chemical

components of the strains were also separated by examining the specimen at various

temperatures in a specially designed thermal chamber. Using the measurements on the

[016] panel as input, the process induced residual stresses in the [02/902] 2s, [03/90] 2s,

[02/452] 2s were then predicted. The predicted residual stress was as high as 95.3% of the

tensile strength along the cross fiber direction in the [02/902] 2s laminated composite. In

this chapter, an independent method was employed to validate the CRM by using an

unsymmetric laminate. The CLT (Classical Laminate Theory) was first employed to

predict the curvature of the [04/9041 laminate of AS4/3501-6 using the process induced

strain measurements from the [016] unidirectional lamina. The curvature of the [04/90412

laminate manufactured with AS4/3501-6 prepreg was then measured using the shadow

moire method. The validation was achieved by comparing the prediction with the

experimental measurements. Additionally, the process induced strain measurements

were also conducted on [02/902]2s, [03/90] 2s, and [02/452] 2s laminated composites of

AS4/3501-6 respectively to validate the CRM and the residual stress prediction. The

same methodology used for predicting the residual stresses was also used to predict the







72


process induced strains. The prediction was compared with the measurements to fulfilled

the validation.


Before cure


After cure


Figure 5.1 Unsymmetric laminated composite panel before and after cure.


90
S90
0

0
21-1
_____________________0


V 90+t


NI


-1 ..N


Figure 5.2 The coordinate system of the [02/902]s laminated composite.


90


I










Validation of CRM Using Unsymmetric Laminated Composites


Predicting Curvature with CLT


A bending-stretching coupling exists in unsymmetric laminated composites. This

causes a curvature of the laminate because each layer of the composite tends to contract

differently along the two orthogonal directions during processing. An example of a

curved unsymmetric composite is illustrated in Figure 5.1. In this study, the curvature of

a [04904]2 laminate of AS4/3501-6 was calculated with CLT (Classical Laminate Theory)

based on the process induced strain of the [016] measured with CRM. Figure 5.2

illustrates the coordinate system used in this analysis. The constitutive relations are

x(k) (k) (k)
( (ak) (ky) ) (5.1)
xy llamxy urn _xy


(k)
lxi
where a' k) is the stress matrix of the kth layer in the laminate. Ok denotes the fiber
( k


direction of the kth layer. The strain matrix of the kth layer lamina, with no constraints,

is calculated from Eq. (5.2).

'(k) [ 1
um x um 1
I (k,) = [T]. (5.2)
u Ok unik2
Yun _xy 0

The strain matrix of the laminate is defined as


lamx x x
i -^*^<^ (-3
y,,o <0










where is the curvature matrix of the laminate.


The force resultants along the cross section of the lamina are given in Eq. (5.4)

N, (T(k) (T 4k)
Ny N-h/2 y zz--- J^l
h2{ (k) dz g k { )dz{ (5.4)



Combining Eqs. (5. 1), and (5.3) in Eq. (5.4), the following equation results.


y ,akmy .)_y duz
xY lm_xy Yum _xy








e }+[ ]. + { } 2-2 ]Ok E [ _2 dz
= [A].- o +[B] Zkj 2 k un_2 dz



=[A]. + h/2 k 2 dz (5.5)
Yo 0

Here [A] is the laminate extensional stiffness and [B] is the bending-stretching coupling

stiffness. They are only related to material properties. Their definitions are given in Eqs.

(5.6) and (5.7).

N
[A]= fk k dz (5.6)
k=l k-1










[B]= k 'kZdz (5.7)
k=l

Similarly, the resultant moments are derived in Eq. (5.8).


{ { fh2 {Na {zd X { { {zdz{
Y J-h/2 I Jzk-1
M (k) k=1 k (k)



I lam x un _x

lamxy [un _xy

0 C
N x x uni-1
k k l- *+Z -+Z Y _2 )Zdz







= [B]. {o +[D]. y k 1 I2 k -un2 Zdz





C k =1 k
Since there are no [B]external forces applied to the laminate, the dz (58)



where [D] is the laminate bending stiffness which is only a function of material

properties. It is defined as


[D]= -k k Z2dz (5.9)


Since there are no external forces applied to the laminate, the resultant stresses derived in


Eqs. (5.5) and (5.8) are equal to 0.










x x un 1
[A]. 20 +[B]. -k[rk --un dz=0 (5.10)




[B- ]. +[D].- y -C 2 T.[unz. Zdz= (5.11)



Among Eqs. (5.10) and (5.11), only 3 mid-plane strains and 3 laminate curvatures

are unknowns. They were solved from the 6 equations using a program written in

Mathcad.


Laminated composite


Moir g------rille I
Moire grille I \


Proj ector


Camera


Figure 5.3 Schematic of the shadow moire experiment.





















Figure 5.4 Shadow moire fringe pattern of the AS4/3501-6 [04/90412 (3"x8") laminate.





Measuring Curvature Using the Shadow Moire Method

Three [0M90412 laminates of AS4/3501-6 were manufactured in separate autoclave

runs according to the manufacturer recommended vacuum bag lay up and curing profile,

which were described in early chapter. The specimen dimension was 76.2 mm x 203.2

mm (3 in x 8 in). The same size of bleeder material was used in order to keep a

consistent fiber volume fraction of the laminate with all the other specimens

manufactured for this research. The specimens were first painted with flat white paint as

the shadow moire method required. The specimen painting and curvature measuring

were done within 5 hours after the curing process to minimize moisture effects. Shadow

moire is a full field optical method. It is suitable for measuring relative large out-of-

plane deformation. Figure 5.3 illustrates the schematic of the shadow moire experiment.

In this experiment, a 7.87 line/mm (200 line/inch) grille was used. It gave a 0.127 mm

(0.005 inch) out-of-plane displacement sensitivity. One of the shadow moire fringe

patterns is illustrated in Figure 5.4. The fringe patterns were analyzed along the

horizontal centerline of the specimen. The out-of-plane displacement w, which is the









relative distance between the flat grille and the specimen surface, was calculated using

Eq. (5.12).

n
W=f (5.12)


Where n is the fringe order and f is the moire grille frequency. Each data point was

recorded in the form of (x,,ww). The least squares method was adopted to curve-fit all

the data points in the form of Eq. (5.13).

w = C x2 + Cxc 2 (5.13)

By including all of the data points, Eq. (5.13) transforms to


x2 x1 1
X2 X2 1 2
C0
S c, (5.14)
c2
X2 X1 1 W



If defining

x2 x 1
x2 x2 1

[x]= (5.15)


x2 1
x~x~ 1









W2


[w]= = (5.16)






[c]= c1 (5.17)
C2

Eq. (5.14) becomes

[x]- [c]= [W] (5.18)

Based on the least squares method

I[xy x]. [c]= I[xy [w]

([X 1X X [x] [c] = ([x] [x-I [X [W]

[C]= x-f([X [X)-[XY. [W] (5.19)

After calculating the coefficient matrix [C], the curvature of the panel was determined

using

=- = -2c (5.20)

Results

Table 5.1 lists both the analytically predicted and the experimentally determined

curvature cx of the AS4/3501-6 [04/90412 laminated composite. The prediction and









Table 5.1 Curvature of the AS4/3501-6 [04/90412 laminate.


measurements showed excellent agreement because all the three measured curvatures

were less than 6% difference than the predicted value. This verified that the process

induced unidirectional measurements using CRM on [016] AS4/3501-6 panels are valid.

Validation of the CRM Using Symmetric Laminates


Prediction of Process Induced In-Plane Dimensional Distortions

In Chapter 4, the equilibrium, compatibility, and constitutive relations were used

to establish the equations for predicting the residual stresses in laminated composites with

various stacking sequences. Among the unknowns in those equations, there are several

strain components as well as the residual stress components. The strain components were

deformations of the lamina that resulted from residual stresses. They could be solved

along with the unknown residual stress components. Based on the compatibility

relations, the process induced strains of the laminate could be calculated using those

solved strain components.


Prediction Run 1 Run 2 Run 3


K, (1/m) -0.521 -0.502 -0.492 -0.527


Difference (%) 3.64 5.57 1.15










[02/90,212 laminate of AS4/3501-6

As described in Chapter 4, eight equations were established. They are equilibrium

relation Eq. (4.1), compatibility relations Eq. (4.6), and constitutive relations Eq. (4.8)


J cross 0_x cross 90 x
and Eq. (4.9). Eight unknowns, which included across_ _y cross_90_y
0 0


cross 0 res x .cross 90 res x
..cross_ 0res_y and E cross 90 res_y were solved for using a program written in Mathcad.
0 0

According to the compatibility relations illustrated in Figure 4.5, the process induced

strains were calculated using Eq. (5.21),


cross cr ross 0 res [x umr 1
cross y cross 0 resy un (5.21)
0 0 0


cross x
where Ecro ssy is the process induced strain matrix of the [02/9022s cross ply laminate.
0


cross 90 res x
At elevated temperatures, the strain components E cross_90_res_y were determined using
0

the same way as the residual stresses at the elevated temperatures. The methodology was

described earlier in Chapter 4. The same equation as Eq. (5.21) was used for calculating

the process induced strains at elevated temperature except that all the strain components

were replaced by the corresponding strains at elevated temperature.









[03/901,s laminate of AS4/3501-6

For the [03/90]2s unbalanced cross ply laminate of AS4/3501-6, there are also 8

independent equations established from equilibrium (Eq. (4.14)), compatibility (Eq.

(4.15)) and constitutive relations (Eq. (4.17) and (4.18)). The 8 unknowns were solved

from the equations by using a Mathcad program as described in the last chapter. They

unbalanced 0 x unbalanced 90 x
are the residual stresses unbalanced_0_y >, unbalanced90_y and the strains
0 0


Unbalanced 0 res x unbalanced 90 res x
unbalanced 0 resy and unbalanced_90_res_y that were caused by residual stresses in the
0 0

lamina. By studying the compatibility relations of the lamina of the [03/9012S laminate

(Figure 4.7), the process induced strains on this unbalanced cross ply laminate

Unbalanced x
unbalanced y were determined using Eq. (5.22).
0


Unbalanced x unbalanced 0 res x umn 1
Unbalanced y unbalanced_ 0 resy um 2 (5.22)
0 0 0

The residual strains in the lamina at elevated temperatures were calculated by the residual

stresses as described in last chapter. The corresponding stress and strain components at

elevated temperature were substituted into Eq. (5.22) to determine the process induced

strains in the [03/9012S laminate of AS4/3501-6.










[02/45,212 laminate of AS4/3501-6

The equilibrium relations (Eq. (4.19)), the constitutive relations (Eq. (4.20) and

(4.21)) and compatibility relations (Eq. (4.22)) established 12 independent equations. A

total of 12 unknowns were solved for from those equations with the Mathcad program


[ angle 0_ res _x
used in Chapter 4. The solved unknowns included the lamina strains angle __res_y '

I angle 0 res xy


angle_45_res_x
angle _45_res_y which were caused by the residual stresses. By analyzing the
Angle _45 _res _xy

compatibility relations illustrated in Figure 4.9, the process induced strains on the

[ angle x 1
[02/452]2s laminate angle_ y were calculated using Eq. (5.23).

Angle _xy


anglex angle_0_res_x um 1
E angle_y { angle_0_res_y +Eumn_ 2 (5.23)
Yanglexy angle _0_res _xy 0


When calculating the process induced strains at elevated temperatures, the same

equations (Eq. (5.23)) were used and strain components in the equations were replaced

with corresponding strains at elevated temperatures.

Measurement of Process Induced In-Plane Dimensional Distortions


Specimen manufacture


Three types of lay-ups were manufactured. They were the [02/90212s cross ply

laminate, the [03/90] 2S unbalanced cross ply laminate and the [02/452] 2s angle ply

laminate. Two specimens were manufactured in separate autoclave runs for each type.









The prepreg of AS4/3501-6 was chosen from the same lot of prepreg that was used to

manufacture the [016] unidirectional composite. The dimension of the specimens was

101.6 mm x 101.6 mm (4 inch x 4 inch). Moire diffraction grating was attached to the

specimen during the curing process using CRM as described in Chapter 3. The same size

of Astrositall tools was used in this study as used for the [016] unidirectional laminate. In

addition, the specimens were cured in the autoclave with the same vacuum bag lay-ups

(Figure 3.2) and curing profile (Figure 3.3) too.

Process induced strain measurement on the laminates

The process induced strains at room temperature were measured within 6 hours

after each autoclave run using the interferometery set-up illustrated in Figure 3.9. The

moire fringe recording and analyzing procedures were the same as described in Chapter

3. The autoclave tool gratings were used to tune the moire interferometer. Room

temperature moire fringe patterns of the [02/902,]s cross ply laminate are illustrated in

Figure 5.5. Rotation carriers were added on the V field for easier fringe counting. Figure

5.6 illustrates the moire fringe patterns of the [03/90],s unbalanced cross ply laminate and

the [02/45,]2s angle ply laminate. The angle ply laminate showed very dense fringes on

the V displacement field. The fringe pattern was still readable after being enlarged with

photographic equipment. Specimens were also placed inside the thermal chamber

(Figure 3.12) and were heated and cooled for two cycles. The average heating and

cooling rate was no more than 20C/min. The thermal chamber was placed in front the

interferometer, which is illustrated in Figure 3.9, to measure the deformation at various

temperatures. The same procedure as that described in Chapter 3 when studying the

















[02/90212S Specimen 1


20C


x,U


V +Rotation carrier




Figure 5.5 Moire fringe patterns of the AS4/3501-6 [02/90212s laminate at room
temperature.






86




[03/90]2s Specimen 1












U V



y,V








[02/4522S Specimen 1




200C







U V


Figure 5.6 Moire fringe patterns of the AS4/3501-6 [03/9012S and [02/45212s laminates at
room temperature.









thermal deformation on the unidirectional lamina were used in this experiment. The

moire interferometer was tuned to null with the specimen grating when the specimen was

in the chamber. Moire fringe patterns were photographed every 30 minutes during the

heating and cooling cycle. Relative deformations were determined after analyzing the

fringes using Eqs. (3.1), (3.2), and (3.3). Those values are the deformation at elevated

temperature with respect to the apparent measurement at room temperature. The absolute

deformations were determined by subtracting the room temperature measurements from

the high temperature measurement and added to the actual strain at room temperature.

Figure 5.7 illustrates the moire fringe patterns of [02/90212S laminate at various

temperatures while moire fringe patterns of the [03/9012S and the [02/45212s laminates at

various temperatures are illustrated in Figure 5.8 and Figure 5.9 respectively. Rotation

carrier fringe patterns were added to some of the fringe patterns to add convenience for

fringe analysis. Rotation did not disturb the normal strain analysis. Because the rotation

carriers were achieved by adding rigid body in-plane rotation to the specimen and a four-

beam interferometer was used, values with the same magnitude but opposite signs were


added to -Nx and aN When calculating the shear strains using Eq. (3.3), the rotation
ay ax

parts are cancelled. Therefore, the rotation carriers did not affect the shear strain

calculation either. Process induced strain and temperature relations of the [02/90212S,

[03/9012S, and the [02/45212S were illustrated in Figure 5.10, Figure 5.11, and Figure 5.12

respectively.









[02/90212S Specimen 1

Heating 1 @ 20C










U+Carrier


U+Carrier


U+Carrier


V+Carrier


Heating 1 @ 1760C










V+Carrier


Cooling 2 @ 111C


V+Carrier


Figure 5.7 Moire fringe patterns of the AS4/3501-6 [02/90212s laminate at various
temperature.

















[03/90]2s Specimen 1


Heating 1 @ 122c (


























Heating 1 @ 171cC


V+Carrier


V+Carrier


oling 2 @ 76'


y,V


x,U


V+Carrier


Figure 5.8 Moire fringe patterns ofAS4/3501-6 [03/901]2s laminate at various

temperature.


U+Carrier


U+Carrier


... .... ... .. .. C o
.... ... ....
. ........ .. .
.... ... ...
.. ...... ...... ..... ..... .
... .. .....
..... ....... .... ... .. .....

.. ...... .. .. ....
. ...... ........ ..... .. .. ... . ..... .. ....
.... ... ... .. .. .... .....
..... ... ..
..... ... .. .... ..... .
'. ": ... ...... ... .. . .... ....... .
.... . .. .. ....
. ...... .. ............. .
...... ......
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