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Temperature Dependent Mechanical Properties of Composite Materials and Uncertainties in Experimental Measurements

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Title:
Temperature Dependent Mechanical Properties of Composite Materials and Uncertainties in Experimental Measurements
Copyright Date:
2008

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Subjects / Keywords:
Composite materials ( jstor )
Diffraction patterns ( jstor )
Laminates ( jstor )
Residual stress ( jstor )
Room temperature ( jstor )
Shear modulus ( jstor )
Shear stress ( jstor )
Specimens ( jstor )
Temperature dependence ( jstor )
Temperature measurement ( jstor )

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University of Florida
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University of Florida
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7/30/2007

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TEMPERATURE DEPENDENT MECHANICAL PROPERTIES OF COMPOSITE
MATERIALS AND UNCERTAINTIES IN EXPERIMENTAL MEASUREMENTS















By

LUCIAN M. SPERIATU


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


2005

































Copyright 2005

by

Lucian M. Speriatu
































This dissertation is dedicated to my family.















ACKNOWLEDGMENTS

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

friendship. I would also like to thank my other committee members, Dr. Raphael Haftka,

Dr. Nicolae Cristescu, Dr. Bhavani Sankar and Dr. Fereshteh Ebrahimi, for their advice.

I thank William Schulz, Donald Myers, Thomas Singer, Dr. Leishan Chen, Ryan

Karkkainen, Dr. Theodore Johnson, and Ron Brown for their assistance in my efforts

throughout the years.
















TABLE OF CONTENTS

page

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

LIST OF TA BLES .............................. .......... .. .... ............ ........ .. ............ .. vii

L IS T O F F IG U R E S ........ .................. .. ................................................ .......... ........ v iii

LIST OF SYMBOLS AND ABBREVIATIONS ..................................................... xii

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

CHAPTER

1 IN TR OD U CTION ............................................... .. ......................... ..

1.1 B background .................... .. .............................. ........ .. .... .......... 1
1.2 M oire Interferom etry ............................................................ ......................... 4
1.3 Digital Image Processing and Fringe Analysis................................ ..... ......6
1.4 Temperature Dependent M easurements ...................................... ............... 8
1.5 Research M otivation and Objectives................................................................... 9

2 TEMPERATURE DEPENDENT TRANSVERSE MODULUS
EXPERIMENTAL MEASUREMENTS ........ .......................12

2.1 Introduction ....................................... .. ... ..... ....... .. ............ 12
2.2 Characterization of Transverse M odulus.............................. .. .......... ........ 14
2.3 Experim mental Setup.................. .... .......... ... .......... .... ............. 15
2.4 Experimental Procedure and Results...... .................... ..............24
2.5 Conclusions.............................31... .........31
2.6 D discussion and Future W ork ........................................ .......................... 32

3 TEMPERATURE DEPENDENT SHEAR MODULUS EXPERIMENTAL
M E A SU R E M E N T S ................................................ ......... .............. .......................36

3.1 Characterization of Shear M odulus ........................................... ............... 36
3.2 Double Notch Shear Specimen (DNSS) for G12 Testing...............................39
3.3 Experim mental Setup.................. .... .......... ... ............ .... ............. 47
3.4 Experimental Procedure and Results...................................... ......... ............... 47
3 .5 C o n clu sio n s.................................................. ................ 5 3









3.6 D discussion and Future W ork ........................................ .......................... 54

4 RESIDUAL STRESSES IN LAMINATED COMPOSITES.................................58

4.1 Introduction .............................................................................. 58
4.2 Cure Referencing M ethod................................. ........................................ 59
4.3 Residual Stresses and CTE Measurements....................................................63
4 .3.1 D ata A naly sis............ ...................................................... ...... .... .... 64
4.3.2 Experim ental R esults........................................................ ............... 68
4 .4 C o n clu sio n s....................................................... ................ 7 3
4.5 D discussion and Future W ork ........................................ .......................... 74

5 EXPERIMENTAL CHARACTERIZATION OF LOADING IMPERFECTION
ON THE BRAZILIAN DISK SPECIMEN......... ..................... 76

5.1 Introduction ............................................................................ .................... .........76
5.2 Experim ental Procedure................................................ ............................ 78
5.3 E xperim mental R results ........................................................... ......................... 83
5.3.1 Angle Dependent Displacement Fields ............................................... 83
5.3.2 Comparison to the FEA ................................ ............... 85
5.3.3 Plastic Zones Ahead of the Crack Tips ............ ................................. 87
5.4 Effect of Load Misalignment in the Linear Range ..........................................89
5.5 Effect of Load Misalignment in the Plastic Range.................... ...... .........94
5.6 J-Integral Estimation Procedure, Experimental Analysis..................................95
5.7 A lignm ent Procedure ................................................................. ............... 99
5.8 Discussions and Recommendations ............... ............................................ 104
5 .9 C o n clu sio n s................................................. ................ 10 5

6 REDUCING UNCERTAINTIES IN EXPERIMENTAL MEASUREMENTS TO
REDUCE STRUCTURAL WEIGHT ........................................... ............... 106

6.1 Experimental Errors and Uncertainty ...................................... ............... 106
6.2 Reducing Uncertainties in Experimental Measurements..................................109
6.3 Uncertainty Analysis for E2 and G12 Measurements .................... ........110
6 .4 C on clu sion s...................................................... ................ 12 4
6.5 D discussion and Future W ork ........................................ ......................... 124

7 CONCLUSIONS ................................... .. .. ........ .. ............127

APPENDIX: MATLAB CODE FOR PLOTTING TEMPERATURE VS.
TRANSVERSE MODULUS:........................................... ......... ....129

L IST O F R E FE R EN C E S ......... .. ................... ..................................... .......................134

BIO GRA PH ICAL SK ETCH .................................... ........... ................. .....................142
















LIST OF TABLES


Table page

2-1 Width and average thickness measurements for all tested specimens ...................27

2-2 The mean, standard variation and coefficient of variation at each temperature for
all tested specim ens .............................................. .. ........ .. ........ .... 31

3-1 Length and average thickness measurements for all tested specimens ..................50

3-2 The mean, standard variation and coefficient of variation at each temperature for
all tested specim en s .. ........................................................... .. .. .......... .... 53

4-1 Strain at cure temperature due to chemical shrinkage (CS)...................................70

6-1 U uncertainty from the load cell.................................................................... ..... 112

6-2 Percent difference found in measuring known weights ................ ................ 112

6-3 Uncertainty from measuring the width and thickness of the specimens ..............13

6-4 Percent difference found in measuring temperature ............................................114

6-5 Measurement variability of cross-sectional area in few specimens ....................1.17

6-6 Percent difference in E2 by including specimens with different speed of testing .119
















LIST OF FIGURES


Figure page

1-1 X -33 reusable launch vehicle ....................................................

1-2 Schematic description of four-beam moire interferometer to record the Nx and Ny
fringe patterns, which depict the Uand Vdisplacement fields ................................6

1-3 Failure of the outer skin of the LN2 tank of the X-33 RLV...............................10

1-4 Effect of Sltlt variability on tank wall thickness................................................... 11

2-1 Experimental setup: MTI testing machine, environmental chamber, data
acquisition system ........................... .................. ................... .. ..... 16

2-2 Detailed drawing of the grip, top (left) and side (right) views..............................17

2-3 Front (left) and side (right) views detailed drawings of the connecting rod............17

2-4 Detailed drawing of the aluminum alignment fixture, top (left) and side (right)
v iew s ...................................... .................................................... 1 8

2-5 3D AutoCAD schematic of one of the two grips ..............................................18

2-6 Schematic view of the alignment fixture for specimens with grips .........................19

2-7 Detailed drawing of the alignment fixture for specimens with grips, top (left)
and side (right) view s ...................... ...... ............ ................... .. ...... 20

2-8 Alignment fixture with specimen and grips .................................. ............... 21

2-9 Gripping fixture and specimen in alignment tool..................................................21

2-10 Thermal chamber and LN2 dewar................................ ......................... ........ 22

2-11 Rohacell thermal chamber with specimen, open (left) and closed (right)...............23

2-12 Transverse modulus panel with cut specimens ................................ ............... 25

2-13 Quarter-bridge circuit diagram ...................................................... ..... .......... 26

2-14 Transverse modulus as a function of temperature for all tested specimens ............29









2-15 Linear fit for the transverse modulus as a function of temperature..........................30

2-16 Transverse modulus as a function of temperature with linear fit and extra data
fro m literate re .................................................................. ................ 3 4

3-1 Iosipescu's specim en in the loading fixture........................................ ..................38

3-2 Variation of Gx with the fiber orientation angle ............................................. 41

3-3 Shear stress (S12) distribution for specimen with 00 oriented notches ...................44

3-4 Transverse stress (S22) distribution for specimen with 00 oriented notches.............44

3-5 Shear stress (S12) distribution for specimen with 450 oriented notches ...................44

3-6 Transverse stress (S22) distribution for specimen with 450 oriented notches...........45

3-7 Shear stress (S12) distribution for specimen with 600 oriented notches ...................45

3-8 Transverse stress (S22) distribution for specimen with 600 oriented notches...........45

3-9 Shear stress (S12) distribution for specimen with rounded notches........................46

3-10 Transverse stress (S22) distribution for specimen with rounded notches .................46

3-11 Shear stress (S12) distribution for the DNSS specimen..........................................47

3-12 Transverse stress (S22) distribution for the DNSS specimen............................ 47

3 -13 D N S S sp ecim en s ........................................................................... ....................4 8

3-14 The shear gage ................................ ........ .. ........ ......... 49

3-15 H alf-bridge circuit diagram ......................................................... .............. 49

3-16 Shear modulus as a function of temperature for all tested specimens....................52

3-17 Linear fit through the data points for the shear modulus as a function of
tem perature ..................................... ................................ ........... 52

3-18 Shear modulus as a function of temperature with linear fit and extra data from
th e literate re ................................................... ................ 5 7

4-1 Schematic of the replication technique ........... ...............................................61

4-2 Method of attaching the diffraction grating to the composite in the autoclave........62

4-3 Cure cycle for laminated composites in autoclave............................................62









4-4 Typical horizontal and vertical fringe patterns................................. .....................64

4-5 Example of counting fringes to determine surface strains ....................................65

4-6 CCD cam era ............................................................... ... .... ......... 66

4-7 Specially designed stage for fringe shifting .................................. ............... 67

4-8 Experim mental setup for fringe shifting ........................................ .....................68

4-9 Temperature dependent average strains for different laminate configurations........69

4-10 Temperature dependent CTEs for different laminate configurations.....................70

4-11 Effect of chemical shrinkage on residual stress calculation.............. ........... 72

4-12 Effect of chemical shrinkage and temperature dependent properties on residual
stress calculation ......................................................................73

5-1 Schematic description of the Brazilian disk............................................79

5-2 Loading fixture, actual specimen and digital inclinometer.............................. 81

5-3 Tilting fixture, interferometer and digital inclinometer .......................................82

5-4 Front (a) and side (b) view description of the specimen for in-plane and out-of-
plane m isalignm ent cases ........................................ ...................... .....................82

5-5 Displacement fields for mode I loading, U (a) and V (b) ........................................84

5-6 Displacement fields for mixed mode loading, U (a) and V (b) ................................84

5-7 Displacement fields for mode II loading, U (a) and V (b) .......................................85

5-8 Comparison between Moire (top) and FEA (bottom) results for U (a) and V (b)
displacem ent fields, m ode I loading................................. .......................... 86

5-9 Comparison between Moire (top) and FEA (bottom) results for U (a) and V (b)
displacement fields, mixed mode loading ........................................... ..........87

5-10 Horizontal and vertical fringe patterns showing the plastic zones formed around
the crack tip for m ode I loading ........................................ ......................... 88

5-11 Horizontal and vertical fringe patterns showing the plastic zones formed around
the crack tip for mode II loading ................ ............... ... ............... 88

5-12 Effect of in-plane misalignment on before and after misalignment.........................90

5-13 Effect of out-of-plane misalignment before and after misalignment .....................91









5-14 Effect of in-plane misalignment on the V field ....................................................93

5-15 Effect of out-of-plane misalignment on the V field ...........................................93

5-16 Horizontal and vertical fringe patterns showing the plastic zones around the
crack tips for an intentionally misaligned specimen loaded in mode I ..................94

5-17 Horizontal and vertical fringe patterns showing the plastic zones around the
crack tips for an intentionally misaligned specimen loaded in mode II...................95

5-18 Strains values at different data points along the path for an in-plane misaligned
specim en ..................................... .................................. ......... 96

5-19 Strains values at different data points along the path for an out-of-plane
m isaligned specim en ......................... ....... .... .. ...... ............ 97

5-20 Upper and lower crack J-integral difference variation with in-plane
m isalignm ent ............................................................... .. .... ......... 98

5-21 Upper and lower crack J-integral difference variation with out-of-plane
m isalignm ent ............................................................... .. .... ......... 99

5-22 Front view of aluminum Brazilian disk specimen with attached strain gages and
le a d w ire s ..................................................................... 1 0 0

5-23 Schematic description of the alignment procedure, step 1...................................102

5-24 Schematic description of the alignment procedure, step 2...................................102

5-25 Schematic description of the alignment procedure, step 3................................... 102

6-1 Variation of Ex/E12 with fiber orientation ........... ..............................114

6-2 Variation of Gx with fiber orientation............................. ............... 115

6-3 Speed of testing effect on the transverse modulus .............. ...... .................... 118

6-4 Transverse modulus variation with temperature for two runs of the same
specimen ............... ....... ....................... .................. 120

6-5 Transverse modulus with 1.29% error bars...............................................122

6-6 Shear m odulus with 1.40% error bars ........................................ ............... 123















LIST OF SYMBOLS AND ABBREVIATIONS

A Cross-sectional area

ASTM American Society for Testing and Materials

BDS Brazilian Disk Specimen

CCD Charge Coupled Device

CLT Classical Lamination Theory

CNC Computerized Numerical Control

COD Crack opening displacement

CRM Cure Reference Method

CS Chemical shrinkage

CTEx Coefficient of thermal expansion in the x-direction

CTEy Coefficient of thermal expansion in the y-direction

CV Coefficient of Variation

DNSS Double Notch Shear Specimens

E1 Lamina elastic modulus in fiber direction

E2 Lamina elastic modulus in transverse direction

EDM Electrical Discharge Machining

f Frequency of the diffraction grating

FEA Finite Element Analysis

FO Fiber orientation

G12 Lamina shear modulus









LN2 Liquid nitrogen

M Misalignment

MTI Measurements Technology Inc.

NASA National Aeronautics and Space Administration

Nx Fringe order in x-direction

Ny Fringe order in y-direction

OAP Optimized Angle Ply

P Applied load

PEMI Portable Engineering Moire Interferometer

Q Ply stiffness matrix

R2 Regression coefficient

RLV Reusable Launch Vehicle

S12 Shear stress

S22 Transverse stress

SCXI Signal Conditioning eXtensions for Instrumentation

Sn- Sample standard deviation

T Temperature

t Thickness of the specimen

T, Temperature

T2 Temperature

TD Temperature dependent

Td Temperature diode

tip Uncertainty in the thickness measurements from instrument precision









tuv Uncertainty in the thickness measurements from user variability

U Horizontal displacement

UNI Unidirectional

V Vertical displacement

w Width of the specimen

wip Uncertainty in the width measurements from instrument precision

wuv Uncertainty in the width measurements from user variability

x-y Coordinate system aligned with laminate 0 (x) and 90 (y) directions

Shear strain in the x-y coordinate system

AT Temperature difference

1-2 Coordinate system aligned with lamina fiber (1) and transverse (2) directions

a Experimentally measured CTE

+45 Measured strain in the +450 direction

E2 Transverse strain

E2ult Ultimate transverse strain

e-45 Measured strain in the -45 direction

Echem Chemical shrinkage vector of a unidirectional panel, 3x1

Eun Strain vector on a unidirectional panel in the x-y system, 3x1

Ex Strain in the x-direction

Ey Strain in the y-direction

esg Uncertainty in the strain gage

0 Angle between x-y and 1-2 coordinate systems

v12 Lamina Poisson's ratio.










a2 Transverse stress

Ures Residual stress vector in the 1-2 coordinate system, 3x1

r Shear stress















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

TEMPERATURE DEPENDENT MECHANICAL PROPERTIES OF COMPOSITE
MATERIALS AND UNCERTAINTIES IN EXPERIMENTAL MEASUREMENTS

By

Lucian M. Speriatu

August 2005

Chair: Peter Ifju
Major Department: Mechanical and Aerospace Engineering

A new method for efficient determination of multiple material property values and

improved techniques for reduction in experimental uncertainty were developed for use on

composite and lightweight materials that perform under extreme temperatures and

sustained load. The method calls for use of tension specimens only in determining the

material properties, using a specially designed chamber with both cryogenic and high

temperature testing capabilities. Mechanical properties of fiber reinforced composite

materials were determined, such as transverse modulus (E2) and shear modulus (G12).

Specially designed double notch tension specimens and shear strain gages were used to

determine the shear properties in composites in a unique and more efficient way. A

robust set of data from cryogenic to elevated temperatures for the two material properties

of fiber reinforced composite materials was obtained and reported.

The fracture behavior of single crystal metallic materials was also investigated at

room temperature. The Brazilian Disk Specimen (BDS) was proposed to study mode I,









mode II and mixed mode fracture of these materials. During the study, questions arose

concerning the effect of load misalignment on the stress field at the crack tip and crack

propagation. To isolate the loading effects from the crystallographic effects, a systematic

experimental study was conducted on aluminum specimens to characterize the effect of

load misalignment and specimen orientation in the linear range as well as in the plastic

range.














CHAPTER 1
INTRODUCTION

In the development of new structural materials, it is first required to perform a

detailed mechanical characterization to be able to implement these materials into an

improved, optimized component design. Current techniques require several different tests

and specimen types to achieve a complete thermo-mechanical characterization.

Furthermore, each test and specimen is subject to inherent error types that led to

uncertainty in material property values. Thus, the current paper aims to establish a new

method for efficient determination of multiple material property values, as well as

improved techniques for reduction in experimental uncertainty.

1.1 Background

One of the primary goals of engineers has been to develop new lighter materials

with improved properties, such as strength, toughness and heat resistance, which can be

used in the design of engineering structures. One answer came in the form of so called

composite material [1], which is by definition a material that consists of two or more

materials combined at the macroscopic scale and that is superior to the constituents

themselves.

Fiber reinforced composites are a special type of composite that have become more

and more popular these days, since it has been demonstrated that some materials are

stronger in the fiber form than in the bulk form. Fiber reinforced composites offer

numerous advantages over the conventional materials, but they also have shortcomings









such as poor material performance in the transverse direction and poor out-of-plane

properties.

Although the basic man-made composites have been around for thousands of years,

the introduction of fiber-reinforced composites in structural design in 1960s has

generated the need to develop new testing methods and procedures to characterize these

materials. Assessment of their performance under thermo-mechanical loading would

increase their reliability and allow for a better design of engineering structures, especially

those in aerospace applications.

Although these laminated fiber reinforced composite materials were predicted to

become the materials of choice in such applications, aluminum is still predominantly

used. This is partially due to the lack of experimental data in the mechanical properties of

composites and is also because their behavior is not yet fully understood.

In the pursuit of space exploration, efforts have been underway to replace the aging

space shuttle with a newly developed reusable launch vehicle (RLV). This vehicle would

provide a reduction in the cost of launching payloads into space from $10,000 to $1,000

per pound. This would be possible only by reducing the overall structural weight of the

vehicle by using lightweight materials such as fiber reinforced composites.

This vehicle would also have to be entirely self-contained throughout the mission.

The development of the X-33 reusable launch vehicle [2], shown in Fig. 1-1, tried to

achieve all those goals.

The X-33 had two internal liquid hydrogen fuel tanks made of composite materials.

While the choice of such materials in this application seemed appropriate at the time, the

preflight testing in the fall of 1999 at NASA Marshall Space Flight Center for verification









of the tanks at cryogenic loading condition of -4230F revealed micro-cracking that later

led to failure of the liquid hydrogen tanks.





















Figure 1-1. X-33 reusable launch vehicle

Recently, Bechel et al. [3] performed a study on different polymer matrix

composites, including the IM7/977-2 that was used in the X-33 project, by thermally

cycling the structural composites from cryogenic to elevated temperatures. The

investigated composites rapidly developed micro cracks when subjected to combined

cycling, i.e., cryogenic to elevated temperatures.

Thus to safely use fiber reinforced composites in such applications, we need a

methodology to predict multiple mechanical properties of fiber reinforced materials as a

function of temperature as well as to understand their temperature dependent behavior.

The determination of elastic constants of a composite material is significantly more

complicated than the determination of these constants for an isotropic material. In view of

the fact that design of composite structures achieves a reduction in weight and an









improvement in strength and toughness, a major effort has to be put in the development

of standard test methods for material property characterization.

1.2 Moire Interferometry

Even though laminated composites are widely used in aerospace applications

because of their high strength-to-weight ratio, there are numerous shortcomings that

designers have to overcome when using such materials. One important shortcoming is the

development of the residual stresses within the laminate. These stresses form due to the

matrix solidification around the reinforcement or due to mismatch in the coefficients of

thermal expansion between the fiber and the matrix.

A non-destructive method is used in conjunction with the moire interferometry [4]

technique to determine the surface strains and the coefficients of thermal expansion in

laminated composites, as will be explained in Chapter 4. Because the moire

interferometry technique plays a key role in the determination of accurate temperature

dependent residual stresses in laminated composites it was considered necessary to

introduce the method and present its principle of operation.

Moire interferometry is a laser based optical technique that combines the concepts

of optical interferometry and geometrical moire. It is a full-field technique capable of

measuring the in-plane displacements with very high sensitivity (sub-micron level). This

measurement technique uses the interference effect between a (virtual) reference grating

and a specimen grating to magnify the surface deformations and creates a moire fringe

pattern which is related to surface displacements. The relationship between fringe order

and displacement is shown in Eqs. (1-1) and (1-2):


U(x,y)= N (x,y) (1-1)









V(x,y)= 1 N,(x,y) (1-2)
f

where Uand V are the horizontal and vertical displacement fields, Nx and Ny are the

fringe orders corresponding to the horizontal and vertical displacement fields, andfis the

frequency of the reference grating.

Using the relationships between displacements and engineering strains we get Eqs.

(1-3) to (1-5):


E=U_ IlNlx (1-3)
ax x f Ox


; (1-4)


8U V 1 O8N oN,
7 =-- +- =I +x-Y- (1-5)
8y ax f 8y ax

where ex,Sy, are the strains in the x andy directions respectively, and ", is the shear strain.

A schematic description of the moire interferometry is presented in Fig. 1-2.

There are numerous configurations of optical and mechanical components that

produce the four beams illustrated in Fig. 1-2. The entire ensemble that produces these

four-beams is called a moire interferometer.

The applications of the moire interferometry include determination of the thermal

deformations in microelectronic devices, determination of the coefficient of thermal

expansion, characterization of the fiber-reinforced polymer matrix composite materials,

fracture mechanics, micro-mechanics.

Moire interferometry has also been used to validate models, estimate reliability,

and identify design weakness.











x


5,4

Figure 1-2. Schematic description of four-beam moire interferometer to record the Nx and
Ny fringe patterns, which depict the Uand Vdisplacement fields

1.3 Digital Image Processing and Fringe Analysis

The result of the moire interferometry technique appears as a set of fringe patterns,

or contour maps, of displacement. These fringe patterns have to be documented, analyzed

and interpreted. For many years, the analysis of the fringe patterns was performed by

locating the positions and numbering the fringes manually. Because of the development

and decreasing cost of the digital image processing equipment [5], the digital image

fringe pattern techniques are increasingly used in acquiring strains and stresses. The

reasons for implementing this method are to improve the accuracy, to improve the speed,









and to automate the process. Ultimately, it is the intent to eliminate the human factor by

automatically detecting the positions of the fringes.

The digital image processing system consists of a CCD camera and a frame

grabber. The CCD camera is used to scan the fringe pattern. The frame grabber, which is

a video digitizer, digitizes the image and stores it into the computer memory. Then by

using different techniques, the fringe order is calculated and an image output is produced.

This combination of the digital camera, frame grabber and computer made it very easy to

record and manipulate the images.

These image manipulations are performed on the individual pixels. Many fringe

analysis procedures were developed based on different algorithms [6]. Ultimately the

fringe pattern dictates the validity and applicability of a specific algorithm. For

complicated fringe patterns and with a high fringe frequency, the algorithm used may not

detect the fringes accurately, which can lead to erroneous results. An image of a simple

fringe pattern with low fringe frequency is easier to manipulate and provides more

accurate output.

Recently, more powerful algorithms and procedures were developed to

dramatically reduce the output errors, making this automated fringe analysis a quick and

efficient tool in the analysis of the moire fringe patterns.

This is why digital image processing is increasingly used in applications that

require the use of moire interferometry but is not limited to this area. In a recent paper by

Kishen et al. [7], biomedical engineers have investigated the human dentine using a

digital speckle pattern interferometer and thermography, in conjunction with an advanced

digital fringe processing technique, to analyze its deformation when subjected to









temperature changes. Spagnolo et al. [8] presented a full digital speckle photography to

measure free convection in liquids together with a fast Fourier transform algorithm to

compute the fringe patterns and speckle displacement, and Ramesh et al. [9] investigated

the possibility of using the hardware features of a color image processing system for

automated photo elastic data acquisition. And although the greater part of the researchers

are simply users of the digital image processing systems, there is continuous research

undergoing for the improvement in both the hardware and the algorithms used, thus

increasing the accuracy of the method. In the end, an automation of the method for an

easier manipulation of the results as well as a more accurate output is obtained.

1.4 Temperature Dependent Measurements

Some of the latest applications in aerospace engineering require that new structural

materials perform under extreme temperature and load conditions; therefore a huge effort

is made to characterize the thermo-mechanical behavior of such materials. Temperature

dependent experimental measurements on composite and lightweight materials remain

relatively undeveloped. To correctly predict their behavior as well as to be able to

integrate them into an optimization scheme to perform probabilistic analysis and design,

the temperature dependence must be known accurately.

Unfortunately, there is not enough information available on the temperature

dependent mechanical properties of different materials used in aerospace applications.

This is usually because no standard methods exist that will help researchers determining

these properties. Another important reason is that current methods and techniques are

inefficient and expensive giving little option to designers; they are forced to use in the

design of engineering structures room temperature properties and minimum information

collected at cryogenic and elevated temperatures. Temperature dependent data









measurements, for fiber reinforced composite materials in particular, are unexploited and

some of the temperature dependent data for material properties such as shear and

transverse moduli are of special interest.

1.5 Research Motivation and Objectives

Composite materials are increasingly used in aerospace applications. A recent goal

of NASA was to replace the aged space shuttle with lighter vehicles that can achieve a

ten times reduction in the cost of the payload by incorporating composite and lightweight

materials in the vehicle's design. Since composites have a high strength-to-weight ratio,

all-composite tanks for cryogenic storage have become of great interest for researchers.

However, NASA's X-33 project, which incorporated LN2 tanks made of fiber-reinforced

composites, unfortunately failed, as seen in Fig. 1-3, because of microcracking of the

tank walls. Lack of information about material behavior under extreme temperatures and

sustained load was one of the main contributors to this failure. At the moment, besides

working on new manufacturing techniques and novel curing processes, substantial effort

is underway to characterize the temperature-dependent behavior of fiber reinforced

composite materials.

Thus, there is currently a need for methods and techniques to perform simpler and

more efficient tests on composite materials to determine their temperature dependent

mechanical properties. This paper aims to develop such a method for efficient

determination of different material property values as a function of temperature, before

the implementation of the laminated composites in engineering structures.

On the other hand, measurement variability is a key factor that accounts for an

increased safety factor to ensure reliability.











































Figure 1-3. Failure of the outer skin of the LN2 tank of the X-33 RLV

This variability in the material properties translates into a heavier vehicle. A

previous LN2 tank optimization study, as discussed in Chapter 4, showed the effect of

variability on tank wall thickness. Fig. 1-4 shows that by reducing the variability in the

ultimate transverse tensile strength (12ult) by 10%, the thickness is reduced by about 15%

for the same probability of failure of 1 in 1,000,000. Thus, using a probabilistic design,

which is based on the probability of failure, we can minimize the weight of the vehicle.






11



100
-*- Nominal
10 ---- 10% reduction in variability


10-2 i


4 1 0 .3 14


S10- -
r -4
Z 10 % %




10
10-


10-7


0.06 0.08 0.1 0.12 0.14 0.16

Thickness (in)
Figure 1-4. Effect of E2ult variability on tank wall thickness

The objectives of this dissertation are to establish a simple and more efficient

testing method for determination of multiple material property values as a function of

temperature, to improve techniques for reduction in experimental uncertainty, as well as

to reduce the variability and uncertainty in the experimental measurements.














CHAPTER 2
TEMPERATURE DEPENDENT TRANSVERSE MODULUS EXPERIMENTAL
MEASUREMENTS

2.1 Introduction

Temperature dependent experimental measurements on composite and lightweight

materials remain relatively undeveloped. To correctly predict the behavior of these

materials, as well as to be able to integrate them into an optimization scheme to perform

probabilistic analysis and design, the temperature dependence must be known accurately.

Takeda et al. [10] employed three-dimensional finite elements to examine the

thermo-mechanical behavior of cracked G- 11 woven glass/epoxy laminates with

temperature-dependent material properties under tension at cryogenic temperatures.

Experimental studies [11-14] investigated the mechanical properties and the behavior of

different materials under cryogenic temperatures and Schultz [15] looked at the

mechanical, thermal and electrical properties of fiber reinforced composites at cryogenic

temperatures. In a study by Baynham et al. [16] the transverse mechanical properties of

glass reinforced composites at 4K were reported from tests using an improved specimen

design and also using finite element modeling techniques, and data on the properties of

composites at 4 K in a biaxial shear/tension situation were recorded for the first time.

In the past decade there were relatively a few studies on the temperature effects on

the mechanical properties of fiber-reinforced composites to investigate their applicability

for cryogenic use. Hussain et al. [17] studied the interface behavior and mechanical

properties of carbon fiber reinforced epoxy composites at room and liquid nitrogen









temperature. Glass [18] looked at the Gore-Tex woven fabric's mechanical properties and

determined them at ambient, elevated, liquid nitrogen, and liquid helium temperatures in

hope that they can contain gaseous helium at 60 psi. Shindo et al. [19] studied the

cryogenic compressive properties of G-1OCR and SL-ES30 glass-cloth/epoxy laminates

for superconducting magnets in fusion energy systems and experimentally investigated

the effects of temperature and specimen geometry on the compressive properties, and

Horiuchi et al. [20] considered carbon reinforced fiber plastics as supports for cold

transportable nuclear magnetic resonance cryostat and found the performance and

reliability of the cryostat to be acceptable.

But the mechanical properties of different materials used in aerospace applications

are usually determined at room temperature and used as a reference in the design of

engineering structures even when they are used in extreme environments. Sometimes

only a few data points are collected, usually one point at cryogenic temperature, one at

room temperature, and one at elevated temperature. However, this is not enough to

determine an accurate basic fitting curve of the investigated material property as a

function of temperature unless the trend is proved linear. Temperature dependent data

measurements, for fiber reinforced composite materials in particular, are unexploited and

some of the temperature dependent data for material properties such as shear and

transverse moduli are of special interest. Special configuration fiber reinforced

composites such as the IM7/977-2 of the X-33 reusable launch vehicle require systematic

experimental testing from cryogenic to elevated temperatures before it can be safely

implemented in an engineering structure that can withstand thermo-mechanical loading.

Unfortunately, an investigation of graphite/epoxy laminates for suitability of cryogenic









fuel applications was performed only after the failure of the X-33 project. Roy et al. [21]

examined the IM7/PETI-5 graphite/epoxy cross-ply laminate system to predict COD and

permeability in polymer matrix composites, and Bechel et al. [22] performed a study on

different polymer matrix composites, including the IM7/977-2 that was used in the X-33

project, to investigate micro cracking development due to thermal cycling from cryogenic

to elevated temperatures.

Future work on this problem seems to concentrate on the infusion of nano-particles

in the fiber reinforced polymeric materials to enhance their resistance to thermal cycling

induced stresses [23]. However, there is currently a need for methods and techniques to

perform more simple and efficient tests on composite materials to determine their

temperature dependent mechanical properties. This paper aims to develop such a method

for efficient determination of different material property values as a function of

temperature, before the implementation of the laminated composites in the engineering

structures.

2.2 Characterization of Transverse Modulus

ASTM 3039 [24] is currently the standard testing procedure for determining room

temperature longitudinal modulus and transverse modulus of composite materials.

However, since the goal of this research was to determine temperature dependent

transverse and shear moduli, a new and efficient experimental method was developed to

determine such material properties of composite materials as a function of temperature.

The method is capable of performing multiple tests such as El, E2 and G12, using a single

experimental setup. Temperature dependent mechanical properties such as E2 and G12 of

unidirectional IM7/977-2 panels were investigated and reported in this paper. This









chapter presents a characterization of the transverse modulus for the IM7/977-2 material

system.

2.3 Experimental Setup

The proposed testing method, which follows the ASTM 3039 guidelines for

material property determination of composite materials, had to be designed with the

understanding that we were dealing with extreme temperatures. Consequently,

improvements and additions to the ASTM setup were implemented resulting in the

development of a new testing procedure.

The setup consists of a compression-tension MTI type machine, a testing chamber,

an environmental chamber that regulates the temperature inside the testing chamber, a

liquid nitrogen (LN2) dewar, and a data acquisition system. Fig. 2-1 shows the entire

experimental setup.

A 30K compression/tension-testing machine from MTI Phoenix was used.

Since testing was performed under extreme temperature conditions, and since the

current ASTM grips present a large thermal mass, the first thing that had to be addressed

was the design of new, special grips that would be suitable for such application.

The mechanical drawings of the newly designed grips are shown in Fig. 2-2

through 2-4 and Fig. 2-5 shows a 3D AutoCAD schematic of the assembly. Each grip

assembly consists of a few elements; the main part is the one referred here as grip. There

are two such parts in the assembly. Each grip has a 1" x 1.8" grooved area that is

machined to achieve maximum gripping power. Also the design of the grips accounted

for obtaining a uniform distribution of the load to the specimen through the tabs attached

at the ends.



































t figure 2-1. Experimental setup: MIII testing machine, environmental chamber, data
acquisition system

One of the two grips has two drilled holes while the other one has two taped holes

that accommodate two 0.375" bolts. Both parts are heat-treated for hardness. On the

upper part of the grips there are holes that allow for a 0.5" diameter pin to go through and

hold in place a rod that connects to the MTI machine. Since the standard ASTM grips

have an alignment system that makes sure the load goes through the mid-plane of the

specimen, the newly designed grips were fitted with a so called alignment fixture that

achieves the same thing.

An aluminum block was machined using EDM, to slide on the connecting rod;

when pushed down the wedge type alignment fixture positions the two grips at same

distance from the center insuring that load goes through the mid-plane of the specimen.




























- 0.3S75



0.7750



00.3750

"- RO,2500


0,5000





L.5000

RO.10DO







0,7750







i4WLi


Figure 2-2. Detailed drawing of the grip, top (left) and side (right) views



















3,0000
00,5000 -

00500-------






005000


S 1.000

Figure 2-3. Front (left) and side (right) views detailed drawings of the connecting rod









1,5000



0,4000 0,5000 1,0000
7;


S 1,0000 0,5000

Figure 2-4. Detailed drawing of the aluminum alignment fixture, top (left) and side
(right) views


rod that connects to
the MTI machine


4 -- alignment fixture



S-.----- pin


grip


Figure 2-5. 3D AutoCAD schematic of one of the two grips









Because of misalignment concerns, an alignment fixture was also designed to align

the specimen with the grips. Misalignment is a very important factor that has to be

accounted for when testing materials. It can induce errors that are substantial to cause

premature failure or failure in a mode and/or direction that does not match prediction.

Since the temperature dependent transverse modulus determination procedure requires

the use of strain gages and since eliminating misalignment in the loading fixture

translates into eliminating errors read by the gages, it was considered necessary to have

such alignment fixture. This also achieves a more easy and efficient way to set up the

fixture with the grips and specimen for testing. Fig. 2-6 through 2-9 show the alignment

fixture with the grips and the specimen prepared for alignment.


Figure 2-6. Schematic view of the alignment fixture for specimens with grips





















































0.7650
i





2 3175


RaLnx --


LMftdO -


*6 A(0 -


7.90I]


C M O--


a s96: ---1


]9g[MIO 2D.MiiOD


Figure 2-7. Detailed drawing of the alignment fixture for specimens with grips, top (left)
and side (right) views












- --I.


Figure 2-8.


/ ->!ft
/P~D


fixture with specimen and grips


pr~c~


Figure 2-9. Gripping fixture and specimen in alignment tool

To regulate the temperature of the testing chamber, a liquid nitrogen (LN2) dewar

was attached to a Sun Systems Model EC12 environmental chamber, as seen in Fig. 2-10.

Using the incorporated heating elements and by taking in LN2, this chamber can easily

regulate the temperature in our range of interest, i.e., between -200C and +200C degrees.

Special insulated hoses connect the environmental chamber to the testing (thermal)


_ .. .









chamber and a blower transports the regulated air from the environmental chamber to the

testing chamber.

The testing (thermal) chamber was made of Rohacell 110-IG foam; this material

proved to have very good thermal insulation properties. The material proved also to be

very efficient and inexpensive; although it was designed to be a disposable chamber, only

one was machined and used for testing because it exhibited no deformation and/or lose of

properties even after numerous cryogenic to high temperature cycles. CNC machining of

the Rohacell foam was also very fast and efficient.

The thermal chamber was placed around the specimen and grips, as seen in Fig. 2-

11; tension straps helped holding it in place.


Figure 2-10. Thermal chamber and LN2 dewar
































Figure 2-11. Rohacell thermal chamber with specimen, open (left) and closed (right)

All MTI testing machines are equipped with a data acquisition system; however for

this application a new data acquisition system had to be implemented to accommodate all

the inputs such as strain gages, thermocouples, load cell, environmental chamber. In

order to do that, controls from the machine had to be redirected towards a more powerful

computer with SCXI modules from National Instruments. Regular setup for MTI type

machines cannot accommodate such application unless a custom built setup is requested

at the time of purchase. Therefore some modifications had to be made here; the crosshead

controls as well as displacement rate control were transferred from the MTI machine to

the new control system.

Thus a control box had to be installed; simply by turning ON/OFF a few switches,

the operator can switch from manual to new computer controls. An additional motorized

potentiometer was installed such that by turning the power ON the crosshead









displacement rate is automatically adjusted by the computer. The control box gives the

operator the choice of running the old data acquisition system, the new data acquisition

system or just having manual controls of the testing machine.

A NI SCXI-1121 four channel module was used to read gages, control loading, and

read the diode temperature sensor.

2.4 Experimental Procedure and Results

Specimens for temperature dependent transverse modulus determination were

prepared according to the ASTM 3039 standard and NASA recommendations. In order to

accommodate our newly designed grips and to allow a smother transition of the applied

loads to the test section, specimens were made longer than the standard suggested length.

Thus 12" long specimens were used. These specimens were obtained from 12" x 12", 18

layer unidirectional panels that were produced in our lay-up facilities. The panels made of

IM7/977-2 prepreg material were produced in the autoclave following the cure cycle, as

explained in Chapter 4, which was used for the RLV.

Using a diamond cutting wheel and then a surface grinder, four 12" x 1.6" x

1/16"strips of G-10 fiberglass were cut. We then bonded them to the panel using Hysol

9394 epoxy following the curing cycle supplied by the manufacturer. These fiberglass

strips provide tabs to the material. Attaching fiberglass strips to the entire panel was

considered over individual ones because of efficiency as well as future reduction in data

variability. These panels with the tabs were cut into 1.15" wide coupons using a

diamond-cutting wheel, as seen in Fig. 2-12. A surface grinder was then used to grind

both edges of the coupons to insure all the flaws produced during the cutting procedure

would be removed. These flaws are dangerous because they can initiate failure sooner

than expected. The process also allowed the specimens to reach a nominally width of









1.000" thus controlling better the cross-sectional area. The final dimensions of the

coupons were 12" x 1" x 0.9". Each panel and each coupon cut from the panel was

labeled such that a future variability analysis would be possible. This is described in

Chapter 6.

























Figure 2-12. Transverse modulus panel with cut specimens

Strain gaging technique is widely used today in many applications. As any

experimental technique strain gaging has its advantages and disadvantages. Used

correctly, the technique can accurately determine the surface strain on the object where

they are attached.

Strain gages are made of a very thin wire bonded to a foil (backing). When attached

to materials that experience mechanical and/or thermal loads, the strain gage will also

experience them. Consequently, a change in resistance of the gage will appear that can be

read using a quarter bridge configuration as shown in Fig. 2-13. This change in resistance








is then related back to strain. In extreme temperature conditions the gage itself and the

backing foil expand or contract and the strain values that are produced have to be

subtracted or added to the strains exhibited by the material tested. The contribution of this

so called apparent strain can be as much as 10%-15%. There are a few techniques that

allow removing this apparent strain. The technique that was used in this project will be

explained later on in this chapter.


RL
RR



V E V
1 R2


Figure 2-13. Quarter-bridge circuit diagram

Gage selection was made to handle the large temperature range, nominally +200C.

Therefore, WK-13-250BG-350 custom unidirectional gages were obtained through the

Vishay Micromeasurements Group. All the other required supplies to attach the gages to

the specimen, such as the M-Bond 610 epoxy adhesive, were also obtained from Vishay.

Specimens were prepared according to NASA recommended procedures for strain

gage application and ASTM standard.

Each specimen was first abraded, with varying grits of sand paper.

All the surface flaws were removed and a smooth finish surface was obtained to

allow for good gage adhesion.

The surface was cleaned with acetone and then two perpendicular marks were

inscribed for gage alignment with the specimen.









Acetone was used again for cleaning then any remaining impurities were removed

by dusting the air off the surface.

Thickness and width measurements were taken across the perpendicular mark on

the specimen. Three thickness measurements were taken, one in the center and two at

each side, according to the ASTM standard. The average of those three determined the

thickness of the specimen.

Table 2-1 shows the width and average thickness of each specimen:

Table 2-1. Width and average thickness measurements for all tested specimens
Specimen Width (in) Average
thickness (in)
p2-1 0.08050 1.00100
p2-2 0.09000 0.98700
p2-3 0.08800 0.99500
p2-4 0.08650 1.00250
p2-5 0.09000 1.00100
p2-7 0.08300 0.99500
p2-8 0.09000 0.99600
p2-9 0.08900 1.00100
p3-1 0.08400 0.99950
p3-2 0.08700 0.99970
p3-3 0.08683 0.99850
p3-4 0.08663 1.00180
p3-5 0.08700 1.00100
p4-1 0.08365 1.00030
p4-2 0.08656 1.00120
p4-3 0.08796 0.99985
p4-4 0.08761 1.00055


Using a microscope, a gage and strain relief tabs were aligned to the inscribed

marks then a Teflon tape was used to temporarily attach them to the specimen. The

undersides of the gage and strain relief tabs were exposed and together with the









specimen's surface they were coated with a thin layer of M-Bond 610 adhesive. After a

ten-minute drying period the gage and the tab were placed back on the specimen and

clamped with uniform pressure. The specimen was cured for three hours at 1210C then

post-cured for another two hours at 1350C.

Once the specimen was gaged, wires were soldered to the tabs and connected to the

SCXI module, it was fixed to the grips using the alignment fixture. A temperature diode

was taped to the specimen together with the environmental chamber's thermocouple. The

entire ensemble was positioned into the MTI machine then the specially designed testing

chamber was placed around it and connected to the environmental chamber.

The actual test was started and run as follows: a Labview program developed for

this application was initiated which turned ON the environmental chamber and

commanded it to reach -165C degrees. A blower circulated the air from the

environmental chamber to the testing chamber to cool down the specimen inside it. Once

it reached the commanded temperature, the specimen was allowed to soak for 23 minutes

to reach an equilibrium temperature. When the equilibrium temperature was reached, the

load cell and strain gages were zeroed out using the Labview program developed, then

the specimen was loaded to 200 lb and unloaded to 0 lb for five consecutive times. Each

specimen was tested at approximately 250C intervals, from -165C to +1500C.

After all the 14 measurements were recorded, a Matlab code [appendix]

manipulated the data to obtain the average slope of the five curves at each temperature.

Knowing the slope and the cross-sectional area allowed for transverse modulus

determination such as in Eqs. (2.1) to (2-3):

2 = E2E2 (2-1)










(2-2)


(2-3)


E2 =A
AE2


where P is the applied load and A is the cross-sectional area of the specimen. Thus the

transverse modulus is obtained from the slope of the load vs. strain curve, divided by the

cross-sectional area of the specimen.

Fig. 2-14 shows all the temperature dependent transverse modulus curves for all

tested specimens and Fig. 2-15 shows a linear fit through all the data points. This basic

fitting will be used in Chapter 4 to predict residual stresses for different laminate

configurations.


1.2 -


1.1 -


x 1101


0.9


0.8


-200 -100 0 100 200

Temperature (oC)
Figure 2-14. Transverse modulus as a function of temperature for all tested specimens









x 0101
1.3-1-1--
S* experimental data
basic linear fitting
1.2 ,


w 1.1
c3


9 1 1



S0.9
0.8



O-00 -100 0 100 200

Temperature (oC)
Figure 2-15. Linear fit for the transverse modulus as a function of temperature

The equation of the straight line and the regression coefficient are presented in Eqs.

(2-4) and (2-5):

E2(T)= -0.016127 T+ 9.6744 GPa (2-4)

R2 = 0.9746 (2-5)

For statistical purposes, the coefficients of variation (CV) were computed for all the

tests and presented in Table 2-2. ASTM standard requires also that this data be

determined every time a series of tests are conducted. The average transverse modulus

and the standard deviation are used to compute the coefficients of variation at each

temperature. The formulae used will be presented in Chapter 6, where a more detailed

statistical and uncertainty analysis will be performed.









Table 2-2. The mean, standard variation and coefficient of variation at each temperature
for all tested specimens
Temperature (C) Mean E2 SN-1 CV %
-165 1.25E+10 1.67E+08 1.33
-145 1.22E+10 1.40E+08 1.15
-125 1.19E+10 1.74E+08 1.46
-100 1.14E+10 2.20E+08 1.93
-75 1.07E+10 1.73E+08 1.61
-50 1.02E+10 1.61E+08 1.58
-25 9.81E+09 1.83E+08 1.87
+0 9.42E+09 1.93E+08 2.05
+25 9.00E+09 1.66E+08 1.85
+50 8.64E+09 1.46E+08 1.69
+75 8.40E+09 1.48E+08 1.77
+100 8.19E+09 1.66E+08 2.03
+125 7.92E+09 2.10E+08 2.65
+150 7.55E+09 1.60E+08 2.12


2.5 Conclusions

A new and efficient method was developed for temperature dependent material

property determination. The method was used to successfully determine the transverse

modulus as a function of temperature for the unidirectional IM7/977-2 composite

material. The method is fully automated and once a test is started do not require

supervision. Specimens were easily fabricated using our facilities. Over twenty tests were

performed during which the method proved to be very repeatable. A robust set of data

was obtained using 14 points along the temperature range, i.e., -165C to +1500C for

each specimen. Each single test lasted approximately 9 hours and used less than half of

tank of LN2. An increased number of data points, up to 28, can be used from a single LN2

tank, thus without requiring any user intervention, if a more accurate representation of the

transverse modulus is desired.









Besides characterizing the material behavior, the transverse modulus property of

the IM7/977-2 will be used in a modified Classical Lamination Theory (CLT) Matlab

code developed at the University of Florida; together with other mechanical properties

this will be useful to predict more accurately the behavior of multidirectional laminates.

2.6 Discussion and Future Work

This chapter described in details the experimental setup and procedure developed to

obtain the temperature dependent transverse modulus for a particular fiber-reinforced

polymer matrix composite material. The newly devised method was employed to test

more than fifteen different specimens to obtain a robust set of data.

Figure 2-15 shows the nonlinear behavior of the material investigated. Although a

straight line was fitted through the data points and the equation was used later on to

predict residual stresses, a higher order polynomial will be more representative. One can

also speculate how the material will behave outside the temperature range where data was

collected. Other polymer matrix composite materials that have been tested [53] at

cryogenic temperatures showed a pronounced deviation from linearity in the modulus

starting at liquid nitrogen temperature all the way to liquid helium temperatures. One

possible explanation would be crack formation and crack propagation within the

laminate. The temperature range initially considered for this research was from liquid

nitrogen temperatures (-1960C) to cure conditions (+1820C). However, the actual tests

were performed from -165C to approximately +155C. At the lower end of the

temperature range, imperfect insulation of the system, including the testing chamber, did

not allow the specimen to efficiently reach an equilibrium temperature below -1700C. In

the future a better insulation of the system and/or use of liquid helium should be









considered to be able to perform more tests and obtain data below -1650C; this will also

provide more data to identify the best fitting method to accurately predict material

behavior. Close to cure temperatures, the resin will reach the glass transition temperature

which will probably change the properties of the composite. However, since no other

measurements are taken after the elevated temperature data is collected there is no reason

why the temperature range should not be increased. On the other hand, performing tests

above +155C would probably show a huge drop in the modulus but the information

would not be vital since the material was intended for cryogenic environments only.

The author searched through the literature to find experimental data for the

IM7/977-2 material to compare its findings but unfortunately found [3] extremely limited

data. Only two data points are available, one at room temperature and the other one at

liquid nitrogen temperature. These two points are shown in Fig. 2-16 together with the

data obtained at University of Florida. When a straight line is fitted through those data

points, a better match with the data from Wright Patterson AFB is obtained. A significant

difference will be obtained when a higher order polynomial will be used.

Two questions surfaced once the comparison was performed: first, which data is

accurate and therefore should be trusted and second, since the specimens were first

subjected to cryogenic temperatures and then the data was collected, does the thermal

history affect the room temperature measurements? With respect to which data is more

accurate, the author stands by the current findings. In Chapter 6, it will be shown that the

method was calibrated and then tested on aluminum specimens with extremely good

results. For liquid nitrogen temperature, a real comparison cannot be performed since no

experimental data was obtained. Future work should concentrate on obtaining such data.











experimental data
basic linear fitting
1.2 U Wright Pat AFB data


UJ 1.1


o 1 "


0.9
,I-
S0.8


0.7
-200 -100 0 100 200

Temperature (oC)
Figure 2-16. Transverse modulus as a function of temperature with linear fit and extra
data from literature

But the room temperature measurements are of special interest since they might be

a function of cycling the material from cryogenic to elevated temperatures. As

mentioned, the specimens tested here were first exposed to cryogenic temperatures and

then data was collected as temperatures were increased. This seems to affect the modulus

and create the material nonlinearity. Comparing room temperature values with the Wright

Pat AFB data a considerable difference was observed. Recently, tests have been

performed at room temperature only to investigate this phenomenon. Preliminary results

are much closer to the Wright Patterson AFB data. In the future, new tests should be

performed starting at room temperature going down to cryogenic temperatures as well as

from room temperatures to elevated temperatures to further investigate this aspect.






35


One of the objectives of this research was to reduce the scatter in the data to allow

for design optimization. This objective was accomplished since the method reduced

scatter in the data with most of the coefficients of variation below 2%; the other study [3]

showed 3% 5% scatter in the data. A reduction in variability would enable optimization

through probabilistic design. The grips design with alignment capabilities, the alignment

fixture for proper axial loading of the specimen as well as meticulous calibration of the

entire system were part of the reason for such achievement.














CHAPTER 3
TEMPERATURE DEPENDENT SHEAR MODULUS EXPERIMENTAL
MEASUREMENTS

3.1 Characterization of Shear Modulus

Due to the orthotropic behavior of most composite materials, the measurement of

the shear properties has been a problem of special interest for a number of years. A

variety of test methods [25] were developed to determine those properties. However, they

all have some disadvantages, making them less than ideal. Shear characterization of

laminated composites has been particularly challenging, because there is no standard test

method available. Thus, a recognized need exists for a simple, efficient, and inexpensive

test method for determination of shear properties in composites.

The continuing advances in the development of new structural materials, especially

those of fiber-reinforced composites, are leading to more consistent thermo-mechanical

response characteristics. However, often times in trying to implement composite

materials to aerospace applications, we find discrepancies in the test data obtained using

different test methods that may be related to the correct interpretation of the test results;

and this is especially true in the case of shear modulus for anisotropic composites.

It has been generally recognized that the shear properties of fiber composites are

more difficult to determine than the other elastic properties. This is due to the fact that for

highly anisotropic fiber-reinforced composite materials, a state of pure shear stress is

very difficult to attain.









Numerous papers are available in the literature presenting different results for

determining the shear properties of composite materials. Chan et al. [26] presented in

their paper a sensitivity analysis of six shear and bending tests for determining the

interlaminar shear modulus of fiber composites. Papadakis et al. [27] presented the strain

rate effects on the shear mechanical properties of a highly oriented thermoplastic

composite material. Most of the results that are published in the literature have been

obtained using conventional mechanical tests such as the one presented by Marin et al.

[28] where they determined G12 by means of the off-axis test. The interesting part of this

paper though is that they considered the gripping effect influence on the mechanical

property in question, to reproduce the most reliable clamped conditions and thus to

accurately present their results.

However, the ideal shear test method is one that requires small and easily fabricated

specimens, it is simple to conduct, and is capable of determining both shear strength and

shear stiffness at the same time.

There are currently many methods available to measure the shear properties of

various composite materials, including the + 45' test, the off-axis tensile test, thin-walled

tube torsion test, solid rode torsion test, rail shear test plate twist test, split-ring shear test,

and others but they are difficult to run, they are not applicable to any material and they

are not capable of measuring both shear modulus and shear strength simultaneously.

Also, tests like the off-axis test works well only for unidirectional, continuous fiber

composites, the rail shear test induces stress concentrations at the specimen edges, the

plate twist and split-ring shear tests measure only shear modulus, and the short beam

shear test measure only shear strength.









Applying torsional loading to thin-walled tube specimens produce the most

uniform shear-stress state in a material; however, this method is not commonly used

because tubular specimens are very expensive to manufacture.

The losipescu [29] shear test method, introduced by Nicolae losipescu in Romania

in the early 1960s, is considered the most promising shear test method because the

specimens are easily made and both shear modulus and shear strength can be obtained.

This method attempts to achieve a state of pure shear stress of the test section of the

specimen by applying two counteracting force couples; it has been developed for use on

isotropic materials but it was extended to composite materials testing by Adams and

Walrath [30] of the University of Wyoming. Fig. 3-1 shows a specimen loaded in an

losipescu fixture.


























Figure 3-1. Iosipescu's specimen in the loading fixture









3.2 Double Notch Shear Specimen (DNSS) for G12 Testing

Due to the Iosipescu method's popularity, extensive work has been performed for

the past fifty years and researchers reported obtaining good results when using the

method. For this reason, ASTM conducted a study [31] to determine its feasibility as a

standard method for laminated composites. The results showed a substantial variation in

the shear modulus compared to the variation of the longitudinal and transverse moduli for

comparable materials. The study also revealed that the shear stress and shear strain

distributions in the test section of the Iosipescu specimen were not uniform; they were

also dependent on the orthotropy of the material tested, specimen configuration and

loading condition.

The specimens sometimes exhibit twisting during loading, adding and subtracting

shear strain on the faces of the specimen; when following the recommendations by

Adams and Walrath of using a small centrally located strain gage rosette, the measured

shear modulus is inaccurate.

Researchers [32-33] have tried to overcome most of the shortcomings by improving

the method. Depending on the material tested, the Iosipescu shear test method was

modified by improving the specimen geometry and the fixture. A special strain gage

called the "shear gage" was developed by Ifju et al. [34] in collaboration with Prof. Post

and Micro-Measurements Division of the Vishay Measurements Group Inc [35]. Ifju also

improved the specimen geometry. His contributions led to the significant reduction of the

coefficient of variation in shear modulus within each material system. He also

demonstrated that the newly developed shear gage is insensitive to normal stress in the

test section; this means that a state of pure shear stress in the test section does not have to

be achieved in order to get accurate results.









A complete and accurate knowledge of mechanical properties of composites is very

important in the design of new engineering structures. Iosipescu method proved very

efficient in determining some of their properties, namely the shear properties, as such

presented in papers by Chiang et al. [36] where hybrid composites are investigated, and

in a more comprehensive study by Odegard et al. [37] in which shear strength for

unidirectional composites was determined using the losipescu method and the off-axis

test, and then compared with the finite element method where they accounted for the non-

linear material behavior. Whether unidirectional composites, textile composites [38] or

brittle materials [39] were investigated, losipescu method presented numerous

advantaged over the common mechanical tests available.

Although many improvements to the losipescu method have been implemented,

characterization of shear properties in composites remains a challenging task. When

trying to determine the shear properties as a function of temperature we are confronted

with new problems. Special test chambers have to be used when testing at cryogenic and

elevated temperatures. The fixture required to conduct the losipescu shear test is too

bulky, needs a lot of space thus imposing large and expensive test chambers and the test

itself is very difficult to conduct in these conditions.

There are two tension tests namely the 45 degree test or the off-axis test that could

have been used in conjunction with the experimental setup explained in Chapter 2. These

two tests are the only existing tension shear tests that can compare to the newly

developed method presented in this chapter. However these tests are not standard

methods but guides and have also a few disadvantages making them less attractive for

temperature dependent testing. The 45 degree test requires E1 and E2 properties in order









to determine G12 and the off-axis test does not produce pure shear in the test section. Also

the lay-up configuration makes these tests susceptible to measurement error due to fiber

orientation and gage alignment. Both tests are very sensitive to load misalignment and

gage positioning.

Therefore the off-axis behavior of composite materials had to be accounted for

since it can increase the variability in the experimental measurements. Looking at the

variation of the engineering constant G12 with the fiber orientation angle 0 in Fig. 3-2, it

can be observed that considerable error can be obtained from such tests if fiber and/or

gage alignment is off by more than a few degrees.


0 15 30 45 60

E (degree)
Figure 3-2. Variation of Gxy with the fiber orientation angle









Most importantly these two tests cannot evaluate the shear properties of

multidirectional laminates or randomly oriented chopped fiber composites.

This calls for the development of a new shear test method for efficient temperature-

dependent determination of shear modulus. The proposed method would use double

notch tension specimens designed such that a uniform shear stress state would be

obtained in the test section.

The new method would be easy to conduct, the specimens would be easy to

fabricate and would require limited fixturing and consequently a small testing chamber.

Most importantly this new method would allow for multiple property values

determination such as longitudinal, transverse and shear moduli, using the same

methodology and experimental setup. The main idea was to design a specimen from a

similar geometry as for one used in an El or E2 test, and that would exhibit a uniform

shear stress state in the test section. To achieve that, Finite Element Analysis (FEA)

method was employed in the design of so called double notch shear specimens. FEA

analysis was performed to determine the optimal specimen geometry such that a uniform

shear stress state is obtained in the test section. The specimens would also have to be easy

to fabricate and machine as well as very inexpensive. The test method was design such

that by a simple swap of the specimens an El or E2 test to a G12 test could be performed.

Thus using the same procedure as explained for the transverse modulus tests we would be

able to determine shear properties of unidirectional IM7/977-2 graphite epoxy.

The geometry of the specimens was first created using AutoCAD 2004 and then

imported into ABAQUS. This allowed creating even very complicated models in an

easier and faster way. ABAQUS 6.4 was used to perform the shear specimens' analysis.









The process of designing a specimen that would exhibit a uniform shear stress in the test

section was one of trial and error.

However, a few parameters were imposed such as length, width and thickness to be

able to use the same setup as previously discussed for transverse modulus. Consequently

the only modification to the specimen geometry was the two notches that were cut in the

center. Another fixed parameter was the distance between the two notches. The shear

gages that would be attached were 0.45" long, therefore the distance between the notches

had to be the same. One concern was that premature failure would be initiated if the

transverse stresses next to the tip of the notches were higher than the shear stresses. For

this reason the geometry was constructed such that the stresses would gradually feed into

the test section.

The numerical analysis was performed as follows: a 2D part was created from the

sketch imported from AutoCAD. Then the mechanical properties were introduced. Using

the "Lamina" type option in ABAQUS, the elastic constants namely El, E2, V12, G12, G13

and G23 were specified.

The lamina orientation was given such that to coincide with the longitudinal

direction of the specimen. One end of the specimen was constrained in all 6 DOF and the

other end was given a displacement in the x-direction while constrained in y-direction as

well as to rotate in x-y plane.

The model was then meshed and submitted for analysis. Results of shear stress

(S12) and transverse stress (S22) were interpreted and presented below.

The first geometry that was investigated is presented in Figs. 3-3 and 3-4. The two

notches are parallel to each other and perpendicular to the specimen. Fig. 3-3 shows the









shear stress (S12) distribution while Fig. 3-4 shows transverse stress (S22) distribution.

From this numerical analysis it can be seen that the stress state is not entirely uniform

over the entire test section, stress direction does not match fiber direction and S22 is quite

large compared to S12.


Figure 3-3. Shear stress (S12) distribution for specimen with 00 oriented notches


Figure 3-4. Transverse stress (S22) distribution for specimen with 00 oriented notches

The second geometry investigated is presented in Figs. 3-5 and 3-6. The notches

are again parallel to each other but oriented at 450 with the specimen. Here the stress state

is more uniform and the transverse stresses are lower than in the previous case.


Figure 3-5. Shear stress (S12) distribution for specimen with 450 oriented notches












-.. ... ... --'
,' -a i I,



Figure 3-6. Transverse stress (S22) distribution for specimen with 450 oriented notches

Variations of this geometry were analyzed by modifying the notch thickness, notch

shape, notch length, and/or the notch orientation. The process was entirely trial and error

but fortunately not time consuming; consequently it allowed for numerous numerical

simulations to be able to identify the best geometry.

From all these trials, only the one presented in Figs. 3-7 and 3-8, where notches are

oriented at 60 degrees, was interesting from the point of view of the results obtained.



[ l i .. I..


'-~- ; : ::


Figure 3-7. Shear stress (S12) distribution for specimen with 600 oriented notches









Figure 3-8. Transverse stress (S22) distribution for specimen with 600 oriented notches

In all previous examples stress concentration appeared around the tip's notches; to

eliminate this problem one simple solution would be to increase the radius of the notch.
eliminate this problem one simple solution would be to increase the radius of the notch.






46


However that will result in eliminating more material around the test section and the

specimens will be very fragile thus braking before it could be tested. An alternative

solution is presented in Fig. 3-9 and Fig. 3-10. On the other hand the shape of the notches

was considered difficult to machine at the time and a more conservative approach was

used.

, -,I II' 4,' I ---
"- l -_ -- ,1 }_1 i.,'.' !.



I y L .
I ,, .. l


Figure 3-9. Shear stress (S12) distribution for specimen with rounded notches




I.








Fig. 3-11 and Fig. 3-12 show the stress distribution for the geometry chosen to be

machined. The two notches are quarter circles with a radius equal to half the width of the

specimen. The width of the notches was choused to be 0.1875".

The shear stress distribution is very uniform across the test section and the

transverse stresses are lower than the shear stresses.

This geometry was preferred over all the others investigated because its simpler

geometry would also allow for easy specimen machining.






47











Figure 3-11. Shear stress (S12) distribution for the DNSS specimen











Figure 3-12. Transverse stress (S22) distribution for the DNSS specimen

3.3 Experimental Setup

The same experimental setup that was used in determining the transverse modulus

was employed here, namely an MTI type machine, a testing chamber, an environmental

chamber that regulates the temperature inside the testing chamber, a liquid nitrogen (LN2)

dewar, and a data acquisition system. The only change was in the data acquisition system

where in one SCXI module a few switches where interchanged to read a half bridge

configuration.

3.4 Experimental Procedure and Results

Specimens for temperature dependent shear modulus determination were first

machined using a carbide mill on a CNC machine. However the end result did not

satisfied since material flaking and delamination was present next to the notches. The

alternative was waterjet machining of the specimens. This allowed for faster, cheaper but
.... ...... b ,, ... dlil _r~r~d~~lf '" ,',, ,J-I] -#!'Y" '- .. & fJ............

: :-+:,, -- L:-- :,I',,.',iF: IIIIIi~
.. : - .... + -- -, ... .- .. ,-'
.....1#-jj ~ ,.,.,,,, -4g :L



















altrnaiv was wa, e mahiin of.the specimes Thsalwe __ aseceaeu









most importantly a more accurate and flake free cut of the specimens. It was also a one-

time process eliminating the need for first cutting specimens to a 1" width and grinding

the edges before cutting the notches as it would have been necessary if a milling machine

was used. Most importantly it insured that all the specimens were cut at the same angle

with respect to the fiber direction thus helping reduce measurement variability. Fig. 3-13

shows 12 DNSS specimens that were cut from 2 panels.


















Figure 3-13. DNSS specimens

These specimens were then prepared and the tests were conducted according to the

ASTM 5379 standard and NASA recommendations that were discussed in Chapter 2.

Gage selection was made to handle the large temperature range, nominally 200'C.

Therefore, C-040621-A custom shear gages were obtained through the Vishay

Micromeasurements Group. Fig. 3-14 shows a schematic of the shear gage and as it can

be seen it is a composed of two gages with the grid at +450 and -45' respectively. The

gage was connected to the data acquisition system in a half bridge configuration, as

presented in Fig. 3-15.
presented in Fig. 3-15.








All the other required supplies to attach the gages to the specimen, such as the M-

Bond 610 epoxy adhesive, were also obtained from Vishay.

Shear specimens were also prepared according to NASA recommendation

procedures for strain gage application and ASTM standard. Each test section was first

abraded, with varying grits of sand paper to remove all surface flaws and to smooth finish

the surface. It was then cleaned with acetone and marks were inscribed for gage

alignment with the specimen.


c


Figure 3-14. The shear gage






2 I


RL I 14
R++


Rt- ,Ii(-


Figure 3-15. Half-bridge circuit diagram


c






I II









Then any remaining impurities were removed with acetone and by dusting the air

off the surface.

Thickness and length measurements were taken across the test section of the

specimen. Three thickness measurements were taken and the average was used in

determining the cross-sectional area. Table 3-1 shows the length and the average

thickness of each test section.

Table 3-1. Length and average thickness measurements for all tested specimens
Specimen Length (in) Average
thickness (in)
p5-1 0.43095 0.09415
p5-2 0.42610 0.08705
p5-3 0.41155 0.09055
p5-4 0.42400 0.08818
p5-5 0.43020 0.08903
p5-6 0.42515 0.08888
p6-1 0.41140 0.08843
p6-2 0.42120 0.08850
p6-3 0.42150 0.08477
p6-4 0.42480 0.09097
p6-5 0.42060 0.08755
p6-6 0.42030 0.09030


Using a microscope, a gage and strain relief tabs were aligned to the inscribed

marks then a Teflon tape was used to temporary attach them to the specimen.

The undersides of the gage and strain relief tabs were exposed and together with the

specimen's surface they were coated with a thin layer of M-Bond 610 adhesive.

After a ten-minute drying period the gage and the tabs were placed back on the

specimen and clamped with uniform pressure.









Specimens were cured for three hours at 1210C then post-cured at 1350C for

another two hours. Once the specimen was gaged and wires were soldered to the tabs and

connected to the SCXI module it was fixed to the grips using the alignment fixture.

The temperature diode was taped to the specimen together with the environmental

chamber's thermocouple. The entire ensemble was positioned into the MTI machine then

the testing chamber was placed around it and connected to the environmental chamber,

and data was extracted using the Labview program as explained in Chapter 2.

This time shear specimens were loaded only up to 90 lb to avoid premature failure.

Each specimen was again tested at approximately 250C intervals, from -165C to

+1500C.

The Matlab code [appendix] manipulated the data to obtain the average slope of the

five curves at each temperature. Slope and the cross-sectional area allowed for shear

modulus determination as presented in Eqs. (3-1) to (3-4):

S= G12y (3-1)

7 = +45 + 45 (3-2)

P
r =- (3-3)
A

P
G12 = (3-4)
Ay

where P is the applied load and A is the cross-sectional area of the specimen.

Fig. 3-16 shows the entire temperature dependent shear modulus curves for all

tested specimens and Fig. 3-17 shows a linear fit through all the data points. Again this

basic fitting will be used in Chapter 4 to predict residual stresses for different laminate

configurations.










x109


0


-100 0 100


Temperature (C)
Figure 3-16. Shear modulus as a function of temperature for all tested specimens


x109


100 0 100


Temperature (C)
Figure 3-17. Linear fit through the data points for the shear modulus as a function of
temperature


6.5 F


5.5 F


4.5 k


I I


3.0
- 0


-200









The equation of the straight line and the regression coefficient are presented in Eqs.

(3-5) and (3-6):

G12(T)=-0.012231.T+5.5399 GPa (3-5)

R2 = 0.98768 (3-6)

For statistical purposes the coefficients of variation (CV) were computed for all the

tests and presented in Table 3-2.

As explained for the transverse modulus in Chapter 2, the average value and

standard deviation were first determined, then the coefficients of variation were

calculated at each of the fourteen temperatures.

Table 3-2. The mean, standard variation and coefficient of variation at each temperature
for all tested specimens
Temperature (C) Mean G12 SN-1 CV %
-165 7.57E+09 8.91E+07 1.18
-145 7.36E+09 1.58E+08 2.15
-125 7.18E+09 1.90E+08 2.65
-100 6.92E+09 1.63E+08 2.36
-75 6.44E+09 2.09E+08 3.25
-50 6.07E+09 1.74E+08 2.87
-25 5.75E+09 1.38E+08 2.39
0 5.47E+09 1.23E+08 2.25
+25 5.15E+09 8.71E+07 1.69
+50 4.87E+09 1.09E+08 2.25
+75 4.66E+09 9.20E+07 1.97
+100 4.44E+09 8.60E+07 1.94
+125 4.17E+09 8.91E+07 2.14
+150 3.72E+09 1.29E+08 3.46


3.5 Conclusions

A new method was developed and used to successfully determine the shear

modulus as a function of temperature for the unidirectional IM7/977-2 composite









material. The method uses specially designed tension specimens to produce a shear stress

state in the test section. FEA was employed to optimize the specimen geometry.

Specimens were easily fabricated from panels produced using schools facilities and then

waterjet machined to obtain the final geometry. Over ten tests were performed during

which the method proved to be very repeatable. A robust set of data was obtained using

14 points along the temperature range, i.e., -165C to +1500C for each specimen. The

method is fully automated and once a test is started do not require supervision.

The method is unique because it uses double notch tension specimens to produce

shear in composite materials. Specimens are easier to fabricate and the variability in the

experimental measurements is reduced because the method is not as sensitive to load

misalignment with fiber orientation or gage positioning. Multidirectional or chopped

fiber composites can be investigated. The method can also be extended to other materials

as well.

However in this project the method was used to extract information from

unidirectional composites and the results were used in predicting the behavior of

multidirectional composites.

Besides characterizing the material behavior, the shear modulus property of the

IM7/977-2 will be used in a modified Classical Lamination Theory (CLT) Matlab code to

predict the behavior of multidirectional laminates.

3.6 Discussion and Future Work

Chapter 3 described a practical new method to determine in-plane shear properties

of fiber reinforced polymer matrix composite materials. Since a reduction in data

variability was one of the main concerns in this research, techniques such as the off-axis









tests, which showed scatter in the data, were not the first choice. The Iosipescu method,

which is the most popular and commonly used technique, was also inappropriate for

temperature dependent tests because of the bulky fixture required. The author had to

come up with a simpler, more efficient technique that uses a unique specimen which can

produce a uniform shear stress state in the test section. Another important factor in

determining accurate shear properties in composites is the use of shear gages, as shown in

previously published papers [31-34]. The parabolic distribution of the shear strains in the

test section of the Iosipescu specimens can lead to scatter in the data when small,

unidirectional, centrally located strain gages are used. The shear gage has been shown to

reduce the scatter and improve the accuracy of the results by integrating the shear strain

over the entire test section. Therefore it was imperative to use shear gages in conjunction

with the newly developed double notch shear specimen.

The newly devised technique was employed to test more than ten different

specimens to obtain a robust set of data. As for the transverse modulus data, Fig. 3-17

shows the nonlinear behavior of the material investigated. A straight line was also fitted

through the data points and the equation was used later on to predict residual stresses.

However, in this case the residuals are smaller than in the transverse modulus case

although a higher order polynomial will fit the data much better. A comparison of the

transverse modulus with the shear modulus data shows that there is a correlation between

the material behaviors. The data seems to deviate from linearity around -75C and then

come back around +750C. Although in the case of shear modulus the residuals are much

smaller when a straight line is fitted through the data points, the same trend was observed

on both properties. It is not known why this phenomenon occurs, but it is speculated that









the thermal history is the primary cause. The phenomenon might not occur if tests are

performed from room to cryogenic or room to elevated temperatures. Future tests should

be performed to investigate this phenomenon.

The same paper [3] mentioned in Chapter 3 presented shear modulus data for the

IM7/977-2 material. Again only two data points are available, one at room temperature

and the other one at liquid nitrogen temperature. These two points are shown in Fig. 3-18

together with the data obtained at University of Florida. In this case a straight line will

better predict the value obtained by the Wright Patterson AFB at liquid nitrogen

temperature but will not agree with the room temperature value. Significant difference

will be obtained when a higher order polynomial will be used. As in the case of

transverse modulus, it was found that the shear modulus at room temperature is higher

when the specimens were first subjected to cryogenic temperatures but still lower than

the one presented by the Wright Patterson AFB. Nevertheless it should be remembered

that 0 Iosipescu specimens over-predict the modulus; therefore it is the author's believe

that the results obtained in this paper are much closer to the real value. The coefficient of

variation obtained from all the specimens tested at room temperature is around 1.7%.

This is a tremendous reduction in variability from 4% -9% when Iosipescu specimens are

used.

More tests should be performed in the future to have a better approximation of the

real shear modulus. Iosipescu specimens fitted with shear gages should be tested at room

temperature and compared to the double notch shear specimens. This process has already

been started and the data shows good agreement.






57


x109
8
S+ experimental data
7.5- basic linear fitting
a Wright Pat AFB data




+ 0





S4.5-

4-

.-00 -100 100 200

Temperature ("C)
Figure 3-18. Shear modulus as a function of temperature with linear fit and extra data
from the literature

Future work should also concentrate in determining the shear modulus for different

laminate configurations to compare the experimental results with the classical laminate

theory prediction.














CHAPTER 4
RESIDUAL STRESSES IN LAMINATED COMPOSITES

4.1 Introduction

Engineers face new challenges every day in the design and manufacturing

processes of structures and machine components. Often times their work is wasted when

those components or structures fail not due to the applied loads but from residual stresses

[40]. These residual stresses form during fabrication operations.

Metals develop residual stresses during processes such as welding, casting, rolling,

forging and assembly. In laminated composites they form due to the matrix solidification

around the reinforcement or due to the mismatch in the coefficients of thermal expansion

[41] between the fiber and matrix and in the plies of a stacked laminate.

Residual stresses are difficult to measure nondestructively and they add to the live

loads. In aerospace applications, the composites have to endure sudden temperature

changes, from cryogenic to high temperature, thus having to sustain thermal load above

the mechanical load.

Generally, most materials expand when they are heated. The coefficient of thermal

expansion (CTE) measures their rate of expansion. For example, silicon has a coefficient

of thermal expansion approximately five times smaller than copper and eight times lower

than aluminum (6061). Hence low expansion materials such as silicon cannot be bonded

directly to high expansion ones like aluminum or copper without experiencing high

stresses. There is also the case of graphite fibers that actually contract as they are

heated. Since a composite material is composed of two or more materials they are









likewise subjected to large mismatches in CTE that lead to thermal residual stresses.

Therefore determination of the CTE and residual stresses is critical. A better prediction of

how the laminate composite will behave can be made if those quantities are accurately

determined.

Analysis of the residual stresses was performed on single fiber composites [42],

fiber reinforced laminated composites or layered ceramic composites, and results present

the effect of thermal loading on the total carrying load such as in the papers by Benedikt

et al. [43], Gungor [44] or Tomaszewski [45]. The effect of residual stress on the

toughening behavior of TiB2/SiCw composites was investigated by Jianxin [46], who

found out that considerable improvement in the high-temperature fracture toughness was

observed up to 12000C due to the relaxation of the thermal residual stresses caused by the

thermal expansion mismatch between SiC whisker and TiB2. Qianjung et al. [47]

investigated metal-ceramic functionally gradient materials, and used moire interferometry

to report the residual stress distribution in such materials.

Current practices [48-49] for residual stress determination include both destructive

and non-destructive techniques such as hole-drilling methods, ultrasonic techniques, X-

ray and photomechanical techniques.

For composites in particular, there are destructive techniques like hole-drilling

method, cutting method, ply sectioning method, and non-destructive techniques like

embedded strain gages, X-ray diffraction or CRM.

4.2 Cure Referencing Method

A new experimental technique called the Cure Referencing Method [50] was

recently developed at the University of Florida by Peter Ifju and his research group to









measure residual stress in composites. This non-destructive testing method used in

conjunction with the moire interferometry technique is capable of full-field

measurements of the surface strains.

The method uses high frequency diffraction gratings attached to the laminated

composite during the curing process that act as a reference to the free stress state prior to

resin solidification.

The process of attaching gratings to the laminated composite involves several steps

which are rigorously explained in the paper by Ifju et al. [51] published in the Journal of

Experimental Mechanics. The replication procedure is shown in Fig. 4-1.

The end result of the replication procedure is an autoclave tool with a diffraction

grating, two layers of aluminum and an epoxy film on top. This tool is then used to

transfer the grating to the composite panel in the autoclave during curing process.

Fig. 4-2 shows the method of attaching the diffraction grating to the composite in

the autoclave.

The curing process is initiated using a cure cycle like the one shown in Fig. 4-3.

The laminated composite goes from an uncured state at room temperature to fully

cured at high temperature.

Separating the tool from the composite panel at elevated temperature when the

composite is fully cured, the grating is able to record the free stress state that existed in

the composite before building up residual stress as it cools down to room temperature.

This newly developed method has been employed to determine the residual stresses

and coefficients of thermal expansion (CTE) in composite materials.

The IM7/977-2 material was investigated and reported as follows.












Make a silicone rubber
grating mold


High

Replicate the intermediate
grating using high temp, epoxy



Vacutun deposit
aluminum onto the intermediate
grating

High to

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


Silicone rubber
grating


RPg. Silicone rubber
grating
Intermediate grating
(high temp. epoxy)

Intermediate grating
(high temp. epoxy)
Aluminum deposition



p Intermediate grating
(high temp. epoxy)

Autoclave tool
(high temp. epoxy
on Astrosital)


Vacuum deposit
aluminum onto the autoclave
tool grating


M High tmp.

Cast a thin film onto CE
the autoclave tool grating
using high temp. epoxy


High temp.
S high pr 1
Transfer the epoxy film
onto the composite panel
during cure in the autoclave


Composite preprcg


- Autoclave tool


Figure 4-1. Schematic of the replication technique












Porous release film Breather ply


bag Vacuum line


Non-porous release film


.3501-6 Epoxy layer
Evaporated aluminum
3501-6 Epoxy layer

Astrosital autoclave tool


Figure 4-2. Method of attaching the diffraction grating to the composite in the autoclave


Cure
Temp




E
I-


Uncured
high
viscosity
liquid

RTL


Transiton
to solid


Fully
cured


Pollmerizatlon
begins *
Uncured low
viscosity liquid

*I I


Hold
Matrix Cure


Fiber
Wet-out


Figure 4-3. Cure cycle for laminated composites in autoclave


Time









4.3 Residual Stresses and CTE Measurements

The failure of X-33 reusable launch vehicle showed that the behavior of the new

advanced structural composite materials is not yet fully understood. Lack of information

about the material properties of those materials played a key role in the failure of the

liquid hydrogen tanks and of the project itself.

Temperature dependent measurements to characterize composite materials are

missing from the literature thus limited data is obtained and then used in the design of the

new engineering structures. The X-33 project marked a set-back for the development and

implementation of new advanced structural composite materials to aerospace

applications. Consequently, the composite community focused on determining the failure

causes of the project and on obtaining the correct and complete information of the

different material properties therefore trying to fill the void that exists in the literature

about the temperature dependent material properties of composite materials.

Under the supervision and guidance of Peter Ifju at the University of Florida, the

ESALab research team started an experimental study on residual stresses in laminated

composites as a function of temperature. Materials used in the study were unidirectional

laminated composites, [0]13, the RLV configuration [52], [45/903/-45/03]s, and a special

optimized angle ply (OAP) configuration, [+25n]s presented by Qu [53] to account for

both thermal and mechanical loading. The IM7/977-2 prepreg was used to fabricate the

panels. In our lay-up facility, 4" x 4" panels were layed-up using different configurations

as mentioned. They were then placed in a special oven with vacuum capabilities and left

to cure following the curing cycle provided by the manufacturer.

The CRM technique was employed to determine the coefficients of thermal

expansion and the residual stresses of these materials. The extensive previous work









performed on CRM led to improvements in the grating replication. The first three steps in

the Fig. 4-1 were eliminated, reducing the time needed to replicate a grating on the

composite panels by approximately 72 hours, thus making the method more efficient.

Once the grating was transferred to the composite panel, moire interferometry was

employed to document the surface strains. Fringe patterns, as seen in Fig. 4-4, were

photographed and recorded for analysis.


















Figure 4-4. Typical horizontal and vertical fringe patterns

4.3.1 Data Analysis

Once the fringe patterns have been recorded they could be analyzed to determine

the surface strains. Fringe patterns contain displacement information thus the fringe order

(N) is directly related to the displacement of the composite panel. 1200 lines/mm

diffraction gratings were used thus giving this method a displacement sensitivity of 0.417

microns.

The relationship between fringe order and displacement and between displacements

and engineering strains were presented in Eqs. (1-1) to (1-5).








These equations were used to determine the surface strains at room temperature on

each tested specimen. This provided the reference point for the temperature dependent

residual stress and CTE measurements.

These measurements were obtained by hand calculations. The analysis of the fringe

patterns was performed manually by locating the positions and numbering the fringes, as

can be seen in Fig. 4-5. This process however is very slow and has the potential of

increasing the measurement error. Thus a new system has to be used in the future to

eliminate the human factor. This system which is called digital image processing for

fringe analysis has been successfully implemented in the ESALab at the University of

Florida.


Y
5 0 5




















Figure 4-5. Example of counting fringes to determine surface strains









Because of the development and decreasing cost of the digital image processing

equipment, the digital image fringe pattern techniques are increasingly used in acquiring

strains and stresses. The reasons for implementing this method are to improve the

accuracy, to improve the speed, and to automate the process. Ultimately, it will eliminate

the human factor by automatically detecting the positions of the fringes.

An Insight Firewire CCD camera, as seen in Fig. 4-6, and a frame grabber were

acquired from Disagnostic Instruments Inc. The CCD camera is used to scan the fringe

pattern. The frame grabber, which is a video digitizer, digitizes the image and stores it

into the computer memory. This combination of the digital camera, frame grabber and

computer made it very easy to record and manipulate the images.


















Figure 4-6. CCD camera

Different algorithms are available to obtain image manipulations on the individual

pixels. However, these algorithms require the fringe patterns to be shifted before they

could be analyzed. One possible solution for shifting fringe patterns is by displacing

either the specimen or the interferometer simultaneously in the horizontal and vertical

directions.









This can be achieved by building a stage as the one in Fig. 4-7 that can withstand

the weight of the interferometer. The stage is specially designed and has four aluminum

tubes connecting two aluminum plates, on the bottom and top. The tubes are precisely

machined and attached to the plates at 450

Magnet wire of 0.007" in diameter with special enamel coating for high

temperature was wrapped exactly 200 times around each of the four aluminum tubes then

connected together with strain gage wire to complete the circuit.























Figure 4-7. Specially designed stage for fringe shifting

A 0-35 V, 0-5 Amp adjustable power supply, from Pyramid, model PS-32 lab was

connected to the circuit. By turning the power ON and increasing the voltage, the current

going through the magnet wire heats the aluminum tubes, which will then expand thus

raising the interferometer in a 45 degree direction. Fig. 4-8 shows the entire ensemble

including the PEMI interferometer sitting on the stage as well as the power supply.

































Figure 4-8. Experimental setup for fringe shifting

A sequence of images of the shifted fringe pattern is recorded from which a special

algorithm calculates the horizontal and vertical displacement fields. Thus the newly

implemented system is able to determine faster the full-field displacements. An

automation of the method for an easier manipulation of the results as well as a more

accurate output is obtained. This system will be used in the future for the analysis of the

fringe patterns.

4.3.2 Experimental Results

Moire interferometry was used to analyze and determine the surface strains at room

temperature. Because CRM uses this optical technique to determine the surface strains of

the laminates, the fog created at cryogenic temperatures makes it very difficult to take

measurements. For this reason, strain gages were attached to the laminates and a new

procedure [54] for cryogenic temperature measurements was developed. The relative






69

strains were obtained and superimposed with the strains obtained via CRM at room

temperature. Several panels for each of the configurations mentioned above were tested.

Results of the average surface strains are presented in Fig. 4-9.


2000

0


-2000-


S-4000

S-6000
^ -UNI x
-8000 UNly
SOAPx
OAP y
-10000 PLV x
S- > R L V y
-12000
-200 -100 0 100 200

Temperature (oC)
Figure 4-9. Temperature dependent average strains for different laminate configurations

It is commonly assumed that when a cured polymer matrix composite is returned to

the cure temperature, the stresses in the material completely disappear. Looking at the

strain vs. temperature data in Fig. 4-9 it is evident that the tested panels still exhibit

surface strains after they were heated to cure temperature.

This strain difference is the result of a one-time phenomenon, namely chemical

shrinkage (CS). Table 4-1 shows the surface strain on the specimens at cure temperatures

due to chemical shrinkage.






70

Table 4-1. Strain at cure temperature due to chemical shrinkage (CS)
Specimen type x-direction (microstrains) y-direction (microstrains)
UNI 108 -2712.5
RLV -126.6 -9.25
OAP 476.9 -2026.9

Having the surface strain information on the composite panels at each temperature,

the coefficients of thermal expansion can be calculated using Eqs. (4-1) and (4-2), where

T1 and T2 are two different temperatures:


CTEX =
( 7


CTE, =
lii


E,(T )


(4-1)


(4-2)


The temperature dependent CTEs are presented in Fig. 4-10:


40

35

30

25

20


-100


100


200


Temperature (C)
Figure 4-10. Temperature dependent CTEs for different laminate configurations


--UNIx
--- UNI y
--- OAP x
-- OAP y
SRLV x
RLV y
-- -- fit UNI x
----- fit UNI y "









A linear fit was obtained for the CTE of unidirectional composites in both x andy

directions. These basic fits will be used later on together with the transverse and shear

properties to predict the behavior of multidirectional composites. The two equations, Eqs.

(4-3) and (4-4) are:

CTEUN = a,(T)= 0.0014T+ 0.4232 UE (4-3)
IC

CTEUN = a,(T)= 0.0429T +22.167 (4-4)
YC

Residual stress can be calculated within each ply of the composite panel using the

classical lamination theory. First the residual strain was calculated for each ply

orientation using Eq. (4-5):

{Cres.k =[ra]{inm}-{C,} (4-5)

where rk is the transformation matrix from the 1-2 coordinate system to the ply

coordinate system, cEam is the laminate strain vector and SE,, is the strain vector for the

unidirectional composite. Then the constitutive relation, Eq. (4-6), was used to determine

the residual stress:

{ [ore }k []k { }k (4-6)

where Q is the stiffness matrix of the composite as defined in Eq. (4-7):

SEl v12E2(T) 0
Q(T = E2 (T 2 E2 (T) E2 (T) 0 (4-7)
l -2 12 0 0 G12()


The program used includes previously measured temperature dependent transverse

and shear information, as it can be seen in Eq. (4-7), as well as the effect of chemical

shrinkage. The strain due to chemical shrinkage adds up to the residual strain calculation









and has a huge effect on residual stresses. This quantity which is neglected in the

classical lamination theory is critical in the residual stress prediction as it can be observed

in Fig. 4-11.


100
--+-- RLV 00 layer w/o CS
---- 25 layer w/o CS
80- -- +250 layer w CS
S-*- RLV 0 layer w CS


60


0,












Figure 4-11. Effect of chemical shrinkage on residual stress calculation

The residual stress in the RLV 00 and OAP +250 worst case layers are plotted with

and without including chemical shrinkage. It can be observed that in both cases the

stresses are under-predicted. Furthermore the temperature dependent properties were

included in the stiffness matrix and predictions are presented in Fig. 4-12.

The effect of temperature dependent shear properties can be neglected for normal

residual stresses and only transverse properties influence the prediction. RLV panels

exhibit higher residual stress than the OAPs.











100
--+-- RLV 00 layer w CS
---RLV 0' layer w CS, TD E2, G12
80 -- +25 layer w CS, TD E2,G12
--"* .-- 25 layer w CS
--'-- s22 ultimate
-------------- --a--
O 60-. .
LL U----,,~


40
U) -6



20 9




-200 -100 0 100 200

Temperature (C)
Figure 4-12. Effect of chemical shrinkage and temperature dependent properties on
residual stress calculation

Comparing the different laminates is observed that the worst case layer in the RLV

reached the failure strength in the transverse direction very close to subzero temperatures;

therefore use of such configuration was totally inappropriate in the X-33 project since

microcracks will develop as residual stresses build up and produce failure.

4.4 Conclusions

Temperature dependent residual stress and CTE measurements were acquired for

different laminate configurations using improved CRM. Room temperature

measurements were acquired with moire interferometry techniques and then strain gages

were used to record surface strains from cryogenic temperatures to cure conditions Moire

interferometry plays a key role since surface strains at room temperature provide the









reference point for the temperature dependent measurements. Thus the accuracy of the

temperature dependent residual stresses and CTEs depend on the accuracy of the data

recorded at room temperature. Fringe patterns were manually analyzed but in the future a

new system that has been implemented will be used. This system called the Digital Image

Processing for fringe analysis will try to eliminate the human factor by reducing some of

the errors and most importantly will also automate and speed the process.

Residual stresses were determined using a modified classical lamination theory that

includes chemical shrinkage effect and temperature dependent transverse and shear

properties. Non- inclusion of chemical shrinkage effect under-predicts the residual

stresses and can lead to premature failure of the composite.

4.5 Discussion and Future Work

Residual stresses are very important to be determined because they can predict

failure of the composite material. Results obtained in this paper show first of all that the

stacking sequence used in the X-33 project was not the right choice and emphasizes the

importance of the design optimization.

Temperature dependent properties should definitely be included in the residual

stress prediction; they accounted for a 20% increase in the residual stresses in the worst

case ply of the RLV configuration. However, only the transverse modulus was a factor in

predicting residual stresses in the transverse direction. The shear modulus did not affect

the results; but this does not mean that the data was obtained in vain or that in the future

this quantity should be omitted. Preliminary data show that shear modulus plays an

important role in determining residual shear stress, and in predicting the behavior of the

multi-directional laminates from the modified classical laminate theory.









In the future, once more data is obtained over a larger temperature range, the

prediction can be improved. Also, instead of approximating the data with straight lines,

the equations from a high order polynomial should be included in the Matlab code that

calculates the stresses. This will slightly modify the results.

Failure strength of the composite in the transverse direction was partially

determined here, as presented in Fig. 4-12. However, only a few data points were

obtained at cryogenic and room temperatures and the scatter in the data was considerable.

Therefore the straight line used to approximate the data should not be entirely trusted

until enough tests are performed across the temperature range.

Tests were performed on the same specimens that were tested to obtain transverse

modulus, and they did not always fail in the test section; this can lead to miscalculation of

the cross-sectional area and thus ultimate stress. In the future special specimens should be

used. The width of the test section should be smaller than the width of the specimen to

produce failure in that region.














CHAPTER 5
EXPERIMENTAL CHARACTERIZATION OF LOADING IMPERFECTION ON THE
BRAZILIAN DISK SPECIMEN

The chapter represents a small portion of a broader experimental program to

characterize single crystal metallic materials. These are the materials of choice for

maximizing creep resistance in environments of extreme temperatures and sustain load,

such as that of turbine blades in fuel pump assemblies. In order to utilize single crystal

materials in such applications, the fracture behavior must be thoroughly understood. This

endeavor requires mode I, mode II and mixed mode testing on all effected

crystallographic planes. Tests ultimately would be performed at temperatures up to

7000C and pressures up to 5000psi. Due to the size of the test chamber and expense of

the specimen material it was imperative that the specimens be compact. Because of these

testing requirements the Brazilian Disk specimen was selected to be investigated.

5.1 Introduction

For over half a century, the Brazilian Disk specimen [55] has been intensively used

to characterize the mechanical properties of different materials.

The specimen was initially used in 1947 to determine the fracture toughness in

rocks. Early versions of the specimen were approximately 2 in. in diameter and a

thickness equal to the radius. Subsequent researchers developed a "flattened" center crack

disk type specimen. This newly developed specimen, which was much thinner and had a

pre-existing crack at the center, proved to have many advantages and soon became a very

popular testing tool in fracture mechanics. Because the specimen provides a wide range









of mode mixity, considerable material property information can be obtained from one

specimen geometry.

Analytical solutions for this indirect (Brazilian) testing method are available in the

literature, such as presented by Claesson et al. [56] who calculated the stress field and

tensile strength of anisotropic rocks using elastic parameters measured in the laboratory

or by Exadaktylos et al. [57] who calculated the stresses and strains at any arbitrary point

in the disc.

Shetty et al. [58-62] used the method to determine the fracture toughness of

different materials, Atkinson et al. [63] used the Brazilian test to determine the combined

mode fracture. Mixed-mode fracture was also investigated by researchers like Petrovic

[64], Marshall [65], Suresh et al. [66-67], Awaji et al. [68]. Paul [69] presented a

numerical solution for tests on the Brazilian Disk specimen. Khan et al. [70], Kukreti et

al. [71], Narasimhan et al. [72] developed finite element programs for the prediction of

initiation, crack growth or ultimate fracture and many others [73-83] performed tests and

analysis on cracked specimens and presented solutions on the behavior of cracks, stress

distribution or fracture toughness of different materials under different loading.

Recent published papers such as the one by Ayatollahi et al. [84] presents results on

the fracture toughness ratio KIIc/KIc that is calculated for two brittle materials and is

compared with the relevant published experimental results obtained from fracture tests on

the cracked Brazilian disc specimen. Wang et al. [85] have used a flattened Brazilian disc

specimen to determine the elastic modulus, tensile strength and fracture toughness of

marbles and again in a different paper Wang at al. [86] presented analytical and

numerical results for the flattened Brazilian disc specimen. Al-Shayea et al. [87]









presented the effects of confining pressure and temperature on mixed-mode fracture

toughness of a limestone rock. Huang et al. [88] determined the fracture toughness of

orthotropic materials and Banks-Sills et al. [89] developed a methodology to determine

the interface fracture toughness in composites.

The Brazilian specimen became the configuration of choice during an experimental

program to assess single crystal materials for slip plane determination under mixed mode

loading. However, questions surfaced concerning the effects of specimen alignment. And

since there is a void in the literature on this subject, a systematic experimental study was

conducted to determine how specimen misalignment (both out-of-plane and in-plane)

affected the strain and displacement fields. For test purposes, an aluminum specimen was

investigated in order to isolate the loading effects from the crystallographic effects.

Additionally, a finite element analysis (FEA) program was developed to model the

specimen. Altogether, the experimental program at the University of Florida concentrated

on: providing angle dependent displacement fields, comparing experimental results to

FEA, providing full-field analysis of the plastic zones ahead of the crack tips, studying

the effect of misalignment in the linear range and in the plastic range.

5.2 Experimental Procedure

Aluminum (7075-T6) Brazilian disk specimens, shown in Fig. 5-1, were machined

with a diameter of 1.1 in (27.94 mm) and thickness of 0.09" (2.286 mm). A notch of 0.3"

x 0.01" (7.62 mm x 0.254 mm) was cut in the center of each specimen using Electrical

Discharge Machining (EDM). Moire interferometry was used to document displacement

fields on the surface of the specimens. A phase type diffraction grating, crossed line with

a nominal frequency of 1200 lines/mm (30480 lines/in) was replicated on the surface of

the specimen as necessary for the moire tests. It was oriented such that the lines were






79

parallel and perpendicular to the notch (Fig. 5-1). A custom loading fixture was

fabricated that had adjustment capabilities for both in-plane and out-of-plane

misalignment for intentionally inducing load misalignment as shown in Fig. 5-2. The top

portion of the fixture remained fixed. By rotating the left most adjustment screw, the

lower portion of the fixture produced out-of-plane misalignment. By rotating the right

most adjustment screw the fixture produced in-plane misalignment. Since the grating was

fixed to the specimen and the specimen was loaded along angle 0, ranging from 0 to 27,

the moire interferometer was required to be oriented at the angle 0. Thus a second fixture,

Fig. 5-3, was also fabricated for tilting capability to allow the moire interferometer to

orient with the specimen.


P P
p






C


grating for moire 06



0.09 in

P IP


Figure 5-1. Schematic description of the Brazilian disk

The Brazilian disk specimen was then loaded by means of a compression testing

machine (MTI type). Once the grating was attached to the specimen and the specimen









was placed in the loading fixture, the process of obtaining the displacement fields was

initiated.

First, the interferometer (an IBM PEMI compact interferometer) was positioned on

the specially designed fixture and rotated to the notch angle 0 (between 0 and 27 degrees)

for which displacement fields were recorded. To achieve this, a digital inclinometer with

0.1 degree accuracy, placed on top of the interferometer, was used for angle

measurements. Then, while looking through the interferometer's window, the specimen

was rotated until the first and second order diffraction dots emerging from the grating

were grouped into one dot. This is the standard procedure for tuning the PEMI

interferometer. Next, using the interferometer's fine tuning screws, null field

displacements were obtained. Once this was achieved for both U and V fields, load was

gradually applied up to a point where a dense fringe pattern was observed and pictures

were recorded.

One of the main objectives of this project was to determine the displacement fields

for various specimen orientations, 0. The advantage of a center notch disk specimen is

that mode I, mode II and mixed mode are present by running a simple compression test

using a single specimen geometry.

Fig. 5-1 illustrates how load was applied to the specimen in order to obtain mode I,

mode II and mixed mode loading. When loaded in the direction of the notch (i.e., the

direction of the notch matches the direction of the loading) pure mode I is obtained. For

the angle between the load and the direction of the notch of about 27 deg. pure mode II is

obtained. Loading at any angle between 0 and 27 deg. will produce a combination of the

two modes (mixed mode).









Tests were conducted for cases with no load misalignment. Full displacement fields

were documented and analyzed; after gaining confidence in the results, additional tests

were conducted for the misalignment cases. Misalignment was obtained using a special

fixture with tilting capabilities.

Fig. 5-2 shows the actual specimen positioned in the loading fixture. A special

guiding device placed the specimen at the same location every time a test is conducted.

Adjusting screws on the bottom part of the fixture allowed for in-plane and out-of-plane

load misalignment.


guiding fixture




digital inciinometer....













adjusting screws


Figure 5-2. Loading fixture, actual specimen and digital inclinometer

Fig. 5-3 shows a close up of the experimental setup with the moire interferometer

placed on top of the tilting fixture and in front of the specimen. The digital inclinometer

placed on top of the moire interferometer was used to record the angles at which the

specimen was loaded.























Figure 5-3. Tilting fixture, interferometer and digital inclinometer
Fig. 5-4 shows a schematic description (front and side view) of how load was

applied to achieve misalignment. In-plane misalignment (3) can be achieved by rotating

the bottom part of the fixture in the plane of the specimen, Fig. 5-4(a), while rotating the

bottom part of the fixture in a plane perpendicular to the specimen's surface, out-of-plane

misalignment (y) is achieved Fig. 5-4(b).

P0 P








PH
P : P

(a) 1' (b)
Figure 5-4. Front (a) and side (b) view description of the specimen for in-plane and out-
of-plane misalignment cases









5.3 Experimental Results

5.3.1 Angle Dependent Displacement Fields

Using the method described, tests were conducted and displacement fields were

documented and analyzed. Because the displacement fields are notch angle dependent, all

cases, at 20 increments were considered for a full and complete analysis but only a few

are presented in this paper due to space consideration.

Fig. 5-5 shows the horizontal and vertical moire interferometry fringe patterns for

pure mode I loading. The symmetric fringe patterns obtained indicate that load was

applied correctly i.e., in the direction of the notch. Analyzing the fringe pattern from the

U displacement field, Fig. 5-5(a) we can observe that in fact the notch is opening as

expected for this type of specimen in pure mode I loading. Also, the exact number of

fringes on a certain gage length around both of the crack tips, Fig. 5-5(b) and again the

symmetry of the fringe patterns indicate that the fixture was aligned properly with the

specimen and no misalignment was induced.

Fig. 5-6 shows the fringe patterns for the mixed mode loading. Analyzing the fringe

patterns from both U field, Fig. 5-6(a) and V field, Fig. 5-6 (b), we can see that both

modes are present and although the notch was still opening under the applied load, the

influence of the mode II was dominant. Shear, as the predominant effect, is indicated by

the fringes that almost align to the direction of the notch Fig. 5-6(b). Symmetry again

indicated good alignment of the specimen with the load applied.

Fig. 5-7 presents the case of pure mode II loading. Fringe patterns in the V field,

Fig. 5-7 (b), parallel to the direction of the notch are indication of shear between the two

regions.




Full Text

PAGE 1

TEMPERATURE DEPENDENT MECHANIC AL PROPERTIES OF COMPOSITE MATERIALS AND UNCERTAINTIES IN EXPERIMENTAL MEASUREMENTS By LUCIAN M. SPERIATU A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2005

PAGE 2

Copyright 2005 by Lucian M. Speriatu

PAGE 3

This dissertation is dedicated to my family.

PAGE 4

ACKNOWLEDGMENTS I would like to thank my advisor, Dr. Peter Ifju, for his support, advice and friendship. I would also like to thank my other committee members, Dr. Raphael Haftka, Dr. Nicolae Cristescu, Dr. Bhavani Sankar and Dr. Fereshteh Ebrahimi, for their advice. I thank William Schulz, Donald Myers, Thomas Singer, Dr. Leishan Chen, Ryan Karkkainen, Dr. Theodore Johnson, and Ron Brown for their assistance in my efforts throughout the years. iv

PAGE 5

TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................iv LIST OF TABLES ............................................................................................................vii LIST OF FIGURES .........................................................................................................viii LIST OF SYMBOLS AND ABBREVIATIONS .............................................................xii ABSTRACT .....................................................................................................................xvi CHAPTER 1 INTRODUCTION........................................................................................................1 1.1 Background .............................................................................................................1 1.2 Moir Interferometry ..............................................................................................4 1.3 Digital Image Processing and Fringe Analysis .......................................................6 1.4 Temperature Dependent Measurements .................................................................8 1.5 Research Motivation and Objectives ......................................................................9 2 TEMPERATURE DEPENDENT TRANSVERSE MODULUS EXPERIMENTAL MEASUREMENTS....................................................................12 2.1 Introduction ...........................................................................................................12 2.2 Characterization of Transverse Modulus ..............................................................14 2.3 Experimental Setup ...............................................................................................15 2.4 Experimental Procedure and Results ....................................................................24 2.5 Conclusions ...........................................................................................................31 2.6 Discussion and Future Work ................................................................................32 3 TEMPERATURE DEPENDENT SHEAR MODULUS EXPERIMENTAL MEASUREMENTS....................................................................................................36 3.1 Characterization of Shear Modulus ......................................................................36 3.2 Double Notch Shear Specimen (DNSS) for G Testing 12 ......................................39 3.3 Experimental Setup ...............................................................................................47 3.4 Experimental Procedure and Results ....................................................................47 3.5 Conclusions ...........................................................................................................53 v

PAGE 6

3.6 Discussion and Future Work ................................................................................54 4 RESIDUAL STRESSES IN LAMINATED COMPOSITES.....................................58 4.1 Introduction ...........................................................................................................58 4.2 Cure Referencing Method .....................................................................................59 4.3 Residual Stresses and CTE Measurements ...........................................................63 4.3.1 Data Analysis ..............................................................................................64 4.3.2 Experimental Results ..................................................................................68 4.4 Conclusions ...........................................................................................................73 4.5 Discussion and Future Work ................................................................................74 5 EXPERIMENTAL CHARACTERIZATION OF LOADING IMPERFECTION ON THE BRAZILIAN DISK SPECIMEN................................................................76 5.1 Introduction ...........................................................................................................76 5.2 Experimental Procedure ........................................................................................78 5.3 Experimental Results ............................................................................................83 5.3.1 Angle Dependent Displacement Fields ......................................................83 5.3.2 Comparison to the FEA ..............................................................................85 5.3.3 Plastic Zones Ahead of the Crack Tips ......................................................87 5.4 Effect of Load Misalignment in the Linear Range ...............................................89 5.5 Effect of Load Misalignment in the Plastic Range ...............................................94 5.6 J-Integral Estimation Procedure, Experimental Analysis .....................................95 5.7 Alignment Procedure ............................................................................................99 5.8 Discussions and Recommendations ....................................................................104 5.9 Conclusions .........................................................................................................105 6 REDUCING UNCERTAINTIES IN EXPERIMENTAL MEASUREMENTS TO REDUCE STRUCTURAL WEIGHT......................................................................106 6.1 Experimental Errors and Uncertainty .................................................................106 6.2 Reducing Uncertainties in Experimental Measurements ....................................109 6.3 Uncertainty Analysis for E and G Measurements 2 12 ..........................................110 6.4 Conclusions .........................................................................................................124 6.5 Discussion and Future Work ..............................................................................124 7 CONCLUSIONS ......................................................................................................127 APPENDIX: MATLAB CODE FOR PLOTTING TEMPERATURE VS. TRANSVERSE MODULUS:...................................................................................129 LIST OF REFERENCES .................................................................................................134 BIOGRAPHICAL SKETCH ...........................................................................................142 vi

PAGE 7

LIST OF TABLES Table page 2-1 Width and average thickness measurements for all tested specimens .....................27 2-2 The mean, standard variation and coefficient of variation at each temperature for all tested specimens ..................................................................................................31 3-1 Length and average thickness measurements for all tested specimens ....................50 3-2 The mean, standard variation and coefficient of variation at each temperature for all tested specimens ..................................................................................................53 4-1 Strain at cure temperature due to chemical shrinkage (CS) .....................................70 6-1 Uncertainty from the load cell ................................................................................112 6-2 Percent difference found in measuring known weights .........................................112 6-3 Uncertainty from measuring the width and thickness of the specimens ................113 6-4 Percent difference found in measuring temperature ...............................................114 6-5 Measurement variability of cross-sectional area in few specimens .......................117 6-6 Percent difference in E2 by including specimens with different speed of testing .119 vii

PAGE 8

LIST OF FIGURES Figure page 1-1 X-33 reusable launch vehicle .....................................................................................3 1-2 Schematic description of four-beam moir interferometer to record the N and N fringe patterns, which depict the U and V displacement fields x y ..................................6 1-3 Failure of the outer skin of the LN2 tank of the X-33 RLV .....................................10 1-4 Effect of variability on tank wall thickness 2 ult .......................................................11 2-1 Experimental setup: MTI testing machine, environmental chamber, data acquisition system ....................................................................................................16 2-2 Detailed drawing of the grip, top (left) and side (right) views .................................17 2-3 Front (left) and side (right) views detailed drawings of the connecting rod ............17 2-4 Detailed drawing of the aluminum alignment fixture, top (left) and side (right) views .........................................................................................................................18 2-5 3D AutoCAD schematic of one of the two grips .....................................................18 2-6 Schematic view of the alignment fixture for specimens with grips .........................19 2-7 Detailed drawing of the alignment fixture for specimens with grips, top (left) and side (right) views ...............................................................................................20 2-8 Alignment fixture with specimen and grips .............................................................21 2-9 Gripping fixture and specimen in alignment tool .....................................................21 2-10 Thermal chamber and LN2 dewar ............................................................................22 2-11 Rohacell thermal chamber with specimen, open (left) and closed (right) ................23 2-12 Transverse modulus panel with cut specimens ........................................................25 2-13 Quarter-bridge circuit diagram .................................................................................26 2-14 Transverse modulus as a function of temperature for all tested specimens .............29 viii

PAGE 9

2-15 Linear fit for the transverse modulus as a function of temperature ..........................30 2-16 Transverse modulus as a function of temperature with linear fit and extra data from literature ...........................................................................................................34 3-1 Iosipescus specimen in the loading fixture .............................................................38 3-2 Variation of G with the fiber orientation angle xy .....................................................41 3-3 Shear stress (S) distribution for specimen with 0 oriented notches 12 .....................44 3-4 Transverse stress (S) distribution for specimen with 0 oriented notches 22 .............44 3-5 Shear stress (S) distribution for specimen with 45 oriented notches 12 ...................44 3-6 Transverse stress (S) distribution for specimen with 45 oriented notches 22 ...........45 3-7 Shear stress (S) distribution for specimen with 60 oriented notches 12 ...................45 3-8 Transverse stress (S) distribution for specimen with 60 oriented notches 22 ...........45 3-9 Shear stress (S) distribution for specimen with rounded notches 12 ..........................46 3-10 Transverse stress (S) distribution for specimen with rounded notches 22 .................46 3-11 Shear stress (S) distribution for the DNSS specimen 12 ............................................47 3-12 Transverse stress (S) distribution for the DNSS specimen 22 ....................................47 3-13 DNSS specimens ......................................................................................................48 3-14 The shear gage ..........................................................................................................49 3-15 Half-bridge circuit diagram ......................................................................................49 3-16 Shear modulus as a function of temperature for all tested specimens ......................52 3-17 Linear fit through the data points for the shear modulus as a function of temperature ...............................................................................................................52 3-18 Shear modulus as a function of temperature with linear fit and extra data from the literature ..............................................................................................................57 4-1 Schematic of the replication technique ....................................................................61 4-2 Method of attaching the diffraction grating to the composite in the autoclave ........62 4-3 Cure cycle for laminated composites in autoclave ...................................................62 ix

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4-4 Typical horizontal and vertical fringe patterns .........................................................64 4-5 Example of counting fringes to determine surface strains .......................................65 4-6 CCD camera .............................................................................................................66 4-7 Specially designed stage for fringe shifting .............................................................67 4-8 Experimental setup for fringe shifting .....................................................................68 4-9 Temperature dependent average strains for different laminate configurations ........69 4-10 Temperature dependent CTEs for different laminate configurations .......................70 4-11 Effect of chemical shrinkage on residual stress calculation .....................................72 4-12 Effect of chemical shrinkage and temperature dependent properties on residual stress calculation ......................................................................................................73 5-1 Schematic description of the Brazilian disk .............................................................79 5-2 Loading fixture, actual specimen and digital inclinometer ......................................81 5-3 Tilting fixture, interferometer and digital inclinometer ...........................................82 5-4 Front (a) and side (b) view description of the specimen for in-plane and out-of-plane misalignment cases .........................................................................................82 5-5 Displacement fields for mode I loading, U (a) and V (b) ........................................84 5-6 Displacement fields for mixed mode loading, U (a) and V (b) ................................84 5-7 Displacement fields for mode II loading, U (a) and V (b) .......................................85 5-8 Comparison between Moir (top) and FEA (bottom) results for U (a) and V (b) displacement fields, mode I loading .........................................................................86 5-9 Comparison between Moir (top) and FEA (bottom) results for U (a) and V (b) displacement fields, mixed mode loading ................................................................87 5-10 Horizontal and vertical fringe patterns showing the plastic zones formed around the crack tip for mode I loading ...............................................................................88 5-11 Horizontal and vertical fringe patterns showing the plastic zones formed around the crack tip for mode II loading ..............................................................................88 5-12 Effect of in-plane misalignment on before and after misalignment .........................90 5-13 Effect of out-of-plane misalignment before and after misalignment .......................91 x

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5-14 Effect of in-plane misalignment on the V field ........................................................93 5-15 Effect of out-of-plane misalignment on the V field .................................................93 5-16 Horizontal and vertical fringe patterns showing the plastic zones around the crack tips for an intentionally misaligned specimen loaded in mode I ....................94 5-17 Horizontal and vertical fringe patterns showing the plastic zones around the crack tips for an intentionally misaligned specimen loaded in mode II ...................95 5-18 Strains values at different data points along the path for an in-plane misaligned specimen ...................................................................................................................96 5-19 Strains values at different data points along the path for an out-of-plane misaligned specimen ................................................................................................97 5-20 Upper and lower crack J-integral difference variation with in-plane misalignment ............................................................................................................98 5-21 Upper and lower crack J-integral difference variation with out-of-plane misalignment ............................................................................................................99 5-22 Front view of aluminum Brazilian disk specimen with attached strain gages and lead wires ................................................................................................................100 5-23 Schematic description of the alignment procedure, step 1 .....................................102 5-24 Schematic description of the alignment procedure, step 2 .....................................102 5-25 Schematic description of the alignment procedure, step 3 .....................................102 6-1 Variation of E/E with fiber orientation x 12 ..............................................................114 6-2 Variation of G with fiber orientation xy ...................................................................115 6-3 Speed of testing effect on the transverse modulus .................................................118 6-4 Transverse modulus variation with temperature for two runs of the same specimen .................................................................................................................120 6-5 Transverse modulus with 1.29% error bars ............................................................122 6-6 Shear modulus with 1.40% error bars ....................................................................123 xi

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LIST OF SYMBOLS AND ABBREVIATIONS A Cross-sectional area ASTM American Society for Testing and Materials BDS Brazilian Disk Specimen CCD Charge Coupled Device CLT Classical Lamination Theory CNC Computerized Numerical Control COD Crack opening displacement CRM Cure Reference Method CS Chemical shrinkage CTE x Coefficient of thermal expansion in the x-direction CTE y Coefficient of thermal expansion in the y-direction CV Coefficient of Variation DNSS Double Notch Shear Specimens E 1 Lamina elastic modulus in fiber direction E 2 Lamina elastic modulus in transverse direction EDM Electrical Discharge Machining f Frequency of the diffraction grating FEA Finite Element Analysis FO Fiber orientation G 12 Lamina shear modulus xii

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LN 2 Liquid nitrogen M Misalignment MTI Measurements Technology Inc. NASA National Aeronautics and Space Administration N x Fringe order in x-direction N y Fringe order in y-direction OAP Optimized Angle Ply P Applied load PEMI Portable Engineering Moir Interferometer Q Ply stiffness matrix R 2 Regression coefficient RLV Reusable Launch Vehicle S 12 Shear stress S 22 Transverse stress SCXI Signal Conditioning eXtensions for Instrumentation S n-1 Sample standard deviation T Temperature t Thickness of the specimen T 1 Temperature T 2 Temperature TD Temperature dependent Td Temperature diode tip Uncertainty in the thickness measurements from instrument precision xiii

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tuv Uncertainty in the thickness measurements from user variability U Horizontal displacement UNI Unidirectional V Vertical displacement w Width of the specimen wip Uncertainty in the width measurements from instrument precision wuv Uncertainty in the width measurements from user variability x-y Coordinate system aligned with laminate 0 (x) and 90 (y) directions xy Shear strain in the x-y coordinate system T Temperature difference 1-2 Coordinate system aligned with lamina fiber (1) and transverse (2) directions Experimentally measured CTE +45 Measured strain in the +45 direction 2 Transverse strain 2 ult Ultimate transverse strain 45 Measured strain in the -45 direction chem Chemical shrinkage vector of a unidirectional panel, 3x1 uni Strain vector on a unidirectional panel in the x-y system, 3x1 x Strain in the x-direction y Strain in the y-direction sg Uncertainty in the strain gage Angle between x-y and 1-2 coordinate systems 12 Lamina Poissons ratio. xiv

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2 Transverse stress res Residual stress vector in the 1-2 coordinate system, 3x1 Shear stress xv

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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 TEMPERATURE DEPENDENT MECHANICAL PROPERTIES OF COMPOSITE MATERIALS AND UNCERTAINTIES IN EXPERIMENTAL MEASUREMENTS By Lucian M. Speriatu August 2005 Chair: Peter Ifju Major Department: Mechanical and Aerospace Engineering A new method for efficient determination of multiple material property values and improved techniques for reduction in experimental uncertainty were developed for use on composite and lightweight materials that perform under extreme temperatures and sustained load. The method calls for use of tension specimens only in determining the material properties, using a specially designed chamber with both cryogenic and high temperature testing capabilities. Mechanical properties of fiber reinforced composite materials were determined, such as transverse modulus (E 2 ) and shear modulus (G 12 ). Specially designed double notch tension specimens and shear strain gages were used to determine the shear properties in composites in a unique and more efficient way. A robust set of data from cryogenic to elevated temperatures for the two material properties of fiber reinforced composite materials was obtained and reported. The fracture behavior of single crystal metallic materials was also investigated at room temperature. The Brazilian Disk Specimen (BDS) was proposed to study mode I, xvi

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mode II and mixed mode fracture of these materials. During the study, questions arose concerning the effect of load misalignment on the stress field at the crack tip and crack propagation. To isolate the loading effects from the crystallographic effects, a systematic experimental study was conducted on aluminum specimens to characterize the effect of load misalignment and specimen orientation in the linear range as well as in the plastic range. xvii

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CHAPTER 1 INTRODUCTION In the development of new structural materials, it is first required to perform a detailed mechanical characterization to be able to implement these materials into an improved, optimized component design. Current techniques require several different tests and specimen types to achieve a complete thermo-mechanical characterization. Furthermore, each test and specimen is subject to inherent error types that led to uncertainty in material property values. Thus, the current paper aims to establish a new method for efficient determination of multiple material property values, as well as improved techniques for reduction in experimental uncertainty. 1.1 Background One of the primary goals of engineers has been to develop new lighter materials with improved properties, such as strength, toughness and heat resistance, which can be used in the design of engineering structures. One answer came in the form of so called composite material [1], which is by definition a material that consists of two or more materials combined at the macroscopic scale and that is superior to the constituents themselves. Fiber reinforced composites are a special type of composite that have become more and more popular these days, since it has been demonstrated that some materials are stronger in the fiber form than in the bulk form. Fiber reinforced composites offer numerous advantages over the conventional materials, but they also have shortcomings 1

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2 such as poor material performance in the transverse direction and poor out-of-plane properties. Although the basic man-made composites have been around for thousands of years, the introduction of fiber-reinforced composites in structural design in 1960s has generated the need to develop new testing methods and procedures to characterize these materials. Assessment of their performance under thermo-mechanical loading would increase their reliability and allow for a better design of engineering structures, especially those in aerospace applications. Although these laminated fiber reinforced composite materials were predicted to become the materials of choice in such applications, aluminum is still predominantly used. This is partially due to the lack of experimental data in the mechanical properties of composites and is also because their behavior is not yet fully understood. In the pursuit of space exploration, efforts have been underway to replace the aging space shuttle with a newly developed reusable launch vehicle (RLV). This vehicle would provide a reduction in the cost of launching payloads into space from $10,000 to $1,000 per pound. This would be possible only by reducing the overall structural weight of the vehicle by using lightweight materials such as fiber reinforced composites. This vehicle would also have to be entirely self-contained throughout the mission. The development of the X-33 reusable launch vehicle [2], shown in Fig. 1-1, tried to achieve all those goals. The X-33 had two internal liquid hydrogen fuel tanks made of composite materials. While the choice of such materials in this application seemed appropriate at the time, the preflight testing in the fall of 1999 at NASA Marshall Space Flight Center for verification

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3 of the tanks at cryogenic loading condition of -423F revealed micro-cracking that later led to failure of the liquid hydrogen tanks. Figure 1-1. X-33 reusable launch vehicle Recently, Bechel et al. [3] performed a study on different polymer matrix composites, including the IM7/977-2 that was used in the X-33 project, by thermally cycling the structural composites from cryogenic to elevated temperatures. The investigated composites rapidly developed micro cracks when subjected to combined cycling, i.e., cryogenic to elevated temperatures. Thus to safely use fiber reinforced composites in such applications, we need a methodology to predict multiple mechanical properties of fiber reinforced materials as a function of temperature as well as to understand their temperature dependent behavior. The determination of elastic constants of a composite material is significantly more complicated than the determination of these constants for an isotropic material. In view of the fact that design of composite structures achieves a reduction in weight and an

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4 improvement in strength and toughness, a major effort has to be put in the development of standard test methods for material property characterization. 1.2 Moir Interferometry Even though laminated composites are widely used in aerospace applications because of their high strength-to-weight ratio, there are numerous shortcomings that designers have to overcome when using such materials. One important shortcoming is the development of the residual stresses within the laminate. These stresses form due to the matrix solidification around the reinforcement or due to mismatch in the coefficients of thermal expansion between the fiber and the matrix. A non-destructive method is used in conjunction with the moir interferometry [4] technique to determine the surface strains and the coefficients of thermal expansion in laminated composites, as will be explained in Chapter 4. Because the moir interferometry technique plays a key role in the determination of accurate temperature dependent residual stresses in laminated composites it was considered necessary to introduce the method and present its principle of operation. Moir interferometry is a laser based optical technique that combines the concepts of optical interferometry and geometrical moir. It is a full-field technique capable of measuring the in-plane displacements with very high sensitivity (sub-micron level). This measurement technique uses the interference effect between a (virtual) reference grating and a specimen grating to magnify the surface deformations and creates a moir fringe pattern which is related to surface displacements. The relationship between fringe order and displacement is shown in Eqs. (1-1) and (1-2): yxNfyxUx,1, (1-1)

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5 yxNfyxVy,1, (1-2) where U and V are the horizontal and vertical displacement fields, N x and N y are the fringe orders corresponding to the horizontal and vertical displacement fields, and f is the frequency of the reference grating. Using the relationships between displacements and engineering strains we get Eqs. (1-3) to (1-5): xNfxUxx1 (1-3) yNfyVyy1 (1-4) xNyNfxVyUyxxy1 (1-5) where x y are the strains in the x and y directions respectively, and xy is the shear strain. A schematic description of the moir interferometry is presented in Fig. 1-2. There are numerous configurations of optical and mechanical components that produce the four beams illustrated in Fig.1-2. The entire ensemble that produces these four-beams is called a moir interferometer. The applications of the moir interferometry include determination of the thermal deformations in microelectronic devices, determination of the coefficient of thermal expansion, characterization of the fiber-reinforced polymer matrix composite materials, fracture mechanics, micro-mechanics. Moir interferometry has also been used to validate models, estimate reliability, and identify design weakness.

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6 Figure 1-2. Schematic description of four-beam moir interferometer to record the N x and N y fringe patterns, which depict the U and V displacement fields 1.3 Digital Image Processing and Fringe Analysis The result of the moir interferometry technique appears as a set of fringe patterns, or contour maps, of displacement. These fringe patterns have to be documented, analyzed and interpreted. For many years, the analysis of the fringe patterns was performed by locating the positions and numbering the fringes manually. Because of the development and decreasing cost of the digital image processing equipment [5], the digital image fringe pattern techniques are increasingly used in acquiring strains and stresses. The reasons for implementing this method are to improve the accuracy, to improve the speed,

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7 and to automate the process. Ultimately, it is the intent to eliminate the human factor by automatically detecting the positions of the fringes. The digital image processing system consists of a CCD camera and a frame grabber. The CCD camera is used to scan the fringe pattern. The frame grabber, which is a video digitizer, digitizes the image and stores it into the computer memory. Then by using different techniques, the fringe order is calculated and an image output is produced. This combination of the digital camera, frame grabber and computer made it very easy to record and manipulate the images. These image manipulations are performed on the individual pixels. Many fringe analysis procedures were developed based on different algorithms [6]. Ultimately the fringe pattern dictates the validity and applicability of a specific algorithm. For complicated fringe patterns and with a high fringe frequency, the algorithm used may not detect the fringes accurately, which can lead to erroneous results. An image of a simple fringe pattern with low fringe frequency is easier to manipulate and provides more accurate output. Recently, more powerful algorithms and procedures were developed to dramatically reduce the output errors, making this automated fringe analysis a quick and efficient tool in the analysis of the moir fringe patterns. This is why digital image processing is increasingly used in applications that require the use of moir interferometry but is not limited to this area. In a recent paper by Kishen et al. [7], biomedical engineers have investigated the human dentine using a digital speckle pattern interferometer and thermography, in conjunction with an advanced digital fringe processing technique, to analyze its deformation when subjected to

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8 temperature changes. Spagnolo et al. [8] presented a full digital speckle photography to measure free convection in liquids together with a fast Fourier transform algorithm to compute the fringe patterns and speckle displacement, and Ramesh et al. [9] investigated the possibility of using the hardware features of a color image processing system for automated photo elastic data acquisition. And although the greater part of the researchers are simply users of the digital image processing systems, there is continuous research undergoing for the improvement in both the hardware and the algorithms used, thus increasing the accuracy of the method. In the end, an automation of the method for an easier manipulation of the results as well as a more accurate output is obtained. 1.4 Temperature Dependent Measurements Some of the latest applications in aerospace engineering require that new structural materials perform under extreme temperature and load conditions; therefore a huge effort is made to characterize the thermo-mechanical behavior of such materials. Temperature dependent experimental measurements on composite and lightweight materials remain relatively undeveloped. To correctly predict their behavior as well as to be able to integrate them into an optimization scheme to perform probabilistic analysis and design, the temperature dependence must be known accurately. Unfortunately, there is not enough information available on the temperature dependent mechanical properties of different materials used in aerospace applications. This is usually because no standard methods exist that will help researchers determining these properties. Another important reason is that current methods and techniques are inefficient and expensive giving little option to designers; they are forced to use in the design of engineering structures room temperature properties and minimum information collected at cryogenic and elevated temperatures. Temperature dependent data

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9 measurements, for fiber reinforced composite materials in particular, are unexploited and some of the temperature dependent data for material properties such as shear and transverse moduli are of special interest. 1.5 Research Motivation and Objectives Composite materials are increasingly used in aerospace applications. A recent goal of NASA was to replace the aged space shuttle with lighter vehicles that can achieve a ten times reduction in the cost of the payload by incorporating composite and lightweight materials in the vehicles design. Since composites have a high strength-to-weight ratio, all-composite tanks for cryogenic storage have become of great interest for researchers. However, NASAs X-33 project, which incorporated LN 2 tanks made of fiber-reinforced composites, unfortunately failed, as seen in Fig. 1-3, because of microcracking of the tank walls. Lack of information about material behavior under extreme temperatures and sustained load was one of the main contributors to this failure. At the moment, besides working on new manufacturing techniques and novel curing processes, substantial effort is underway to characterize the temperature-dependent behavior of fiber reinforced composite materials. Thus, there is currently a need for methods and techniques to perform simpler and more efficient tests on composite materials to determine their temperature dependent mechanical properties. This paper aims to develop such a method for efficient determination of different material property values as a function of temperature, before the implementation of the laminated composites in engineering structures. On the other hand, measurement variability is a key factor that accounts for an increased safety factor to ensure reliability.

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10 Figure 1-3. Failure of the outer skin of the LN2 tank of the X-33 RLV This variability in the material properties translates into a heavier vehicle. A previous LN 2 tank optimization study, as discussed in Chapter 4, showed the effect of variability on tank wall thickness. Fig. 1-4 shows that by reducing the variability in the ultimate transverse tensile strength ( 2 ult ) by 10%, the thickness is reduced by about 15% for the same probability of failure of 1 in 1,000,000. Thus, using a probabilistic design, which is based on the probability of failure, we can minimize the weight of the vehicle.

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11 Figure 1-4. Effect of 2 ult variability on tank wall thickness The objectives of this dissertation are to establish a simple and more efficient testing method for determination of multiple material property values as a function of temperature, to improve techniques for reduction in experimental uncertainty, as well as to reduce the variability and uncertainty in the experimental measurements.

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CHAPTER 2 TEMPERATURE DEPENDENT TRANSVERSE MODULUS EXPERIMENTAL MEASUREMENTS 2.1 Introduction Temperature dependent experimental measurements on composite and lightweight materials remain relatively undeveloped. To correctly predict the behavior of these materials, as well as to be able to integrate them into an optimization scheme to perform probabilistic analysis and design, the temperature dependence must be known accurately. Takeda et al. [10] employed three-dimensional finite elements to examine the thermo-mechanical behavior of cracked G-11 woven glass/epoxy laminates with temperature-dependent material properties under tension at cryogenic temperatures. Experimental studies [11-14] investigated the mechanical properties and the behavior of different materials under cryogenic temperatures and Schultz [15] looked at the mechanical, thermal and electrical properties of fiber reinforced composites at cryogenic temperatures. In a study by Baynham et al. [16] the transverse mechanical properties of glass reinforced composites at 4K were reported from tests using an improved specimen design and also using finite element modeling techniques, and data on the properties of composites at 4 K in a biaxial shear/tension situation were recorded for the first time. In the past decade there were relatively a few studies on the temperature effects on the mechanical properties of fiber-reinforced composites to investigate their applicability for cryogenic use. Hussain et al. [17] studied the interface behavior and mechanical properties of carbon fiber reinforced epoxy composites at room and liquid nitrogen 12

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13 temperature. Glass [18] looked at the Gore-Tex woven fabrics mechanical properties and determined them at ambient, elevated, liquid nitrogen, and liquid helium temperatures in hope that they can contain gaseous helium at 60 psi. Shindo et al. [19] studied the cryogenic compressive properties of G-10CR and SL-ES30 glass-cloth/epoxy laminates for superconducting magnets in fusion energy systems and experimentally investigated the effects of temperature and specimen geometry on the compressive properties, and Horiuchi et al. [20] considered carbon reinforced fiber plastics as supports for cold transportable nuclear magnetic resonance cryostat and found the performance and reliability of the cryostat to be acceptable. But the mechanical properties of different materials used in aerospace applications are usually determined at room temperature and used as a reference in the design of engineering structures even when they are used in extreme environments. Sometimes only a few data points are collected, usually one point at cryogenic temperature, one at room temperature, and one at elevated temperature. However, this is not enough to determine an accurate basic fitting curve of the investigated material property as a function of temperature unless the trend is proved linear. Temperature dependent data measurements, for fiber reinforced composite materials in particular, are unexploited and some of the temperature dependent data for material properties such as shear and transverse moduli are of special interest. Special configuration fiber reinforced composites such as the IM7/977-2 of the X-33 reusable launch vehicle require systematic experimental testing from cryogenic to elevated temperatures before it can be safely implemented in an engineering structure that can withstand thermo-mechanical loading. Unfortunately, an investigation of graphite/epoxy laminates for suitability of cryogenic

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14 fuel applications was performed only after the failure of the X-33 project. Roy et al. [21] examined the IM7/PETI-5 graphite/epoxy cross-ply laminate system to predict COD and permeability in polymer matrix composites, and Bechel et al. [22] performed a study on different polymer matrix composites, including the IM7/977-2 that was used in the X-33 project, to investigate micro cracking development due to thermal cycling from cryogenic to elevated temperatures. Future work on this problem seems to concentrate on the infusion of nano-particles in the fiber reinforced polymeric materials to enhance their resistance to thermal cycling induced stresses [23]. However, there is currently a need for methods and techniques to perform more simple and efficient tests on composite materials to determine their temperature dependent mechanical properties. This paper aims to develop such a method for efficient determination of different material property values as a function of temperature, before the implementation of the laminated composites in the engineering structures. 2.2 Characterization of Transverse Modulus ASTM 3039 [24] is currently the standard testing procedure for determining room temperature longitudinal modulus and transverse modulus of composite materials. However, since the goal of this research was to determine temperature dependent transverse and shear moduli, a new and efficient experimental method was developed to determine such material properties of composite materials as a function of temperature. The method is capable of performing multiple tests such as E 1 E 2 and G 12, using a single experimental setup. Temperature dependent mechanical properties such as E 2 and G 12 of unidirectional IM7/977-2 panels were investigated and reported in this paper. This

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15 chapter presents a characterization of the transverse modulus for the IM7/977-2 material system. 2.3 Experimental Setup The proposed testing method, which follows the ASTM 3039 guidelines for material property determination of composite materials, had to be designed with the understanding that we were dealing with extreme temperatures. Consequently, improvements and additions to the ASTM setup were implemented resulting in the development of a new testing procedure. The setup consists of a compression-tension MTI type machine, a testing chamber, an environmental chamber that regulates the temperature inside the testing chamber, a liquid nitrogen (LN 2 ) dewar, and a data acquisition system. Fig. 2-1 shows the entire experimental setup. A 30K compression/tension-testing machine from MTI Phoenix was used. Since testing was performed under extreme temperature conditions, and since the current ASTM grips present a large thermal mass, the first thing that had to be addressed was the design of new, special grips that would be suitable for such application. The mechanical drawings of the newly designed grips are shown in Fig. 2-2 through 2-4 and Fig. 2-5 shows a 3D AutoCAD schematic of the assembly. Each grip assembly consists of a few elements; the main part is the one referred here as grip. There are two such parts in the assembly. Each grip has a 1 x 1.8 grooved area that is machined to achieve maximum gripping power. Also the design of the grips accounted for obtaining a uniform distribution of the load to the specimen through the tabs attached at the ends.

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16 Figure 2-1. Experimental setup: MTI testing machine, environmental chamber, data acquisition system One of the two grips has two drilled holes while the other one has two taped holes that accommodate two 0.375 bolts. Both parts are heat-treated for hardness. On the upper part of the grips there are holes that allow for a 0.5 diameter pin to go through and hold in place a rod that connects to the MTI machine. Since the standard ASTM grips have an alignment system that makes sure the load goes through the mid-plane of the specimen, the newly designed grips were fitted with a so called alignment fixture that achieves the same thing. An aluminum block was machined using EDM, to slide on the connecting rod; when pushed down the wedge type alignment fixture positions the two grips at same distance from the center insuring that load goes through the mid-plane of the specimen.

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17 Figure 2-2. Detailed drawing of the grip, top (left) and side (right) views Figure 2-3. Front (left) and side (right) views detailed drawings of the connecting rod

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18 Figure 2-4. Detailed drawing of the aluminum alignment fixture, top (left) and side (right) views grip alignment fixture rod that connects to the MTI machine pin grip alignment fixture rod that connects to the MTI machine pin Figure 2-5. 3D AutoCAD schematic of one of the two grips

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19 Because of misalignment concerns, an alignment fixture was also designed to align the specimen with the grips. Misalignment is a very important factor that has to be accounted for when testing materials. It can induce errors that are substantial to cause premature failure or failure in a mode and/or direction that does not match prediction. Since the temperature dependent transverse modulus determination procedure requires the use of strain gages and since eliminating misalignment in the loading fixture translates into eliminating errors read by the gages, it was considered necessary to have such alignment fixture. This also achieves a more easy and efficient way to set up the fixture with the grips and specimen for testing. Fig. 2-6 through 2-9 show the alignment fixture with the grips and the specimen prepared for alignment. Figure 2-6. Schematic view of the alignment fixture for specimens with grips

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20 Figure 2-7. Detailed drawing of the alignment fixture for specimens with grips, top (left) and side (right) views

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21 Figure 2-8. Alignment fixture with specimen and grips Figure 2-9. Gripping fixture and specimen in alignment tool To regulate the temperature of the testing chamber, a liquid nitrogen (LN 2 ) dewar was attached to a Sun Systems Model EC12 environmental chamber, as seen in Fig. 2-10. Using the incorporated heating elements and by taking in LN 2 this chamber can easily regulate the temperature in our range of interest, i.e., between -200C and +200C degrees. Special insulated hoses connect the environmental chamber to the testing (thermal)

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22 chamber and a blower transports the regulated air from the environmental chamber to the testing chamber. The testing (thermal) chamber was made of Rohacell 110-IG foam; this material proved to have very good thermal insulation properties. The material proved also to be very efficient and inexpensive; although it was designed to be a disposable chamber, only one was machined and used for testing because it exhibited no deformation and/or lose of properties even after numerous cryogenic to high temperature cycles. CNC machining of the Rohacell foam was also very fast and efficient. The thermal chamber was placed around the specimen and grips, as seen in Fig. 2-11; tension straps helped holding it in place. Figure 2-10. Thermal chamber and LN2 dewar

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23 Figure 2-11. Rohacell thermal chamber with specimen, open (left) and closed (right) All MTI testing machines are equipped with a data acquisition system; however for this application a new data acquisition system had to be implemented to accommodate all the inputs such as strain gages, thermocouples, load cell, environmental chamber. In order to do that, controls from the machine had to be redirected towards a more powerful computer with SCXI modules from National Instruments. Regular setup for MTI type machines cannot accommodate such application unless a custom built setup is requested at the time of purchase. Therefore some modifications had to be made here; the crosshead controls as well as displacement rate control were transferred from the MTI machine to the new control system. Thus a control box had to be installed; simply by turning ON/OFF a few switches, the operator can switch from manual to new computer controls. An additional motorized potentiometer was installed such that by turning the power ON the crosshead

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24 displacement rate is automatically adjusted by the computer. The control box gives the operator the choice of running the old data acquisition system, the new data acquisition system or just having manual controls of the testing machine. A NI SCXI-1121 four channel module was used to read gages, control loading, and read the diode temperature sensor. 2.4 Experimental Procedure and Results Specimens for temperature dependent transverse modulus determination were prepared according to the ASTM 3039 standard and NASA recommendations. In order to accommodate our newly designed grips and to allow a smother transition of the applied loads to the test section, specimens were made longer than the standard suggested length. Thus 12 long specimens were used. These specimens were obtained from 12 x 12, 18 layer unidirectional panels that were produced in our lay-up facilities. The panels made of IM7/977-2 prepreg material were produced in the autoclave following the cure cycle, as explained in Chapter 4, which was used for the RLV. Using a diamond cutting wheel and then a surface grinder, four 12 x 1.6 x 1/16strips of G-10 fiberglass were cut. We then bonded them to the panel using Hysol 9394 epoxy following the curing cycle supplied by the manufacturer. These fiberglass strips provide tabs to the material. Attaching fiberglass strips to the entire panel was considered over individual ones because of efficiency as well as future reduction in data variability. These panels with the tabs were cut into 1.15 wide coupons using a diamond-cutting wheel, as seen in Fig. 2-12. A surface grinder was then used to grind both edges of the coupons to insure all the flaws produced during the cutting procedure would be removed. These flaws are dangerous because they can initiate failure sooner than expected. The process also allowed the specimens to reach a nominally width of

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25 1.000 thus controlling better the cross-sectional area. The final dimensions of the coupons were 12 x 1 x 0.9. Each panel and each coupon cut from the panel was labeled such that a future variability analysis would be possible. This is described in Chapter 6. Figure 2-12. Transverse modulus panel with cut specimens Strain gaging technique is widely used today in many applications. As any experimental technique strain gaging has its advantages and disadvantages. Used correctly, the technique can accurately determine the surface strain on the object where they are attached. Strain gages are made of a very thin wire bonded to a foil (backing). When attached to materials that experience mechanical and/or thermal loads, the strain gage will also experience them. Consequently, a change in resistance of the gage will appear that can be read using a quarter bridge configuration as shown in Fig. 2-13. This change in resistance

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26 is then related back to strain. In extreme temperature conditions the gage itself and the backing foil expand or contract and the strain values that are produced have to be subtracted or added to the strains exhibited by the material tested. The contribution of this so called apparent strain can be as much as 10%-15%. There are a few techniques that allow removing this apparent strain. The technique that was used in this project will be explained later on in this chapter. Figure 2-13. Quarter-bridge circuit diagram Gage selection was made to handle the large temperature range, nominally C. Therefore, WK-13-250BG-350 custom unidirectional gages were obtained through the Vishay Micromeasurements Group. All the other required supplies to attach the gages to the specimen, such as the M-Bond 610 epoxy adhesive, were also obtained from Vishay. Specimens were prepared according to NASA recommended procedures for strain gage application and ASTM standard. Each specimen was first abraded, with varying grits of sand paper. All the surface flaws were removed and a smooth finish surface was obtained to allow for good gage adhesion. The surface was cleaned with acetone and then two perpendicular marks were inscribed for gage alignment with the specimen.

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27 Acetone was used again for cleaning then any remaining impurities were removed by dusting the air off the surface. Thickness and width measurements were taken across the perpendicular mark on the specimen. Three thickness measurements were taken, one in the center and two at each side, according to the ASTM standard. The average of those three determined the thickness of the specimen. Table 2-1 shows the width and average thickness of each specimen: Table 2-1. Width and average thickness measurements for all tested specimens Specimen Width (in) Average thickness (in) p2-1 0.08050 1.00100 p2-2 0.09000 0.98700 p2-3 0.08800 0.99500 p2-4 0.08650 1.00250 p2-5 0.09000 1.00100 p2-7 0.08300 0.99500 p2-8 0.09000 0.99600 p2-9 0.08900 1.00100 p3-1 0.08400 0.99950 p3-2 0.08700 0.99970 p3-3 0.08683 0.99850 p3-4 0.08663 1.00180 p3-5 0.08700 1.00100 p4-1 0.08365 1.00030 p4-2 0.08656 1.00120 p4-3 0.08796 0.99985 p4-4 0.08761 1.00055 Using a microscope, a gage and strain relief tabs were aligned to the inscribed marks then a Teflon tape was used to temporarily attach them to the specimen. The undersides of the gage and strain relief tabs were exposed and together with the

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28 specimens surface they were coated with a thin layer of M-Bond 610 adhesive. After a ten-minute drying period the gage and the tab were placed back on the specimen and clamped with uniform pressure. The specimen was cured for three hours at 121C then post-cured for another two hours at 135C. Once the specimen was gaged, wires were soldered to the tabs and connected to the SCXI module, it was fixed to the grips using the alignment fixture. A temperature diode was taped to the specimen together with the environmental chambers thermocouple. The entire ensemble was positioned into the MTI machine then the specially designed testing chamber was placed around it and connected to the environmental chamber. The actual test was started and run as follows: a Labview program developed for this application was initiated which turned ON the environmental chamber and commanded it to reach -165C degrees. A blower circulated the air from the environmental chamber to the testing chamber to cool down the specimen inside it. Once it reached the commanded temperature, the specimen was allowed to soak for 23 minutes to reach an equilibrium temperature. When the equilibrium temperature was reached, the load cell and strain gages were zeroed out using the Labview program developed, then the specimen was loaded to 200 lb and unloaded to 0 lb for five consecutive times. Each specimen was tested at approximately 25C intervals, from -165C to +150C. After all the 14 measurements were recorded, a Matlab code [appendix] manipulated the data to obtain the average slope of the five curves at each temperature. Knowing the slope and the cross-sectional area allowed for transverse modulus determination such as in Eqs. (2.1) to (2-3): 222 E (2-1)

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29 AP2 (2-2) 22APE (2-3) where P is the applied load and A is the cross-sectional area of the specimen. Thus the transverse modulus is obtained from the slope of the load vs. strain curve, divided by the cross-sectional area of the specimen. Fig. 2-14 shows all the temperature dependent transverse modulus curves for all tested specimens and Fig. 2-15 shows a linear fit through all the data points. This basic fitting will be used in Chapter 4 to predict residual stresses for different laminate configurations. Figure 2-14. Transverse modulus as a function of temperature for all tested specimens

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30 Figure 2-15. Linear fit for the transverse modulus as a function of temperature The equation of the straight line and the regression coefficient are presented in Eqs. (2-4) and (2-5): GPaTTE 6744.9016127.02 (2-4) 9746.02R (2-5) For statistical purposes, the coefficients of variation (CV) were computed for all the tests and presented in Table 2-2. ASTM standard requires also that this data be determined every time a series of tests are conducted. The average transverse modulus and the standard deviation are used to compute the coefficients of variation at each temperature. The formulae used will be presented in Chapter 6, where a more detailed statistical and uncertainty analysis will be performed.

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31 Table 2-2. The mean, standard variation and coefficient of variation at each temperature for all tested specimens Temperature (C) Mean E 2 S N-1 CV % -165 1.25E+10 1.67E+08 1.33 -145 1.22E+10 1.40E+08 1.15 -125 1.19E+10 1.74E+08 1.46 -100 1.14E+10 2.20E+08 1.93 -75 1.07E+10 1.73E+08 1.61 -50 1.02E+10 1.61E+08 1.58 -25 9.81E+09 1.83E+08 1.87 +0 9.42E+09 1.93E+08 2.05 +25 9.00E+09 1.66E+08 1.85 +50 8.64E+09 1.46E+08 1.69 +75 8.40E+09 1.48E+08 1.77 +100 8.19E+09 1.66E+08 2.03 +125 7.92E+09 2.10E+08 2.65 +150 7.55E+09 1.60E+08 2.12 2.5 Conclusions A new and efficient method was developed for temperature dependent material property determination. The method was used to successfully determine the transverse modulus as a function of temperature for the unidirectional IM7/977-2 composite material. The method is fully automated and once a test is started do not require supervision. Specimens were easily fabricated using our facilities. Over twenty tests were performed during which the method proved to be very repeatable. A robust set of data was obtained using 14 points along the temperature range, i.e., -165C to +150C for each specimen. Each single test lasted approximately 9 hours and used less than half of tank of LN 2 An increased number of data points, up to 28, can be used from a single LN 2 tank, thus without requiring any user intervention, if a more accurate representation of the transverse modulus is desired.

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32 Besides characterizing the material behavior, the transverse modulus property of the IM7/977-2 will be used in a modified Classical Lamination Theory (CLT) Matlab code developed at the University of Florida; together with other mechanical properties this will be useful to predict more accurately the behavior of multidirectional laminates. 2.6 Discussion and Future Work This chapter described in details the experimental setup and procedure developed to obtain the temperature dependent transverse modulus for a particular fiber-reinforced polymer matrix composite material. The newly devised method was employed to test more than fifteen different specimens to obtain a robust set of data. Figure 2-15 shows the nonlinear behavior of the material investigated. Although a straight line was fitted through the data points and the equation was used later on to predict residual stresses, a higher order polynomial will be more representative. One can also speculate how the material will behave outside the temperature range where data was collected. Other polymer matrix composite materials that have been tested [53] at cryogenic temperatures showed a pronounced deviation from linearity in the modulus starting at liquid nitrogen temperature all the way to liquid helium temperatures. One possible explanation would be crack formation and crack propagation within the laminate. The temperature range initially considered for this research was from liquid nitrogen temperatures (-196C) to cure conditions (+182C). However, the actual tests were performed from -165C to approximately +155C. At the lower end of the temperature range, imperfect insulation of the system, including the testing chamber, did not allow the specimen to efficiently reach an equilibrium temperature below -170C. In the future a better insulation of the system and/or use of liquid helium should be

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33 considered to be able to perform more tests and obtain data below -165C; this will also provide more data to identify the best fitting method to accurately predict material behavior. Close to cure temperatures, the resin will reach the glass transition temperature which will probably change the properties of the composite. However, since no other measurements are taken after the elevated temperature data is collected there is no reason why the temperature range should not be increased. On the other hand, performing tests above +155C would probably show a huge drop in the modulus but the information would not be vital since the material was intended for cryogenic environments only. The author searched through the literature to find experimental data for the IM7/977-2 material to compare its findings but unfortunately found [3] extremely limited data. Only two data points are available, one at room temperature and the other one at liquid nitrogen temperature. These two points are shown in Fig. 2-16 together with the data obtained at University of Florida. When a straight line is fitted through those data points, a better match with the data from Wright Patterson AFB is obtained. A significant difference will be obtained when a higher order polynomial will be used. Two questions surfaced once the comparison was performed: first, which data is accurate and therefore should be trusted and second, since the specimens were first subjected to cryogenic temperatures and then the data was collected, does the thermal history affect the room temperature measurements? With respect to which data is more accurate, the author stands by the current findings. In Chapter 6, it will be shown that the method was calibrated and then tested on aluminum specimens with extremely good results. For liquid nitrogen temperature, a real comparison cannot be performed since no experimental data was obtained. Future work should concentrate on obtaining such data.

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34 Figure 2-16. Transverse modulus as a function of temperature with linear fit and extra data from literature But the room temperature measurements are of special interest since they might be a function of cycling the material from cryogenic to elevated temperatures. As mentioned, the specimens tested here were first exposed to cryogenic temperatures and then data was collected as temperatures were increased. This seems to affect the modulus and create the material nonlinearity. Comparing room temperature values with the Wright Pat AFB data a considerable difference was observed. Recently, tests have been performed at room temperature only to investigate this phenomenon. Preliminary results are much closer to the Wright Patterson AFB data. In the future, new tests should be performed starting at room temperature going down to cryogenic temperatures as well as from room temperatures to elevated temperatures to further investigate this aspect.

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35 One of the objectives of this research was to reduce the scatter in the data to allow for design optimization. This objective was accomplished since the method reduced scatter in the data with most of the coefficients of variation below 2%; the other study [3] showed 3% 5% scatter in the data. A reduction in variability would enable optimization through probabilistic design. The grips design with alignment capabilities, the alignment fixture for proper axial loading of the specimen as well as meticulous calibration of the entire system were part of the reason for such achievement.

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CHAPTER 3 TEMPERATURE DEPENDENT SHEAR MODULUS EXPERIMENTAL MEASUREMENTS 3.1 Characterization of Shear Modulus Due to the orthotropic behavior of most composite materials, the measurement of the shear properties has been a problem of special interest for a number of years. A variety of test methods [25] were developed to determine those properties. However, they all have some disadvantages, making them less than ideal. Shear characterization of laminated composites has been particularly challenging, because there is no standard test method available. Thus, a recognized need exists for a simple, efficient, and inexpensive test method for determination of shear properties in composites. The continuing advances in the development of new structural materials, especially those of fiber-reinforced composites, are leading to more consistent thermo-mechanical response characteristics. However, often times in trying to implement composite materials to aerospace applications, we find discrepancies in the test data obtained using different test methods that may be related to the correct interpretation of the test results; and this is especially true in the case of shear modulus for anisotropic composites. It has been generally recognized that the shear properties of fiber composites are more difficult to determine than the other elastic properties. This is due to the fact that for highly anisotropic fiber-reinforced composite materials, a state of pure shear stress is very difficult to attain. 36

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37 Numerous papers are available in the literature presenting different results for determining the shear properties of composite materials. Chan et al. [26] presented in their paper a sensitivity analysis of six shear and bending tests for determining the interlaminar shear modulus of fiber composites. Papadakis et al. [27] presented the strain rate effects on the shear mechanical properties of a highly oriented thermoplastic composite material. Most of the results that are published in the literature have been obtained using conventional mechanical tests such as the one presented by Marin et al. [28] where they determined G 12 by means of the off-axis test. The interesting part of this paper though is that they considered the gripping effect influence on the mechanical property in question, to reproduce the most reliable clamped conditions and thus to accurately present their results. However, the ideal shear test method is one that requires small and easily fabricated specimens, it is simple to conduct, and is capable of determining both shear strength and shear stiffness at the same time. There are currently many methods available to measure the shear properties of various composite materials, including the 45 test, the off-axis tensile test, thin-walled tube torsion test, solid rode torsion test, rail shear test plate twist test, split-ring shear test, and others but they are difficult to run, they are not applicable to any material and they are not capable of measuring both shear modulus and shear strength simultaneously. Also, tests like the off-axis test works well only for unidirectional, continuous fiber composites, the rail shear test induces stress concentrations at the specimen edges, the plate twist and split-ring shear tests measure only shear modulus, and the short beam shear test measure only shear strength.

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38 Applying torsional loading to thin-walled tube specimens produce the most uniform shear-stress state in a material; however, this method is not commonly used because tubular specimens are very expensive to manufacture. The Iosipescu [29] shear test method, introduced by Nicolae Iosipescu in Romania in the early 1960s, is considered the most promising shear test method because the specimens are easily made and both shear modulus and shear strength can be obtained. This method attempts to achieve a state of pure shear stress of the test section of the specimen by applying two counteracting force couples; it has been developed for use on isotropic materials but it was extended to composite materials testing by Adams and Walrath [30] of the University of Wyoming. Fig. 3-1 shows a specimen loaded in an Iosipescu fixture. Figure 3-1. Iosipescus specimen in the loading fixture

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39 3.2 Double Notch Shear Specimen (DNSS) for G 12 Testing Due to the Iosipescu methods popularity, extensive work has been performed for the past fifty years and researchers reported obtaining good results when using the method. For this reason, ASTM conducted a study [31] to determine its feasibility as a standard method for laminated composites. The results showed a substantial variation in the shear modulus compared to the variation of the longitudinal and transverse moduli for comparable materials. The study also revealed that the shear stress and shear strain distributions in the test section of the Iosipescu specimen were not uniform; they were also dependent on the orthotropy of the material tested, specimen configuration and loading condition. The specimens sometimes exhibit twisting during loading, adding and subtracting shear strain on the faces of the specimen; when following the recommendations by Adams and Walrath of using a small centrally located strain gage rosette, the measured shear modulus is inaccurate. Researchers [32-33] have tried to overcome most of the shortcomings by improving the method. Depending on the material tested, the Iosipescu shear test method was modified by improving the specimen geometry and the fixture. A special strain gage called the shear gage was developed by Ifju et al. [34] in collaboration with Prof. Post and Micro-Measurements Division of the Vishay Measurements Group Inc [35]. Ifju also improved the specimen geometry. His contributions led to the significant reduction of the coefficient of variation in shear modulus within each material system. He also demonstrated that the newly developed shear gage is insensitive to normal stress in the test section; this means that a state of pure shear stress in the test section does not have to be achieved in order to get accurate results.

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40 A complete and accurate knowledge of mechanical properties of composites is very important in the design of new engineering structures. Iosipescu method proved very efficient in determining some of their properties, namely the shear properties, as such presented in papers by Chiang et al. [36] where hybrid composites are investigated, and in a more comprehensive study by Odegard et al. [37] in which shear strength for unidirectional composites was determined using the Iosipescu method and the off-axis test, and then compared with the finite element method where they accounted for the non-linear material behavior. Whether unidirectional composites, textile composites [38] or brittle materials [39] were investigated, Iosipescu method presented numerous advantaged over the common mechanical tests available. Although many improvements to the Iosipescu method have been implemented, characterization of shear properties in composites remains a challenging task. When trying to determine the shear properties as a function of temperature we are confronted with new problems. Special test chambers have to be used when testing at cryogenic and elevated temperatures. The fixture required to conduct the Iosipescu shear test is too bulky, needs a lot of space thus imposing large and expensive test chambers and the test itself is very difficult to conduct in these conditions. There are two tension tests namely the degree test or the off-axis test that could have been used in conjunction with the experimental setup explained in Chapter 2. These two tests are the only existing tension shear tests that can compare to the newly developed method presented in this chapter. However these tests are not standard methods but guides and have also a few disadvantages making them less attractive for temperature dependent testing. The degree test requires E 1 and E 2 properties in order

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41 to determine G 12 and the off-axis test does not produce pure shear in the test section. Also the lay-up configuration makes these tests susceptible to measurement error due to fiber orientation and gage alignment. Both tests are very sensitive to load misalignment and gage positioning. Therefore the off-axis behavior of composite materials had to be accounted for since it can increase the variability in the experimental measurements. Looking at the variation of the engineering constant G 12 with the fiber orientation angle in Fig. 3-2, it can be observed that considerable error can be obtained from such tests if fiber and/or gage alignment is off by more than a few degrees. Figure 3-2. Variation of G xy with the fiber orientation angle

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42 Most importantly these two tests cannot evaluate the shear properties of multidirectional laminates or randomly oriented chopped fiber composites. This calls for the development of a new shear test method for efficient temperature-dependent determination of shear modulus. The proposed method would use double notch tension specimens designed such that a uniform shear stress state would be obtained in the test section. The new method would be easy to conduct, the specimens would be easy to fabricate and would require limited fixturing and consequently a small testing chamber. Most importantly this new method would allow for multiple property values determination such as longitudinal, transverse and shear moduli, using the same methodology and experimental setup. The main idea was to design a specimen from a similar geometry as for one used in an E 1 or E 2 test, and that would exhibit a uniform shear stress state in the test section. To achieve that, Finite Element Analysis (FEA) method was employed in the design of so called double notch shear specimens. FEA analysis was performed to determine the optimal specimen geometry such that a uniform shear stress state is obtained in the test section. The specimens would also have to be easy to fabricate and machine as well as very inexpensive. The test method was design such that by a simple swap of the specimens an E 1 or E 2 test to a G 12 test could be performed. Thus using the same procedure as explained for the transverse modulus tests we would be able to determine shear properties of unidirectional IM7/977-2 graphite epoxy. The geometry of the specimens was first created using AutoCAD 2004 and then imported into ABAQUS. This allowed creating even very complicated models in an easier and faster way. ABAQUS 6.4 was used to perform the shear specimens analysis.

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43 The process of designing a specimen that would exhibit a uniform shear stress in the test section was one of trial and error. However, a few parameters were imposed such as length, width and thickness to be able to use the same setup as previously discussed for transverse modulus. Consequently the only modification to the specimen geometry was the two notches that were cut in the center. Another fixed parameter was the distance between the two notches. The shear gages that would be attached were 0.45 long, therefore the distance between the notches had to be the same. One concern was that premature failure would be initiated if the transverse stresses next to the tip of the notches were higher than the shear stresses. For this reason the geometry was constructed such that the stresses would gradually feed into the test section. The numerical analysis was performed as follows: a 2D part was created from the sketch imported from AutoCAD. Then the mechanical properties were introduced. Using the Lamina type option in ABAQUS, the elastic constants namely E 1 E 2 12 G 12 G 13 and G 23 were specified. The lamina orientation was given such that to coincide with the longitudinal direction of the specimen. One end of the specimen was constrained in all 6 DOF and the other end was given a displacement in the x-direction while constrained in y-direction as well as to rotate in x-y plane. The model was then meshed and submitted for analysis. Results of shear stress (S 12 ) and transverse stress (S 22 ) were interpreted and presented below. The first geometry that was investigated is presented in Figs. 3-3 and 3-4. The two notches are parallel to each other and perpendicular to the specimen. Fig. 3-3 shows the

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44 shear stress (S 12 ) distribution while Fig. 3-4 shows transverse stress (S 22 ) distribution. From this numerical analysis it can be seen that the stress state is not entirely uniform over the entire test section, stress direction does not match fiber direction and S 22 is quite large compared to S 12 Figure 3-3. Shear stress (S 12 ) distribution for specimen with 0 oriented notches Figure 3-4. Transverse stress (S 22 ) distribution for specimen with 0 oriented notches The second geometry investigated is presented in Figs. 3-5 and 3-6. The notches are again parallel to each other but oriented at 45 with the specimen. Here the stress state is more uniform and the transverse stresses are lower than in the previous case. Figure 3-5. Shear stress (S 12 ) distribution for specimen with 45 oriented notches

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45 Figure 3-6. Transverse stress (S 22 ) distribution for specimen with 45 oriented notches Variations of this geometry were analyzed by modifying the notch thickness, notch shape, notch length, and/or the notch orientation. The process was entirely trial and error but fortunately not time consuming; consequently it allowed for numerous numerical simulations to be able to identify the best geometry. From all these trials, only the one presented in Figs. 3-7 and 3-8, where notches are oriented at 60 degrees, was interesting from the point of view of the results obtained. Figure 3-7. Shear stress (S 12 ) distribution for specimen with 60 oriented notches Figure 3-8. Transverse stress (S 22 ) distribution for specimen with 60 oriented notches In all previous examples stress concentration appeared around the tips notches; to eliminate this problem one simple solution would be to increase the radius of the notch.

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46 However that will result in eliminating more material around the test section and the specimens will be very fragile thus braking before it could be tested. An alternative solution is presented in Fig. 3-9 and Fig. 3-10. On the other hand the shape of the notches was considered difficult to machine at the time and a more conservative approach was used. Figure 3-9. Shear stress (S 12 ) distribution for specimen with rounded notches Figure 3-10. Transverse stress (S 22 ) distribution for specimen with rounded notches Fig. 3-11 and Fig. 3-12 show the stress distribution for the geometry chosen to be machined. The two notches are quarter circles with a radius equal to half the width of the specimen. The width of the notches was choused to be 0.1875. The shear stress distribution is very uniform across the test section and the transverse stresses are lower than the shear stresses. This geometry was preferred over all the others investigated because its simpler geometry would also allow for easy specimen machining.

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47 Figure 3-11. Shear stress (S 12 ) distribution for the DNSS specimen Figure 3-12. Transverse stress (S 22 ) distribution for the DNSS specimen 3.3 Experimental Setup The same experimental setup that was used in determining the transverse modulus was employed here, namely an MTI type machine, a testing chamber, an environmental chamber that regulates the temperature inside the testing chamber, a liquid nitrogen (LN 2 ) dewar, and a data acquisition system. The only change was in the data acquisition system where in one SCXI module a few switches where interchanged to read a half bridge configuration. 3.4 Experimental Procedure and Results Specimens for temperature dependent shear modulus determination were first machined using a carbide mill on a CNC machine. However the end result did not satisfied since material flaking and delamination was present next to the notches. The alternative was waterjet machining of the specimens. This allowed for faster, cheaper but

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48 most importantly a more accurate and flake free cut of the specimens. It was also a one-time process eliminating the need for first cutting specimens to a 1 width and grinding the edges before cutting the notches as it would have been necessary if a milling machine was used. Most importantly it insured that all the specimens were cut at the same angle with respect to the fiber direction thus helping reduce measurement variability. Fig. 3-13 shows 12 DNSS specimens that were cut from 2 panels. Figure 3-13. DNSS specimens These specimens were then prepared and the tests were conducted according to the ASTM 5379 standard and NASA recommendations that were discussed in Chapter 2. Gage selection was made to handle the large temperature range, nominally C. Therefore, C-040621-A custom shear gages were obtained through the Vishay Micromeasurements Group. Fig. 3-14 shows a schematic of the shear gage and as it can be seen it is a composed of two gages with the grid at +45 and -45 respectively. The gage was connected to the data acquisition system in a half bridge configuration, as presented in Fig. 3-15.

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49 All the other required supplies to attach the gages to the specimen, such as the M-Bond 610 epoxy adhesive, were also obtained from Vishay. Shear specimens were also prepared according to NASA recommendation procedures for strain gage application and ASTM standard. Each test section was first abraded, with varying grits of sand paper to remove all surface flaws and to smooth finish the surface. It was then cleaned with acetone and marks were inscribed for gage alignment with the specimen. Figure 3-14. The shear gage Figure 3-15. Half-bridge circuit diagram

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50 Then any remaining impurities were removed with acetone and by dusting the air off the surface. Thickness and length measurements were taken across the test section of the specimen. Three thickness measurements were taken and the average was used in determining the cross-sectional area. Table 3-1 shows the length and the average thickness of each test section. Table 3-1. Length and average thickness measurements for all tested specimens Specimen Length (in) Average thickness (in) p5-1 0.43095 0.09415 p5-2 0.42610 0.08705 p5-3 0.41155 0.09055 p5-4 0.42400 0.08818 p5-5 0.43020 0.08903 p5-6 0.42515 0.08888 p6-1 0.41140 0.08843 p6-2 0.42120 0.08850 p6-3 0.42150 0.08477 p6-4 0.42480 0.09097 p6-5 0.42060 0.08755 p6-6 0.42030 0.09030 Using a microscope, a gage and strain relief tabs were aligned to the inscribed marks then a Teflon tape was used to temporary attach them to the specimen. The undersides of the gage and strain relief tabs were exposed and together with the specimens surface they were coated with a thin layer of M-Bond 610 adhesive. After a ten-minute drying period the gage and the tabs were placed back on the specimen and clamped with uniform pressure.

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51 Specimens were cured for three hours at 121C then post-cured at 135C for another two hours. Once the specimen was gaged and wires were soldered to the tabs and connected to the SCXI module it was fixed to the grips using the alignment fixture. The temperature diode was taped to the specimen together with the environmental chambers thermocouple. The entire ensemble was positioned into the MTI machine then the testing chamber was placed around it and connected to the environmental chamber, and data was extracted using the Labview program as explained in Chapter 2. This time shear specimens were loaded only up to 90 lb to avoid premature failure. Each specimen was again tested at approximately 25C intervals, from -165C to +150C. The Matlab code [appendix] manipulated the data to obtain the average slope of the five curves at each temperature. Slope and the cross-sectional area allowed for shear modulus determination as presented in Eqs. (3-1) to (3-4): 12G (3-1) 4545 (3-2) AP (3-3) APG12 (3-4) where P is the applied load and A is the cross-sectional area of the specimen. Fig. 3-16 shows the entire temperature dependent shear modulus curves for all tested specimens and Fig. 3-17 shows a linear fit through all the data points. Again this basic fitting will be used in Chapter 4 to predict residual stresses for different laminate configurations.

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52 Figure 3-16. Shear modulus as a function of temperature for all tested specimens Figure 3-17. Linear fit through the data points for the shear modulus as a function of temperature

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53 The equation of the straight line and the regression coefficient are presented in Eqs. (3-5) and (3-6): GPaTTG 5399.5012231.012 (3-5) 98768.02R (3-6) For statistical purposes the coefficients of variation (CV) were computed for all the tests and presented in Table 3-2. As explained for the transverse modulus in Chapter 2, the average value and standard deviation were first determined, then the coefficients of variation were calculated at each of the fourteen temperatures. Table 3-2. The mean, standard variation and coefficient of variation at each temperature for all tested specimens Temperature (C) Mean G 12 S N-1 CV % -165 7.57E+09 8.91E+07 1.18 -145 7.36E+09 1.58E+08 2.15 -125 7.18E+09 1.90E+08 2.65 -100 6.92E+09 1.63E+08 2.36 -75 6.44E+09 2.09E+08 3.25 -50 6.07E+09 1.74E+08 2.87 -25 5.75E+09 1.38E+08 2.39 0 5.47E+09 1.23E+08 2.25 +25 5.15E+09 8.71E+07 1.69 +50 4.87E+09 1.09E+08 2.25 +75 4.66E+09 9.20E+07 1.97 +100 4.44E+09 8.60E+07 1.94 +125 4.17E+09 8.91E+07 2.14 +150 3.72E+09 1.29E+08 3.46 3.5 Conclusions A new method was developed and used to successfully determine the shear modulus as a function of temperature for the unidirectional IM7/977-2 composite

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54 material. The method uses specially designed tension specimens to produce a shear stress state in the test section. FEA was employed to optimize the specimen geometry. Specimens were easily fabricated from panels produced using schools facilities and then waterjet machined to obtain the final geometry. Over ten tests were performed during which the method proved to be very repeatable. A robust set of data was obtained using 14 points along the temperature range, i.e., -165C to +150C for each specimen. The method is fully automated and once a test is started do not require supervision. The method is unique because it uses double notch tension specimens to produce shear in composite materials. Specimens are easier to fabricate and the variability in the experimental measurements is reduced because the method is not as sensitive to load misalignment with fiber orientation or gage positioning. Multidirectional or chopped fiber composites can be investigated. The method can also be extended to other materials as well. However in this project the method was used to extract information from unidirectional composites and the results were used in predicting the behavior of multidirectional composites. Besides characterizing the material behavior, the shear modulus property of the IM7/977-2 will be used in a modified Classical Lamination Theory (CLT) Matlab code to predict the behavior of multidirectional laminates. 3.6 Discussion and Future Work Chapter 3 described a practical new method to determine in-plane shear properties of fiber reinforced polymer matrix composite materials. Since a reduction in data variability was one of the main concerns in this research, techniques such as the off-axis

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55 tests, which showed scatter in the data, were not the first choice. The Iosipescu method, which is the most popular and commonly used technique, was also inappropriate for temperature dependent tests because of the bulky fixture required. The author had to come up with a simpler, more efficient technique that uses a unique specimen which can produce a uniform shear stress state in the test section. Another important factor in determining accurate shear properties in composites is the use of shear gages, as shown in previously published papers [31-34]. The parabolic distribution of the shear strains in the test section of the Iosipescu specimens can lead to scatter in the data when small, unidirectional, centrally located strain gages are used. The shear gage has been shown to reduce the scatter and improve the accuracy of the results by integrating the shear strain over the entire test section. Therefore it was imperative to use shear gages in conjunction with the newly developed double notch shear specimen. The newly devised technique was employed to test more than ten different specimens to obtain a robust set of data. As for the transverse modulus data, Fig. 3-17 shows the nonlinear behavior of the material investigated. A straight line was also fitted through the data points and the equation was used later on to predict residual stresses. However, in this case the residuals are smaller than in the transverse modulus case although a higher order polynomial will fit the data much better. A comparison of the transverse modulus with the shear modulus data shows that there is a correlation between the material behaviors. The data seems to deviate from linearity around -75C and then come back around +75C. Although in the case of shear modulus the residuals are much smaller when a straight line is fitted through the data points, the same trend was observed on both properties. It is not known why this phenomenon occurs, but it is speculated that

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56 the thermal history is the primary cause. The phenomenon might not occur if tests are performed from room to cryogenic or room to elevated temperatures. Future tests should be performed to investigate this phenomenon. The same paper [3] mentioned in Chapter 3 presented shear modulus data for the IM7/977-2 material. Again only two data points are available, one at room temperature and the other one at liquid nitrogen temperature. These two points are shown in Fig. 3-18 together with the data obtained at University of Florida. In this case a straight line will better predict the value obtained by the Wright Patterson AFB at liquid nitrogen temperature but will not agree with the room temperature value. Significant difference will be obtained when a higher order polynomial will be used. As in the case of transverse modulus, it was found that the shear modulus at room temperature is higher when the specimens were first subjected to cryogenic temperatures but still lower than the one presented by the Wright Patterson AFB. Nevertheless it should be remembered that 0 Iosipescu specimens over-predict the modulus; therefore it is the authors believe that the results obtained in this paper are much closer to the real value. The coefficient of variation obtained from all the specimens tested at room temperature is around 1.7%. This is a tremendous reduction in variability from 4% -9% when Iosipescu specimens are used. More tests should be performed in the future to have a better approximation of the real shear modulus. Iosipescu specimens fitted with shear gages should be tested at room temperature and compared to the double notch shear specimens. This process has already been started and the data shows good agreement.

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57 Figure 3-18. Shear modulus as a function of temperature with linear fit and extra data from the literature Future work should also concentrate in determining the shear modulus for different laminate configurations to compare the experimental results with the classical laminate theory prediction.

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CHAPTER 4 RESIDUAL STRESSES IN LAMINATED COMPOSITES 4.1 Introduction Engineers face new challenges every day in the design and manufacturing processes of structures and machine components. Often times their work is wasted when those components or structures fail not due to the applied loads but from residual stresses [40]. These residual stresses form during fabrication operations. Metals develop residual stresses during processes such as welding, casting, rolling, forging and assembly. In laminated composites they form due to the matrix solidification around the reinforcement or due to the mismatch in the coefficients of thermal expansion [41] between the fiber and matrix and in the plies of a stacked laminate. Residual stresses are difficult to measure nondestructively and they add to the live loads. In aerospace applications, the composites have to endure sudden temperature changes, from cryogenic to high temperature, thus having to sustain thermal load above the mechanical load. Generally, most materials expand when they are heated. The coefficient of thermal expansion (CTE) measures their rate of expansion. For example, silicon has a coefficient of thermal expansion approximately five times smaller than copper and eight times lower than aluminum (6061). Hence low expansion materials such as silicon cannot be bonded directly to high expansion ones like aluminum or copper without experiencing high stresses. There is also the case of graphite fibers that actually contract as they are heated. Since a composite material is composed of two or more materials they are 58

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59 likewise subjected to large mismatches in CTE that lead to thermal residual stresses. Therefore determination of the CTE and residual stresses is critical. A better prediction of how the laminate composite will behave can be made if those quantities are accurately determined. Analysis of the residual stresses was performed on single fiber composites [42], fiber reinforced laminated composites or layered ceramic composites, and results present the effect of thermal loading on the total carrying load such as in the papers by Benedikt et al. [43], Gungor [44] or Tomaszewski [45]. The effect of residual stress on the toughening behavior of TiB2/SiCw composites was investigated by Jianxin [46], who found out that considerable improvement in the high-temperature fracture toughness was observed up to 1200C due to the relaxation of the thermal residual stresses caused by the thermal expansion mismatch between SiC whisker and TiB2. Qianjung et al. [47] investigated metal-ceramic functionally gradient materials, and used moir interferometry to report the residual stress distribution in such materials. Current practices [48-49] for residual stress determination include both destructive and non-destructive techniques such as hole-drilling methods, ultrasonic techniques, X-ray and photomechanical techniques. For composites in particular, there are destructive techniques like hole-drilling method, cutting method, ply sectioning method, and non-destructive techniques like embedded strain gages, X-ray diffraction or CRM. 4.2 Cure Referencing Method A new experimental technique called the Cure Referencing Method [50] was recently developed at the University of Florida by Peter Ifju and his research group to

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60 measure residual stress in composites. This non-destructive testing method used in conjunction with the moir interferometry technique is capable of full-field measurements of the surface strains. The method uses high frequency diffraction gratings attached to the laminated composite during the curing process that act as a reference to the free stress state prior to resin solidification. The process of attaching gratings to the laminated composite involves several steps which are rigorously explained in the paper by Ifju et al. [51] published in the Journal of Experimental Mechanics. The replication procedure is shown in Fig. 4-1. The end result of the replication procedure is an autoclave tool with a diffraction grating, two layers of aluminum and an epoxy film on top. This tool is then used to transfer the grating to the composite panel in the autoclave during curing process. Fig. 4-2 shows the method of attaching the diffraction grating to the composite in the autoclave. The curing process is initiated using a cure cycle like the one shown in Fig. 4-3. The laminated composite goes from an uncured state at room temperature to fully cured at high temperature. Separating the tool from the composite panel at elevated temperature when the composite is fully cured, the grating is able to record the free stress state that existed in the composite before building up residual stress as it cools down to room temperature. This newly developed method has been employed to determine the residual stresses and coefficients of thermal expansion (CTE) in composite materials. The IM7/977-2 material was investigated and reported as follows.

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61 Figure 4-1. Schematic of the replication technique

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62 Figure 4-2. Method of attaching the diffraction grating to the composite in the autoclave Figure 4-3. Cure cycle for laminated composites in autoclave

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63 4.3 Residual Stresses and CTE Measurements The failure of X-33 reusable launch vehicle showed that the behavior of the new advanced structural composite materials is not yet fully understood. Lack of information about the material properties of those materials played a key role in the failure of the liquid hydrogen tanks and of the project itself. Temperature dependent measurements to characterize composite materials are missing from the literature thus limited data is obtained and then used in the design of the new engineering structures. The X-33 project marked a set-back for the development and implementation of new advanced structural composite materials to aerospace applications. Consequently, the composite community focused on determining the failure causes of the project and on obtaining the correct and complete information of the different material properties therefore trying to fill the void that exists in the literature about the temperature dependent material properties of composite materials. Under the supervision and guidance of Peter Ifju at the University of Florida, the ESALab research team started an experimental study on residual stresses in laminated composites as a function of temperature. Materials used in the study were unidirectional laminated composites, [0] 13 the RLV configuration [52], [45/90 3 /-45/0 3 ] s and a special optimized angle ply (OAP) configuration, [ n ] s presented by Qu [53] to account for both thermal and mechanical loading. The IM7/977-2 prepreg was used to fabricate the panels. In our lay-up facility, 4 x 4 panels were layed-up using different configurations as mentioned. They were then placed in a special oven with vacuum capabilities and left to cure following the curing cycle provided by the manufacturer. The CRM technique was employed to determine the coefficients of thermal expansion and the residual stresses of these materials. The extensive previous work

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64 performed on CRM led to improvements in the grating replication. The first three steps in the Fig. 4-1 were eliminated, reducing the time needed to replicate a grating on the composite panels by approximately 72 hours, thus making the method more efficient. Once the grating was transferred to the composite panel, moir interferometry was employed to document the surface strains. Fringe patterns, as seen in Fig. 4-4, were photographed and recorded for analysis. Figure 4-4. Typical horizontal and vertical fringe patterns 4.3.1 Data Analysis Once the fringe patterns have been recorded they could be analyzed to determine the surface strains. Fringe patterns contain displacement information thus the fringe order (N) is directly related to the displacement of the composite panel. 1200 lines/mm diffraction gratings were used thus giving this method a displacement sensitivity of 0.417 microns. The relationship between fringe order and displacement and between displacements and engineering strains were presented in Eqs. (1-1) to (1-5).

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65 These equations were used to determine the surface strains at room temperature on each tested specimen. This provided the reference point for the temperature dependent residual stress and CTE measurements. These measurements were obtained by hand calculations. The analysis of the fringe patterns was performed manually by locating the positions and numbering the fringes, as can be seen in Fig. 4-5. This process however is very slow and has the potential of increasing the measurement error. Thus a new system has to be used in the future to eliminate the human factor. This system which is called digital image processing for fringe analysis has been successfully implemented in the ESALab at the University of Florida. Figure 4-5. Example of counting fringes to determine surface strains

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66 Because of the development and decreasing cost of the digital image processing equipment, the digital image fringe pattern techniques are increasingly used in acquiring strains and stresses. The reasons for implementing this method are to improve the accuracy, to improve the speed, and to automate the process. Ultimately, it will eliminate the human factor by automatically detecting the positions of the fringes. An Insight Firewire CCD camera, as seen in Fig. 4-6, and a frame grabber were acquired from Disagnostic Instruments Inc. The CCD camera is used to scan the fringe pattern. The frame grabber, which is a video digitizer, digitizes the image and stores it into the computer memory. This combination of the digital camera, frame grabber and computer made it very easy to record and manipulate the images. Figure 4-6. CCD camera Different algorithms are available to obtain image manipulations on the individual pixels. However, these algorithms require the fringe patterns to be shifted before they could be analyzed. One possible solution for shifting fringe patterns is by displacing either the specimen or the interferometer simultaneously in the horizontal and vertical directions.

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67 This can be achieved by building a stage as the one in Fig. 4-7 that can withstand the weight of the interferometer. The stage is specially designed and has four aluminum tubes connecting two aluminum plates, on the bottom and top. The tubes are precisely machined and attached to the plates at 45. Magnet wire of 0.007 in diameter with special enamel coating for high temperature was wrapped exactly 200 times around each of the four aluminum tubes then connected together with strain gage wire to complete the circuit. Figure 4-7. Specially designed stage for fringe shifting A 0-35 V, 0-5 Amp adjustable power supply, from Pyramid, model PS-32 lab was connected to the circuit. By turning the power ON and increasing the voltage, the current going through the magnet wire heats the aluminum tubes, which will then expand thus raising the interferometer in a 45 degree direction. Fig. 4-8 shows the entire ensemble including the PEMI interferometer sitting on the stage as well as the power supply.

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68 Figure 4-8. Experimental setup for fringe shifting A sequence of images of the shifted fringe pattern is recorded from which a special algorithm calculates the horizontal and vertical displacement fields. Thus the newly implemented system is able to determine faster the full-field displacements. An automation of the method for an easier manipulation of the results as well as a more accurate output is obtained. This system will be used in the future for the analysis of the fringe patterns. 4.3.2 Experimental Results Moir interferometry was used to analyze and determine the surface strains at room temperature. Because CRM uses this optical technique to determine the surface strains of the laminates, the fog created at cryogenic temperatures makes it very difficult to take measurements. For this reason, strain gages were attached to the laminates and a new procedure [54] for cryogenic temperature measurements was developed. The relative

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69 strains were obtained and superimposed with the strains obtained via CRM at room temperature. Several panels for each of the configurations mentioned above were tested. Results of the average surface strains are presented in Fig. 4-9. Figure 4-9. Temperature dependent average strains for different laminate configurations It is commonly assumed that when a cured polymer matrix composite is returned to the cure temperature, the stresses in the material completely disappear. Looking at the strain vs. temperature data in Fig. 4-9 it is evident that the tested panels still exhibit surface strains after they were heated to cure temperature. This strain difference is the result of a one-time phenomenon, namely chemical shrinkage (CS). Table 4-1 shows the surface strain on the specimens at cure temperatures due to chemical shrinkage.

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70 Table 4-1. Strain at cure temperature due to chemical shrinkage (CS) Specimen type x-direction (microstrains) y-direction (microstrains) UNI 108 -2712.5 RLV -126.6 -9.25 OAP 476.9 -2026.9 Having the surface strain information on the composite panels at each temperature, the coefficients of thermal expansion can be calculated using Eqs. (4-1) and (4-2), where T 1 and T 2 are two different temperatures: 2121TTTTCTExxx (4-1) 2121TTTTCTEyyy (4-2) The temperature dependent CTEs are presented in Fig. 4-10: Figure 4-10. Temperature dependent CTEs for different laminate configurations

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71 A linear fit was obtained for the CTE of unidirectional composites in both x and y directions. These basic fits will be used later on together with the transverse and shear properties to predict the behavior of multidirectional composites. The two equations, Eqs. (4-3) and (4-4) are: C 4232.00014.01 TTCTEUNIx (4-3) C 167.220429.02 TTCTEUNIy (4-4) Residual stress can be calculated within each ply of the composite panel using the classical lamination theory. First the residual strain was calculated for each ply orientation using Eq. (4-5): resklamunik (4-5) where k is the transformation matrix from the 1-2 coordinate system to the ply coordinate system, lam is the laminate strain vector and uni is the strain vector for the unidirectional composite. Then the constitutive relation, Eq. (4-6), was used to determine the residual stress: resreskkQ k (4-6) where Q is the stiffness matrix of the composite as defined in Eq. (4-7): TGTETETEETEEETQ12221221221221100001 (4-7) The program used includes previously measured temperature dependent transverse and shear information, as it can be seen in Eq. (4-7), as well as the effect of chemical shrinkage. The strain due to chemical shrinkage adds up to the residual strain calculation

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72 and has a huge effect on residual stresses. This quantity which is neglected in the classical lamination theory is critical in the residual stress prediction as it can be observed in Fig. 4-11. Figure 4-11. Effect of chemical shrinkage on residual stress calculation The residual stress in the RLV 0 and OAP worst case layers are plotted with and without including chemical shrinkage. It can be observed that in both cases the stresses are under-predicted. Furthermore the temperature dependent properties were included in the stiffness matrix and predictions are presented in Fig. 4-12. The effect of temperature dependent shear properties can be neglected for normal residual stresses and only transverse properties influence the prediction. RLV panels exhibit higher residual stress than the OAPs.

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73 Figure 4-12. Effect of chemical shrinkage and temperature dependent properties on residual stress calculation Comparing the different laminates is observed that the worst case layer in the RLV reached the failure strength in the transverse direction very close to subzero temperatures; therefore use of such configuration was totally inappropriate in the X-33 project since microcracks will develop as residual stresses build up and produce failure. 4.4 Conclusions Temperature dependent residual stress and CTE measurements were acquired for different laminate configurations using improved CRM. Room temperature measurements were acquired with moir interferometry techniques and then strain gages were used to record surface strains from cryogenic temperatures to cure conditions Moir interferometry plays a key role since surface strains at room temperature provide the

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74 reference point for the temperature dependent measurements. Thus the accuracy of the temperature dependent residual stresses and CTEs depend on the accuracy of the data recorded at room temperature. Fringe patterns were manually analyzed but in the future a new system that has been implemented will be used. This system called the Digital Image Processing for fringe analysis will try to eliminate the human factor by reducing some of the errors and most importantly will also automate and speed the process. Residual stresses were determined using a modified classical lamination theory that includes chemical shrinkage effect and temperature dependent transverse and shear properties. Noninclusion of chemical shrinkage effect under-predicts the residual stresses and can lead to premature failure of the composite. 4.5 Discussion and Future Work Residual stresses are very important to be determined because they can predict failure of the composite material. Results obtained in this paper show first of all that the stacking sequence used in the X-33 project was not the right choice and emphasizes the importance of the design optimization. Temperature dependent properties should definitely be included in the residual stress prediction; they accounted for a 20% increase in the residual stresses in the worst case ply of the RLV configuration. However, only the transverse modulus was a factor in predicting residual stresses in the transverse direction. The shear modulus did not affect the results; but this does not mean that the data was obtained in vain or that in the future this quantity should be omitted. Preliminary data show that shear modulus plays an important role in determining residual shear stress, and in predicting the behavior of the multi-directional laminates from the modified classical laminate theory.

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75 In the future, once more data is obtained over a larger temperature range, the prediction can be improved. Also, instead of approximating the data with straight lines, the equations from a high order polynomial should be included in the Matlab code that calculates the stresses. This will slightly modify the results. Failure strength of the composite in the transverse direction was partially determined here, as presented in Fig. 4-12. However, only a few data points were obtained at cryogenic and room temperatures and the scatter in the data was considerable. Therefore the straight line used to approximate the data should not be entirely trusted until enough tests are performed across the temperature range. Tests were performed on the same specimens that were tested to obtain transverse modulus, and they did not always fail in the test section; this can lead to miscalculation of the cross-sectional area and thus ultimate stress. In the future special specimens should be used. The width of the test section should be smaller than the width of the specimen to produce failure in that region.

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CHAPTER 5 EXPERIMENTAL CHARACTERIZATION OF LOADING IMPERFECTION ON THE BRAZILIAN DISK SPECIMEN The chapter represents a small portion of a broader experimental program to characterize single crystal metallic materials. These are the materials of choice for maximizing creep resistance in environments of extreme temperatures and sustain load, such as that of turbine blades in fuel pump assemblies. In order to utilize single crystal materials in such applications, the fracture behavior must be thoroughly understood. This endeavor requires mode I, mode II and mixed mode testing on all effected crystallographic planes. Tests ultimately would be performed at temperatures up to 700C and pressures up to 5000psi. Due to the size of the test chamber and expense of the specimen material it was imperative that the specimens be compact. Because of these testing requirements the Brazilian Disk specimen was selected to be investigated. 5.1 Introduction For over half a century, the Brazilian Disk specimen [55] has been intensively used to characterize the mechanical properties of different materials. The specimen was initially used in 1947 to determine the fracture toughness in rocks. Early versions of the specimen were approximately 2 in. in diameter and a thickness equal to the radius. Subsequent researchers developed a flattened center crack disk type specimen. This newly developed specimen, which was much thinner and had a pre-existing crack at the center, proved to have many advantages and soon became a very popular testing tool in fracture mechanics. Because the specimen provides a wide range 76

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77 of mode mixity, considerable material property information can be obtained from one specimen geometry. Analytical solutions for this indirect (Brazilian) testing method are available in the literature, such as presented by Claesson et al. [56] who calculated the stress field and tensile strength of anisotropic rocks using elastic parameters measured in the laboratory or by Exadaktylos et al. [57] who calculated the stresses and strains at any arbitrary point in the disc. Shetty et al. [58-62] used the method to determine the fracture toughness of different materials, Atkinson et al. [63] used the Brazilian test to determine the combined mode fracture. Mixed-mode fracture was also investigated by researchers like Petrovic [64], Marshall [65], Suresh et al. [66-67], Awaji et al. [68]. Paul [69] presented a numerical solution for tests on the Brazilian Disk specimen. Khan et al. [70], Kukreti et al. [71], Narasimhan et al. [72] developed finite element programs for the prediction of initiation, crack growth or ultimate fracture and many others [73-83] performed tests and analysis on cracked specimens and presented solutions on the behavior of cracks, stress distribution or fracture toughness of different materials under different loading. Recent published papers such as the one by Ayatollahi et al. [84] presents results on the fracture toughness ratio K IIc /K Ic that is calculated for two brittle materials and is compared with the relevant published experimental results obtained from fracture tests on the cracked Brazilian disc specimen. Wang et al. [85] have used a flattened Brazilian disc specimen to determine the elastic modulus, tensile strength and fracture toughness of marbles and again in a different paper Wang at al. [86] presented analytical and numerical results for the flattened Brazilian disc specimen. Al-Shayea et al. [87]

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78 presented the effects of confining pressure and temperature on mixed-mode fracture toughness of a limestone rock. Huang et al. [88] determined the fracture toughness of orthotropic materials and Banks-Sills et al. [89] developed a methodology to determine the interface fracture toughness in composites. The Brazilian specimen became the configuration of choice during an experimental program to assess single crystal materials for slip plane determination under mixed mode loading. However, questions surfaced concerning the effects of specimen alignment. And since there is a void in the literature on this subject, a systematic experimental study was conducted to determine how specimen misalignment (both out-of-plane and in-plane) affected the strain and displacement fields. For test purposes, an aluminum specimen was investigated in order to isolate the loading effects from the crystallographic effects. Additionally, a finite element analysis (FEA) program was developed to model the specimen. Altogether, the experimental program at the University of Florida concentrated on: providing angle dependent displacement fields, comparing experimental results to FEA, providing full-field analysis of the plastic zones ahead of the crack tips, studying the effect of misalignment in the linear range and in the plastic range. 5.2 Experimental Procedure Aluminum (7075-T6) Brazilian disk specimens, shown in Fig. 5-1, were machined with a diameter of 1.1 in (27.94 mm) and thickness of 0.09 (2.286 mm). A notch of 0.3 x 0.01 (7.62 mm x 0.254 mm) was cut in the center of each specimen using Electrical Discharge Machining (EDM). Moir interferometry was used to document displacement fields on the surface of the specimens. A phase type diffraction grating, crossed line with a nominal frequency of 1200 lines/mm (30480 lines/in) was replicated on the surface of the specimen as necessary for the moir tests. It was oriented such that the lines were

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79 parallel and perpendicular to the notch (Fig. 5-1). A custom loading fixture was fabricated that had adjustment capabilities for both in-plane and out-of-plane misalignment for intentionally inducing load misalignment as shown in Fig. 5-2. The top portion of the fixture remained fixed. By rotating the left most adjustment screw, the lower portion of the fixture produced out-of-plane misalignment. By rotating the right most adjustment screw the fixture produced in-plane misalignment. Since the grating was fixed to the specimen and the specimen was loaded along angle ranging from 0 to 27, the moir interferometer was required to be oriented at the angle Thus a second fixture, Fig. 5-3, was also fabricated for tilting capability to allow the moir interferometer to orient with the specimen. PP yx P P 1.1 in 0.01 in0.09 in yx yx yx 0.3 in PP yx P P 1.1 in 0.01 in0.09 in yx yx yx 0.3 in grating for moir PP yx P P 1.1 in 0.01 in0.09 in yx yx yx 0.3 in PP yx P P 1.1 in 0.01 in0.09 in yx yx yx 0.3 in grating for moir Figure 5-1. Schematic description of the Brazilian disk The Brazilian disk specimen was then loaded by means of a compression testing machine (MTI type). Once the grating was attached to the specimen and the specimen

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80 was placed in the loading fixture, the process of obtaining the displacement fields was initiated. First, the interferometer (an IBM PEMI compact interferometer) was positioned on the specially designed fixture and rotated to the notch angle (between 0 and 27 degrees) for which displacement fields were recorded. To achieve this, a digital inclinometer with 0.1 degree accuracy, placed on top of the interferometer, was used for angle measurements. Then, while looking through the interferometers window, the specimen was rotated until the first and second order diffraction dots emerging from the grating were grouped into one dot. This is the standard procedure for tuning the PEMI interferometer. Next, using the interferometers fine tuning screws, null field displacements were obtained. Once this was achieved for both U and V fields, load was gradually applied up to a point where a dense fringe pattern was observed and pictures were recorded. One of the main objectives of this project was to determine the displacement fields for various specimen orientations, The advantage of a center notch disk specimen is that mode I, mode II and mixed mode are present by running a simple compression test using a single specimen geometry. Fig. 5-1 illustrates how load was applied to the specimen in order to obtain mode I, mode II and mixed mode loading. When loaded in the direction of the notch (i.e., the direction of the notch matches the direction of the loading) pure mode I is obtained. For the angle between the load and the direction of the notch of about 27 deg. pure mode II is obtained. Loading at any angle between 0 and 27 deg. will produce a combination of the two modes (mixed mode).

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81 Tests were conducted for cases with no load misalignment. Full displacement fields were documented and analyzed; after gaining confidence in the results, additional tests were conducted for the misalignment cases. Misalignment was obtained using a special fixture with tilting capabilities. Fig. 5-2 shows the actual specimen positioned in the loading fixture. A special guiding device placed the specimen at the same location every time a test is conducted. Adjusting screws on the bottom part of the fixture allowed for in-plane and out-of-plane load misalignment. Figure 5-2. Loading fixture, actual specimen and digital inclinometer Fig. 5-3 shows a close up of the experimental setup with the moir interferometer placed on top of the tilting fixture and in front of the specimen. The digital inclinometer placed on top of the moir interferometer was used to record the angles at which the specimen was loaded.

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82 Figure 5-3. Tilting fixture, interferometer and digital inclinometer Fig. 5-4 shows a schematic description (front and side view) of how load was applied to achieve misalignment. In-plane misalignment () can be achieved by rotating the bottom part of the fixture in the plane of the specimen, Fig. 5-4(a), while rotating the bottom part of the fixture in a plane perpendicular to the specimens surface, out-of-plane misalignment () is achieved Fig. 5-4(b). P P P P (a)(b) Figure 5-4. Front (a) and side (b) view description of the specimen for in-plane and out-of-plane misalignment cases

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83 5.3 Experimental Results 5.3.1 Angle Dependent Displacement Fields Using the method described, tests were conducted and displacement fields were documented and analyzed. Because the displacement fields are notch angle dependent, all cases, at 2 increments were considered for a full and complete analysis but only a few are presented in this paper due to space consideration. Fig. 5-5 shows the horizontal and vertical moir interferometry fringe patterns for pure mode I loading. The symmetric fringe patterns obtained indicate that load was applied correctly i.e., in the direction of the notch. Analyzing the fringe pattern from the U displacement field, Fig. 5-5(a) we can observe that in fact the notch is opening as expected for this type of specimen in pure mode I loading. Also, the exact number of fringes on a certain gage length around both of the crack tips, Fig. 5-5(b) and again the symmetry of the fringe patterns indicate that the fixture was aligned properly with the specimen and no misalignment was induced. Fig. 5-6 shows the fringe patterns for the mixed mode loading. Analyzing the fringe patterns from both U field, Fig. 5-6(a) and V field, Fig. 5-6 (b), we can see that both modes are present and although the notch was still opening under the applied load, the influence of the mode II was dominant. Shear, as the predominant effect, is indicated by the fringes that almost align to the direction of the notch Fig. 5-6(b). Symmetry again indicated good alignment of the specimen with the load applied. Fig. 5-7 presents the case of pure mode II loading. Fringe patterns in the V field, Fig. 5-7 (b), parallel to the direction of the notch are indication of shear between the two regions.

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84 P P y,v P P (a) (b) Figure 5-5. Displacement fields for mode I loading, U (a) and V (b) x,u P P y,v P P (a) Figure 5-6. Displacement fields for mixed mode loading, U (a) and V (b) x,u (b)

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85 P P y,v P P (a) Figure 5-7. Displacement fields for mode II loading, U (a) and V (b) x,u (b) The top and bottom portions of the specimens were not damaged nor did plastic deformation occur at the loading points as it would seem from the pictures. During the successive testing on the specimen as it was rotated from 0 to 27 deg, the diffraction grating attached to the specimen was altered locally in contact with the loading fixture and thus did not diffract the light perpendicular to the specimens surface, a necessary condition for the moir interferometry technique for the in-plane strains. This effect did not alter the strain field near the crack tip. 5.3.2 Comparison to the FEA Using the same conditions as in the experimental study, contour plots of the displacement fields were obtained from a FEA program. Due to symmetry of the specimen, superposition of the patterns was chosen to present the results.

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86 Figs. 5-8 and 5-9 show a comparison of the fringe patterns obtained by moir interferometry (top) and contour plots obtained by the FEA program (bottom) for U, Fig. 5-8(a) & Fig. 5-9 (a) and V, Fig. 5-8(b) & Fig. 5-9(b) displacement fields for mode I and mixed mode loading respectively. Results show a very good agreement between numerical and experimental results. Cases from 0 to 27 deg were also compared revealing very good agreement between results. More attention to fine details, such as thicker contour lines or better adjustment of the contour intervals would result in a near perfect matching of the results. Having performed the comparison and gaining confidence in using the program, material properties could be implemented in the program for future characterization of the single crystal material behavior. P Figure 5-8. Comparison between Moir (top) and FEA (bottom) results for U (a) and V (b) displacement fields, mode I loading P P x,u y,v P P P P (a) (b) P P P

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87 P P y,v P P Figure 5-9. Comparison between Moir (top) and FEA (bottom) results for U (a) and V (b) displacement fields, mixed mode loading 5.3.3 Plastic Zones Ahead of the Crack Tips Another objective of this experimental study was to determine the strain fields ahead of the crack tips and to document the effect of load misalignment on crack propagation. Again, using the method described, tests were conducted on aluminum specimens at loads exceeding the aluminum yield point, resulting in the appearance of plastic zones. A limited number of tests were conducted for this case and the horizontal and vertical fringe patterns were obtained for both mode I and mode II loading. Fig. 5-10 shows the horizontal, Fig. 5-10(a), and vertical, Fig. 5-10(b), moir interferometry fringe patterns obtained in mode I loading, after load was removed. Analysis of the fringe patterns shows that the notch remained opened after load was removed. Additionally the alignment of the plastic zone was oriented with zones of maximum shear stress, at approximately 45. x,u (b) (a)

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88 Fig. 5-11 shows the horizontal, Fig. 5-11(a), and vertical, Fig. 5-12(b), moir interferometry fringe patterns obtained in mode II loading, after load was removed. Analyzing the fringe patterns we can observe that the material sheared straight ahead of the crack tip, as expected. (a) (b) Figure 5-10. Horizontal and vertical fringe patterns showing the plastic zones formed around the crack tip for mode I loading (a) (b) Figure 5-11. Horizontal and vertical fringe patterns showing the plastic zones formed around the crack tip for mode II loading

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89 5.4 Effect of Load Misalignment in the Linear Range Because a full investigation on the Brazilian disk specimen was not yet performed, a systematic study was conducted here to document the effect of load misalignment on the strain field around the crack tip. Using the special fixture designed for this project, misalignment was intentionally induced to document and measure the effects on the U and V displacement fields. The fixture was capable of inducing loading misalignment of angle up to four degrees for both in-plane and out-of-plane cases. A digital inclinometer with 0.1 degree accuracy was used for angle measurements. Using the procedure explained earlier, specimens were loaded in mode I at 350 lb and fringe patterns were documented and analyzed. In the V displacement fields it was observed that misalignment affected the fringe patterns and subsequently the strain field around the crack tip. On the other hand, the U displacement field showed little change as a function of misalignment. Also from the method described for inducing in-plane and out-of-plane misalignment it was obvious that the strain field around the top part of the specimen (crack tip) was not affected in any way as no load misalignment was induced but only the strain field around the bottom part of the specimen (crack tip) was affected. Fig. 5-12 shows the horizontal and vertical fringe patterns before and after in-plane load misalignment. It can be observed that the in-plane load misalignment produced a shift in the fringe pattern i.e., the fringe pattern moved to where the load was applied. It changed the loading mode from mode I to mixed mode loading but the effect on the strain field around the crack tip was barely noticeable. Fig. 5-13 shows the horizontal and vertical fringe patterns before and after out-of-plane load misalignment. The out-of-plane load misalignment produced a greater effect resulting in considerably lower strain around the crack tip.

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90 U displacement P Figure 5-12. Effect of in-plane misalignment on before and after misalignment y,v x,u V displacement P P P P P P P P P P P P P P P P P P P P P P P P P P P

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91 U displacement P Figure 5-13. Effect of out-of-plane misalignment before and after misalignment y,v x,u P V displacement P P P P P P P P P P P P P P P P P P P P P P P P

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92 To quantify the effect of load misalignment, surface strains were computed ahead of the crack tips, on gages perpendicular to the crack for the strain in the x-direction and in the direction of the crack for the strain in the y-direction for a near perfect aligned specimen and specimens with load misalignment. The loading fixture was specially designed for intentionally inducing load misalignment only on the bottom half portion of the Brazilian Disk specimen and did not induced any load misalignment on the top half portion of the specimen. Thus, the fringe pattern for the top portion of an intentionally misaligned specimen remained identical with the one for a near perfect aligned specimen. To minimize the error, the fringe patterns for the top and the bottom half portions of the specimens were analyzed and compared. Strains on the surface of the specimens were determined using the strain-displacement relationships defined in Eqs. (1-3) and (1-4). Figs. 5-14 and 5-15 show the difference in strain, in percentage, at the crack tips (top and bottom) vs. the misalignment angle, in degrees. For zero degree angle the strain difference around the crack tips is zero as it should be in the case of no misalignment. As we increase the angle, the strain difference increases. A 28% difference was recorded for the maximum in-plane misalignment angle and 50% for the maximum out-of-plane misalignment angle. This strain difference corresponds to an applied load of 350 lbs and was computed ahead of the crack tips on a gage of approximately 10 mm.

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93 Figure 5-14. Effect of in-plane misalignment on the V field Figure 5-15. Effect of out-of-plane misalignment on the V field

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94 5.5 Effect of Load Misalignment in the Plastic Range The same tests were also conducted for loads above the yield point of aluminum to document the effect of load misalignment on the strain field around the crack tip. Figs. 5-16 and 5-17 show the horizontal and vertical fringe patterns for a misaligned specimen ( = 4) loaded in pure mode I and pure mode II respectively. Analyzing the patterns we can observe that although the symmetry of the fringes was not perfectly preserved at the bottom part of the specimen, the difference in strain around the crack tips of the specimens was small, in the range of 10% for the largest misalignment. Figure 5-16. Horizontal and vertical fringe patterns showing the plastic zones around the crack tips for an intentionally misaligned specimen loaded in mode I

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95 Figure 5-17. Horizontal and vertical fringe patterns showing the plastic zones around the crack tips for an intentionally misaligned specimen loaded in mode II 5.6 J-Integral Estimation Procedure, Experimental Analysis For the last few decades, substantial amount of research has been extended to determine J-integral value for different engineering materials. Since J-integral value quantifies better the fracture behavior of the investigated material, and also gives a better indication of effect of load misalignment, an experimental analysis is performed to estimate its values ahead of the crack tips. Moir interferometry full-field displacement fields are used for this prediction. Both the horizontal and vertical displacement fields are used in this experimental analysis. The same fringe patterns that were previously presented for the misalignment cases are analyzed.

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96 Since J-integral is path independent, a convenient path is chosen ahead of the crack tips but making sure the paths from the horizontal and vertical fields overlap to be able to calculate the partial derivatives of u and v with respect to x and y. To acquire a better estimation of the J-integral value, around thirty data points were investigated along the path. First the partial derivatives and then strains were determined using Eqs. (1-3) to (1-5). Figs. 5-18 and 5-19 show the strain values obtained at different data points along the path ahead of the crack tip for an in-plane and out-of-plane misaligned specimen respectively. Figure 5-18. Strains values at different data points along the path for an in-plane misaligned specimen

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97 Figure 5-19. Strains values at different data points along the path for an out-of-plane misaligned specimen Once these quantities were determined, the engineering constants for 7075-T6 aluminum, Youngs modulus, Poissons ratio and shear modulus were employed to determine the stresses at each of those locations. J-integral values were obtained at each point using the following Eqs. (5-1) to (5-5) and then integrated over the entire path. dsxuTdyUJii0 (5-1) dsndyx (5-2) dsxunnUJijijx0 (5-3) dsxvnxunnUJyxyxxx0 (5-4)

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98 xyxyyyxxU210 (5-5) where U 0 is the strain energy density, is a closed contour followed counter clockwise, T i is the tension vector (traction) perpendicular to in an outside direction, , u are the stress, strain and displacement field respectively, ds is an element of and n is the unit vector normal to The J-integral was calculated ahead of the upper crack tip, where no misalignment was induced, as well as ahead of the bottom crack tip were misalignment was induced. The difference between the two values at different misalignment angles is plotted and presented in Fig. 5-20 and Fig. 5-21. As it can be observed, a difference in the two values exists, leading us again to the conclusion that misalignment can produce unexpected failure as well as in a direction that does not match prediction. Figure 5-20. Upper and lower crack J-integral difference variation with in-plane misalignment

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99 Figure 5-21. Upper and lower crack J-integral difference variation with out-of-plane misalignment 5.7 Alignment Procedure Because load misalignment was observed to be a very important factor when testing a Brazilian disk specimen, a common alignment procedure is proposed here to better assist future center-crack disk test users, to eliminate errors that initiate due to loading misalignment, and to avoid possible failure propagation in a direction that does not match prediction. The alignment procedure should be easy and inexpensive to implement as well as very efficient in obtaining near perfect alignment. The experimental setup as proposed in this paper requires an alignment fixture, a 0.001 thick shim of about 5 x 5, a Brazilian disk specimen, strain gages, a strain indicator box and multi-channel box. First, an alignment fixture as the one in Fig. 5-2, has to be designed and machined. The material investigated will determine the size and shape, i.e., a more robust fixture is

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100 required for high failure strength materials. Circular rods were used in this project simply because they were available. Also this application required optical access to the diffraction grating attached to the specimen; subsequently, some material was removed at the ends of the two rods. Thus for a regular test this would not be required nor necessary. The fixture has to pivot about a single point allowing both in-plane and out-of-plane adjustments. Springs are to be used to hold in place the fixture and two screws with rounded heads and thin threads would allow for fine-tuning the fixture. Very importantly, the surfaces of the two rods, between which the disk would be loaded, have to be perfectly flat as well as perfectly parallel to each other to insure that load misalignment is not induced through such imperfections in the loading fixture. The top part of the loading fixture that connects to the crosshead of the testing machine must be in the plane of the testing machine and in perfect vertical position. Second, a Brazilian disk specimen, preferably aluminum, has to be gaged with four relatively small gages, as in Fig. 5-22, one gage ahead of each crack tip on both faces of the specimen. Gaging procedure and information on materials required as well as purchasing such materials can be obtained on the Internet from Vishays web site. Figure 5-22. Front view of aluminum Brazilian disk specimen with attached strain gages and lead wires

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101 When choosing the gages a few things have to be considered. The smaller the gages the better alignment can be obtained assuming that all four gages are perfectly aligned with crack direction as well as positioned at the same distance from the crack tips. Non-symmetry in the strain fields due to material imperfections can also affect the gage readings. Since gages reading errors are enormous even for very small misalignment angles, and since small misalignment commonly occur with gage application, a compromise has to be obtained between size of the gages and the degree of alignment that can be obtained. In this paper, EA-06-062AK-120 gages were selected and used in a quarter bridge configuration; a 10x microscope was used to align the gages. The following alignment procedure assumes that all the steps will be followed exactly and enough consideration is given to gage application. Fig. 5-23 shows a schematic of the alignment procedure. Once the fixture is fabricated, the disk is gaged and all the other requirements are fulfilled, near perfect alignment of the Brazilian disk specimen testing fixture can be achieved by doing the following: Step 1: move down the crosshead of the MTI type testing machine until the two rods of the loading fixture almost get into contact (Fig. 5-23) Step 2: insert a shim between the two rods and further move down the crosshead until near contact is achieved (Fig. 5-24) Step 3: rotate the shim in the horizontal plane and observe where is does not move (Fig. 5-25). That indicates where contact between the two surfaces of the rods occurs. Note that full contact between top and bottom surfaces would not be attained. This is due to initial misalignment of the fixture.

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102 Figure 5-23. Schematic description of the alignment procedure, step 1 Figure 5-24. Schematic description of the alignment procedure, step 2 Figure 5-25. Schematic description of the alignment procedure, step 3

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103 Step 4: while continuously rotate the shim in the horizontal plane, using the two screws on the alignment fixture adjust it both in-plane and out-of-plane such that the shim would get in full contact with the surfaces. This would be indicated by the fact that the shim cannot rotate at all; once this is achieved, the loading fixture is near perfectly aligned. Step 5: using the strain indicator, zero out the strains in all four gages on the calibration Brazilian disk specimen. Move up the crosshead and place the disk in the loading fixture. Load the specimen in mode I i.e., the direction of the crack has to match the direction of the load, up to a convenient load level and read the strains. If all the previous steps were followed exactly and gages on the disk were carefully attached then strain readings from all four gages would be very close to each other. Step 6: using the adjustment screws fine tune the loading fixture such that all four gages read the same strain. Remarks: 1. This research found that once steps 1 through 4 are performed near perfect alignment is achieved. Using a very sensitive technique namely the moir interferometry technique, the vertical displacement fields ahead of the crack tips have been analyzed and the results showed a difference of less than 1.5 fringes (0.6255 microstrains). 2. If shims are not used but only a calibration disk, obtaining same strain values in all four gages is very difficult and time consuming. 3. The calibration disk is very important to verify alignment but some might argue that gage alignment will introduce measurement errors and that misalignment of the

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104 gages will translate in a misalignment of the testing fixture. Therefore a skilled technician with training in strain gage application should attach the gages on the calibration disk. 4. The calibration specimen should be a choice rather than a requirement. 5.8 Discussions and Recommendations As it was observed from the study, loading misalignment is a very important factor that has to be accounted for when testing a Brazilian disk specimen in the linear range. Experiments showed that only strain in the y-direction is affected by misalignment and the out-of-plane load misalignment produced the largest effect. Considerable strain difference occurs between 0 and 1 degree. Because erroneous results can be obtained even for small misalignment angles it is recommended that alignment be given considerable attention when running the test. On the other hand, above the linear range, stress redistribution occurred, from the plastic deformation at the contact zone, and near symmetry at the notch was observed. The misalignment study suggests that when testing brittle materials, obtaining near perfect alignment is critical. The resulting misalignment can lead to crack propagation along a path that does not match prediction. However, for ductile materials that lead to plastic deformation and shear banding, the alignment is not that critical because of stress redistribution at the contact zones. An alignment procedure was presented to minimize errors associated with loading imperfection of the Brazilian disk specimen. A special, adjustable loading fixture is required to obtain near perfect loading. The current study on aluminum specimens was used to obtain confidence in a FEA model that is being extended to include anisotropy and crystallographic effects for single crystal materials. It proved to be efficient to decouple the material effects (crystal

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105 orientation with respect to the notch orientation and loading direction) with the overall understanding and analysis of the specimen and loading conditions. In the future, single crystal metallic alloy specimens will be tested in the conditions experience in service. 5.9 Conclusions The Brazilian disk specimen has been proposed to characterize the fracture behavior of single crystal materials. This type of specimen provides a wealth of information about mode I, mode II and mixed mode loading in simple compression. A systematic study was conducted to determine the effects of loading misalignment on the stress field around crack tip and crack propagation. Experimental results showed that while in the linear range, on the strain field in the y-direction, around the tip of the crack, the in-plane load misalignment had a smaller effect than the out-of-plane loading misalignment and negligible effect on the strain field in the x-direction. In the linear range at the material there was a noticeable effect on the strain field at the notch tip. In the plastic range however, the effect diminished.

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CHAPTER 6 REDUCING UNCERTAINTIES IN EXPERIMENTAL MEASUREMENTS TO REDUCE STRUCTURAL WEIGHT Scientists have always tried to determine and verify the laws of physics through observations and experiments. For engineers in particular, understanding the laws of physics helps to improve their design and most importantly prevents catastrophic failure of the structures or machine components. In the case of failure, the cost of replacement is sometimes prohibitive. Thus experimental measurements are taken in the design stage to determine the behavior of the individual materials used as well as of the structure itself. 6.1 Experimental Errors and Uncertainty Composite and lightweight materials are relatively new and have not been fully tested, thus their behavior is not yet fully understood. Their material properties have to be experimentally determined [90] to be implemented in an optimization scheme to perform probabilistic analysis and design. In trying to determine these properties, laboratory measurements cannot be performed with perfect certainty [91]. In general, we assume that a true value exists, and we attempt to determine that value using our best resources. When we repeat a measurement, a slightly different result is obtained the second time due to a combination of errors. The error cannot be completely eliminated but the order of magnitude can be reduced thus approximating better the true value. To know the degree of uncertainty in the experimental measurements we need to know the types of errors and ways to reduce errors thus to perform an error analysis [92]. 106

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107 We can classify the errors as personal, systematic and random. Personal errors are unavoidable but they can be easily corrected. Most of the systematic errors come from the imperfect calibration of the measuring instruments therefore detecting these errors is very difficult. Faulty reading of the measuring instruments by the user is another important source for systematic errors. Random errors are due to the irregular variations during the experiments such as temperature fluctuation. All these errors can be either eliminated or reduced by repeating the measurement. Increasing the number of measurements will provide a better estimate of the true value. Accuracy and precision are also two important parameters in experimental measurements. The first parameter, accuracy, refers to how close the measurement comes from the true value. Precision refers to how close together the measurements are. In order to obtain high accuracy we need that our measurements to be very precise. However, even if we are able to perform our experimental measurements with high accuracy and precision and to eliminate all the experimental error, there is still uncertainty in the material property itself. For instance, fiber volume fraction can vary in the specimen or the specimen has defects from the manufacturing process or curing process. These are the most important uncertainties that have to be determined in order to optimize structural design, but unfortunately this is a very difficult task. Thus, an experimental optimization is to be performed, and experimental procedures have to be developed to reduce the uncertainties in experimental measurements. As mentioned earlier, many researchers have determined different material properties using a variety of mechanical test methods as well as comparing the experimental results with those from the analytical and numerical solutions. It was

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108 obvious that some of the results in question were neither 100% accurate nor precise, due to different errors as pointed out in this chapter. Thus, error analysis helped identify the errors and then improve the experimental results that followed. An abundant number of papers [93-96] are available in the literature, depicting the types and sources of errors, as well as the effects of parameter uncertainties for optimization and design of experiments. There are also papers that dealt with the uncertainty and design of optimal experiments for the estimation of elastic constants, such as Frederiksens paper [97], in which the author investigated a technique for the identification of orthotropic elastic constants and addresses the parameter uncertainty due to errors in measurements. In two other papers he also investigated the temperature dependence for orthotropic material moduli [98] and material parameters in anisotropic plates [99]. Wamelen et al. [100] used optimal design of laminated specimens to evaluate composite failure criteria. Different techniques useful in the structural optimization are also available in the literature. Lombardi et al. [101] published a paper that describes a technique for design under uncertainty based on the worst-case-scenario technique of anti-optimization and applied the method to the optimization of a simple supported laminate composite, a simple beam problem and a more complex real-life structure. Elishakoff et al. [102] looked at structural design under bounded uncertainty-optimization with anti-optimization and Gangadharan et al. [103] used the anti-optimization to compare alternative structural models. Adali et al. [104-105] considered the minimum weight design of symmetric angle-ply laminates under multiple uncertain loads as well as multi objective optimization of laminated plates for maximum pre-buckling, buckling and post-buckling strength.

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109 6.2 Reducing Uncertainties in Experimental Measurements All measurements have some degree of uncertainty. In this experimental study we have tested different materials and we have obtained experimental results. Because of the uncertainties in experimental measurements we expect to have errors but at the same time we are trying to reduce them to estimate better the true values of the measured quantities. The paper aims to improve the accuracy of the experimental data by introducing new procedures and through recommendations on how to avoid experimental error in the process of data acquisition. Part of the data obtained in this study will be used to perform structural optimization. Thus an optimization of experimental design [106] would achieve a significant reduction in structural weight. First, the Brazilian Disk specimen was investigated at room temperature. This type of specimen is intensively used in fracture mechanics because considerable information about material properties can be obtain by running a simple compression test. Tests on this type of specimen are usually conducted without considering the error that comes from the effect of load misalignment. In our study on aluminum specimens we have tried to reduce the experimental error by investigating the effect of load misalignment on the strain field ahead of the crack tip and crack propagation. It has been shown that load misalignment has a significant effect on the strain field ahead of the crack tip and crack propagation. Poor alignment of the loading fixture can induce as high as 50% error in the calculated strain ahead of the crack tip thus it is a very important factor that has to be accounted for when testing a Brazilian disk specimen in the linear range. Considerable error occurs between 0 and 1 of out-of-plane load misalignment as it was observed in Fig. 5-15 in Chapter 5. This suggests that when testing brittle

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110 materials, obtaining near perfect alignment is critical. The resulting misalignment can lead to crack propagation along a path that does not match prediction. Because erroneous results can be obtained even for small misalignment angles it is recommended that alignment be given considerable attention when running the test. One way of avoiding load misalignment errors is obtained by attaching two strain gages ahead of each crack tip of the specimen. Adjusting the loading fixture such that both gages will read the same strain will eliminate these errors. The second part of this experimental study concentrated on obtaining temperature dependent material properties for laminated composites. Residual stresses and CTEs were previously obtained as a function of temperature. Part of the error that exists in these results comes from composite manufacturing, lay-up and curing processes, but most of the error is due to the implementation of the CRM and strain gage methods. In the replication process, alignment of the grating is critical. Tuning the interferometer, documenting and reporting the results can also lead to erroneous results. In the future part of these errors can be reduced using the digital image processing for fringe analysis that was implemented as described in Chapter 4. A new test for determination of transverse properties was developed as well as for shear properties using double notch shear specimens and shear gages. A detailed uncertainty analysis was performed and reported as follows. 6.3 Uncertainty Analysis for E 2 and G 12 Measurements A new and unique test method for temperature dependent material property determination on composite materials has been developed as explained in Chapter 2 and Chapter 3. Using this newly developed method, we have determined the transverse modulus and shear modulus as a function of temperature of the IM7/977-2 material.

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111 However, questions might surface concerning the accuracy of the results and variability and uncertainty of our measurements. Before any composite specimens were tested, a validation of the method was required. An aluminum 6063-T5 bar was CNC machined to determine the transverse modulus and then the shear modulus using the geometry obtained from the FEA analysis. The two moduli were determined using the experimental setup and methodology explained in Chapters 2 and 3. Results were compared to the data sheet of the aluminum material. A 0.8% difference was found for the transverse modulus and less than 0.4% difference was obtained for the shear modulus. For the composite specimens manufacturing variability and measurement error are a few sources of this uncertainty. Some of these errors are unavoidable, but the objective is to analyze the greatest sources of error and to quantify the final uncertainty. The uncertainty associated with the applied load is dependent on the capabilities of the load cell being used. In this experiment an Interface SM series 1000lb load cell was used. The error sources include instrument precision, measurement nonlinearity, hysteresis, and nonrepeatability. The load cell used for the experiments had an accuracy of + 0.4 lb full scale. Measurement nonlinearity is the uncertainty of transforming the electronic response to a quantifiable load. For this load cell, the nonlinearity was + 0.3% full scale. + 0.2% error was used for hysteresis, which is the lagging effect in the measurements. Finally, the nonrepeatability of getting the same reading was + 0.2%. Creep effects were neglected since the loading occurred on a relatively small time interval. Table 6-1 shows the uncertainty due to the load cell.

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112 Table 6-1. Uncertainty from the load cell Instrument precisions Variability 0.4 lb Measurement nonlinearity Variability 0.3 % Hysteresis Variability 0.2 % Nonrepeatability Variability 0.2 % Sanity checks were often performed before tests. After the load cell would be tarred, different weight of known values would be added and measured. With the remark that those weights were not metrological approved, the measured values were very close to the values inscribed on them. Table 6-2 shows the percent difference found in measuring different weights. Table 6-2. Percent difference found in measuring known weights Run Known weight Determined weight value Difference 1 25 lbs 24.92 lbs 0.32 % 2 30 lbs 29.89 lbs 0.37 % 3 52.05 lbs 52.71 lbs 1.23 % The cross-sectional area calculation is broken down into its basic components width (w) and thickness (t). Instrument precision, user variability, and tooling variability are the three contributors of uncertainty in the area. Instrument resolution is 0.00005in and accuracy of 0.0001 in for a digital micrometer used in these experiments. The same micrometer was used to measure the width and thickness; therefore this error is the same for both. However a few of the first measurements of the specimens used in transverse modulus determination were taken using a regular micrometer with a lower resolution of 0.001 in. Therefore in the final uncertainty analysis the lower resolution will be used.

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113 Table 6-3 shows the uncertainty due to instrument resolution, accuracy, and user variability. Table 6-3. Uncertainty from measuring the width and thickness of the specimens Instrument resolution Variability 0.00005 in Tooling accuracy Variability 0.0001 in User variability (width) Measurement variability 0.00035 in User variability (thickness) Measurement variability 0.0005 in Both unidirectional and shear strain gages were custom ordered to allow operation over a wide range of temperatures with minimum error output. Resolution of the strain gages was assumed to be 1 microstrains. Strain gage alignment was assumed to be less than 2 degrees. Alignment of the gages was obtained by inscribing marks on the specimens then looking through a microscope the gage would be positioned such that the edges would follow exactly the marks. For transverse modulus tests, a 2 degrees misalignment of the strain gage will produce less than 1% measurement error. Attaching two gages on both sides of the specimen eliminates some of this measurement error; the average value is used in computing the modulus. Inspection of the recorded strain values was performed on all tests and specimens with large strain difference have been eliminated from the analysis. A temperature diode with a 0.1C resolution, as given by the manufacturer, was used in addition to the thermocouple in the environmental chamber. The reading from this diode was used as a reference in recording the data.

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114 At the beginning of the tests the diode was calibrated; but to verify its precision, two separate tests were later performed. The diode was submersed into boiling water and then into liquid nitrogen; results obtained are presented in Table 6-4. Table 6-4. Percent difference found in measuring temperature Run Temperature Recorded value Difference 1 LN 2 (-196C) -195.462C 0.27 % 2 Boiling water (+100C) +100.187C 0.19 % The composite specimens were manufactured in the lab and cured in the autoclave. Lay-up angle error occurs when the person manufacturing these specimens does not place each lamina in its correct orientation. For a simple unidirectional specimen, the ply variation was estimated to be + 2degrees. Figs. 6-1 and 6-2 show the variation of E x /E 2 and G xy /G 12 respectively with the fiber orientation angle. Figure 6-1. Variation of E x /E 12 with fiber orientation

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115 Figure 6-2. Variation of G xy with fiber orientation The plots show that variation of E 2 and G 12 with fiber orientation for small misalignment is negligible in the order 0.17% and 0.29% respectively when unidirectional laminates are tested. However, if we were considering testing a more complicated laminate the variation could be as large as 5%. Therefore, the uncertainty would also be much greater. Besides measurement variability in the micrometer, measurement variability is present when a single person or multiple persons try to measure the thickness or width of the specimens. This variability can be present due to defects in the surface or on the edges, due to positioning the instrument in different locations or due to improper use of the micrometer.

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116 To quantify this variability a few specimen measurements were taken and coefficient of variation was computed as per ASTM standards D3039 and D5379, where x is the sample mean (average), Eq. (6-1), s n-1 is the sample standard deviation, Eq. (6-2), CV is the sample coefficient of variation in %, Eq. (6-3), n is the number of specimens and x i is the measured or derived property. nxxnii1 (6-1) 11221nxnxsnin (6-2) xsCVn1100 (6-3) Five specimens were selected. One of them was intentionally chosen to have small surface defects, namely p2-7, that were not completely removed by sand abrading. Measurements were taken using a Starrett digital micrometer, model 734XFL, with a resolution of 0.00005 and accuracy of .0001. Table 6-5 shows the variability of cross-sectional area from repeated measurements on the same specimens. This comes from user variability in measuring width and thickness of the specimens.

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117 Table 6-5. Measurement variability of cross-sectional area in few specimens Specimen x1 x2 x3 Mean Standard Deviation CV % P2-4 t1 0.0883 0.08835 0.08825 0.0883 5E-05 0.057 t2 0.0873 0.0873 0.0872 0.087267 5.7735E-05 0.066 t3 0.0869 0.087 0.0871 0.087 1E-04 0.115 t ave 0.0875 0.08755 0.087517 0.087522 2.54588E-05 0.029 w 1.0018 1.00185 1.0018 1.001817 2.88675E-05 0.003 area 0.087658 0.087712 0.087674 0.087681 2.7905E-05 0.032 P2-5 t1 0.09045 0.09045 0.0905 0.090467 2.88675E-05 0.032 t2 0.08995 0.08995 0.08995 0.08995 1.69967E-17 0 t3 0.09 0.08995 0.08995 0.089967 2.88675E-05 0.032 t ave 0.090133 0.090117 0.090133 0.090128 9.6225E-06 0.011 w 1.0003 1.00035 1.00035 1.000333 2.88675E-05 0.003 area 0.09016 0.090148 0.090165 0.090158 8.62448E-06 0.010 P2-6 t1 0.08975 0.08975 0.0897 0.089733 2.88675E-05 0.032 t2 0.0891 0.0891 0.08905 0.089083 2.88675E-05 0.032 t3 0.08955 0.08955 0.0896 0.089567 2.88675E-05 0.032 t ave 0.089467 0.089467 0.08945 0.089461 9.6225E-06 0.011 w 0.99745 0.99735 0.99735 0.997383 5.7735E-05 0.006 area 0.089239 0.08923 0.089213 0.089227 1.29752E-05 0.015 P2-7 t1 0.08305 0.083 0.0835 0.083183 0.000275379 0.331 t2 0.0831 0.083 0.0834 0.083167 0.000208167 0.250 t3 0.0842 0.0843 0.08445 0.084317 0.000125831 0.149 t ave 0.08345 0.083433 0.083783 0.083556 0.000197437 0.236 w 0.99535 0.99505 0.9952 0.9952 0.00015 0.015 area 0.083062 0.08302 0.083381 0.083154 0.000197414 0.237 P3-9 t1 0.0898 0.0898 0.0898 0.0898 0 0 t2 0.0889 0.08855 0.08865 0.0887 0.000180278 0.203 t3 0.0873 0.0871 0.08705 0.08715 0.000132288 0.152 t ave 0.088667 0.088483 0.0885 0.08855 0.000101379 0.114 w 0.99655 0.99635 0.99655 0.996483 0.00011547 0.012 area 0.088361 0.08816 0.088195 0.088239 0.000107178 0.121 where t 1 t 2 t 3 are the thickness measurements at three different locations, and x 1 x 2 x 3 represent three separate measurements at the same locations. Thickness (t 1 t 2 t 3 ) and width (w) were measured then the average thickness (t ave ) and area were computed. Area is used in modulus determination, so that any variability will directly affect the modulus variability. The table shows in general a very small coefficient of variation for the cross-sectional area of the specimens, with the exception of the one where surface

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118 flows where not completely removed. ASTM standard recommends that tests for transverse modulus as well as shear modulus determination to be performed at a nearly constant strain rate in the gage section. The strain rate should be selected to produce failure within 1 to 10 minutes. If strain control is not available on the testing machine, the load should be adjusted such that it produces a constant strain rate. For constant head speed tests, a standard head displacement rate of 0.05/min is suggested. For this project, load was adjusted before each test. However during the investigation, it was observed that two specimens were tested at different rates, one approximately 37% slower (dashed line with square marker) and the other 60% slower (triangular marker) as in Fig. 6-3. Even though the two specimens were not included in the analysis it is important to show the effect of speed of testing on the transverse modulus. Figure 6-3. Speed of testing effect on the transverse modulus

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119 Table 6-6 shows how the two measurements affect the temperature dependent transverse modulus. The second column was obtained from fitting a straight line through the specimens without including the two runs while the third column includes all the specimens. Considerable error is produced above room temperature when the ASTM standard is not followed. Table 6-6. Percent difference in E2 by including specimens with different speed of testing Temp C E2 w/o specimens E2 with specimens % difference -165 1.2335E+10 1.2353E+10 0.15 -150 1.2094E+10 1.2114E+10 0.17 -125 1.169E+10 1.1716E+10 0.22 -100 1.1287E+10 1.1318E+10 0.27 -75 1.0884E+10 1.092E+10 0.33 -50 1.0481E+10 1.0522E+10 0.39 -25 1.0078E+10 1.0124E+10 0.45 0 9674449066 9725427620 0.52 25 9271273183 9327260423 0.60 50 8868097301 8929093226 0.68 75 8464921418 8530926029 0.77 100 8061745536 8132758832 0.87 125 7658569653 7734591635 0.98 150 7255393771 7336424438 1.10 Several other concerns surfaced as listed below but their effects were found to be negligible. Repeatability of the method was imperative if accurate results and minimum variability would need to be obtained. Fig. 6-4 shows the transverse modulus versus temperature for two runs on the same specimens. The results are in very good agreement considering the fact that during a single run the specimen is tested very close to cure temperatures therefore probably initiating a post cure of the resin. Soak time was increased to observe if results change; the compared tests showed insignificant difference (less than 0.5%). Temperature variation during data acquisition was on the order of 2 microstrains for the full 3000 microstrains scale used in slope determination. Bending

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120 and gage misalignment errors had minimum effects as observed from the readings on the two gages attached to each specimen. Cross-sectional area variability coming from width and thickness measurements taken by multiple users on the same specimens were found to be in the same order of magnitude as the ones taken by one user. No correlation was found between final measured data and the different panel or different gagging techniques used. This was expected since only unidirectional panels were tested. The two previous plots in Fig. 6-2 and Fig. 6-3 indicate such thing. Figure 6-4. Transverse modulus variation with temperature for two runs of the same specimen All these effects were minimized as a result of carefully panning and executing the experiments. Each lamina was properly aligned within the laminate. The cure process was monitored to insure that vacuum was drawn into the vacuum bag, no fluctuation in

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121 pressure occurred, and the temperature profile matched the one that was given by the manufacturer. During the strain gage implementation it was insured that gages are aligned with the direction of the fibers within the laminate. Through design and machine processes of the grips, minimum or no bending and/or twisting occurred during transverse and shear moduli determination by properly aligning the specimens with the loading fixture. Temperature probes were calibrated to insure accuracy of the reading. Speed of testing was adjusted in accordance to ASTM standards to reduce the measurement variability and the method was verified to insure it is repeatable. A digital micrometer with increased resolution and accuracy was acquired for thickness and width measurements. Taking into consideration the factors discussed, the uncertainty due to random errors in the transverse modulus can be calculated as, Eq. (6-4) to (6-7): 222222222MUTdUUtUwUPUEUMTDtwPE (6-4) where U P is the uncertainty contribution from load cell precision, U w is the uncertainty contribution from instrument precision and user variability on width measurements, U t is the uncertainty contribution from instrument precision and user variability on thickness measurements, U is the uncertainty contribution from strain gage resolution, U Td is the uncertainty contribution from temperature diode precision, and U M is the uncertainty contribution from fiber orientation as well as gage misalignment. 2222222222220004.391390221.040008.120001 087.000035.0087.0001.0998.00005.0998.0001.02004.02EEEUE (6-5)

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122 GMFOTdsgtuvtipwuvwipPEEEEEEEEEEEU689.2689.2 629.775.2562.1 432.1751.260.160.4222 (6-6) %29.122EUE (6-7) The plot for the temperature dependent transverse modulus with 1.29% error bars is shown in Fig. 6-5. Figure 6-5. Transverse modulus with 1.29% error bars For the shear modulus the uncertainty can be estimated as, Eq. (6-8) to (6-11): 22222221212MUTdUUtUwUPUGUMTDtwPG (6-8)

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123 22222222221230007.891390377.040008.130001 087.000035.0087.0001.0450.00005.0450.0001.01004.012EEGUG (6-9) GMFOTdsgtuvtipwuvwipPEEEEEEEEEEEU641.8641.8 629.7711.1562.1 432.1623.1694.456.1222 (6-10) %40.122EUE (6-11) The plot for the temperature dependent shear modulus with 1.40% error bars is shown in Fig. 6-6. Figure 6-6. Shear modulus with 1.40% error bars

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124 6.4 Conclusions In order to estimate the true values of the material properties of different materials, we need to find the types of errors and their sources. We also have to measure the experimental errors to determine the uncertainties in those measurements so we can design new and improved experimental methods and techniques. Implementing these new techniques, as well as taking multiple measurements will provide a better estimate of the true value and will reduce the coefficient of variation. Brazilian Disk Specimen was investigated and the effect of loading misalignment was documented and reported. Considerable measurement error can be obtained if tests are performed on a misaligned specimen. Material can behave totally different than expected which could lead to premature failure. Mechanical properties of composite materials were also determined and the error sources as well as the measurement variability were investigated here in detail. Thickness variability proved to be the most important factor to affect both transverse modulus and shear modulus. A detailed analysis of its effect was performed and reported here. In the future, all the transverse modulus and shear modulus measurements will be performed on an increased number of specimens and taking into consideration all the factors previously discussed. Only a repetition of sufficient measurements will guarantee a reduction in the coefficient of variation that can be low enough to be used in a structural optimization. 6.5 Discussion and Future Work This chapter tried to identify the type of errors and determine their influence on the measured transverse and shear moduli data. As stated in the beginning of this dissertation, a reduction in the data variability can substantially improve the overall

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125 design. Numerous reasons that can induce error and increase variability were discussed, but only the nine most significant were considered in the uncertainty analysis. The reduction in data variability obtained in this research is a direct consequence of the preventive measures taken before each test, including a complete calibration of the acquisition system. Using unidirectional laminates can significantly reduce errors associated with fiber and gage orientation. A better load cell might also lead to better results. A special thermocouple with high precision, such as the one used in this project should be used to measure the temperature, and calibration should be mandatory. From the uncertainty analysis that was performed in this chapter, it was found that the main contributor was the uncertainty from measuring the thickness of the specimens. From all the uncertainty components used, thickness accounted for around 70% 80% of the variability in the data. Since in this project a combination of micrometers was used for thickness measurements, one with a higher precision than the other, the uncertainty from the lower resolution instrument was used in the analysis. In the future, measurements will be taken using a very precise digital micrometer and thus minimize the effect on moduli variability. Nevertheless, the thickness will remain the main contributor to uncertainty. Instead of determining the cross sectional area as per ASTM standard (using three measurements across the test section) the number of measurements should be increased to nine, with three measurements across three different positions that will cover the area where the strain gage will be attached. There are also other methods that can be considered to accurately determine the cross-sectional area, although they might be expensive and time consuming.

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126 An increased scatter in the data was observed at elevated temperatures. One of the explanations could be the strain rate effect. Unfortunately, all the measurements that were taken for this research did not record the strain rate. Instead displacement control was used as per ASTM standard. The speed of testing effects that were shown in Fig. 6-4 indicates that the moduli are very sensitive to different strain rates at elevated temperatures. In the future, Labview program should be modified the current program for strain rate data acquisition to allow for better control of the testing machine. This should reduce the scatter and make it easier to identify measurement error from measurement variability.

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CHAPTER 7 CONCLUSIONS The author of this dissertation was concerned with the lack of temperature dependent material properties of composite and lightweight materials. Consequently a new and efficient method was designed and implemented, and the E 2 and G 12 properties of the IM7/977-2 composite material were determined as a function of temperature. This new method is unique because it uses tension specimens of special geometry for shear modulus determination and can determine the longitudinal, transverse and shear properties using a single experimental setup. Specimens are also very inexpensive and easy to fabricate. The method is fully automated and does not require supervision during the test. A robust set of data from cryogenic to elevated temperatures was obtained for the transverse modulus as well as shear modulus. The method proved to be repeatable and the scatter in the measured data was very low. A detailed uncertainty analysis was performed to determine measurement error and measurement variability in these measurements. Using a previously developed method, namely CRM, surface strains and CTEs for different laminate configurations were determined at room temperature and recorded for future analysis. The CRM method was improved by reducing the number of steps required to replicate a diffraction grating onto a composite panel as required. A digital fringe analysis system was implemented that could be used in the future to determine the surface strains on composites. The CRM provided the reference point for temperature 127

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128 dependent measurements. Strain gages were used in conjunction with the CRM to determine the surface strains over a large temperature range. These strains were superimposed to the reference point obtained via CRM. This allowed calculation of CTEs and chemical shrinkage as a function of temperature. A CLT Matlab code was employed to predict residual stresses in composites using information obtained from unidirectional laminates. Two lay-up sequences were investigated, one used in the RLV for the cryogenic tank application, and one used in an optimization study for the same application. Results showed that considerable residual stress occurred in the RLV configuration and the residual stress alone without any mechanical loads surpassed the ultimate transverse strength of the composite. The residual stress in the OAP configuration was considerable lower. The fracture behavior of single crystal metallic materials was also investigated at room temperature. The Brazilian Disk Specimen (BDS) was proposed to study mode I, mode II and mixed mode fracture of these materials. A systematic experimental study was conducted on aluminum specimens to characterize the effect of load misalignment and specimen orientation in the linear range as well as in the plastic range. A substantial difference in the strain ahead of the misaligned crack tip was observed that could lead to premature failure or crack propagation in a direction that does not match prediction. The information will be useful in predicting more accurately the fracture behavior of lightweight materials.

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APPENDIX MATLAB CODE FOR PLOTTING TEMPERATURE VS TRANSVERSE MODULUS: clear all; close all; save data.out -ascii for i=1:14 s=sprintf('a%d.txt',i); m=load(s); [E2,T]=de2t(m); save data.out T E2 -ASCII -append clear all close all end clear all; close all load data.out; n=data; for i=1:2:28 T(i)=n(i,1); end for i=2:2:28 E2(i)=n(i,1); end Temp=nonzeros(T); E_2=nonzeros(E2); plot(Temp,E_2) 129

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130 SUBROUTINE FOR DETERMINING THE SLOPE: function [E2,T]=de2t(m); % FIND SIZE s = size(m); ss = s(1,1); % FIND FORCE AND AVERAGE STRAIN AND AVERAGE TEMPERATURE for i = 1:1:ss; x_1(i) = m(i,2); x_2(i) = m(i,3); x(i) = (x_1(i)+x_2(i))/2; %average strain y(i) = m(i,1); %load t(i) = m(i,4); %temperature end max_load = max(y); max_strain = max(x); tave = sum(t)/ss; %average temperature %area = input('input cross-section area area = '); % minload = input('input the minimum acceptable value for load (default value = 20 lb) min = '); minload = 20; % maxload = input('input the maximum acceptable value for load (default value = 130 lb) max = '); maxload = 190; % FIND LOWER LIMITS for i = 1:ss; if y(i) > minload & y(i) < 40 ll(i) = y(i); li(i)=i; end end LLL=nonzeros(li); size_LLL = size(LLL); ss_size_LLL1 = size_LLL(1,1); ss_size_LLL2 = size_LLL(1,2); if ss_size_LLL1 == 1 ss_size_LLL = ss_size_LLL2; else ss_size_LLL = ss_size_LLL1; end for k=1:1:ss_size_LLL-1 if LLL(k+1)-LLL(k) == 1 LLLi(k) = LLL(k); else LLLi(k) = 0; mmm(k) = k; end

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131 end MMM=nonzeros(mmm); MMM2=MMM(2); MMM4=MMM(4); MMM6=MMM(6); MMM8=MMM(8); LLLfi = [LLLi(1), LLLi(MMM2+1), LLLi(MMM4+1), LLLi(MMM6+1), LLLi(MMM8+1)]; %FIND UPPER LIMITS for i = 1:ss; if y(i) > max_load-50 & y(i) < maxload ul(i) = y(i); ui(i)=i; end end LUL=nonzeros(ui); size_LUL = size(LUL); ss_size_LUL1 = size_LUL(1,1); ss_size_LUL2 = size_LUL(1,2); if ss_size_LUL1 == 1 ss_size_LUL = ss_size_LUL2; else ss_size_LUL = ss_size_LUL1; end for uk=1:1:ss_size_LUL-1 if LUL(uk+1)-LUL(uk) == 1 LULi(uk) = LUL(uk); else LULi(uk) = 0; nnn(uk) = uk; end end NNN=nonzeros(nnn); NNN1=NNN(1); NNN3=NNN(3); NNN5=NNN(5); NNN7=NNN(7); NNN9=NNN(9); LULfi = [LULi(NNN1-1)+1, LULi(NNN3-1)+1,LULi(NNN5-1)+1, LULi(NNN7-1)+1,LULi(NNN9-1)+1]; %PLOT FORCE VS STRAIN plot(x,y) hold on; %FIT CURVES for j1=LLLfi(1):1:LULfi(1) x1(j1) = x(j1); y1(j1) = y(j1);

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132 end for j2=LLLfi(2):1:LULfi(2) x2(j2) = x(j2); y2(j2) = y(j2); end for j3=LLLfi(3):1:LULfi(3) x3(j3) = x(j3); y3(j3) = y(j3); end for j4=LLLfi(4):1:LULfi(4) x4(j4) = x(j4); y4(j4) = y(j4); end for j5=LLLfi(5):1:LULfi(5) x5(j5) = x(j5); y5(j5) = y(j5); end x1nz = nonzeros(x1); y1nz = nonzeros(y1); x2nz = nonzeros(x2); y2nz = nonzeros(y2); x3nz = nonzeros(x3); y3nz = nonzeros(y3); x4nz = nonzeros(x4); y4nz = nonzeros(y4); x5nz = nonzeros(x5); y5nz = nonzeros(y5); p1 = polyfit(x1nz,y1nz,1); f1 = polyval(p1,x1nz); plot(x1nz,y1nz,x1nz,f1,'-r','LineWidth',2) p2 = polyfit(x2nz,y2nz,1); f2 = polyval(p2,x2nz); plot(x2nz,y2nz,x2nz,f2,'-r','LineWidth',2) p3 = polyfit(x3nz,y3nz,1); f3 = polyval(p3,x3nz); plot(x3nz,y3nz,x3nz,f3,'-r','LineWidth',2) p4 = polyfit(x4nz,y4nz,1); f4 = polyval(p4,x4nz); plot(x4nz,y4nz,x4nz,f4,'-r','LineWidth',2) p5 = polyfit(x5nz,y5nz,1); f5 = polyval(p5,x5nz); plot(x5nz,y5nz,x5nz,f5,'-r','LineWidth',2) average_slope = (p1(1)+p2(1)+p3(1)+p4(1)+p5(1))/5; T = tave; area = 0.09*.987; E2=average_slope*6894.7*1e6/area;

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133 mlp=max_load*.85; msp=max_strain*.1; mlp1=max_load*.1; msp1=max_strain*.5; %DISPLAY DATA text(msp,mlp,sprintf('E2 (Pa) = %d',E2)) text(msp1,mlp1,sprintf('Temp (C) = %d',T)) title('E2 at temperature T') ylabel('Force (lb)') xlabel('Strain (microstrains)')

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BIOGRAPHICAL SKETCH Lucian Speriatu was born in Bucharest, Romania, in 1976. He began his undergraduate education at the University Politehnica of Bucharest in the Department of Engineering Sciences. A few years later he received a three months scholarship to study at Darlington College of Technology in England. He graduated in 1999 with a Bachelor of Science degree in mechanical engineering. From 1999 to 2000, he worked as a mechanical engineer and later was promoted to project manager of the Industrial Division Equipment of TehnoEM Ltd., Bucharest, Romania, and led the successful completion of several projects in the area of industrial metrology. In August 2000, he was admitted to the graduate program in the Department of Aerospace Engineering, Mechanics and Engineering Sciences at the University of Florida. He served as a Graduate Research Assistant under the guidance of Dr. Peter Ifju, working in the area of experimental stress analysis. 142