processinduced stresses and deformations in woven composites manufactured by resin transfer moulding

Process-Induced Stresses and Deformations

in Woven Composites Manufactured by Resin

Transfer Moulding

Loleï Khoun

July, 2009

Department of Mechanical Engineering

McGill University, Montréal

A thesis submitted to McGill University

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

©Loleï Khoun, 2009

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“I may not have gone where I intended to go,

But I think I have ended up where I needed to be”

Douglas Adams (1952 – 2001)

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Abstract

This work investigated the factors leading to the generation of process-induced

stresses and deformations in woven composites manufactured by Resin Transfer

Moulding (RTM). Both intrinsic and extrinsic mechanisms were examined. First,

a comprehensive methodology was applied to characterize the thermal,

chemorheological and thermomechanical properties of the CYCOM 890RTM

epoxy resin. The developed models were essential to establish a clear

understanding of the resin behaviour during the processing conditions. Then, the

thermomechanical properties of 5-Harness satin woven fabrics were investigated

using a micromechanical approach. Different fibre volume fractions between 50%

and 62%, corresponding to typical volume fractions used in the RTM process,

were examined. These thermomechanical properties were compared to the

properties of equivalent unidirectional crossply laminates in order to validate the

use of crossply configuration to model the behaviour of woven fabric laminate.

The developed resin models and the fibre properties were then implemented in a

finite element software, ABAQUS/COMPRO in order to predict the evolution of

the laminate properties during the RTM process. Fibre Bragg Grating sensors

were then used to characterize experimentally the tool-part interaction occurring

during the RTM process. The separation of the composite from the mould during

the cool down period was measured by the optical sensors. The maximal shear

stress allowed by the laminate before the debonding was estimated to be 140 kPa

for a steel mould. The observed tool-part interaction was simulated using

frictional contact conditions at the composite/mould interface in a finite element

analysis. Finally, using the ABAQUS/COMPRO interface, the manufacturing of a

composite structure by RTM was modelled, taking into account simultaneously

the intrinsic and extrinsic mechanisms examined. This case study demonstrates

the capacity of the process modelling approach to predict the process-induced

strains, stresses and deformations of three-dimensional woven composite parts

manufactured by the RTM process. The use of such a modelling tool is essential

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for industrial purposes to significantly reduce the design time and manufacturing

cost.

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Résumé

Ce travail étudie les facteurs conduisant au développement de contraintes et

déformations résiduelles induites par le procédé d’injection sur renforts dans le

cas de composites à renforts tissés. Les mécanismes intrinsèques ainsi

qu’extrinsèques ont été pris en considération. Tout d’abord, une méthodologie a

été utilisée pour caractériser les propriétés thermo-chimiques et thermo-

mécaniques de la résine époxy CYCOM 890RTM. Le développement de modèles

mathématiques pour décrire les différentes propriétés est une étape essentielle

pour comprendre clairement l’évolution du comportement de la résine lors du

procédé de fabrication. Ensuite, les propriétés thermo-mécaniques d’un tissu satin

de 5 ont été examinées en utilisant une approche de micromécanique sur un motif

élémentaire. Différentes fractions volumiques de fibre entre 50% et 62%,

correspondant aux fractions volumiques de fibre typiquement utilisées pour le

procédé d’injection sur renfort, ont été étudiées. Les propriétés ont été comparées

aux propriétés obtenues pour des laminés unidirectionnels croisés équivalents. En

général, les propriétés des deux configurations sont comparables. Ceci justifie

l’utilisation des propriétés de fibre unidirectionnelle dans une configuration

croisée pour simuler le comportement d’un laminé à renfort tissé satin de 5. Les

modèles des propriétés de la résine et des fibres ont été ensuite implémentés dans

un logiciel d’éléments finis, ABAQUS/COMPRO, afin de prédire l’évolution des

propriétés du laminé pendant le procédé d’injection sur renforts. Des fibres

optiques à réseaux de Bragg ont été également utilisées pour caractériser

expérimentalement les interactions entre le composite et le moule générées

pendant le procédé. Les fibres optiques saisirent la séparation entre le composite

et le moule pendant le refroidissement. La contrainte de cisaillement maximale

que le composite peut endurer avant le décollement a été estimée à 140 kPa. Cette

interaction entre le composite et le moule a été ensuite simulée par une analyse

d’éléments finis en utilisant une condition de contact par friction à l’interface

composite/moule. Finalement, la fabrication d’une structure composite par le

procédé d’injection sur renfort a été simulée en tenant en compte, simultanément,

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les mécanismes intrinsèques et extrinsèques étudiés. Ce cas d’étude démontre la

capacité d’utiliser le principe de la modélisation de procédé pour prédire les

déformations et contraintes résiduelles générées par le procédé de fabrication pour

des pièces composite tissées tridimensionnelles. L’utilisation d’un tel outil

numérique est essentielle pour des applications industrielles afin de diminuer les

temps de conception ainsi que les coûts de fabrication.

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Acknowledgements

Je tiens tout d’abord à adresser mes remerciements les plus sincères à mon

superviseur, Prof. Pascal Hubert. Ses précieux conseils, son support et ses

encouragements tout au long du projet ont été la clé d’une expérience de

recherche enrichissante et mémorable.

I would like to deeply acknowledge Timotei Centea for his precious help for the

resin characterization. I would like also to sincerely thank Tadayoshi Yamanaka

and Dr. Krishna Challagulla for their valuable help and advice on the unit cell

analysis.

Je remercie sincèrement Jonathan Laliberté pour son aide précieuse pour les

montages expérimentaux ainsi que ses conseils tout au long du projet et son

infinie patience. J’aimerai également remercier le Dr. Véronique Michaud et le

Dr. Rui de Oliveira pour leur accueil chaleureux au Laboratoire de technologie

des composites et polymères de l’EPFL, ainsi que de m’avoir permis d’enrichir

mon expérience dans le domaine des fibres optiques.

I am grateful to Anthony Floyd and Robert Courdji from Convergent

Manufacturing Technologies Inc. for their endless help and invaluable advice with

the process modelling simulations.

Je remercie également de tout mon cœur ma famille qui m’a toujours encouragée

à aller de l’avant et à poursuivre mes ambitions. Je n’aurais pas pu arriver là où

j’en suis sans leurs constants encouragements et conseils.

I would like to gratefully thank all the members of the Composite Materials and

Structures Laboratory for their invaluable friendship and their support throughout

my studies.

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Finally, I would like to acknowledge the financial support from the Consortium

for Research and Innovation in Aerospace in Quebec (CRIAQ) and the Natural

Sciences and Engineering Research Council of Canada (NSERC). I would like

also to acknowledge the industrial and academic partner of this project: Bell

Helicopter Textron, Delastek, the Aerospace Manufacturing Technology Centre

of the National Research Council of Canada (NRC-AMTC) and École

Polytechnique.

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Table of contents

Abstract............. .................................................................................................... iv

Résumé………. ..................................................................................................... vi

Acknowledgements ............................................................................................ viii

Table of contents ................................................................................................... x

List of Figures .....................................................................................................xiv

List of Tables.... ................................................................................................ xxiv

List of Symbols ................................................................................................. xxvi

CHAPTER 1 Introduction ................................................................................... 1

1.1 Introduction ................................................................................... 1

1.2 Motivations .................................................................................... 5

1.3 Project objectives and thesis outline ............................................. 6

CHAPTER 2 Literature Review and Objectives ................................................. 8

2.1 Material behaviour during the cure ............................................... 8

2.1.1 Resin behaviour ............................................................................. 8

2.1.2 Composite thermomechanical properties .................................... 22

2.1.3 Fibre architecture behaviour ........................................................ 27

2.2 Sources of residual stresses and deformations ............................ 31

2.2.1 Thermal strains ............................................................................ 32

2.2.2 Resin volumetric cure shrinkage ................................................. 34

2.2.3 Tool-part interaction .................................................................... 36

2.2.4 Property gradients: temperature, degree-of-cure and fibre volume

fraction ........................................................................................ 38

2.2.5 Secondary effects ........................................................................ 39

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2.3 Process modelling ....................................................................... 40

2.3.1 Heat transfer and cure kinetics .................................................... 42

2.3.2 Flow and compaction .................................................................. 43

2.3.3 Stresses development .................................................................. 44

2.3.4 COMPRO Component Architecture (CCA) ............................... 47

2.4 Literature review summary and objectives ................................. 48

CHAPTER 3 Characterization of the Resin Thermomechanical Properties ..... 52

3.1 Characterization methodology .................................................... 52

3.2 Thermal stability and cure kinetics (step 1 and 2) ...................... 53

3.2.1 Thermal stability (step 1) ............................................................ 53

3.2.2 Cure kinetics (step 2) ................................................................... 55

3.3 Rheological behaviour (step 3a) .................................................. 60

3.4 Glass transition temperature (step 3b) ......................................... 64

3.5 Volumetric changes during cure (step 4a and 4b) ....................... 66

3.5.1 Cure shrinkage (step 4a) .............................................................. 66

3.5.2 Coefficient of thermal expansion (step 4b) ................................. 80

3.6 Elastic modulus (step 4c) ............................................................ 84

3.7 Summary and discussion ............................................................. 88

CHAPTER 4 Thermomechanical properties of fabric composites ................... 91

4.1 Unit cell models .......................................................................... 93

4.1.1 Unidirectional unit cell ................................................................ 93

4.1.2 Crossply unit cell ......................................................................... 94

4.1.3 5-harness satin unit cell ............................................................... 95

4.2 Boundary conditions ................................................................... 99

4.2.1 Periodic constraints ..................................................................... 99

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4.2.2 Loading cases ............................................................................ 101

4.3 Thermomechanical properties ................................................... 103

4.3.1 Determination of the thermomechanical properties .................. 103

4.3.2 Unidirectional unit cell thermomechanical properties .............. 104

4.3.3 Crossply and 5-harness satin unit cells thermomechanical

properties ................................................................................... 107

4.3.4 Evolution of the 5-HS unit cell stresses during the cure cycle .. 115

4.4 Summary and discussion ........................................................... 119

CHAPTER 5 Investigation of the tool-part interaction by fibre Bragg grating

sensors ....................................................................................... 121

5.1 Fibre Bragg grating sensor principle ......................................... 122

5.2 Experimental procedure ............................................................ 125

5.2.1 RTM process ............................................................................. 125

5.2.2 FBG sensors .............................................................................. 128

5.3 Experimental results .................................................................. 129

5.3.1 Measured in-plane strains: cure cycle 1 .................................... 129

5.3.2 Measured in-plane strains: cure cycle 2 .................................... 133

5.3.3 Laminate coefficient of thermal expansion ............................... 137

5.3.4 Maximum shear stress determination ........................................ 138

5.4 Tool-part interaction modelling ................................................ 140

5.4.1 Geometry and finite element mesh ............................................ 141

5.4.2 Material model .......................................................................... 142

5.4.3 Boundary conditions ................................................................. 143

5.4.4 Numerical results ....................................................................... 146


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CHAPTER 6 Numerical case study: dimensional stability of carbon epoxy

cylinders ................................................................................... 167

6.1 Numerical model ....................................................................... 167

6.1.1 Geometry and finite element mesh ............................................ 168

6.1.2 Material models ......................................................................... 169

6.1.3 Boundary conditions ................................................................. 170

6.2 Results and discussion ............................................................... 171

6.2.1 Temperature and degree-of-cure ............................................... 172

6.2.2 Strains and stresses results ........................................................ 174

6.2.3 Spring-in variation ..................................................................... 186


CHAPTER 7 Conclusions and Future Work ................................................... 195

References......... ................................................................................................. 200

Appendix A Complements on Material Characterization .............................. 211

A.1. DSC measurements .................................................................... 211

A.2. Rheological measurements......................................................... 212

A.3. Solid samples preparation for the rheometer in torsion mode ... 217

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List of Figures

Figure 1-1: Composite manufacturing processes as a function of production rate

and part complexity [2].................................................................................. 1

Figure 1-2: RTM process ........................................................................................ 3

Figure 1-3 RTM phenomena interactions ............................................................... 3

Figure 2-1: State transition and property evolution of the CYCOM 890RTM

epoxy resin during a typical cure cycle. a) Degree-of-cure, viscosity and

glass transition temperature, b) Relative volume variation and elastic

modulus ....................................................................................................... 10

Figure 2-2: Volumetric change of the CYCOM 890RTM epoxy resin during a

typical cure cycle ......................................................................................... 11

Figure 2-3: Example of construction of the compliance master curve using the

principle of time-temperature superposition [62] ........................................ 21

Figure 2-4: Loading on the representative volume element to determine the elastic

constants: a) longitudinal load, b) transverse load, c) in-plane shear load .. 22

Figure 2-5: Comparison of experimental values of the transverse Young’s

modulus with the predicted values using the strength of materials approach,

the semi-empirical approach and the elastic approach as a function of the

fibre volume fraction: a) 0 <Vf <1, b) 0.45< Vf <0.75 [67] ......................... 25

Figure 2-6: Comparison of experimental values of the in-plane shear modulus

with the predicted values using the strength of materials approach, the semi-

empirical approach and the elastic approach as a function of the fibre

volume fraction: a) 0< Vf <1, b) 0.45< Vf <0.75 [67] .................................. 26

Figure 2-7: Main weave configurations. a) Plain weave, b) Twill weave and ..... 28

Figure 2-8: Schematic view of the three analytical models for an 8-harness satin.

a) Mosaic model, b) Crimp model, c) Bridging model (adapted from [73]) 29

Figure 2-9 Shape variations due to process-induced stresses: a) spring-in

deformation, b) warpage deformation ......................................................... 32

Figure 2-10: Schematic explanation of the spring-in variation as a function of the

resin state, below or above Tg (adapted from [99]) .................................. 34

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Figure 2-11: Process-induced warpage mechanism due to tool-part interaction

[107] ............................................................................................................ 36

Figure 2-12: Process-induced warpage mechanism due to fibre volume fraction

gradient ........................................................................................................ 39

Figure 2-13: Process modelling modular approach .............................................. 41

Figure 2-14: Schematic representation of the coordinate systems in ply and the

global orientation ......................................................................................... 45

Figure 2-15: ABAQUS/COMPRO structure ........................................................ 47

Figure 2-16: Summary of the investigations on process-induced stresses and

deformations ................................................................................................ 48

Figure 3-1: Characterization procedure for the thermoset resin ........................... 53

Figure 3-2: Resin weight variation with temperature from a TGA dynamic test at

20°C/min ...................................................................................................... 54

Figure 3-3: Resin weight variation for three hour at 180ºC .................................. 55

Figure 3-4: Typical heat flow of a Dynamic Scanning Calorimetry dynamic test at

2ºC/min ........................................................................................................ 56

Figure 3-5: Comparison of experimental data and predicted cure kinetics model

for isothermal tests: a) degree-of-cure with the time, b) cure rate as a

function of the degree-of-cure ..................................................................... 57

Figure 3-6: Cure rate as a function of inverse absolute temperature at low degree-

of-cure (α = 0.1) under isothermal conditions ............................................. 58

Figure 3-7: Ultimate degree-of-cure under isothermal conditions as a function of

the glass transition temperature ................................................................... 59


for dynamic tests .......................................................................................... 60

Figure 3-9: Evolution of the measured and predicted viscosity with temperature

for rheological dynamic tests at three temperature rates ............................. 61

Figure 3-10: Evolution of the measured and predicted viscosity with time for

rheological isothermal tests ......................................................................... 62

Figure 3-11: Determination of the gel point at 180ºC .......................................... 62

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Figure 3-12: Comparison of glass transition temperatures measured with

Modulated Differential Scanning Calorimeter, Thermo Mechanical

Analyzer and rheometer in torsion mode and the predicted values obtained

with the DiBenedetto model ........................................................................ 66

Figure 3-13: Shrinkage measurement methods set-up: a) modified rheology, b)

gravimetric. .................................................................................................. 70

Figure 3-14: Gap and normal force variation for a typical modified rheology test

for an isothermal cure at 180ºC ................................................................... 71

Figure 3-15: Evolution of the measured resin shrinkage by the modified rheology

method and predicted values with time under isothermal conditions ......... 72


method and the predicted values as a function of the degree-of-cure under

isothermal conditions ................................................................................... 73

Figure 3-17: Resin weight and temperature variation for a typical gravimetric test






Figure 3-20: Evolution of the measured resin shrinkage by gravimetric method

and predicted values with time under isothermal conditions ...................... 76

Figure 3-21: Measured and predicted cure shrinkage for isothermal tests with the

gravimetric method ...................................................................................... 76

Figure 3-22: Comparison of the two shrinkage measurement methods with

degree-of-cure at 160ºC ............................................................................... 78





Figure 3-25: Resin relative dimensional change with temperature of a neat resin

sample with an initial degree-of-cure 1 of 0.883 ....................................... 81

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Figure 3-26: Resin relative dimensional change during the heating part of cycle 3

at 3ºC/min .................................................................................................... 82

Figure 3-27: Variation of the coefficient of thermal expansion with the degree-of-

cure before and after the glass transition ..................................................... 83

Figure 3-28: Evolution of the measured and predicted CTE as a function of T*,

for 3ºC/min heating rate up to different temperatures ................................. 84

Figure 3-29: Evolution of the elastic modulus with temperature and time for a

resin sample with an initial degree-of-cure 1 of 0.846 .............................. 86

Figure 3-30: Resin modulus model as a function of difference between

instantaneous and glass transition temperature (T*=T-Tg) ......................... 87

Figure 3-31: Measured and predicted elastic modulus with time under two curing

temperatures, 160ºC and 180ºC ................................................................... 88

Figure 4-1: Applied methodology to determine the thermomechanical properties

of the unidirectional crossply and 5-harness woven fabric unit cells .......... 92

Figure 4-2: Unidirectional unit cell finite element model..................................... 94

Figure 4-3: Crossply unit cell finite element model ............................................. 95

Figure 4-4: a) Cross-section of a 4 plies laminate, G30-500 6k carbon

fibre/CYCOM 890RTM epoxy resin, observed by optical microscope (x50),

b) detail of a yarn ......................................................................................... 96

Figure 4-5: 5-harness satin unit cell: a) unit cell finite element model and

dimensions, b) yarn dimensions, c) schematic representation of the fibre

orientation along a yarn ............................................................................... 99

Figure 4-6: Unit cell faces, edges and corners notations .................................... 100

Figure 4-7: Boundary conditions: a) for an axial loading, b) for a shear loading, c)

for a thermal loading.................................................................................. 102

Figure 4-8: Axial and shear stress distributions of the unidirectional unit cell at

70% fibre volume fibre .............................................................................. 106

Figure 4-9: Axial and shear stress distributions of the crossply unit cell at 70%

fibre volume fraction ................................................................................. 109

Figure 4-10: Axial and shear stress distributions of the 5-HS unit cell at 70% fibre

volume fraction .......................................................................................... 110

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Figure 4-11: Elastic modulus comparison for the crossply unit cell and the 5-

harness satin unit cell ................................................................................. 111

Figure 4-12: Shear modulus comparison for the crossply unit cell and the 5-


Figure 4-13: Poisson’s ratios comparison for the crossply unit cell and the 5-


Figure 4-14: In-plane coefficients of thermal expansion comparison for the

crossply unit cell and the 5-harness satin unit cell .................................... 113

Figure 4-15: Through-thickness coefficients of thermal expansion comparison for

the crossply unit cell and the 5-harness satin unit cell .............................. 113

Figure 4-16: Stresses in the three directions of a half 5-HS unit cell (Vf = 50%) at

the gel point (t = 70 minutes) .................................................................... 116


the end of the isotherm (t = 120 minutes) .................................................. 117


the end of the cool down (t = 275 minutes) ............................................... 118

Figure 5-1: Schematic representation of the open and closed mould processes, a)

before the cure, b) at the end of the cure ................................................... 121

Figure 5-2: Phase mask grating technique (adapted from [150])....................... 124

Figure 5-3: RTM steel mould: a) mould opened, b) perform inside the mould .. 126

Figure 5-4: RTM experimental set-up ................................................................ 127

Figure 5-5: Applied cure cycle to the RTM process ........................................... 127

Figure 5-6: Preconditioned fibre Bragg grating sensor ....................................... 128

Figure 5-7: FBG sensors position in the laminate .............................................. 129

Figure 5-8: FBG sensor relative wavelength variation and temperature during cure

cycle 1 ........................................................................................................ 130

Figure 5-9: In-situ strain variation during cure cycle 1 ...................................... 131

Figure 5-10: In-situ strain variation from the injection to the end of cure cycle 1

................................................................................................................... 131

Figure 5-11: In-situ strain variation with the temperature for cure cycle 1 ........ 133

Figure 5-12: FBG sensor relative wavelength variation during cure cycle 2 ..... 135

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Figure 5-13: In-situ strain variation during cure cycle 2 from the injection to the

end of the cool down ................................................................................. 135

Figure 5-14: In-situ strain variation with the temperature for the cool down of cure

cycle 2 ........................................................................................................ 136

Figure 5-15: Comparison of the strain variation at the laminate mid-thickness for

the two cure cycles. ................................................................................... 136

Figure 5-16: Temperature and strain variation during the post-cure of the laminate

................................................................................................................... 138

Figure 5-17: Shear stress formation due to the mismatch of the thermal expansion

between the composite and the mould at the cool down ........................... 139

Figure 5-18: Composite plate and steel mould finite element model: a) finite

element mesh of the laminate, b) finite element mesh of the mould and the

laminate, c) close-up of the laminate finite element mesh in the mould, d)

schematic position of the analyzed element .............................................. 142

Figure 5-19: Schematic representation of the critical shear stress evolution with a

stick-slip behaviour ................................................................................... 145

Figure 5-20: Evolution of the temperature and the degree-of-cure at the laminate

mid-thickness at the position A for cure cycle 1 ....................................... 147


mid-thickness at the position A for cure cycle 2 ....................................... 147

Figure 5-22: Temperature and degree-of-cure field at different times: 0 minutes,

60 minutes, 120 minutes, and 917 minutes ............................................... 148

Figure 5-23: In-plane strain evolution at the laminate mid-thickness for cure cycle

1 in the case of no bonding (model A) and perfect bonding (model B) ..... 150


1 using contact interactions (model C) ...................................................... 150

Figure 5-25: Through-thickness strain evolution at the laminate mid-thickness for

cure cycle 1 in the case of no bonding (model A) and perfect bonding (model

B) ............................................................................................................... 151


cure cycle 1 using contact interactions (model C) ..................................... 151

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Figure 5-27: In-plane strain evolution with the temperature at the laminate mid-

thickness for cure cycle 1 in the case of no bonding (model A) and perfect

bonding (model B) ..................................................................................... 153


thickness for cure cycle 1 using contact interactions (model C) ............... 153

Figure 5-29: Through-thickness strain evolution with the temperature at the

laminate mid-thickness for cure cycle 1 in the case of no bonding (model A)

and perfect bonding (model B) .................................................................. 154

Figure 5-30: Through-thickness strain evolution with temperature at the laminate

mid-thickness for cure cycle 1 using contact interactions (model C) ........ 154

Figure 5-31: Comparison of the in-plane strain evolution at the laminate mid-

thickness for cure cycle 1 obtained experimentally and numerically in the

case of no bonding (model A) and perfect bonding (model B) and frictional

contact (model C)....................................................................................... 156

Figure 5-32: Comparison of the in-plane strain evolution with temperature during

the cool down at the laminate mid-thickness for cure cycle 1 obtained

experimentally and numerically in the case of no bonding (model A), perfect

bonding (model B) and frictional contact (model C) ................................. 157


2 in the case of no bounding (model A) and perfect bounding (model B) . 158


2 using contact interactions (model C) ...................................................... 159


cure cycle 2 in the case of no bounding (model A) and perfect bounding

(model B) ................................................................................................... 159


cure cycle 2 using contact interactions (model C) ..................................... 160

Figure 5-37: In-plane strain evolution with temperature at the laminate mid-

thickness for cure cycle 2 in the case of no bounding (model A) and perfect

bounding (model B) ................................................................................... 161

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thickness for cure cycle 2 using contact interactions (model C) ............... 161


laminate mid-thickness for cure cycle 2 in the case of no bounding (model

A) and perfect bounding (model B)............................................................ 162


mid-thickness for cure cycle 2 using contact interactions (model C) ........ 162


thickness for cure cycle 2 obtained experimentally and numerically in the

case of no bonding (model A) and perfect bonding (model B) and frictional

contact (model C)....................................................................................... 164




bonding (model B) and frictional contact (model C) ................................. 165

Figure 6-1: Finite element models and boundary conditions: a) RTM finite

element mesh, b) close-up of the laminate mesh, c) schematic position of the

analyzed elements A and B ....................................................................... 169

Figure 6-2: Predicted temperatures at point A at different locations through the

composite thickness ................................................................................... 172

Figure 6-3: Predicted degree-of-cure at point A at different locations through the

composite thickness ................................................................................... 173

Figure 6-4: Temperature, glass transition temperature and degree-of-cure

evolutions for the RTM process at point A at the mid-thickness of the

composite ................................................................................................... 173

Figure 6-5: Radial strain evolution of the [0º]8 laminate at the interfaces for the

RTM process with a steel mandrel at position A....................................... 175



Figure 6-7: Radial strain evolution of the [+30/-30/-30/+30]s laminate at the

interfaces for the RTM process with a steel mandrel at position A .......... 176

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Figure 6-10: Radial stress evolution of the [0º]8 laminate at the interfaces for the




Figure 6-12: Radial stress evolution of the [+30/-30/-30/+30]s laminate at the






Figure 6-15: Schematic representation of the composite debonding, depending of

the material orientation .............................................................................. 182

Figure 6-16: Evolution of the contact pressure at position A and B for the ....... 183


RTM process with an aluminum mandrel at position A ............................ 184


RTM process with an aluminum mandrel at position A ............................ 184


interfaces for the RTM process with an aluminum mandrel at position A 185





Figure 6-22: Schematic representation of the deformations occurring after the

stresses released a) spring-in, b) warpage ................................................. 187

Figure 6-23: Effect of the resin shrinkage and the laminate layup on the spring-in

value at the end face .................................................................................. 192

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Figure 6-24: Effect of the laminate layup and the mandrel material on the spring-

in value at the end face .............................................................................. 193

Figure A-1: Dynamic test reproducibility at 1ºC/min and 2ºC/min temperature

ramp ........................................................................................................... 211

Figure A-2: Isothermal test reproducibility at 160ºC, 170ºC, 180ºC and 190ºC 212

Figure A-3: Strain sweep test performed at 1Hz frequency in oscillatory mode 213

Figure A-4: Time sweep performed at 15% strain and 1Hz in oscillatory mode 213

Figure A-5: Viscosity tests at 170ºC at 15% strain and 1Hz in oscillatory mode

................................................................................................................... 214


................................................................................................................... 214


................................................................................................................... 215

Figure A-8: Dynamic viscosity tests for a temperature ramp of 1ºC/min at 15%

strain and 1Hz in oscillatory mode ............................................................ 215





Figure A-11: Glass transition temperature measurement process. The arrows

correspond to one of the three glass transition temperature indicators [155]

................................................................................................................... 218

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List of Tables

Table 2-1: Studies on process-induced stresses and deformations for the RTM

process ......................................................................................................... 50

Table 3-1: Cure kinetic model constants............................................................... 59

Table 3-2: Viscosity model constants ................................................................... 64

Table 3-3: DiBenedetto model constants .............................................................. 65

Table 3-4: Curve fitting constants for the shrinkage model obtained by the

modified rheology method (Eq. 3-10) and R2 values for isothermal

experiments .................................................................................................. 73

Table 3-5: Bilinear curve fitting constants for the shrinkage model obtained by the

gravimetric method (Eq. 3-11) .................................................................... 77

Table 3-6: Coefficient of thermal expansion model constants ............................. 84

Table 3-7: Parameters values of the elastic modulus model ................................. 88

Table 4-1: Types of reinforcement and their fibre volume fractions .................... 92

Table 4-2: Carbon fibre and epoxy resin thermomechanical properties ............... 93

Table 4-3: Measured dimensions of a 5-harness satin unit cell ............................ 96

Table 4-4: Nominal ply thickness as a function of the fibre volume fraction ...... 97

Table 4-5: Dimensions and characteristics of the preliminary and final 5-harness

satin unit cell ................................................................................................ 98

Table 4-6: Comparison of the numerical and analytical values obtained for the

nine engineering constants and the coefficients of thermal expansion of the

unidirectional unit cell ............................................................................... 105

Table 4-7: Engineering constants and coefficients of thermal expansion obtained

for the crossply unit cell for different fibre volume fractions ................... 107


for the 5-harness satin unit cell for different fibre volume fractions ......... 108

Table 4-9: Experimental values of the coefficients of thermal direction obtained

by TMA for a 5-Harness satin unit cell with Vf = 59.4% .......................... 115

Table 4-10: Composite shrinkage coefficients for the 5-harness satin unit cell at

62%, 55% and 50% fibre volume fractions ............................................... 119

-xxv-

Table 5-1: Coefficient of thermal expansion measured at the post cure ............. 138

Table 5-2: Maximum shear stress for the two cure cycle ................................... 140

Table 5-3: Material properties used as input for the FE models ......................... 143

Table 5-4: Numerical curve gradients obtained with the different models for the

in-plane and through-thickness strains for the cure cycle 1 ...................... 155

Table 5-5: Comparison of the experimental and predicted curve gradients

obtained with the different models for the in-plane strains ....................... 157


in-plane and through-thickness strains during the cure cycle 2................. 163


obtained with the different models for the in-plane strains ....................... 165

Table 6-1: Material properties used as input for the FE models ......................... 170

Table 6-2: Coefficients of thermal expansion of the laminates .......................... 182

Table 6-3: Process-induced dimensional changes for the different laminate layups

................................................................................................................... 188

Table 6-4: Composite cure shrinkage coefficients in the longitudinal, hoop and

radial directions ......................................................................................... 189

Table 6-5: Analytical spring-in values for the different laminate layups ........... 190

Table A-1: Pre-cured plaque information ........................................................... 217

Table A-2: Degree-of-cure evolution for samples used for the glass transition

temperature measurements ........................................................................ 219

Table A-3: Degree-of-cure evolution for samples used for the tensile modulus

measurements ............................................................................................ 219

-xxvi-

List of Symbols

Latin Symbols

A Area; constant

Fibre areal weight

a Shift factor; constant

B Constant

b Constant

C Stiffness; constant

Cp Specific heat

CTE Coefficient of thermal

expansion

E Elastic modulus; edge node;

constant

Ea Activation energy

Eν Viscous activation energy

Ek Kinetic activation energy

F Face nodes

FN Normal force

G Shear modulus

H Heat flow

HT Total heat of reaction

h Heat transfer coefficient;

parallel plates gap; height

K Bulk modulus; FBG

sensitivity; constant

KT Effective plane strain bulk

modulus

Preform permeability tensor

k Arrhenius constants

kk Rheology constant

kij Thermal conductivity tensor

L Length

l Thickness; length

m Reaction order; mass;

constant

N Corner nodes

n Reaction order; number of

plies; effective refractive index

P Pressure

Generated heat

R Universal gas constant

RF Reaction force

r Radius

S Compliance

T Temperature; transformation

matrix; constant

Tg Glass transition temperature

T* Difference between the

instantaneous cure temperature and

the glass transition temperature

t Time; thickness

u Displacement

V Volume

Vf Fibre volume fraction

Darcy velocity vector

Resin velocity vector

w Width; warpage

YVf Yarn fibre volume fraction

-xxvii-

Greek symbols

Λ Period

Ф Fibre bed porosity

α Degree-of-cure

Normalized degree-of-cure

ε Strain, shrinkage

η Viscosity

θ Angle

Constant

λ Fitting parameter

λB Bragg wavelength

µ Dynamic viscosity;

coefficient of friction

ν Poisson’s ratio

ρ Density

σ Stress

Fibre bed effective stress

τ Shear stress

Composite shrinkage

coefficient

Subscrits:

agp After gel point

app Applied

B Grating

c Composite; cure; critical

crit Critic

f Fibre; final

fl Fluid

gel Gelation

glass Glassy state

H Host material

i i-direction; initial; inflection

j j-direction

L Longitudinal; Linear

l In-plane

M Mechanical

max Maximum

q Quenched

RT room temperature

r Resin; radial

ref Reference

S Shrinkage

s Solid; surface

T Temperature

t Transverse

th Thermal

tot Total

ult Ultimate

V volumetric

α Degree-of-cure

ε Strain

θ Hoop direction

0 Initial; at 0K

Superscript

S Shrinkage

0 Uncured

∞ Fully cured

-1-

CHAPTER 1 Introduction

1.1 Introduction

The development of preimpregnated reinforcements (prepregs) and autoclave

moulding have opened doors to high performance composite structures. They

enable the manufacturing of composite parts with high mechanical properties,

high fibre volume fraction (up to 70%) and low void content. However, with the

autoclave process, the material and equipment costs remain very high. Over the

last decade, the composite industry has aimed to produce high quality parts at low

cost and reduced time. Therefore, out-of-autoclave processes (OOAP) have been

increasingly considered to manufacture high performance composite structures as

an alternative to the well established autoclave process [1]. As shown in Figure

1-1, most of the OOAP allow the production of equally or more complex

composite parts than those manufactured by autoclave, with a higher production

rate.

Figure 1-1: Composite manufacturing processes as a function of production rate

and part complexity [2]

-2-

Among them, the use of Resin Transfer Moulding (RTM) to manufacture

composite parts for aerospace applications has significantly increased in recent

years. As part of the Liquid Composite Moulding (LCM) process family, RTM

was first developed in the 1950’s by the US Navy to produce a 28-ft long boat in

fibre glass/polyester. After many years dedicated to marine applications, it is now

widely used in diverse industries such as automotive, marine, transportation and

aerospace [3, 4].

This closed mould process presents many advantages over the autoclave process

[5, 6]:

The material and equipment costs are low (30-50% of the autoclave

process cost).

It enables the production of large and complex composite structures with

short cure cycles (approximately 50% of the autoclave process time) and

high consistency.

It allows the use of a wide variety of resin systems and reinforcements.

Composite parts manufactured by RTM typically have a good surface

finish on all sides while maintaining tight geometrical tolerances.

Mechanical properties comparable to autoclave processed parts can be

achieved with fibre volume fraction up to 60%

As it is a closed mould process, the emission of volatiles remains low.

The RTM process consists of five main steps (Figure 1-2). In the first step or

preforming (1), dry reinforcements are assembled in a preform whose shape is

close to the desired part geometry. Then the preform is placed into the mould and

compacted when the mould is closed (2). The mould is afterwards pre-heated to

the cure temperature (3). Once the required temperature is reached, the resin is

injected into the mould cavity through the injection port, impregnating the

preform. The excess resin flows outside the mould through the vent port (4). The

heat of the mould activates the polymerization to cure the resin. Once the resin is

fully cured, the part is removed from the mould (5).

-3-

Four main physical and chemical phenomena are involved during the RTM

process: heat transfer, flow and compaction, cure and residual stresses

development. As shown in Figure 1-3, these phenomena involve several key

material properties and their interaction affects the final properties of the

composite structure.

Figure 1-2: RTM process

Figure 1-3 RTM phenomena interactions

The RTM process produces parts with high consistency which is an advantage for

high production rate applications. However, at every step of the process, several

phenomena can affect the part quality and dimensions [5]. During the preforming

-4-

stage and compaction, the preform manipulation and deformation, when the

mould is closed, can cause: fibre displacements, changes in fibre orientation and

non-uniform fibre volume fraction distribution. Then fibre motions, porosity and

dry spot formation can occur during the injection phase and mould filling. Finally,

residual stresses develop during the curing stage leading to shape distortions after

demoulding and sometimes leading to the formation of micro-cracks or

delaminations.

In order to predict such phenomena and defects, many studies on RTM

simulations have been carried out. In a recent review on RTM modelling, the

RTM simulation approaches were divided into two main categories: the

simulation of the mould filling stage and the simulation of the process cycle [7].

Simulations of the mould filling stage have been extensively investigated. These

simulations determine the flow front location at any time and the filling time as a

function of the part geometry, the resin and preform properties, and the inlet/vent

positions. The studies typically investigate the following aspects [8-23]:

The prediction of the flow front location, the fibre impregnation and the

void content.

The prediction of the mould filling time.

The prediction of the pressure, temperature and degree-of-cure distribution

in the composite during the mould filling.

The optimization of the process parameters such as the injection pressure,

the resin flow rate, the mould temperature, the inlet and vent positions.

The first simulations only considered isothermal conditions [8-15] and were later

extended to non-isothermal conditions [16-20] in order to take into account the

resin cure kinetics and the heat transfer between the resin and the mould. These

simulations can be used as a useful tool for the design and optimization of the

RTM mould.

On the other hand, fewer studies have been performed on the simulations of the

entire RTM process cycle. These simulations allow the prediction of the evolution

-5-

of the degree-of-cure and the development of the residual stresses and eventual

shape distortions during the cure cycle with [16, 17] and without considering the

mould filling stage [24-26]. The different phenomena and interactions occurring

during the process (Figure 1-3), as well as the evolution of the composite

constituent material properties have to be taken into account simultaneously in

order to be realistic and accurate.

1.2 Motivations

For aerospace applications, dimensional stability is one of the major issues as

tight tolerances are required. While highly distorted parts are rejected entirely,

smaller distortions lead to unwanted stresses as the part is forced to fit the

assembly geometry. One decade ago, most of the knowledge in composite

manufacturing was based on rule-of-thumb and experience. When a part presented

some distortions, the tool geometry was modified so that the composite part met

the shape requirements. This approach worked well for simple and similar

geometries. However for new and complex parts, such a process took several

iterations, increasing production time and cost. Nowadays, both process

experience and modelling analysis are employed in industry to predict the strength

and failure properties of complex composite parts before the actual part

manufacturing, leading to significant reduction in time and cost to produce

components. While design and stress analyses are now well established in the

aerospace industry, process modelling is proving to be also attractive, especially

for well known and extensively employed process, such as autoclave. However,

this procedure is not as developed and common for out-of-autoclave processes.

In order to predict the final geometry and final properties of a new or complex

composite structure, one has to simulate the entire cure cycle and take into

account both intrinsic and extrinsic mechanisms that can influence the structure

properties. Intrinsic refers to material and part geometry related mechanisms. The

property differences between the polymeric matrix and the reinforcement as well

-6-

as the property differences in the longitudinal, transverse and through-thickness

directions have a significant influence on the development of residual stresses. In

addition, the resin change from a liquid to a solid, as the cure progresses, leads to

significant variations of its constitutive properties such as the degree-of-cure, the

volumetric changes and the elastic modulus. The evolution of these properties

affects as well the residual stresses and deformations. On the other hand, extrinsic

describes the tool and process related mechanisms, such as the tool-part

interaction or the cure cycle (time, temperature, pressure) that can have an effect

on the final properties of the composite structure.

Hence, it is crucial to clearly understand the different phenomena, involved in

composite manufacturing, leading to process-induced stresses and part shape

change. Development of accurate material constitutive models, process modelling

and a comprehensive understanding of both intrinsic and extrinsic mechanisms

are key elements to achieve this purpose.

1.3 Project objectives and thesis outline

The main research objective of this thesis is to investigate the different parameters

leading to process-induced deformations, including thickness variations and part

distortions, of woven composite parts manufactured by RTM. Once the different

mechanisms are well understood, process modelling can be applied to predict the

process-induced deformations. To achieve this goal, the present research is

organized into the following chapters.

Chapter 2 presents a detailed literature review on the material behaviour during

the cure cycle and the process-induced stresses and dimensional stability in

composite manufacturing. Based on this knowledge, the specific objectives of the

thesis are formulated.

-7-

Chapter 3 and Chapter 4 are related to the material characterization. Chapter 3

describes the methodological approach developed to characterize the processing

properties of thermoset resins. The methodology was applied to define the

thermal, chemorheological and thermomechanical properties of a particular RTM

one-part epoxy. Chapter 4 analyses the influence of the fibre architecture

(unidirectional, crossply, 5-harness satin weave) on the composite

thermomechanical properties.

Chapter 5 examines the tool-part interaction mechanisms experimentally and

numerically for panels manufactured by RTM.

Chapter 6 presents a case study on dimensional stability including the diverse

factors studied in the previous chapters.

Finally, the contributions of this study and recommendations for future studies are

presented in Chapter 7.

-8-

CHAPTER 2 Literature Review and Objectives

This chapter contains a comprehensive literature review on residual stresses and

deformation induced during the manufacturing process of composite structures.

First an overall description of the evolution of the material behaviour during the

cure is presented. The resin properties having an effect on the strain and stress

development are described in detail. Some investigations of the influence of the

fibre architecture are presented as well. Then the different sources of process-

induced stresses and deformations are highlighted. From the literature review, the

specific objectives of this thesis are stated.

2.1 Material behaviour during the cure

2.1.1 Resin behaviour

During the processing of composite material, the thermoset resin evolves from a

low molecular weight liquid material to a crosslinked macromolecular solid

structure. In its liquid state, the thermoset resin consists of monomers. Then as the

polymerization is initiated by a catalyst or heat for example, the monomer

molecules react, crosslink and grow longer. As the crosslinking process

progresses, the long polymer chains join up to form a three-dimensional network.

At that moment, the resin evolves in a gel/rubbery state where the polymer chains

remain mobile. Finally, when most of the crosslinks have formed and the three-

dimensional network is fully established, the resin is in a solid/glassy state and the

motion of the polymer chains is very restrained. The crosslinking process is

quantified by the degree of conversion or degree-of-cure. This variable varies

from 0 to 1, 0 corresponding to the uncured state with no crosslink and 1

representing the fully cured state where the three-dimensional network is totally

developed.

-9-

Figure 2-1 shows the evolution of the resin properties for a typical cure cycle for

the RTM process. As the cure progresses, the degree-of-cure of the resin

increases, leading to an increase of the glass transition temperature and the resin

viscosity. From Figure 2-1-a, the resin undergoes its liquid-rubbery

transformation when the viscosity reaches an infinite value. This gelation occurs

after 70 minutes at 180ºC, at a degree-of cure of 0.7. After that point, as shown in

Figure 2-1-b, the resin elastic modulus starts to develop and the resin can sustain

strains and stresses without flowing. The resin also begins to shrink, due to the

polymer network formation. However, its behaviour remains highly viscoelastic,

and the generated strains and stresses can be relaxed to some extent. As the

polymerization advances more, the glass transition temperature, Tg, passes the

curing temperature and the vitrification happens 50 minutes later at a degree-of-

cure of 0.93. A significant increase in the resin elastic modulus can be observed at

the vitrification. At that stage, the resin is in its glassy state, and behaves like an

elastic solid. The generated stresses cannot be relaxed any more. The gel point

and the vitrification time depend of the type of resin and the cure cycle used; the

resin may go through the vitrification during the isotherm or at the cool down.

-10-

Figure 2-1: State transition and property evolution of the CYCOM 890RTM

epoxy resin during a typical cure cycle. a) Degree-of-cure, viscosity and glass

transition temperature, b) Relative volume variation and elastic modulus

-11-

Also, as seen in Figure 2-1-b, significant changes in volume take place as the cure

progresses. The different mechanisms leading to volumetric change are illustrated

in Figure 2-2 for a cube of resin with an initial volume of 1 cm3:

Step a-b: as the temperature increases to reach the curing temperature of 180ºC,

the volume of the resin increases due to thermal expansion.

Step b-c: at the isothermal curing temperature, the volume of the resin decreases

due to the chemical shrinkage resulting from the formation of the chemical

network.

Step c-e: during the temperature cool-down, the volume of the resin decreases due

to the thermal contraction. The dashed line represents the path of a resin passing

the vitrification transition during the cool down. The resin coefficient of thermal

expansion (CTE) is much higher in its rubbery state (above Tg, step c-d’) than in

its glassy state (below Tg, step d’-e’).

Figure 2-2: Volumetric change of the CYCOM 890RTM epoxy resin during a

typical cure cycle

Hence, a comprehensive understanding of the resin behaviour during the cure, and

an accurate characterization of the evolution of its properties (cure kinetics,

-12-

viscosity, glass transition temperature, volumetric changes, elastic modulus) is

essential to understand the development of residual stresses and deformations.

The next sub-sections present the main models found in the literature to describe

these properties.

2.1.1.1 Cure kinetics

A variety of cure kinetic models have been proposed to describe the cure

behaviour of several types of resin. They can be divided into two categories:

mechanistic models and phenomenological models.

Mechanistic models are based on the knowledge of how the chemical molecules

react with one another during the cure. Due to the complexity of the

polymerization reaction, such models can be very difficult to obtain. Also they

require the details of the resin chemical formula which is not always available

from the manufacturer. Phenomenological models describe the cure reaction

ignoring the details of the chemical reaction. Generally, phenomenological

models are preferred to describe the curing behaviour of thermoset resins.

Phenomenological cure kinetics models are usually determined using a

Differential Scanning Calorimeter (DSC) under dynamic and isothermal

conditions. The dynamic scans measure the total heat of reaction released during

the cure whereas isothermal scans are used to monitor the heat flow during a

series of isothermal cures. The measured heat generated by the resin is then

converted into cure rate based on the assumption that the rate of reaction, ,

is proportional to the rate of the heat flow, :

Eq. 2-1

where HT is the total exothermic heat of reaction. The degree-of-cure of the resin

(α) can be obtained by integrating the area under the curve of cure rate versus time

as follows:

-13-

Eq. 2-2

Then resin cure kinetics models relate the rate of cure as a function of time,

temperature and degree-of-cure.

The simplest cure kinetic model is expressed by an n-order equation [27]:

Eq. 2-3

where n is the reaction order and k is the rate constant following an Arrhenius

temperature dependency:

Eq. 2-4

where EA is the activation energy and R is the gas constant.

Nevertheless, this model is too simple to realistically describe the various

reactions taking place during the cure and the transitions (gelation, vitrification)

the material undergoes.

Kamal and Sourour [28, 29] developed the following autocatalytic cure kinetic

model for the epoxy and unsaturated polyester resin systems:

Eq. 2-5

where k1 and k2 are the rate constants following the Arrhenius relationship, and n

and m are catalytic constants.

When the thermoset resin goes through the glass transition, the reaction slows

down rapidly and changes to a diffusion controlled mode. As a consequence, the

final degree-of-cure and the rate of cure will be lower than those predicted. In

order to take into account the phenomenon of vitrification, Gonzalez-Romero and

Castillas [30] introduced a new parameter αmax in the equation, which corresponds

to the maximum degree-of-cure the resin can reach due to the diffusion:

-14-

Eq. 2-6

An alternative way to model the switch from a kinetics-dominated to a diffusion-

dominated reaction is to add a diffusion factor, f(α,T), to the cure kinetics

equation:

Eq. 2-7

Khanna and Chanda [31] defined a diffusion factor as follows:

Eq. 2-8

where αc is the critical degree-of-cure when the reaction change to diffusion

control, and C is a constant.

Cole et al. [32] extended this diffusion factor by expressing the critical degree-of-

cure as a function of the temperature:

Eq. 2-9

where αC0 is the critical degree-of-cure at T=0K and αCT is a constant taking into

account the increase in critical degree-of-cure with the temperature.

Hubert et al. [33] used this diffusion factor with the cure kinetic model from Lee

et al. [34]:

Eq. 2-10

Using this model, they demonstrated much better prediction of the cure behaviour

after the vitrification of epoxy resin than achieved using regular models.

2.1.1.2 Rheological behaviour

The resin rheological behaviour describes the evolution of the resin viscosity as a

function of many variables such as the temperature, the resin cure, the shear rate

or the filler properties. The viscosity is influenced by the thermal effect and the

cure effect in opposite way. First, the viscosity decreases as the temperature

-15-

increases due to the thermal effect, as shown in Figure 2-1-a. Then the viscosity

reaches a minimum value. In liquid injection processes, the resin is usually

injected in the mould at this minimum viscosity point in order to allow the resin to

flow and better impregnate the reinforcement. As the temperature or time

increases, the curing reaction starts and the viscosity increases due to the network

formation to finally reach an infinite value at the gel point. The viscosity is

usually measured using a rheometer with different types of geometry, such as

parallel plate, cone and plate, or rotational cylinder.

Similar to the cure kinetic, many models have been developed to capture the cure

effect on the viscosity of thermoset resins. A simple empirical isothermal model

was first developed by Kamal and Sourour [28] for epoxy resins:

Eq. 2-11

where η is the viscosity, η0 is the initial viscosity and is a constant. However,

this model doesn’t take into account the gel point.

Castro and Macosko developed a model expressing the evolution of the viscosity

as a function of the degree-of-cure and the gel point [35]:

Eq. 2-12

where α is the degree-of-cure, αgel is the degree-of-cure at gel point, A and B are

constants.

Kamal developed also a viscosity model based on the Arrhenius relation for

epoxy resins [29]:

Eq. 2-13

where n is the reaction order, Ev is the viscous activation energy, kk is a rate

constant and Ek is the kinetic activation energy.

-16-

2.1.1.3 Glass transition temperature

The glass transition temperature (Tg) significantly affects the resin mechanical

properties as it changes from its rubbery to its glassy state. One of the most

common techniques to characterize Tg uses a modulated DSC (MDSC), where Tg

is identified by a step change in the specific heat [36, 37]. Thermo Mechanical

Analysis (TMA) is another widely used method of measuring the Tg, as a

significant change in the coefficient of thermal expansion is noticed when the

resin goes through the glass transition (Figure 2-2).

The DiBenedetto equation is the most commonly used relationship when

modelling the evolution of Tg with the degree-of-cure for thermoset resins [37-

42]. The relationship is expressed as follows:

Eq. 2-14

where Tg is the glass transition temperature, and are the glass transition

temperatures of uncured and fully cured resin respectively, is the degree-of-cure

and is a constant used as a fitting parameter valued between 0 and 1. Other

researchers fit empirical models to express the variation of Tg with the degree-of-

cure [37].

2.1.1.4 Volumetric changes

As described in Figure 2-2, volumetric changes during the cure can be categorized

as thermal and chemical contributions. The thermal contribution describes the

expansion and contraction due to change in temperature. The chemical

contribution represents the contraction due to the cure shrinkage.

Coefficient of Thermal Expansion

The coefficients of thermal expansion are usually measured by Thermo

Mechanical Analyzer (TMA) [43]. This method allows the measurement of the

CTE above and below Tg. In order to capture the evolution of the resin thermal

-17-

expansion during the cure, Hill et al. [44] expressed first the volume variation of

the resin as a function of the temperature and/or the degree-of-cure:

Eq. 2-15

Eq. 2-16

where CTEr,gel and CTEr,cured are the coefficients of thermal expansion of the

gelled and fully cured resin respectively, and a0 and b0 are linear fit with

temperature.

Ruiz and Trochu [43] expressed also the resin coefficient of thermal expansion as

a function of the temperature and the degree-of-cure in the following manner:

Eq. 2-17

where CTEr,agp is the resin coefficient of thermal expansion after the gel point and

is normalized degree-of-cure given by the following equation:

Eq. 2-18

where αagp is the degree-of-cure after the gel point and αult is the ultimate degree-

of-cure.

Shrinkage

The volumetric cure shrinkage describes the contraction of the resin during the

polymerization, due to the network formation. It is the result of the change from

Van der Waals links to smaller but stronger covalent links between the molecules

as the cure progresses. In the following, volumetric cure shrinkage will be

referred as shrinkage for purposes of brevity.

Measurement of the shrinkage development along the entire curing process is

challenging, as the resin changes from the liquid to the rubbery state and finally

the glassy state. The standard ASTM D2566-79 method to measure resin

shrinkage is based on the resin volume variation before and after the cure without

taking into account the change of resin coefficient of thermal expansion from the

-18-

rubbery to the glassy state [45]. This limitation significantly underestimates the

magnitude of the shrinkage as shown in Figure 2-2. Water or mercury

dilatometers are the most common instruments used to measure shrinkage based

on volume dilatometry [44, 46-48]. With a water-based dilatometer, results may

be influenced by water absorption of the resin and temperature variation [48].

Pycnometers are also employed to measure the volumetric chemical change in a

dry state [49]. However, this method allows only the measurement of the final

shrinkage and not its development during the cure. Non-volumetric dilatometry

methods usually measure the linear shrinkage and rely on various assumptions to

calculate the volumetric shrinkage. The non-volumetric methods regroup various

methods, such as the shadow Moire method [50], Dynamic Mechanical Analysis

(DMA), Thermo Mechanical Analysis (TMA) [51, 52], online monitoring using

LVDT transducers and optical sensors embedded in the resin [53, 54], modified

rheology method [55] or gravimetric method [56].

From these experiments, empirical models have been developed in order to

predict the amount of shrinkage as a function of the degree-of-cure, the radical

concentration or the curing temperature. Linear relationships between the

shrinkage and the degree-of-cure were derived for both polyester and epoxy resin

systems and the total shrinkage was found to be independent of the curing

temperature [44, 55-57].

2.1.1.5 Resin Elastic modulus

Elastic modulus models are important to describe the evolution of the resin

mechanical behaviour during the cure, as the material goes through its liquidy-

rubbery and rubbery-glassy transitions. Dynamic Mechanical Analyzer (DMA) is

a common technique to measure the evolution of the elastic modulus with the

degree-of-cure. Different loading fixtures such as single or double cantilever and

three-point bending can be used on non-cured or pre-cured resin sample [57, 58].

Elastic and viscoelastic models are usually employed to capture this behaviour.

-19-

Elastic models

Despite the known viscoelastic behaviour of the resin throughout a majority of the

cure process, elastic models can predict, most of the time, the process-induced

stresses realistically. According the Svanberg and Holmberg [41], glassy-rubbery

transition are well described by elastic models whereas incremental elastic model

better captures rubbery-glassy transition. Using an incremental approach, Bogetti

and Gillespie [57], Golestanian and El-Gizawy [24], Huang et al. [59] and

Johnston et al. [60] used cure-dependent elastic models to compute resin elastic

modulus during the entire cure. A linear correlation between the resin modulus

and the degree-of-cure was reported in [24, 57, 59]:

Eq. 2-19

where and are the uncured and fully cured modulus of the resin

respectively and α is the degree-of-cure.

In order to capture more accurately the rubbery-glassy transition, Johnston et al.

[60] and Curiel and Fernlund [58] relate the resin modulus with the variable T*,

equal to the difference between the curing temperature and the instantaneous glass

transition temperature, with the following formulation [60]:

Eq. 2-20

where and have the same definition as before, T1 and T2 are constants

representing the onset and the completion of the glass transition. In that case, the

variable T* is expressed as follows:

Eq. 2-21

where is the glass transition temperature of the uncured resin, is a

constant and α is the degree-of-cure.

-20-

Similarly, Ruiz and Trochu [43] take into account the resin elastic modulus

dependence with the degree-of-cure and glass transition temperature using two

functions Fr(α) and Wr(Tg) as follow:

Eq. 2-22

Eq. 2-23

Eq. 2-24

where the subscripts r, c and agp stand for resin, composite and after gel point,

is the normalized degree-of-cure defined in Eq. 2-18, c, d, e, h are some constants

and is the normalized temperature expressed in the following manner:

Eq. 2-25

Where Tg is the glass transition temperature and Tref is a reference temperature.

Viscoelastic models

Viscoelastic models are more realistic than elastic models, as they take into

account the stress relaxation occurring in the resin rubbery state. Wiersma et al.

[61] used both elastic and viscoelastic modulus models to predict the spring-in of

L-shape composite parts and observed closer agreement with the experimental

results using the viscoelastic model. However, the viscoelastic models are more

difficult to develop. Extensive material characterization is needed to determine the

different model variables. Also, for simulation purpose, they lead to long

computational time and heavy computational resources.

Generally, the variation of the modulus or compliance versus time or frequency is

obtained from a series of experiments at specific temperatures and degree-of-cure.

Then each experiment at a specific temperature and degree-of-cure can be shifted

from a factor a, to form the master curve. This shift factor accounts for the

temperature and/or degree-of-cure dependence of the relaxation time. Figure 2-3

describes this time-temperature principle of superposition to get the compliance

master cure.

-21-

Figure 2-3: Example of construction of the compliance master curve using the

principle of time-temperature superposition [62]

William, Landel and Ferry [63] defined first a temperature shift factor aT , as

follows:

Eq. 2-26

where C1 and C2 are material dependent constants, and Tref is the reference

temperature.

This model was used in similar or modified forms in many studies [39, 62, 64-66].

Similarly, Simon et al. [39] developed a conversion shift factor to describe the

dependency of the relaxation time with the degree-of-cure:

Eq. 2-27

-22-

where C and are constants, is the glass transition temperature as a

function of the degree-of-cure and is the glass transition temperature at

the reference degree-of-cure.

2.1.2 Composite thermomechanical properties

Contrary to the resin, the fibres do not react during the cure and their properties

remain constant. Knowing the properties of the composite constituents, i.e. resin

and fibre, micromechanic analytical relations can be used to determine the elastic

moduli and coefficients of thermal expansion of a unidirectional lamina.

For the determination of the elastic properties, the simplest approach used is the

strength of materials approach or rule of mixtures [67]. For this, the following

assumptions are made:

Perfect bonding between the fibres and the matrix.

The fibres are continuous and parallel.

The fibre and the matrix are assumed to be linear elastic materials and

follow Hookes’s law.

The fibres have a uniform strength.

The composite is free of voids.

Considering the representative volume element (RVE) of a fibre surrounded by a

matrix presented in Figure 2-4, and subjected to longitudinal, transverse or in-

plane shear loads, the composite elastic constants can be expressed by the

following equations in the ply orientation.

Figure 2-4: Loading on the representative volume element to determine the elastic

constants: a) longitudinal load, b) transverse load, c) in-plane shear load

-23-

The longitudinal Young’s modulus:

Eq. 2-28

The transverse Young’s modulus:

Eq. 2-29

The major Poisson’s ratio:

Eq. 2-30

The in-plane shear modulus:

Eq. 2-31

where the subscripts f and r stand for the fibre and resin properties respectively,

Vf is the fibre volume fraction, E is the elastic modulus, ν is the Poisson’s ratio

and G is the shear modulus.

With this approach, the predicted values of the longitudinal Young’s modulus E1

and the major Poisson’s ratio ν12 agree well with the experimental data. However,

the predicted values of the transverse Young’s modulus E2 and the in-plane shear

modulus G12 are generally lower than the experimental data [67].

In order to obtain better prediction in the transverse direction, Halphin and Tsai

[68] developed semi-empirical models taking into account the fibre geometry and

the packing geometry. Hashin and Rosen [69] and Whitney and Riley [70]

developed elastic constant relations based on the elastic approach and defining the

effective elastic modulus in terms of the strain energy. Bogettie and Gillespie [57]

and Johnston et al. [60] used this micromechanic elastic approach to compute the

evolution of the composite elastic constant during the cure cycle. In that case, the

elastic constants were expressed as follows:

The longitudinal Young’s modulus:

Eq. 2-32

-24-

The transverse Young’s modulus:

Eq. 2-33

The in-plane shear modulus:

Eq. 2-34

The transverse shear modulus:

Eq. 2-35

The major Poisson’s ratio:

Eq. 2-36

The transverse Poisson’s ratio:

Eq. 2-37

The effective plane strain bulk modulus:

Eq. 2-38

-25-

Figure 2-5: Comparison of experimental values of the transverse Young’s

modulus with the predicted values using the strength of materials approach, the

semi-empirical approach and the elastic approach as a function of the fibre

volume fraction: a) 0 <Vf <1, b) 0.45< Vf <0.75 [67]

-26-

Figure 2-6: Comparison of experimental values of the in-plane shear modulus

with the predicted values using the strength of materials approach, the semi-

empirical approach and the elastic approach as a function of the fibre volume

fraction: a) 0< Vf <1, b) 0.45< Vf <0.75 [67]

Figure 2-5 and Figure 2-6 compared the experimental values of the transverse

Young’s modulus and the in-plane shear modulus respectively with the predicted

values from the micromechanic approaches. The Halphin-Tsai semi-empirical and

the elastic approaches better capture the experimental data whereas, as mentioned

previously, the strength of materials approach predicts lower values.

-27-

Using the strength of materials approach, the composite coefficients of thermal

expansion can be also expressed as function of the properties of the resin and the

fibre in the ply orientation:

Eq. 2-39

Eq. 2-40

As the effect of the shrinkage is similar to a contraction, Eq. 2-39 and Eq. 2-40

can be similarly used to determine the longitudinal and transverse effective

shrinkage of the composite.

2.1.3 Fibre architecture behaviour

For a composite with unidirectional fibres, the laminate mechanical properties can

be predicted using the Classical laminate Theory (CLT). In the case of LCM

process, such as RTM, the use of woven textile reinforcements increased

significantly in the past decades. Woven reinforcements have higher drapability

and better impact resistance than unidirectional fibres that qualify them as good

candidates to manufacture complex structures. Woven fabrics are characterized by

a recurrent in-plane pattern of the interlaced region. Typically, the three main

configurations are plain, twill and satin weaves, as shown in Figure 2-7. In the

plain weave pattern, a warp yarn is interlaced over and under the weft yarns

(Figure 2-7-a), whereas in the twill weave motif, a warp yarn is woven over two

weft yarn and under one weft yarn (Figure 2-7-b). In the satin weave architecture,

the warp yarn is intertwined over ng consecutive weft yarn (ng>2) and under one

weft yarn (Figure 2-7-c). For the satin weave, the number of consecutive weft

yarns ng defined the name of the architecture as (ng + 1)-harness satin weave.

-28-

Figure 2-7: Main weave configurations. a) Plain weave, b) Twill weave and

c) 5-harness satin weave

Hence, to predict the thermomechanical properties of woven composites, more

parameters have to be taken into account. The fibre architecture geometry, the

fibre undulation or the resin distribution throughout the bundles can affect the

mechanical and failure properties of the composite.

Various analytical and numerical approaches have been carried out to investigate

the thermomechanical properties of 2D fabric reinforcements. Analytical models

are generally based on the Classical Laminate Theory. Ishikawa and Chou [71-75]

developed three analytic models to predict the stiffness and coefficient of thermal

expansion of woven fabric composites. The first model, called the mosaic model,

described the fabric as an assemblage of asymmetrical crossply laminates, as

shown in Figure 2-8-a. In that case, no fibre undulation was taken into account.

Therefore, the mosaic model gave good predictions for fabrics with few interlaced

regions, such as satin fabric. The second model, called the crimp model,

accounted for the fibre undulation and fibre continuity (Figure 2-8-b). It used

shape functions to describe the fibre undulation. The crimp model is more suitable

for plain weave composite. Finally the bridging model was developed for satin

woven fabrics in order to describe the properties difference between the straight

threads regions and the interlaced regions (Figure 2-8-c). The straight threads

-29-

region A, B, D, and E have higher in-plane stiffness than the interlaced region C,

and plays the role of bridge for the load transfer. However these models only

considered the undulation in one direction and restrict the two-dimensional (2D)

woven structure to one dimension.

Figure 2-8: Schematic view of the three analytical models for an 8-harness satin.

a) Mosaic model, b) Crimp model, c) Bridging model (adapted from [73])

Naik and Shembekar [76-78] and Naik and Ganesh [79-81] developed a 2D

woven fabric model to predict the elastic properties and the coefficient of thermal

expansion of plain weave reinforcements at the ply and laminate level. The fibre

architecture geometry in the ply, as well as the position of the different plies in the

laminate, with respect to each other, was considered. Their results demonstrated

that the elastic moduli were affected by the undulation length, the ply thickness,

the gap between two adjacent yarns and the laminate configuration. The elastic

-30-

moduli increased with an increase in the undulated length and a decrease in the

ply thickness. Shifts of plies in the laminate configuration gave better in-plane

elastic properties. Also, depending on the fibre architecture and the material

system, an optimum gap could be determined to improve the elastic properties of

the woven composite. The results obtained for the CTE of plain weave woven

laminates were compared to the properties of unidirectional and crossply

laminates. For the same fibre volume fraction, the CTE of the plain-weave

composite were higher than the unidirectional one. But it could be lower or higher

than the CTE of the crossply laminate depending of the fabric strand crimp.

Overall, the authors determined that in the case of plain weave woven fabric,

higher fibre volume fraction and lesser crimp gave a lower CTE and Poisson’s

ratio but higher Young’s and shear moduli. Their analytical results were then

confirmed experimentally [82]. In addition, Hahn and Pandey [83] used geometry

efficiency factors to develop a micromechanics model including the fibre

architecture parameters to predict the thermoelastic properties of plain weave

woven composite.

More recently, finite element analyses (FEA) were used to determine the

mechanical properties of woven composites. The advantage of FEA is that it

provides information on the internal strains, stresses and displacements generated

in the woven fabric. Generally, the analysis is reduced to the behaviour of the

smaller representative element or unit cell. Then periodic boundary conditions are

applied to the unit cell so that it represents the entire reinforcement. Glaessgen et

al. [84] developed a unit cell model to study the internal displacements, strains

and stresses in plain weave composite under axial load. To reduce the

computational time, the global/local finite element method was used in different

studies to model textile composite: a coarse mesh is used on the global structure

and a more refined mesh is applied on local region where rapid changes can occur

[85-87]. Dasgupta and Bhandarkar [88] investigated the influence of the fibre

volume fraction on thermomechanical properties of plain weave composite using

a 3D unit cell model. Their results showed that the stiffness increased with the

-31-

fibre volume fraction whereas the CTE and the Poisson’s ratio decreased. This is

in agreement with some experimental studies [82]. Lomov et al. also validated the

FEA unit cell approach using full-field strain measurement on carbon/epoxy

woven composites and glass/polypropylene woven composites [89]. Finally, the

unit cell representation of woven composite was also used in the analysis and

prediction of process-induced stresses and deformation [24, 25, 59]. For this last

purpose, Svanberg et al. used a “knock down factor” as an alternative method to

reduce the fibre longitudinal modulus and compensate for the fibre weave [26].

The design of the fabric unit cell can be facilitated using textile modelling

software such as WiseTex [90], developed by the Composite Material Group of

the Leuven University, or TexGen [91], developed by Textile Composite Research

group at the University of Nottingham. Knowing the yarn properties, the yarn

interlacing pattern and the yarn spacing within the unit cell, these softwares

determine the unit cell geometry and properties, such as the areal density, the

local fibre content and the fibre orientation. The unit cell geometry can also be

meshed and exported in traditional finite element software to compute the fabric

mechanical properties.

2.2 Sources of residual stresses and deformations

Residual stresses and deformations are one of the major concerns in composite

manufacturing. Residual stresses can lead to a reduction of the composite

structure performance such as strength and fatigue life, and can initiate cracks in

the matrix. As mentioned in CHAPTER 1 section 1.2, the assemblage of

composite structures with deformations can be problematic or impossible, leading

to the reject of the part. The sources of residual stresses and their effects on

composite structures have been widely investigated for over three decades.

Overall four main mechanisms have been identified [92]:

Thermal strains

Resin chemical shrinkage

Tool-part interaction

-32-

Temperature, degree-of-cure and fibre volume fraction gradient

Typically, three common shape variations can occur in a composite part due to

process-induced stresses:

Spring-in or spring-out (Figure 2-9-a), defined as variation of closed

angle, spring-in being a reduction of the initial angle, whereas spring-out

is an increase of the initial angle.

Warpage (Figure 2-9-b), defined as a bending of a flat laminate.

Laminate thickness variations

Figure 2-9 Shape variations due to process-induced stresses: a) spring-in

deformation, b) warpage deformation

In the next sections, the mechanisms leading to the shape distortions are discussed

in more detail.

2.2.1 Thermal strains

Thermal strains were the first studied and probably the most well understood

causes of residual stresses [64, 93-96]. Thermal strains describe the strains arising

due to the difference in thermal expansion at three scales: firstly, between the

matrix and the fibre at the constituent level, second between the longitudinal and

transversal direction at the ply level and finally, between the in-plane and out-of-

plane direction at the laminate level.

-33-

Polymeric matrices have usually higher thermal expansion than fibres (typical

CTE polymer = 50-100 x10-6

ºC-1

, typical CTE fibre = -1-15 x10-6

ºC-1

). This

difference in thermal expansion creates stresses at the microscale between the

matrix and the fibre with a variation of temperature. This micromechanical

stresses can affect the strength and failure of the composite structure, but should

not lead to significant distortions, as their effects remain small and local [92].

At the ply level, the CTE difference between the longitudinal and transverse

directions generates in-plane stresses and deformations in laminates. These

residual stresses and deformations can be predicted and avoided using the

Classical Laminate Theory. For example, using symmetric laminates can prevent

non-symmetric coupling, whereas balance lay-up or crossply laminates can

prevent shear-normal coupling. Finally antisymmetric laminates and crossply

laminates can prevent bending-twisting coupling.

Finally, at the laminate level, the thermal expansion difference between in-plane

direction, dominated by the fibres, and through-thickness direction, dominated by

the matrix, results in the change of curvature for angled laminates. This

phenomenon is also known as spring-in (Figure 2-9-a).

A simple analytical equation, developed by Radford, predicts the angle variation,

, as a function of the temperature variation, , and the in-plane and through-

thickness composite thermal expansion coefficients, and respectively

[97]:

Eq. 2-41

From this equation, it can be predicted that the higher the temperature variation

( is, the higher the spring-in value should be. However, it does not

take into account the difference of the coefficients of thermal expansion above

and below the glass transition temperature, which was shown to be significant in

section 2.1.1.4. Svanberg and Holmberg [98] and Ersoy et al. [99] demonstrated

that the spring-in could increase or decrease with ΔT, depending when the resin

goes through its glass transition. Figure 2-10 describes the paths the resin can take

-34-

while cooling down from the same curing temperature (Tcure). If the resin goes

through its glass transition and reaches its glassy state during the dwell, it will

follow the path A-B during the cool-down, with a glassy CTE. On the other hand,

if the resin does not go through its glass transition, it will still be in a rubbery state

by the end of the isotherm. The resin will then cool-down following the path A-C-

D. The glass transition happens at C, with a significant decrease in CTE. So, for

the same ΔT, the spring-in can be different.

Figure 2-10: Schematic explanation of the spring-in variation as a function of the

resin state, below or above Tg (adapted from [99])

2.2.2 Resin volumetric cure shrinkage

As explained previously, shrinkage is a contraction of the resin due to the

formation of the 3D crosslinked network. In the composite, its effect will be then

more significant in the matrix dominant direction (transverse direction at the ply

level and through-thickness direction at the laminate level). Thus, the shrinkage

difference between the longitudinal and through-thickness directions acts similar

to the thermal contraction (Section 2.2.1) on the residual stresses and

deformations and is a source of spring-in. Shrinkage also has a significant effect

-35-

on composite surface finish quality and can lead to surface defects such as ripples,

sink marks or fabric print through [100].

In order to take into account the effect of shrinkage in the prediction of the spring-

in angle, Radford [97] modified the previous developed analytic equation (Eq.

2-41) as follows:

Eq. 2-42

where ϕl and ϕt are the in-plane and through-thickness composite shrinkage

respectively.

Recently, Ersoy et al. adjusted Eq. 2-25 to take also into account the difference of

resin behaviour before and after the temperature of glass transition [99]:

Eq. 2-43

where and are the in-plane and through-thickness composite

thermal expansion coefficients in the rubbery state, and are the

in-plane and through-thickness composite thermal expansion coefficients in the

glassy state, Tg is the glass transition temperature, Tq is the quenched temperature

and TRT is the room temperature. As previously, ϕl and ϕt are the in-plane and

through-thickness composite shrinkage.

The consideration of shrinkage as a significant cause for residual stresses and

deformation was not always addressed and has evolved considerably in the past

few decades. At first, shrinkage was supposed to have a negligible effect on

residual stresses [42, 64, 93, 94, 96]. Researchers assumed that shrinkage

occurred while the resin was in its rubbery state, and therefore the arising

chemical strains were simply relaxed by the viscoelastic property of the resin in

that state. However, Lange.et al. [101] established that this was not true for all

-36-

resin systems. Using a bi-layer beam bending technique, they measured the built-

up of residual stresses for an epoxy and an acrylate. While the epoxy developed

stress only on cooling below Tg, the acrylate system generated stresses during the

cure above Tg. Many other researchers [41, 57, 97-99, 102-106] took into account

the chemical strains to predict the residual stresses and deformations, even when

the viscoelastic behaviour of the resin was taken into consideration [40, 61].

When taken into account, experimental and numerical studies determined that the

cure shrinkage increased the spring-in value [61, 99, 106].

2.2.3 Tool-part interaction

Tool-part interaction takes into account the effect of the mould on the laminate.

Figure 2-11 presents the tool-part interaction mechanism leading to shape

deformation. During the heat-up of the cure cycle, the mould stretches the

laminate (a), generating shear stresses at the interface between the mould and the

composite and through-thickness stress gradient in the laminate (b). These

interfacial stresses and through-thickness stress gradient generally lead to a

bending of the laminate away from the mould at the demoulding (c). This

particular bending of a flat panel is also known as warpage.

Figure 2-11: Process-induced warpage mechanism due to tool-part interaction

[107]

-37-

The common tool materials used in composite manufacturing are steel and

aluminum and carbon/epoxy. As both steel and aluminum have coefficients of

thermal expansion much higher than the composite, warpage is often observed at

the demoulding stage with these types of mould. On the contrary, composite

moulds create lower shear stresses as they have a low coefficient of thermal

expansion and their behaviour is similar to the part itself. However, composite

moulds are not as stiff and durable as metallic moulds and the part geometry

might not be as reliable.

Radford [102] and Svanberg [98] first introduced the notion of tool-part

interaction. They observed that in the case of the autoclave and RTM process an

increase of the spring-in value that could not be explained by the presence of

thermal or chemical strains. Svanberg [41, 103] developed then numerical models

to predict the observed values of spring-in. Different boundary conditions were

used to simulate the effect of the tool, and frictional contact behaviour appeared to

give the closest agreement with the experiments. Twigg et al [107, 108] studied

experimentally and numerically the effect of tool-part interaction on induced

warpage of unidirectional laminate manufactured by autoclave. An empirical

relationship was used to relate the autoclave pressure and the part aspect ratio to

the induced warpage. The increase of the autoclave pressure increases the residual

stresses or the deformation as it amplifies the contact with the mould, and

therefore the effect of the tool-part interaction. Numerically, the tool-part

interaction was simulated by introducing a “shear layer” between the mould and

the composite part whose elastic properties could be changed to adjust the

property of the interface. Twigg et al. [109] also developed an experimental

approach to quantify the interfacial shear stress during the cure of composite by

autoclave. They defined the interface condition as a combination of stick-slip

behaviour. Potter et al. [110] investigated the presence of residual strains by

measuring the curvature of unidirectional laminate cured in autoclave. Tools were

specially designed to impose an interaction with the composite part. They found

that the high expansion of the mould was the driving factor to induce stress in the

-38-

surface layer of the prepreg and then through the thickness of the prepreg. De

Oliveira et al. [111] investigated experimentally the influence of the mould

material on the development of residual strains using fibre Bragg grating optic

sensors in unidirectional and crossply laminates manufactured by autoclave. In

both cases, they observed higher strains for moulds with higher thermal

expansion. Also, the effect of the autoclave pressure were similar to the one

observed by Twigg et al. [107]. Finally, Fernlund et al. [112, 113] studied the

effect of the tool surface. They found that the use of a FEP release film in addition

to release agent decreased the spring-in and demonstrates the strong influence of

the tool even with the use of release agent.

2.2.4 Property gradients: temperature, degree-of-cure and fibre

volume fraction

Temperature and degree-of-cure through-thickness gradients in the laminate are

generally an issue for thick composite laminates. Usually negligible in thin

laminate, significant temperature gradients can arise in thicker parts as a result of

exothermic resin reaction and low composite thermal conductivity in the

transverse direction. Temperature gradient results in degree-of-cure gradient as

well. Gillespie [57], Huang [59] and Ruiz [104] determined that for thick

composites, temperature and cure progression path affects the magnitude of the

residual stresses and deformation. Actually, high temperature processes produce

an outside-to-inside cure progression, as the composite surfaces cure before the

core. This leads to high residual stresses in the laminate and potentially resulting

in matrix cracking. On the contrary, low temperature process generates an inside-

to-outside cure progression. This type of cure pattern reduces the residual stresses,

but results in long cure progress and low mechanical properties as the part might

not be fully cured. Finally, one-side cure progression, using different temperatures

at the composite surfaces, reduces the process time and the magnitude of the

residual stresses. However, this configuration creates an unsymmetrical residual

stresses distribution and warpage might happen at the demoulding. Therefore,

cure cycles, different from the traditional one used for thin parts, should be used

-39-

to avoid such gradients. Optimized cure strategies based on in-situ temperature

measurements and control of the mould temperature have been proposed for the

autoclave [114, 115], RTM [104, 116] and filament wound structures [117].

The through-thickness fibre volume fraction variation has also an influence on

thin laminates [118]. Such a phenomenon is observed in vacuum bagging

processes, such as autoclave, where the bleeder absorbs the excess of resin while

increasing the fibre volume fraction of the ply at the composite surface. On the

contrary, the ply in contact with the tool is resin rich and has a lower fibre volume

fraction. Radford [119] demonstrates that this fibre volume fraction gradient

creates some warpage in the case of flat panel, as shown in Figure 2-12. Also it

generates an increase in the spring-in angle for convex tooling, but a decrease of

the spring-in value for concave tooling. Similar results have been observed by

Huang et al. [120] and Darrow [118].

Figure 2-12: Process-induced warpage mechanism due to fibre volume fraction

gradient

2.2.5 Secondary effects

Other effects such as the part geometry (shape, thickness, length, corner radius),

or cure cycle (cooling ramp rate, one hold or two holds) can also have an effect on

-40-

the composite part distortion. However, some disagreements exist on the effect of

certain parameters.

Concerning the part geometry, some researchers found experimentally [102, 107,

113] and numerically [121-123] that higher value of spring-in and warpage

occurred for thinner parts, but others did not see a significant difference [61].

Similarly, the effect of the corner radius seems to be controversial. Dong [121]

predicted linear increase of the spring-in with the radius, but others observed only

a small contribution [118, 120]. Jain [105] determined that for a radius-to-

thickness ratio above 1, the spring-in was independent of the radius or the

thickness of the laminate. In addition, the part length also tends to increase the

overall spring-in [107, 113].

The effect of the cure cycle on spring-in was investigated by Fernlund et al. [112,

113]. A two-hold cure cycle with the gelation occurring and the end of the first

hold generated more spring-in than a one-hold cure cycle. However, the cooling

rate did not seem to influence the spring-in value [98].

Most of these secondary effects are the result of the interaction of the four

primary effects explained above. For example the effect of different cure cycles is

related to the state of the resin (rubber or glass) and the coefficient of thermal

expansion in that physical state. Or the effect of the corner radius is related to the

tool-part interaction and the thermal and chemical strains. Therefore, depending

on which primary effects are interacting, the results can be contradictory.

2.3 Process modelling

The sources of residual stresses are multiple and caused by different phenomena.

Hence, in order to consider all these effects, the entire process has to be examined.

Process modelling has been widely used in order to take into account different

phenomena leading the residual stresses and deformations for the entire cure

cycle. The main approach applied in process modelling is to divide the process in

sub-models to study some phenomena independently. An incremental finite

element method (FEM) can be then used in each sub-model to solve the governing

-41-

equations. Generally, for composite manufacturing, the process can be divided

into three independent sub-models: heat transfer and cure kinetics, flow and

compaction, and stress development as shown in Figure 2-13. The material

property models as well as the process variables are the external inputs of the sub-

analyses. The coupling of the sub-model is ensured by using the output of one

sub-model as input for the following sub-model. First developed by Loos and

Springer [96], this approach has been then applied by many other researchers for

the autoclave process [42, 57, 59-61, 64, 95, 122, 124, 125] and the RTM process

[25, 26, 41, 103, 104].

Figure 2-13: Process modelling modular approach

-42-

2.3.1 Heat transfer and cure kinetics

The governing equation solved in this analysis is the Fourier’s heat conduction

equation:

Eq. 2-44

where ρ is the composite density, Cp is the composite specific heat, kij are the

components of the composite thermal conductivity tensor, T is the temperature

and t is the time. is the heat generated during the exothermic chemical reaction

and is related to the resin cure kinetic as follows:

Eq. 2-45

As presented previously in the paragraph 2.1.1.1, the cure rate can be described by

various cure kinetic model.

Initial conditions are then applied to the temperature and the degree-of-cure:

Eq. 2-46

Different boundary conditions such as convective, adiabatic or prescribed

temperature can be applied at the external surface of the system:

Eq. 2-47

where Ts and are the temperature and the normal derivative of the

temperature at the external surface, h is the convective heat transfer coefficient

and T(t) is the cure cycle applied during the process.

An incremental finite element method is then employed to solve the heat transfer

equation with the applied initial and boundary conditions. Thus, the heat transfer

analysis computes the variation of degree-of-cure in the laminate and the change

of temperature in the laminate and the mould using the material properties and the

process cure cycle.

-43-

2.3.2 Flow and compaction

In this analysis, both the behaviour of the composite constituent, the resin and the

reinforcement have to be considered. The general approach to model the resin

flow through the fibre reinforcement is to consider it as flow through a porous

media using Darcy’s law [126]:

Eq. 2-48

where is the Darcy velocity vector, µ is the resin viscosity, is the preform

permeability tensor and is the pressure gradient. As mentioned in paragraph

2.1.1.2, the resin viscosity is a function of the degree-of-cure and the temperature.

The Darcy velocity vector is related to the resin velocity vector as follows:

Eq. 2-49

where ф is the fibre bed porosity.

Eq. 2-48 is valid in the permanent flow regime and saturated porous media, such

as an autoclave process. Assuming a linear resin flow, it can be also generalized

to unsaturated porous media like in the RTM process. In that case, is the Darcy

velocity vector at the unsaturated flow front, is the unsaturated permeability

tensor, which is a function of the fibre volume fraction (Vf) and the fibre

saturation, and is the pressure gradient between the injection points and the

unsaturated flow front [127].

As the flow front advances, the reinforcement is compressed by the resin pressure.

This causes a change in fibre volume fraction which affects significantly the

permeability. The compaction behaviour of the reinforcement is generally

represented by the effective stress formulation used in soil mechanics [128]

expressed as follows:

Eq. 2-50

where σ(t) is the applied stress, is the fibre bed effective stress and P is the resin

pressure.

-44-

In order to solve the coupled equations, initial conditions are applied to the fibre

volume fraction, the resin pressure and the fibre bed effective stress:

Eq. 2-51

Different boundary conditions can be also applied to specify the pressure and the

permeability at the edge of the laminate. An incremental finite element method is

then employed to solve the Darcy’s law and the fibre bed compaction equations

with the applied initial and boundary conditions.

In this work, the RTM process is modelled after the injection phase, once the

preform is fully saturated by the resin. Therefore, the resin flow and the fibre bed

compaction were not considered.

2.3.3 Stresses development

The governing equations of the stress analysis are based on the classical laminated

plate theory. Considering the laminate as a two-dimensional orthotropic material,

the compliance relationship in the ply orientation can be written as follows:

Eq. 2-52

where the subscript l and t refer to the longitudinal and transverse directions, [εxyz]

and [σxyz] are the laminate strains and stresses in the material directions. [S] is the

compliance matrix expressed as follows:

Eq. 2-53

where El and Et are the longitudinal and transverse moduli, νlt and νtl are the

Poisson’s ratio and Glt is the shear modulus.

If the material coordinate system is different from the global coordinate system,

this relation can be transformed to the global coordinate system using the

transformation matrix [T]:

-45-

Eq. 2-54

where [S’] is the compliance matrix in the global coordinate system. The

transformation matrix [T] is expressed as a function of θ which is the angle

difference between the ply coordinate (l, t) to the global coordinate (1,2,3) as

shown in Figure 2-14:

Eq. 2-55

Figure 2-14: Schematic representation of the coordinate systems in ply and the

global orientation

Then, the stiffness relationship can be determined by inverting the compliance

matrix:

Eq. 2-56

where [C’ij] is the stiffness matrix in the global coordinate.

Therefore, the stiffness matrix is a function of the elastic properties of the ply

which can be determined using the micromechanic approaches (Eq. 2-28 to Eq.

2-37) presented in paragraph 2.1.2.

As presented in paragraph 2.2, during the process, strains arise due to thermal and

chemical effects, and the total strain in the laminate is the summation of the

strains caused by these two effects:

Eq. 2-57

-46-

Eq. 2-58

Eq. 2-59

where CTEi and i are the composite coefficients of thermal expansion and

composite cure shrinkage respectively, computed from the micromechanic model

(Eq. 2-39 and Eq. 2-25), ΔT is the temperature variation and is the resin

shrinkage strain variation.

A finite element incremental method is then employed to solve these equations,

assuming that the fibre properties are constant or only function of the temperature

and the resin behaves as a “cure-hardening instantaneous linear elastic” (CHILE)

material. For a given increment, knowing the field of degree-of-cure and

temperature from the heat transfer analysis, the instantaneous composite elastic

constants can be computed using the resin elastic modulus model and the

micromechanic approach. Similarly, the thermal and chemical strains can be

computed for a given increment knowing the resin thermal and shrinkage

behaviour with the temperature and the degree-of-cure and using the

micromechanic approach. The stresses in the laminate can be then calculated from

the classical laminated theory Eq. 2-56. Then the laminate strains and stresses

development during the cure cycle are obtained by adding the total strains and

stresses of the consecutive increments:

Eq. 2-60

Eq. 2-61

In this manner, the evolution of the strains and stresses can be computed for the

entire cure cycle, taking into account the thermomechanical properties of the

composite constituents.

-47-

2.3.4 COMPRO Component Architecture (CCA)

In this work, the commercial finite element software ABAQUS and the COMPRO

Component Architecture (CCA) were used to model the RTM process based on

the approach described above. The CCA, developed by Convergent

Manufacturing Technology Inc., is a subroutine allowing the interface between

the material properties and the ABAQUS finite element solver as shown in Figure

2-15. Using the material model database, it computes the evolution of the material

properties (resin, fibre and composite) at each increment as described above, and

transfers them to the ABAQUS finite element solver which computes the strains

and stresses using the classical laminated plate theory. Due to the ABAQUS

structure, two analyses are required to model the manufacturing process. First, a

heat transfer analysis is performed to determine the temperature and degree-of-

cure fields of each integration point in the model. Then, a stress analysis is solved,

using the temperature and degree-of-cure history computed in the previous

analysis, to determine the strains, stresses and displacements caused by the cure

cycle.

Figure 2-15: ABAQUS/COMPRO structure

-48-

2.4 Literature review summary and objectives

As presented from the previous sections, process-induced stresses and

deformations have been widely studied experimentally, analytically and

numerically. Figure 2-16 presents a brief summary of the different aspects

investigated in the past researches on process-induced stresses and deformations.

Figure 2-16: Summary of the investigations on process-induced stresses and

deformations

-49-

The following conclusions can be drawn:

1) The majority of the studies concerned the autoclave process (Figure 2-16-

a). Only few addressed the issue of residual stresses and dimension change

for the RTM process.

2) The different sources of process-induced stresses and deformations are

clearly identified in the literature (Figure 2-16-b). The main investigations

focussed on the thermal strains, the resin cure shrinkage and the tool-part

interaction. However, in a majority of case, these different aspects were

not considered simultaneously.

3) Most of them focused on unidirectional carbon reinforcements and epoxy

resin (Figure 2-16-c). Despite their increasingly use in the industry, only

few researches investigated the woven reinforcements and the effect of the

fibre architecture on the development of the residual stresses.

4) Finally, most of these studies considered simple geometries, such as flat or

angled structures and few examined more complex structures (Figure

2-16-d).

Concerning the RTM process, Table 2-1 details the main studies carried out on

the process-induced stresses and deformations. Most of the works were performed

on glass fibre reinforcements with epoxy resin and took into account the effect of

the thermal strains and the resin shrinkage. However the effect of the tool-part

interaction was not very well investigated.

The importance of the development of constitutive material models was also

addressed in the first section of this literature. Accurate material models are

essential in order to capture more realistically the behaviour and evolution of the

material during the manufacturing process.

-50-

Table 2-1: Studies on process-induced stresses and deformations for the RTM

process

Sou

rces

of

resi

du

al

stre

sses

Oth

er

Fib

re

wav

ines

s

Tem

per

atu

re

gra

die

nt

Tem

per

atu

re

gra

die

nt,

Vf,

Geo

met

ry

Deg

ree-

of-

cure

an

d V

f

gra

die

nt

Tool-

part

inte

ract

ion

Per

fect

bo

nd

ing

X

Sh

rin

kage

X

X X

X

Th

erm

al

stra

ins

X

X

X

X

X

Mate

rial

epoxy /

5H

S

Car

bon w

oven

fabri

c

Epoxy /

Gla

ss

woven

fab

ric

Poly

este

r /

Unid

irec

tional

gla

ss f

ibre

Epoxy /

Unid

irec

tional

gla

ss f

ibre

Poly

este

r /

gla

ss

mat

and n

on

crim

p g

lass

fab

ric

Geo

met

ry

Tap

ered

geo

met

ry

L-s

hap

ed

bra

cket

,

C-s

par

stru

cture

Fla

t pan

el

Sin

gle

stif

fener

stru

cture

Fla

t pan

el

Exp

erim

enta

l

/ N

um

eric

al

Nu

mer

ical

Ex

per

imen

tal

and

num

eric

al

Nu

mer

ical

Nu

mer

ical

Ex

per

imen

tal

and

num

eric

al

Ref

eren

ces

Gole

stania

n a

nd

El-

Gaza

wy

[24, 25]

Sva

nber

g a

nd

Holm

ber

g

[26, 41, 98

, 103]

Anto

nucc

i et

al.

[116]

Dong e

t al.

[121]

Ruiz

and T

roch

u

[43, 10

4]

-51-

In the light of the above, the current thesis investigates the process-induced

residual stresses and deformation of 5-harness satin woven composite structures

manufactured by RTM. In order to achieve this goal, the following objectives

were considered:

1) Resin characterization: implementation of a methodical approach to

characterize the processing properties of the RTM one-part epoxy resin

and develop the resin constitutive models.

A particular emphasis should be set on the volumetric cure shrinkage and

the thermal expansion of the resin and the composite, as these parameters

have a significant influence on the dimensional stability.

2) Effect of the fibre architecture: Investigation of the influence of the 5-

harness satin carbon reinforcement architecture on the composite

thermomechanical properties.

3) Tool-part interaction: Investigation of the tool-part interaction for the

RTM process experimentally using fibre Bragg grating sensors (FBG) and

numerically using a finite element modelling.

4) RTM process modelling: Implementation of the constitutive material

models into a finite element model to predict the geometrical variations

such as spring-in or warpage. The main sources of residual stresses and the

different phenomena involved in the RTM process are taken into account

simultaneously.

-52-

CHAPTER 3 Characterization of the Resin Thermomechanical Properties As presented in CHAPTER 2, accurate material constitutive models are essential

in order to realistically capture the behaviour and evolution of the material during

the manufacturing process. In this chapter, the characterization steps and the

development of the material constitutive models of a commercial epoxy resin are

detailed. Supplied by Cytec, the CYCOM 890RTM epoxy [129] is a low viscosity

resin developed especially for the RTM process. It is a one part system reacting at

high temperature. It can be injected at 80ºC with a viscosity of 0.390 Pa.s, and its

typical cure cycle is two hours at 180ºC. No complete characterization has

previously been performed on the CYCOM 890RTM epoxy, and no constitutive

material models were available in the literature.

3.1 Characterization methodology

Figure 3-1 presents the methodical approach developed in order to investigate the

processing properties of thermoset resins and applied on the CYCOM 890RTM

epoxy resin. First, thermal stability tests are conducted to determine the resin

temperature processing window (step 1). The curing behaviour is then

investigated in order to obtain the evolution of the degree-of-cure, α, as a function

of time and temperature (step 2). The resin rheological behaviour (step 3a) and the

glass transition temperature Tg (step 3b), are then measured as a function of the

degree-of-cure. Next, knowing the resin rheological behaviour, the cure

shrinkage, εV, is determined as a function of the degree-of-cure (step 4a). The

coefficient of thermal expansion (step 4b) and the resin modulus (step 4c) are

expressed as a function of the glass transition temperature. Finally, the developed

material constitutive models can be implemented in any finite element software

(step 5) to predict the final properties of a composite structure as a function of the

cure cycle used.

-53-

Figure 3-1: Characterization procedure for the thermoset resin

The next sections present in details the characterization steps and the development

of the material constitutive models.

3.2 Thermal stability and cure kinetics (step 1 and 2)

3.2.1 Thermal stability (step 1)

Tests performed

Thermal stability tests were carried out on a Thermal Gravimetric Analyzer

(TGA) Q500 from TA Instruments. A temperature ramp at 20ºC/min from 25ºC to

700ºC was applied to a 12.24 mg sample. The sample was under nitrogen from

-54-

25ºC to 550ºC and air from 550ºC to 700ºC. A three-hours isothermal test was

also performed at 180ºC under nitrogen.

Results and Analysis

The corresponding weight variation, under the dynamic and isothermal

conditions, is presented in Figure 3-2 and Figure 3-3 respectively. For RTM

processing, the temperature will not exceed 200ºC. At this temperature, a weight

loss of 1.2% caused by the evaporation of volatiles present in the resin was

measured under dynamic conditions. The resin thermal stability was confirmed by

a weight loss of less than 2.1% after a three hours isothermal experiment at 180ºC.

Therefore, the resin is not subjected to significant degradation during its typical

cure cycle.

Figure 3-2: Resin weight variation with temperature from a TGA dynamic test at

20°C/min

-55-

Figure 3-3: Resin weight variation for three hour at 180ºC

3.2.2 Cure kinetics (step 2)

Tests performed

The resin cure kinetics was measured with a Modulated Differential Scanning

Calorimeter (MDSC) Q100 from TA Instruments. The testing conditions were

chosen based on typical processing conditions suggested by the manufacturer.

Dynamic scans with heating rates of 1ºC/min and 2°C/min, from 25ºC to 250ºC,

and isothermal scans at 160ºC, 170ºC, 180ºC and 190°C, were performed on

uncured neat resin sample. Isothermal tests were followed by a dynamic ramp in

temperature in order to measure the residual heat of reaction. Each testing

condition was carried out up to three times in order to verify the result

reproducibility (Appendix A). As mention in the literature review, CHAPTER 2,

section 2.1.1.1, the measured heat, generated while the resin reacts, can be related

to its cure rate and the degree-of-cure. The cure kinetic model is then the relation

that expresses the cure rate as a function of the degree-of-cure.

-56-

Results and analysis

Figure 3-4 shows the heat flow profile measured by DSC during a dynamic

experiment. The total heat of reaction, HT, was calculated by integrating the area

under the curve. For this epoxy resin, the average HT is 430 25 J/g for 4

samples. Each sample weights 5.25 0.1 g. Figure 3-5 present the evolution of

the degree-of-cure and the cure rate for the isothermal tests. The maximum cure

rate is obtained for a degree-of-cure of 0.5. At temperatures lower than 180ºC, the

degree-of-cure does not reach 1.0 due to the diffusion effect. Therefore, the

autocatalytic cure model with a diffusion factor, developed by Hubert et al. was

chosen to describe the evolution of the degree-of-cure with time and temperature

[33]. This model, expressed by the following equation, gave a good correlation

with the experimental data:

Eq. 3-1

where k is a rate constant following an Arrhenius temperature dependency:

Eq. 3-2

Figure 3-4: Typical heat flow of a Dynamic Scanning Calorimetry dynamic test at

2ºC/min

-57-


for isothermal tests: a) degree-of-cure with the time, b) cure rate as a function of

the degree-of-cure

From Eq. 3-1 and Eq. 3-2, the activation energy Ea was determined by calculating

the slope of versus 1/T at low degree-of-cure ( = 0.1), as shown in

Figure 3-6. Using the data under isothermal conditions, as presented in Figure 3-7,

-58-

a linear relationship was observed between the ultimate degree-of-cure ( max) and

the glass transition temperature Tg. C0 and CT were defined as the fitting

parameters from the linear fit. The step change in the specific heat (Cp) measured

by modulated DSC was used to identify Tg. The other parameters, A, n, m, and C

were calculated using a least squares non-linear regression between the cure rate

and the degree-of-cure for all tested temperature conditions. The values are

presented in Table 3-1.

Figure 3-6: Cure rate as a function of inverse absolute temperature at low degree-

of-cure (α = 0.1) under isothermal conditions

-59-

Figure 3-7: Ultimate degree-of-cure under isothermal conditions as a function of

the glass transition temperature

Table 3-1: Cure kinetic model constants

Model constants

A (s-1

) 58528

Ea (J/mol) 68976

n 0.6

m 0.63

C 15.66

αC0 -0.90

αCT (K-1

) 0.0039

Figure 3-5 compares the experimental data measured by DSC for four isothermal

temperatures with the predictions obtained with the kinetics model (Eq. 3-1). The

variations of the resin degree-of-cure with time and the rate of cure as a function

of the degree-of-cure are presented in Figure 3-5-a and Figure 3-5-b, respectively.

The cure kinetics model accurately predicts the resin cure evolution for the

different isothermal cases considered. The goodness of fit is reflected by R2

values above 0.965 as shown in Figure 3-5-b. The prediction for the dynamic

conditions is presented in Figure 3-8. A good agreement for the cure rate

-60-

prediction is obtained up to 190ºC and 220ºC at temperature ramp of 1ºC/min and

2ºC/min respectively. After those points, the cure kinetic model predicts a faster

decrease in cure rate than measured experimentally. Since the processing

temperature is below 190ºC, this discrepancy is not a point of concern.


for dynamic tests

3.3 Rheological behaviour (step 3a)

Tests performed

Rheological measurements were performed with an AR2000 rheometer from TA

Instruments. Since this epoxy was not previously characterized, the Linear

Viscoelastic Region (LVR) was first determined. A strain sweep test is initially

performed, followed by a time sweep test. These two tests are presented in

Appendix A. For this particular epoxy, the optimal oscillatory conditions to

remain in the LVR were found at 15% strain and 1Hz.

-61-

Dynamic scans at heating rates of 1°C/min, 2°C/min and 3°C/min and isothermal

scans at temperatures of 80°C, 170°C, 180°C and 190°C were performed on

uncured neat resin sample, using a 40 mm parallel plate geometry in oscillatory

mode at 15% strain and 1 Hz. Each testing condition was carried out up to five

times in order to verify the result reproducibility Appendix A.


Figure 3-9 and Figure 3-10 show the evolution of the viscosity under different

dynamic and isothermal conditions. First the resin viscosity decreases as the

temperature increases, until it reaches a minimum value. After a certain time, the

viscosity increases quickly. This sharp increase in viscosity corresponds to the gel

transition. The equality between the storage and loss shear moduli, G’ and G”,

was used as criterion to determine the gel point [130]. As shown in Figure 3-11, at

the curing temperature of 180ºC, the gel point occurred around 72 minutes in

average.

Figure 3-9: Evolution of the measured and predicted viscosity with temperature

for rheological dynamic tests at three temperature rates

-62-

Figure 3-10: Evolution of the measured and predicted viscosity with time for

rheological isothermal tests

Figure 3-11: Determination of the gel point at 180ºC

A model taking into account the influence of both the temperature and the degree-

of-cure was used to characterize the rheological behaviour of the resin. The

-63-

following equation presents the modified gel model used to describe the evolution

of the resin viscosity [131]:

Eq. 3-3

Eq. 3-4

where is the degree-of-cure at the gel point, and Aµi, Eµi, A’, B’ and C’ are

constants. From the temperature-time history measured for each rheological test,

the degree-of-cure of the resin was calculated using the cure kinetics model (Eq.

3-1) and the gel point was determined as αgel = 0.7. Although this value can seem

relatively high for an epoxy resin, similar results were obtained by O’Brien and

White [38]. Furthermore, this resin was developed for the RTM process which

requires a long gel time in order to maximize injection time. Eq. 3-4 can be also

expressed as a linear relationship between the viscosity and the inverse of the

temperature:

Eq. 3-5

From Eq. 3-5, a linear regression was then used to calculate the constants Aµ1, Eµ1

and Aµ2, Eµ2, using the dynamic data and the isothermal data respectively before

the gel point. The other parameters, A’, B’ and C’ were calculated using a least

squares non-linear regression between the viscosity and the temperature. The

values of the different parameters are reported in Table 3-2.

Figure 3-9 and Figure 3-10 compare the predicted and measured viscosity

evolution with time and temperature. The viscosity model (Eq. 3-3) accurately

predicts the onset of resin gelation and the evolution of resin viscosity with

temperature and degree-of-cure, with a R2 value superior to 0.80. From Figure

3-10, it is shown that the resin remains liquid even after three hours at the

recommended injection temperature of 80°C. A typical RTM injection lasts less

than 30 minutes, so no gelation will occur during this time.

gel

-64-

Table 3-2: Viscosity model constants

Model constants

Aµ1 (Pa.s) 9.81x10-19

Aµ2 (Pa.s) 6.41x10-3

Eµ1 (J/mol) 115305

Eµ2 (J/mol) 12074

A’ -0.5

B’ 1

C’ 3.5

αgel 0.7

3.4 Glass transition temperature (step 3b)

Tests performed

Three different methods were used to measure the glass transition temperature:

MDSC, TMA and the rheometer in torsion mode.

With the MDSC technique, Tg is identified by a step change in the specific heat,

during the dynamic ramp following an isothermal test, whereas with the TMA, it

is identified by a change in CTE.

Using the rheometer in torsion mode, the glass transition temperature can be

determined by observing the three modulus based indicators: the onset of a sharp

drop in the storage modulus G’, the peak in the loss modulus G” and the peak in

the tan δ. A succession of dynamic tests was performed at 5ºC/min to 180ºC

followed by a short isotherm in an oscillatory mode at 0.1% strain and 1Hz on

solid samples pre-cured to an initial degree-of-cure 1, manufactured as explained

in Appendix A. The chosen heating rate of 5ºC/min was low enough to ensure

thermal equilibration between the rheometer and the sample but high enough to

avoid large changes in degree-of-cure at higher temperatures. Once the glass

transition temperature was measured, the sample was cured to a known degree-of-

cure 2 and quickly cooled down to room temperature. The procedure was then

repeated from 2 to a higher 3 and so on, so that the Tg was measured for

different values of degree-of-cure (Table A-2).

-65-


The evolution of the Tg with the degree-of-cure was modeled with the

DiBenedetto equation (Eq. 2-14). , the parameter associated with fully cured

resin, was determined as the highest recorded glass transition temperature. , the

glass transition temperature of uncured resin, was determined by MDSC testing,

by heating an uncured resin sample from -50ºC to 25ºC. The fitting parameter λ

was calculated using a least squares non-linear regression between the values of

Tg determined at the peak of tan δ and the degree-of-cure. The DiBenedetto

constants are presented in Table 3-3. This model accurately predicts the evolution

of the glass transition temperature, with a R2 value of 0.999. The value of the

fitting parameter is close to the expected value found by other researchers for

thermosetting resins ( = 0.4 [132]).

Table 3-3: DiBenedetto model constants

Model constants

(ºC) -14.23

(ºC) 213.75

0.396

Figure 3-12 compares the predicted and measured glass transition temperatures

with the degree-of-cure. The DiBenedetto equation captures the trend of the Tg

obtained with different methods well. Differences between the testing methods

were expected as the glass transition passage does not affect thermodynamic and

mechanical properties at the same point, but rather occurs over a range of

temperatures.

-66-

Figure 3-12: Comparison of glass transition temperatures measured with

Modulated Differential Scanning Calorimeter, Thermo Mechanical Analyzer and

rheometer in torsion mode and the predicted values obtained with the DiBenedetto

model

3.5 Volumetric changes during cure (step 4a and 4b)

As explained in CHAPTER 2, the volumetric changes of a thermoset resin are a

combination of chemical effects (shrinkage) and thermal effects (coefficient of

thermal expansion, CTE). Since volumetric changes are one of the main causes of

dimensional variability and residual stress development during the cure of

composite materials, a special attention was set on their characterization.

3.5.1 Cure shrinkage (step 4a)

Two different methods, the modified rheology method and the gravimetric

method, were applied to measure the shrinkage of the CYCOM 890RTM epoxy

resin.

-67-

Principle

The modified rheology method [55] is a simple test, easy to setup. It measures the

shrinkage after the gel point using a rheometer with parallel plate geometry. A

controlled normal force is applied to maintain the contact between the plates and

the resin sample while the gap variation between the parallel plates is measured.

The linear shrinkage is first determined based on the change in gap between the

parallel plates (i.e. sample thickness) with the following equation:

Eq. 3-6

where εL is the linear shrinkage, is the resin Poisson’s ratio, h is the value of the

gap at a given time and h0 is the initial value of the gap. Assuming that the in-

plane strains in the resin are zero and that the resin is incompressible ( = 0.5), the

linear shrinkage can be converted to volumetric shrinkage with the following

equation:

Eq. 3-7

where is the volumetric shrinkage, h0 is the initial value of the gap and h is the

value of the gap at a given time.

The gravimetric method, more complex, measures the change in buoyancy of a

resin in a known fluid at a controlled cure temperature to determine the shrinkage

[56]. It is based on the Archimedean principle which links the mass, the volume

and the density of solid bodies immersed in liquid as follows:

Eq. 3-8

where ms is the mass of the solid, mfl is the mass of the fluid, ms(air) is the mass of

the solid in air, ms(fl) is the mass of the solid in the fluid, ρs is the density of the

solid and ρfl is the density of the fluid.

v

-68-

During cure under isothermal conditions, resin shrinkage causes an increase in

density that can be detected by the change in buoyancy. The buoyancy is

monitored by measuring the apparent change in weight of the immersed sample.

Therefore, the shrinkage can be expressed as follows:

Eq. 3-9

where is the apparent resin weight change, ρfl,Tfl is the density of the fluid

at the actual fluid temperature Tfl and Vr,Tc is the volume of the uncured resin at

the curing temperature Tc.

Tests performed

For the modified rheology method, the shrinkage measurements were performed

with an AR2000 rheometer from TA Instruments with 25 mm diameter plates as

shown in Figure 3-13-a. The initial sample thickness was 1 mm ± 0.05 mm. Tests

were carried out at three different isothermal cure temperatures, 160ºC, 170ºC and

180ºC, to avoid thermal expansion phenomena, and the normal force was set to

0.1N. Three to four experiments were performed for each temperature for

reproducibility purposes.

The experimental procedure was divided in two steps. In the first step, the

rheometer was set in a gap control mode as the resin was in its liquid state: the

value of the gap was controlled and kept constant to his initial value h0 and no

normal force was applied. The maximum strain was set at 15% with a frequency

of 1Hz in order to be in the Linear Viscoelastic Region (LVR) of this epoxy resin.

When the viscosity reached 500 Pa.s, the second step or normal force control

mode was initiated. In this step, the resin has gelled and can withstand pressure

without flowing. The normal force (FN) was kept constant to 0.1N, a maximum

torque of 500 µN.m at a frequency of 30 Hz was also applied and the actual gap h

was measured.

The gravimetric method required pre-experiment preparation and was delicate to

operate as sources of error can be easily introduced. According to Schoutens

rr VV

-69-

[133], the main sources of error of common immersion techniques are: air bubbles

adhesion to the sample surface causing an artificial increase in buoyancy, effect of

surface tension on the wire supporting the specimen and temperature fluctuation.

In this study, the experimental procedure developed by Li et al. [56] shown in

Figure 3-13-b, was modified as follows. Two resin samples were immersed

simultaneously in one litre of Dow Corning 200-100 silicone fluid at constant

temperature. The samples had a mass of 2.45 ± 0.1 g to minimize temperature

changes due to the exothermal curing reaction. One specimen was linked to an

Ohaus precision scale, model AV114C, with a capacity of 110g ± 0.0001g, used

for the weight measurement. The second resin specimen had a type K

thermocouple embedded for resin temperature monitoring. A thermocouple was

also immersed in the silicone fluid. High temperature Nylon 6 bagging film was

used to enclose the resin. In their experimental set-up, Li et al. were moulding thin

silicone bags with a silicone mould rubber. These bags had first to be pre-

conditioned before use as they were swelling in silicone oil. They were then

sealed using machined aluminum plugs and a binding sleeve. In order to decrease

the time of this preparation phase, Nylon 6 bagging film was used and came out

to be more user-friendly while meeting the required specifications. The Nylon 6

bagging film appeared to have a better dimensional stability in the silicone fluid

with the temperature and to be resilient enough to pick up any volumetric change.

Therefore no pre-conditioning was needed before running experiments. Its

standard thickness inferior to 0.1 mm allowed a quick heat up of the resin to the

curing temperature as well as a quick dissipation of the exothermic heat. It can be

used for cure up to 205ºC. An impulse bag sealer was used to seal it, so that no

external material was introduced to close the bags and entrapped air was easily

removed. Nylon bags were hanged from the weight below hook with a steel wire

and a Kevlar thread. The steel wire was used to avoid surface tension effect and

fluid absorption and minimize potential source of error. Kevlar thread was used to

link the scale to the steel wire and avoid heat transfer to the scale. A heating

blanket regulated by temperature controllers was used to heat up the silicone bath

two hours before the experiment in order to have a uniform fluid temperature.

-70-

Experiments were carried out at 160ºC, 170ºC and 180ºC for three to four hours.

Three to four tests were performed for each temperature for reproducibility

purposes. A data acquisition system from National Instruments (NI 9211) was

used to record the temperatures and a RS232 cable was used to connect the

precision scale to the computer. A Labview interface was used to simultaneously

record the temperatures and the apparent weight.

Figure 3-13: Shrinkage measurement methods set-up: a) modified rheology, b)

gravimetric.


Figure 3-14 shows the parallel plate gap and the normal force variation during a

typical modified rheology test at 180ºC. During the gap control, the normal force

increased, implying an expansion of the resin sample. As the rheometer

temperature was kept constant, this expansion was caused by the heat released

during the exothermic reaction creating locally an increase in temperature. A K-

type thermocouple placed at the center of the plate, in the middle of the sample,

measured a 1ºC increase of the resin temperature and confirmed this phenomenon.

Nevertheless, the increase in temperature occurred during the first hour of the

experiment when the resin was liquid. As the shrinkage was measured during the

normal force control step, for more than four hours, this variation of temperature

did not affect the results. In the normal force control step, the normal force was

set to 0.1N. The gap started to decrease due to the shrinkage until it reached a

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constant value. The shrinkage was then calculated using the gap variation in Eq.

3-7.

Figure 3-14: Gap and normal force variation for a typical modified rheology test

for an isothermal cure at 180ºC

Figure 3-15 shows the measured variation of shrinkage with time for samples at

three isothermal temperatures (160ºC, 170ºC, 180ºC). The average total

volumetric shrinkage was 3.36% ± 0.2% which is in the range usually found for

epoxy resins (2%-7%) [51, 56]. The curing temperature had not a significant

influence on the total volumetric shrinkage which was consistent with the work by

Haider et al. [55] and Li et al. [56]. Figure 3-16 presents the shrinkage as a

function of the degree-of-cure, obtained from Dynamic Scanning Calorimetry

(DSC) experimental data. After the gel point, the variation of the shrinkage is a

linear function of the degree-of-cure which is in agreement with previous studies

[44, 55, 56]. Thus the resin shrinkage can be modelled as follows:

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Eq. 3-10

where α is the resin degree-of-cure, αgel is the degree-of-cure at gelation, εV is the

volumetric shrinkage, and A” is a constant. The degree-of-cure at gelation, αgel =

0.7, was determined from the cure kinetic model (section 3.2.2). For each

temperature, the constant A” was calculated using a least squares method for

linear regression. The fitting constants and the R2 values are listed in Table 3-4.

As shown in Figure 3-15 and Figure 3-16, this model agreed overall well with the

experimental data at 170ºC and 180ºC. However, at 160ºC, the model

underestimated the shrinkage where the shrinkage onset occurred before αgel =

0.7. The shrinkage occurring before αgel is not taking into account by the model,

which explains the difference between the measured and predicted values at that

temperature.


method and predicted values with time under isothermal conditions

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method and the predicted values as a function of the degree-of-cure under

isothermal conditions

Table 3-4: Curve fitting constants for the shrinkage model obtained by the

modified rheology method (Eq. 3-10) and R2 values for isothermal experiments

Isothermal experiments A” (%) R2

160ºC

170ºC

180ºC

Average

12.29

12.68

12.28

12.42

0.993

0.995

0.995

Figure 3-17 to Figure 3-19 show the temperatures and sample apparent weight

variation recorded during the gravimetric method. First, the apparent weight

decreased as the resin sample expanded and reached the isothermal temperature

equilibrium. After 20 to 30 minutes, the apparent weight started to increase due to

the shrinkage development until it reached a maximum. At 160°C, the exotherm

due to the curing reaction was negligible (<1ºC). At 170ºC and 180ºC, an increase

of the resin temperature of 3ºC and 6ºC respectively was noticeable. The

temperature increase caused a thermal expansion of the sample, and therefore

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increased the sample buoyancy while decreasing its apparent weight. However, no

decrease of the resin apparent weight was visible as the exotherm occurred. Thus,

the effect of the thermal expansion was considered negligible compared to the

shrinkage and thus was not accounted in the calculation.





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The variation of the shrinkage, computed from the weight change (Eq. 3-9), with

time and degree-of-cure is presented in Figure 3-20 and Figure 3-21, respectively.

As in the previous method, the degree-of-cure was obtained from DSC

experimental data (section 3.2.2). The result of Figure 3-21 corroborates the

conclusion obtained with the previous method: curing temperature has no

influence on the evolution of the shrinkage. The resin shrinkage followed a bi-

linear relationship with the degree-of-cure expressed as follows:

Eq. 3-11

where α is de degree-of-cure, αi is the degree-of-cure at the inflection point, εV is

the volumetric shrinkage and A1, B1, C1 and D1 are the model constants. A least

squares method for linear regression was used to calculate the constant A1, B1, C1

and D1 reported in Table 3-5.

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Figure 3-20: Evolution of the measured resin shrinkage by gravimetric method

and predicted values with time under isothermal conditions

Figure 3-21: Measured and predicted cure shrinkage for isothermal tests with the

gravimetric method

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Table 3-5: Bilinear curve fitting constants for the shrinkage model obtained by the

gravimetric method (Eq. 3-11)

Linear equation 1 Linear equation 2 Inflection

A1 (%) B1 (%) R2 C1 (%) D1 (%) R

2 i

160ºC

170ºC

180ºC

Average

7.78

7.86

8.64

8.10

-0.40

-0.54

-0.13

-0.35

0.994

0.992

0.996

13.93

19.38

22.85

18.72

-4.69

-9.58

-11.99

-8.75

0.986

0.990

0.984

0.70

0.77

0.82

0.77

The rate of volumetric shrinkage increased after the inflection point (A=8.10%

and C=18.72% before and after the inflection point respectively). The resin

reached a volumetric shrinkage of 6% before the transition point and kept

increasing up to 10%. Therefore it can be assumed that the change in the

volumetric cure shrinkage rate at the inflection point corresponded to the gelation

phenomenon. Similar results have been observed in previous studies for a MY750

epoxy resin [56] or nonconductive adhesives with a thermomechanical analyzer

[51]. The change in shrinkage rate can be related to the polymer chain movement

and molecular rearrangement. Before the gelation, polymer chains are free to

move and rearrange and the induced deformation can be accommodated by the

resin flow. After the gelation, the resin transforms from liquid to solid and

develops a mechanical modulus. Molecular rearrangement remains significant but

the mobility of the polymers chains is greatly reduced. At this point, the

deformations induced by the molecular rearrangement cannot be dissipated by the

resin flow inducing a higher shrinkage rate.

Figure 3-22 to Figure 3-24 compare the evolution of the shrinkage obtained with

the modified rheology and the gravimetric methods. The modified rheology

method measured only the shrinkage after the gel point. From Figure 3-21, it

appears that the shrinkage measured with the gravimetric method was actually

5.39% ± 0.4% at the gel point (αgel = 0.7). Therefore, an initial shrinkage of

5.39% was added to the results obtained by the modified rheology method. The

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shrinkage after the gel point measured by the two methods was in good agreement

especially at 160ºC and 170ºC. At 180ºC, the rate of the shrinkage increase

measured with the gravimetric method was slightly higher compared to the

modified rheology method. This phenomenon could be explained by the small

exotherm taking place at 180ºC (Figure 3-19). The 6.5°C temperature overshoot

could lead to an increase of the cure rate and consequently the shrinkage rate.

Also, the potential release of the volatiles present in the resin in form of gas was

not taken into consideration for the shrinkage characterization using the

gravimetric method. The release of the volatiles can indeed affect the sample

buoyancy leading to an increase in the apparent weight and therefore an increase

in the measured shrinkage. Even if very low void level was observed on the cured

sample at the end of test, this issue might explain the shrinkage discrepancy

observed between the modified rheology method and the gravimetric method.


degree-of-cure at 160ºC

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These results validate the use of a simple method, the modified rheology method,

to measure the shrinkage after gelation. However, the gravimetric method

demonstrates that the shrinkage occurring before gelation is not negligible and can

represent up to one half of the total shrinkage. The arising shrinkage before

gelation does not induce residual stresses as the resin is in the liquid state and can

flow. However, shrinkage prior to gelation can lead to surface finish defects such

as fabric print through in closed-mould process (i.e. Resin Transfer Moulding)

where no pressure is applied after the injection to the composite part to

compensate the shrinkage effect.

3.5.2 Coefficient of thermal expansion (step 4b)

Tests performed

Tests were carried on a TMA 2940 from TA Instruments. The influence of the

curing temperature and the degree-of-cure was investigated using fully and

partially cured resin samples. The samples were prepared with the rheometer with

40mm plates. Release agent was applied on each plate to ensure an easy

demolding. The curing temperatures considered were 160ºC, 170ºC and 180ºC,

and the influence of the degree-of-cure was observed after the gel point, from α =

0.8 to α =1. Then the 40mm disk was cut in smaller samples of about 5mm by 5

mm and 1mm thick. Three to four cycles from room temperature up to 250ºC,

then back down to room temperature, at a rate of 3ºC/min were performed for

each sample. A normal force of 0.05N was applied on the probe in order to

maintain contact with the sample.


Figure 3-25 and Figure 3-26 show a typical experiment applied on one sample and

the determination of its CTE. From Figure 3-25, a difference between the first

cycle and the two last cycles can be noticed. During the first cycle, both thermal

expansion and cure shrinkage occur due to the advancement of the degree-of-cure

with temperature. During the last two cycles, the relative dimensional changes,

, are similar, only thermal expansion takes place. Thus, the CTEs were

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measured using the heating part of the cycles excepting cycle 1. Figure 3-26

represents the heating part of cycle 3. The sample relative dimensional change

evolves linearly with the temperature and the slope corresponds to its CTE. The

curve inflection corresponds to the glass transition of 197ºC. As expected, the

resin CTE increases as the sample evolves from the glassy to the rubbery state.

Figure 3-25: Resin relative dimensional change with temperature of a neat resin

sample with an initial degree-of-cure 1 of 0.883

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Figure 3-26: Resin relative dimensional change during the heating part of cycle 3

at 3ºC/min

Figure 3-27 presents the variation of the measured coefficient of thermal

expansion with the degree-of-cure, after the gel point, from α = 0.8 to α = 1. It can

be noticed that the CTE remains constant with the degree-of-cure below the glass

transition temperature, but decreases with the degree-of-cure above the glass

transition temperature. Below Tg, the resin is in its glassy stage, the movement of

molecules is very limited. The network formation has no influence on the

expansion of the resin. The CTE remains low and constant with the increase of the

degree-of-cure. However, above Tg, the movement of the molecules increases and

is less limited. In this case, the network formation will have a bigger influence on

the molecule mobility by reducing it. Due to this higher mobility, the CTE above

Tg is higher than the CTE below Tg, and decreases with the increase of the degree-

of-cure.

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Figure 3-27: Variation of the coefficient of thermal expansion with the degree-of-

cure before and after the glass transition

The glass transition temperature is thus an important parameter for the evolution

of the CTE. Taking example from the expression of elastic modulus as a function

of T* [58, 60], the evolution of the CTE was plotted as a function of the difference

between the instantaneous and glass transition temperature, T*=T-Tg, in Figure

3-28. The same reasoning used for the evolution of the CTE with the degree-of-

cure can be employed. Far below Tg, the CTE remains low and constant with the

increase of temperature as the movement of the polymer chain is limited.

However, as the temperature increases and get closer to the glass transition

temperature, the movement of the molecules increases and the CTE starts to

increase linearly. The following model was developed to describe this evolution

using least squares method for linear regression:

Eq. 3-12

where CTEglass is the resin CTE in the glassy state, A0 and T’ are two constants.

The model constants are expressed in Table 3-6.

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Figure 3-28: Evolution of the measured and predicted CTE as a function of T*,

for 3ºC/min heating rate up to different temperatures

Table 3-6: Coefficient of thermal expansion model constants

Model constants

CTEglass (ºC-1

) 5.97 10-5

A0 (ºC-2

) 7.54 10-6

T’ (ºC) -20.4

3.6 Elastic modulus (step 4c)

Tests performed

The torsion mode of the rheometer was used to capture the evolution of the elastic

modulus with the cure. As described previously in section 3.4, this method

enables to follow the change of the shear moduli, G’ and G” with the temperature.

Knowing the cure kinetics of the epoxy resin, the shear moduli can be related to

the degree-of-cure as well. Then, assuming that the resin is isotropic and that the

variation of the Poisson’s ratio with the temperature and the degree-of-cure has a

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negligible influence on the shear modulus [43, 57], the shear modulus can be

related to the tensile modulus with the following equation:

Eq. 3-13

where E is the tensile modulus, G is the shear modulus and is the Poisson’s

ratio.

The manufacturer’s data sheet listed a room-temperature tensile modulus E of 3.1

GPa, and the average shear modulus G of the resin at room temperature was

measured to be 1.30 GPa. Therefore, using Eq. 3-13, the Poisson’s ratio was

determined to be 0.2, which is in the expected range for cured epoxy resins.

Partially cured neat resin samples to a known degree-of-cure 1 (Table A-3),

manufactured using the same method as described in Appendix A, were tested

with specific cure cycles designed to reach a fully cured state.


As expected, and shown in Figure 3-29, the evolution of the modulus was very

sensitive the glass transition temperature. A significant decrease in the modulus

was observed as soon as the sample reached the glass transition region and

changed from glassy to rubbery state (T>Tg). Then the modulus remained low

until vitrification. Once the specimen passes the vitrification (T<Tg), its elastic

modulus started to increase as it evolved from the rubbery to the glassy state.

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Figure 3-29: Evolution of the elastic modulus with temperature and time for a

resin sample with an initial degree-of-cure 1 of 0.846

As the glass transition temperature is an important factor in the evolution of the

modulus, a resin modulus model was developed as a function of the difference

between the instantaneous cure and glass transition temperature, T*=T-Tg [58, 60]

and can be represented as shown in Figure 3-30. This model can be expressed as

follows:

Eq. 3-14

with using Eq.2-14.

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Table 3-7 presents the values of the fitting parameters obtained with the least

squares non linear regression method which give the best agreement with the

experimental data. Figure 3-31 compares the experimental and predicted resin

modulus obtained at 160ºC and 180ºC. Overall, the model captured both the onset

of the modulus decrease due to the glass transition and the vitrification at different

curing temperatures, with R2 values above 0.78.

This model neglects the viscoelastic characteristic of the resin. This can be

justified due to the slow curing process of the studied resin, which enables the

relaxation of the internal stresses generated before the vitrification. On the

contrary, in the case of a fast curing material system, the generated internal

stresses don’t have time to be relaxed and a modulus viscoelastic model have to

be considered.

Figure 3-30: Resin modulus model as a function of difference between

instantaneous and glass transition temperature (T*=T-Tg)

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Table 3-7: Parameters values of the elastic modulus model

Parameters Values

gel

T1

T2

T3

T4

E1

E2

E3

E4

AM

KM

0.700

-150ºC

-15.18ºC

-7ºC

5ºC

3.20 109 Pa

1.50 109 Pa

1.11 109 Pa

1.30 107 Pa

9.0 107 Pa

0.4ºC

Figure 3-31: Measured and predicted elastic modulus with time under two curing

temperatures, 160ºC and 180ºC

3.7 Summary and discussion

In this chapter, a comprehensive methodology was applied to characterize the

processing properties of the CYCOM 890RTM epoxy resin. The detailed

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procedure and techniques presented can be applied to intensive characterization

purpose of a wide range of thermoset resins.

The model parameters obtained from each characterization technique showed

close agreement with the experimental data.

1) A cure kinetics model taking into account the diffusion phenomena was

found to accurately predict resin cure kinetics behaviour for the Resin

Transfer Moulding processing condition range.

2) A chemorheological model was developed to accurately predict the onset

of resin gelation and the evolution of resin viscosity with temperature and

degree-of-cure.

3) The DiBenedetto equation was found to describe the cure dependence of

Tg well.

4) A two-phase linear model was used to predict the cure shrinkage

behaviour of the resin before and after the gel point in the same processing

condition range. A change in the shrinkage rate was detected due to the

liquid-solid transition.

5) Finally, two models taking into account the influence of Tg were

determined to describe the coefficient of thermal expansion and the elastic

modulus evolution during the cure, respectively. Far below Tg, the CTE

remained constant, whereas a linear variation of the CTE was found for

temperatures close and above Tg.

Two different methods were used to characterize to resin shrinkage. The first

method, a modified rheology method, involved a simple procedure to measure the

volumetric shrinkage after gelation with a rheometer and parallel plate geometry.

The second more complex method used the change in buoyancy of an immersed

sample in a fluid at constant temperature to determine the volumetric shrinkage

during the entire cure. Both methods measured the same amount of shrinkage

after gelation. Depending on the resin system and its manufacturing process, it is

possible to define which characterization method is more suitable to perform

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shrinkage measurement using two parameters: the degree-of-cure at gel point,

αgel, and the gel time, tgel.

1) For low αgel or short tgel (αgel < 0.2 or tgel < 10 min), the modified rheology

method is more appropriate to characterize the shrinkage evolution of the

resin. In that case, most of the shrinkage will occur after the gelation, and

the modified rheology method will be a simple but accurate way to capture

its evolution. As this method does not require sample preparation, even

resin with shorter processing window (tgel < 5 min) can be tested.

2) For high αgel or long tgel (αgel > 0.5 or tgel > 30 min), the gravimetric

method, less user friendly, is more appropriate as up to half of the total

shrinkage can occur before gelation and need to be measured. Resin

systems with long gel time are more suitable as the sample preparation can

take up to 10 minutes.

3) For intermediate αgel or tgel values, both methods can be used depending

on the amount of information desired.

This phenomenal approach provides a clear understanding of the resin processing

behaviour. In the next chapters, the developed material models will be then

implemented in a finite element software, ABAQUS/COMPRO CCA, to solve

coupled thermochemical-stress processing problems, to predict the final properties

of a composite structure manufactured by RTM.

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CHAPTER 4 Thermomechanical properties of fabric composites

After a detailed characterization of the resin properties, this chapter outlines the

influence of the fibre architecture on the elastic and thermal properties of

composite material. The reinforcement investigated in this study was a 5-harness

satin woven reinforcement made of G30-500 6k carbon fibre [134, 135].

The properties of woven fabric composite are usually modelled using the

properties of unidirectional crossply laminates. The influence of the fibre

waviness is therefore not taking into account. In order to verify the validity of this

assumption and determine how the fibre waviness affects the composite

properties, the thermomechanical properties of a 5-harness woven fabric and a

unidirectional crossply reinforcement were investigated using a micromechanical

approach on periodic units or unit cells with the finite element method. Knowing

the properties of the composite constituents (fibre and resin), the analysis of the

unit cell or smallest representative volume element (RVE) enables the

determination of the global properties of the composite structure. Three fibre

volume fractions (Vf) typical for the RTM process (between 50% and 62%) were

analyzed. For both unit cells, the fibre arrangement in the yarns was assumed to

be similar and follow a hexagonal packing. Table 4-1 presents the different types

of reinforcement studied and their respective fibre volume fractions. In order to

achieve the desired fibre volume fraction for the unit cells, the yarn fibre volume

fraction had to be modified as reported in Table 4-1. The following methodology

was then used to determine the thermomechanical properties of the crossply and

5-HS woven fabric unit cell as shown in Figure 4-1.

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Table 4-1: Types of reinforcement and their fibre volume fractions

Unit cell

Unit cell fibre

volume fraction

(Vf)

Yarn fibre volume

fraction (YVf)

Unidirectional crossply

62% 86%

55% 77%

50% 70%

5-Harness satin (5HS) woven

fabric

62% 86%

55% 77%

50% 70%

Figure 4-1: Applied methodology to determine the thermomechanical properties

of the unidirectional crossply and 5-harness woven fabric unit cells

The yarn thermomechanical properties were first determined using the properties

of the G30-500 6k carbon fibre and the cured CYCOM 890RTM epoxy listed in

Table 4-2 in the hexagonal unidirectional unit cells. The epoxy resin was

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considered isotropic and the carbon fibres orthotropic. The yarn fibre volume

fraction investigated were 70%, 77% and 86%. Then, these computed yarn

properties were used as input to the unidirectional crossply and 5-HS woven unit

cells at 50%, 55% and 62% fibre volume fraction.

Table 4-2: Carbon fibre and epoxy resin thermomechanical properties

Carbon fibre

G30-500 6k [134, 135]

Epoxy resin

CYCOM 890RTM [129]

E1,f = 230 GPa

E2,f = E3,f = 22 GPa Er = 3.1 GPa

ν12,f = ν13,f = 0.3

ν23,f = 0.35 νr = 0.3

G12,f = G13,f = 22 GPa

G23,f = 8.15 GPa Gr = 1.2 GPa

CTE1,f = -0.7x10-6

ºC-1

CTE2,f = CTE3,f = 8x10-6

ºC-1

CTEr = 55x10

-6 ºC

-1

*The subscripts f and r stand for fibre and resin respectively.

1, 2 and 3 correspond to the three principal direction of the material

4.1 Unit cell models

4.1.1 Unidirectional unit cell

An dimensionless unidirectional unit cell was modelled with a hexagonal packing

as seen in Figure 4-2. A circular cross section was assumed for the fibres.

Keeping a constant size for the unit cell, the fibre radius r was modified in order

to obtain the required Vf using the following relation:

Eq. 4-1

where L, w and h are the length, width and height of the unit cell.

The calculated radius values are presented in Figure 4-2 to obtain the 70%, 77%

and 86% fibre volume fraction required.

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The global coordinate system of the unit cell is represented by the axes (1, 2, 3).

Two material sections were defined for the resin and the fibre and a local

rectangular coordinate system (x, y, z) was created to apply the carbon fibre

orthotropic properties. This local system was based on three fixed points of the

geometry A, B and C, where A is the origin, B is a point lying on the x-axis and C

a point lying on the y-axis. The unit cell was meshed using 28990, 35640 and

30320 three-dimensional solid elements, type C3D8. The C3D8 element is an 8-

node linear brick element used for stress/displacement problems. Its degrees-of-

freedom are the displacements in the x-, y- and z- directions.

Figure 4-2: Unidirectional unit cell finite element model

4.1.2 Crossply unit cell

The dimensionless crossply unit cell model and its dimensions are shown in

Figure 4-3. Again a circular cross section was assumed for the fibres. In order to

achieve the desired fibre volume fraction, the fibre radius was kept constant and

the yarn fibre volume fraction was varied as described in Table 4-1. 68800 three-

dimensional 8-node solid elements, type C3D8, were used. Two material sections

were defined for the resin and the fibre. In order to identify the fibre orientations,

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two local rectangular coordinate systems, (x, y, z) and (x’, y’, z’), were created,

based on two sets of three fixed points of the geometry. The points A, B and C

were used to define the (x, y, z) coordinate system, and A’, B’ and C’ the (x’, y’,

z’) one, where A and A’ correspond to the origin, B and B’ are points lying on the

x and x’-axes respectively, and C and C’ define the y and y’-axes.

Figure 4-3: Crossply unit cell finite element model

4.1.3 5-harness satin unit cell

The development of the 5-harness satin woven unit cell was done in three steps.

First, the dimensions of actual unit cells were observed and measured. Then the

measured dimensions were applied to a preliminary unit cell model. From the YVf

and Vf obtained with this preliminary model, the dimension of the unit cell were

adjusted to the desired Vf.

Three unit cells were cut from a four plies laminate, manufactured by RTM with

the G30-500 6k 5HS carbon fibre and the CYCOM 890RTM epoxy. The length,

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width and thickness were first measured using a digital calliper. The cross section

of one unit cell was then observed under an optical microscope with the

magnification x50 in order to obtain the yarn dimensions. The cross section is

shown in Figure 4-4 wherein ellipsoidal yarn cross sections were observed. The

measured unit cell dimensions are reported in Table 4-3.

Figure 4-4: a) Cross-section of a 4 plies laminate, G30-500 6k carbon

fibre/CYCOM 890RTM epoxy resin, observed by optical microscope (x50), b)

detail of a yarn

Table 4-3: Measured dimensions of a 5-harness satin unit cell

Dimensions

Length (mm) 11.89 0.085

Width (mm) 11.21 0.151

Thickness (mm) 1.33 0.006

Yarn width (mm) 2.28 0.04

Yarn thickness (µm) 178 0.128

The laminate fibre volume fraction was determined to 62% using the following

equation [136]:

Eq. 4-2

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where is the fabric ply areal weight, ρf is the fibre density, n is the number of

plies and t is the laminate thickness. A fabric ply areal weight of 370 g/m2 and the

fibre density of 1.78 g/cm3 were provided by the manufacturer. Similarly, the

nominal ply thickness can be determined for each considered fibre volume

fraction using Eq. 4-2, as reported in Table 4-4.

Table 4-4: Nominal ply thickness as a function of the fibre volume fraction

Fibre volume fraction (Vf) Ply thickness (mm)

62% 0.34

55% 0.38

50% 0.42

Average 0.38

From these observations, a preliminary 5-harness satin fibre architecture was

developed with the following dimensions 11 mm x 11 mm x 0.38 mm. Because of

the 5-harness satin pattern, five yarns with a 170 µm thickness were positioned

along both the width and the length with a 0.2 mm gap in between the adjacent

yarns. This led to a yarn with a 2 mm width. The 5-harness satin architecture was

then created using TexGen [91], a software dedicated to the modelling of textile

structure in three dimensions. Based on the volumes generated by TexGen, the

YVf was estimated for each desired Vf using the following relationship:

Eq. 4-3

As shown in Table 4-5, it appeared that the 5-harness unit cell with the dimension

cited previously resulted in yarn fibre volume fraction of 95% for a global fibre

volume fraction of 62%. This YVf seems too high and not representative of what

can happen experimentally. Therefore the dimensions of the unit cell were slightly

modified to 12 mm x 12 mm x 0.36 mm. The gap between the adjacent strands

was set to 0.05 mm leading to a yarn width of 2.35 mm. With these modifications,

the yarn fibre volume fraction decreased to 86% at a fibre volume fraction of

62%, which seems more realistic.

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The unit cell volumes were then imported and meshed in a finite element

software. The mesh and the dimensions of the final unit cell are presented in

Figure 4-5. Once again, two material sections were defined for the resin and the

fibres and two local rectangular coordinate systems, (x, y, z) and (x’, y’, z’), were

created in order to identify the fibre orientations. To account for the fibre

waviness, these local systems were defined using the local numbering of each

element, so that the out-of-plane axes remained always normal to the element

surface, as shown in Figure 4-5-c. 11872 three-dimensional solid 8-node

elements, type C3D8, were used to mesh the geometry.

Table 4-5: Dimensions and characteristics of the preliminary and final 5-harness

satin unit cell

Preliminary 5-HS unit cell Final 5-HS unit cell

Vf (%) 62 55 50 62 55 50

Unit cell length

(mm) 11 11 11 12 12 12

Thickness

(mm) 0.38 0.38 0.38 0.36 0.36 0.36

Yarn width

(mm) 2 2 2 2.35 2.35 2.35

Yarn thickness

(µm) 170 170 170 170 170 170

Gap (mm) 0.2 0.2 0.2 0.05 0.05 0.05

Yarn volume

(mm3)

29.87 29.87 29.87 37.24 37.24 37.24

Unit cell volume

(mm3)

45.98 45.98 45.98 51.84 51.84 51.84

Yarn volume

fraction (%) 95 85 77 86 77 70

-99-

Figure 4-5: 5-harness satin unit cell: a) unit cell finite element model and

dimensions, b) yarn dimensions, c) schematic representation of the fibre

orientation along a yarn

4.2 Boundary conditions

4.2.1 Periodic constraints

The unit cell is a periodic unit representative of the global composite structure. In

other words, the global composite structure can be represented by a succession of

in-plane adjacent identical unit cells. Therefore continuity in displacement must

be satisfied at the unit cell boundaries to ensure that the adjacent unit cells cannot

be separated or superposed [137-140]. This means that the opposite faces of the

unit cell should deform identically and remain parallel to each other to maintain

the periodicity for any loading conditions. In order to fulfill this condition,

periodic constraints were applied on the nodes of the opposite faces. This required

-100-

first that the number of nodes on opposite faces and their distribution were

identical. Once an identical node distribution was ensured using the same mesh

seed on opposite faces, a simple program written in MATLAB was used to pair

the nodes having the same in-plane position, on opposite faces and edges. Then,

constraint equations were applied in term of displacements on each pair of nodes

to ensure the periodicity in the three global directions.

In the following, ui represents the displacement in the ith

-direction (i=1,2,3), Fj

represents the nodes on the face j, excluding the edges and corners nodes, Ekl

corresponds to the nodes located on the edge sharing the faces k and l, excluding

the corners nodes, and finally, Njkl stands for the corner node sharing the faces j, k

and l. The described notations are illustrated in Figure 4-6.

Figure 4-6: Unit cell faces, edges and corners notations

Then, the periodic constraint equations for the opposite faces were defined as

follows [137]:

Eq. 4-4

Eq. 4-5

Eq. 4-6

-101-

These equations ensure that the opposite faces F1 and F2, F3 and F4, F5 and F6

remain parallel for any loading conditions.

The periodic constraints on the opposite edges, to ensure that they remain parallel

for any boundary conditions, were expressed in the following manner [137]:

Eq. 4-7

Eq. 4-8

Eq. 4-9

Eq. 4-10

Eq. 4-11

Eq. 4-12

Eq. 4-13

Eq. 4-14

Eq. 4-15

4.2.2 Loading cases

Each model was loaded under seven different cases: three axial strains, three shear

strains and one temperature change to determine the nine engineering constants

and the coefficients of thermal expansion in the three directions. The axial and

shear strains were applied through fixed displacements on the corner nodes of the

unit cell.

-102-

Figure 4-7: Boundary conditions: a) for an axial loading, b) for a shear loading, c)

for a thermal loading

The axial strains simulated material tensile tests in the three global directions 1, 2

and 3. Normal displacements ui were applied to each corner nodes of the faces F2,

F4 and F5 while the opposite faces F1, F3 and F6 were fixed in the three directions.

For example, in the 1-direction, the corner nodes of F1 are fixed in the three

directions, while identical displacements u1 were applied at each nodes of F2 in

the 1-direction. The displacement of the corner nodes of F2 was also prevented in

the directions 2 and 3 as shown in Figure 4-7-a. These axial loadings enable the

determination of the three elastic moduli E1, E2 and E3 and the Poisson’s ratio ν12,

ν13 and ν23.

The shear strains were simulated by applying tangential displacements uj to each

corner nodes of the faces F2, F4, F5 while the opposite face F1, F3 and F6 were

-103-

constrained in the three directions. For example for the shear load in the 1-2

direction, the corner nodes of F1 were fixed in the three directions, and the corner

nodes of F2 were subjected to a displacement u2 in the 2-direction. The corner

nodes of F2 were also constraint in the directions 1 and 3 as shown in Figure 4-7-

b. These shear loads allow the determination of the shear moduli G12, G13 and G23.

Finally, an increase in temperature from 25ºC to 150ºC was applied to the unit cell

models in order to determine the coefficients of thermal expansion in the three

global directions. Each corner nodes of the faces F1, F3 and F6 were fixed in the

direction 1, 2 and 3 respectively as shown in Figure 4-7-c.

4.3 Thermomechanical properties

4.3.1 Determination of the thermomechanical properties

4.3.1.1 Elastic properties

Using the Hooke’s law, the constant of the stiffness matrix were first determined:

Eq. 4-16

For each loading cases, knowing the applied axial displacement ui or tangential

displacement uj, and the dimension of the unit cell li, the applied strain to the unit

cell, εij, was determined as follows:

Eq. 4-17

The stresses were calculated by dividing the reaction forces obtained at the fixed

corner nodes by the area of the face they belong.

Eq. 4-18

-104-

Once all the independent constants of the stiffness matrix were calculated, the

stiffness matrix was inversed to obtain the compliance matrix. From the

compliance matrix, the elastic moduli, shear moduli and Poisson’s ratio can be

extracted using Eq. 4-19.

Eq. 4-19

4.3.1.2 Coefficients of thermal expansion

The coefficient of thermal expansion in the ith

-direction, CTEi, is the ratio between

the strain in the ith

-direction, , and the variation in temperature, ΔT, as expressed

below:

Eq. 4-20

Similarly as mentioned previously, the strain was calculated using Eq. 4-17,

where the displacement ui,j corresponds to the measured displacement at the

corner nodes due to the thermal load.

4.3.2 Unidirectional unit cell thermomechanical properties

Table 4-6 presents the values of the elastic and shear moduli, Poisson’s ratios and

coefficients of thermal expansion, obtained numerically with the method

described above, in the case of the unidirectional unit cell. The material properties

of the carbon fibre and the epoxy resin, listed in Table 4-2, were used as input for

-105-

the finite element model. As expected, the elastic and shear moduli increase with

an increase in the fibre volume fraction, whereas the coefficients of the thermal

expansion decrease with an increase in fibre volume fraction.

Table 4-6: Comparison of the numerical and analytical values obtained for the

nine engineering constants and the coefficients of thermal expansion of the

unidirectional unit cell

Vf = 86% Vf = 77% Vf = 70%

Numerical

results

Theoretical

values

Numerical

results

Theoretical

values

Numerical

results

Theoretical

values

E1 (GPa) 198.18 198.23 177.95 177.81 161.76 161.93

E2 (GPa) 14.83 11.87 11.73 9.16 9.98 7.78

E3 (GPa) 14.82 11.87 11.73 9.16 9.98 7.78

ν12

ν13

ν23

0.300

0.300

0.354

0.300

0.300

-

0.300

0.300

0.356

0.300

0.300

-

0.300

0.300

0.362

0.300

0.300

-

G12 (GPa) 10.47 6.42 6.78 4.41 5.29 3.55

G13 (GPa) 10.45 6.42 6.78 4.41 5.29 3.55

G23 (GPa) 5.49 - 4.33 - 3.66 -

CTE1

(x10-6

ºC-1

) -0.57 -0.58 -0.47 -0.47 -0.37 -0.38

CTE2

(x10-6

ºC-1

) 14.32 16.88 19.44 22.58 23.50 27.01

CTE3

(x10-6

ºC-1

) 14.32 16.88 19.44 22.58 23.50 27.01

The numerical property values were compared to the analytical values obtained

with the strength material approach presented in CHAPTER 2, section 2.1.2. As

expected the analytical values underestimate the material mechanical properties in

the transverse direction, and good agreements were found in the longitudinal

direction. The stress distributions for the unidirectional unit cell at 70% fibre

volume fraction are presented in Figure 4-8 for the axial and shear loadings.

Similar stress distributions were observed at 77% and 86% fibre volume fractions.

-106-

Figure 4-8: Axial and shear stress distributions of the unidirectional unit cell at

70% fibre volume fibre

These elastic constants and coefficients of thermal expansion, obtained from the

unidirectional models, were used as input for the yarn properties at different fibre

volume fractions in the crossply and 5-harness satin models.

-107-

4.3.3 Crossply and 5-harness satin unit cells thermomechanical

properties

The material properties of the epoxy resin listed in Table 4-2 were used as input

for the resin properties for the finite element models. In those models, the yarn

fibre arrangement was assumed to be hexagonal, and the yarn fibre volume

fractions different from 1. Therefore, as explained previously, the material

properties of the unidirectional models, listed in Table 4-6, were used as input for

the fibre properties in the finite element models.


for the crossply unit cell for different fibre volume fractions

Vf = 62% Vf = 55% Vf = 50%

Yarn Vf 86% 77% 70%

E1 (GPa) 76.78 68.83 62.29

E2 (GPa) 76.78 68.83 62.29

E3 (GPa) 9.93 8.71 7.94

ν12

ν13

ν23

0.037

0.369

0.369

0.035

0.374

0.374

0.035

0.380

0.380

G12 (GPa) 4.96 3.91 3.36

G13 (GPa) 3.60 3.09 2.77

G23 (GPa) 3.60 3.09 2.77

CTE1 (x10-6

ºC-1

) 1.75 2.12 2.50

CTE2 (x10-6

ºC-1

) 1.76 2.14 2.52

CTE3 (x10-6

ºC-1

) 35.77 41.51 46.09

-108-


for the 5-harness satin unit cell for different fibre volume fractions

Vf = 62% Vf = 55% Vf = 50%

Yarn Vf 86% 77% 70%

E1 (GPa) 74.24 65.95 59.44

E2 (GPa) 74.31 65.95 59.44

E3 (GPa) 9.50 8.42 7.72

ν12

ν13

ν23

0.059

0.380

0.380

0.056

0.384

0.384

0.054

0.388

0.388

G12 (GPa) 7.32 4.95 3.97

G13 (GPa) 3.32 2.91 2.65

G23 (GPa) 3.32 2.91 2.65

CTE1 (x10-6

ºC-1

) 1.62 2.04 2.49

CTE2 (x10-6

ºC-1

) 1.62 2.03 2.48

CTE3 (x10-6

ºC-1

) 37.55 42.92 47.31

Table 4-7 and Table 4-8 present the engineering constants and the coefficients of

thermal expansion of the crossply unit cell and the 5-harness satin unit cell

respectively. As expected, the properties of the crossply and the 5-harness satin

are orthotropic with E1=E2, ν13=ν23, G13=G23 and CTE1=CTE2. In both cases, the

elastic properties of the unit cells increased with an increase in the fibre volume

fraction, whereas the coefficients of thermal expansion decreased with Vf. The

stress distributions, in the case of axial and shear loadings, of the crossply and 5-

HS unit cells at 50% fibre volume fraction are presented in Figure 4-9 and Figure

4-10 respectively. Similar stress distributions were observed at 55% and 62%

fibre volume fractions.

-109-

Figure 4-9: Axial and shear stress distributions of the crossply unit cell at 70%

fibre volume fraction

-110-

Figure 4-10: Axial and shear stress distributions of the 5-HS unit cell at 70% fibre

volume fraction

Figure 4-11 to Figure 4-15 compare the value of the elastic moduli, the shear

moduli, Poisson’s ratios and the coefficients of thermal expansion obtained for the

crossply and 5-harness satin unit cells. From Figure 4-11, it can be noticed that

the in-plane elastic moduli, E1 and E2, are slightly smaller for the 5-harness satin

unit cell than for the equivalent unidirectional crossply unit cell. This is due to the

fibre undulation that reduces the fibre strength in the in-plane directions. No

difference between the two unit cells was noticed for the through-thickness elastic

modulus E3 because of the matrix-dominated behaviour in that direction.

On the other hand, the in-plane shear modulus G12 is noticeably higher for the 5-

harness satin than for the crossply as shown in Figure 4-12. This behaviour is

caused by the yarn interlacing in the 5-harness satin woven reinforcement. As for

the through-thickness elastic modulus, the out-of-plane shear moduli, G13 and G23,

are comparable for the crossply and 5-harness satin composites. An in-plane

-111-

modulus of 64 GPa and an in-plane shear modulus of 4.3 GPa were determined

experimentally by the manufacturer for a 55% fibre volume fraction carbon epoxy

laminate with the CYCOM 890RTM epoxy resin and a 5HS woven fabric with

similar properties to the G30-500 6k carbon fibre. These experimental values are

similar to the one obtained numerically.

As presented in Figure 4-13, the in-plane 5-harness satin Poisson’s ratio values,

ν12, are higher than those of the corresponding crossply laminate at the same Vf,

again as a result of the fibre undulation. Similarly the out-of-plane Poisson’s ratio

values, ν13 and ν23, are higher for the 5-harness satin composite than the crossply

unit cell.

Finally, concerning the thermal properties presented in Figure 4-14 and Figure

4-15, the 5-harness satin laminate gives slightly higher through-thickness CTEs

than the crossply laminate, and comparable in-plane CTE were observed.

Figure 4-11: Elastic modulus comparison for the crossply unit cell and the 5-

harness satin unit cell

-112-

Figure 4-12: Shear modulus comparison for the crossply unit cell and the 5-


Figure 4-13: Poisson’s ratios comparison for the crossply unit cell and the 5-


-113-

Figure 4-14: In-plane coefficients of thermal expansion comparison for the

crossply unit cell and the 5-harness satin unit cell

Figure 4-15: Through-thickness coefficients of thermal expansion comparison for

the crossply unit cell and the 5-harness satin unit cell

-114-

These results are in agreement with previous experimental and numerical studies

on the thermomechanical behaviour of plain weave fabric composites by Naik and

Ganesh [79-82]. Their investigation demonstrates that the thermomechanical

properties of plain weave laminate are dependent of the architecture strand crimp

and the gap between adjacent strands. Lower strand crimp results in lower CTE

values for the plain weave laminate compare to the crossply laminate and the

Young’s modulus of woven laminate with small gap is slightly smaller than the

one the of crossply laminate with the corresponding Vf. The 5-harnes satin model

can be considered as a low strand crimp woven laminate, and therefore the results

obtained agree well with those conclusions.

The coefficients of thermal expansion were also measured experimentally. Four

5-harness satin plies laminate, with the layup [(0/90)(90/0)]s was manufactured by

RTM. The fibre volume fraction, Vf, was related to the cured specimen thickness

using Eq. 4-2. The sample thickness was measured at three to five different

locations with a calliper. A fibre volume fraction of 59.4% was determined. Using

a precision diamond saw, the laminate was cut into 12x12 mm unit cells. Then,

TMA tests were carried out to measure the coefficients of thermal expansion in

the three directions. A force of 0.05N was applied to the probe to ensure a

constant contact with the composite sample. Three cycles from room temperature

up to 220ºC, then back down to room temperature, at a rate of 3ºC/min were

performed for each sample. The results are reported in

Table 4-9 and Figure 4-14 and Figure 4-15. The experimental values are greater

than the numerical values but remain in the same order of magnitude. This

difference might be because the fibre volume fraction of the laminate

manufactured by RTM is smaller than the one calculated by Eq. 2-25, due to the

presence of voids or resin rich areas.

-115-

Table 4-9: Experimental values of the coefficients of thermal direction obtained

by TMA for a 5-Harness satin unit cell with Vf = 59.4%

CTE CTE1

(x10-6

ºC-1

) CTE2

(x10-6

ºC-1

)

CTE3

(x10-6

ºC-1

) CTE3

(x10-6

ºC-1

)

T<Tg T>Tg

Test 1 Heating 2 3.337 3.669 52.98 178.6

Cooling 2 3.140 3.765

Heating 3 3.132 3.733 52.12 188.4

Cooling 3 3.110 3.730

Test 2 Heating 2 2.997 3.563 56.03 190.3

Cooling 2 3.000 3.441

Heating 3 2.975 3.503 54.69 191.6

Cooling 3 3.081 3.492

Average 3.096 3.612 53.95 187.2

Standard

deviation 0.1169 0.1272 1.746 5.907

4.3.4 Evolution of the 5-HS unit cell stresses during the cure cycle

Using the finite element software ABAQUS and the COMPRO Component

Architecture (CCA), the evolution of the stresses in the 5-harness satin unit cell

during a typical cure cycle of the epoxy resin can be predicted. A heat transfer

analysis was first performed, followed by a stress analysis. The

stress/displacement elements (C3D8), used for the stress analysis, were replaced

by 8-node linear brick heat transfer elements (DC3D8) in the heat transfer

analysis. This type of element only has the temperature as degree of freedom. The

simulated cure cycle was two hours at 180ºC followed by a cool down to 25ºC at

1ºC/min. The material constitutive models of the one-part epoxy resin, CYCOM

890RTM, developed in CHAPTER 3, were implemented in the COMPRO CCA

material database. The properties of the yarn, presented in Table 4-6, were used as

the fibre properties in the finite element model. Figure 4-16 to Figure 4-18 show

the stresses in the x-, y-, and z-directions at different times for a 5-HS unit cell

with a 50% fibre volume fraction and 70% yarn fibre volume fraction. In order to

-116-

observe the state of stress inside the unit cell, the model was cut in two along the

(yz) plane. Before the gel point, no stresses were present in the unit cell. Small

compressive stresses arose after the gel point due to the resin shrinkage at the

fibre overlap. The compressive stresses increased during the isotherm with a

maximum compressive stress around -20 MPa at the end of the temperature hold

in the three directions. At the end of the cure cycle, the fibres remained in

compression with stresses around -50 to -100 MPa. The resin is in tension in the

in-plane direction and in compression in the through-thickness direction. Similar

results were obtained for the 55% and 62% fibre volume fraction 5-HS unit cell.


the gel point (t = 70 minutes)

-117-


the end of the isotherm (t = 120 minutes)

-118-


the end of the cool down (t = 275 minutes)

From these results, the composite shrinkage coefficients c can be as well

estimated using the dimension variations of the unit cell Δli during the cure as

follows:

Eq. 4-21

where l is the unit cell initial dimension, Δl is the change in dimension between

the gel point and the end of the isotherm and the subscript i represent the principal

directions x, y and z.

-119-

The composite shrinkage coefficients of the 5-harness satin unit cell, for the three

fibre volume fraction investigated, are reported in Table 4-10. Due to the

influence of the fibres, the in-plane composite shrinkage coefficients are small. In

the direction 3, the behaviour of the composite is dominated by the resin.

Therefore, the composite shrinkage coefficient is greater in that direction, and

decreases as the fibre volume fraction increases.

Table 4-10: Composite shrinkage coefficients for the 5-harness satin unit cell at

62%, 55% and 50% fibre volume fractions

Vf = 62% Vf = 55% Vf = 50%

Yarn Vf 86% 77% 70%

c,1 (x10-6

m/m) 8.33 8.33 8.33

c,2 (x10-6

m/m) 8.33 8.33 8.33

c,3 (x10-3

m/m) 2.47 2.51 2.54


In this chapter, the thermomechanical properties of 5-harness satin woven

laminate were investigated and compared to an equivalent unidirectional crossply

laminate using a micromechanical approach. Various fibre volume fractions were

investigated corresponding to typical volume fraction used in the RTM process.

The following trends were observed:

1) Elastic modulus: due to the fibre waviness, the in-plane moduli of the

5-harness satin laminate, E1 and E2, are a slightly smaller than a

unidirectional crossply laminate with the same fibre volume fraction,

and the through-thickness moduli, E3, are very comparable.

2) Shear modulus: the in-plane shear modulus of the 5-harness satin

laminate, G12, is noticeably higher than the crossply one, especially

with for high fibre volume fraction because of the yarn interlacing

effect. The out-of-plane shear moduli, G13 and G23, remain

comparable.

-120-

3) Poisson’s ratio: because of the fibre undulation, the in-plane 5-harness

satin Poisson’s ratio, ν12, is higher than the corresponding crossply

laminate at the same Vf. The out-of-plane Poisson’s ratio, ν13 and ν23

are comparable for the two unit cells.

4) Coefficient of thermal expansion: the 5-harness satin laminate gives

a slightly higher through-thickness CTEs than the crossply laminate

and a comparable in-plane CTE.

These results demonstrate that the properties of the 5-harness satin woven fabric

and the equivalent unidirectional crossply laminate are slightly different but

overall comparable. This validates the use of the properties of unidirectional fibre

to model the behaviour of this type of fabric architecture. Using the

ABAQUS/COMPRO CCA platform, the evolution of the stress in the 5-harness

satin unit cell was also predicted and the composite shrinkage coefficients were

determined.

The thermomechanical properties of the unidirectional fibre with a YVf of 70%

will be therefore implemented with the detailed properties of the resin in the

ABAQUS/COMPRO CCA platform in order to predict the properties of a 5-

harness satin carbon/epoxy composite structure at 50% fibre volume fraction.

-121-

CHAPTER 5 Investigation of the tool-part interaction by fibre Bragg grating sensors

This chapter focuses on the influence of the tool-part interaction on the process-

induced stresses. As explained in CHAPTER 2, section 2.2.3, most of the studies

investigating the tool-part interaction focused on open mould process (i.e

autoclave or vacuum bag processes) whereas few studies have been conducted on

the effect of tool-part interaction for closed mould processes such as RTM.

However, the interaction between the mould and the laminate is quite different for

these two processes as shown in Figure 5-1.

Figure 5-1: Schematic representation of the open and closed mould processes, a)

before the cure, b) at the end of the cure

Autoclave or vacuum bagging processes consist of a flexible membrane and a

solid mould whereas the RTM process consist of two solid moulds with a constant

-122-

cavity volume. At the beginning of both processes, the laminate and the mould

cavity have the same thickness t0. In the case of the autoclave process, an external

pressure Pa is applied to the flexible membrane during the entire cure cycle,

leading to a compaction of the laminate. The contact between the composite

structure and the solid mould is maintained until the end of the cure cycle. For the

RTM process, the pressure is applied to the resin through the injection pressure,

Pinj, at the beginning of the cure cycle. During the cure, the resin cure shrinkage

decreases the laminate thickness to a value t. As the mould cavity remains

constant with a thickness t0, this can lead to a loss of contact between the mould

and the composite part and poor surface finish [100, 141]. This phenomenon does

not happen in the autoclave process due to the autoclave pressure Pa applied

continuously to the flexible membrane and compensates for changes in laminate

thickness. This difference of the tool-part interaction mechanism might have an

influence on the process-induced stresses and laminate deformations. Therefore

the tool-part interaction was investigated in the RTM process using fibre Bragg

grating optic sensors and then modelled using finite element method. The

experiments were carried out at the laboratory of Polymer and Composite

Technology from the École Polytecnique Fédérale de Lausanne (EPFL) in

Switzerland.

5.1 Fibre Bragg grating sensor principle

Strain gauges are a common method to measure the strain development

throughout the cure cycle [92, 109]. However, it is difficult to embed the strain

gauges into composite laminates and they are usually mounted on the tool.

Alternatively, fibre optic sensors appear to be an interesting method to measure

in-situ, the development of the residual strains during composite manufacturing

[111, 125, 142-148], as well as the material transition (gel point, glass transition)

[143] or the degree-of-cure [149]. Their advantage over strain gauges is that they

can be easily integrated in the composite at the performing stage of the

manufacturing. Small and non-intrusive, they have also a minimal impact on the

-123-

mechanical properties of the composite. Different kind of fibre optic sensors can

be used, such as fibre Bragg grating (FBG) sensors [111, 125, 143, 147, 148],

extrinsic Fabry-Perot interferometric (EFPI) sensors [142, 144, 146, 149] or

FBG/EFPI hybrid sensors [145]. In this work, FBG sensors were used to measure

the development of internal strain in a composite laminate manufactured by RTM,

as the cure progresses.

A fibre Bragg grating (FBG) sensor is an optical fibre with a periodic

modification of the core refractive index along the fibre. A phase mask technique

is commonly used to imprint the periodic pattern to the optical fibre. This

technique uses the optical fibre photosensitivity property: by exposing an optical

fibre under ultraviolet light, its refractive index can be modified permanently.

Figure 5-2 details the phase mask technique. A piece of silica glass, transparent to

ultraviolet light, with a grating pattern with a period of Λmask on one side is used as

a phase mask. When ultraviolet light passes through the mask, it is diffracted by

mask grating pattern. When the UV diffracted beams reach the optical fibre, they

photoimprint, i.e. change locally its refractive index, with a grating period ΛB,

equal to half of the pattern period ( ). Then, when a source of light is

connected to the optical fibre with a FBG, only a narrow-band of the signal is

reflected with the Bragg wavelength λB, given by [150]:

Eq. 5-1

where n is the effective refractive index of the core and ΛB is the grating period.

-124-

Figure 5-2: Phase mask grating technique (adapted from [150])

Any change in the optical fibre properties which varies the grating period or the

refractive index, such as strain or temperature, will then change the Bragg

wavelength. In the case of an axial applied strain Δεapp and a temperature change

ΔT, the Bragg wavelength shift ΔλB can be related to both the temperature T and

the strain ε, as follows:

Eq. 5-2

where Kε and KT are the strain and temperature sensitivities of the optic sensor and

αf is the fibre optic coefficient of thermal expansion.

When the FBG optic sensor is embedded in a host structure of a different material,

such as a composite laminate, and assuming a perfectly bounded interface

between the two, the thermal strain of the host structure can influence the

response of the FBG sensor [111]. Eq. 2-25 can be then modified as follows:

Eq. 5-3

-125-

where Δεtot is the total strain transferred to the optical fibre and Δεth is the thermal

strain experienced by the host material that can be expressed in the following

manner:

Eq. 5-4

where CTEH is the coefficient of thermal expansion of the host material.

5.2 Experimental procedure

5.2.1 RTM process

Radial injections were carried out at constant pressure in a rectangular steel mould

to manufacture carbon/epoxy laminates with a 50% fibre volume fraction and the

following dimensions: 34.5 cm x 24.5 cm x 0.2 cm. Figure 5-3 and Figure 5-4

present the mould and the RTM set-up. Six heating cartridges on each side of the

mould (top and bottom) were used to apply the desired cure cycle. The mould

surface was treated with release agent (Frekote 770-NC) and flexible silicone

joints were used to seal the mould. Five plies of 5-harness satin G30-500 6k

carbon fabric [134, 135] were stacked with the following layup

[(0/90)(90/0)(0/90)(0/90)(90/0)]. The preform was debulked 30 minutes under

vacuum to remove the eventual entrapped air. Once the preform was placed into

the mould, the mould was closed and the system was preheated at 180ºC prior the

resin injection. Vacuum was as well applied to the mould cavity in order to

facilitate the resin injection. The CYCOM 890RTM one-part epoxy resin [129]

was not degassed before the injection but preheated at 80ºC in the injector to

reach its optimal viscosity and injected in the mould with injection pressure of

0.35MPa. The filling time was less than 5 minutes for all injected plates.

Two cure cycles were applied as shown in Figure 5-5:

- Cure cycle 1 : 2 hours isotherm at 180ºC (CYCOM 890RTM epoxy

typical cure cycle)

- Cure cycle 2: two holds cure cycle, 2 hours at 170ºC following by 30

minutes at 190ºC.

-126-

The cure cycle 2 was designed so that the resin reaches the gel point during the

first temperature hold and to determine the influence of the cure cycle on the

development of the internal strain. Two plates were manufactured for each cycle.

Figure 5-3: RTM steel mould: a) mould opened, b) perform inside the mould

-127-

Figure 5-4: RTM experimental set-up

Figure 5-5: Applied cure cycle to the RTM process

After the cure, the laminates were placed in an oven and subjected to a set of 15

minutes isotherms at 35ºC, 50ºC and 70ºC with 1ºC/min temperature ramp in

-128-

between. Using the FBG already embedded in the laminate, the strain variation

was measured during these particular conditions in order to determine the

coefficient of thermal expansion of the cured laminate.

5.2.2 FBG sensors

The FBG sensors were provided by Technica SA. Their initial wavelength was

1562 0.5 nm with a bandwidth inferior to 0.3 nm, and a diameter of 210 5 µm.

Their strain and temperature sensitivity (Kε and KT) were 7.7x10-7

µε-1

and

6.92x10-6

ºC-1

respectively.

Previous studies reported a decrease in the fibre optic response followed by a

stabilisation while ramping up the temperature [151]. In order to assure the

thermal stability of the Bragg wavelength with temperature, a preconditioning or

pre-annealing is then necessary. It consists of heating the FBG in an oven at

elevated temperature to accelerate the decay phenomenon and reach the moment

where the Bragg wavelength remains stable with temperature. As the curing

temperature of the composite is 180ºC, the FBG sensors were preconditioned 24

hours at 200ºC in an oven before use. Figure 5-6 shows a FBG sensor after

preconditioning.

Figure 5-6: Preconditioned fibre Bragg grating sensor

After the preconditioning, the initial optical fibre wavelength, λB0, was recorded

prior embedding the sensor in the laminate. For each laminate, three FBG sensors

were positioned at the center of the laminate, through the thickness of the

-129-

laminate, at the bottom, middle and top surface, as shown in Figure 5-7. A

thermocouple type K was also placed in the mould cavity to monitor the

temperature of the composite part inside the mould. An optical sensing

interrogator sm125-500 from Micron Optics was used to monitor the variation of

the FBG wavelength λB during the entire cure.

Figure 5-7: FBG sensors position in the laminate

5.3 Experimental results

For each cure cycle, two plates were manufactured. However, in some cases, the

connection between some of the FBG and the optical sensing interrogator failed

during the experiment and the wavelength variation was not recorded entirely.

Therefore, in the following, only the experiments where the data of the three FBG

were completely recorded are presented. Nevertheless, the experiments with the

partial data were compared to the one with the full set of data, and showed good

agreement.

5.3.1 Measured in-plane strains: cure cycle 1

Figure 5-8 presents the wavelength variation of the three FBG sensors during the

entire cure cycle. The wavelength variation was set to zero at the beginning of the

recording (t=0 minutes). First, the wavelength increased as the mould heated-up

and the sensors expanded with the temperature. Then a decrease in the wavelength

was observed at the injection due to the temperature gradient between the mould

and the resin. As the resin was colder than the mould, the sensors contracted when

-130-

the resin reached them. During the isotherm, the wavelength remained constant

and it decreased at the cool down. A wavelength discontinuity was observed at

around 250 minutes in the cool down which corresponds to a separation of the

composite from the mould, as explained in the following.

Figure 5-8: FBG sensor relative wavelength variation and temperature during cure

cycle 1

Using Eq. 5-3, the total strain variations (Δεtot) in the laminate during the cure

were calculated and plotted in Figure 5-9. During the mould heat-up stage, before

the resin injection, the FBG sensor is not bonded to the dry fibres. As there is not

fixed contact points between the sensor and the fabric, the strain occurring in the

fabric might not be totally transferred to the FBG, and the measured strain might

not be consistent and reliable. For these reasons, the strains were then set to zero

at the beginning of the injection as shown in Figure 5-10. Also, once the resin is

injected, the strain transfer between the composite and the FBG sensor might not

be optimum up to the gel point, as the resin acts as a viscous liquid before that

point. Thus the data provided by the FBG sensors before the gel point have to be

-131-

used with caution. For this epoxy resin, the gel point occurs around 70 minutes

after the injection at 180ºC.

Figure 5-9: In-situ strain variation during cure cycle 1

Figure 5-10: In-situ strain variation from the injection to the end of cure cycle 1

-132-

Overall, the composite remained in compression during the cure. Small

compressive strains were introduced in the laminate at the injection (around -50

µε). Then the strain remained constant during the two hour isotherm at 180ºC.

Since the FBG sensors captured the in-plane strains, the resin shrinkage was not

clearly observable. During the cool down, a strain discontinuity was observed at

around 250 minutes or 150ºC. This behaviour corresponded to the composite plate

separation from the mould because of the coefficient of thermal expansion (CTE)

mismatch between the composite and the steel tool. Figure 5-11, showing the

strains as a function of temperature confirmed this assumption.

The evolution of the strain with the temperature was linear with two different

slopes before and after the discontinuity. A slope of 15.3x10-6

ºC-1

, corresponding

to the CTE of steel, was measured before the discontinuity (150°C<T<180°C).

The slope changed to 4.46x10-6

ºC-1

after the discontinuity (25°C<T<150°C). This

value is in the order of magnitude of the in-plane coefficient of thermal expansion

of the composite with a 50% fibre volume fraction (CTE1 = 2.49x10-6

ºC-1

, CTE2

= 2.48x10-6

ºC-1

), as seen in CHAPTER 4, Table 4-8. Thus, during the cool down,

the composite followed the thermal contraction of the steel mould until the shear

stress at the interface mould/composite becomes too high and the laminate

separated from the mould. A similar phenomenon was as well observed for

laminate manufactured by the autoclave [111]. At the end of the cool down, the

composite remained in compression with the value of the residual strain around -

700 µε.

-133-

Figure 5-11: In-situ strain variation with the temperature for cure cycle 1

From Figure 5-10, the strain variation at the top and middle of the laminate

appeared to be slightly higher than in the bottom of the laminate. However, this

observation was not repeatable from one laminate to another. Actually, the FBG

response can be also influenced by the FBG position and its local interaction with

the woven fabric. For example, the alignment of the FBG with respect to the fibre

orientation has an influence on the strain measurement. This parameter is difficult

to control in the RTM process as the resin flowing in the preform can modify the

FBG initial position. Therefore, in that case, we can assume that the alignment of

the middle FBG sensors was slightly different from the top and bottom ones. As

the plate is only 2 mm thick, the strain variation at different position through the

thickness should be similar.

5.3.2 Measured in-plane strains: cure cycle 2

The same approach was applied to the cure cycle 2. The influence of the cure

cycle on the development of the internal strain was then observed. Figure 5-12

presents the relative wavelength variation for the cure cycle 2. Similarly as in cure

-134-

cycle 1, the wavelength increased first as the mould temperature increased. Then a

small decrease in wavelength is observed when the resin is injected into the

mould. The wavelength remained constant during the first isotherm at 170ºC and

increased as the temperature increased to the second isotherm at 190ºC. During

the cool down, the wavelength decreased, and a discontinuity was observed at

around 350 minutes. Using Eq. 5-3, the strain variation was then extracted and set

to zero at the injection, as shown in Figure 5-13. Small compressive strains

around -50 µε were introduced at the injection. The strain remained constant

during the first isotherm, and increased at the second hold due to the part

expansion with temperature. During the cool down, a stain variation is noticed at

around 350 minutes or 150ºC that again corresponded to the separation of the

composite from the mould. The debonding occurred at the same temperature as

for the cure cycle 1. The evolution of the strain with the temperature in Figure

5-14 also confirms this behaviour. From 190ºC to 150ºC, the composite behaved

similarly as the steel mould with a thermal expansion of 12.6x10-6

ºC-1

. After the

discontinuity, from 140ºC to 25ºC to thermal expansion changes to 4.34x10-6

ºC-1

,

which is in the order of magnitude of the in-plane composite CTE as seen

previously. At the end of the cool down, the composite remained in compression

with the value of the residual strain around -700 µε. As suggested previously, the

difference between the strain measurements through the thickness might be due to

a change of the FBG position at the injection or during the cure cycle.

-135-

Figure 5-12: FBG sensor relative wavelength variation during cure cycle 2

Figure 5-13: In-situ strain variation during cure cycle 2 from the injection to the

end of the cool down

-136-

Figure 5-14: In-situ strain variation with the temperature for the cool down of cure

cycle 2

Figure 5-15: Comparison of the strain variation at the laminate mid-thickness for

the two cure cycles.

-137-

Figure 5-15 compares the strain variation obtained for the two cure cycles at the

laminate mid-thickness. The change in cure cycle did not seem to affect the

laminate properties as well as the interaction between the mould and the

composite plate. The debonding occurred at the same temperature and similar in-

plane strains were obtained at the end of the two cure cycles.

5.3.3 Laminate coefficient of thermal expansion

The laminates with the embedded FBG sensors were heated up in an oven and

subjected to a succession of isotherms and temperature ramps at 1ºC/min. The

measured strain and the temperature are plotted in Figure 5-16. Then the

coefficients of thermal expansion were determined for each ramps as well as the

cool down by measuring the slope of the strain with the temperature and were

reported in Table 5-1. Overall, the in-plane coefficient of thermal expansion of the

laminate (CTEc) was around 2.5x10-6

ºC-1

. This value is in agreement with the in-

plane coefficients of thermal expansion obtained numerically with the 50% 5-

harness satin woven unit cell model reported in Table 4-8 (CTE1 = 2.49x10-6

ºC-1

,

CTE2 = 2.48 x10-6

ºC-1

) and confirms the validity of the micromechanical

approach used in CHAPTER 4. This value is lower than the value in the mould

after the separation of the laminate from the mould (Figure 5-11 and Figure 5-14).

Thus, it can be assumed that, after the separation, a small interaction between the

laminate and the mould still remains as the apparent composite CTE in the mould

is higher than the CTE obtained for a free standing laminate.

-138-

Figure 5-16: Temperature and strain variation during the post-cure of the laminate

Table 5-1: Coefficient of thermal expansion measured at the post cure

Laminate CTE (cure cycle 1)

(ºC-1

)

Laminate CTE (cure cycle 2)

(ºC-1

)

FBG middle* FBG top

* FBG bottom

* FBG top

*

Heating ramp 1 1.62 10-6

2.14 10-6

2.05 10-6

1.53 10-6


2.56 10-6

2.66 10-6

2.06 10-6


2.73 10-6

2.89 10-6

1.49 10-6

Cool down 2.59 10-6

3.30 10-6

2.77 10-6

1.31 10-6

Average 2.18 10-6

2.68 10-6

2.59 10-6

1.60 10-6

*As the optical sensing interrogator had only four inputs, only two FBG per plate were linked to

the device.

5.3.4 Maximum shear stress determination

From these experiments, the maximum shear stress that the composite can sustain

before the separation of the laminate from the mould can be determined. Figure

5-17 describes the development of the shear stress at the mould/composite

interface, due to the difference in coefficient of thermal expansion between the

mould and the composite.

-139-

Figure 5-17: Shear stress formation due to the mismatch of the thermal expansion

between the composite and the mould at the cool down

The shear stress τ is related to the composite in-plane stress σC, which is related to

the composite mechanical strain εC,M by the composite Young’s modulus EC, as

follows:

Eq. 5-5

where t is the laminate thickness and L0 is the laminate length. The value of the

elastic modulus, determined in CHAPTER 4 for the 5-harness satin woven unit

cell at 50% fibre volume fraction (Table 4-8, E1 = 59.44GPa), was assumed to be

the Young’s modulus of the composite Ec.

The mechanical strain is the difference between the total strain εC,tot measured by

the top and bottom FBG sensors and the free thermal expansion εC,TH as expressed

below:

Eq. 5-6

-140-

where CTEC is the in-plane coefficient of thermal expansion of the composite

determined experimentally using the FBG and ΔT is the temperature variation.

The total strain corresponds to the maximum strain variation sustained by the

laminate at the interface before the separation, and was measured as follows:

Eq. 5-7

where εtot,i and εtot,f are the total strains measured by the top and bottom FBG

sensors at the beginning of the cool down and before the strain discontinuity, as

shown in Figure 5-10 and Figure 5-13.

The different values obtained for the maximum shear stress were reported in

Table 5-2. Using Eq.3, the residual stress in the composite were estimated around

-20 MPa at the end of the process.

Table 5-2: Maximum shear stress for the two cure cycle

Maximum shear

stress (kPa)

Cure cycle 1

Maximum shear

stress (kPa)

Cure cycle 2

FBG bottom 134 128

FBG top 136 170

Average 140 18

5.4 Tool-part interaction modelling

The RTM process and the tool-part interaction between the composite and the

mould was then investigated numerically using the commercial finite element

software ABAQUS and the COMPRO Component Architecture (CCA)

subroutine. As explained in CHAPTER 2 section 2.3.4, a heat transfer analysis

was first performed, followed by a stress analysis. In each analysis, three steps

were defined: an isothermal cure, a cool down and the demoulding. The

demoulding of the part was simulated by removing all the tooling element and

constraints from the composite part.

-141-

5.4.1 Geometry and finite element mesh

A 2 mm thick composite plate and a steel rectangular mould were modelled using

the actual dimensions of the RTM mould and the manufactured composite plate.

Due to the problem symmetry, only one quarter of the system was analyzed as

shown in Figure 5-18-a. A 1 cm gap between the mould and the composite sides

was added to allow the composite part to expand and not exceed the tool

boundaries (Figure 5-18-b). From Chapter 4, it was noticed that the properties of a

5-Harness fabric ply can approximate fairly well by an equivalent [0/90] non-

crimp fabric. Therefore, five plies 5-Harness satin laminate

[(0/90)(90/0)(0/90)(0/90)(90/0)] at 50% fibre volume fraction was modelled by

ten unidirectional layers with the following layup [0/90/90/0/0/90/0/90/90/0]. At

0º, the fibre were oriented in the length of the plate, as shown in Figure 5-18-c.

Ten elements were used for each layer through the composite thickness. Three-

dimensional 8-node solid elements were used: DC3D8 for the heat transfer

analysis and C3D8 for the stress analysis. The plate and the mould were meshed

with 8160 and 8640 elements respectively.

-142-

Figure 5-18: Composite plate and steel mould finite element model: a) finite

element mesh of the laminate, b) finite element mesh of the mould and the

laminate, c) close-up of the laminate finite element mesh in the mould, d)

schematic position of the analyzed element

5.4.2 Material model

The material constitutive models of the one-part epoxy resin, CYCOM 890RTM,

developed in CHAPTER 3, were implemented in the COMPRO CCA material

data base. The properties of the fibre with yarn fibre volume fraction of 70%,

developed in CHAPTER 4 (Table 4-6) were used as input in the finite element

model and are presented in Table 5-3. The fibre properties were assumed constant

and independent from the cure cycle. As the cure progresses, the thermoset resin

evolves from a liquid state to a rubber state and finally a glass state. Therefore,

three sets of properties (Liquid, Rubber and Glass) were used for the epoxy resin

to account for these transformations for the elastic modulus and the coefficient of

thermal expansion. For convergence purpose, the resin elastic modulus was set to

-143-

13 MPa in the liquid state. A smaller modulus led to a non convergence of the

simulation. As presented in CHAPTER 2, the resin was supposed to behave like a

cure hardening instantaneous linear elastic (CHILE) material during the entire

simulation. Table 5-3 presents also the properties of steel used for the RTM

mould.

Table 5-3: Material properties used as input for the FE models

CYCOM 890RTM Epoxy

Resin

G30-500 6k

Carbon Fibre

(YFV=70%)

Steel

Liquid Rubber Glass

Density (kg/m3) 1220 1220 1220 1790 7833

El (GPa) 1.3.10-2

- 3.2 162 230

Et (GPa) 1.3.10-2

- 3.2 9.92 230

Poisson ratio 0.2 0.2 0.2 0.3 0.2

CTE l

(10-6

m/m.ºC) 350 130 55 -0.36 12

CTE t

(10-6

m/m.ºC) 350 130 55 22 12

Max. volumetric

shrinkage (%) - - 3.36 - -

5.4.3 Boundary conditions

5.4.3.1 Displacements

In order to reproduce the model symmetry, the displacements of the nodes located

on the symmetric planes (xz) and (yz) were fixed in the directions 2 and 1

respectively. The bottom corner node, located at the intersection of the two

symmetric planes, was fixed in the direction 3 as well to prevent the possible rigid

body motion. The top and bottom mould surfaces were fixed in the z-direction in

order to simulate the press that kept the cavity thickness constant and the two-part

mould fixed in the RTM process. The mould top surface constraint in the z-

-144-

direction was then removed during the cool down to allow the mould contraction.

No initial pressure was applied to the mould or the composite part.

5.4.3.2 Temperature

The two cure cycles (cure cycle 1 and cure cycle 2) applied in the experiment

were used as temperature input for the numerical analysis. The temperature field

was applied to the top and bottom element layer of the mould to simulate the

heating cartridges. The heat was then transferred to the entire mould and the

composite part by conduction. The mould was assumed adiabatic during the

isotherm. During the cool down, the natural convection was applied by defining a

heat transfer coefficient of 10 W/m2ºC on the mould external surfaces. The

preform was assumed completely saturated with resin at the beginning of the

simulation. In the experiment, the resin was injected at 80ºC in a mould preheated

at 180ºC. Injection simulations using the software PAM-RTM showed that at the

end of the injection, once the part was totally impregnated, the average

temperature of the composite was around 160ºC. Therefore, in the process

modelling simulation, the initial composite temperature was set at 160ºC to

account for this initial temperature gradient and the initial mould temperature was

set to the curing temperature at 180ºC. Finally, the injection simulation predicted

a filling time less than 1 minute, which is too short for the resin to start reacting.

Thus, the initial degree-of-cure of the epoxy resin was set to 0.001 in the curing

simulation.

5.4.3.3 Contact interactions

In the stress analysis, three different types of contact interaction were used to

model different behaviours between the laminate and the mould.

Model A: no bonding

Model A analyzed the behaviour of the composite laminate alone, with no contact

constraints. In this analysis, the mould was not modelled as shown in Figure 5-18-

-145-

a, and the cure cycle was applied directly to the laminate. This analysis gives the

behaviour of the composite plate in a free standing condition.

Model B: perfect bonding

Model B investigated the behaviour of a composite laminate perfectly bonded to

the mould (Figure 5-18-b). This was ensured by having coincident and equivalent

nodes at the interface between the composite part and the mould.

Model C: frictional contact

Model C examined the effect of contact interaction at the interface of the

composite laminate and the mould (Figure 5-18-b). In order to take into account

the possible interaction between the mould and the composite part, contact

constraints were applied on the composite surfaces in contact with the mould.

Contact constraints were defined as follows: “hard” contact relationships were

applied to prevent the transfer of tensile stresses across the interface and minimize

the surface interpenetration. A stick-slip behaviour was introduced using the

classical isotropic Coulomb friction model, , and a shear stress limit

τmax. The Coulomb friction model expresses the critical shear stress τcrit at which

the surfaces in contact start to slide as a function of the pressure of contact P and

the coefficient of friction µ. By introducing τmax, the sliding then occurs as soon as

the magnitude of the equivalent shear stress reaches the minimum between τmax

and µP, , as shown in Figure 5-19. The maximum shear

stress determined previously was used (Table 5-2) as the shear stress limit. From

the literature review, the coefficient of friction was set to 0.3 [109].

Figure 5-19: Schematic representation of the critical shear stress evolution with a

stick-slip behaviour

-146-

5.4.4 Numerical results

For the different finite element models, the results were reported at the position A,

located as shown in Figure 5-18-c. This position corresponded approximately to

the experimental position of the FBG sensors and was representative of the strain

variations of the composite structure. The temperature and degree-of-cure were

analyzed at the centroid of the element located at the laminate mid-thickness. As

three FBG sensors were positioned in the experimental set-up at the top, mid-

thickness and bottom of the laminate, the computed total strains were analyzed

similarly at the element centroid of the laminate top, middle and bottom layers.

However, as the total strains were very similar for the three positions, only the

total strain at the laminate mid-thickness was plotted in the graph for clarity

purposes. Similarly, the strain in the mould at the top and bottom interface with

the laminate were analysed but only the strain of top of the mould was plotted.

The total strains included the thermal and mechanical strains.

5.4.4.1 Temperature and degree-of-cure

Figure 5-20 and Figure 5-21 show the evolution of the predicted composite

temperature and the degree-of-cure for the two cure cycles at the laminate mid-

thickness. Using the DiBenedetto equation (Eq. 2-11) the glass transition

temperature was also predicted. In both cases, a negligible cure exotherm was

predicted (<1ºC during the isotherm). The gel point occurred at αgel = 0.7 in the

isotherm part at 69 minutes for the cure cycle 1 and at 105 minutes for the cure

cycle 2. In both case, the vitrification occurs before the cool down, which means

that at the end of the isotherms, the resin is in the glassy state. After the isotherm,

the part cooled down slowly by natural convection. A maximum degree-of-cure of

0.97 and 0.99 was reached at the end of the cure cycle 1 and cure cycle 2

respectively. Also, as shown in Figure 5-22, the predicted temperatures were

uniform over the entire mould and laminate during the cure cycle 1 and no

degree-of-cure gradient was present in the laminate. Similar results were observed

for cure cycle 2.

-147-


mid-thickness at the position A for cure cycle 1


mid-thickness at the position A for cure cycle 2

-148-

Figure 5-22: Temperature and degree-of-cure field at different times: 0 minutes,

60 minutes, 120 minutes, and 917 minutes

5.4.4.2 Strain results

Cure cycle 1

Figure 5-23 and Figure 5-24 present the evolution of the total in-plane strains for

the three different types of tool-part interactions (no bonding, perfect bonding,

and frictional contact) for the cure cycle 1, while Figure 5-25 and Figure 5-26

show the total strain evolution in the through-thickness direction.

In each case, the laminate expanded first as its temperature increased from 160ºC

to 180ºC in less than two minutes. As the behaviour of the laminate in the

through-thickness direction is dominated by the matrix, the expansion was 10 to

-149-

20 times higher in that direction than the in-plane direction. In the in-plane

direction, a greater expansion was noticed for the model C, where the frictional

contact interactions were used, with a maximum in-plane strain of 190 µε and 270

µε in the directions 1 and 2 respectively. When the laminate was perfectly bonded

to the mould in model B, the expansion was only 50 µε and 90 µε in the two in-

plane directions. Actually, in the case of the perfect bonding, the nodes at the

interface mould/laminate share the material properties of the mould and the

laminate. Therefore the mould prevented the composite expansion as its initial

temperature was already set to the curing temperature (180ºC). On the other hand,

using frictional contact properties allows the laminate to expand more as the

interface is constituted of two nodes with independent properties. In the through-

thickness direction, the maximum strain was obtained for the non bonded

laminate (model A) with a free expansion of 10888 µε. For the model B and model

C, a through-thickness strain around 4000 µε was reached, as the mould restrained

the free expansion of the laminate.

After 60 minutes into the cure, a decrease in the in-plane and through-thickness

strains was observed (Figure 5-24 to Figure 5-27) corresponding to the resin

shrinkage occurring after the gel point.

Then, during the cool down, the temperature decrease led to a decrease in the in-

plane and through-thickness strains in the composite. From Figure 5-23, it can be

noticed that in the case of a perfect bonding (model B), the laminate followed the

contraction behaviour of the mould in the in-plane directions with a final total

strain of -1760 µε. The free standing laminate (model A) contracted less with a

final strain of -550 µε. For the model C, Figure 5-24, the evolution of the total

strain during the cool down was situated in between the one obtained for model A

and model B. No strain discontinuity was observed during the cool down. In the

through-thickness direction, the laminate total strain for the perfect bonding and

frictional contact models evolved similarly, and reached final total strains of -

5200 µε and -5700 µε respectively.

-150-


1 in the case of no bonding (model A) and perfect bonding (model B)


1 using contact interactions (model C)

-151-


cure cycle 1 in the case of no bonding (model A) and perfect bonding (model B)


cure cycle 1 using contact interactions (model C)

-152-

Figure 5-27 to Figure 5-30 present the total strain evolution with the temperature

in the in-plane and through-thickness directions at the laminate mid-thickness.

Overall, the total strain decreased linearly with the temperature. Similar to the

experimental section, the laminate thermal contraction was analysed by measuring

the slope of the curve. In the in-plane direction, a slope of 3.6x10-6

ºC-1

was

measured in the case of the model A, which is of the order of magnitude of the in-

plane coefficient of thermal the coefficient of the laminate with a 50% fibre

volume fraction as seen previously. For the model B, the measured slope was

12x10-6

ºC-1

corresponding to the CTE of the steel mould. Therefore, in a case of

perfect bonding (model B), the laminate behaved like the mould and followed its

thermal contraction. When the frictional contact constraints were applied, a

bilinear curve was noticed for the evolution of the composite strain with the

temperature. Two slopes, 9.25x10-6

ºC-1

and 3.40x10-6

ºC-1

were measured before

and after the inflection respectively. The value after the inflection is similar to the

slope obtained in the model A and corresponds to the laminate CTE. The value

obtained before the inflection is close to the CTE of the mould. Hence, during the

cool down, the composite followed the thermal contraction of the steel mould

until the shear stress at the interface mould/composite reached the maximum shear

stress allowed and the laminate then debonded from the mould. The inflection

corresponded to a transition from a bonded to a debonded laminate. In the

through-thickness direction, the laminate behaved similarly for the three boundary

conditions with a slope around 60x10-6

ºC-1

, which is in the order of magnitude of

the through-thickness composite CTE measured numerically in CHAPTER 4,

Table 4-8 (CTE3 = 47.31 x10-6

ºC-1

). The slopes obtained for the different models

were summarized in Table 5-4.

-153-


thickness for cure cycle 1 in the case of no bonding (model A) and perfect bonding

(model B)


thickness for cure cycle 1 using contact interactions (model C)

-154-


laminate mid-thickness for cure cycle 1 in the case of no bonding (model A) and

perfect bonding (model B)


mid-thickness for cure cycle 1 using contact interactions (model C)

-155-


in-plane and through-thickness strains for the cure cycle 1

Steel

mould Model A Model B Model C

ε1= ε2= ε3 ε1 ε2 ε3 ε1 ε2 ε3 ε1 ε2 ε3

Slope 1

(x10-6

) 12 3.6 3.6 62 12 12 54 9.2 7.0 64

Slope 2

(x10-6

) - - - - - - - 3.4 3.4 -

Temperature

at the

discontinuity (ºC)

- - - 144 144 -

The predicted in-plane strains where then compared to the experimental strains

obtained with the FBG sensors. Figure 5-31 shows the comparison of the in-plane

total strains with time at the laminate mid-thickness. Contrary to the predicted

results, small compressive strains around -50 µε were introduced in the laminate

after the injection. In the experiment, the mould and the preform were preheated

at 180ºC, and the resin was then injected at 80ºC. Thus, when the resin reached

the FBG sensors, the resin temperature was lower than the preform and mould

temperature, leading to a contraction of the FBG sensors. In the numerical models

however, the laminate was assumed fully impregnated at the beginning of the

simulation with an initial temperature of 160ºC. As the initial mould temperature

was set to 180ºC, the composite then expanded due to the positive temperature

gradient. Also as mentioned previously, contrary to the measured results, no strain

discontinuity was predicted for any of the three models. Nevertheless, during the

cool down, the evolution of the strain predicted using frictional contact (model C)

is similar to the evolution of the measured strain after the discontinuity. Figure

5-32 compares the in-plane total strain evolution with temperatures during the

cool down obtained numerically and experimentally. The obtained experimental

and numerical slopes are reported in Table 5-5. It can be observed from Figure

5-32 that model A and model B captured the trend of the strain evolution after and

before the experimental discontinuity respectively. This confirms that the

-156-

discontinuity corresponds to a separation of the laminate from the mould. Model

C does not show a strain discontinuity but presents a transition from the

composite behaviour before and after the strain change. The strain inflection

occurs almost at the same temperature than the strain discontinuity. From these

results, the frictional contact boundary conditions appeared to capture better the

evolution of the in-plane composite strain measured by FBG sensors developed

during the resin transfer moulding process.


thickness for cure cycle 1 obtained experimentally and numerically in the case of

no bonding (model A) and perfect bonding (model B) and frictional contact (model

C)

-157-




bonding (model B) and frictional contact (model C)


obtained with the different models for the in-plane strains

Slope 1

(x10-6

ºC-1

) Slope 2

(x10-6

ºC-1

) Temperature at

discontinuity (ºC)

Experiment 15.3 4.46 150

Model A 3.6 - -

Model B 12 - -

Model C 9.2 3.4 144

Cure cycle 2

Similar trends were observed for cure cycle 2. The evolution of the total in-plane

and through-thickness strains for the three different types of tool-part interaction

are reported in Figure 5-33 to Figure 5-36. In each case, the laminate expanded a

-158-

first time as the temperature increased from 160ºC to 170ºC followed by a second

time from 170ºC to 190ºC at 120 minutes. Similarly to cure cycle 1, a greater

expansion was observed for model C in the in-plane direction with a maximum in-

plane strain of 410 µε and 480 µε in the directions 1 and 2 respectively at the

second hold, compared to 295 µε and 325 µε in the two in-plane directions in

model B. In the through-thickness direction, the maximum strain of 5444 µε was

obtained for model A, corresponding to its free expansion. Due to the mould

restriction, a through-thickness strain around 2000 µε was reached for the model B

and model C. The resin shrinkage occurred then after 110 minutes into the cure as

shown in Figure 5-35 and Figure 5-36. In that case, the gelation occurred at the

end of the first isotherm.

During the cool down period, the composite in-plane and through-thickness total

strains decrease with the temperature. The final in-plane total strains were slightly

higher than the one obtained with the cure cycle 1, whereas the through-thickness

total strain were lower than the one obtained with cure cycle 1. Again no strain

discontinuity was observed.


2 in the case of no bounding (model A) and perfect bounding (model B)

-159-


2 using contact interactions (model C)


cure cycle 2 in the case of no bounding (model A) and perfect bounding (model B)

-160-


cure cycle 2 using contact interactions (model C)

The total strain evolution with the temperature in the in-plane and through-

thickness directions at the laminate mid-thickness are presented in Figure 5-37 to

Figure 5-40. Overall, the total strain decreased linearly with the temperature. The

measured slopes are reported in Table 5-6. A behaviour similar to the one

observed for the cure cycle 1 was found for the cure cycle 2. Model A and Model

B correspond to the behaviour of a free laminate and a bonded laminate

respectively. Model C shows a transition from a bonded to a debonded laminate as

the slope evolves from 8.8x10-6

ºC-1

to 4.6x10-6

ºC-1

in the in-plane direction. The

transition happened around 175ºC. In the through-thickness direction, the

laminate behaved similarly for the three different conditions with a slope around

60x10-6

ºC-1

, which is in the order of magnitude of the through-thickness

composite CTE measured numerically in CHAPTER 4, Table 4-8 (CTE3 = 47.31

x10-6

ºC-1

).

-161-

Figure 5-37: In-plane strain evolution with temperature at the laminate mid-

thickness for cure cycle 2 in the case of no bounding (model A) and perfect

bounding (model B)


thickness for cure cycle 2 using contact interactions (model C)

-162-


laminate mid-thickness for cure cycle 2 in the case of no bounding (model A) and

perfect bounding (model B)


mid-thickness for cure cycle 2 using contact interactions (model C)

-163-


in-plane and through-thickness strains during the cure cycle 2

Steel

mould Model A Model B Model C

ε1= ε2= ε3 ε1 ε2 ε3 ε1 ε2 ε3 ε1 ε2 ε3

Slope 1

(x10-6

) 12 3.6 3.6 62 12 12 34 8.8 7.3 58

Slope 2

(x10-6

) - - - - - - - 4.6 4.4 -

Temperature

at the

discontinuity (ºC)

- - - 174 179 -

The comparisons between the experimental and numerical values at the laminate

mid-thickness for cure cycle 2, as a function of the time and the temperature

variations, are presented in Figure 5-41 and Figure 5-42 respectively. As

mentioned previously, no strain discontinuity was predicted for any of the three

numerical models. Nevertheless, the model using a perfect bonding (model B)

agrees reasonably well with the experiment up to the discontinuity. After the

discontinuity, the evolution of the numerical strain using frictional contact (model

C) is similar to the evolution of the measured strain. From the evolution of the

strain with the temperature (Figure 5-42) and Table 5-7 that present the measured

experimental and numerical slopes, it is clear that model A and model B captured

again the trend of the strain evolution after and before the experimental

discontinuity respectively. Model C shows a transition from the composite

behaviour before and after the strain change; however, this transition happened at

the higher temperature than in the experiment. This difference might be due to the

way the resin is modelled in the simulation. In the numerical analysis, the resin

was modelled as an elastic material. However, in reality, the resin behaves like a

viscoelastic material, allowing the developed strain to relax before the

vitrification. Thus, the mechanical strains generated as the gelled resin is heated

up to the second hold of cure cycle 2, are not relaxed in the simulation. This

induces an earlier separation of the composite from the mould compare to the

-164-

experiment. Nevertheless, from these results, the frictional contact seems to better

capture the evolution of the in-plane composite strain developed during the resin

transfer moulding process and the eventual debonding measured by FBG sensors.


thickness for cure cycle 2 obtained experimentally and numerically in the case of

no bonding (model A) and perfect bonding (model B) and frictional contact (model

C)

-165-




bonding (model B) and frictional contact (model C)


obtained with the different models for the in-plane strains

Slope 1

(x10-6

ºC-1

) Slope 2

(x10-6

ºC-1

) Temperature at

discontinuity (ºC)

Experiment 15.3 4.46 150

Model A 3.6 - -

Model B 12 - -

Model C 8.8 4.6 175

-166-


In this chapter, the tool-part interaction between the laminate and the mould in the

RTM process was investigated experimentally and numerically and the following

conclusions can be underlined:

1) FBG sensors, embedded in the laminate, were successfully used to

measure in-situ the composite in-plane strain evolution during the entire

cure. They also captured the debonding of the composite from the mould

occurring during the cool down due to the coefficient of thermal expansion

mismatch between the laminate and the mould.

2) The maximum shear stress allowed before the debonding of the laminate

from the mould was measured and estimated to be 140 kPa.

3) The tool-part interaction was modelled using three different boundary

conditions: no bonding, perfect bonding and frictional contact. Only the

frictional contact conditions applied at the interface between the laminate

and the mould predicted the debonding occurring at the cool down of the

cure cycle and described well the strain development in the composite

laminate. The predicted separation occurred at the same temperature as the

experimental one for cure cycle 1.

These results demonstrate the capacity of predicting complex tool-part

interactions using frictional contact constraints in finite element analysis.

-167-

CHAPTER 6 Numerical case study: dimensional stability of carbon epoxy cylinders

In this chapter the different factors leading to process-induced strains and stresses

and shape distortions studied previously, such as the resin cure-dependent

properties and volumetric shrinkage (CHAPTER 3), the composite thermal strain

(CHAPTER 4) and the tool-part interaction (CHAPTER 5) are taken into account

simultaneously to compute the process-induced strains, stresses and deformations

of a composite part manufactured by RTM.

Structural shells parts are common in many fields such as aerospace, automotive

or sport industries. Using metallic insert or bladder, such parts can be

manufactured by RTM. However, it can be delicate as the internal mandrel can be

difficult to extract from the shell composite structure. Hence, a hollow cylinder

manufactured by RTM with a metallic insert was used as a case study and a

demonstrator of the numerical capabilities. A three-dimensional finite element

model based on ABAQUS/COMPRO CCA platform was used to analyze

numerically the spring-in and thickness variation of a cylinder manufactured by

RTM. The effect of the thermal strains and the volumetric chemical shrinkage was

introduced in the analysis through the resin and fibre material constitutive models

developed in CHAPTER 3 and CHAPTER 4. Frictional constraints were as well

implemented to simulate the tool-part interactions as described in CHAPTER 5.

The influence of the laminate layup and the mandrel material on the process-

induced deformations was also investigated.

6.1 Numerical model

In order to simulate the RTM process a heat transfer analysis followed by a stress

analysis were performed. Each analysis was divided in four steps. First an

-168-

isothermal cure took place followed by a cool down. Then the demoulding of the

part was simulated by removing the tooling elements (external mould and

mandrel) and the constraints and boundary conditions on the mould. Finally, the

cylinder residual stresses were released by removing one plane of symmetry to

simulate a longitudinal cutting [152]. The cylinder deformation due to the stress

release and the final thickness were then examined.

6.1.1 Geometry and finite element mesh

A 2 mm thick cylinder composite on a 10 cm diameter internal mandrel was

modelled as shown in Figure 6-1. Only a quarter of the cylinder was analyzed due

to the problem symmetry (Figure 6-1-a). The laminate was modelled with 8 plies

and 50% fibre volume fraction. Eight elements were used through the composite

thickness (Figure 6-1-b). Two unidirectional laminates, [0º]8 and [90º]8 and three

symmetric angle-ply laminates [+θ/-θ/-θ/+θ]s with θ equal to 30º, 45º and 60º were

considered. At 0º, the fibres were oriented in the axial direction of the cylinder

(Figure 6-1-c). Three-dimensional 8-node solid elements were used: DC3D8 for

the heat transfer analysis and C3D8 for the stress analysis. The plate was meshed

with 6480 elements and the moulds were meshed with 9922 and 11858 elements

for the external mould and the mandrel respectively.

-169-

Figure 6-1: Finite element models and boundary conditions: a) RTM finite

element mesh, b) close-up of the laminate mesh, c) schematic position of the

analyzed elements A and B

6.1.2 Material models

The properties of the composite material G30-500/CYCOM 890RTM,

characterized previously in CHAPTER 3 and CHAPTER 4 were used. Similarly

as in CHAPTER 5, the carbon fibre properties were taken with 70% yarn fibre

volume fraction (Table 4-6). Table 6-1 summarizes the material properties used as

input in the finite element models. The properties of steel were used for the

external mould. In order to study the effect of the mandrel material on the residual

stresses and deformations, steel and aluminum properties were applied to the

mandrel. The steel and aluminum properties used in this study are also presented

in Table 6-1.

-170-

Table 6-1: Material properties used as input for the FE models

CYCOM 890RTM Epoxy

Resin

G30-500

Carbon

Fibre

Steel Aluminum

Liquid Rubber Glass

Density (kg/m3) 1220 1220 1220 1790 7833 2700

El (GPa) 1.3.10-2

- 3.2 162 230 73

Et (GPa) 1.3.10-2

- 3.2 9.92 230 73

Poisson ratio 0.2 0.2 0.2 0.3 0.2 0.33

CTE l

(10-6

m/m.ºC) 350 130 55 -0.36 12 24.3

CTE t

(10-6

m/m.ºC) 350 130 55 22 12 24.3

Max. volumetric

shrinkage (%) - - 3.36 - - -

6.1.3 Boundary conditions

6.1.3.1 Displacements

In order to reproduce the model symmetry, the displacements of the nodes located

on the symmetric planes (xy), (xz) and (yz) were fixed in the directions 3, 2 and 1

respectively. These nodal constraints prevented as well the possible rigid body

motion. During the isothermal step, the top external mould surface was also fixed

in three directions in order to simulate the press that kept the cavity thickness

constant and the two-part mould fixed. This last constraint was then removed

during the cool down to allow the mould contraction. Finally, in the last step, in

order to simulate the cylinder longitudinal cutting, the symmetric plane (xz) was

removed.

6.1.3.2 Temperature

The typical cure cycle for the epoxy system was used: 120 minutes isotherm at

180ºC followed by a cool down to 25°C by natural convection. In a typical RTM

process, the resin was injected at 80ºC in a mould preheated at 180ºC. Thus, the

-171-

initial composite temperature in the finite element analysis was set to 160ºC in the

simulation to account for this initial temperature gradient. The mould was

assumed adiabatic during the isotherm. During the cool down, the natural

convection was applied by defining a heat transfer coefficient of 10 W/m2ºC on

the mould external surfaces. The preform was assumed to be completely saturated

with resin at the beginning of the simulation and the initial degree-of-cure of the

epoxy resin was set to 0.001. Finally, no initial external pressure was applied to

the mould.

6.1.3.3 Contact constraints

As discussed in CHAPTER 5 section 5.3.4, contact constraints were applied on

the composite surfaces in contact with the mould to take the tool-part interactions

between the mould and the composite part. Frictional constraints as defined in

section 5.4.3.3 were applied with a shear stress limit of 140 kPa and a coefficient

of friction of 0.3. It was assumed that these contact conditions were the same for

the aluminum mandrel. At the demoulding of the part, all the contact constraints

were removed.

6.2 Results and discussion

In all the finite element models, the results were observed at the positions A and

B, located as shown in Figure 6-1-c. These positions were representative of the

strain and stress variations of the composite structure. For both positions, in the

thermal analysis, the temperature was analyzed at the nodes and the degree-of-

cure was analyzed at the centroid of the element. In the stress analysis, the total

strains and stresses were analyzed at the element centroid of the inner and outer

layers of the composite part (Figure 6-1-b). The total strains include the thermal

and mechanical strains.

-172-

6.2.1 Temperature and degree-of-cure

Figure 6-2 and Figure 6-3 show the evolution of the predicted temperature and

degree-of-cure at the top, center and bottom center of the composite during the

cure cycle at the location A. A negligible cure exotherm was predicted (<1ºC

during the isotherm) for the RTM process. The predicted temperatures were

uniform over the entire part during the cure cycle and no degree-of-cure gradient

was present. The gel point occurred after 70 minutes at αgel = 0.7 in the middle of

the isotherm as shown in Figure 6-4. The vitrification also happened in the

isotherm, 40 minutes after the gelation, when the glass transition temperature goes

over the curing temperature. After the isotherm, the part cooled down slowly by

natural convection. A maximum degree-of-cure of 0.97 was reached at the end of

the cure.

Figure 6-2: Predicted temperatures at point A at different locations through the

composite thickness

-173-

Figure 6-3: Predicted degree-of-cure at point A at different locations through the

composite thickness

Figure 6-4: Temperature, glass transition temperature and degree-of-cure

evolutions for the RTM process at point A at the mid-thickness of the composite

-174-

6.2.2 Strains and stresses results

Figure 6-5 to Figure 6-9 and Figure 6-10 and Figure 6-14 show the evolution of

the total strains and stresses in the radial direction at the position A for the

different laminates at the part interfaces: external mould/composite outer surface

and mandrel/composite inner surface (Figure 6-1-b). The two angle-ply laminates

[+30/-30/-30/+30]s and [+60/-60/-60/+60]s behaved similar to the [+45/-45/-

45/+45]s laminate and in the following only the significant difference in behaviour

will be mentioned.

In all cases, the composite expands first as its temperature increases from 160ºC

to 180ºC from 0 to 2 minutes. A greater expansion for the 0º than the 90º laminate

was noticed with a maximum radial strain of 3470 µε versus 1245 µε,

respectively, as the presence of fibre in the hoop direction for the 90º laminate

prevented the radial expansion [153]. The expansion of the 45 angle-ply

laminate was situated in between with a radial strain of 3220 µε. Similar values to

the 45 angle-ply laminate were found for the 30º and 60º angle-ply laminates.

A decrease in the expansion was noticed as the ply angle became closer to the

orientation at 90º due to the effect of the fibre in the hoop direction.

This thermal expansion led to the development of compressive stresses in the

tools as shown in Figure 6-10 to Figure 6-14. Compressive stresses were built up

in the composite as well, as the external mould and the mandrel were preventing

the composite expansion. As the radial strains were smaller for the 90º laminate,

the resulting radial stresses remained also lower than the one in the 0º

unidirectional and angle-ply laminates. The maximum radial stresses were around

-22 MPa for the unidirectional laminate at 0º and the angle-ply laminates, and -9

MPa at 90º.

After 60 minutes of cure, a decrease in strain can be observed in Figure 6-8. This

corresponds to the resin shrinkage strain occurring after the gel point. The

shrinkage led to the release of the radial compressive stresses in the composite

and the tools, but not enough to eliminate the contact between the composite and

the moulds except for the [90º]8 laminate. In that case, the radial stresses in the

-175-

laminate and the moulds became very low and the radial stress in the mandrel

reached almost zero during the isotherm at 90 minutes.

During the cool down after 120 minutes, the laminates contracted more than the

steel tool as the radial strains in the composites remained lower than the radial

strains in the mandrel and the external mould. As the temperature decreases, the

radial stresses of the laminates decrease in magnitude, independently of the layup.


RTM process with a steel mandrel at position A

-176-




interfaces for the RTM process with a steel mandrel at position A

-177-





-178-





-179-





-180-



The separation of the composite cylinder from the mould can be noticed when the

radial stresses at the interface of the mandrel or the external mould became almost

zero. As shown in Figure 6-10 to Figure 6-14 and mentioned previously, the

laminate oriented at 90º separated first from the mandrel during the isotherm at

around 90 minutes due to the resin shrinkage. The 0º unidirectional laminate and

the angle-ply laminates separated from the tool during the cool down. [0º]8

debonded at around 302 minutes or 92ºC. The angle-ply laminates separated at

285 minutes, 352 minutes and 335 minutes for the 60º, 45º and 30º ply angles

respectively, as reported in Table 6-2. In that case, the separation of the composite

from the tool was caused primarily by the difference in their coefficient of thermal

expansion.

Table 6-2 presents the coefficients of thermal expansion in the radial, hoop and

longitudinal direction of the five laminates. The laminate CTEs were determined

using the dimension variations Δli of the laminate generated by the FEA during

the cool down as follows:

-181-

Eq. 6-1

where the subscripts r, θ and L stands for the radial, hoop and longitudinal

directions respectively, and l is the initial laminate length at the beginning of the

cool down. For the composite oriented at 0º, the transverse CTEs of the

composite, in the hoop (CTEc,θ) and radial (CTEc,r) directions, are equal and

greater than the mould CTE (CTEc,θ = CTEc,r > CTEsteel). Therefore, during the

cool down, the composite contracted more than the mould, leading to a debonding

of the composite from the external mould and compressive stresses in the mandrel

as shown in Figure 6-10. For the laminate at 90º, the composite CTE in the hoop

direction is dominated by the behaviour of the fibre, and is then smaller than the

CTE of the mould. However, it remains greater than the CTE of the mould in the

through-thickness direction (CTEc,r > CTEsteel > CTEc,θ ). Hence, as the part

cooled down, the composite contraction in the hoop direction was smaller than the

mould contraction, locking the composite part in the external mould. Then, the

composite part debonded from the mandrel as its contraction was greater in the

through-thickness direction. This mechanism is schematically represented in

Figure 6-15. Depending on the ply angle value, the symmetric angle-ply laminates

behaved similarly to the 0º or 90º unidirectional laminate. The [+30/-30/-30/+30]s

laminate separated from the external mould as its CTE values followed the same

trend as the 0º laminate compared to the CTE of the mould, while the [+45/-45/-

45/+45]s and [+60/-60/-60/+60]s laminates behaved like the 90º laminate and

debonded from the mandrel.

-182-

Table 6-2: Coefficients of thermal expansion of the laminates

Layup CTEc,L

(10-6

ºC-1

) CTEc,θ

(10-6

ºC-1

)

CTEc,r (10

-6 ºC

-1)

Separation

from: Debonding time

(min)

Mandrel Steel Aluminum

[0º]8 -0.16 31.4 31.4 External

mould 302 170

[+30/-30/

-30/+30]s -3.5 20.8 38.6

External

mould 335 150

[+45/-45/

-45/+45]s 4.1 4.1 43.1 Mandrel 352 150

[+60/-60/

-60/+60]s 20.8 -3.5 38.6 Mandrel 285 145

[90º]8 31.4 -0.16 31.4 Mandrel 90 90

Figure 6-15: Schematic representation of the composite debonding, depending of

the material orientation

The radial strain and stress evolutions obtained for the position B were similar to

those observed at position A. However, it was noticed that the separation of the

laminate from the mould happened earlier than at position A. This means that the

debonding happens from the side of the composite part (position B) towards the

centre (position A). By analyzing the evolution of the contact pressure at the

-183-

interface, as shown in Figure 6-16 for the 45º angle-ply laminate, it was noticed

that the contact pressure at position B became null 30 minutes earlier than at

position A, which confirms the previous assumption. A similar phenomenon was

observed experimentally by Twigg et al. [109] on plate manufactured by

autoclave.

Figure 6-16: Evolution of the contact pressure at position A and B for the

[+45/-45/-45/+45]s laminate during the RTM process with a steel mandrel

Figure 6-17 to Figure 6-21 present the evolution of the radial stress of the five

laminates for the RTM process with a mandrel in aluminum. The values of the

radial stresses in the composite and the mould were similar to the values obtained

with a mandrel in steel. The same debonding mechanism occurred for the five

laminates. However, as the aluminum CTE is greater than the steel CTE, the

aluminum mandrel contracted more than the steel mandrel; and the separation of

the composite from the mould occurred earlier as presented in Table 6-2.

-184-


RTM process with an aluminum mandrel at position A


RTM process with an aluminum mandrel at position A

-185-


interfaces for the RTM process with an aluminum mandrel at position A



-186-



From these simulations, the ease of demoulding can be anticipated by observing

the state of stress in the external mould and the mandrel. For example, a difficult

demoulding can be expected for the [0]8 and [+30/-30/-30/+30]s laminates as the

mandrel remained in compression at the end of the cure with the value in the order

of -500 kPa.

6.2.3 Spring-in variation

The simulation of the cylinder radial cutting by removing a plane of symmetry

released the residual stresses and generated some spring-in and warpage in the

structure as shown in Figure 6-22.

The spring-in was calculated by evaluating the angle variation θ1. In an angled

composite laminate, such as L-shape bracket, Albert and Fernlund determined that

the spring-in was a combination of a corner component and a flange warpage

component [113]. Hence, for the cylinder, the measured spring-in would be then

equivalent to the spring-in corner component in an angled composite laminate.

-187-

The cylinder warpage was caused by the generation of shear stress at the interface

between the mould and the composite during the heat-up of the cure cycle, while

the mould stretches the laminate [107]. The warpage (w) was determined by

evaluating the bending of the cylinder. A positive value means that the cylinder

warps away from the mandrel. The spring-in, thickness and warpage variations

are presented in Table 6-3. In order to estimate the influence of the resin

shrinkage on the deformation, the finite element analyses were also computed

with 0% of resin volumetric shrinkage.

Figure 6-22: Schematic representation of the deformations occurring after the

stresses released a) spring-in, b) warpage

The analytical values of spring-in were calculated using the equations (Eq. 2-41

and Eq. 2-25) developed by Radford [97] taking into account the temperature

change, the thermal expansion of the composite in the in-plane and through-

thickness directions, as well as the cure shrinkage. It should be noticed that the in-

plane direction defined by Radford corresponds to the hoop direction defined in

this work. Therefore, the CTEc,θ and CTEc,r determined in Table 6-2 were used as

the CTEl and CTEt in Eq. 2-41 and Eq. 2-25.

-188-

Table 6-3: Process-induced dimensional changes for the different laminate layups

Warp

age

(mm

) Alu

min

um

man

dre

l

-4.1

x10

-3

-1.6

x10

-2

8.0

x10

-3

3.1

x10

-2

-1.4

x10

-2

Ste

el

man

dre

l

8.5

x10

-4

-2.6

x10

-2

8.8

x10

-3

3.9

x10

-2

-1.5

x10

-2

No

shri

nk

age

-7.7

x10

-3

-7.1

x10

-2

1.3

x10

-2

8.4

x10

-2

5.7

x10

-2

Th

ick

nes

s (m

m) A

lum

inu

m

man

dre

l

1.9

937

1.9

928

1.9

901

1.9

888

1.9

895

1.9

877

1.9

890

1.9

873

1.9

842

1.9

858

Ste

el

man

dre

l

1.9

914

1.9

907

1.9

890

1.9

878

1.9

887

1.9

870

1.9

877

1.9

867

1.9

842

1.9

858

No

shri

nk

age

1.9

977

1.9

968

1.9

981

1.9

950

1.9

972

1.9

934

1.9

954

1.9

917

1.9

922

1.9

871

Sp

rin

g-i

n (

º) A

lum

inu

m

man

dre

l

0.0

4

0.0

6

0.2

7

0.2

6

0.4

9

0.5

1

0.5

7

0.6

3

0.7

0

0.6

7

Ste

el

man

dre

l

0.0

5

0.0

7

0.2

7

0.2

6

0.5

2

0.5

3

0.6

0

0.6

6

0.7

0

0.6

6

No

shri

nk

age

0.0

2

0.0

2

0.1

4

0.1

1

0.2

3

0.2

7

0.2

9

0.4

1

0.4

2

0.5

4

Face

Sym

.

Fa

ce

En

d

face

Sym

.

Fa

ce

En

d

face

Sym

.

Fa

ce

En

d

face

Sym

.

Fa

ce

En

d

face

Sym

.

Fa

ce

En

d

face

Layu

p

[0º]

8

[+30/-

30/

-30/+

30] s

[+45/-

45/

-45/+

45] s

[+60/-

60/

-60/+

60] s

[90º]

8

-189-

The chemical shrinkages of the composite in the three directions were determined

using the dimension variations of the laminate Δli during the cure as follows:

Eq. 6-2

Only the shrinkage occurring after the resin vitrification, when the resin had build

up a significant elastic modulus, was assumed to contribute to the residual

stresses. Actually, before the vitrification, most of the generated strain can be

relaxed due to the resin viscous behaviour. A similar assumption was used in

[113] to estimate the shrinkage components. The composite cure shrinkage

coefficients are reported in Table 6-4. The hoop and radial chemical shrinkage of

the composite were used as l and t respectively in Eq. 2-25. The analytical

spring-in values are then summarized in Table 6-5.

Table 6-4: Composite cure shrinkage coefficients in the longitudinal, hoop and

radial directions

Layup c,L (10-5 m/m)

c,θ (10-5 m/m)

c,r (10-5 m/m)

[0º]8 0 7.99 7.99

[+30/-30/-30/+30]s -1.30 6.39 10.72

[+45/-45/-45/+45]s 0.89 0.89 13.71

[+60/-60/-60/+60]s 6.15 -1.30 10.72

[90º]8 7.98 0 7.99

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Table 6-5: Analytical spring-in values for the different laminate layups

Layup [0]8 [+30/-30/

-30/+30]s

[+45/-45/

-45/+45]s

[+60/-60/

-60/+60]s [90]8

CTEc,θ (10

-6 ºC

-1)

31.4 20.8 4.1 -3.5 -0.16

CTEc,r (10

-6 ºC

-1)

31.4 38.6 43.1 38.6 31.4

c,θ (10

-5m/m)

7.99 6.39 0.89 -1.30 0

c,r (10

-5m/m)

7.99 10.72 13.71 10.72 7.99

ΔT (ºC) 150 150 150 150 150

θTH (º) 0.0 0.242 0.531 0.572 0.428

θS (º) 0.0 0.004 0.012 0.011 0.007

θ (º) 0.0 0.246 0.543 0.583 0.435

Figure 6-23 shows the influence of the layup on the spring-in. The spring-in was

negligible for the laminate oriented at 0º and increased as the fibre orientation

follows the curvature of the composite part. Nevertheless, the values of the

spring-in remain small (< 1º). The results demonstrate as well the significant

influence of the resin shrinkage on the spring-in, as an increase up to 50% was

observed in the numerical spring-in values due to the shrinkage strain. The

numerical spring-in values were compared to the analytical values predicted by

the Radford equations (Eq. 2-41 and Eq. 2-25). Overall, the analytical and

numerical spring-in values followed the same trend. The numerical values of the

spring-in, taking into account the effect of the shrinkage, are in reasonable

agreement with the analytical values of the total spring-in ((θTH + θS). Good

agreements are observed as well for the unidirectional laminates without the

influence of the shrinkage. However, more discrepancy can be observed between

the analytical and numerical spring-in of the angle-ply laminates without

considering the resin shrinkage.

Considering now the values of the spring-in taking into account the effect of the

shrinkage, the difference between the analytical and numerical values might be

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due to the effect of the mould interaction, which was not considered with the Eq.

2-25. This demonstrates that the tool-part interaction has a possible influence on

the process-induced deformations. From Figure 6-23, the effect of the tool-part

interaction seems more important for the [+60/-60/-60/+60]s and [90]8 laminates.

In those configurations, this laminates present the maximal CTE difference with

the mould in the hoop direction. This CTE mismatch can generate a through-

thickness stress gradient which is released when the cylinder is cut, leading to an

increase in spring-in. Nevertheless, the tool-part interaction does not seem to be a

major mechanism leading to the cylinder spring-in variation. Similar conclusions

were observed experimentally for autoclaved L-shape composite brackets [113],

where the tool-part interaction affected more significantly the flange warpage

component than the corner component.

From Table 6-3, a difference can be noticed between the spring-in reported at the

symmetric face and the end face of the cylinder. This difference was due to a

bending of the cylinder in the longitudinal direction. As the stresses are released,

the cylinder warps away from the mould leading to a greater spring-in at the free

end of the cylinder as shown in Figure 6-22. The values of the warpage are also

reported in Table 6-3.

Figure 6-24 compares the spring-in values obtained with a steel and an aluminum

mandrel. The change of the mandrel material does not affect the spring-in

significantly. In the case of open mould processes, such as autoclave or filament

winding, previous studies observed higher composite strains and spring-in using

moulds with higher thermal expansion [111, 113, 154]. For this type of processes,

the mould stretched the laminate during the initial heat-up of the cure cycle,

generating shear stresses at the interface between the mould and the composite

and high through-thickness stress gradient in the laminate. These interfacial

stresses and through-thickness stress gradients were locked in the composite as it

cured and led to residual stresses and deformations at the demoulding. For the

RTM process, the mould was preheated to the curing temperature before the

injection. Hence, there is only a small amount of stress gradients that remains

locked in the composite during the cure due to the mould expansion. This explains

-192-

that the change of mandrel material from steel to aluminum does not affect the

residual stresses and the spring-in for the RTM process. Finally, the thickness

variation is negligible (<1%) for all simulations.

Figure 6-23: Effect of the resin shrinkage and the laminate layup on the spring-in

value at the end face

-193-

Figure 6-24: Effect of the laminate layup and the mandrel material on the spring-

in value at the end face


In this chapter, a numerical study was performed to analyse the dimensional

stability of representative composite part manufactured by the RTM process. Five

different laminate sequences were investigated. The cure-dependent factors, such

as thermal strain and volumetric shrinkage, as well as tool-part interactions were

taken into account simultaneously to compute the process-induced strains and

stresses and deformations. The following conclusions emphasized:

1) The simulations captured the possible debonding of the composite from

the mould due to the tool-part interaction and the difference in thermal

expansion coefficient and the shrinkage strain. In most cases, this

debonding occurred during the cool down of the cure cycle. However, for

the [90]8 laminate, the separation happened during the isotherm primarily

due to the significant effect of the shrinkage in the radial direction. The

ease of demoulding (mandrel extraction) was also estimated by analyzing

-194-

the state of stresses in the moulds at the end of the cure and was found to

be dependent of the material properties and the laminate layup.

2) The process-induced deformations were predicted for the different layup

configurations. As expected, these results showed the significant

contribution of the thermal strain and the shrinkage strain on the spring-in

variation. However, the tool-part interaction do not seem to be a major

mechanism leading to process-induced deformations in the case of the

RTM process.

3) For the thermal boundary conditions tested, representative of the RTM

process, the change of the mandrel material did not have a notable

influence on the process-induced deformations.

This process modelling approach can be applied to determine to process-induced

deformations of different geometry configurations, such as L-shape or C-shape

brackets.

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CHAPTER 7 Conclusions and Future Work

This work investigated the factors leading to the generation of process-induced

stresses and deformations in woven composites manufactured by Resin transfer

Moulding. Both intrinsic and extrinsic mechanisms were examined. The

contributions of this work are summarized as follows.

1) A comprehensive methodology was developed to characterize the

processing properties of thermoset resin systems. As a case study, this

phenomenal approach was then applied for the characterization of a

specific epoxy resin, CYCOM 890RTM epoxy resin. Empirical models

were developed in order to determine the evolution of the resin property

(cure kinetics, viscosity, glass transition temperature, cure shrinkage,

coefficient of thermal expansion and elastic modulus) for any temperature

cycle. These models were essential to establish a clear understanding of

the resin behaviour during the processing conditions. Among the different

chemo-physical resin properties, a particular effort was involved in the

measurement of the resin cure shrinkage. Two measurement methods were

improved and validated. It was determined that the total cure shrinkage of

CYCOM 890RTM epoxy resin was 10%, of which 3.4% occurred after the

gel point. It was then assume that only the resin cure shrinkage happening

after the vitrification, when the resin has developed a significant elastic

modulus, would induce residual stresses. The developed models were then

implemented in finite element software in order to solve coupled

thermochemical-stress processing problems and predict the evolution of

laminate properties during the manufacturing process.

2) The thermomechanical properties of 5-Harness satin woven fabrics

were investigated numerically using a micromechanical approach.

-196-

Unit cells or periodic units representative of the global composite structure

were developed for the different laminate configurations and periodic

boundary conditions were applied to ensure the continuity in displacement

at the unit cell boundaries. The elastic constants and coefficient of thermal

expansion were determined for different fibre volume fractions

corresponding to typical volume fraction used in the RTM process and

compared to equivalent unidirectional crossply laminates. Overall, the

thermomechanical properties of a 5-HS woven fabric laminate are very

comparable to an equivalent unidirectional crossply laminate. The main

difference results in the in-plane shear modulus G12 which is higher than

the crossply one due to the yarn interlacing effect. This validates the use of

the properties of unidirectional fibre in a crossply configuration to model

the behaviour of 5-harness satin woven fabric laminate. The properties of

the unidirectional fibre were therefore implemented in the finite element

software to predict the properties of the 5-harness satin woven laminate

during the manufacturing process.

3) Fibre Bragg Grating sensors were used to characterize the tool-part

interaction for the RTM process. The optic sensors captured the

separation of the composite from the mould due to their difference in

coefficient of thermal expansion during the cool down period. The

maximum shear stress stand by the laminate before the debonding was

estimated to be 140 kPa for a steel mould. Finite element analyses were

used to simulate the tool-part interaction. Different boundary conditions

were applied at the composite/mould interface. The frictional contact

conditions, using the maximum shear stress observed experimentally,

successfully predicted the measured composite in-plane strain

development as well as the separation of the laminate from the mould for

the RTM process. This frictional contact constraint was then used in the

process modelling to simulate the tool-part interaction occurring during

the RTM process.

-197-

4) Finally, taking simultaneously into account the intrinsic and extrinsic

mechanisms investigated and mentioned above, the RTM process was

then modelled. The developed epoxy resin properties models, the carbon

fibre unidirectional properties, as well as the investigated frictional contact

conditions were implemented in a numerical case study to compute the

process-induced strains, stresses and deformations generated during the

RTM process. The effect of the laminate sequences and the mould

material were also investigated. The simulations predicted a debonding of

the laminate mainly due to the coefficient of thermal expansion mismatch

between the composite and the mould. However, depending of the

laminate layup, the cure shrinkage can have a significant influence on the

separation of the laminate from the mould during the process. The

predicted process-induced deformations varied with the laminate

sequences. A maximum spring-in was found for the 60º angle-ply

laminate and the 90º unidirectional laminate due to the maximal difference

between their longitudinal and transversal properties. A significant

increase of the spring-in value with the resin shrinkage was observed.

Contrary to the autoclave process, the results showed a small influence of

the tool-part interaction for the RTM process, and the change of the

mandrel material did not affect the value of the spring-in. The numerical

total spring-in agreed reasonably well with the corresponding analytical

values. This case study also validates the use of an existing process

modelling approach, originally developed for the autoclave process,

for three-dimensional composite parts manufactured by the RTM

process.

In conclusion, a predictive tool to simulate the strains, stresses and deformation

generated during the RTM process was developed. This process modelling tool

accounts for the resin cure-dependent properties developed in CHAPTER 3, the

composite properties investigated in CHAPTER 4 and the tool-part interaction

-198-

examined in CHAPTER 5. This process modelling approach was then applied to a

numerical case study in CHAPTER 6, establishing the efficacy of this tool to

predict the process-induced deformations. This approach can be then applied to

various 3D geometry configurations and/or manufacturing processes,

demonstrating the potential value of this work for industrial purposes.

For future work on the investigation of the process-induced deformations in

woven composite manufactured by RTM, further studies could be carried out in

order to examine different issues that arose during the course of this project:

1) Micromechanics constitutive laws for the thermomechanical properties of

woven fabric could be developed. Actually, it was demonstrated in

CHAPTER 4 that the properties of the 5-HS woven fabric were similar to

an equivalent unidirectional crossply configuration. However, this might

not be true for a plain weave or twill woven architecture where the fibre

waviness is more dominant. With the increasing use of woven fabric in

industry, the implementation of the “true” woven fabric properties in the

COMPRO CCA platform would expend greatly its modelling capabilities

and increase the results accuracy. Further experimental validation of the

unit cell approach by characterizing the fabric properties at various fibre

volume fractions would be also interesting to carry out.

2) The use of FBG sensors for complementary experiments could be carried

out to investigate the effect of the parameters that were examined

numerically (i.e. laminate layup and the mould material). Also, pressure

sensors could be added in the experimental set-up in order to measure the

pressure variation during the RTM process.

3) Further validation of the RTM process modelling could be investigated

using an extensive experiment approach. As different mechanisms leading

to the process-induced stress occurred simultaneously, experimental set-

-199-

ups should be developed in order to isolate each effect individually. Also,

the effect of more extrinsic parameters such as the laminate layup, the tool

material, the composite geometry or the cure cycle could be investigated

experimentally.

4) This RTM process modelling could be also combined with mould filling

simulations in order to take into account the effect of the resin flow, the

fibre permeability and the fibre compaction on the process-induced strains,

stresses and deformations.

-200-

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Appendix A Complements on Material Characterization

Appendix A regroups some extra information on diverse aspect of the material

characterization.

A.1. DSC measurements

Figure A-1 and Figure A-2 show the test reproducibility under dynamic and

isothermal conditions.

Figure A-1: Dynamic test reproducibility at 1ºC/min and 2ºC/min temperature

ramp

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Figure A-2: Isothermal test reproducibility at 160ºC, 170ºC, 180ºC and 190ºC

A.2. Rheological measurements

Figure A-3 and Figure A-4 present the strain sweep and time sweep tests

performed in order to determine the LVR. From these results, the resin LVR was

determined at 15% strain and 1Hz frequency.

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Figure A-3: Strain sweep test performed at 1Hz frequency in oscillatory mode

Figure A-4: Time sweep performed at 15% strain and 1Hz in oscillatory mode

Figure A-5 to Figure A-7 show the reproducibility of the rheological tests under

isothermal conditions, and Figure A-8 to Figure A-10 show the reproducibility of

the rheological tests under dynamic conditions. Overall, for each condition, the

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gel point occurred at the same time. The value of the minimal viscosity varied a

little but not significantly.



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strain and 1Hz in oscillatory mode

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A.3. Solid samples preparation for the rheometer in

torsion mode

Neat resin plaques were pre-cured in an oven on an aluminum plaque with an

embedded K thermocouple. The thermocouple readings, acquired every 30

seconds and automatically fed into the cure kinetics and viscosity models allowed

real-time tracking of the degree-of-cure. When the desired post-gelation degree-

of-cure 1 was attained, the plaques were removed from the oven and quickly

cooled. Once at room temperature, the plaques were cut using a ceramic saw and

polished with sandpaper into samples approximately 45mm long, 13mm wide and

1.5mm thick. The exact dimensions of each specimen were measured before

testing. As the resin exhibits a very low fracture toughness close to the gel point,

the sample were pre-cured above = 0.8, so that they did not break in the

rheometer during the torsion test. Table A-1 presents the details of the pre-cured

solid plaque. The three first plaques where used to determine the fully cured

behaviour of the resin. Plaques 4 and 5 were used to measure the evolution of Tg

and the elastic modulus with the temperature and the degree-of-cure. The final

column of Table A-1 provides the total number of specimens cut form each

plaque. Note that not all specimens cut were used to obtain final data. Some were

used to test different approaches or testing conditions while others were simply

invalidated due to inadequate quality or known experimental errors.

Table A-1: Pre-cured plaque information

Plaque Isotherm time

(min)

Isotherm

temp (ºC) α1

Nb. of

samples

1

2

3

4

5

320

320

320

154

150

160

170

180

180

180

0.95

0.98

1

0.847

0.827

5

4

4

4

4

To measure the evolution of the glass transition temperature, the pre-cured

samples was heated at 5ºC/min in the rheometer while its degree of cure was

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tracked by means of the cure kinetics model as shown in Figure A-11. .Once the

resin passed the glass transition temperature (2), determined by one of the three

modulus based indicators, the resin was brought to the manufacturer

recommended cure temperature of 180ºC and allowed to isothermally reach a

desired degree of cure α2, as shown at (3). Then, the sample was quickly removed

from the rheometer and cooled. The procedure was then repeated from α2 to a

higher α3 and so on to measure the Tg for different values of degree-of-cure.

Figure A-11: Glass transition temperature measurement process. The arrows

correspond to one of the three glass transition temperature indicators [155]

Table A-2 summarizes the degree-of-cure evolution the samples underwent during

the experiments. α1 denotes the pre-cure degree of cure right after removal from

the oven. Samples from plaques 4 and 5 were eventually cured to high values, so

as to confirm the results of plaques 1, 2 and 3.

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Table A-2: Degree-of-cure evolution for samples used for the glass transition

temperature measurements

Plaque Sample α1 α2 α3 α4 α5

1 a 0.95 0.95

b 0.95 0.95

2 a 0.98 0.98

b 0.98 0.98

3 a 1 1

b 1 1

c 1 1

4 a 0.847 0.9 0.91

b 0.847 0.87 0.931 0.961 0.981

5 a 0.827 0.883 0.915 0.936

b 0.827 0.926 0.969

Table A-3 shows the evolution of the degree-of-cure during the tensile modulus

experiments. These experiments were carried out under isothermal conditions at

180ºC and 160ºC.

Table A-3: Degree-of-cure evolution for samples used for the tensile modulus

measurements

Plaque Sample α1 α2

4 c 0.847 0.991

5 c 0.827 0.998

processinduced stresses and deformations in woven composites manufactured by resin transfer moulding

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