Flow Induced Alignment in Composite Materials

380 Pages·1997·26.21 MB·English

by  T. D. Papathanasiou

Flow-in duced a Ii gn m ent in corn posite materiaI s

Flow-induced
alignment
in composite
materials
Edited by
T D Papathanasiou and D C Guell
WOODHEAD PUBLISHING LIMITED
Cambridge England
Published by Woodhead Publishing Limited
Abington Hall, Abington
Cambridge CB 1 6AH, England
First published 1997 Woodhead Publishing Ltd
0 1997, Woodhead Publishing Ltd
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British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library.
ISBN 1 85573 254 8
Designed by Geoff Green
Typeset by Techset Composition Limited, Salisbury, Wiltshire.
Printed by St Edmundsbury Press, Suffolk, England.
CONTENTS
Preface xi
List of authors xv
1 Flow-induced alignment in composite materials:
current applications and future prospects 1
DCGUELL and ABENARD
1.1 A brief survey of composites i
1.1.1 Brief history of composite materials 3
1.1.2 An overview of aligned-fiber composites 4
1.1.3 Benefits of aligned short-fiber reinforcement 6
1.1.4 Flow-induced fiber alignment 9
1.1.5 Applications of aligned-fiber composites 11
1.1.6 Types of fiber reinforcement 12
1.1.7 Critical fiber length 16
1.1.8 Processing issues in aligned-fiber composites 18
1.2 Flow processes for producing aligned-fiber polymer matrix
composites 21
1.2.1 Processing of thermoplastic polymer composites 22
1.2.2 Thermosets 28
1.2.3 Aligned fiber mats 28
1.2.4 Blends of liquid crystal polymers and thermoplastics 29
1.3 Flow processes for producing aligned-fiber metal-matrix
composites 30
1.4 Flow processes for producing aligned-fiber ceramic-matrix
composites 32
1.5 Future prospects 34
References 37
vi CONTENTS
2 Fiber-fiber and fiber-wall interactions during the flow
of non-dilute suspensions 43
S RANGANATHAN and S G ADVANI
2.1 Introduction 43
2.2 Single fiber motion 46
2.3 Orientation characterization 48
2.4 Fiber-fiber interactions 51
2.4.1 Early work 51
2.4.2 Diffusion models 53
2.4.3 Slender body theory-based solution 58
2.4.4 Stokesian dynamics 61
2.4.5 Computer simulations/full numerical solutions 63
2.5 Concentrated suspensions 64
2.6 Fiber-wall interactions 65
2.7 Summary and outlook 70
References 71
3 Macroscopic modelling of the evolution of fibre
orientation during flow 77
N PHAN-THIEN and R ZHENG
3.1 Introduction 77
3.2 Theory 80
3.2.1 Evolution equations 80
3.2.2 Anisotropic fluid models 86
3.3 Numerical methods 90
3.3.1 The boundary element method 90
3.3.2 Solution of the evolution equations 91
3.4 Applications 92
3.4.1 Flow past a sphere 93
3.4.2 Injection moulding 98
3.5 Conclusions 105
Acknowledgement 106
Bibliography 106
4 Flow-induced alignment in injection molding of
fiber-reinforced polymer composites 112
T D PAPATHANASIOU
4.1 Introduction 112
4.2 The injection molding process 114
4.2.1 Overview 114
4.2.2 Modeling of mold filling 117
CONTENTS vii
4.2.3 Velocity profiles in mold filling 121
4.3 Experimental observations of fiber orientation in injection
molding 126
4.3.1 Filling patterns with fiber-reinforced melts 126
4.3.2 Skin-core structure 127
4.3.3 Other influences 137
4.4 Prediction of fiber orientation in injection molding 148
4.4.1 Modeling strategies: prediction of fiber orientation 148
4.4.2 Modeling strategies: effect of fibers on flow kinematics 154
4.4.3 Parametric sensitivity studies 157
4.5 Conc 1 u s io n 160
References 160
5 Control and manipulation of fibre orientation in
large scale processing 166
P S ALLAN and M J BEVIS
5.1 Introduction 166
5.2 Application of SCORIM for weldline strength enhancement 166
5.2.1 Copolyester LCP-containing glass fibres 169
5.2.2 High temperature cure DMC 171
5.3 Application of SCORIM for physical property enhancement 174
5.3.1 Glass fibre-reinforced polypropylene 174
5.3.2 Glass fibre filled copolyester 177
5.4 Control of porosity in thick-section mouldings 183
5.4.1 Control of porosity and fibre orientation in a variable
cross-section bar 183
5.4.2 Moulding and characterization of a thick-section moulding
representing an actuation support structure 185
5.5 Control of fibre orientation in a selection of mould geometries 191
5.5.1 Injection moulded plaque 193
5.5.2 Injection moulded fin 193
5.5.3 Multicavity SCORIM for the production of moulded rings 193
5.6 Extensions of the shear controlled orientation concept 195
References 202
6 Theory and simulation of shear flow-induced
microstructure in liquid crystalline polymers 203
A D REY
6.1 Introduction 203
6.2 Shear flow-induced orientation phenomena in rod-like
nematic polymers 204
6.2.1 Leslie-Ericksen continuum theory of nematics 204
viii CONTENTS
6.2.2 Orientation modes and multistability 207
6.2.3 Pattern formation under forced convection 21 1
6.2.4 Non-equilibrium defect structures 213
6.3 Shear flow-induced molecular alignment phenomena in
rod-like nematic polymers 218
6.3.1 Tensor continuum theory 218
6.3.2 Alignment-orientation coupling 220
6.4 Conclusions 228
Acknowledgments 228
References 228
7 Mesostructural characterisation of aligned fibre
composites 230
A R CLARKE. N C DAVIDSON and G ARCHENHOLD
7.1 Introduction 230
7.1.1 Definition of the measurement problem 230
7.1.2 Comparison of measurement techniques 233
7.1.3 Characterisation parameters of fibre orientation states 234
7.2 Optical reflection microscopy 236
7.2.1 Sample preparation 236
7.2.2 Overview of microscope and image analyser 237
7.2.3 An automated large area high spatial resolution design 237
7.3 Confocal laser scanning microscopy 244
7.3.1 Basic principles 245
7.3.2 Operational modes for three-dimensional reconstruction 247
7.4 Measurement errors in optical microscopy 252
7.4.1 Noise in pixellated images 252
7.4.2 Intrinsic fibre ellipticity 252
7.4.3 Minimising orientation errors by large angle sectioning 253
7.4.4 Confocal laser scanning microscope and the apparent depth
problem 256
7.4.5 Stereological issues 258
7.5 Characterisation studies of fibre reinforced composites 26 1
7.5.1 Geometrical coefficients 26 1
7.5.2 Fibre length distributions 263
7.5.3 Nearest neighbour angular anisotropy 266
7.5.4 Fibre misalignments and fibre curvature 270
7.5.5 Power spectral density of fibre waviness 274
7.6 Future developments 276
7.6.1 Low level voidag- e determination 278
7.6.2 Pattern matching between successive two-dimensional sections 280
7.6.3 Automation of three-dimensional CLSM for large volume
studies 283
CONTENTS ix
7.6.4 Automated ultrasonic testrig for elastic constants
determination 284
7.6.5 Concluding remarks 287
Acknowledgements 287
References 288
8 Materials property modelling and design of short
fibre composites 293
R BROOKS
8.1 Introduction 293
8.2 Modelling the stiffness of fully aligned materials 294
8.2.1 Bounds on moduli 294
8.2.2 Self-consistent models 295
8.2.3 Mori-Tanaka model 297
8.2.4 Halpin-Tsai model 30 1
8.2.5 Comparison between models 305
8.3 Effect of fibre aspect ratio on stiffness 308
8.4 Effect of constituent properties on stiffness 310
8.5 Modelling the effect of fibre orientation 312
8.5.1 Introduction 312
8.5.2 Transversely isotropic subunit 313
8.5.3 Transformation of properties and the aggregate model 315
8.5.4 Orientation averaging using tensors 316
8.6 Application in design and some results 317
8.7 Conclusions 320
References 321
9 Micromechanical modelling in aligned-fiber
composites: prediction of stiffness and permeability
using the boundary element method 324
T D PAPATHANASIOU and M S INGBER
9.1 Introduction 3 24
9.2 Boundary element method 330
9.2.1 Consideration of dispersed fibers 33 1
9.2.2 Massively parallel implementation 333
9.3 Representative results 336
9.3.1 Stiffness of an elastic rod reinforced with short fibers 336
9.3.2 Stokes’ flow across arrays of aligned fibers 343
9.4 Conclusion 350
Literature 352
Index 357