Table Of ContentMechanical Properties of Polycarbonate
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Series Editor
Piotr Breitkopf
Mechanical Properties of
Polycarbonate
Experiment and Modeling for Aeronautical
and Aerospace Applications
Weihong Zhang
Yingjie Xu
First published 2019 in Great Britain and the United States by ISTE Press Ltd and Elsevier Ltd
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ISBN 978-1-78548-313-4
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Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Chapter 1. Experimental Studies of Mechanical Properties of
Polycarbonate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1. Uniaxial compression tests at various strain rates . . . . . . . . . . . . . 2
1.1.1. Experimental setup of quasi-static uniaxial compression tests . . . 2
1.1.2. Experimental setup of dynamic uniaxial compression tests . . . . . 4
1.1.3. Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2. Uniaxial tension tests at various strain rates . . . . . . . . . . . . . . . . . 13
1.2.1. Experimental setup of quasi-static uniaxial tension tests . . . . . . . 13
1.2.2. Experimental setup of dynamic uniaxial tension tests . . . . . . . . 14
1.2.3. Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.3. Quasi-static uniaxial compression tests at various temperatures . . . . . 24
1.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.5. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Chapter 2. Constitutive Models of Polycarbonate . . . . . . . . . . . . . 29
2.1. Introduction to constitutive models for polycarbonate . . . . . . . . . . 30
2.1.1. Linear viscoelastic model . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.1.2. Viscoplastic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2. Damage-based elastic–viscoplastic model for polycarbonate . . . . . . 42
2.2.1. Damage mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.2.2. Helmholtz free energy . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.2.3. Fundamental laws of thermodynamics . . . . . . . . . . . . . . . . . 45
2.2.4. Constitutive equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.3. Calibration of model parameters . . . . . . . . . . . . . . . . . . . . . . . 51
vi Mechanical Properties of Polycarbonate
2.4. Numerical integration algorithm . . . . . . . . . . . . . . . . . . . . . . . 55
2.4.1. Time-discrete framework . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.4.2. A simplified integration algorithm of the time-discrete model . . . 56
2.5. Implementation of the constitutive model in LS-DYNA . . . . . . . . . 59
2.6. Numerical examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.6.1. Single-element tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.6.2. Cylinder compression simulation . . . . . . . . . . . . . . . . . . . . 72
2.7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2.8. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Chapter 3. Impact Simulation of Polycarbonates in Aeronautical and
Aerospace Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.1. Simulation methodology and experimental verification . . . . . . . . . . 80
3.1.1. Impact simulation methodology . . . . . . . . . . . . . . . . . . . . . 80
3.1.2. Gas gun impact tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.1.3. Gas gun impact simulations . . . . . . . . . . . . . . . . . . . . . . . . 89
3.2. Impact simulation in aeronautical and aerospace applications . . . . . . 92
3.2.1. Polycarbonate windshield under bird impact . . . . . . . . . . . . . . 92
3.2.2. Polycarbonate visor under debris impact . . . . . . . . . . . . . . . . 104
3.3. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
3.4. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Chapter 4. Integrated Simulation of Injection Molding Process and
Mechanical Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.1. Yield stress modeling from thermal history . . . . . . . . . . . . . . . . . 114
4.1.1. Govaert’s yield stress model . . . . . . . . . . . . . . . . . . . . . . . 114
4.1.2. Experimental validations of the yield stress model . . . . . . . . . . 118
4.2. Setup of the Izod impact test . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.3. Integrated simulation framework . . . . . . . . . . . . . . . . . . . . . . . 121
4.4. Integrated simulation of the injection molding process and
Izod impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.4.1. Prediction of yield stress based on the injection molding
simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.4.2. Constitutive model with the processing-induced inhomogeneity
of yield stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
4.4.3. Impact simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.4.4. Simulation results and comparisons with experiments . . . . . . . . 127
4.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.6. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Contents vii
Chapter 5. Process Optimization of the Injection Molding for
High Mechanical Performance . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.1. Integrated simulation framework of an astronaut’s helmet visor . . . . 135
5.1.1. Simulation of the injection molding process . . . . . . . . . . . . . . 136
5.1.2. Residual stress analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.1.3. Yield stresses and constitutive model . . . . . . . . . . . . . . . . . . 139
5.1.4. Impact simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.2. BP neural network model . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.2.1. Generation of training data . . . . . . . . . . . . . . . . . . . . . . . . 144
5.2.2. Training of the neural network . . . . . . . . . . . . . . . . . . . . . . 145
5.2.3. Neural network testing . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.3. Process optimization by the particle swarm optimization algorithm . . 147
5.3.1. Optimization problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5.3.2. Basis of the PSO algorithm . . . . . . . . . . . . . . . . . . . . . . . . 148
5.3.3. Variable limits handling strategy . . . . . . . . . . . . . . . . . . . . . 149
5.3.4. Optimization result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
5.5. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
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Preface
Polycarbonate is a kind of thermoplastic polymer with high transparency,
high ductility, impact resistance and lightweightness. It has been widely used
in transparent products of aeronautical and aerospace systems, including
aircraft windshields, canopies and astronaut helmet visors. In order to design
these products to satisfy complex service conditions, we should have a good
understanding of the mechanical properties of polycarbonate that depend on
a variety of factors such as strain rate, temperature and even the processing
conditions. From the viewpoint of experiments, it is almost impossible to
have a comprehensive understanding of the mechanical behavior of
polycarbonate products and their evolution rules under various loading
conditions. A promising way is to develop numerical modeling techniques.
With the support of the National Key Research Program and the National
Natural Science Foundation of China, our research group has been devoted
to the development of numerical modeling techniques for studying the
mechanical properties of polycarbonate with emphasis on aeronautical and
aerospace applications. The main content of this book covers experimental
characterization, material modeling, finite element simulation as well as the
integrated analysis and design method for polycarbonate. This book contains
six chapters:
– the Introduction briefly presents the properties, processing and
applications of polycarbonate. The purpose and layout of this book is also
presented;
– Chapter 1 presents the experiment facilities and methods used to
characterize the mechanical properties of polycarbonate;
