Properties for Design of Composite Structures

Neil McCartney graduated with a PhD in Mathematics from Manchester University in 1968 and spent the whole of his career at the National Physical Laboratory (NPL) undertaking theoretical research associated with many aspects of materials science. He is currently an Emeritus Senior NPL Fellow. For many years he studied damage initiation and growth in unidirectional fibre reinforced composites and their laminates, with applications to multi-layered materials involving metals, ceramics, and polymers. His current work includes modelling of polymer electrolyte membrane fuel cells and batteries, and of multi-layered piezoelectric systems subject to mechanical, thermal, and electrical stimulation. He was Visiting Professor in the Department of Materials Science and Engineering, University of Surrey, March 1995 to 31 August 2010, and Visiting Professor in the Centre for Collaborative Research, The University of Tokyo, Japan, 1 February to 8 May 1999. He is a Fellow of the Institute of Mathematics and its Applications and a Chartered Mathematician.

Preface vii

About the Companion Website ix

1 Introduction 1

2 Fundamental Relations for Continuum Models 5

3 Maxwell’s Far-field Methodology Applied to the Prediction of Effective Properties of Multiphase Isotropic Particulate Composites 43

4 Maxwell’s Methodology for the Prediction of Effective Properties of Unidirectional Multiphase Fibre-reinforced Composites 65

5 Reinforcement with Ellipsoidal Inclusions 97

6 Properties of an Undamaged Single Lamina 111

7 Effective Thermoelastic Properties of Undamaged Laminates 129

8 Energy Balance Approach to Fracture in Anisotropic Elastic Material 163

9 Ply Crack Formation in Symmetric Cross-ply Laminates 189

10 Theoretical Basis for a Model of Ply Cracking in General Symmetric Laminates 223

11 Ply Cracking in Cross-ply Laminates Subject to Biaxial Bending 249

12 Energy-based Delamination Theory for Biaxial Loading in the Presence of Thermal Stresses 271

13 Energy Methods for Fatigue Damage Modelling of Laminates 297

14 Model of Composite Degradation Due to Environmental Damage 329

15 Maxwell’s Far-field Methodology Predicting Elastic Properties of Multiphase Composites Reinforced with Aligned Transversely Isotropic Spheroids 345

16 Debonding Models and Application to Fibre Fractures and Matrix Cracks 379

17 Interacting Bridged Ply Cracks in a Cross-ply Laminate 425

18 Theoretical Basis for a Model of Ply Cracking in General Symmetric Laminates 447

19 Stress-transfer Mechanics for Biaxial Bending 479

Appendix A: Solution for Shear of Isolated Spherical Particle in an Infinite Matrix 503

Appendix B: Elasticity Analysis of Two Concentric Cylinders 510

Appendix C: Gibbs Energy per Unit Volume for a Cracked Laminate 518

Appendix D: Crack Closure Conditions for Laminates 523

Appendix E: Derivation of the Solution of Nonlinear Equations 531

Appendix F: Analysis for Transversely Isotropic Cylindrical Inclusions 536

Appendix G: Recurrence Relations, Differential Equations and Boundary Conditions 541

Appendix H: Solution of Differential Equations 546

Appendix I: Energy Balance Equation for Delamination Growth 551

Appendix J: Derivation of Energy-based Fracture Criterion for Bridged Cracks 554

Appendix K: Numerical Solution of Integral Equations for Bridged Cracks 560

Index 565