Fracture Mechanics in Layered and Graded Solids: Analysis Using Boundary Element Methods

Abstract

Preface: In general, all solid materials can be considered as non-homogeneous because their properties can vary with locations in a three-dimensional space. One special type of solid material is characterized by the variations of its physical and mechanical components, structures and properties along only one given coordinate; the material properties have very small or no variations in any other direction perpendicular to the given coordinate. These types of solid materials are called functionally graded materials (FGMs). Since 1983, the second author of this book has devoted much of his research to understanding the elasticity of a multilayered medium and has achieved important results. One of these results is the analytical and closed-form formulation of fundamental solutions for a multilayered elastic medium and a transversely isotropic bi-material. These solutions can be applied to investigate and analyze many problems in multilayered media encountered in the science and engineering disciplines using the BEM. Since 2000, the authors have dedicated their efforts to the development of the new BEMs based on these fundamental solutions under the funding of The University Grants Committee of Hong Kong, The University of Hong Kong and the National Natural Science Foundation of China. This book brings together the descriptions of the new boundary element formulation based on the two fundamental solutions and new analyses and results for the fracture me chanics of layered and functionally graded materials. This method overcomes the mathematical degeneration that is associated with the solitary use of the displacement boundary integral equation for cracked bodies by developing the multi-region and single-region methods of BEMs. Effective implementation of the methods is detailed, devoting special attention to the description of accurate algorithms for the evaluation of various singular integrals in the boundary element formulations. The layered discretization technique is used to simulate the variations of the material property of FGMs with depth. The proposed numerical methods, together with fracture mechanics theories, are used to calculate the stress intensity factors of three-dimensional cracks in FGMs and to analyze the crack growth. The influence of the material parameters and crack dimensions on the fracture properties has been analyzed and quantified. The new material presented in this book is supported by recent articles published in relevant peer-reviewed journals in English or Chinese.