The Theory of Materials Failure

Abstract This book provides a complete and comprehensive development of failure theory for homogeneous materials. The resultant failure criteria to be used for applications with isotropic materials are calibrated by only two properties: the uniaxial tensile and compressive strengths, T and C. From these data the entire family of failure envelopes can be generated for all states of stress. The account begins with a historical survey that includes the efforts of many of history's greatest scientists. The complete inadequacy for general applications of all the historical forms are detailed. The center point of the book is the derivation of the failure theory for isotropic materials. The new and enabling technical insight is that of an organizing principle whereby the entire spectrum of isotropic materials types can be characterized by their strengths ratio, T/C, with stress being non-dimensionalized by C. Two coordinated but competitive failure criteria then emerge. One of several unique features of the book is a full and complete treatment of ductile versus brittle behavior for isotropic materials. Along with the experimental evaluation of the failure theory, many examples of failure behavior and applications are presented. The relationship to fracture mechanics is also included. The overall coverage is very broad, but with no compromise in quality or rigor. Reasonably extensive treatments are given for fiber composites failure as well as investigations into microscale and nanoscale aspects of failure. The book is completed with a probe into damage models and a fairly complete derivation of probabilistic failure and life prediction.