The Theory of Materials Failure

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Product Description

A complete and comprehensive theory of failure is developed for homogeneous and isotropic materials. The full range of materials types are covered from very ductile metals to extremely brittle glasses and minerals. Two failure properties suffice to predict the general failure conditions under all states of stress. With this foundation to build upon, many other aspects of failure are also treated, such as extensions to anisotropic fiber composites, cumulative damage, creep and
fatigue, and microscale and nanoscale approaches to failure.

The Theory of Materials Failure Review

This book is concerned with the development of materials failure theory that has the mathematical and physical basis. It is not an all inclusive review, but rather a discriminating exposition on this difficult subject. The lack of such books has long been recognized and it is often thought that such a book could never be written, but by exercising the highest possible scientific standard and drawing from his vast experience and knowledge, Dr. Christensen has finally succeeded in presenting such a book.

The author started with a historical account and critical reviews of the widely known failure theories. He then moved on to the development of a tensor-based, multi-dimensional failure theory for isotropic materials, and convincingly demonstrated that their complicated failure phenomena could be described by only two material constants, T and C, the uniaxial tensile and compressive strengths, respectively. This set the tone for the presentation of subsequent topics, with each built upon the foundation of the preceding ones. Along the way, experimental evaluation, theoretical applications, ductile to brittle transition, and precise definition of yield stress and failure stress, are all introduced with great rigor. While the main contribution of this book can be said to be on the isotropic materials, theories for anisotropic fiber-reinforced composites is also well presented. In addition, some fracture mechanics, nanomechanics, cumulative damage, and probabilistic failure, are also discussed.

This book contains sixteen chapters, as follows.

Chapters 1 & 2: Perspectives and history; Chapter 3: The baselines of isotropic failure theory; Chapters 4 & 5: New perspectives of failure theories for isotropic materials. This is the heart of the book. Chapters 6 & 7: Evaluations and applications; Chapter 8: Ductile to brittle transition. This is a special feature of the book. Chapter 9: Precise definition of yield stress and failure stress; Chapter 10: Fracture mechanics; Chapters 11-13: Failure theories and micromechanics of anisotropic fiber composites; Chapters 14-16: Nanomechanics, cumulative damage, and probabilistic failure theories.

This book, entitled "The Theory of Material Failure", can be suitably cast in the context of "Theory of Elasticity" by Timoshenko and Goodier, "Mathematical Theory of Elasticity" by Sokolnikoff, and "The Mathematical Theory of Plasticity" by Hill. With this book, the trilogy of elasticity, plasticity, and failure in solid mechanics is now completed.

The book is well suited for instruction of upper-level undergraduates and graduate students, and for researchers. Practicing engineers will also find it useful in structural designs and analysis.

Overall this is an excellent book, extremely well written. It is resourceful, and the style of presentation is inspiring. I highly recommend it to readers.

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