Fracture mechanics. With an introduction to micromechanics.

*(English)*Zbl 1110.74001
Mechanical Engineering Series. Berlin: Springer (ISBN 3-540-24034-9/hbk). xii, 319 p. (2006).

This textbook is an extended English edition of three previous German editions. The book is divided into ten chapters. The introductory chapter 1 includes basic concepts, ideas, principles, constitutive equations and criteria of solids mechanics, restricting mostly to isotropic elastic and plastic materials subjected to infinitesimal deformations. Chapter 2 is devoted to a brief outline of classical fracture and failure hypothesis for materials under static loading. Interrelations of micro- and macroscopic aspects of fracture are briefly discussed in chapter 3. The next chapter is devoted to a macroscopic description of fracture processes on the basis of linear fracture mechanics. Here, the main modes of fracture are considered and the concepts of stress intensity factors and energy release rates are introduced. The classical methods of weight functions and energy balance are applied to different fracture problems, and the basic concept of \(J\)-integral is discussed in detail. Then, the authors present different behavior types of cracks, connected with plastic zone near crack tip, crack stability, mixed-mode loading, fatigue processes and existence of interfaces. Finally, the crack in ferroelectric material is considered. Chapter 5 investigates problems of elastic-plastic fracture mechanics in the framework of rate-independent plasticity (i.e. perfect plasticity or total strain theory) and monotonic loading. The analysis focuses mainly on plane problems for mode-I loading cracks. The considered problems are connected with estimation of \(J\)-integral and statement of fracture criteria on its basis. The phenomenon of creep fracture, taking place quasistatically without inertia effects is studied in chapter 6. The fracture concepts of the crack initiation and growth are presented for viscoelastic materials in linear and nonlinear cases under small-scale creep conditions.

Chapter 7 presents dynamic fracture problems for brittle materials, described by linear elasticity theory. The analysis is devoted to two typical problems: (i) the stationary (i.e. non-propagating) crack under dynamic loading, and (ii) the fast running crack. The consideration of fracture is based on already established quantities such as the \(K\)-factors and the energy release rate. The important chapter 8 introduces fundamental concepts and methods of micromechanics (representative volume element, homogenization, averaging, effective properties, etc.). Beginning from Eshelby’s approach, the modern and broadly used models and methods (Mori-Tanaka model, self-consistent method, differential scheme, etc.) are discussed in the framework of boundary value problems for an representative volume element. Then, extremal principles of elasticity theory are presented, which allow to derive from energetic expressions sharp upper and lower bounds for the effective properties. This chapter mainly focuses on linear elastic material behavior, but a brief introduction into the treatment of elastic-plastic and thermoelastic materials is also given. Chapter 9 presents elementary concepts of damage mechanics, focusing only on the simplest cases of brittle and ductile damage under monotonic loading. The final chapter 10 deals with basic concepts of probabilistic fracture mechanics. The analysis is restricted to brittle materials, the strength properties of which display especially strong scatter and depend on volume of a testing specimen. The consideration is based on Weibull approach to brittle fracture.

In total, this textbook is a well brief presentation of modern concepts and methods of fracture mechanics in both macro- and microscales. The book may be recommended to students, researchers and industry practitioners interested in theoretical backgrounds of fracture mechanics.

Chapter 7 presents dynamic fracture problems for brittle materials, described by linear elasticity theory. The analysis is devoted to two typical problems: (i) the stationary (i.e. non-propagating) crack under dynamic loading, and (ii) the fast running crack. The consideration of fracture is based on already established quantities such as the \(K\)-factors and the energy release rate. The important chapter 8 introduces fundamental concepts and methods of micromechanics (representative volume element, homogenization, averaging, effective properties, etc.). Beginning from Eshelby’s approach, the modern and broadly used models and methods (Mori-Tanaka model, self-consistent method, differential scheme, etc.) are discussed in the framework of boundary value problems for an representative volume element. Then, extremal principles of elasticity theory are presented, which allow to derive from energetic expressions sharp upper and lower bounds for the effective properties. This chapter mainly focuses on linear elastic material behavior, but a brief introduction into the treatment of elastic-plastic and thermoelastic materials is also given. Chapter 9 presents elementary concepts of damage mechanics, focusing only on the simplest cases of brittle and ductile damage under monotonic loading. The final chapter 10 deals with basic concepts of probabilistic fracture mechanics. The analysis is restricted to brittle materials, the strength properties of which display especially strong scatter and depend on volume of a testing specimen. The consideration is based on Weibull approach to brittle fracture.

In total, this textbook is a well brief presentation of modern concepts and methods of fracture mechanics in both macro- and microscales. The book may be recommended to students, researchers and industry practitioners interested in theoretical backgrounds of fracture mechanics.

Reviewer: I. A. Parinov (Rostov-na-Donu)