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About this book

New developments in the applications of fracture mechanics to engineering problems have taken place in the last years. Composite materials have extensively been used in engineering problems. Quasi-brittle materials including concrete, cement pastes, rock, soil, etc. all benefit from these developments. Layered materials and especially thin film/substrate systems are becoming important in small volume systems used in micro and nanoelectromechancial systems (MEMS and NEMS). Nanostructured materials are being introduced in our every day life. In all these problems fracture mechanics plays a major role for the prediction of failure and safe design of materials and structures. These new challenges motivated the author to proceed with the second edition of the book.

The second edition of the book contains four new chapters in addition to the ten chapters of the first edition. The fourteen chapters of the book cover the basic principles and traditional applications, as well as the latest developments of fracture mechanics as applied to problems of composite materials, thin films, nanoindentation and cementitious materials. Thus the book provides an introductory coverage of the traditional and contemporary applications of fracture mechanics in problems of utmost technological importance.

With the addition of the four new chapters the book presents a comprehensive treatment of fracture mechanics. It includes the basic principles and traditional applications as well as the new frontiers of research of fracture mechanics during the last three decades in topics of contemporary importance, like composites, thin films, nanoindentation and cementitious materials. The book contains fifty example problems and more than two hundred unsolved problems. A "Solutions Manual" is available upon request for course instructors from the author.

Table of Contents

Frontmatter

Chapter 1. Introduction

Abstract
The mechanical design of engineering structures usually involves an analysis of the stress and displacement fields in conjunction with a postulate predicting the event of failure itself. Sophisticated methods for determining stress distributions in loaded structures are available today. Detailed theoretical analyses based on simplifying assumptions regarding material behavior and structural geometry are undertaken to obtain an accurate knowledge of the stress state. For complicated structure or loading situations, experimental or numerical methods are preferable. Having performed the stress analysis, we select a suitable failure criterion for an assessment of the strength and integrity of the structural component.
Emmanuel E. Gdoutos

Chapter 2. Linear Elastic Stress Field in Cracked Bodies

Abstract
Fracture mechanics is based on the assumption that all engineering materials contain cracks from which failure starts. The estimation of the remaining life of machine or structural components requires knowledge of the redistribution of stresses caused by the introduction of cracks in conjunction with a crack growth condition. Cracks lead to high stresses near the crack tip; this point should receive particular attention since it is here that further crack growth takes place. Loading of a cracked body is usually accompanied by inelastic deformation and other nonlinear effects near the crack tip, except for ideally brittle materials. There are, however, situations where the extent of inelastic deformation and the nonlinear effects are very small compared to the crack size and any other characteristic length of the body. In such cases the linear theory is adequate to address the problem of stress distribution in the cracked body. Situations where the extent of inelastic deformation is pronounced necessitate the use of nonlinear theories and will be dealt with in the next chapter.
Emmanuel E. Gdoutos

Chapter 3. Elastic-Plastic Stress Field in Cracked Bodies

Abstract
The linear elastic analysis of the stress field in cracked bodies, dealt with in the preceding chapter, applies, strictly speaking, only to ideal brittle materials for which the amount of inelastic deformation near the crack tip is negligible. In most cases, however, there is some inelasticity, in the form of plasticity, creep or phase change in the neighborhood of the crack tip. A study of the local stress fields for the three modes of loading showed that they have general applicability and are governed by the values of three stress intensity factors. In other words, the applied loading, the crack length and the geometrical configuration of the cracked bodies influence the strength of these fields only through the stress intensity factors. We can have two cracked bodies with different geometries, crack lengths and applied loads with the same mode. The stress and deformation fields near the crack tip will be the same if the stress intensity factors are equal.
Emmanuel E. Gdoutos

Chapter 4. Crack Growth Based on Energy Balance

Abstract
When a solid is fractured new surfaces are created in the medium in a thermodynamically irreversible manner. Material separation is caused by the rupture of atomic bonds due to high local stresses. The phenomenon of fracture may be approached from different points of view, depending on the scale of observation. At one extreme is the atomic approach where the phenomena of interest take place in the material within distances of the order of 10−7 cm. At the other extreme is the continuum approach, which considers material behavior at distances greater than 10−2 cm. In the atomic approach, the problem is studied using the concepts of quantum mechanics; the continuum approach uses the theories of continuum mechanics and classical thermodynamics. The complex nature of fracture prohibits a unified treatment of the problem, and the existing theories deal with the subject either from the microscopic or from the macroscopic point of view. A major objective of fracture mechanics is to bridge the gap between these two approaches.
Emmanuel E. Gdoutos

Chapter 5. Critical Stress Intensity Factor Fracture Criterion

Abstract
When a solid is fractured, work is performed to create new material surfaces in a thermodynamically irreversible manner. In Griffith’s theory of ideally brittle materials, the work of fracture is spent in the rupture of cohesive bonds. The fracture surface energy γ, which represents the energy required to form a unit of new material surface, corresponds to a normal separation of atomic planes. For the fracture of polycrystals, however, the work required for the creation of new surfaces should also include: dissipation associated with nonhomogeneous slip within and between the grains; plastic and viscous deformation; and possible phase changes at the crack surfaces. The energy required for the rupture of atomic bonds is only a small portion of the dissipated energy in the fracture process. There are situations where the irreversible work associated with fracture is confined to a small process zone adjacent to the crack surfaces, while the remaining material is deformed elastically. In such a case the various work terms associated with fracture may be lumped together in a macroscopic term R (resistance to fracture) which represents the work required for the creation of a unit of new material surface. R may be considered as a material parameter. The plastic zone accompanying the crack tip is very small and the state of affairs around the crack tip can be described by the stress intensity factor.
Emmanuel E. Gdoutos

Chapter 6. J-integral and Crack Opening Displacement Fracture Criteria

Abstract
A number of investigators have proposed the mathematical formulation of elastostatic conservation laws as path independent integrals of some functionals of the elastic field over the bounding surface of a closed region. For notch problems, Rice [6.1] introduced the two-dimensional version of the conservation law, a path independent line integral, known as the J-integral. The present chapter is devoted to the theoretical foundation of the path independent J-integral and its use as a fracture criterion. The critical value of the opening of the crack faces near the crack tip is also introduced as a fracture criterion.
Emmanuel E. Gdoutos

Chapter 7. Strain Energy Density Failure Criterion: Mixed-Mode Crack Growth

Abstract
So far, we have studied growth of a crack only for the case when the load is applied normal to the crack and such that the crack propagates in a self-similar manner. However, often the loads are not aligned to the orientation of the crack. In such cases, the crack-tip stress field is no longer governed by a single opening-mode stress intensity factor K I but by a combination of the three stress intensity factors K I, K II, and K III. Moreover, the direction of crack initiation is not known a priori but depends on a failure criterion involving some combination of K I, K II, and K III. As a rule the crack follows a curved path.
Emmanuel E. Gdoutos

Chapter 8. Dynamic Fracture

Abstract
The analysis of crack systems considered so far concerned only quasi-static situations in which the kinetic energy is relatively insignificant compared with the other energy terms and can be omitted. The crack was assumed either to be stationary or to grow in a controlled stable manner, and the applied loads varied quite slowly. The present chapter is devoted entirely to dynamically loaded stationary or growing cracks. In such cases rapid motions are generated in the medium and inertia effects become important.
Emmanuel E. Gdoutos

Chapter 9. Fatigue and Environment-Assisted Fracture

Abstract
It was first realized in the middle of the nineteenth century that engineering components and structures often fail when subjected to repeated fluctuating loads whose magnitude is well below the critical load under monotonic loading. Early investigations were primarily concerned with axle and bridge failures which occurred at cyclic load levels less than half their corresponding monotonic load magnitudes. Failure due to repeated loading was called “fatigue failure”.
Emmanuel E. Gdoutos

Chapter 10. Micromechanics of Fracture

Abstract
The phenomenon of fracture of solids may be approached from different viewpoints depending on the scale of observation. At one extreme is the atomic approach where the phenomena take place in the material within distances of the order of 10−7 cm; at the other extreme is the continuum approach which models material behavior at distances greater than 10−2 cm. In the atomic approach, the problem is studied using the concepts of quantum mechanics; the continuum approach uses the theories of continuum mechanics and classical thermodynamics. A different approach should be used to explain the phenomena that take place in the material between these two extreme scales: movement of dislocations; formation of subgrain boundary precipitates, slip bands, grain inclusions and voids. The complex nature of the phenomenon of fracture prohibits a unified treatment of the problem, and the existing theories deal with the subject either from the microscopic or the macroscopic point of view. Attempts have been made to bridge the gap between these two approaches.
Emmanuel E. Gdoutos

Backmatter

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