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2011 | Book

Elements of solid mechanics Read chapter Read first chapter

Fracture Mechanics

With an Introduction to Micromechanics

Authors: Dietmar Gross, Thomas Seelig

Publisher: Springer Berlin Heidelberg

Book Series : Mechanical Engineering Series

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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About this book

Concerned with the fundamental concepts and methods of fracture mechanics and micromechanics, Fracture Mechanics primarily focuses on the mechanical description of the fracture process; however, material specific aspects are also discussed. The presentation of continuum mechanical and phenomenological foundations is followed by an introduction into classical failure hypotheses. A major part of the book is devoted to linear elastic and elastic-plastic fracture mechanics. Further subjects are creep fracture, dynamic fracture mechanics, damage mechanics, probabilistic fracture mechanics, failure of thin films and fracture of piezoelectric materials. The book also contains an extensive introduction into micromechanics. Self-contained and well-illustrated, this text serves as a graduate-level text and reference.

Table of Contents

Frontmatter
Chapter 1. Elements of solid mechanics
Abstract
This chapter summarizes basic concepts and equations of solid mechanics. It is selfevident that this outline cannot be complete but is limited to a necessary minimum. For more detailed descriptions the reader is referred to the literature, and selected textbooks are listed at the end of the chapter (Section 1.6). The reader with some knowledge of elasticity and plasticity may skip this part and jump directly to the next chapter.
Dietmar Gross, Thomas Seelig
Chapter 2. Classical fracture and failure hypotheses
Abstract
In this chapter, a brief outline on classical fracture and failure hypotheses for materials under static loading will be given. The word classical this context means in that most of these so-called strength hypotheses are already quite old. Partially they date back to considerations made at the end of the 19th or the beginning of the 20th century and they are inseparably associated with the development of solid mechanics at that time. Through modern fracture mechanics they have been pushed into the background, as far as research is regarded. However, because of their wide spreading which, last but not least, is due to their simplicity, they are still of remarkable importance.
Dietmar Gross, Thomas Seelig
Chapter 3. Micro and macro phenomena of fracture
Abstract
Origins and phenomena of fracture are manifold. The reason for this can be found in the fact that the phenomena are predominantly determined by the microscopic properties of a material which in turn vary extensively from material to material. In this book, emphasis is placed on a continuum-mechanical description of macroscopic fracture behavior. Nevertheless, it is beneficial to have a certain understanding of microscopic events. Therefore, both microscopic and macroscopic aspects are briefly discussed in this chapter. The former have only exemplary character and focus on phenomena in crystalline or polycrystalline materials which includes the large class of metals.
Dietmar Gross, Thomas Seelig
Chapter 4. Linear fracture mechanics
Abstract
We now turn to the description of the crack behavior. From a macroscopic, continuum mechanical viewpoint, we consider a crack as a cut in a body. Its opposite boundaries are the crack surfaces which are also called crack faces or crack flanks (Fig. 4.1). In general they are traction-free. The crack ends at the crack front or crack tip.
Dietmar Gross, Thomas Seelig
Chapter 5. Elastic-plastic fracture mechanics
Abstract
When a test specimen or a structural component consisting of a ductile material and containing a crack is loaded, plastic flow starts in the vicinity of the crack tip. As a consequence, the crack tip becomes increasingly blunted with increasing load and the crack opens. At the same time the plastic zone grows and may, depending on the material and geometry, extend over large regions or the entire specimen until at some critical load crack initiation takes place. In such a situation of large-scale yielding linear elastic fracture mechanics can no longer be applied and parameters and fracture concepts such as the K–concept based on linear elastic material behavior become meaningless. Fracture parameters and concepts then are needed which account for plastic flow of the material in larger regions outside the process zone.
Dietmar Gross, Thomas Seelig
Chapter 6. Creep fracture
Abstract
Various materials display a time-dependent behavior which is the source of phenomena such as creep or relaxation. These processes typically take place quasistatically, i.e., so slow that inertia forces do not play any role. If a component made of such a material contains a crack and is loaded, time-dependent deformations occur especially in the vicinity of the crack tip due to the locally high stresses. This may cause a delay of crack initiation until some critical crack-tip deformation is attained. Creep of the material at the crack tip, however,may also lead directly to creep crack growth.
Dietmar Gross, Thomas Seelig
Chapter 7. Dynamic fracture mechanics
Abstract
So far, our investigations of crack initiation and propagation have always been based on the assumption of quasistatic conditions. This is no longer justified when inertia forces or high strain rates significantly affect the fracture behavior. It is, for instance, well known that a material is more likely to fail under impulsive dynamic loading than in case of a slowly applied load. One reason for this is the different material behavior: plastic or viscous flow is increasingly suppressed at higher loading rates and a material often behaves more brittle in the dynamic case than in the static case. This and possibly different failure mechanisms in the process zone may lead to a change of the fracture toughness. Another reason is due to the fact that the inertia forces in case of dynamic loading can cause higher stresses in the vicinity of a crack tip than in the corresponding quasistatic case.
Dietmar Gross, Thomas Seelig
Chapter 8. Micromechanics and homogenization
Abstract
On close inspection, e.g., through a microscope, all real materials show a multitude of heterogeneities even if they macroscopically appear to be homogeneous. These deviations from homogeneity may exist in form of cracks, voids, particles, or regions of a foreign material, layers or fibers in a laminate, grain boundaries, or irregularities in a crystal lattice. Here they shall be referred to as defects in a generalized sense. Subject ofmicromechanical investigations is the behavior of these heterogeneities or defects as well as their effect on the overall properties and performance of amaterial. For instance, heterogeneities of any kind can locally act as stress concentrators and thereby lead to the formation and coalescence of microcracks or voids as a source of progressive material damage (see Section 3.1.2 and Chapter 9).
Dietmar Gross, Thomas Seelig
Chapter 9. Damage mechanics
Abstract
Real materials often contain already in the initial state a multitude of defects such as microcracks or voids. In the course of a deformation process these internal cavities may grow and coalesce while at the same time further material separation takes place by the creation of new microdefects at stress concentrators (e.g. inclusions, grain boundaries, inhomogeneities). This causes a change of the macroscopic properties of the material and its strength decreases. Such a process of structural deterioration of a material which results from the creation, growth and coalescence of microdefects is called damage. In its final stage it leads to a complete loss of the material’s integrity and to the formation of a macroscopic crack.
Dietmar Gross, Thomas Seelig
Chapter 10. Probabilistic fracture mechanics
Abstract
The failure analysis of a structure proceeds on the basis of a fracture or failure criterion. A typical example is the criterion of brittle fracture K I = K Ic which states that failure does not take place for K I < K Ic . Application of such a criterion in the deterministic sense requires all involved quantities to be exactly known. This, however, is not always the case. For instance, the in-service loading conditions of a technical component as well as the material’s fracture toughness K Ic may scatter. Also the location, size, and orientation of cracks is sometimes not precisely known. If these details are neglected and only ‘averaged’ quantities are employed the deterministic analysis may lead to rather vague results.
Dietmar Gross, Thomas Seelig
Backmatter
Metadata
Title
Fracture Mechanics
Authors
Dietmar Gross
Thomas Seelig
Copyright Year
2011
Publisher
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-19240-1
Print ISBN
978-3-642-19239-5
DOI
https://doi.org/10.1007/978-3-642-19240-1

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