Principles of Fracture Mechanics

Grain boundaries Path of crack prop ation 

For tensile loading, computation of maximum stress at a crack tip 

If it is assumed that a crack is similar to an elliptical hole through a plate and is oriented perpendicular to the applied stress, the maximum stress, cr, occurs at the crack tip and may be approximated by 

Sometimes the ratio o-Jo-q is denoted the stress concentration factor K,  

Note that stress amplification is not restricted to these microscopic defects it may occur at macroscopic internal discontinuities (e.g., voids or inclusions), sharp corners, scratches, and notches. 

---

The discussion of fracture mechanics will be divided in two parts. First, basic principles of fracture mechanics will be described. Second, the application of fracture mechanics concepts to composite materials will be discussed. In both parts, the basic approach is that of Wu [6-12],... 

In this article after a brief review of elementary principles of fracture mechanics, certain issues concerning the applications to graded materials are identified and some exanqiles are given. 

The test, nevertheless, does have several important features. First, it is accepted by a large technical audience and is in common use. Second, it is a reproducible test, mostly because of the work of the ASTM. Finally, the impact results for various materials are spread over two orders of magnitude. When this spread is compared with the signal to noise ratio, the material range is impressive. Attempts are made to set up this ubiquitous test method on a firm platform based on the principles of fracture mechanics. 

When building a model to predict the mechanical behavior of heterogeneous materials based on polypropylene, the basic principle of fracture mechanics should be considered that fracture is induced in a material when an energy threshold on the weakest zones is reached. It is also well accepted that such energy threshold consists of at least two components necessary energy to initiate a craze and the necessary energy to propagate it. 

Adhesive joints usually fail by the initiation and propagation of flaws and, since the basic tenet of continuum fracture mechanics is that the strength of most real solids is governed by the presence of flaws, the application of such theories to adhesive joint failure has received considerable attention. The reader is referred to reviews for detailed discussions of the general principles of fracture mechanics and to on the application of fracture mechanics to the failure of adhesive joints ". ... 

R. J. Sanford, Principles of Fracture Mechanics, Prentice Hall, 2003. 

The proposed failure theory for slow crack growth Is a probabilistic methodology based on the principles of fracture mechanics. Component failure probability starts at the fast fracture probability and deteriorates with time. In addition to the fast fracture material constants, two additional constants representing the deterioration of mean strength with time are determined from testing. The approach considers both area and volume reliabilities. The software for this task Is completed and incorporated Into the CARES code. 

Fracture mechanics was first applied by A. A. Griffith (1921) as an approach to the analysis and evaluation of the material s behaviour. For the basic principles of fracture mechanics and its present development, the reader is referred to one of a number of available books and manuals Anderson (2005). It is sufficient here to recall a few of the most important notions necessary for considerations of the brittle matrix composites. 

The well-known Griffith s theory constitutes the principle of fracture mechanics. In fracture mechanics, the fracture of a brittle material is caused by the increase of tension-stress at the edges of micro-cracks (disfigurements) in the material. The breaking strength of a catalyst follows the Griffith equation. 

The formation and destruction of an adhesive joint have been shown to be nonequilibrium and non-thermodynamic processes. In the past several years, the principles of fracture mechanics have been employed to study the breaking of an adhesive joint several papers on this subject are published in this volume on Adhesion Science and Technology. ... 

A notable feature of this experimental arrangement is the non-linear relationship that holds between force P and angle 0, a measure of deformation, Eq. (24). Provided that the system is elastic, the principles of fracture mechanics can be applied to systems that follow nonlinear relations between load and deflection. Another example is given in the next section. 

Essentially, continuum fracture mechanics is the study of the strength of a structure which contains a flaw, usually considered as an elliptical crack. The theories were originally developed for the cohesive fracture of materials, and several reviews [1 ] have been published on this subject, but a large body of work has also been reported on extending the principles of fracture mechanics... 

Using principles of fracture mechanics, it is possible to show that the critical stress cr required for crack propagation in a brittle material is described by the expression... 

Principles of fracture mechanics developed in Section 8.5 also apply to brittle and quasi-brittle polymers the susceptibility of these materials to fracture when a crack is present may be expressed in terms of the plane strain fracture toughness. The magnitude of Kjc depends on characteristics of the polymer (molecular weight, percent crystallinity, etc.), as well as on temperature, strain rate, and the external environment. Representative values of for several polymers are given in Table 8.1 and Table B.5, Appendix B. 

One of the purposes of this paper is to differentiate between surface free energy and fracture surface energy. Thus, several basic principles of fracture mechanics are discussed with reference to the Griffith s energy-b J nce concept and the Irwin-Orowan s plastic-zone concept. We also define several frequently misused terms, e.g., effective fracture surface energy, fracture energy and fracture toughness. Actual values of related parameters are presented to illustrate the applicability of fracture mechanics to the selection of polymers for structural materials. 

---