7 - Crack propagation and fracture mechanics

Summary

The object of the chapter In the absence of plastic strain, the problem of brittle fracture by extension of cracks can be presented in a thermodynamic framework, analogous to that of elastoplasticity. This means that the fracture criterion (or the criterion of crack propagation) replaces the plasticity criterion. One important notion is the notion of mechanical field singularity (displacement, stresses).

Introduction and elementary notions

We are interested in the problem of fracture, a phenomenon that occurs, more or less violently, under monotonic loading (whereas fatigue concerns cyclical loading). More specifically, we are interested in the problem of cracking, that is, the progagation of macroscopic cracks (of size of the order of one millimetre), whereas the beginning of cracking belongs to the microscopic and to the metal analyses which will not be examined here. (Microscopic cracks are one cause of damage – see Chapter 10.) The aim of this study is to arrive at a formulation of the crack-propagation laws, based upon fracture criteria and the definition of the conditions that may insure resistance to this fracture. We are certainly aware of the interest that such a subject implies for industry; it suffices to think about aeronautical engines and nuclear installations. Actually, our main interest is brittle fracture, that is, the kind that occurs without considerable plastic strain (i.e. the separation mechanism of crystallographic facets through cleavage), whereas ductile rupture is produced by different mechanisms accompanied by great plastic strains).