Griffith-Irwin fracture criterion

Inserting Eq. (12.4) into Eq. (12.5) gives the so-called Griffith-Irwin fracture criterion... 

It is assumed that the limit equilibrium state is reached if cracks develop and increase on the surface of the body volume under action of external loadings. In linear fracture mechanics, Irwin s force criterion and an equivalent Griffith s energy criterion completely determine the equilibrium condition of a continuum elastic body with a crack [9],... 

Irwin proposed the concept of quasi-elastic fracture, which allows us to extend the limits of applicability of Griffith s theory [11], Irwin s criterion is valid not only for brittle materials, but also for elastic-plastic materials with significant plastic deformation developing until the moment of actual destruction of a material. 

The basis of another theory is the triggering of a fracture at pre-existing cracks in the substrate or within the film according to the so-called Griffith-Irwin criterion [25,86] ... 

According to fracture mechanics, catastrophic fracture (fast crack growth) occurs at the Griffith-Irwin criterion (Lawn, 1993) given by... 

Irwin has reviewed fracture mechanics as applied to adhesive systems. Griffith was the first to apply fracture mechanics to solids. His formulation of fracture mechanics begins with Eq. (54) above, except that the fracture criterion in his formulation was the amount of energy expended to create... 

This approach was later modified independently by Irwin (51,52) and Oro-wan and Weld (53) and Orowan (54) by including a strain energy release rate term to account for changes caused by small-seale plastic deformations at the crack tip and surfaces. Below, an expression is derived using the modified Griffith criterion for the occurrence of spontaneous fracture of a brittle material depicted in Fig. 6.1. 

In many particular cases, there is a direct correspondence between the Irwin and Griffith criteria, as was noted above an connection with the result in (4.27). However, the latter criterion has the distinct advantage that the energy release rate can often be determined, or at least estimated, without the need for a complete solution of the boundary value problem for the stress field in the body. For this reason, it is selected as the basis for the present discussion. Many of its special features and numerous extensions of the basic concept will become evident in the sections that follow, in the course of discussing various issues concerned with delamination and fracture in thin film configurations. 

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