Griffith-Irwin criterion

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... 

Assuming the Griffith-Irwin criterion (Eq. 13), one can calculate crack sizes corresponding to the measured strength values. Values obtained in this fashion are tabulated... 

If, however, the criterion (lb) or (3b) holds, then the system can be treated by Griffith-Irwin (29,30) crack theory, as extended by Good (24) to interfacial separation. That treatment yields the expression. 

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. 

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. 

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... 

Alternatively to the Griffith s energy criterion, In the 1950s Irwin calculated the stresses in the vicinity of a crack tip based on linear elasticity theory. He introduced a constant, K, the stress intensity factor, to characterize the magnitude of the stress field. If K (Kj in mode I) reaches a critical value Kc (Kjc), then the crack will propagate in the material Kjc is generally expressed in MPam. ... 

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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