Griffith fracture criterion

In a disordered solid, as modelled by the percolation model (discussed in Section 1.2) with intact bond concentration p on a lattice, there occur various vacancy clusters (voids), or pre-existing cracks, of different sizes and shapes. The typical crack size in such a percolating solid being of the size of the correlation length (see Section 1.2.1) the application of the Griffith fracture criterion gives (Chakrabarti 1988, Ray and Chakrabarti 1985a,b) from equation (3.4)... 

The first fracture criterion was defined by Griffith, supposing that fracture occurs when sufficient energy is released (from the stress field) by growth of the... 

The point to notice is that a threshold level of stored energy in the bond is necessary before AG -> 0 and thus before the forward reaction can proceed. This stored energy is, of course, equal to AG and thus (when normalised) to the surface energy of the material. Thus we see that the kinetic model of fracture requires a minimum energy supply equal to the surface energy, which is the fracture criterion employed by Griffith. No contradiction therefore exists between the kinetic and Griffith theories. 

The concept of quasi-brittle fracture implies that some materials that exhibit the characteristics of plastic materials at standard test, collapse in tests of the sample with a crack due to the quasi-brittle mechanism, that is, plastic deformation is concentrated in a narrow layer near the tip of a crack. For such materials, Griffith s criterion is relevant instead of the value of the surface energy to introduce the work of plastic deformation at the crack tip. 

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] ... 

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

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

To understand ductile-to-brittle transitions, the Rice criterion in which the ratio between the surface energy (Griffith fracture energy) and the unstable stacking fault energy is often... 

Figure 6.1 Griffith-Orowan fracture criterion. (Courtesy of Prof. A. T. DiBene-detto.)...

The Griffith-Orowan criterion for spontaneous fracture is defined as the critical crack depth at which the slope dUj/da changes abruptly to negative values as shown in Fig. 6.1. Mathematically, this condition corresponds to... 

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... 

Equation (8.50) is known as Griffith s fracture criterion. It includes a critical value of the strain energy release rate, denoted Gjc, and the latter is determined by the surface parameter w. The subscript T is used in the literature to indicate reference to the opening mode V of Fig. 8.30 and to discriminate it from other possible modes of loading. From Eqs. (8.49) and (8.50) follows the critical value of the tensile stress, as... 

Griffith s criterion for brittle fracture involves a remarkably simple expression. It is straightforward to relate the energy release rate to the stress intensity factors introduced above to describe the stresses and displacements in the neighborhood of the crack. In particular, for mode / loading in plane strain, the energy release rate Gi and the stress intensity factor A / are related by... 

The similarity between elastic and extending viscoelastic cracks carries over to the criteria for crack extension. In Sect. 4.6, the implications of an energy balance criterion for the growth of a crack in a viscoelastic body are explored. The condition obtained depends only on the initial values of the relaxation functions and takes the same form as that derived by Griffith for an elastic body. There follows, in Sect. 4.7, a demonstration valid in viscoelasticity, that the above condition may be expressed in terms of critical values of the stress intensity factors, which in turn are expressed in terms of distributions of cohesive forces at the crack ends. In this way, Barenblatt s elastic fracture criterion has been extended to viscoelasticity. 

Earthquake Mechanisms and Stress Field, Fig. 5 Griffith failure criterion, (a) Scheme of a cylindrical specimen with a fracture created by loading with stresses tri > (72 = left) and the corresponding Mohr s circle diagram (right), (b) Position of different... 

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