Griffith’s criterion

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. 

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 first summand in this equation is identical to the Hertzian contact radius defined in Eq. (8.39), the second and the third one are due to the adhesive interaction and lead to an increased contact radius compared to the adhesionless case. By using again Griffith s criterion (8.33) in combination with Eq. (8.63), we obtain the equation for the JKR indentation... 

Thus, the fracture criterion remains the same as that for the Griffith s criterion ... 

The transition between cohesive and adhesive failure in a simple bi-material joint has been studied by Kendall (1975). Based on Griffith s energy approach, a criterion is derived for deflection along the interface for a short crack for an isotropic material... 

The eneigy criterion arising from Griffith s work implies that fracture occurs when sufficient energy is released by the growth of the crack to supply the requirements of new fracture surface. The eneigy released comes from the stored elastic or potential... 

Using fracture mechanics and the Griffith s energy criterion, Chow et al. have derived an analytical relation to determine the interfacial fracture energy between a brittle film and a polymeric substrate. 

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. 

From Griffith s energy failure criterion, the termais constant, which implies that strength... 

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. ... 

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... 

The energy criterion for fracture is simply an extension of Griffith s hypothesis which describes quasi-static crack propagation as the conversion of the work done, Wd, by the external force and the available elastic energy stored in the bulk of the specimen, U, into surface free energy, y. It may be written ... 

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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