Brittle fracture - Griffith criterion

What remains to be established is a criterion that will differentiate between the tendency of the solid to respond to external loading by brittle fracture or ductile deformation. This is not an easy task, because it implies a connection between very complex processes at the atomistic level and the macroscopic response of the solid in fact, this issue remains one of active research at present. Nevertheless, phenomenological theories do exist which capture the essence of this issue to a remarkable extent. In an early work, Griffith developed a criterion for the conditions under which brittle fracture will occur [140]. He showed that the critical rate of energy per unit area Gi, required to open an existing crack by an infinitesimal amount in mode I loading is given by 

This can be generalized to the case of a small extension of the crack by Sa, by introducing the energy release rate Gt related to this extension  

The total energy of the solid E is given by the internal energy plus any additional energy cost introduced by the presence of surfaces on either side of the crack plane, which, per unit width of the crack, is 

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 

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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. 

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. 

Griffith criterion The Griffith criterion states that the fracture strength of a brittle solid is solely determined by its elastic properties, its surface tension and the crack or flaw size being in the material... 

The energetic criterion, according to which the crack development into a mechanically solicited composite releases a certain amount of elastic energy that is stocked in material and can be evaluated. When its level attains a critical value, G, the cracks will propagate until the material s fracture. The critical energy of propagation represents an intricate characteristic of material, and in the case of brittle fracture, the Griffith criterion can be ex-... 

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. 

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. 

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... 

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