Brittle crack growth modeled as the forced separation of chemical bonds within a K-field

The focus here is the growth of a planar crack in a brittle material under two dimensional plane strain conditions. The stress field surrounding the crack edge is presumed to be an elastic stress intensity factor field, or K-field, as is characteristic of such systems. However, as the observation point within the K-field approaches the crack edge, that field gradually gives way to a zone of material separation that is coplanar with the crack and that is characterized as a region of chemical bond breaking. The separation zone is spanned by a large number of identical atomic or molecular bonds resisting the influence of the surrounding stress field. The trailing edge of that zone coincides with the physical crack edge. By describing the collective response of these bonds in terms of the behavior of a generic bond and the statistical concept of survival probability, the process of material separation is followed to its end with no further requirement of a material failure condition. In this way, the physical process of material separation is related directly to the commonly measured fracture parameters for brittle materials.