A note on pseudo-cohesive behavior in quasi-bidimensional brittle fracture

This paper addresses the study of a planar crack in a plate with a slightly curved crack front, as found in most nominally plane strain tests. Rather than trying to make a full three dimensional analysis of the elastic fields, we look for a systematic procedure to project the three-dimensional features on the plane of the plate. This is achieved by though-the-thickness averaging of the stress and displacement fields. It is shown that the resulting fields are pseudo-cohesive, which means that their expressions are formally identical to those corresponding to a traditional cohesive zone. The results for two simple cases are given to illustrate the pseudo-cohesive behavior, although general results are derived as obvious consequences of the averaging process. The general procedure to carry out the analysis for any kind of crack front shape is indicated, and the application to special cases such as fatigue-grown cracks in metals and stably growing cracks in brittle polymers is shortly discussed.