The form and position of the core region: Its influence on the fracture criteria

Abstract

A comparative study of the fracture criteria based on energy concept indicated their relationships concerning the physical laws on which they are founded. Although the maximum strain energy release rate or G-criterion is based on sound physical concepts, the computational procedures necessary to define exactly the angle of crack extension for an arbitrary angled crack presents a formidable amount of calculations. On the other hand, the minimum strain energy density or S-criterion and the maximum dilatational or T-criterion are compared and their affinities have been established. It was shown that only in the cases when the total strain energy density is due to its distortional component both criteria coincide. Furthermore, the shape of the so-called core region, which normally in all criteria is assumed as a small circle, is one of the main causes of discrepancies of the results of the various criteria. On the contrary, an initial yield locus, which for the Mises yield criterion, takes a kidney-like shape, becomes the most logical locus on which a criterion should be tested. The T-criterion, using this yield locus as core region, is closer to reality and yields satisfactory results in the elastic, as well as in the small-scale yielding regions of loading.