The independence of the [formula omitted] from the strength anisotropy of the materials

Abstract

The validity of the maximum dilatational strain energy density (SED) or T- criterion was shown up to now for brittle materials, where the elastic version of the criterion applies, or for ductile materials where the HRR-singular plastic field was used for defining the components of elastic energy and plastic work. However, none of the well established criteria has faced the real situation of engineering materials, the so-called strength differential effect, according to which, although the materials may even by isotropic, however, they always present different strengths in tension and compression. The SD-effect can be described by convenient failure loci. In this paper it was shown that, by applying the T- criterion to the most generalized failure criterion, which is the elliptic paraboloid failure criterion, this gives the same conditions concerning the angle of initiation of propagation of the crack and equal ratios between the components of the dilatational and the distortional components of SED either for the singular or the two-term solution of the stress distribution around the oblique internal crack in an infinite plate. Then, the T- criterion remains independent and invariant from the type of solution of the elastic problem and the form of the yield and failure locus assumed for the material of the plate.