On the Failure Locus of Isotropic Materials in the Stress Triaxiality Space

The aim of this paper is to contribute to the prediction of the failure of materials (ductile and brittle) with a single criterion (rule) not violating the assumptions of continuum mechanics. In this work, the failure behavior of isotropic materials is connected with the ability of a material to store elastic strain energy from the very start of loading until its fracture. This elastic strain energy is known that is separated in a distortional and a dilatational part. So, when one of these quantities takes a critical value, then the material fails either by slip or by cleavage. The behavior of a material is described with regard to the secant elastic moduli depending on both unit volume expansion Θ and equivalent strain $ɛeq$⁠. This dependence enlightens, in physical terms, the different reaction of materials in normal and shear stresses. T-criterion is applied for the prediction of failure in a series of experiments that took place to an aluminum alloy (Al-5083) and to PMMA (Plexiglas). A single criterion was used for two totally different materials and the predictions are quite satisfactory. This work is a step toward the direction of using one criterion in order to explain and predict failure in materials independently of the plastic strain that developed before fracture.