Failure criteria for isotropic bodies revisited

Abstract

Existing failure criteria for isotropic bodies are reconsidered in this paper and compared with modern versions taking into account either the influence of the strength differential effect or the influence of the internal dilation of the materials on yielding and therefore the contribution of the hydrostatic component of stress in failure. Modern criteria are expressed by quadric polynomials whose coefficients constitute convenient terms of the failure tensor of the material which for the isotropic body is defined by the respective failure stresses in simple tension and compression. Among the different expressions for the respective failure tensor polynomial of a material the paraboloid of revolution failure locus is the most convenient, since it fulfils the requirements of invariancy relative to any reference coordinate system, it is flexible and yields a unique solution for each loading path while it is unambiguously defined in the stress space. Furthermore, it is in conformity with basic physical laws and the extensive experience that the hydrostatic stress constitutes a safe loading path for the material. Experimental evidence with all varieties of isotropic materials corroborates the theory upon which the criterion is based. Finally, a failure criterion, based on void coalescence mechanisms inside the material, which also takes into consideration the influence of internal dilation of the material and therefore it depends on the hydrostatic component of stresses, is presented. This criterion is an improvement of the Gurson-McClintock criterion which permits a judicial determination of the coefficients of the respective quadric polynomial expressing it, since it belongs to the broad family of criteria based on energy principles.