FAILURE CRITERIA FOR ISOTROPIC BODIES REVISITED

Existing failure criteria for isotropic bodies are reconsidered in thi s paper and compared with modern Versions taking into account either t he influence of the strength differential effect or the influence of t he internal dilation of the materials on yielding and therefore the co ntribution of the hydrostatic component of stress in failure. Modern c riteria are expressed by quadric polynomials whose coefficients consti tute convenient terms of the failure tenser of the material which for the isotropic body is defined by the respective failure stresses in si mple tension and compression. Among the different expressions for the respective failure tenser polynomial of a material the paraboloid of r evolution failure locus is the most convenient, since it fulfils the r equirements of invariancy relative to any reference coordinate system, it is flexible and yields a unique solution for each loading path whi le it is unambiguously defined in the stress space. Furthermore, it is in conformity with basic physical laws and the extensive experience t hat the hydrostatic stress constitutes a safe loading path for the mat erial. 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 ma terial, which also takes into consideration the influence of internal dilation of the material and therefore it depends on the hydrostatic c omponent of stresses, is presented. This criterion is an improvement o f the Gurson-McClintock criterion which permits a judicial determinati on of the coefficients of the respective quadric polynomial expressing it, since it belongs to the broad family of criteria based on energy principles.