Gurson's Criterion and Its Derivation Revisited

This paper revisits Gurson's (Gurson, A., 1975, Plastic Flow and Fracture Behavior of Ductile Materials Incorporating Void Nucleation, Growth, and Interaction, Ph.D. thesis, Brown University, Rhode Island; Gurson, 1977, Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I-Yield Criteria and Flow Rules for Porous Ductile Media, ASME J. Eng. Mater. Technol., 99, pp. 2-15) classical limit-analysis of a hollow sphere made of some ideal-plastic von Mises material and subjected to conditions of homogeneous boundary strain rate (Mandel (Mandel, J., 1964, Contribution Theorique a l'Etude de l'Ecrouissage et des Lois d'Ecoulement Plastique, Proceedings of the 11th International Congress on Applied Mechanics, Springer, New York, pp. 502-509) and Hill (Hill, R., 1967, The Essential Structure of Constitutive Laws for Metal Composites and Polycrystals, J. Mech. Phys. Solids, 15, pp. 79-95)). Special emphasis is placed on successive approximations of the overall dissipation, based on a Taylor expansion of one term appearing in the integral defining it. Gurson considered only the approximation based on the first-order expansion, leading to his well-known homogenized criterion; higher-order approximations are considered here. The most important result is that the correction brought by the second-order approximation to the first-order one is significant for the porosity rate, if not for the overall yield criterion. This bears notable consequences upon the prediction of ductile damage under certain conditions.