The aim of this paper is to extend the classical Gurson (1977) analysis of a hollow rigid ideal-plastic sphere loaded axisymmetrically to an ellipsoidal volume containing a confocal oblate ellipsoidal cavity. An “expansion” velocity field satisfying conditions of homogeneous boundary strain rate is used to derive a two-field estimate of the overall yield criterion. The latter is shown to be reducible, with a few approximations, to a Gurson-like criterion depending on the “shape parameter” of the cavity. The accuracy of this estimate is assessed through comparison with some results derived from a numerical minimization procedure. An approximate evolution equation for the shape parameter is also presented; comparison with some finite element simulations suggests a slight modification of the theoretical formula leading to considerably enhanced agreement.
Approximate Models for Ductile Metals Containing Nonspherical Voids—Case of Axisymmetric Oblate Ellipsoidal Cavities
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Gologanu, M., Leblond, J., and Devaux, J. (July 1, 1994). "Approximate Models for Ductile Metals Containing Nonspherical Voids—Case of Axisymmetric Oblate Ellipsoidal Cavities." ASME. J. Eng. Mater. Technol. July 1994; 116(3): 290–297. https://doi.org/10.1115/1.2904290
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