Homogenized Gurson-type behavior equations for strain rate sensitive materials

In this paper, the classical Gurson model for ductile porous media is extended for strain-rate-dependent materials. Based on micromechanical considerations, approximate closed-form macroscopic behavior equations are derived to describe the viscous response of a ductile metallic material. To this end, the analysis of the expansion of a long cylindrical void in an ideally plastic solid introduced by McClintock (J Appl Mech 35:363, 1968) is revisited. The classical Gurson yield locus has been modified to explicitly take into account the strain rate sensitivity parameter for strain rate power-law solids. Two macroscopic approaches are proposed in this work. Both models use the first term of a Taylor series expansion to approximate integrals to polynomial functions. The first proposed closed-form approach is analytically more tractable than the second one. The second approach is more accurate. In order to compare the proposed approximate Gurson-type macroscopic functions with the behavior of the original Gurson yield locus, numerical finite element analyses for cylindrical cells have been conducted for a wide range of porosities, triaxialities, and strain rate sensitivity parameters. The results presented evidence that, for large values of the rate sensitivity parameters, the proposed extended Gurson-type models have the important quality to better predict the behavior of rate sensitive materials than the classical one. They also provide simpler and accurate alternatives to more traditional viscoplastic models.