A shear modified enhanced Gurson constitutive relation and implications for localization

Abstract

The most widely used phenomenological constitutive relation to model ductile failure of structural metals at room temperature is based on the work of Gurson (1977) and has the advantage of having both a micromechanics basis and sufficient simplicity to enable complex engineering calculations to be carried out. The predictions of this framework have been most successful in circumstances where the stress triaxiality, the ratio of mean normal stress to Mises effective stress, is relatively large. For stress states with smaller values of stress triaxiality, the predictive capability has typically been much reduced. We present a shear modified enhanced Gurson constitutive relation that combines the shear modification of Nahshon and Hutchinson (2008) with the second porosity concept of Gologanu et al. (1994). This maintains both the connection with micromechanics and the computational simplicity. The predictive capability of the framework is illustrated by the good agreement with cell model calculations for localization of deformation over a wide range of stress states. Strain localization analyses with an initial porosity imperfection predict that for axisymmetric stress states with a superposed hydrostatic tension, the minimum critical strain for the onset of localization follows the onset of coalescence, as defined within the context of the constitutive model here, if the value of the stress triaxiality is sufficiently small. For an imposed shear stress state with a superposed hydrostatic tension, the minimum critical strain for the onset of localization is predicted to precede the onset of coalescence. A strong sensitivity of the critical strain for localization of deformation to the strain or stress range over which void nucleation occurs is also predicted, with void nucleation and localization of deformation essentially coinciding for sufficiently abrupt nucleation.