Gurson revisited and multiscale-multimechanisms modeling

Abstract

Ductile fracture of metallic alloys is mainly attributed to initiation, growth and coalescence of micrometric voids. In 1977, Gurson’s kinematic limit analysis of the hollow sphere provided an analytical upper bound of the yield surface in the case of fully plastic flow: Gurson’s famous porous plasticity model. But in the case of flow with a conical rigid section, Gurson only fitted an empirical equation to his ”data points”. In 2004, the numerical limit analysis methods developed by Pastor et al. pointed out the existence of a corner of the yield surface on the hydrostatic axis that is not obtained with the empirical equation. The two parameters of Rousselier’s thermodynamically-derived model provide a good fit to Gurson’s data points in both cases of fully plastic flow and flow with rigid section, simultaneously. It is of utmost importance for ductile fracture modeling as void coalescence involves a transition from fully plastic flow to flow with rigid section. This model yield surface shows a corner with the right slope $-3/2$ corresponding to void coalescence and strain localization in a band normal to the main loading direction. In shear-dominated loadings, rotation and flattening of micrometric voids is also observed. It is usually modeled either with uncoupled failure criteria or with porous plasticity. In the first approach, criteria depending on the third invariant of the stress tensor: the Lode variable, have been developed. In porous plasticity, a second porosity was added to the yield criterion by Gologanu, Madou, Leblond and Morin (1993, 1994, 2012). In this work, the two approaches are combined with a very simple equation for the second porosity evolution depending on the Lode variable. The novelty lies in applying void nucleation, growth, rotation and flattening models also to the secondary nanometric voids that are observed inside the grains and in microscopic shear bands. At this latter scale, a modified Lode variable is used depending on the resolved shear and normal stresses of each slip system. Multiscale modeling is thus required. The dissipative Coulomb-Rousselier-Luo (2014) failure model at the slip system scale is also considered for ductile fracture without voids observed in aluminum alloys. The use of reduced texture polycrystalline models is a good compromise between macroscopic plasticity and crystal plasticity finite element method. Finite element calculations of a notched specimen are performed to illustrate the effects of the various damage models.