Ductile Failure Under Combined Tension and Shear: Simulation Using A Gurson-Type Porous Plasticity Model

Abstract

A modification of the Gurson–Tvergaard’s yield function based on the micromechanics analysis of the plastic deformation of the porous materials containing spherical empty voids arranged in cubic arrays was proposed by Sean McElwain et al. [2006a, Yield criterion for porous materials subjected to complex stress states, Acta Materialia, 54, 1995–2002; 2006b, Yield functions for porous materials with cubic symmetry using different definitions of yield, Advanced Engineering Materials, 8, 870–876]. The derived yield function possesses in particular the distinctiveness to explicitly depend upon the third stress invariant. On another note, a phenomenological modification of the well-known Gurson–Tvergaard–Needleman (GTN) isotropic hardening model that incorporates damage accumulation under shearing was proposed by Nahshon and Hutchinson, [2008, Modification of the Gurson model for shear failure, European Journal of Mechanics A/Solids, 27, 1–17]. This model incorporates only one extra parameter to account for damage under shear-dominated loadings. In this work, the quasi-static ductile damage and failure behavior of a butterfly specimen is numerically studied using a further extension of this model based on both of the above modifications. To this end, a stress integration algorithm based on the general backwards-Euler return algorithm has been implemented into a finite element code. The simulations show that the proposed extended damage evolution model can capture both the tension and shear failure mechanisms. As long as the softening initiation of the considered specimen is not reached, the computational fracture results highlight the similarities and almost have perfect agreement with those provided by the use of the GTN model. This observation holds for tension-dominated deformation and shear-dominated deformation as well. However, for the later loading, discrepancy shows up at the onset of softening and especially as soon as the failure of material is triggered.