Rupture model based on non-associated plasticity

Abstract

This research work is about modeling the mechanical behavior of metallic sheets of AA6016 up to rupture using non-associated flow rule. Experiments were performed at room temperature in uniaxial tension and simple shear in different directions according to the rolling direction and an additional hydraulic bulge test. The anisotropy of the material is described by a Yld2000-2d yield surface [1], calibrated by stress ratios, and a plastic potential represented by Hill1948 [2], calibrated using Lankford coefficients. That way, the former is able to reproduce the yield stresses in different directions and the latter is able to reproduce the deformations in different directions as well [3], [4]. Indeed, the non-associated flow rule allows for the direction of the plastic flow not to be necessarily normal to the yield surface.Concerning the rupture, the macroscopic ductile fracture criterion DF2014 was used [5]. It indirectly uses the three invariants of the stress tensor by using the three following parameters: the stress triaxiality η, the Lode parameter L and the equivalent plastic strain to fracture ∈f−p. In order to be consistent with the plastic model and to add more flexibility to the p criterion, the equivalent stress σ¯ and the equivalent strain to fracture ∈f−p have been substituted respectively as Yld2000-2d and Hill1948 in the DF2014 fracture criterion. The parameters for the fracture criterion were obtained by optimization and the fracture locus can be plotted in the (η,L,∈−p) space. The damage indicator D is then numerically predicted with respect of average strain values. A good correlation with the experimental results is obtained.