Lode-dependent second porosity in porous plasticity for shear-dominated loadings

Abstract

Ductile fracture of metallic alloys in shear-dominated loadings 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 GTN yield criterion. In this work, the two approaches are combined with a very simple equation for the second porosity evolution depending on the Lode variable. The new model involves two material parameters. They determine the intensity of the Lode effect and could be calibrated with several specimen geometries in which the Lode variable ranges from zero to some intermediate value (positive or negative). Finite element calculations of a notched KAHN specimen are performed with the Rousselier porous plasticity model (polycrystalline version). The model without the Lode effect first includes the Coulomb-Rousselier-Luo failure model at the slip system scale for ductile damage in shear, in agreement with the experimental load-notch opening displacement curve of an aluminum alloy sheet and with observations of the fracture mechanisms at the micro-scale. Then the Lode effect is also included. The damage mechanisms involved in the different resulting cracks are discussed: flat tensile crack in the notch plane, shear lips on the two specimen surfaces and slant crack, in relation with the local Lode variable. The load-displacement curve softening depends on the model parameters.