3D finite element simulation of deep drawing with damage development

The elasto-plastic constitutive equation accounting for isotropic hardening coupled with material damage has been implemented in the finite element code ABAQUS. A damage variable, which was defined in meso-scale, was used to reveal the effects of micro-defects within the material. With an explicit integration scheme, deep drawing of a mild steel square cup was simulated using the ABAQUS with a specially designed VUMAT subroutine. The three-dimensional brick element was adopted to build-up the finite element model, and the contact and friction between the blank and tool were taken into consideration. The forming process of deep drawing is a non-proportional loading one, so that the accumulated damage state variable depends on the strain path, or in other words, the loading history. The damage evolution and the wrinkle formation under the influences of Coulomb friction and the blank holding force were analyzed and discussed. Experiments have been conducted to investigate the effect of blank holding force on wrinkling, and determine the position of crack initiation. Experimental results are in good agreement with the predicted ones.