Numerical simulation of fracture in cup drawing

Abstract

Prediction of the initiation of ductile fracture in deep drawing allows a prior modification of the process which can result in a defect-free final product. This paper deals with the prediction of fracture initiation in deep drawn cup using Lemaitre’s continuum damage mechanics model. The damage is incorporated in the constitutive equation through the principle of strain equivalence. The damage is evaluated using the damage growth law proposed by Lemaitre. An in-house 3D finite element formulation is employed for the analysis. Finite element formulation is based on updated Lagrangian approach. Logarithmic strain measure is used. The incremental stress is made objective by evaluating it in a frame rotating with the material particle. The material is assumed to be elasto-plastic with isotropic strain hardening using von Mises yield criterion. Modified Newton-Raphson iterative technique is used to solve the nonlinear incremental equations. The fracture location predicted by the present formulation is in agreement with the results reported in the literature.