Finite element prediction of fracture onset in sheet metal forming using a ductile damage model

Abstract

The ability to predict the formability limit of sheet metal forming processes is of paramount importance as the finite deformation in these processes is restricted by geometric instabilities due to necking, strain localization and consequent ductile fracture. Although forming limit diagrams, associated with finite element simulations, are currently available, or are easy to implement, in powerful commercial codes, when complex strain paths are involved, very often combined with an anisotropic behaviour, these predictions fail to give the right answer. Ductile failure is a result of internal degradation described throughout metallographic observations by the nucleation, growth and coalescence of voids and micro-cracks that may lead to macroscopic collapse. The fact that internal degradation (or damage) accompanies large plastic deformation suggests that these two dissipative processes, although different in nature, influence each other and should, therefore, be coupled at the constitutive level. Consequently the theory of Continuum Damage Mechanics may provide a better insight to the physical phenomenon and play a significant role in the study of the formability and fracture onset in sheet metal forming processes. To address these problems a damage model is introduced in a commercial code. This model is based on the enhanced Lemaitres ductile damage evolution law, which includes a distinction between rates of damage growth observed for states of stress with identical triaxiality but stresses of opposite sign (tension and compression), and is coupled with Hills orthotropic plasticity criterion. The resulting constitutive equations are implemented and assessed for the prediction of fracture onset in sheet metal forming processes. A numerical example has been carried out in order to assess the capability of the implemented model in necking prediction and its results were compared with experimental ones.