Development of a damage-based criterion for ductile fracture prediction in sheet metal forming

Abstract

Abstract A second-order continuity tensor ψ is proposed to characterize the state of anisotropic damage in ductile sheet metal during a forming process. The continuity tensor can be determined from the effective elastic stiffness matrix and it satisfies the requirement of symmetry for derivation of the effective elastic stiffness matrix and it satisfies the requirement of symmetry for derivation of the effective stress tensor, the effective elastic strain tensor and the effective elastic stiffness tensor. The corresponding anisotropic damage constitutive relations are formulated to model the damage-failure process for sheet metal. Hence, the expressions of the specific damage energy release rate Y , taking into account damage anisotropy and stress triaxiality, have been derived by means of decomposing Y into a hydrostatic and a deviatoric part. The damage evolution equation is established in terms of a Lemaitre’s type plastic damage dissipation potential and plastic stress–strain relation. The minimum principal component of continuity ψ II is taken as the predominant factor governing the damage failure process. A damage-based criterion, which is a non-linear function of the equivalent plastic strain, the triaxiality factor and the continuity threshold, is finally derived for the prediction of fracture strains. An example of the biaxial stretching of steel sheet has been used to demonstrate how the criterion can be applied to predict the fracture limit. The results show that the predicted values are in agreement with experimental values.