Phenomenological uncoupled ductile fracture model considering different void deformation modes for sheet metal forming

A mathematical model of ductile fracture behavior is devised by considering fracture incipience as a void deformation limit phase. To this end, two major void deformation modes, viz., void dilation and void elongation/rotation are carefully considered in the model. Void dilation is governed by the normalized first principal stress, whereas void elongation/rotation is characterized by the normalized maximum shear stress. To model the ductile damage accumulation process caused by plastic deformation, the above two void deformation modes are carefully combined with a strain-based nonlinear void nucleation function in an integral framework, with model parameters with clear physical meanings being introduced. Through hypothesis of a proportional loading, a 3D fracture surface function is obtained. The 3D fracture surface is calibrated using a robust experimental-numerical approach for a dual-phase steel (DP780) sheet. In addition, the fracture data of two aluminum alloys are used for construction of their 3D fracture surfaces. The acceptable deviation of the predictions from the experimental results confirms the good prediction performance of the proposed model for various metals under the distinctly different stress states that often manifest in sheet metal forming processes. Moreover, scanning electron microscopy analysis of the DP780 specimens further demonstrates that the proposed model expresses a reasonable correlation between the stress state, void evolution, and material ductility.