Gradient damage model for ductile fracture introducing degradation of damage hardening modulus: implementation and experimental investigations

This study presents a gradient damage model for ductile fracture, in which the damage hardening modulus is degraded by the accumulation of plastic deformation and the volume expansion caused by negative hydrostatic pressure. The proposed model fulfills the thermodynamic requirements, and the governing equations are derived from energy minimization principles. Two parameter studies are carried out to confirm the basic performance of the proposed model, in which some typical ductile fracture responses are demonstrated by changing parameters for degrading the damage hardening modulus. Also, a series of numerical experiments are presented to reveal the ability of the proposed model to successfully simulate the fracture tests of advanced high strength steel sheets with different tensile strengths. It is indeed confirmed by the close agreement with experimental results that the proposed model is capable of realizing the breaking elongation, the transitional behavior from unstable to stable crack propagations, and the corresponding load–displacement curves. Also, the model successfully reproduces and predicts the crack initiation positions in notched specimens with different notch radii.