A phase field model for ductile fracture considering the strain rate, stress triaxiality and Lode angle parameter

Ductile materials exhibit rate-dependent behaviors when subjected to different loading rates, particularly during impact and explosion events. In order to investigate the high strain rate behaviors of metal materials, a phase field model considered the rate-dependent threshold for effective plastic work is proposed. And the presented model couples the influences of the stress triaxiality and Lode angle parameter on failure behaviors. Later, a single element is modeled to demonstrate the impacts of the model in predicting stress-strain relations under varying loading rates. To illustrate the impacts of the Lode angle parameter on load-displacement responses, rectangular notch specimens are used. Next, the presented model is employed to mimic the shear fracture of hat-shaped specimens at different strain rates based on the split Hopkinson pressure bar tests, and the model parameters are calibrated by comparing the strain waveforms between the simulations and experiments. The numerical results indicate the developed model is capable of accurately reproducing the shear ductile fracture of the hat-shaped specimens under high strain rates.