Variational crack phase-field model for ductile fracture with elastic and plastic damage variables

Abstract

Based on the study on characteristic features of existing crack phase-field (PF) models for ductile fracture, we propose a new model endowed with elastic and plastic damage variables. In the review part, the emphasis is placed on the plastic driving force and degrading fracture toughness that enable PF models to represent damage evolution in elastoplastic materials. Attention is also paid to the damage evolution tendency in terms of the definition of the yield function. Based on the reviewed features, we originally formulate the proposed model, which separately accommodates two damage variables for elasticity and plasticity. Its constitutive work density consists of elastic, plastic hardening, and damage hardening components. Evolution laws for plasticity and damage are derived by using separate threshold (yield) functions while having similar formats so that those for damage hold variational and thermodynamic consistencies. Also, the proposed model is equipped with thresholds and coefficients to control the amount of damage driving force. Several numerical examples are presented to demonstrate the characteristic features of the proposed model and the ability to mimic the typical fracture behavior of elastoplastic materials.