Fracture Investigation of the Ductile Materials Using Phase-Field Model

Abstract

Phase-field models have been the subject of a great deal of research in recent years. Investigations have revealed that the phase-field model is capable of generating complex crack patterns. This is gained by replacing the sharp discontinuities with a scalar phase damage field comprising the diffuse crack topology. In the previous models, cracks are blurred into the surrounding areas due to introducing dependency of degradation function to a single parameter, strain threshold. The stable crack initiation and propagation require estimation of complex higher-order degradation function, which should be solved either by a new iteration scheme or using extremely small loading increment. However, this demands considerably high computational cost. In this study, the nonlinear coupled system comprising the linear momentum equation and the diffusion-type equation governing the phase-field evolution is solved concurrently through a Newton-Raphson approach. Moreover, an improved degradation function and staggered iteration scheme are solved by a one-step paradigm is proposed. Such that the computational costs can be reduced, and the stability of crack propagation can be improved. A phase-field model for ductile fracture is carried out in the commercial finite element software Abaqus by means of UEL and UMAT subroutines. Post-processing of simulation results is implemented through an added subroutine implemented in the visualization module. Several benchmark problems show the proposed model's ability to reproduce some essential phenomenological characteristics of ductile fracture as documented in the experimental literature.