Modelling Brittle Fractures with Finite Elements: A Time-independent Phase-field Model

Abstract

The objective of this paper is to propose a 2-D time-independent phase-field model with validating its performance as well as applying it for simulating existing representative experiments. Firstly, the section of the literature review provides an overview of quasi-brittle material and brittle fracture behaviours, as well as the existing FE models from both discontinuous and continuous approaches for simulating fracture behaviours. Next, the governing equations of the proposed phase-field model are determined, which are based on traditional Griffith’s theory as well as a specific variational method evolved from that. The proposed model is implemented in Abaqus. In particular, the implementation is achieved by using the User Subroutine in order to take the phase-field into account. The proposed model is validated by simulating a pure-tension and a pure shear test. In this part, not only the effect of discretisation but also the effects of length parameter and energy release rate has been discussed, of which the latter effect is exclusive in phase-field method. Finally, the validated model is used for simulating two sets of existing experiments, including a mixed-mode test and a series of Brazilian disks test. The results in both validation and simulation part indicate that the proposed model can successfully simulate both crack initiation and propagation in these cases, and good qualitative agreement with theoretical or experimental results can be observed.