An assessment of the phase field formulation for crack growth

The phase field description for crack growth and fracture is an attractive alternative to numerical methods based on discrete representations of cracks, since the phase field methodology avoids the numerically challenging monitoring of the discontinuities introduced by the crack. In particular, for the simulation of complex crack growth topologies and application to coupled systems, e.g. with thermal or electrical fields, the phase field method has shown promise. However, an accurate prediction of the crack growth initiation is mandatory for a reliable simulation of crack trajectories both in terms of load history and the path followed through the material. In this work, we therefore investigate predictions of crack growth derived from the phase field method and compare them with established relations from fracture mechanics. To implement the phase field method for crack growth, a parallelized finite element method computer code using adaptive mesh refinement is developed and implemented. Results from it are presented. For these results, pre-existing cracks are introduced into the finite element model in two ways, including their representation as discrete discontinuities and as heterogeneities in the phase field order parameter.