Effective fracture toughness in phase-field models for interface fracture

<p dir="ltr">When applying the phase-field fracture model (PFFM) to interface fracture, the diffuse phase-field damage interferes with the surrounding bulk material, artificially increasing the apparent interface fracture toughness (assuming the bulk material has a higher fracture toughness). This effect can be mitigated by using an effective fracture toughness value. However, existing analytical expressions in the literature for effective fracture toughness neglect the history of tensile elastic strain energy during loading, which is shown here to be a crucial factor, even for a crack in a homogeneous material. In this work, the phase-field damage profile around an interface crack is derived from first principles, explicitly accounting for tensile elastic strain energy. The effective fracture toughness is then evaluated using a variation of the established energy dissipation balance approach. Finite-element method (FEM) simulations are conducted to model crack propagation in various configurations using the PFFM. First, the effective fracture toughness is determined empirically by tuning it until the apparent toughness matches the interface material’s fracture toughness. Second, the FEM results are compared against three new mathematical models developed in this work, and the current best model from the literature, considering effective fracture toughness and crack phase-field damage profiles. Although all the new mathematical models show good agreement with FEM results, one model in particular, which modifies sharp crack theory to approximate the tensile elastic strain energy in the PFFM, shows particularly strong agreement with FEM results in all regards, and outperforms models that disregard tensile elastic strain energy. This model can be used to accurately and efficiently pre-compute effective fracture toughness for PFFM simulations.