This paper proposes a diffused approach to approximate failure at interfaces that physically occupy negligible space compared to the bulk material. For an interface diffused over a certain length, we derive an effective interface fracture toughness based on the diffused length and the fracture toughness of the bulk and the interface. Our derivation ensures the energetic equivalence between the sharp and the diffused representations of interface.

We verified the critical energy release rates in a steadily propagating tensile fracture example as well as the critical fracture pressure and the crack length evolution in toughness dominated hydraulic fracturing. The proposed model does not require any changes in existing implementation of phase-field models. The only requirement is to assign the analytically calculated effective interface fracture toughness over a diffused sub-domain.