Effective fracture toughness in phase-field models for mode-II interface fracture: A maximum energy envelope method

Modelling shear-driven interface fracture is essential for predicting interfacial failure in composites and bonded structures. When applying the phase-field fracture method to these problems, the diffuse phase-field damage interferes with the (usually tougher) surrounding bulk material, artificially delaying crack propagation. While pre-computing an effective fracture toughness to mitigate this effect has been successful for mode-I loading, current methodologies are insufficient for mode-II fracture. The effective toughness calculation relies on accurately predicting the phase-field damage field, which is governed by the history function—the historical maximum of the strain energy density (SED). The mode-I approach approximates the history function using a vertical slice through a modified total SED field from sharp crack theory, which is not appropriate for asymmetric shear fields. Here, an analytical anisotropic split of the total SED approximation based on the volumetric strain distribution mirrors the numerical implementation. Further, a maximum energy envelope method is derived. By exploiting the scale-invariant properties of sharp crack theory, this method captures peak SED values experienced at each material point. The resulting maximum energy profile is used to solve for the phase-field damage profile and determine effective fracture toughness values via an energy balance approach. Finite element method simulations of various end-loaded split tests demonstrate that, while previous approximations fail, the proposed maximum energy envelope method recovers the true material fracture toughness with excellent accuracy across all shear propagation cases. This establishes a robust framework for simulating pure shear interface cracks, providing the foundation to accurately predict mixed-mode failure in heterogeneous materials. • Model enables efficient pre-computation of mode-II effective fracture toughness. • Anisotropic split of analytical strain energy density to match numerical method. • New maximum energy envelope method derived for history function prediction. • Captures true peak strain energy density in asymmetric shear fields. • Effective fracture toughness model validated on various shear-loaded configurations.