Mixed-mode fracture assessment of functionally graded materials using rule of mixtures and equivalent stress intensity factor concept

Purpose This paper aims to evaluate mixed-mode fracture behavior in alumina/zirconia functionally graded materials (FGMs) by integrating the rule of mixtures with the equivalent stress intensity factor (SIF) concept. Design/methodology/approach An algorithmic procedure is implemented in ANSYS Parametric Design Language (APDL) that couples the finite element method, displacement-extrapolation technique (DET) and a crack box method with Barsoum singular elements. Tanaka’s formulation and a local fracture angle criterion govern crack propagation, while material gradation follows a spatial power law function (P-FGM) under a homogeneous element modeling strategy. An edge-cracked plate under mixed-mode loading serves as the case study. Findings Simulated SIFs (KI, KII), equivalent SIF (Keq), fracture toughness (KIC) and bifurcation angles show consistent trends across varying volume fraction indices and critical load levels. The proposed strategy provides excellent results under crack growth conditions. Originality/value This work combines multiple fracture-analysis techniques within a single ANSYS APDL algorithm, incorporating DET, crack box and Tanaka’s model in a P-FGM context. The result is a robust, automated tool for precise fracture parameter extraction in FGMs with complex geometries.