This paper presents a phase-field model to analyze thermal-mismatch fracture behavior in functionally graded materials (FGMs). By homogenizing fracture resistance via the rule of mixtures , the model accurately captures complex experimental crack patterns in bi-material plates, showing better agreement with experimental data than theoretical models.

The validated model is applied to investigate thermal fractures in circular, square, and triangular FGM plates. It provides a fundamental understanding of fracture mechanisms by analyzing three key aspects: damage fields for crack propagation, principal stress fields in fracture-critical regions, and energy evolution during deformation.