Fracture behavior of thermal mismatch in functionally graded materials using phase-field modeling

A phase-field modeling is presented to study the complex thermal mismatch fracture behavior in functionally graded materials. The fracture resistance in functionally graded materials is homogenized by the rule of mixtures of the energy release rate. For validation, the bi-material plates and rectangular plates coated with functionally graded materials under thermal load are examined and the obtained results are compared with existing theoretical and experimental data. In the bi-material plates, the model captures commonly experimentally observed crack patterns such as the perpendicular crack, benching, and the formation of two pairs of parallel cracks. Additionally, a detailed comparison of the correlation between crack depth and film thickness is conducted among theoretical, experimental, and phase-field model data. Notably, the results of the phase-field model exhibit good agreement with experiments compared to the theoretical model. Subsequently, the model is applied to examine the thermal mismatch fracture behavior in plates of different shapes. The analysis emphasizes three key aspects: (i) examining the damage field to understand crack initiation and propagation, (ii) analyzing the major principal stress field in the coatings to identify fracture-critical regions, and (iii) tracking the evolution of elastic/fracture/total energies to investigate the fracture/deformation behavior. This analysis enhances a fundamental understanding of thermal fracture mechanisms in functionally graded materials and provides a foundation for optimizing materials and structures in various engineering applications.