Study of mixed-mode fracture in functionally graded material using an adaptive phase-field fracture model

This work systematically investigates the mixed-mode fracture propagation in functionally graded materials. The crack trajectory and load-displacement responses were effectively simulated using the mixed-mode phase field approach in combination with an adaptive mesh refinement technique. The mesh refinement is carried out using quadtree decompositions, and the elements with hanging nodes are handled as n-sided polygons. The adaptive implementation is validated by solving benchmark problems from the literature. The adaptive technique demonstrates greater computational efficiency by significantly reducing the number of elements without compromising the accuracy of the solution. This study provides insight into how fracture propagation behavior is influenced by gradient profile, material gradation, crack location, energy release rate, and displacement configuration in uni-directional and bi-directional functionally graded material. Remarkably, it is found that the peak load on the load-displacement graph changes noticeably, and the fracture path remains constant despite variations in the critical energy release rate. Notably, the results show that materials with lower fracture toughness have an early failure when studying a center fractured plate. This thorough examination deepens our understanding of the propagation of mixed-mode cracks and provides insight into improving the analysis and design methodologies for functionally graded materials.