Crack propagation in functionally graded 2D structures: A finite element phase-field study

The finite element phase-field modeling is presented to study the crack propagation in functionally graded (FG) two-dimensional structures. Exploring the influences of the effective parameters of the staggered solver such as load increment and the number of staggered iteration on the phase-field solution and crack propagation analysis of FG structures is the main objective the research undertaken. Based on the concept of FG materials, the material properties are continuously varied along the length and width of the structure according to the Voigt rule of mixture. The finite element phase-field formulation is derived in the variational framework, and the staggered scheme together with the hybrid formulation is implemented to solve the problem and find the crack growth path. Various benchmark problems are modeled and the influences of material distribution pattern, load increment and the number of staggered iteration on the fracture of FG two-dimensional structures are extensively examined. The results revealed that considering large load increment or one staggered iteration considerably overestimate the fracture resistance of FG structures.