Simulations of crack propagation in elastic-plastic graded materials

This paper introduces a criterion suitable for the simulation of crack propagation in elastic-plastic graded materials. It proposes a power-law relationship between the two critical failure parameters, surface separation energy and peak separation stress, which are spatial variants in graded solids. To investigate its feasibility, this criterion is implemented in finite element models and tested under various dynamic failure conditions. First, dynamic crack propagation in double cantilever beam model is considered and the effects of the failure parameters are investigated. The results show crack propagation behavior is highly dependent on the variations of the failure parameters. Evolutions of various energy components are also monitored during the crack growth to evaluate failure characteristics of graded materials. Unlike homogeneous materials, crack propagation in elastic-plastic graded materials never attains a steady state and the fracture energy associated with crack growth continues to vary as the crack propagates through the graded region. In a subsequent analysis, impact failure of a ceramic-metal graded layer is considered. In this case, multiple crack initiate and propagate at various locations. Additionally, different through-thickness compositional gradations are examined to study their effects on cracking profiles and energy absorption characteristics. It is demonstrated that the cracking substantially alters the overall pattern of energy evolutions even though the energy directly consumed by the surface separations remains small. This study concludes that similar approaches can be employed for investigating failure in other inhomogeneous/heterogeneous materials to optimize their design.