Simulation of crack paths in functionally graded materials

One of the main interests of fracture mechanics in functionally graded materials is the influence of such an inhomogeneity on crack propagation processes. Using the Griffith’ energy principle, the change of energy has to be calculated, if the crack starts to propagate. In homogeneous linear-elastic structures (asymptotically precise) formulas for the energy release rate are known, but a direct transfer of these methods to functionally graded materials can lead to very inaccurate results. Moreover, the influence of the inhomogeneity on the crack path cannot be seen. Here, a simple model for functionally graded materials is introduced. For this model, a formula for the change of potential energy is derived, giving detailed information on the effect of the gradation on crack propagation.