Functionally graded materials with periodic internal cracks subjected to transient loading

A periodic array of cracks in a functionally graded material under transient mechanical loading is investigated. Anti-plane shear loading condition is considered. A singular integral equation is derived, in which the crack surface displacement is the unknown function. Numerical results are obtained to illustrate the variations of the stress intensity factors as a function of the crack periodicity for different values of the material nonhomogeneity, either at the transient state or at the steady state. The material non-homogeneity can increase or reduce the stress intensity factors. Comparing with the single crack solution, it can be shown that multiple cracking can reduce the stress intensity factor significantly.