Crack kinking in functionally graded materials due to an initial strain resulting from stress relaxation

Small crack kinking in functionally graded materials (FGMs) subjected to a constant initial strain resulting from stress relaxation is studied. The FGMs are modeled as simply nonhomogeneous materials; that is, the effect of microstructure is neglected and the material property variation is considered to be continuous. The material gradation in the FGMs is taken to be of a power-law type. Systematic finite element calculations are made for the energy release rate of the crack. With regard to the local homogeneity, the toughness is taken to be independent of direction; therefore, the crack propagates along the direction of the maximum energy release rate. It is shown that the crack length and the thickness of the surface zone subjected to the initial strain have a strong effect on the kink direction, whereas the material gradients have little effect.