Displacements, strains and stresses associated with propagating cracks in materials with continuously varying properties

Crack tip stress, strain and displacement fields for a propagating crack along the direction of property gradation in functionally graded materials (FGMs) are obtained through an asymptotic analysis coupled with a displacement potential approach. The analysis for the opening mode is performed assuming two types of property variation: (a) linearly varying shear modulus with constant density, and (b) exponentially varying shear modulus and density. The first six terms in the series expansion of the stress, strain and displacement fields for the dynamic crack are derived to explicitly bring out the influence of nonhomogeneity on the structure of the displacement, strain and stress fields. The analysis revealed that crack tip stress fields retain the inverse square root singularity and only the higher order terms in the expansion are influenced by material inhomogeneity. Using these stress, strain and displacement fields, contours of constant maximum shear stress, constant first stress invariant and constant in-plane displacements are generated and the effect of the nonhomogeneity parameter on these contours is discussed.