Analysis of a propagating crack tip in orthotropic functionally graded materials

Crack tip stress and displacement fields for a propagating crack at constant velocity along a gradient in orthotropic functionally graded materials (OFGMs) with an exponential variation of the shear modulus and density are developed. The crack tip fields are obtained by using wave potentials and the Airy stress function through an asymptotic analysis. Solutions are obtained for orthotropic characteristics of two kinds. Using the stress fields, the effects of material nonhomogeneity on the stress components are investigated. In addition, contours of the constant maximum shear stress at a propagating crack tip are generated and the effects of material nonhomogeneity on the isochromatics are discussed.