A complex variable approach for asymptotic Mode-III crack-tip fields in an anisotropic functionally graded material

This paper addresses asymptotic full crack-tip fields for an anti-plane (Mode-III) stationary crack in an anisotropic functionally graded material. A monoclinic material that has a material symmetry plane is considered. The complex variable approach and the asymptotic analysis are used to solve a perturbed Laplace equation resulting from material anisotropy and gradation. The out-of-plane displacement and stress solutions are provided for a crack in exponentially and linearly graded anisotropic materials by considering material gradation either parallel or perpendicular to the crack. The characteristics of the asymptotic solutions in an anisotropic functionally graded material are compared with those for anisotropic homogeneous and isotropic graded materials. Finally, engineering significance of the present work is discussed.