The mixed mode crack problem in an inhomogeneous orthotropic medium

Abstract

The mixed mode crack problem in plane elasticity for a graded and oriented material is considered. The material property grading is intentional, whereas the property orientation or orthotropy is usually the consequence of material processing. It is assumed that the crack is located in a plane perpendicular to the direction of property grading and the principal axes of orthotropy are parallel and perpendicular to the crack. The four independent engineering constants E11, E22, G12, and ν12 are replaced by a stiffness parameter, E = √E11 E22, a stiffness ratio, δ = (E11/E22)1/4, a Poisson's ratio, ν = √ν12 ν21, and a shear parameter κ0 = (E/2G12) - ν. The corresponding mixed boundary value problem is reduced to a system of integral equations which is solved for various loading conditions and material parameters. The results presented consist of the strain energy release rate, the stress intensity factors and the crack opening displacements. It is found that generally the stress intensity factors increase with increasing material inhomogeneity parameter and shear parameter and with decreasing stiffness ratio.