Multiple crack problems in nonhomogeneous orthotropic planes under mixed mode loading conditions

•Stress analysis is carried out in nonhomogeneous orthotropic planes under mixed mode loading conditions.•Dislocation densities are employed to determine stress intensity factors for multiple cracks.•Formulation is applicable for several different cases of crack configurations and arrangements.

Analytical method based on continuous dislocation technique is developed to examine the mixed mode behavior of a functionally graded orthotropic plane. First, the elastic stress fields in a functionally graded orthotropic infinite plane containing single Volterra types climb and glide edge dislocations are obtained. Using the dislocation solutions, the problem of interacting cracks is reduced to a system of singular integral equations for dislocation density functions on the surfaces of smooth cracks which are solved numerically for the dislocation density. Then, the dislocation density function is applied to calculate the stress intensity factors for several different cases of crack configurations and arrangements.