Mixed mode axisymmetric annular cracks in a finite layer: Off angle crack initiation

The solutions of axisymmetric Volterra type climb and glide edge dislocations are obtained in a layer by means of the Hankel transforms. Utilizing the same procedure, Green’s function solution is obtained for a layer under self-equilibration normal ring traction. The distributed dislocation technique is used to construct integral equations for a system of co-axial annular cracks where the layer is under axisymmetric normal loads. These equations are solved numerically to obtain dislocation density on the cracks surfaces. The results are employed to determine stress intensity factors for annular and penny-shaped cracks and the interaction between two co-axial penny-shaped cracks is studied. Moreover, the stress intensity factors of the interacting cracks are determined such that they can be further used in conjunction with strain energy density (SED) failure criterion to obtain the possible direction of crack initiation that may not be apparent under mixed mode conditions.