Interaction of cracks with dislocations in couple-stress elasticity

In the present work we study the interaction of a finite-length crack with a climb dislocation within the framework of the generalized continuum theory of couple-stress elasticity. Our approach is based on the distributed dislocation technique. Due to the nature of the boundary conditions that arise in couple-stress elasticity, the crack is modeled by a continuous distribution of climb dislocations and constrained wedge disclinations. These distributions produce both standard stresses and couple stresses in the body. The final results are obtained by numerically solving a system of coupled singular integral equations with both Cauchy and logarithmic kernels. The results for the near-tip fields differ in several respects from the predictions of the classical fracture mechanics. In particular, the present results indicate that a cracked solid governed by couple-stress elasticity behaves in a more rigid way (having increased stiffness) as compared to a solid governed by classical elasticity. Also, the stress level at the crack tip region is appreciably higher, within a small zone adjacent to the tip, than the one predicted by classical elasticity while the crack-face displacements and rotations are significantly smaller that the respective ones in classical elasticity.