Interaction between a screw dislocation and a bridged crack with surface elasticity

Abstract

We examine the contribution of crack bridging and surface elasticity to the elastic interaction between a mode III finite crack and a screw dislocation. The surface effect on the crack faces is incorporated by using the continuum-based surface/interface model of Gurtin and Murdoch. The crack faces are subjected to a bridging force which is assumed to be proportional to the crack opening displacement, whereas the bridging stiffness is allowed to vary arbitrarily along the crack. By considering a continuous distribution of both screw dislocations and line forces on the crack, the boundary value problem is reduced to two decoupled first-order Cauchy singular integro-differential equations. After the expansion of the unknown line dislocation and line force densities and the known variable bridging stiffness into Chebyshev polynomials, these singular integro-differential equations are solved numerically using the collocation method. Owing to the incorporation of surface elasticity, the stresses at the crack tips only exhibit the weak logarithmic singularity when the dislocation is located on the real axis where the crack is located, whereas in the case when the dislocation is not on the real axis, the stresses at the crack tips exhibit both the weak logarithmic and the strong square-root singularities. The two densities, the crack opening displacement across the crack faces and the image force acting on the screw dislocation are specifically calculated. We note that crack bridging only exerts an effect on the line dislocation density but has no influence on the line force density. In addition, we demonstrate that both surface elasticity and crack bridging can reduce the strengths of the logarithmic stress singularity at the crack tips and the magnitude of the crack opening displacement across the crack faces. Our results also clearly show that both crack bridging and surface elasticity exert a significant influence on the magnitude and direction of the image force acting on the screw dislocation.