Interaction of a semi-infinite crack with a screw dislocation within Mindlin’s first strain-gradient elasticity

Behavior of dislocations in the vicinity of cracks and the stresses induced in a material due to their interactions have a significant influence on the toughness of that material. As a fundamental problem related to this issue, the present paper is hence devoted to address the interaction of a semi-infinite crack and a straight screw dislocation in an infinite isotropic material within the framework of Mindlin’s first strain-gradient theory. Analytical expressions are determined for the induced displacement and elastic strain fields as well as the image force acting on the dislocation core. Subsequently, the limiting behaviors of the displacement and elastic strain fields in the vicinity of the crack tip are investigated. The current analysis shows that the solution obtained for the displacement field can be represented by a smooth function everywhere in the medium, especially on the slip plane of the dislocation and around the crack tip. Moreover, it is revealed that, according to the adopted theory, all classical singularities of the elastic strain field at the crack tip and dislocation core are eliminated. The obtained results also exhibit clearly the size effect on the induced displacement and elastic strain fields, in particular when the geometrical and material characteristic lengths of the problem are comparable to one another. •Solutions for the elastic fields due to a screw dislocation interacting with a crack.•Determination of the image force acting on the dislocation.•Interpretation of the size effect within Mindlin’s first strain-gradient theory.•Removal of all classical singularities from the elastic strain and stress fields.•Investigation of the asymptotic behavior of the plastic distortion at the crack tip.