Couple-stress effects for the problem of a crack under concentrated shear loading

Abstract

In this paper, we deal with the plane-strain problem of a semi-infinite crack under concentrated loading in an elastic body exhibiting couple-stress effects. The faces of the crack are subjected to a concentrated shear loading at a distance L from the crack tip. This type of loading is chosen since, in principle, shear effects are more pronounced in couple-stress elasticity. The problem involves two characteristic lengths, that is, the microstructural length ℓ and the distance L between the point of application of the concentrated shear forces and the crack tip. The presence of this second characteristic length introduces certain difficulties in the mathematical analysis of the problem: a non-standard Wiener–Hopf equation arises, one that contains a forcing term with unbounded behaviour at infinity in the transformed plane. Nevertheless, an analytic function method is employed that circumvents the aforementioned difficulty. For comparison purposes, the case of a semi-infinite crack subjected to a distributed shear load is also treated in the present study. Numerical results for the dependence of the stress intensity factor and the energy release rate upon the ratio of the characteristic lengths are presented.