Saint-Venant torsion of a circular bar with a non-radial crack incorporating surface elasticity

We analytically investigate the contribution of surface elasticity to the Saint-Venant torsion problem of a circular cylinder containing a non-radial crack. The surface elasticity for the crack faces is incorporated by using the continuum-based surface/interface model of Gurtin and Murdoch. Both internal and edge cracks are studied. By employing the Green's function method, we reduce the original boundary value problem to two coupled first-order Cauchy singular integro-differential equations which can be numerically solved by the Chebyshev polynomials and an adapted collocation method. The analysis indicates that in general the stresses at the crack tips exhibit both the weak logarithmic and the strong square root singularities. The jump in the warping function across the crack faces and the size-dependent torsional rigidity are calculated.