Torsion of an elastic medium containing a nanosized penny-shaped crack with surface effects

Theoretical and experimental studies have revealed that at small length scales, surface effects contribute significantly to overall elastic deformation. In this paper, we analyze a torsional problem for a nanosized penny-shaped crack in an infinite homogeneous isotropic elastic medium with surface elasticity on the boundary of the crack. The resulting model of deformation leads to a nonclassical mixed boundary value problem which is analyzed using the Hankel transform technique leading to a pair of dual integral equations. The latter are solved numerically with the solution demonstrating excellent convergence. We examine the contribution of surface elasticity by comparing the calculated torsional displacement and bulk stresses to their counterparts in the absence of surface elasticity. The influence of surface and bulk shear modulus on the torsional stress intensity factors is analyzed and displayed graphically. Our results show that stress intensity factors are dependent on both the crack size and the bulk/surface material properties, revealing that the presence of surface elasticity may hinder or promote crack growth, depending on whether the surface shear modulus takes positive or negative values. As a check, we also note that our results indeed reduce to the corresponding classical results in the absence of surface elasticity.