Torsional deformation of an infinite elastic solid weakened by a penny-shaped crack in the presence of surface elasticity and Dugdale plastic zone

Abstract

We consider the torsional deformation of an infinite three-dimensional isotropic elastic solid weakened by a penny-shaped crack whose boundary is enhanced by the incorporation of surface elasticity. Furthermore, we assume the presence of a Dugdale-type plastic zone around the crack front. The ensuing elastoplastic problem gives rise to a non-standard mixed boundary value problem which is then reduced to a hypersingular integral equation upon application of the Hankel transform. The hypersingular integral equation is subsequently solved numerically using orthogonal expansions revealing the effects of surface elasticity on the size of the plastic zone and crack-face torsional displacements. Our results demonstrate the effect of surface elasticity on the width of the plastic zone thus providing a significant shielding effect while increasing the load-bearing capacity of the solid in the vicinity of the defect. Our conclusions will be of particular interest when the presence of surface elasticity along a crack boundary is used in enhanced continuum-based models to study fracture at micro- and nano-scales, for example, in the prediction of fracture and failure in micro- and nano-structures.