Torsion of elastic solids with sparse voids parallel to the twist axis

Abstract

With the purpose of investigating a linear elastic solid containing a dilute distribution of cylindrical and prismatic holes parallel to the torsion axis, the full-field solution for an infinite elastic plane containing a single void and subject to torsion is derived. The obtained solution is exploited to derive the analytic expressions for the stress concentration factor related to the presence of an elliptical hole, the stress intensity factor for hypocycloidal holes and star-shaped cracks and the notch stress intensity factor for star-shaped polygons. Special sets of the void location are obtained for which peculiar mechanical behaviours are displayed, such as stress annihilation at some points along the boundary of elliptical voids and stress singularity removal at the cusps or points of hypocycloidal or isotoxal star-shaped polygonal voids. By means of finite-element simulations, it is finally shown that the presented closed-form expressions for the stress intensification provide reliable predictions, even for finite-domain realizations; in particular, the infinite-plane solution remains highly accurate when the the smooth and non-smooth external boundaries are larger than twice and five times the void dimension, respectively. Under these geometrical conditions, the derived analytical expressions represent a valid ‘guide tool’ in mechanical design.