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 (SCF) related to the presence of an elliptical hole, for the Stress Intensity Factor (SIF) for hypocycloidal-shaped hole and star-shaped cracks, and for the Notch Stress Intensity Factor (NSIF) for star-shaped polygons. Special sets of the void location are obtained for which peculiar mechanical behaviours are displayed, such as the stress annihilation at some points along the boundary of elliptical voids and the stress singularity removal at the cusps/points of hypocycloidal shaped/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 and, in particular, the infinite-plane solution remains highly accurate when the size of smooth and non-smooth external boundary is greater 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.