Residual Stresses of Round Steel Rod at Elastoplastic Twisting

Abstract

In the elastoplastic twisting of a rod under the action of an external torque, the cross-section of the rod is divided into two zones: the inner elastic zone and the outer plastic zone. After removing the external loads, we observe the residual deformations and the residual stresses inside the rod that significantly affect on the subsequent mechanical processes at manufacturing the products from the round rod. Under too much twisting, the longitudinal surface fibers of the rod begin to tear, the outer surface of the rod ceases to be cylindrical, and the rod’s cross-section ceases to be flat (the Bernoulli’s hypothesis about the flat sections is violated). Next a rupture of the rod is followed. For the plastic materials, the destruction is caused by the pure shear, and the rupture surface is perpendicular to the axis of the rod. For the brittle materials, the destruction occurs, due to the rupture along the screw surface inclined to the axis of the round rod at the angle of 45. In this paper, the residual stresses of the round rod at twisting are obtained for an elastoplastic medium with linear hardening in depending on the rod’s diameter, the shear modulus, the hardening modulus in shear and the yield strength in shear of the rod’s material.