Elastoplastic deformation of a rotating hollow cylinder with a rigid casing

Abstract

A rotating hollow cylinder with fixed ends is considered, the inner surface of which is free of stresses, and the outer one is fixed from radial movements. It is assumed that the cylinder is made of an ideal isotropic elastoplastic material, and the deformations in it are small and represent the sum of elastic and plastic deformations. Stresses are associated with elastic deformations by Hooke's law. Plastic deformations are determined using the Tresca - Saint-Venant condition and the plastic flow rule associated with it. The cylinder rotation speed first monotonically increases to a maximum value, and then decreases to zero. By using the elastic solution, the dependence is found for the critical rotation speed at which the plastic flow begins. It is established that, depending on the thickness of the cylinder and the Poisson's ratio, plastic flow can begin, either on the inner or on the outer surface of the cylinder. In addition, 3 plastic regions appear in the cylinder at the loading stage, and 4 plastic regions appear at the unloading stage. These regions correspond to two faces and two edges of the Treska prism. For each plastic region, an exact analytical solution of the determining system of equations is found. The system of conditions at the boundaries between the regions providing continuity of the obtained solutions throughout the cylinder is given. Two cases are considered, i.e. the case with a plastic flow which starts first on the inner, and then on the outer surface of the cylinder. Analytical expressions are obtained for rotational speeds at which new regions appear. The relationship between the nucleation rates of the secondary and primary plastic flow is established. The value of the maximum rotation speed sufficient for a complete transition of the cylinder to the state of the secondary plastic flow was also found. It has been revealed that the adding of a rigid casing can significantly increase the resource of an exploited part.