Analytical solution to thermal loading and unloading of a cylinder subjected to periodic surface heating

Abstract

An attempt is made to develop an analytical model for the prediction of thermal loading into a partially plastic state and unloading into an elastic state of a cylinder subjected to periodic boundary condition. The uncoupled theory of thermoelasticity is used as the cylinder is heated or cooled slowly. Transient temperature distribution in the cylinder is obtained by the use of Duhamel's theorem. It is assumed that the ends of the cylinder are free and hence a state of generalized plane strain is operative in the axial direction. An elastic and two plastic regions with different mathematical forms of Tresca's yield condition are formulated and solved analytically. Linearly hardening material behavior is assumed. Sudden unloading approximation is used to model unloading into a plastically predeformed elastic region. The model is verified in comparison to a purely numerical solution and by observing satisfaction of equilibrium, interface, and boundary conditions in every stage of deformation.