Thermal loading and unloading of a solid cylinder subjected to periodic internal energy cycling

摘要

An analytical model is developed to estimate partially plastic loading and unloading behavior of a transient internal energy cycling solid cylinder. The cylinder is initially at zero temperature, but for times greater than zero, heat is generated or consumed internally at a time dependent rate. The transient temperature distribution in the cylinder is obtained by using Duhamel's theorem. As the cylinder is heated or cooled slowly the uncoupled theory of thermal stress is used. Under these circumstances elastic and plastic solutions are obtained in conformity with the generalized plane strain condition. When variable amplitude periodic internal energy cycling occurs within the cylinder, two different plasticization modes may take place depending on the parameters that define the thermal load. Corresponding to these, four plastic solutions based on different mathematical forms of Tresca's yield criterion are derived considering linearly hardening material behavior. Sudden unloading approximation is used to model unloading from partially plastic to plastically predeformed elastic states of stress. 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.