Transient thermoelastoplastic stress analysis for a hollow sphere using the incremental theory of plasticity

An analysis based on the incremental strain theory is formulated for solving the problem of an elastoplastic hollow sphere subjected to a transient temperature distribution. Thermal and material properties are assumed to be temperature dependent and the behaviour of the medium to be characterized by the Ramberg-Osgood stress-strain relation. A method of successive elastic solutions is used to obtain a numerical solution. An illustrative example shows that the effective stress is not a monotonie function of the radius, but is much dependent on the history, gradient, and distribution of the temperature in the hollow sphere. In addition, unloading in the plastically deformed region is confirmed from the detailed discussion on the distribution of strains. As a result, the analysis based on the total strain theory is not permissible for solving this kind of elastoplastic problems subjected to transient thermal loading. In the following analysis the problem is treated in a quasi-static sense and the inertia terms in the thermoelastoplastic equations are neglected.