Temperature Dependent Analysis of Elastoplastic Thermal Stresses by Finite Element Method

Abstract

The finite element formulation was developed for the elastoplastic thermal stress problem by employing a loading function composed of stress, plastic strain and temperature. Then, the technique of utilizing the formulation was discussed. The generalized plastic stress-strain matrix for the strain incremental theory was experssed explicitly in terms of the loading function ; and it was found that the additional nodal force due to the temperature dependence of the loading function should be considered in the matrix equilibrium equation. It was also shown that the transformation stresses during quenching could be analysed by taking account of the dependence of both temperature and cooling velocity on the coefficient of thermal expansion. The formulated analysis was applied to the elastoplastic thermal stress problem of the thick-walled cylinder subjected to an unsteady radial temperature gradient. Good agreement was obtained between the calculated residual stresses and experimental values measured by Sachs' boring-out technique.