Analysis of Elasto-Plastic Thermal Stresses by the Finite Element Method

Abstract

Hereunder is presented a procedure to analyze elasto-plastic thermal stresses by the finite element method. On the finite element analysis of thermal stresses, the equivalent load matrix due to thermal expansion is employed, as the so-called external load matrix. The stiffness matrix in the plastic region is constructed according to Yamada's [Dp] matrix, which is derived from Prandtl-Reuss equation and von Mises yield criterion. A modified Marcal's method gives appropriate stiffness to the element adjacent to the elasto-plastic interface.Attension is to be focused on the analysis of thermal residual stresses. The steps in calculation of the residual stresses are as follows:(1) The elasto-plastic stresses and strains will be determined.(2) The plastic strains will be estimated.(3) The residual stresses will be calculated so as to compensate the remaining plastic strains in the body.Numerical calculation was made of the thermal residual stresses in a cylindrical bar induced by the partial induction quenching. The temperature distribution in the heating and cooling processes was determined by means of the finite difference method. The residual stresses induced in the present case are found to be resultant of two kinds of plastic deformation; one made during the initial heating and the other during the subsequent cooling.The method of calculating the residual stresses by such a technique is applicable to repeated loading.