Accurate Theory for Thermal Elastic-Plastic Analysis to Significantly Shorten Computation Time

Abstract

The thermal elastic-plastic analysis of the transient and residual stresses and the deformations that occur during welding requires a long computation time to obtain accurate results. The reason for this is the necessity for the temperature increment to be sufficiently small to ensure calculation accuracy. In this study, the thermal elastic and thermal elastic-plastic constitutive equations were modified to enable the use of very large temperature increments. Moreover, in the latter constitutive equation, the definition of the differential coefficient of the yield stress when the temperature changes is ingeniously modified to perfectly satisfy the yield condition. The new constitutive equations were introduced into the FEM (Finite Element Method) program. A simple typical problem of thermal elastic-plastic mechanics was analyzed to verify the basic capability of the new theory. Further, to examine the reliability and accuracy of the theory, a complex welding problem was analyzed. The computed welding residual stress and deformation were compared with the accurate results obtained by the usual incremental method using very small temperature increments, and those obtained by ABAQUS. High accuracy was confirmed, and the computation was found to be significantly shortened (reducedby one order) compared to those of the usual incremental method and ABAQUS.