Finite Element Analysis of Welding Processes by Way of Hypoelasticity-Based Formulation

Welding is one of the most important joining processes, and the effect of welding residual stresses in a structure has a great deal of influence on its quality. In spite of such a key interest, the analysis of a welding process has not been successful as in a structural analysis. This is partially because welding involves complex phenomena that are manifested by the phase evolution and by thermomechanical processes as well. In the present study, a hypoelasticity-based formulation is applied to welding processes to determine residual deformation and stresses. Algorithmic consistent moduli for elastoplastic deformations including transformation plasticity are also obtained. Leblond’s phase evolution equation, coupled with the energy equation, is employed to calculate the phase volume fraction; this plays an important role as a constitutive parameter reflecting phase fraction effects in a mechanical constitutive equation. Furthermore, transformation plasticity is taken into account for an accurate evaluation of stress. The influence of the phase transformation and the transformation plasticity on residual stress is investigated by means of numerical analyses using metallurgical parameters in Leblond’s phase evolution equation that are adjusted with respect to various cooling rates in a CCT-diagram. Coding implementation is conducted by way of the ABAQUS user subroutines, DFLUX, UEXPAN, and UMAT. The numerical examples demonstrated that the phase transformation and the transformation plasticity have a significant effect on the residual stress of a welded structure.