Elasto-visco-plastic analysis of welding residual stress

Abstract

In the past three decades, extensive research has focussed on the application of numerical methods for the computation of residual stress. Most commonly, the simulations involved performing weakly coupled thermal mechanical finite element analyses in Lagrangian reference frames assuming rate independent elasto-plastic material response. Nearly all approaches assumed rate independent elasto-plastic material response, which is most appropriate at low to moderately elevated temperatures. At, the high temperatures near the fusion zone, the material response becomes rate dependent and an elasto-visco-plastic model would be more suitable. In 1989, Brown et al. (Int. J. Plast., 1989, 5 , 95–130) proposed a rate dependent constitutive equation (commonly known as Anand's model) to describe the plastic evolution of metals at high temperatures. The objective of this work is twofold: evaluate the suitability of Anand's elasto-visco-plastic model in computing welding residual stress and investigate the feasibility of an Eulerian implementation of Anand's model in modelling welding residual stress. Such an implementation has the potential to reduce computational cost in modelling welding processes, since it is a steady state analysis as compared to the common time incremental Lagrangian analyses. An Eulerian reference frame is also more advantageous in modelling processes with large deformation such as friction stir welding, rolling and extrusion since excessive mesh distortion and re-meshing are no issues as the case of Lagrangian models (Int. J. Mater. Form., 2008, 1 , 1287–1290).