Uncertainty analysis of welding residual stress fields

A fuzzy-set approach is applied in conjunction with a finite element procedure to study the effect of uncertainty in material properties on welding residual stress fields. The study focuses on steels that undergo martensitic transformations during the cool-down part of the weld thermal cycle. Uncoupled thermo-mechanical analysis is performed. Filler metal deposition, various convective–radiative energy losses, and latent heat generation are included in modeling of the welding process. A rate-independent thermo-elasto-plastic material model with nonlinear kinematic hardening is adopted in the study. Account is taken of the metallurgical transformations that occur during the entire weld thermal cycle. The material model is validated by comparing its predictions with existing experimental measurements of the welding residual mechanical fields. Fuzzy logic is then used to study the variability in the residual stress field due to pre-selected ranges of variation in material parameters associated with the martensitic transformations. It is found that the variations in material parameters considered have a significant effect on the welding residual stress field.