Prediction of Joint Line Movement and Temperatures in Friction Stir Spot Welding of DP 980 Steel

Abstract

The friction stir spot welding (FSSW) process is non steady state and therefore lends itself to modeling using a Lagrangian approach. However a 3 dimensional model of this process can be overly time-consuming, particularly when an implicit scheme is used to solve the equilibrium equations that arise from discretization of the continuum body into finite elements. In this paper a novel 2 dimensional, finite element approach was used to model the FSSW process. An updated Lagrangian scheme was employed to predict the flow of the sheet material, subjected to boundary conditions of a descending tool and a fixed backing plate. Material flow was calculated from a velocity field that is two dimensional, but heat generated by friction was computed by an approach where the rotational velocity component from the tool surface was included in the thermal boundary conditions. An isotropic, viscoplastic Norton-Hoff law was used to model the material flow stress as a function of strain, strain rate, and temperature, while a viscoplastic friction law was used to compute the shear stress at the tool/sheet interface. The model predicted welding temperatures to within a few percent of experiment, but welding loads were significantly overpredicted. Comparison with a 3D model of FSSW showed that frictional heating and proportion of total heat generated by friction were similar. It was also shown that the position of the joint interface was reasonably well-predicted by the 2D model, compared to experiment.