Modelling of strain hardening during friction stir welding of stainless steel

Friction stir welding of stainless steel has been modelled using a steady-state, Eulerian formulation that considers coupled viscoplastic flow and heat transfer in three dimensions. The model equations are solved using the finite element method to determine the velocity field and temperature distribution, with a modified Petrov-Galerkin employed to stabilize the temperature distribution. Strain hardening is incorporated using a scalar state variable for the isotropic strength that evolves with deformation as material moves along streamlines of the flow field. The evolution equation for the hardening is integrated along streamlines of the flow field. The influence of pin threads on the friction between the tool and the workpiece was modelled by supplementing the tangential tractions along the pin interface with axial tractions that depend on the pitch of the threads. The formulation is used to conduct a parametric study to determine the influences of various welding parameters on the flow, heating and hardening of the stainless steel. For parameters corresponding to available experimental data, comparisons are drawn between the simulation results and measured values of hardness and temperature.