Modeling strain hardening and texture evolution in friction stir welding of stainless steel

Steady-state friction stir welding of stainless steel has been modeled using an Eulerian formulation that considers coupled viscoplastic flow and heat transfer in the vicinity of the tool pin. Strain hardening is incorporated with a scalar state variable that evolves with deformation as material moves along streamlines of the flow field. 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. The evolution equation for the state variable for strength is integrated along streamlines using an adaptive procedures to determine step size based on the element size. The intense shearing and associated heating lead to complex behavior near the tool pin. The effect of this complex response is demonstrated with the crystallographic texture, which displays a nonmonotonic strengthening and weakening history along streamlines that pass close to the tool pin.