  A methodology is presented for estimating average values for the temperature
and the frictional traction over a tool-workpiece interface using measured
values of force and torque applied to the tool. The approach was developed
specifically for friction stir welding and friction stir processing
applications, but is sufficiently general to be of use in a variety of other
processes that involve sliding contact and heating at a tool-workpiece
interface. The methodology works with a finite element framework that is
intended to predict the evolution of the microstructural state of the workpiece
material as it undergoes a complex thermomechanical history imposed by the
process tooling. We employ a three-dimensional, Eulerian, finite element
formulation; it includes coupling among the solutions for velocity, temperature
and material state evolution. A critical element of the methodology is a
procedure to estimate the tool interface traction and temperature from typical,
measured values of force and torque. The procedure leads naturally to an
intuitive basis for estimating error that is used in conjunction with multiple
meshes to assure convergence. The methodology is demonstrate for a suite of
three experiments that had been previously published as part of a study on the
effect of weld speed on friction stir welding. The probe interface temperatures
and torques are estimated for all three weld speeds and the multi-mesh error
estimation methodology is employed to quantify the rate of convergence.
Finally, comparison of computed and measured power usage is used as a further
validation. Using the converged results, trends in the material flow,
temperature, stress, deformation rate and material state with changing weld
conditions are examined.
