Sensitivity analysis of metal forming processes involving frictional contact in steady state

A simple element to model frictional contact in steady state metal forming processes is presented together with the sensitivity analysis to the friction coefficient in a Coulomb friction law. The interest of such model arises from the analysis of rolling processes and a two dimensional approach to cutting problems, where the contact zone is to be determined, however a stationary state is present in most part of the operation. The flow approach proves to be an adequate method to handle efficiently this situation. The contact elements impose a restriction in the velocity component normal to the boundary and a tangential friction force opposite to the velocity. The parts of the boundary which are not in closed contact are treated as free surfaces, which must fulfill the condition of being streamlines. Sensitivity analysis with respect to the friction coefficient is performed by the Direct Differentiation Method (DDM). The effect of variations in this parameter is discussed for the simulation of an extrusion and a cutting problem.