Multi-scale friction modelling for rough contacts under sliding conditions

In Finite Element (FE) simulations of sheet metal forming (SMF), the coefficient of friction is generally expressed as a constant Coulomb friction. However in reality, the coefficient of friction at the local contact spot varies with the varying operational, deformation and contact conditions. Therefore, it is important to calculate the coefficient of friction under local contact conditions to better evaluate the formability of the sheet metal product. Friction at the local contact spot is largely influenced by the micro-mechanisms occurring at asperity level like shearing in the boundary layer, ploughing, surface deformation of the sheet metal surface and hydrodynamic lubrication. In this paper, a multi-scale contact model is developed for predicting the friction occurring in the SMF processes. The model describes the asperity flattening and ploughing phenomenon between the sheet metal and the tool which is predominant amongst the other friction mechanisms. The change occurring in the surface topography of the sheet metal during the deep drawing processes influences the ploughing process. An asperity flattening model for pure plastic conditions is used to describe this phenomenon. The developed model is analyzed with various sheet metal and tool surfaces. The result shows that the coefficient of friction is very much dependent on the surface topography of the interacting surfaces at low nominal contact pressures. At high nominal contact pressures, the surface topography influences less the friction. The coefficient of friction is also compared with tool surfaces of different roughness, bandwidth and surface lay. The coefficient of friction is found to be high for rough, low bandwidth and transversal anisotropic tool surfaces.