Friction modeling on multiple scales for deep drawing processes

Abstract

A deep drawing process is one of the widely used manufacturing techniques in the automotive industry because of its capability to produce complex shapes with sheet material, often performed using lubricants to ease the forming. Finite Element Methods (FEM) are popularly used at the design stage to predict the formability of the product, the spring-back of the sheet metal product after forming, local thinning/thickening of sheet material and failure of the sheet metal during forming. The performance of the FEM simulations relies on the accuracy of the numerical techniques, material models, contact and friction conditions. Over the past decades, FEM has been largely developed on the aspects of numerical techniques, material and contact algorithms. The coefficient of friction used in the contact formulations is often still the Coulomb friction model, i.e. constant coefficient of friction. The coefficient of friction, however, is generally dependent on the nature of surfaces, material properties as well as the operational and environmental conditions. A friction model has been developed in this research work. This model can be coupled with the FEM simulations in predicting the local coefficient of riction for a deep drawing process. The basic friction mechanisms at the asperity scale taken into account in the model are shearing of the boundary layers, ploughing and shearing of the lubricant film. A contact model has been developed to describe the fully plastic deformation of the surface from a given surface topography, the load at the micro-scale as well as the uniaxial bulk strain. The contact models include the roughness of both the sheet material (for surface deformation) and tool surfaces (for ploughing). A lubrication model has been developed to describe the hydrodynamic flow of the lubricant between the surfaces, taking into account the surface deformation of the sheet as well as the operational conditions like the sliding velocity. The effect of surface lay and lubricant amount applied on the surface is also considered in the model. Further, a deterministic approach for the characterisation of the micro-contacts has been used. This approach is better than traditional statistical methods in terms of geometrical description. The contact model has been further extended to elastic-plastic contact conditions to account for the elastic recovery of the asperities if the sheet surface is subjected to unloading. Experiments have also been carried out to study the shear strength of the boundary layers formed due to the lubricant. It is shown that the shear strength of boundary layers is almost constant if the appropriate contact area is used in the analysis of the experimental data. The coefficient of friction is shown to reduce during the deep drawing processes due to the lubricant pressure generation if the operation conditions and the applied lubricant amount favour hydrodynamic effects. The model shows that the coefficient of friction decreases as the contact pressure increases, which is in accordance with the experiments. The contact model shows that the coefficient of friction is dependent on the surface roughness, bandwidth parameter and surface lay. The coefficient of friction is high for rough, low bandwidth and transversal anisotropic surfaces. The coefficient of friction is low for smooth, high bandwidth and longitudinal anisotropic surfaces. The friction model has been subjected to a validation process with a rotational friction tester. The results of the friction model shows good comparison with the experimental results. The applicability of the developed friction model in a FEM simulation has been demonstrated with a cup drawing FEM simulation which shows the expected evolution of friction conditions during the progression of a deep drawing process.