Numerical simulation of the lubricant performance in tube hydroforming

Due to the high pressures that are involved in tube hydroforming processes, high values of the friction forces are developed and, therefore, lubricants are usually employed to increase the formability of the workpiece. However, different lubrication regimes are observed along the different forming zones which vary with the lubricant layer thickness, applied load and sliding velocity. A constitutive relation that captures these features of tribology between two surfaces separated by an atomically thin layer of lubricant molecules is proposed in this paper.The model defines the tangential stress as sum of two contributions: one purely frictional and the other one of viscous type. The frictional contribution depends on the contact between the asperities, whereas the viscous contribution is described by means of an effective viscosity coefficient that accounts for the thin lubricant layer separating such asperities. The model is implemented in a FE code and validated with a pear-shape expansion test. Comparisons with the Coulomb's law are also presented showing a better performance of the proposed model.