A simple dry friction model for metal forming process

Based on Tabor's friction model, a three-dimensional stress element under a contact contaminant film is proposed to model the dry friction mechanism. The present friction model shows that friction coefficient μ is a function of dimensionless stress ratio σ/K and contact area ratio α. Based on the feature of indentation of hardness test, the σ/K   can be modified as 3αn/2. Moreover, the α can be particularly assumed as a useful hyperbolic function tanh(Cap/σu) in accordance with the experimental observations. The present model could effectively improve the contradiction of two-dimensional case, such as Tabor's friction relation, that friction coefficient equals infinity in sticking state. The improvement is worth noting that the friction coefficient μ of constant friction law, such as Amonton–Coulomb friction law, would be always less than 0.577 (for von-Mises yield criterion) or 0.5 (for Tresca yield criterion) in practical applications. It is thereby possible to better understand and evaluate the friction coefficient of metal forming process in industry necessity.