A Phenomenological Friction Model Capturing Plastic Saturation of Rough Surface Contacts

Introduction: Classical friction laws, including the Amontons–Coulomb model and power-law approximations such as Kragelsky’s, exhibit fundamental limitations at extreme normal pressures. These models predict unphysical vanishing or even negative friction coefficients when extrapolated beyond their validity range, failing to capture the saturation of the real contact area that occurs as surface asperities fully flatten under high loads.

Methods: We propose a novel phenomenological friction model derived from the exponential distribution of asperity heights combined with the two-component adhesion–deformation theory of friction. The model takes the form µ(p) = b₁ + (b₀ − b₁ ) exp(−b₀ p/s), where b₀ and b₁ are the friction coefficients at zero and infinite pressure, respectively, and s is the effective plasticity limit of the contact layer. Building on this formulation, we construct a pressure-dependent generalization of the Stribeck effect, in which the difference between static and kinetic friction is modulated by the proximity to plastic saturation.

Results: The proposed model yields physically correct limiting behavior: µ → b₀ at low pressures and µ → b₁ > 0 at extreme pressures, thereby avoiding the artifacts of classical power laws. Analysis reveals that increasing normal pressure progressively suppresses the static–kinetic friction gap, with the Stribeck effect vanishing entirely in the plastic saturation regime. Three distinct contact regimes are identified — elastic, transitional, and fully plastic saturation — each characterized by qualitatively different energy dissipation behavior.

Conclusions: The model provides a robust, analytically tractable framework for contact mechanics under extreme pressures. It is directly applicable to the design of high-load tribological systems such as sliding bearings, seals, and braking interfaces, as well as to micro-scale contacts in MEMS/NEMS devices.