Static Friction Model of Elastic-Plastic Contact Behavior of Surface With Elliptical Asperities

The friction coefficient $(μ)$ of a contact surface with elliptical asperities is examined at various values of the plasticity index $(ψ)$⁠, the effective radius ratio $(γ)$⁠, the shear-strength-pressure proportionality constant $(c)$⁠, and the dimensionless limiting interfacial shear strength $(τ¯m)$⁠. The results demonstrate that the friction coefficient of the contact system increases with an increasing value of $γ$ but decreases with an increasing value of $ψ$⁠. Furthermore, it is shown that Amonton’s law is applicable for contact systems with either a low $ψ$ and a high $τ¯m$ or a high $ψ$ and a low $τ¯m$⁠. Analyzing the ratio of the nonelastic contact area, it is found that the asperities of a surface characterized by a large $γ$ generally deform elastically at all values of the plasticity index, while those of a surface with a larger $c$ deform plastically, particularly for surfaces with higher values of $τ¯m$ and $ψ$⁠. Finally, an inspection of the critical dimensionless real contact area shows that the contact mode of the surface is determined primarily by the value of the effective radius ratio.