Analytical model of friction behavior during polymer scratching with conical tip

To investigate the effects of the contact geometry, interfacial friction, and substrate recovery on the behavior of polymer scratching using a conical tip, an analytical model is proposed. The normal stress acting on the contact surface between the tip and the substrate is described as a function of the included angle $\theta$, representing the angle between two planes across the axis of the conical tip, and the attack angle $\beta$, representing the angle between the conical surface and the substrate material surface. The effects of the rear contact geometry on the scratch friction between the tip and substrate, represented by recovery angle $\phi$, owing to the instantaneous elastic recovery of the polymer substrate, are also introduced. Validated by the experimental and numerical results from the literature, the proposed analytical model can describe well the scratch coefficient of friction (SCOF), which is defined as the ratio of the tangential force to the normal force. Meaningful guidance is provided to understand the scratch friction behavior.