Viscoelastic friction in sliding a non-cylindrical asperity

Area of Science:

• Tribology
• Materials Science
• Solid Mechanics

Background:

• The behavior of viscoelastic materials under contact and friction is complex.
• Existing analytical models for friction, like Persson's solution, are primarily developed for simpler geometries such as cylindrical punches.

Purpose of the Study:

• To investigate the 2D contact problem of sliding a non-cylindrical punch with a power-law shape (k>2) on a viscoelastic half-plane.
• To evaluate the accuracy of analytical friction solutions in this non-cylindrical, viscoelastic scenario.
• To identify a more accurate approximation for friction coefficients in this complex contact problem.

Main Methods:

• Full boundary element numerical solution was employed.
• Analysis of pressure distribution and friction coefficient under sliding conditions.
• Comparison with existing analytical solutions (Persson's).

Main Results:

• Persson's analytical solution, accurate for cylindrical punches, shows significant qualitative errors for the non-cylindrical punch.
• Despite complex pressure distribution in the viscoelastic regime, the friction coefficient exhibits a simpler trend.
• A first approximation for the friction coefficient can be obtained by normalizing the cylindrical solution with the modulus and mean pressure at zero speed.

Conclusions:

• Analytical friction models need refinement for non-cylindrical geometries in viscoelastic contact.
• A normalized approximation offers a viable first-order solution for friction coefficients in this scenario.
• The study highlights numerical challenges in modeling the sharp flat punch limit.