Transverse and normal interfacial stiffness of solids with randomly rough surfaces

Area of Science:

• Solid Mechanics
• Tribology
• Materials Science

Background:

• Understanding the mechanical behavior of interfaces between contacting solids is crucial in various engineering applications.
• Surface roughness significantly influences the stiffness and frictional properties of these interfaces.
• Existing models often simplify surface topography, necessitating more accurate theoretical frameworks.

Purpose of the Study:

• To theoretically calculate the normal stiffness (K(perpendicular)) and transverse stiffness (K(parallel)) of interfaces between two isotropic solids with randomly rough surfaces.
• To validate theoretical predictions against results from computer simulations.
• To compare the derived theoretical ratio of K(perpendicular)/K(parallel) with established models and experimental data.

Main Methods:

• Employed a theoretical approach combined with computer simulations to model the interface mechanics.
• Calculated normal and transverse stiffness for randomly rough surfaces of isotropic solids.
• Utilized the Poisson ratio (ν) as a key material property in the calculations.

Main Results:

• Theoretical predictions for normal stiffness (K(perpendicular)) showed excellent agreement with computer simulation results.
• The derived theoretical ratio K(perpendicular)/K(parallel) was found to be (2 - ν)/(2 - 2ν).
• The theoretical model's predictions were also compared favorably with experimental ultrasonic data.

Conclusions:

• The theoretical framework accurately predicts the normal stiffness of randomly rough interfaces.
• The calculated stiffness ratio aligns with Mindlin's prediction for single circular contacts, extending it to rough surfaces.
• The study validates the theoretical approach through simulations and experimental ultrasonic measurements, enhancing understanding of interface mechanics.