[Paper Review] Rate and Aging Time Dependent Static Friction of a Soft and Hard Solid Interface

Vinay A. Juvekar, Arun K. Singh|arXiv (Cornell University)|Feb 2, 2016

Adhesion, Friction, and Surface Interactions5 citations

TL;DR

This paper proposes a population balance model of interfacial bonds between a soft solid (e.g., rubber or gel) and a hard surface (e.g., glass) to predict static friction forces that depend on both pulling velocity and aging time. The model predicts that static friction stress scales logarithmically with both velocity and aging time, matching experimental observations and offering a mechanistic explanation for rate- and time-dependent friction in soft materials.

ABSTRACT

In this article, we present a mathematical model that answers a classical question concerning how much force, which is generally called static friction force, will it require to initiate the motion of a soft solid block such as gel, rubber or elastomer on a hard surface for instance glass surface. The model uses population balance of the bonds between the polymer chains of the soft solid and the hard surface to estimate rate and aging time dependent static friction. The model predicts that under certain range of the pulling velocity, the friction stress at the onset of sliding (static friction stress) varies as the logarithm of the pulling velocity, as well as the logarithm of the aging time. These predictions are consistent with the experimental observations.

Motivation & Objective

• To understand the physical origin of static friction in soft solids (e.g., elastomers) on hard surfaces.
• To explain the experimentally observed dependence of static friction on both pulling velocity and aging time.
• To develop a predictive mathematical model based on interfacial bond formation and rupture dynamics.
• To quantify how the strength of static friction evolves with time and loading rate.
• To provide a theoretical framework consistent with experimental data on soft materials.

Proposed method

• The model uses a population balance approach to track the number of interfacial bonds between polymer chains of the soft solid and the hard surface.
• It assumes that new bonds form over time during aging, increasing the number of load-bearing contacts.
• The rate of bond formation is modeled as a function of time, while bond rupture depends on the applied stress and pulling velocity.
• The static friction stress is derived as the stress required to break the total number of bonds at the interface at the onset of sliding.
• The model incorporates logarithmic dependencies on both aging time and pulling velocity through the kinetics of bond formation and rupture.
• Theoretical predictions are derived from the balance of bond formation and rupture rates, leading to a logarithmic scaling of friction stress.

Experimental results

Research questions

• RQ1 How does the static friction force depend on the pulling velocity in soft-solid/hard-surface systems?
• RQ2 How does the static friction force evolve with increasing aging time before sliding?
• RQ3 What is the underlying mechanism linking bond formation dynamics to macroscopic friction behavior?
• RQ4 Why does static friction exhibit logarithmic dependence on both velocity and aging time?
• RQ5 Can a population balance model of interfacial bonds quantitatively reproduce experimental friction trends?

Key findings

• The model predicts that static friction stress scales logarithmically with the pulling velocity, consistent with experimental observations.
• The model predicts that static friction stress also scales logarithmically with aging time, matching experimental data.
• The logarithmic dependence arises from the time-dependent growth of interfacial bonds during aging and their velocity-dependent rupture at the onset of sliding.
• The theoretical predictions are in quantitative agreement with experimental measurements on soft solids like elastomers on glass.
• The model provides a unified explanation for both rate and aging time dependence in static friction through interfacial bond dynamics.
• The results support the hypothesis that static friction in soft materials is governed by the cumulative effect of bond formation and rupture at the interface.