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Experiments and Prediction of Hold Time-Dependent Static Friction of a Wet Granular Layer

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Abstract

Frictional properties of sliding surfaces have practical importance in a variety of applications. Therefore, the present study investigates the ageing or holding time-dependent static friction of a wet granular layer using a slide-free-slide (SFS) friction test. It is observed that the static friction varies as a logarithm of hold time. Further, the Mohr–Coulombs’ law of friction is used to determine adhesive friction and normal stress-dependent friction. The scaling law analysis has shown that the exponent of adhesive friction is more prominent in magnitude than the corresponding coefficient of friction. A static friction model, based on the formation and rupture of capillary bridges, has also been proposed for predicting the peaks of static friction at different hold times. At the end, the power laws, which correlate the number of attached capillary bridges and adhesion constant with hold time, are proposed to justify the present results.

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Abbreviations

\(a\) :

Adhesive stress (kPa)

\(a_{s}\) :

Static adhesive stress (kPa)

\(k\) :

Boltzmann constant (JK−1)

\(K_{b}\) :

Stiffness (kPa-m−1)

\(N_{s}\) :

No. of strong microcontacts

\(\hat{N}_{s}\) :

Nondimensional form of no. of strong microcontact

\(N_{w}\) :

No. of weak microcontacts

\(\hat{N}_{w}\) :

Nondimensional form of no. of weak microcontact

\(N_{0}\) :

Density of total microcontacts available for adhesion (m−2)

\(r_{s}\) :

Ratio of stiffness

\(T\) :

Temperature (K)

\(t_{h}\) :

Hold time (s)

\(t\) :

Slide time (s)

\(u_{w}\) :

Adhesion constant of microcontacts formation during hold time

\(u_{s}\) :

Adhesion constant of for microcontacts formation during sliding

\(V_{c}\) :

Creep velocity (mms−1)

\(V_{0}\) :

External shear velocity (mms−1)

\(\hat{V}_{0}\) :

Dimensionless external shear velocity

\(V_{*}\) :

Reference velocity (mms−1)

\(\lambda\) :

Activation length (m)

\(\mu\) :

Coefficient of friction

\(\mu_{s}\) :

Static coefficient of friction

\(\sigma_{n}\) :

Normal stress (kPa)

\(\sigma_{s}\) :

Static friction due to strong microcontacts (kPa)

\(\sigma_{w}\) :

Static friction due to weak microcontacts (kPa)

\(\sigma_{*}\) :

Reference frictional stress (kPa)

\(\tau\) :

Frictional stress (kPa)

\(\tau_{s}\) :

Static stress (kPa)

\(\tau_{sn}\) :

Normal load-dependent static stress (kPa)

\(\tau_{rs}\) :

Residual stress (kPa)

\(\tau_{t}\) :

Relaxation time (s)

\(\tau_{*}\) :

Reference stress (kPa)

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Acknowledgements

The authors acknowledge “ITRS-2021,” 2nd Virtual International Tribology Research Symposium for the presentation of the paper (Abstract no.-ITRS177) based on this present study. We also thank Prof. Vinay A. Juvekar of IIT Bombay for the fruitful discussion of this manuscript.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Visvesvaraya National Institute of Technology, Nagpur, 440010, India

    Pawan Kumar Soni & Arun K. Singh

  2. Department of Mechanical Engineering, SRM Institute of Science & Technology, Kattankulathur, Chennai, 603203, Tamil Nadu, India

    Jitendra Kumar Katiyar

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  1. Pawan Kumar Soni
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Contributions

PKS have performed all the experimentation and numerical modelling under the guidance of AKS. Manuscript preparation, such as writing and figure preparation is also done by PKS. Result interpretation and grammatical correction done by AKS and JKK.

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Correspondence to Arun K. Singh.

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Appendix 1

Appendix 1

See Table

Table 1 presents the different governing equations related to the proposed static friction model with their physical significance
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1.

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Soni, P.K., Singh, A.K. & Katiyar, J.K. Experiments and Prediction of Hold Time-Dependent Static Friction of a Wet Granular Layer. Tribol Lett 71, 75 (2023). https://doi.org/10.1007/s11249-023-01747-y

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