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Hybrid Atomistic/Continuum Study of Contact and Friction Between Rough Solids

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Abstract

A hybrid simulation method is used to study the effect of atomic structure and self-affine roughness on non-adhesive contact and friction between two-dimensional surfaces. Rough-on-flat and rough-on-rough contact are compared as a function of system size up to several micrometers. In order to contrast elastic and plastic behavior, interactions within the deformable substrate are either harmonic or Lennard-Jones. The ratio of lattice constants in the solids is varied to examine the effect of commensurability. In all cases the true area of contact rises linearly with load, but the slope is much larger than expected from continuum calculations. These calculations considered a continuous distribution of surface heights that is appropriate for large scales, rather than the discrete height distribution of the crystalline surfaces used here. The ratio of contact area to load depends on the ratio of lattice constants in the solids and varies with system size in small systems that deform plastically. While some dislocations are observed, plasticity is dominated by an asperity flattening mechanism where surface atoms are displaced into a lower layer. The kinetic friction rises linearly with load and is independent of system size, as predicted by Amontons’s laws. Variations in friction with commensurability are smaller for rough surfaces than for flat surfaces, because most of the contact area is in small patches. Asperity flattening increases patch sizes and thus the effect of commensurability on friction. Rough-on-rough contact leads to additional friction associated with the local slope of the contacting regions.

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Notes

  1. Note that using the non-linear Lagrangian strain tensor, (u i,j + u j,i + u k,i u k,j)/2, at lowest order does not yield all of the terms for the diagonal stress components in Eq. 3. However, it does yield the quadratic term for the off-diagonal stress, and with ratios of coefficients that are nearly consistent with those determined below.

  2. These exponents are reduced in magnitude by unity from the values in Refs. [43, 44] because of the reduction from 3D to 2D.

  3. In principal there may be a logarithmic dependence on velocity, but the prefactor is expected to be proportional to temperature (Ref. [31]) and should be negligible for the low T considered here.

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Acknowledgments

This material is based upon work supported by the National Science Foundation under Grant No. DMR-0454947. The authors are grateful to Noam Bernstein, Sangil Hyun, and Jean-Francois Molinari for their collaboration in developing the code used here.

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  1. Binquan Luan

    Present address: IBM Physical Sciences Division, PO Box 218, Yorktown Heights, NY, 10598, USA

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  1. Department of Physics and Astronomy, Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD, 21218, USA

    Binquan Luan & Mark O. Robbins

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Correspondence to Mark O. Robbins.

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Luan, B., Robbins, M.O. Hybrid Atomistic/Continuum Study of Contact and Friction Between Rough Solids. Tribol Lett 36, 1–16 (2009). https://doi.org/10.1007/s11249-009-9453-3

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