Research ArticleMATERIALS SCIENCE

What is the origin of macroscopic friction?

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Science Advances  21 Dec 2018:
Vol. 4, no. 12, eaav2268
DOI: 10.1126/sciadv.aav2268
  • Fig. 1 Mica structures, sliding directions, and the potential energy changes along the sliding paths.

    (A) Relaxed structures of the top and side views for D = 0.0 Å under no applied normal stress. The tetrahedral sheets and interlayer potassium ions are shown in the top view. The dashed line indicates the unit area of simulation cell. The cell parameters of the supercell were fixed to a = 5.2026 Å, b = 9.03695 Å, c = 41.41998 Å, α = 90°, β = 95.50°, and γ = 90°. (B) Mica structure and the directions of six sliding paths from paths 1 to 6. (C) Relaxed structures of the top and side views for D = 2.3 Å under no applied normal stress along path 1. (D to I) Theoretical change of the potential energy (V) of an upper mica layer relative to a lower layer with distance (D) along six sliding paths. The line plots show potential energy change along the sliding paths, with the applied normal stresses from 0 to 5.3 GPa encoded by colors. The crystal structures were visualized using VESTA software (25).

  • Fig. 2 Shear stresses along sliding paths.

    Shear stresses along paths 1 (A) and 4 (B) under applied normal stresses from 0 to 5.3 GPa. (C) Average shear stress as a function of the normal stress. Solid lines indicate the results fitted to the linear equation τ = μσn + τ0 by a damped least-squares method. (D) Fitting parameters of τ0 and μ of the six sliding paths.

  • Fig. 3 Shear experiments and a comparison with the theoretical predictions.

    (A) Schematic of the double-direct shear test. Oven-dried mica sheets were embedded between the side and central blocks and placed in a chamber to realize almost 0% of relative humidity by nitrogen atmosphere in the chamber. The depth of all blocks was 40 mm. (B) Experimental friction coefficient as a function of shear displacement along the sliding path 4. The initially applied normal stress of 5 MPa was increased to 60 MPa. (C) Results of double-direct shear tests compared to those derived from the DFT calculations along path 4 (blue line) and the average of paths 1 to 6 (red line). The dashed lines indicate the SD of hardness measurements. The results of each of two experimental runs are plotted as filled circles or open squares. The arrows indicate that these values should increase at steady state. (D) Mica sheets recovered from the double-direct shear tests. White wear particles were observed between the mica sheets. (E) Optical image of the wear particles observed with a polarizing microscope.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/12/eaav2268/DC1

    Supplementary Text

    Fig. S1. Interlayer potential energy EIL along six sliding paths.

    Fig. S2. Shear stresses (τ) along six sliding paths obtained from the derivative with respect to distance of the potential energy curves shown in Fig. 1.

    Fig. S3. A representative nanoindentation profile of a mica cleavage plane.

    Table S1. The list of best-fit parameters of the average shear stress.

    References (2628)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text
    • Fig. S1. Interlayer potential energy EIL along six sliding paths.
    • Fig. S2. Shear stresses (τ) along six sliding paths obtained from the derivative with respect to distance of the potential energy curves shown in Fig. 1.
    • Fig. S3. A representative nanoindentation profile of a mica cleavage plane.
    • Table S1. The list of best-fit parameters of the average shear stress.
    • References (2628)

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