untethered atom · Tribology

How to Calculate Wear Depth: Archard, Abrasive & Fretting Wear Six ways a surface loses material, and two honest routes to a depth in micrometres

Six ways to lose material, zero of them covered by the warranty.

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Cite this page: Tripathy, Manisha. “Wear mechanisms & wear depth.” untethered atom, 2026, https://untetheredatom.com/tribology/wear-mechanisms-and-depth.
BibTeX 
@misc{tripathy2026wearmechanismsweardepth,
  author = {Tripathy, Manisha},
  title  = {Wear mechanisms & wear depth},
  year   = {2026},
  howpublished = {\url{https://untetheredatom.com/tribology/wear-mechanisms-and-depth}},
  note   = {Interactive teaching resource}
}
Last updated 12 August 2026.
Models, assumptions, and where each one stops being true

Every number here comes from a published closed form. Where a source could not be fetched and verified, the number is absent rather than guessed: most visibly, Rabinowicz's compatibility-class wear-coefficient table is not reproduced, because inventing those multipliers would be worse than leaving them out.

Assumptions worth knowing about

Archard assumes fully plastic junctions, so real contact area is load over hardness and the wear coefficient absorbs everything else, including the fact that K is not really a constant, but changes by decades across a mild-to-severe transition. The abrasive model assumes rigid conical grits that all cut; real grits mostly plough, which is why the geometric prediction sits above the measured band. Quinn's model assumes a coherent oxide growing parabolically to a single critical thickness. Finnie's model is one rigid particle cutting a perfectly plastic solid, and predicts zero erosion at normal incidence, which is wrong for every real material. None of these six models applies once the contact reaches the melting point.

References

  1. J. F. Archard, J. Appl. Phys. 24 (1953) 981: adhesive wear; derivation as presented in Cambridge DoITPoMS.
  2. J. A. Williams, Engineering Tribology, OUP 1994: conical abrasive model V = (2tanθ/π)WL/H; cf. E. Rabinowicz, Friction and Wear of Materials, which publishes tanθ/3 for the same physics.
  3. D. Tabor (1954), via G. Pintaude: the Ha/Hs ≥ 1.2 transition; K.-H. Zum-Gahr for the two-body and three-body coefficient ranges.
  4. I. Finnie, Wear 3 (1960) 87: erosion by solid particle impact.
  5. T. F. J. Quinn, NASA-CR-3686 (1983): oxidational wear; the tribological Ap values in Table 3, not the static-oxidation ones.
  6. F. E. Kennedy, "Frictional Heating and Contact Temperatures", ASM Handbook Vol. 18: flash temperature, Peclet number, and the all-speeds interpolation.
  7. G. Lundberg & A. Palmgren, via ISO 281: L10 = (C/P)p.
  8. S. Fouvry, P. Kapsa & L. Vincent: the energy wear law and the At = 0.2 criterion; O. Vingsbo & S. Söderberg, Wear 126 (1988) 131: fretting maps.
  9. ASTM G99, Appendix X1: wear scar and wear track volume, and the 1% / 5% validity bands quoted here.
  10. S. M. Lim & M. F. Ashby, Acta Metall. 35 (1987) 1: the wear-mechanism map whose idea mode 0 borrows, though not its empirical fits.