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Is wear law really Archard's law (1953), or Reye's law (1860) ???

Mike Ciavarella's picture

In 1860 the mathematician and geometer Reye proposed a simple and elegant theory for explaining the consumption of a solid body when it slides with friction on a rough surface [8]. Reye’s model became very popular in Europe (in Italy was promulgated by Panetti [7]), and it is still taught in university courses of applied mechanics. But, strangely enough, this theory has been totally ignored in English and American literature.  Why? A paper from 2001 by Villaggio is interesting to read today.

1. Ferrari, C. and Romiti, A., Meccanica Applicata alle Macchine, Torino, 1966.

2. Galerkin, B.,‘On the analysis of stresses in dams and retaining walls of trapezoidal section’, Sbornik Len.

Inst. 99 (1929) 147–170.

3. Girkmann, K., Fl¨achentragwerke, Springer, Wien, 1959.

4. Goryacheva, I.G.,Contact Mechanics in Tribology, Kluwer, Dordrecht, Boston, London, 1988.

5. Kragelskii, I.V., Friction and Wear, Butterworths, London, 1965.

6. Love, A.E.H., A Treatise on the Mathematical Theory of Elasticity, 4th edn, Cambridge University Press,


7. Panetti, M., Meccanica Applicata, Torino, 1947.

8. Reye, T., ‘Zur Theorie der Zapfenreibung’, Der Civilingenieur 4 (1860) 235–255.

9. Szab´o, I., H¨ohere Technische Mechanik, Springer, Berlin, G¨ottingen, Heidelberg, 1964.

10. Tabor, D., ‘Junction growth in metallic friction’, Proc. R. Soc. A 251 (1959) 378.

11. Worch, G., ‘Elastische Scheiben’, in: Beton-Kalender, II, Berlin, M¨unich, D¨usseldorf, Ernst u. Sohn, 1967,

pp. 1–128. 

PDF icon villaggio_wear.pdf123.77 KB
PDF icon reye_original.pdf967.72 KB


Mike Ciavarella's picture

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.

Mike Ciavarella's picture


dear Alan
 thanks for your contribution.  I think it is worth
reading the original Reye's paper although I am not fluent in German. 
There is a lot of maths, probably even more than Archard's, and less
physics I guess. The figure seem to recollect heat exchangers? It would
be good if any of our german friends could explain, to make a
contribution in this academic but interesting controversy.  Besides, I
read that Villaggio also noticed this strange complete obscurance of
Reye's work.   Villaggio, attached, also goes some way into attempting
to modify Reye-Archard by introducing a friction coeffiient effect for
the von Mises equivalent stress, but I do not know how many people would
buy that, given that wear in the end is all "predicted" only via a very
widely changing empirical coefficient.
PS.  Can I put this conversation into imechanica for the young people there?

On 9 September 2013 15:43, Ponter, Alan R.S. (Prof.) <> wrote:

Dear Mike,


I've resisted joining your discussion of
Archards/Reyes law, but as I knew Jack Archard personally I thought I
should say a few words. Jack was a Reader at Leicester until he retired
in the early 1980's and ran a successful experimental
tribology research program. He was very meticulous and I very much
doubt if he had heard of Reye's work, particularly as it wasn't
published in English.


It is quite common for ideas to appear
independently in different countries over time. It is, after all, not an
nreasonable law to suggest as a possibility. The final attribution is
usually attached to whoever has carries out the critical
experiment that convince the community that it is a valid hypothesis,
i.e. completes the cycle of the scientific method. Jack certainly did
this for his wear law. If Reyes also carried out the critical
experiments then the attribution should be give to them
jointly as independent discoverers. But if Reye only introduced it as a
hypothesis then the attribution remains with Archard as Reye failed to
complete the cycle of the scientific method.


Kindest regards





Mike Ciavarella's picture

Critical length scale controls adhesive wear mechanisms

10 February 2016
03 May 2016
Published online:
06 June 2016


The adhesive wear process remains one of the least understood areas of mechanics. While it has long been established that adhesive wear is a direct result of contacting surface asperities, an agreed upon understanding of how contacting asperities lead to wear debris particle has remained elusive. This has restricted adhesive wear prediction to empirical models with limited transferability. Here we show that discrepant observations and predictions of two distinct adhesive wear mechanisms can be reconciled into a unified framework. Using atomistic simulations with model interatomic potentials, we reveal a transition in the asperity wear mechanism when contact junctions fall below a critical length scale. A simple analytic model is formulated to predict the transition in both the simulation results and experiments. This new understanding may help expand use of computer modelling to explore adhesive wear processes and to advance physics-based wear laws without empirical coefficients.

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