Discussion: “An Asperity Microcontact Model Incorporating the Transition from Elastic Deformation to Fully Plastic Flow” [ASME J. Tribol., 122, No. 1, pp. 86–93 (2000)]¹

The authors have presented an elegant way to overcome a shortcoming of the CEB model by smoothing the transition from elastic to plastic state in a single asperity. Their physical interpretation of the results, however, may be misleading.

On several occasions the authors criticize the CEB results as being “physically unreasonable” e.g., when discussing the differences between the GW and CEB results in Fig. 5 for Ψ=0.7, the authors state that “…The asperity yielding would require increased contact area to support a given contact load than otherwise…”. This statement is a common mistake often made in connection to the contact of rough surfaces. In fact asperity yielding, or fully plastic contact, means that the asperity mean contact pressure has reached the value of the material hardness (see Eq. (9)). The mean contact pressure in the case of an elastic contact is certainly less than the hardness. Obviously with a higher contact pressure a smaller contact area is required to support a given contact load. Hence, for a given hardness, asperity yielding would require less contact area to support a given contact load.

Smaller contact area for a given surface roughness means that fewer asperities are required to carry the load. Hence, higher separation would be expected when the contact is more plastic. This physically realistic behavior contradicts another statement made by the authors in discussing their Fig. 4 that “…the plastic deformation, which is the main feature of the CEB model, should yield a lower separation due to the plastic deformation of the contacting asperities…”. In fact, even the authors present model results in Fig. 4 show increasing separation at a given load, as the contact becomes more plastic and the plasticity index increases.

The experimental and theoretical results of Kucharski et al. were obtained for extreme loading conditions, deep into the plastic regime, when ω is much larger than $ω2.$ Under these extreme plastic conditions the measured experimental approach (which is the opposite of the mean separation), and real contact area should be smaller than the prediction of any elastic-plastic model like the CEB model. Indeed, in Figs. 11 and 12 of Kucharski et al. this is the case. The results that are shown in these figures for the GW model are completely false since the GW model breaks down much before $ω2$ is obtained and hence should not be considered for comparison with the other models. Again, the CEB model is very much physically reasonable.

Finally, it is interesting to note the similar results of the present model and the CEB model as shown in Figs. 4 and 5. This is probably due to the fact that selecting the mean pressure KH in the CEB model for plastically deformed asperities is not such a bad choice after all. Indeed, it overestimates the mean contact pressure of asperities in their early elastic-plastic state where ω is close to $ω1$ but at the same time it underestimates the mean contact pressure of asperities deep into the plastic state where ω is close to $ω2.$ Using an average contact pressure in a statistical model like the CEB for the entire population of plastically deformed asperities seems to have a global smoothing effect equivalent to the empirical smoothing of the contact pressure on individual asperities in the present model.