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are fractal surfaces adhesive? a new attempt on JMPS

Mike Ciavarella's picture

In 2007 I wrote a question in Imechanica, IS THERE NO PULL-OFF FOR ADHESIVE FRACTAL SURFACES?

Clearly, in 2007 this question was too hard to answer.  I pointed there that Fuller and Tabor 1975 asperity theory predicted a weird limit for a true fractal surface, that of no stickiness for any fractal dimension or amplitude, in the limit.

Various theories had been proposed at that time already, like Persson and Tosatti (2001) and Persson (2002), which did not clarify the issue, and today seem to have been abandoned, mostly because they are JKR theories, and JKR requires a high Tabor parameter, which is inconsistent with the "fractal limit" of very fine asperities.

We can say a lot more after data from Pastewka and Robbins in PNAS 2014 have been explored in my BAM model (see e.g. here) which seems to indicate that the main emphasis should be on small rms amplitude of roughness, as intuitive --- and contrary to the suggestion of Pastewka and Robbins -- the contradiction is still not completely understood, although I am close to a clue on what happened.

This latest paper in JMPS studies the problem in the limit of near full contact, and is able to clarify some aspects.

Notice that the Tabor parameter we introduced can be shown to be related to the size of the regions of separation, rather than those in contact, like the original Tabor parameter everyone uses for the sphere.

The generalized Tabor parameter for adhesive rough contacts near complete contactAuthor links open overlay panelMicheleCiavarellaaYangXubRobert L.JacksonbShow morehttps://doi.org/10.1016/j.jmps.2018.08.011Get rights and content Abstract

Recently, the first author has obtained a model for adhesive contact near full contact under the JKR assumptions. The model shows, in the common case of low fractal dimensions, an ‘unbounded’ adhesion enhancement when larger and larger upper “truncation wavenumber” is considered in the spectrum of roughness, i.e. when we increase “magnification”. Here, using a more general Maugis–Dugdale model, we show that a generalized multiscale Tabor parameter can be defined which shows a transition to a non-hysteretic regime, dependent on the root-mean-square (rms) slope of the surface. The contact area returns in the “fractal limit” to the adhesionless one. Two examples of rough surfaces from the literature are considered to show the full dependence on magnification of the adhesive solution. The choice of the truncation of the spectrum remains fundamentally arbitrary. 

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