A very interesting recent paper by Dalvi et al. has demonstrated convincingly with adhesion experiments of a soft material with a hard rough material that the simple energy idea of Persson and ...Tosatti works reasonably well, namely the reduction in apparent work of adhesion is equal to the energy required to achieve conformal contact. We demonstrate here that, in terms of a stickiness criterion, this is extremely close to a criterion we derive from BAM (Bearing Area Model) of Ciavarella, and not very far from that of Violano et al. It is rather surprising that all these criteria give very close results and this also confirms stickiness to be mainly dependent on macroscopic quantities.
•We derive a stickiness criterion from the simple Persson and Tosatti theory of adhesion of rough solids.•We derive another stickiness criterion from the BAM (Bearing Area Model) theory of Ciavarella.•We compare the two derived new criteria with that Violano et al., and Pastewka and Robbins and Muser.•We find Persson–Tosatti, BAM, and Violano criteria give very close results, and are mainly dependent on macroscopic quantities, while Pastewka and Robbins and Muser criteria differ from the previous three in that they depend on the truncation of the spectrum of roughness.
It is known that energy balance is the correct criterion for large enough cracks, as otherwise the limit (cohesive) strength dominates, and this is the reason for many examples in Nature of “flaw ...insensitive” design at very small scales. These concepts have so far been proposed only for elastic materials, neglecting the effect of viscoelasticity. This introduces some novelty: for liquid materials, there is never flaw insensitivity as slow crack propagation occurs in principle at any crack size. On the other hand, for materials with a well defined relaxed modulus, flaw sensitivity can be defined with respect to threshold or very fast speed of propagation, respectively. These concepts are introduced by means of a simple Dugdale model, in which Schapery’s approximation is used. Qualitative comparison with existing theories based on the de Gennes/Persson-Brener model with dissipated energy is made, and large differences are found.
•We define “flaw insensitivity” of viscoelastic materials.•For liquid materials slow crack propagation occurs in principle at any crack size.•A Schapery’s approximation is used to solve the short crack propagation of a central crack in a large plate.
In the present note, we suggest a simple closed form approximate solution to the adhesive contact problem under the so-called JKR regime. The derivation is based on generalizing the original JKR ...energetic derivation assuming calculation of the strain energy in adhesiveless contact, and unloading at constant contact area. The underlying assumption is that the contact area distributions are the same as under adhesiveless conditions (for an appropriately increased normal load), so that in general the stress intensity factors will not be exactly equal at all contact edges. The solution is simply that the indentation is δ=δ1−2wA′/P″ where w is surface energy, δ1 is the adhesiveless indentation, A′ is the first derivative of contact area and P′′ the second derivative of the load with respect to δ1. The solution only requires macroscopic quantities, and not very elaborate local distributions, and is exact in many configurations like axisymmetric contacts, but also sinusoidal waves contact and correctly predicts some features of an ideal asperity model used as a test case and not as a real description of a rough contact problem. The solution permits therefore an estimate of the full solution for elastic rough solids with Gaussian multiple scales of roughness, which so far was lacking, using known adhesiveless simple results. The result turns out to depend only on rms amplitude and slopes of the surface, and as in the fractal limit, slopes would grow without limit, tends to the adhesiveless result – although in this limit the JKR model is inappropriate. The solution would also go to adhesiveless result for large rms amplitude of roughness hrms, irrespective of the small scale details, and in agreement with common sense, well known experiments and previous models by the author.
The detachment of a sphere from a viscoelastic substrate is clearly a fundamental problem. In the case viscoelastic dissipation is concentrated at the contact edge, and the work of adhesion follows a ...quite popular simplified model, Muller has suggested an approximate solution, which however is based on an empirical observation. We revisit Muller's solution and show it leads to very poor fitting of the actual full numerical results, particularly for the radius of contact at pull-off, and we suggest an improved fitting of the pull-off which works extremely well over a very wide range of withdrawing speeds, and correctly converges to the JKR value at very low speeds.
The old asperity model of Fuller and Tabor had demonstrated almost 50 years ago surprisingly good correlation with respect to quite a few experiments on the pull-off decay due to roughness of rubber ...spheres against roughened Perspex plates. We revisit here some features of the Fuller and Tabor model in view of the more recent theories and experiments, finding good correlation can be obtained only at intermediate resolutions, as perhaps in stylus profilometers. In general we confirm qualitatively the predictions of the Persson & Tosatti and Bearing Area Model of Ciavarella, as stickiness depends largely on the long wavelength content of roughness, and not the fine features.
•The old asperity model of Fuller and Tabor had demonstrated surprisingly good correlation.•However, asperity models today are believed to be largely ill-conditioned.•Good correlation can be obtained with the Fuller and Tabor model only at intermediate resolutions.•Stickiness depends largely on the long wavelength content of roughness, and not the fine features.•Multi-instruments measurements should hopefully not be needed.
Classical asperity theories predict, in qualitative agreement with experimental observations, that adhesion is always destroyed by roughness except if the roughness amplitude is extremely small, and ...the materials are particularly soft. This happens for all fractal dimensions. However, these theories are limited due to the geometrical simplification, which may be particularly strong in conditions near full contact. We therefore introduce a simple model for adhesion which aims at being rigorous near full contact, where we postulate there are only small isolated gaps between the two bodies, as an extension of the adhesive-less solution proposed recently by Xu, Jackson, and Marghitu (XJM model) (Xu et al., 2014) 1, using the JKR theory for each gap. The results confirm recent theories in that we find an important effect of the fractal dimension. For D<2.5, the case which includes the vast majority of natural surfaces, there is an expected strong effect of adhesion. Only for large fractal dimensions, D>2.5, it seems that for large enough magnifications a full fractal roughness completely destroys adhesion. These results are partly paradoxical since strong adhesion is not observed in nature except in special cases.
•We introduce a simple model for adhesion rigorous near full contact.•Solution is found postulating constant stress intensity factor on edge of isolated gaps.•Results confirm some previous theories: for fractal dimension D<2.5, strong effect of adhesion.•However strong adhesion is not commonly observed in nature.
The contact between rough surfaces with adhesion is an extremely difficult problem, and the approximation of the DMT theory (to neglect deformations due to attractive forces), originally developed ...for spherical contact of very small radius, is receiving some new interest. The DMT approximation leads to extremely large overestimations of the adhesive forces in the case of spherical contact, except at pull-off. For cylindrical contact, the opposite trend is found for larger contact areas. These findings suggest some caution in solving rough contacts with DMT models, unless the Tabor parameter is really low. Further approximate models like that of Pastewka & Robbins’ may be explained to work only due to a coincidence of error cancellation in their range of parameters.
•The approximation of the DMT theory (to neglect deformations due to attractive forces), is receiving some new interest.•It leads to large overestimations of the adhesive forces in the case of spherical contact, even at relatively small Tabor parameters, except at pull-off.•For cylindrical contact, the opposite trend is found.•This may explain why some partial success has been found for rough contacts in some limited range of parameters.
In the present note, we suggest a single-line equation estimate for adhesion between elastic (hard) rough solids with Gaussian multiple scales of roughness. It starts from the new observation that ...the entire DMT solution for “hard” spheres (Tabor parameter tending to zero) with the Maugis law of attraction can be obtained using the Hertzian relationship load-indentation and estimating the area of attraction as the increase of the bearing area geometrical intersection when the indentation is increased by the Maugis range of attraction. The bearing area model in fact results in a simpler and even more accurate solution than DMT for intermediate Tabor parameters, although it retains one of the assumptions of DMT, that elastic deformations are not affected by attractive forces. Therefore, a solution is obtained for random rough surfaces combining Persson’s adhesiveless asymptotic simple form solution with the bearing area model, which is trivially computed for a Gaussian. A comparison with recent data from extensive numerical computations involving roughness with wavelength from nano to micrometer scale shows that the approximation is quite good for the pull-off in the simulations, and it remarks the primary importance in this regime of a single parameter, the macroscopic well-defined quantity (rms) amplitude of roughness, and small sensitiveness to rms slopes and curvatures.
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