SOME SIMPLE RESULTS ON THE MULTISCALE VISCOELASTIC FRICTION

The coefficient of friction due to bulk viscoelastic losses corresponding to multiscale roughness can be computed with Persson's theory. In the search for a more complete understanding of the parametric dependence of the friction coefficient, we show asymptotic results at low or large speed for a generalized Maxwell viscoelastic material, or for a material showing power law storage and loss factors at low frequencies. The ascending branch of friction coefficient at low speeds highly depends on the rms slope of the surface roughness (and hence on the large wave vector cutoff), and on the ratio of imaginary and absolute value of the modulus at the corresponding frequency, as noticed earlier by Popov. However, the precise multiplicative coefficient in this simplified equation depends in general on the form of the viscoelastic modulus. Vice versa, the descending (unstable) branch at high speed mainly on the amplitude of roughness, and this has apparently not been noticed before. Hence, for very broad spectrum of roughness, friction would remain high for quite few decades in sliding velocity. Unfortunately, friction coefficient does not depend on viscoelastic losses only, and moreover there are great uncertainties in the choice of the large wave vector cutoff, which affect friction coefficient by orders of magnitudes, so at present these theories do not have much predictive capability

Detachment of a rigid flat punch from a viscoelastic material

We show that the detachment of a flat punch from a viscoelastic substrate has a relatively simple behavior, framed between the Kendall's elastic solution at the relaxed modulus and at the instantaneous modulus, and the cohesive strength limit. We find hardly any dependence of the pull-off force on the details of the loading process, including maximum indentation at preload and loading rate, resulting much simpler than the case of a spherical punch. Pull-off force peaks at the highest speeds of unloading, when energy dissipation is negligible, which seems to be in contrast with what suggested by the theories originated by de Gennes of viscoelastic semi-infinite crack propagation which associated enhanced work of adhesion to dissipation. Further qualitative differences with the dissipation-based model occur to explain the finite size effect

On the Effect of a Rate-Dependent Work of Adhesion in the Detachment of a Dimpled Surface

Patterned surfaces have proven to be a valuable design to enhance adhesion, increasing hysteresis and the detachment stress at pull-off. To obtain high adhesive performance, soft materials are commonly, used, which easily conform to the countersurface, such as soft polymers and elastomers. Such materials are viscoelastic; i.e., they show rate-dependent properties. Here, the detachment of two half spaces is studied, one being flat and the other having a dimple in the limit of short range adhesion and a power law rate-dependent work of adhesion, as observed by several authors. Literature results have suggested that the dimpled surface would show pressure-sensitive adhesion, showing two possible adhered states, one weak, in partial contact, and one strong when full contact is achieved. By accounting for a power law rate-dependent work of adhesion, the “weak state” may be much stronger than it was in the purely elastic case, and hence the interface may be much more tough to separate. We study the pull-off detachment stress of the dimpled surface, showing that it weakly depends on the preload, but it is strongly affected by the dimensionless unloading rate. Finally, possible implications of the presented results in the detachment of soft materials from rough substrates are discussed

Friction-induced energy losses in mechanical contacts subject to random vibrations

In this paper, we apply the previously developed Method of Memory Diagrams (MMD) to the description of an axisymmetric mechanical contact with friction subject to random vibrations. The MMD belongs to a family of semi-analytical methods of contact mechanics originating from the classical Cattaneo–Mindlin solution; it allows one to efficiently compute mechanical and energetic responses to complex excitation signals such as random or acoustic ones. For an axisymmetric contact driven by random normal and tan- gential displacements having fractal statistical properties, we calculate the friction-induced mechanical energy loss averaged over a large number of realizations. In the considered problem, this energy depends on a very restrained number of parameters: on the rms of random displacements, on the fractal dimen- sion, and on the upper cut-offfrequency of the fractal spectrum. In addition, a radial distribution of the dissipated energy has been obtained that has a direct relation to wear in the contact system. For small displacement amplitudes, wear should be expected in an annulus inside of a mean contact circle whereas for large displacements it will start at the contact center

Interfacial Dissipative Phenomena in Tribomechanical Systems

The last decade has experienced a tremendous development of several technologies that are likely to shape our future [...

Vectorial Images for "A two-scale FEM-BAM approach for fingerpad friction under electroadhesion"

<p>This dataset contains the figures in Scalable Vector Graphics format (*.svg) that appear in Ref. [1]. This upload is intended to ease the access and reuse of the data published in Ref. [1].</p> <p>[1] Forsbach, F., Heß, M., & Papangelo, A. (2023). A two-scale FEM-BAM approach for fingerpad friction under electroadhesion. <em>Frontiers in Mechanical Engineering</em>, <em>8</em>, 1074393. <a href="https://doi.org/10.3389/fmech.2022.1074393">https://doi.org/10.3389/fmech.2022.1074393</a> </p> <p> </p&gt

Bio-inspired solution for optimal adhesive performance

In recent years there has been a growing interest into high performance bioinspired adhesives. This communication focuses on the adhesive behavior of a rigid cylinder that indents an elastic layer coated on a rigid substrate. With the assumption of short range adhesive interactions (JKR type) the adhesive solution is obtained very easily starting from the adhesiveless one. We show that ultrastrong adhesion (up to theoretical material strength) can be reached in line contact by reducing the thickness of the layer, typically down to the nanoscale size, which suggests a new possible design for "optimal adhesion". Adhesion enhancement occurs as an increase of the actual pull-off force, which is further enhanced by Poisson's ratio effects in the case of nearly incompressible layer. The system studied could be an interesting geometry for an adhesive system, but also a limit case of the more general class of layered systems, or FGMs (Functionally Graded Materials). The model is well suited for analyzing the behavior of polymer layers coated on metallic substrates

Can Wear Completely Suppress Thermoelastic Instabilities?

Thermoelastic instabilities (TEI) occur in sliding bodies at sufficiently high speed because a small thermoelastic disturbance tends to localize the contact, leading to "hot spots." The role that wear plays in TEI has been studied briefly and only on highly idealized cases. We extend and complete in detail a model of Dow and Burton who studied the specific configuration of a blade sliding on a rigid half-space normal to its line of contact. We find there is a limit value of wear coefficient that can be estimated by simple equations, above which TEI is completely eliminated. In the limiting case of non-conducting half-space, it depends linearly on thermal expansion, diffusivity, and friction coefficient and inversely on the conductance of the material of the sliding body. This may not always be in the practical range, but when considering conductance of the half-space, the limit wear can be lowered arbitrarily so as to be viable. In some applications, it may be possible to increase wear to reduce or suppress TEI. Hence, the common assumption of neglecting wear in simulations of sliding contacts with TEI and hotspots should be taken with care, and the present results give some important benchmarks

On notch and crack size effects in fatigue, Paris’ law and implications for Wöhler curves

As often done in design practice, the Wöhler curve of a specimen, in the absence of more direct information, can be crudely retrieved by interpolating with a power-law curve between static strength at a given conventional low number of cycles N0(of the order of 10-103), and the fatigue limit at a “infinite life”, also conventional, typically N∞=2·106or N∞=107cycles. These assumptions introduce some uncertainty, but otherwise both the static regime and the infinite life are relatively well known. Specifically, by elaborating on recent unified treatments of notch and crack effects on infinite life, and using similar concepts to the static failure cases, an interpolation procedure is suggested for the finite life region. Considering two ratios, i.e. toughness to fatigue threshold FK=KIc/∆Kth, and static strength to endurance limit, FR=σR/∆σ0, qualitative trends are obtained for the finite life region. Paris’ and Wöhler’s coefficients fundamentally depend on these two ratios, which can be also defined “sensitivities” of materials to fatigue when cracked and uncracked, respectively: higher sensitivity means stringent need for design for fatigue. A generalized Wöhler coefficient, k’, is found as a function of the intrinsic Wöhler coefficient k of the material and the size of the crack or notch. We find that for a notched structure, k<k’<m, as a function of size of the notch: in particular, k’=k holds for small notches, then k’ decreases up to a limiting value (which depends upon Ktfor mildly notched structures, or on FKand FRonly for severe notch or crack). A perhaps surprising return to the original slope k is found for very large blunt notches. Finally, Paris’ law should hold for a distinctly cracked structure, i.e. having a long-crack; indeed, Paris’ coefficient m is coincident with the limiting value of k’lim. The scope of this note is only qualitative and aims at a discussion over unified treatments in fatigue

On the degree of irreversibility of friction in sheared soft adhesive contacts

A number of authors have experimentally assessed the influence of friction on adhesive contacts, and generally the contact area has been found to decrease due to tangential shear stresses at the interface. The decrease is however generally much smaller than that predicted already by the Savkoor and Briggs 1977 classical theory using “brittle” fracture mechanics mixed mode model extending the JKR (Griffith like) solution to the contact problem. The Savkoor and Briggs theory has two strong assumptions, namely that (i) shear tractions are also singular at the interface, whereas they have been found to follow a rather constant distribution, and that (ii) no dissipation occurs in the contact. While assumption (ii) has been extensively discussed in the Literature the role of assumption (i) remained unclear. We show that assuming entirely reversible slip at the interface with a constant shear stress fracture mechanics model leads to results almost indistinguishable from the Savkoor and Briggs model (and further in disagreement with experiments), hence it is assumption (ii) that critically affects the results. We analyze a large set of experimental data from Literature and show that the degree of irreversibility of friction can vary by orders of magnitude, despite similar materials and geometries, depending on the velocity at which the tangential load is applied.Open access funding provided by Politecnico di Bari within the CRUI-CARE Agreement. A.P. and M.C. acknowledge the support by the Italian Ministry of Education, University andResearch under the Programme Department of Excellence Legge 232/2016 (Grant No. CUP-D94I18000260001). A.P. is thankful to the DFG (German Research Foundation) for funding theproject PA 3303/1-1. A.P. acknowledges support from “PON Ricerca e Innovazione 2014-2020-Azione I.2”—D.D. n. 407, 27/02/2018, bando AIM (Grant No. AIM1895471)