In this work, a numerical method has been developed to investigate the adhesionless contact mechanics between rough surfaces. To solve the elastic problem a boundary elements approach is used with ...self-equilibrated square elements. The domain of integration is discretized developing an “intelligent” adaptive mesh and obtaining a considerable memory saving. The numerical convergence of the method has been verified by comparing the results with the Hertzian solution and by checking the stress probability distribution at the contact interface. The methodology has been then utilized to analyse the contact between an elastic flat substrate and a periodic numerically generated self-affine fractal rigid surface. The fractal surface has been generated by employing spectral methods. The results of our investigation supports the findings of some analytical theories (
Persson, 2001) and numerical findings (
Yang et al., 2006; Hyun et al., 2004; Carbone and Bottiglione, 2008; Campana and Muser, 2007) in terms of linearity between contact area and load and stress probability distributions.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
•Friction-induced vibrations may arise in viscoelastic contacts.•Contact interactions depend on the relative speed and on the indentation depth.•Instability may occur due to negative damping ...terms.•In plane and out-of-plane motion are coupled through the contact interface.•Multiple stable solutions exist in certain range of system parameters.
Self-excited vibrations represent a big concern in engineering, particularly in automotive, railway and aeronautic industry. Many lumped models have been proposed over the years to analyze the stability of such systems. Among the instability mechanisms a falling characteristic of the friction law and mode coupling have been shown to give friction-excited oscillations. The mass-on-moving-belt system has been studied extensively in Literature, very often adopting a prescribed form of the friction law and linearizing the contact stiffness. Instead, in this work, the case of a spherical oscillator excited by a moving viscoelastic halfspace is considered. The friction law and the nonlinear normal contact stiffness have been computed via boundary element numerical simulations for varying substrate velocity and indentation depth, then they have been adopted in time-marching dynamical numerical simulations. It is shown that the horizontal and vertical dynamics of the oscillator are tightly connected each other through the viscoelastic substrate. Furthermore, for certain normal forces/substrate velocity, the system has multiple stable solutions, which may include lift-off of the oscillator, which are selected based solely on the system initial conditions.
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In this paper, we show how the numerical theory introduced by the authors Carbone and Putignano, J. Mech. Phys. Solids 61, 1822 (2013) can be effectively employed to study the contact between ...viscoelastic rough solids. The huge numerical complexity is successfully faced up by employing the adaptive nonuniform mesh developed by the authors in Putignano et al. J. Mech. Phys. Solids 60, 973 (2012). Results mark the importance of accounting for viscoelastic effects to correctly simulate the sliding rough contact. In detail, attention is, first, paid to evaluate the viscoelastic dissipation, i.e., the viscoelastic friction. Fixed the sliding speed and the normal load, friction is completely determined. Furthermore, since the methodology employed in the work allows to study contact between real materials, a comparison between experimental outcomes and numerical prediction in terms of viscoelastic friction is shown. The good agreement seems to validate-at least partially-the presented methodology. Finally, it is shown that viscoelasticity entails not only the dissipative effects previously outlined, but is also strictly related to the anisotropy of the contact solution. Indeed, a marked anisotropy is present in the contact region, which results stretched in the direction perpendicular to the sliding speed. In the paper, the anisotropy of the deformed surface and of the contact area is investigated and quantified.
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CMK, CTK, FMFMET, IJS, NUK, PNG, UM
This review summarizes recent advances in the area of tribology based on the outcome of a Lorentz Center workshop surveying various physical, chemical and mechanical phenomena across scales. Among ...the main themes discussed were those of rough surface representations, the breakdown of continuum theories at the nano- and microscales, as well as multiscale and multiphysics aspects for analytical and computational models relevant to applications spanning a variety of sectors, from automotive to biotribology and nanotechnology. Significant effort is still required to account for complementary nonlinear effects of plasticity, adhesion, friction, wear, lubrication and surface chemistry in tribological models. For each topic, we propose some research directions.
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In the last years, an increasing number of papers has been published in the field of contact mechanics between rough fractal surfaces. The increase in research is motivated by the wide variety of ...natural and industrial processes that involve formation of rough surfaces and interfaces, characterized by self-similarity or self-affine properties on multiple scales. In this paper, the contact between a linear elastic half-space and a rough self-affine fractal rigid surface is studied by employing a numerical method recently developed by the authors (Putignano et al., 2012). The paper aims at investigating the influence of surface parameters as fractal dimensions, mean square slope and mean square roughness on the relation between the contact area, the load and the average separation. The results show that, for relatively small loads, the real contact area–load relationship coefficient of proportionality κ takes the universal value κ=2 independent of the statistical properties and fractal dimension Df of the rough surface. This universal constant is just in between the two values predicted respectively by Bush et al. (1975) and Persson (2001). We also find that the average separation vs. load relation is affected by the fractal dimension Df of the rough surface, as higher Df lead to an increase of the average separation. Finally, in this work, we also study the behavior of the power spectral densities of the elastically deformed surface and of the distribution of local separations. We find that the trend of this quantities is in agreement with recent theoretical predictions.
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In this work, we discuss important improvements of asperity models. Specifically, we assess the predictive capabilities of a recently developed multiasperity model, which differs from the original ...Greenwood and Williamson model by (i) including the coupling between the elastic fields generated by each contact spot, and (ii) taking into account the coalescence among the contact areas, occurring during the loading process. Interaction of the elastic field is captured by summing the contributions, which are analytically known, of the elastic displacements in a given point of the surface due to each Hertzian-like contact spot. The coalescence is instead considered by defining an equivalent contact spot in such a way to guarantee conservation of contact area during coalescence. To evaluate the accuracy of the model, a comparison with fully numerical ‘exact’ calculations and Persson’s contact mechanics theory of elastic rough surfaces is proposed. Results in terms of contact area versus load and separation versus load show that the three approaches give almost the same predictions, while traditional asperity models neglecting coalescence and elastic coupling between contact regions are unable to correctly capture the contact behavior. Finally, very good results are also obtained when dealing with the probability distribution of interfacial stresses and gaps.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
If the nominal contact tractions at an interface are everywhere below the Coulomb friction limit throughout a cycle of oscillatory loading, the introduction of surface roughness will generally cause ...local microslip between the contacting asperities and hence some frictional dissipation. This dissipation is important both as a source of structural damping and as an indicator of potential fretting damage. Here we use a strategy based on the Ciavarella-Jäger superposition and a recent solution of the general problem of the contact of two half spaces under oscillatory loading to derive expressions for the dissipation per cycle which depend only on the normal incremental stiffness of the contact, the external forces and the local coefficient of friction. The results show that the dissipation depends significantly on the relative phase between the oscillations in normal and tangential load—a factor which has been largely ignored in previous investigations. In particular, for given load amplitudes, the dissipation is significantly larger when the loads are out of phase. We also establish that for small amplitudes the dissipation varies with the cube of the load amplitude and is linearly proportional to the second derivative of the elastic compliance function for all contact geometries, including those involving surface roughness. It follows that experimental observations of less than cubic dependence on load amplitude cannot be explained by reference to roughness alone, or by any other geometric effect in the contact of half spaces.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
We investigate the adhesive and adhesiveless contact between a rigid regular wavy profile and an elastic substrate coated with an elastic layer. The contact stiffness is strongly influenced by the ...elasticity and thickness of the coating layer. Specifically, coatings more compliant than the substrate entail larger contact area, and vice versa. Under adhesive conditions, thin soft coatings may lead to complete contact, regardless of the applied load. Moreover, enhanced adhesive strength (toughness) can be achieved at the pull-off by adopting stiff (compliant) coatings. We compare our exact model with the Bec/Tonck model, which is one of the most adopted approximate model for biological tissues contact mechanics. The results show that predictions of the proposed model are in better qualitative agreement with experimental results taken from the literature.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
We analyze the periodic contact between an elastic half-space and two types of rough substrates: (i) a perfect isotropically rough rigid substrate (2D isotropic roughness), and (ii) a perfect ...anisotropically rough rigid substrate, i.e. a substrate with roughness in only one direction (1D roughness). The analysis is carried out with the aid of proprietary codes, that we have developed (both in real and Fourier space) to deal with this type of contacts. Of course, 1D contacts differ from 2D isotropic contacts. However, our results and theoretical arguments suggest a possible criterion to make 2D contacts equivalent to 1D ones from the point of view of contact area and separation calculations. The rule consists in replacing the 2D power spectral density (PSD) of the isotropic surface into an equivalent 1D PSD. Interestingly the transformation rule does not depend on the statistical properties of the surface roughness, hence seems to have a universal character for isotropic surfaces.
► A simple criterion is presented to reduce the dimensionality of rough contacts. ► We find that the condition for equivalence has a very general character. ► The criterion allows to reduce of orders of magnitude the numerical complexity of contact problems.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
Analyses of rough surface contact sometimes study the two-dimensional problem to avoid some of the difficulties of three-dimensional contacts, or to reduce the size of the calculations in numerical ...work. But two-dimensional elastic contacts introduce their own difficulties. The mean real contact pressures will be much lower than in three dimensions, and will depend strongly on the thickness of the ‘slab’ used to represent the elastic half-space.
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