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Register a new userNon-Amontons-Coulomb local friction law of randomly rough contact interfaces with rubber
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Added by
Antoine Chateauminois
Publication date
2017
fields
Physics
and research's language is
English
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We report on measurements of the local friction law at a multi-contact interface formed between a smooth rubber and statistically rough glass lenses, under steady state friction. Using contact imaging, surface displacements are measured, and inverted to extract both distributions of frictional shear stress and contact pressure with a spatial resolution of about 10~$mu$m. For a glass surface whose topography is self-affine with a Gaussian height asperity distribution, the local frictional shear stress is found to vary strongly sub-linearly with the local contact pressure over the whole investigated pressure range. Such sub-linear behavior is also evidenced for a surface with a non Gaussian height asperity distribution, demonstrating that, for such multi-contact interfaces, Amontons-Coulombs friction law does not prevail at the local scale.
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We report on normal contact and friction measurements of model multicontact interfaces formed between smooth surfaces and substrates textured with a statistical distribution of spherical micro-asperities. Contacts are either formed between a rigid textured lens and a smooth rubber, or a flat textured rubber and a smooth rigid lens. Measurements of the real area of contact $A$ versus normal load $P$ are performed by imaging the light transmitted at the microcontacts. For both interfaces, $A(P)$ is found to be sub-linear with a power law behavior. Comparison to two multi-asperity contact models, which extend Greenwood-Williamson (J. Greenwood, J. Williamson, textit{Proc. Royal Soc. London Ser. A} textbf{295}, 300 (1966)) model by taking into account the elastic interaction between asperities at different length scales, is performed, and allows their validation for the first time. We find that long range elastic interactions arising from the curvature of the nominal surfaces are the main source of the non-linearity of $A(P)$. At a shorter range, and except for very low pressures, the pressure dependence of both density and area of micro-contacts remains well described by Greenwood-Williamsons model, which neglects any interaction between asperities. In addition, in steady sliding, friction measurements reveal that the mean shear stress at the scale of the asperities is systematically larger than that found for a macroscopic contact between a smooth lens and a rubber. This suggests that frictional stresses measured at macroscopic length scales may not be simply transposed to microscopic multicontact interfaces.
We study experimentally and theoretically the equilibrium adhesive contact between a smooth glass lens and a rough rubber surface textured with spherical microasperities with controlled height and spatial distributions. Measurements of the real contact area $A$ versus load $P$ are performed under compression by imaging the light transmitted at the microcontacts. $A(P)$ is found to be non-linear and to strongly depend on the standard deviation of the asperity height distribution. Experimental results are discussed in the light of a discrete version of Fuller and Tabors (FT) original model (textit{Proceedings of the Royal Society A} textbf{345} (1975) 327), which allows to take into account the elastic coupling arising from both microasperities interactions and curvature of the glass lens. Our experimental data on microcontact size distributions are well captured by our discrete extended model. We show that the elastic coupling arising from the lens curvature has a significant contribution to the $A(P)$ relationship. Our discrete model also clearly shows that the adhesion-induced effect on $A$ remains significant even for vanishingly small pull-off forces. Last, at the local asperity length scale, our measurements show that the pressure dependence of the microcontacts density can be simply described by the original FT model.
Frictional properties of contacts between a smooth viscoelastic rubber and rigid surfaces are investigated using a torsional contact configuration where a glass lens is continuously rotated on the rubber surface. From the inversion of the displacement field measured at the surface of the rubber, spatially resolved values of the steady state frictional shear stress are determined within the non homogeneous pressure and velocity fields of the contact. For contacts with a smooth lens, a velocity dependent but pressure independent local shear stress is retrieved from the inversion. On the other hand, the local shear stress is found to depend both on velocity and applied contact pressure when a randomly rough (sand blasted) glass lens is rubbed against the rubber surface. As a result of changes in the density of micro-asperity contacts, the amount of light transmitted by the transparent multi-contact interface is observed to vary locally as a function of both contact pressure and sliding velocity. Under the assumption that the intensity of light transmitted by the rough interface is proportional to the proportion of area into contact, it is found that the local frictional stress can be expressed experimentally as the product of a purely velocity dependent term, $k(v)$, by a term representing the pressure and velocity dependence of the actual contact area, $A/A_0$. A comparison between $k(v)$ and the frictional shear stress of smooth contacts suggests that nanometer scale dissipative processes occurring at the interface predominate over viscoelastic dissipation at micro-asperity scale.
This paper reports on the frictional properties of smooth rubber substrates sliding against rigid surfaces covered with various densities of colloidal nano-particles (average diameter 77 nm). Friction experiments were carried out using a transparent Poly(dimethyl siloxane) (PDMS) rubber contacting a silica lens with silica nano-particles sintered onto its surface. Using a previously described methodology (Nguyen textit{et al.}, textit{J. of Adhesion} textbf{87} (2011) 235-250 ), surface shear stress and contact-pressure distribution within the contact were determined from a measurement of the displacement field at the surface of the PDMS elastomer. Addition of silica nano-particles results in a strong, pressure-independent enhancement of the frictional shear stress as compared to the smooth lens. The contribution of viscoelastic losses to these increased frictional properties is analyzed in the light of a numerical model that solves the contact problem between the rubber and the rough surface. An order-of-magnitude agreement is obtained between experimental and theoretical results, the latter showing that the calculation of viscoelastic dissipation within the contact is very sensitive to the details of the topography of the rigid asperities.
We report on a theoretical and experimental investigation of the normal contact of stretched neo-Hookean substrates with rigid spherical probes. Starting from a published formulation of surface Greens function for incremental displacements on a pre-stretched, neo-Hookean, substrate (L.H. Lee textit{J. Mech. Phys. Sol.} textbf{56} (2008) 2957-2971), a model is derived for both adhesive and non-adhesive contacts. The shape of the elliptical contact area together with the contact load and the contact stiffness are predicted as a function of the in-plane stretch ratios $lambda_x$ and $lambda_y$ of the substrate. The validity of this model is assessed by contact experiments carried out using an uniaxally stretched silicone rubber. for stretch ratio below about 1.25, a good agreement is observed between theory and experiments. Above this threshold, some deviations from the theoretical prediction are induced as a result of the departure of the mechanical response of the silicone rubber from the neo-Hokeean description embedded in the model.
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