No Arabic abstract
A MEMS-based sensing device is used to measure the normal and tangential stress fields at the base of a rough elastomer film in contact with a smooth glass cylinder in steady sliding. This geometry allows for a direct comparison between the stress profiles measured along the sliding direction and the predictions of an original textit{exact} bidimensional model of friction. The latter assumes Amontons friction law, which implies that in steady sliding the interfacial tangential stress is equal to the normal stress times a pressure-independent dynamic friction coefficient $mu_d$, but makes no further assumption on the normal stress field. Discrepancy between the measured and calculated profiles is less than 14% over the range of loads explored. Comparison with a test model, based on the classical assumption that the normal stress field is unchanged upon tangential loading, shows that the exact model better reproduces the experimental profiles at high loads. However, significant deviations remain that are not accounted for by either calculations. In that regard, the relevance of two other assumptions made in the calculations, namely (i) the smoothness of the interface and (ii) the pressure-independence of $mu_d$ is briefly discussed.
This paper addresses the issue of the determination of the frictional stress distribution from the inversion of the measured surface displacement field for sliding interfaces between a glass lens and a rubber (poly(dimethylsiloxane)) substrate. Experimental results show that high lateral strains are achieved at the periphery of the sliding contacts. As a consequence, an accurate inversion of the displacement field requires that finite strains and non linear response of the rubber substrate are taken into account. For that purpose, a Finite Element (FE) inversion procedure is implemented where the measured displacement field is applied as a boundary condition at the upper surface of a meshed body representing the rubber substrate. Normal pressure is also determined by the same way, if non-diverging values are assumed at the contact edge. This procedure is applied to linearly sliding contacts as well as on twisting contacts.
Digital Image Correlation is used to study the micromechanics of a multi-contact interface formed between a rough elastomer and a smooth glass surface. The in-plane elastomer deformation is monitored during the incipient sliding regime, i.e. the transition between static and sliding contact. As the shear load is increased, an annular slip region, in coexistence with a central stick region, is found to progressively invade the contact. From the interfacial displacement field, the tangential stress field can be further computed using a numerical inversion procedure. These local mechanical measurements are found to be correctly captured by Cattaneo and Mindlin (CM)s model. However, close comparison reveals significant discrepancies in both the displacements and stress fields that reflect the oversimplifying hypothesis underlying CMs scenario. In particular, our optical measurements allow us to exhibit an elasto-plastic like friction constitutive equation that differs from the rigid-plastic behavior assumed in CMs model. This local constitutive law, which involves a roughness-related length scale, is consistent with the model of Bureau textit{et al.} [Proc. R. Soc. London A textbf{459}, 2787 (2003)] derived for homogeneously loaded macroscopic multi-contact interfaces, thus extending its validity to mesoscopic scales.measurements allow for the first quantitative test of Cattaneo and Mindlin (CM) classical model of the incipient sliding of a smooth interface. Small deviations are observed and interpreted as a result of the finite compliance of the rough interface, a behavior which contrasts with Amontons law of friction assumed to be valid locally in CMs model. We illustrate how these measurements actually provide a method for probing the rheology of the rough interface, which we find to be of the elasto-plastic type.
In this paper, we report on new experimental results on the effects of in-plane surface stretching on the friction of Poly(DiMethylSiloxane) (PDMS) rubber with smooth rigid probes. Friction-induced displacement fields are measured at the surface of the PDMS substrate under steady-state sliding. Then, the corresponding contact pressure and frictional stress distributions are determined from an inversion procedure. Using this approach, we show that the local frictional stress $tau$ is proportional to the local stretch ratio $lambda$ at the rubber surface. Additional data using a triangular flat punch indicate that $tau(lambda)$ relationship is independent on the contact geometry. From friction experiments using pre-stretched PDMS substrate, it is also found that the stretch-dependence of the frictional stress is isotropic, i.e. it does not depend on the angle between stretching and sliding directions. Potential physical explanations for this phenomenon are provided within the framework of Schallamachs friction model. Although the present experiments are dealing with smooth contact interfaces, the reported $tau(lambda)$ dependence is also relevant to the friction of statistically rough contact interfaces, while not accounted for in related contact mechanics models.
Stability of coarse particles against gravity is an important issue in dense suspensions (fresh concrete, foodstuff, etc.). On the one hand, it is known that they are stable at rest when the interstitial paste has a high enough yield stress; on the other hand, it is not yet possible to predict if a given material will remain homogeneous during a flow. Using MRI techniques, we study the time evolution of the particle volume fraction during the flows in a Couette geometry of model density-mismatched suspensions of noncolloidal particles in yield stress fluids. We observe that shear induces sedimentation of the particles in all systems, which are stable at rest. The sedimentation velocity is observed to increase with increasing shear rate and particle diameter, and to decrease with increasing yield stress of the interstitial fluid. At low shear rate (plastic regime), we show that this phenomenon can be modelled by considering that the interstitial fluid behaves like a viscous fluid -- of viscosity equal to the apparent viscosity of the sheared fluid -- in the direction orthogonal to shear. The behavior at higher shear rates, when viscous effects start to be important, is also discussed. We finally study the dependence of the sedimentation velocity on the particle volume fraction, and show that its modelling requires estimating the local shear rate in the interstitial fluid.
One of the most fundamental questions in tribology concerns the area dependence of friction at the nanoscale. Here, experiments are presented where the frictional resistance of nanoparticles is measured by pushing them with the tip of an atomic force microscope. We find two coexisting frictional states: While some particles show finite friction increasing linearly with the interface areas of up to 310,000nm^2, other particles assume a state of frictionless sliding. The results further suggest a link between the degree of surface contamination and the occurrence of this duality.