Showing papers on "Contact area published in 2009"

Friction laws at the nanoscale

Abstract: Macroscopic laws of friction do not generally apply to nanoscale contacts. Although continuum mechanics models have been predicted to break down at the nanoscale, they continue to be applied for lack of a better theory. An understanding of how friction force depends on applied load and contact area at these scales is essential for the design of miniaturized devices with optimal mechanical performance. Here we use large-scale molecular dynamics simulations with realistic force fields to establish friction laws in dry nanoscale contacts. We show that friction force depends linearly on the number of atoms that chemically interact across the contact. By defining the contact area as being proportional to this number of interacting atoms, we show that the macroscopically observed linear relationship between friction force and contact area can be extended to the nanoscale. Our model predicts that as the adhesion between the contacting surfaces is reduced, a transition takes place from nonlinear to linear dependence of friction force on load. This transition is consistent with the results of several nanoscale friction experiments. We demonstrate that the breakdown of continuum mechanics can be understood as a result of the rough (multi-asperity) nature of the contact, and show that roughness theories of friction can be applied at the nanoscale.

Range of Applicability of the Wenzel and Cassie−Baxter Equations for Superhydrophobic Surfaces†

Abstract: The Wenzel and Cassie−Baxter equations depending on the extent of liquid/solid interfacial contact area were generally used to estimate water contact angles on superhydrophobic surfaces. In this study, a simple method is proposed on the criterion to use the Wenzel and Cassie−Baxter equations to evaluate the contact angle results on superhydrophobic surfaces. In this method, the difference between the theoretical (geometric) and experimental contact angle-dependent Wenzel roughness parameter, Δrw, and Cassie−Baxter solid/liquid contact area fraction, ΔfsCB were determined, and the validity of these equations was evaluated. We used the data of eight recent publications where the water drop sits on square and cylindrical pillar structured superhydrophobic model surfaces. We evaluated the contact angle results of 166 patterned samples with our method. We also found that the effect of contact angle error margins was low to vary these parameters. In general, the use of the Wenzel equation was found to be wrong ...

Empirical evaluation for finger input properties in multi-touch interaction

Abstract: Current multi-touch interaction techniques typically only use the x-y coordinates of the human finger's contact with the screen. However, when fingers contact a touch-sensitive surface, they usually approach at an angle and cover a relatively large 2D area instead of a precise single point. In this paper, a Frustrated Total Internal Reflection (FTIR) based multi-touch device is used to collect the finger imprint data. We designed a series of experiments to explore human finger input properties and identified several useful properties such as contact area, contact shape and contact orientation which can be exploited to improve the performance of multi-touch selecting and pointing tasks. Based on the experimental results, we discuss some implications for the design of human finger input interfaces and propose several design prototypes which incorporate these implications. A set of raw data and several concrete recommendations which are useful for the research community are also presented.

Determining the elastic modulus and hardness of an ultra-thin film on a substrate using nanoindentation

Abstract: A data analysis procedure has been developed to estimate the contact area in an elastoplastic indentation of a thin film bonded to a substrate. The procedure can be used to derive the elastic modulus and hardness of the film from the indentation load, displacement, and contact stiffness data at indentation depths that are a significant fraction of the film thickness. The analysis is based on Yu’s elastic solution for the contact of a rigid conical punch on a layered half-space and uses an approach similar to the Oliver-Pharr method for bulk materials. The methodology is demonstrated for both compliant films on stiff substrates and the reverse combination and shows improved accuracy over previous methods.

Is there a biomechanical explanation for anterior knee pain in patients with patella alta? INFLUENCE OF PATELLAR HEIGHT ON PATELLOFEMORAL CONTACT FORCE, CONTACT AREA AND CONTACT PRESSURE

Abstract: The purpose of this study was to test the hypothesis that patella alta leads to a less favourable situation in terms of patellofemoral contact force, contact area and contact pressure than the normal patellar position, and thereby gives rise to anterior knee pain. A dynamic knee simulator system based on the Oxford rig and allowing six degrees of freedom was adapted in order to simulate and record the dynamic loads during a knee squat from 30° to 120° flexion under physiological conditions. Five different configurations were studied, with variable predetermined patellar heights. The patellofemoral contact force increased with increasing knee flexion until contact occurred between the quadriceps tendon and the femoral trochlea, inducing load sharing. Patella alta caused a delay of this contact until deeper flexion. As a consequence, the maximal patellofemoral contact force and contact pressure increased significantly with increasing patellar height (p < 0.01). Patella alta was associated with the highest maximal patellofemoral contact force and contact pressure. When averaged across all flexion angles, a normal patellar position was associated with the lowest contact pressures. Our results indicate that there is a biomechanical reason for anterior knee pain in patients with patella alta.

Indentation of bone tissue: a short review

Abstract: IntroductionBone is a highly hierarchical natural composite material,which mechanical properties are investigated from thephysiological elastic behavior up to impact or fatiguedamage accumulation responsible for traumatic or stressfractures. Each hierarchical level of organization contrib-utes to the global mechanical response of a bone structure:– The mineralized collagen fibril (MCF, 200 nm)– The lamella (2–7 μm)– The bone structural unit (BSU, 60 μm)– Bone tissue, cortical shell, or trabeculae (100–3,000 μm)– Trabecular bone (TB, mm)– Organ (cm)Bone matrix quality becomes a central focus in under-standing the etiology of fractures in diseases such asosteoporosis. Macroscopic indentation was adopted in thefirst half of the 20th century to investigate hardness of boneat the tissue level (compact and trabecular) and wasextended to micro- and nano-indentation in the past 10 yearsto evaluate specific mechanical properties of bone structuralunits and single lamellae, respectively. Over this period oftime, more than 375 papers or reviews were published(Scopus, “*indentation and bone,” June 23rd 2008).Consequently, the objective of this paper is to review therecent progress of indentation techniques to evaluate themechanical properties of human bone at these intermediatelevels of organization.Materials and methodsIndentationIndentation consists in pressing a hard tip with a knownforce into a semi-infinite half-space and measuring directlyor indirectly the contact area. In the classical hardness testperformed at the macroscopic or microscopic level, thecontact area is estimated optically from the imprint createdby the tip on the material and leads to the definition ofhardness as the force divided by this area. The mostcommon hardness measuring indenters are sphere (Brinell,Rockwell), four-sided pyramid (Vickers), and asymmetricpyramid (Knoop).Recent depth-sensing technologies allow for measure-ment of the tip displacement during the indentation processof a semi-infinite half-space with micro- and even nano-precision. Indirect estimation of the contact area is obtainedby preliminary calibration of the tip shape and systemcompliance. Shallow indentation depths down to 100 nmallow for spatial resolution of the measurements in themicron range, and the sample position is typically con-trolled by high-precision motorized tables or piezoelectricscanners. Micro- and nano-indentation tips are often madeof diamond and can be found in spherical, conical, andmost commonly, three-sided pyramidal (Berkovich) shapes.The blunted extremity of the tip has a radius of approxi-mately 100 nm. Spherical tips minimize plastic deformationand damage but are difficult to manufacture, flat puncheslead to high stress concentrations, conical tips have an axialsymmetry that remains in the assumption of most theoret-

Adhesive contact of rough surfaces: Comparison between numerical calculations and analytical theories

Abstract: The authors have employed a numerical procedure to analyse the adhesive contact between a soft elastic layer and a rough rigid substrate. The solution to the problem, which belongs to the class of the free boundary problems, is obtained by calculating Green’s function which links the pressure distribution to the normal displacements at the interface. The problem is then formulated in the form of a Fredholm integral equation of the first kind with a logarithmic kernel. The boundaries of the contact area are calculated by requiring the energy of the system to be stationary. This methodology has been employed to study the adhesive contact between an elastic semi-infinite solid and a randomly rough rigid profile with a self-affine fractal geometry. We show that, even in the presence of adhesion, the true contact area still linearly depends on the applied load. The numerical results are then critically compared with the predictions of an extended version of Persson’s contact mechanics theory, which is able to handle anisotropic surfaces, as 1D interfaces. It is shown that, for any given load, Persson’s theory underestimates the contact area by about 50% in comparison with our numerical calculations. We find that this discrepancy is larger than for 2D rough surfaces in the case of adhesionless contact. We argue that this increased difference might be explained, at least partially, by considering that Persson’s theory is a mean-field theory in spirit, so it should work better for 2D rough surfaces rather than for 1D rough surfaces. We also observe that the predicted value of separation is in agreement with our numerical results as well as the exponents of the power spectral density of the contact pressure distribution and of the elastic displacement of the solid. Therefore, we conclude that Persson’s theory captures almost exactly the main qualitative behaviour of the rough contact phenomena.

Fingerprints are unlikely to increase the friction of primate fingerpads

Abstract: It is generally assumed that fingerprints improve the grip of primates, but the efficiency of their ridging will depend on the type of frictional behaviour the skin exhibits. Ridges would be effective at increasing friction for hard materials, but in a rubbery material they would reduce friction because they would reduce contact area. In this study we investigated the frictional performance of human fingertips on dry acrylic glass using a modified universal mechanical testing machine, measuring friction at a range of normal loads while also measuring the contact area. Tests were carried out on different fingers, fingers at different angles and against different widths of acrylic sheet to separate the effects of normal force and contact area. The results showed that fingertips behaved more like rubbers than hard solids; their coefficients of friction fell at higher normal forces and friction was higher when fingers were held flatter against wider sheets and hence when contact area was greater. The shear stress was greater at higher pressures, suggesting the presence of a biofilm between the skin and the surface. Fingerprints reduced contact area by a factor of one-third compared with flat skin, however, which would have reduced the friction; this casts severe doubt on their supposed frictional function.

3-dimensional curved substrate lamination

Abstract: A method of laminating a surface of a flexible material to a surface of a rigid, curved material. The method includes pressing an area of the surface of the flexible material into the surface of the rigid, curved material with a holder to create a contact area while the flexible material is conformed to the holder, which has a curvature greater than a curvature of the rigid, curved material surface; and changing the contact area between the surface of the flexible material and the surface of the rigid, curved material while maintaining pressure on the contact area until the surface of the flexible material and the surface of the rigid curved material are laminated.

Imparting Ultra‐Low Friction and Wear Rate to Epoxy by the Incorporation of Microencapsulated Lubricant?

Abstract: The incorporation of microcapsules containing lubricant oil into epoxy composites leads to materials with ultra-low friction and wear performance. During sliding wear tests, the capsules are damaged by the asperities of the counterface, releasing the oil to the contact area. The lubrication effect of the released oil and the entrapment of wear particles in the cavities left by the ruptured capsules leads to a significant reduction of both the frictional coefficient and the specific wear rate. The approach provides the merits of fluid lubrication but excludes the drawbacks of external lubrication. A minute amount of lubricant oil is sufficient to improve the tribological properties significantly.

Effect of Different Particle Size Distributions on Solid-State Sintering: A Microscopic Simulation Approach

Abstract: Simulations based on the discrete element method (DEM) are used to investigate the relationship between the distribution of particle sizes and the macroscopic sintering behavior of ceramic powders. This is achieved by generalizing the DEM force laws for solid-state sintering in such a way that sintering of particles with different sizes can be simulated. A generation scheme for initial particle packings with realistic physical properties is presented, which allows for different distributions, ranging from monomodal to normal, log-normal, and bimodal distributions. It is shown that the type and width of the distribution has a significant effect on the strain rates and viscosity during sintering. Broader size distributions lead to reduced sintering rates, although particle rearrangement is enhanced. However, the accelerating effect of rearrangement is overcompensated by an increase of the contact area between particles when the size distribution becomes wider. The simulation results are in good agreement with experimental results on a commercial Al 2 O 3 power.

Forced Response Prediction of Constrained and Unconstrained Structures Coupled Through Frictional Contacts

Abstract: In this paper, a forced response prediction method for the analysis of constrained and unconstrained structures coupled through frictional contacts is presented. This type of frictional contact problem arises in vibration damping of turbine blades, in which dampers and blades constitute the unconstrained and constrained structures, respectively. The model of the unconstrained/free structure includes six rigid body modes and several elastic modes, the number of which depends on the excitation frequency. In other words, the motion of the free structure is not artificially constrained. When modeling the contact surfaces between the constrained and free structure, discrete contact points along with contact stiffnesses are distributed on the friction interfaces. At each contact point, contact stiffness is determined and employed in order to take into account the effects of higher frequency modes that are omitted in the dynamic analysis. Depending on the normal force acting on the contact interfaces, quasistatic contact analysis is initially employed to determine the contact area as well as the initial preload or gap at each contact point due to the normal load. A friction model is employed to determine the three-dimensional nonlinear contact forces, and the relationship between the contact forces and the relative motion is utilized by the harmonic balance method. As the relative motion is expressed as a modal superposition, the unknown variables, and thus the resulting nonlinear algebraic equations in the harmonic balance method, are in proportion to the number of modes employed. Therefore the number of contact points used is irrelevant. The developed method is applied to a bladed-disk system with wedge dampers where the dampers constitute the unconstrained structure, and the effects of normal load on the rigid body motion of the damper are investigated. It is shown that the effect of rotational motion is significant, particularly for the in-phase vibration modes. Moreover, the effect of partial slip in the forced response analysis and the effect of the number of harmonics employed by the harmonic balance method are examined. Finally, the prediction for a test case is compared with the test data to verify the developed method. DOI: 10.1115/1.2940356

Sliding of water droplets on the superhydrophobic surface with ZnO nanorods.

Abstract: In this study, we prepared various superhydrophobic surfaces using ZnO nanorod arrays (ZnO-NR) of different diameters The contact angle was equivalent to the calculated value if it is assuming that the topmost surface of the rods is a solid−liquid contact area On the superhydrophobic ZnO-NR surfaces, the 5 μL water droplets slid down by constant acceleration motion Sliding acceleration was governed by the solid area fraction The resistance force of the actual measurement was consistent with that calculated using the model

A Model for Contact and Static Friction of Nominally Flat Rough Surfaces Under Full Stick Contact Condition model for elastic-plastic nominally flat contacting rough surfaces under combined

Abstract: normal and tangential loading with full stick contact condition is presented. The model incorporates an accurate finite element analysis for contact and sliding inception of a single elastic-plastic asperity in a statistical representation of surface roughness. It includes the effect of junction growth and treats the sliding inception as a failure mechanism, which is characterized by loss of tangential stiffness. A comparison between the present model and a previously published friction model shows that the latter severely underestimates the maximum friction force by up to three orders of magnitude. Strong effects of the normal load, nominal contact area, mechanical properties, and surface roughness on the static friction coefficient are found, in breach of the classical laws of friction. Empirical equations for the maximum friction force, static friction coefficient, real contact area due to the normal load alone and at sliding inception as functions of the normal load, material properties, and surface roughness are presented and compared with some limited available experimental results. DOI: 10.1115/1.2908925

Robotic polishing of precision molds with uniform material removal control

Abstract: In this paper, a uniform material removal (UMR) model is proposed for an automatic mold polishing system (AMPS). Free-form surfaces of mold geometry in IGES format are read and regenerated by the AMPS using the NURBS model. The normal vector, the principal curvatures, and the effective contact area are calculated at any point on the surface. The sensitivity of each factor that influences the material removal is determined by Taguchi experiments. The UMR model is based on maintaining constant velocity and contact pressure by controlling the polishing force according to the effective contact area. Three optical molds were polished using two path patterns with and without UMR control for comparison. The experimental results showed that even the conventional constant-force polishing scheme can achieve nearly the same surface roughness; the surface profile error of the mold with UMR control is less than 1/3 of the mold without UMR control. In addition, the actual material removal depth is less than 5.4% of error compared to the predicted value by the UMR model.

Hybrid Atomistic/Continuum Study of Contact and Friction Between Rough Solids

Abstract: A hybrid simulation method is used to study the effect of atomic structure and self-affine roughness on non-adhesive contact and friction between two-dimensional surfaces. Rough-on-flat and rough-on-rough contact are compared as a function of system size up to several micrometers. In order to contrast elastic and plastic behavior, interactions within the deformable substrate are either harmonic or Lennard-Jones. The ratio of lattice constants in the solids is varied to examine the effect of commensurability. In all cases the true area of contact rises linearly with load, but the slope is much larger than expected from continuum calculations. These calculations considered a continuous distribution of surface heights that is appropriate for large scales, rather than the discrete height distribution of the crystalline surfaces used here. The ratio of contact area to load depends on the ratio of lattice constants in the solids and varies with system size in small systems that deform plastically. While some dislocations are observed, plasticity is dominated by an asperity flattening mechanism where surface atoms are displaced into a lower layer. The kinetic friction rises linearly with load and is independent of system size, as predicted by Amontons’s laws. Variations in friction with commensurability are smaller for rough surfaces than for flat surfaces, because most of the contact area is in small patches. Asperity flattening increases patch sizes and thus the effect of commensurability on friction. Rough-on-rough contact leads to additional friction associated with the local slope of the contacting regions.

Droplets on superhydrophobic surfaces: visualization of the contact area by cryo-scanning electron microscopy.

Abstract: The contact area between liquids and solid surfaces plays the crucial role in the wetting and self-cleaning properties of surfaces. In this study, we have developed a cryo-preparation method to visualize the contact area between liquids and superhydrophobic biological surfaces by scanning electron microscopy. Aqueous liquids that do not crystallize during freezing, such as glycerol and phosphoric acid, were used. First, the samples in contact with the liquid droplets were cooled with liquid nitrogen. After this, the droplets were separated and the contact areas on the frozen droplets were visualized by scanning electron microscopy. The contact areas of droplets on various biological and artificial surfaces with microstructure, nanostructure, and hierarchical structures are shown in detail. It could be shown that spaces between nanostructures were not penetrated by the droplet, which rested only on top of the structures. Measurements of the contact areas showed the largest reduction in the solid−liquid con...