Flat Contacts Research Articles

Multi-asperity contact: A comparison between discrete dislocation and crystal plasticity predictions

Plane strain indentation of single crystals by a periodic array of flat rigid contacts is analyzed. The calculations are carried out, with the mechanical response of the crystal characterized by conventional continuum crystal plasticity or by discrete dislocation plasticity. The properties used in the conventional crystal plasticity description are chosen so that both theories give essentially the same response in uniform plane strain compression. The indentation predictions are then compared, focusing in particular on the effect of contact size and spacing. The limiting cases of frictionless contacts and of perfectly sticking contacts are analyzed. Conventional continuum plasticity predicts a size-independent response. Unless the contact spacing to size ratio is very small, the predicted deformation mode under the contacts is a wedging mechanism of the type described by slip line theory, which is only weakly sensitive to friction conditions. For the micron scale contacts analyzed, discrete dislocation plasticity predicts a response that depends on the contact size as well as on the contact spacing to size ratio. When contacts are spaced sufficiently far apart, discrete dislocation plasticity predicts that the deformation is localized beneath the contacts, whereas for more closely spaced contacts, deformation occurs by shear bands extending relatively far into the crystal. Unless the contacts are sufficiently close together so that the response is essentially one of plane strain compression, the mean contact pressure predicted by discrete dislocation plasticity is substantially greater than that predicted by conventional continuum crystal plasticity and is more sensitive to the friction conditions.

Micro and macro contact mechanics for interacting asperities

Contact of rough surfaces at micro and macro scales is studied in this paper. The asperities at micro scale are characterised by small radius of curvature whereas the waviness is characterised by large radius of curvature. When two rough surfaces come in contact, on the micro scale, of asperities contacts in a very small area leave large gaps between the surfaces; whereas on the macro scale the surfaces conform to each other under the application of load without gaps. Contact at micro scale is modelled by superposition of Hertzian stress fields of individual asperity contacts and the waviness at macro scale is modelled as a mixed boundary problem of rough punch indentation where displacements of uneven profile are prescribed along the region of contact. In both the cases for simplification the roughness is assigned to one surface making the other surface perfectly flat an assumption often made in contact mechanics of rough bodies.The motivation for modelling the asperities at micro scales comes from the preliminary results obtained from photoelastic experiments. Numerical results are presented based on the analytical results available for Hertzian contacts. The motivation for modelling the asperities at macro scales comes from the results available in literature for flat contacts from solving mixed boundary elasticity problems. A condition of full stick is assumed along the contact which is a common assumption made for rough contacts. The numerical results are presented for both the cases of rough contact at micro and macro scales.

An asperity‐based mathematical model for the boundary lubrication of nominally flat metallic contacts

AbstractA mathematical model is presented to study the boundary lubrication of nominally flat metallic contacts. It is developed on the basis of the Greenwood–Williamson model, incorporating key aspects of boundary lubrication in asperity contacts. Four variables are used to describe the asperity contact, including micro‐contact area, pressure, interfacial shear stress and flash temperature. Furthermore, three probability variables are used to define the interfacial state of an asperity junction that may be covered by the lubricant/additive molecules adsorbed on the surface, protected by a chemical film, or in direct contact with no boundary protection. Governing equations for the seven asperity‐level variables are derived based on first‐principle considerations of the asperity deformation, frictional heating and kinetics of boundary films. These equations are solved simultaneously to determine the asperity interfacial state and calculate the contact variables. The asperity‐level solutions are then integrated to formulate the boundary‐lubrication model at the system level with statistical descriptions of the surfaces. Results are presented and analysed including system friction behaviour, surface separation and real area of contact, and the state of boundary lubrication for various operating conditions and surface roughness. Some potential applications of the model are described. The model and the modelling concepts may provide a framework for future boundary‐lubrication analysis, incorporating research advances in contact mechanics, tribochemistry and other related fields. Copyright © 2007 John Wiley & Sons, Ltd.

Contact Shape Controls Adhesion of Bioinspired Fibrillar Surfaces

Following a recent bioinspired paradigm, patterned surfaces can exhibit better adhesion than flat contacts. Previous studies have verified that finer contact structures give rise to higher adhesion forces. In this study, we report on the effect of the tip shape, which was varied systematically in fibrillar PDMS surfaces, produced by lithographic and soft-molding methods. For fiber radii between 2.5 and 25 microm, it is found that shape exerts a stronger effect on adhesion than size. The highest adhesion is measured for mushroom-like and spatular terminals, which attain adhesion values 30 times in excess of the flat controls and similar to a gecko toe. These results explain the shapes commonly found in biological systems, and help in the exploration of the parameter space for artificial attachment systems.

Type 3a and type 3b OFF cone bipolar cells provide for the alternative rod pathway in the mouse retina

The mammalian retina provides several pathways to relay the information from the photoreceptors to the ganglion cells. Cones feed into ON and OFF cone bipolar cells that excite ON and OFF ganglion cells, respectively. In the "classical" rod pathway, rods feed into rod bipolar cells that provide input to both the ON and the OFF pathway via AII amacrine cells. Recent evidence suggests an alternative rod pathway in which rods directly contact some types of OFF cone bipolar cells. The mouse has become an important model system for retinal research. We performed an immunohistochemical analysis on the level of light and electron microscopy to identify the bipolar cells and ganglion cells that are involved in the alternative rod pathway of the mouse retina. 1) We identify a new bipolar cell type, showing that type 3 OFF cone bipolar cells comprise two distinct cell types, that we termed 3a and 3b. Type 3a cells express the ion channel HCN4. Type 3b bipolar cells represent a hitherto unknown cell type that can be identified with antibodies against the regulatory subunit RIIbeta of protein kinase A. 2) We show that both 3a and 3b cells form flat contacts at cone pedicles and rod spherules. 3) Finally, we identify an OFF ganglion cell type whose dendrites costratify with type 3a and 3b bipolar cell axon terminals. These newly identified cell types represent the basis of a neuronal circuit in the mammalian retina that could provide for an alternative fast rod pathway.

Fretting corrosion of tin-plated contacts

The susceptibility of tin-plated contacts to fretting corrosion is a major limitation for its use in electrical connectors. The present paper evaluates the influence of a variety of factors, such as, fretting amplitude (track length), frequency, temperature, humidity, normal load and current load on the fretting corrosion behaviour of tin-plated contacts. This paper also addresses the development of fretting corrosion maps and lubrication as a preventive strategy to increase the life-time of tin-plated contacts. The fretting corrosion tests were carried out using a fretting apparatus in which a hemispherical rider and flat contacts (tin-plated copper alloy) were mated in sphere plane geometry and subjected to fretting under gross-slip conditions. The variation in contact resistance as a function of fretting cycles and the time to reach a threshold value (100 mΩ) of contact resistance enables a better understanding of the influence of various factors on the fretting corrosion behaviour of tin-plated contacts. Based on the change in surface profile and nature of changes in the contact zone assessed by laser scanning microscope (LSM) and surface analytical techniques, the mechanism of fretting corrosion of tin-plated contacts and fretting corrosion maps are proposed. Lubrication increases the life-time of tin-plated contacts by several folds and proved to be a useful preventive strategy.

OFF midget bipolar cells in the retina of the marmoset, Callithrix jacchus, express AMPA receptors

Recent studies suggested that different types of OFF bipolar cells express specific types of ionotropic (AMPA or kainate) glutamate receptors (GluRs) at their contacts with cone pedicles. However, the question of which GluR type is expressed by which type of OFF bipolar cell in primate retina is still open. In this study, the expression of AMPA and kainate receptor subunits at the dendritic tips of flat (OFF) midget bipolar (FMB) cells was analyzed in the retina of the common marmoset, Callithrix jacchus. We used preembedding electron microscopy and double immunofluorescence with subunit-specific antibodies. The FMB cells were labeled with antibodies against the carbohydrate epitope CD15. Cone pedicles were identified with peanut agglutinin. Immunoreactivity for the GluR1 subunit and for CD15 is preferentially located at triad-associated flat contacts. Furthermore, the large majority of GluR1 immunoreactive puncta is localized at the dendritic tips of FMB cells. These results suggest that FMB cells express the AMPA receptor subunit GluR1. In contrast, the kainate receptor subunit GluR5 is not colocalized with the dendritic tips of FMB cells or with the GluR1 subunit. Immunoreactive puncta for the GluR1 subunit are found at all M/L-cone pedicles but are only rarely associated with S-cone pedicles. This is consistent with our recent findings in marmoset retina that FMB cells do not contact S-cone pedicles. The presence of GluR5 clusters at S-cone pedicles indicates that in primate retinas OFF bipolar cells expressing kainate receptor subunits receive some S-cone input.

Surface versus bulk nucleation of dislocations during contact

The indentation of single crystals by a periodic array of flat rigid contacts is analyzed using discrete dislocation plasticity. Plane strain analyses are carried out with the dislocations all of edge character and modeled as line singularities in a linear elastic solid. The limiting cases of frictionless and perfectly sticking contacts are considered. The effects of contact size, dislocation source density, and dislocation obstacle density and strength on the evolution of the mean indentation pressure are explored, but the main focus is on contrasting the response of crystals having dislocation sources on the surface with that of crystals having dislocation sources in the bulk. When there are only bulk sources, the mean contact pressure for sufficiently large contacts is independent of the friction condition, whereas for sufficiently small contact sizes, there is a significant dependence on the friction condition. When there are only surface dislocation sources the mean contact pressure increases much more rapidly with indentation depth than when bulk sources are present and the mean contact pressure is very sensitive to the strength of the obstacles to dislocation glide. Also, on unloading a layer of tensile residual stress develops when surface dislocation sources dominate.

Elastic Contact Induced Self-Organized Patterning of Hydrogel Films

When a flat rigid stamp contacts the surface of a soft hydrogel film, a competition between the adhesive and elastic forces engenders an isotropic, labyrinth pattern on the length scale of 3H, where H is the film thickness, We present here a very simple, self-organized technique for aligning and modulating these patterns by using a patterned stamp and by changing the film thickness and the stamp-film intersurface distance. Many complex structures such as an array of femtoliter beakers and doubly periodic channels are generated from a simple stamp. The elastic nature of the patterns allows in-situ tuning, manipulation, and reconfiguration of structures. The patterns can also be made permanent by drying of the hydrogel.

Platform for Modeling the Boundary Lubrication of Nominally Flat Metallic Contacts

This short paper describes a theoretical platform for modeling the boundary lubrication of nominally flat metallic contacts. The platform is of a general structure with four interrelated modules, each governing one of the four key processes of the problem. It is envisioned to be open ended allowing individual modules to be updated and/or replaced. The product and the outcome may provide an infrastructure for fundamental research in boundary lubrication among theoreticians and experimentalists and across several science/engineering disciplines.

The roughness effect on the frequency of frictional sound

Dry sliding of two bodies in contact generates a wide range of effects like friction, wear, heat and sound among others. The main interest of this study is in the frequency characteristics of the generated sound. In the past, frequency spectrum and sound pressure level with relation to surface topography (surface roughness in particular), have been studied mainly for concentrated contacts like stylus or hemispherical tip pin on a rough surface. Studies on flat–flat contacts were mainly focused on the topography of contacting surfaces and its relation to occurrence or non-occurrence of squeal (high pitch, high sound pressure level sound) in brake systems. The present study aims to clarify the effect of surface roughness on the frequency of non-squealing frictional sound generated in dry flat–flat sliding contact. Sound was generated by the dry contact in rubbing by hand of two rectangular cross-section stainless-steel plates having similar surface roughness. The roughness of the contacting surfaces varied in the range R z = 0.8 –12.4 μm. The sound spectra had 5 peaks (P 1, P 2, P 3, P 4 and P 5) in order of increasing frequency and it was found that the peak frequency was shifted when the roughness of the rubbed surfaces changed. The first peak P 1 was most sensitive to change of surface roughness and it shifted from 3.0 to 4.5 kHz when the maximum surface roughness changed from R z = 1 0.9 to 3.4 μ m . When the surface was relatively rough, this peak was close to the first bending natural frequency of the plate at 2.377 kHz.

Effect of mean stress on fretting fatigue of Ti‐6Al‐4V on Ti‐6Al‐4V

ABSTRACTFretting fatigue tests of Ti‐6Al‐4V on Ti‐6Al‐4V have been conducted to determine the influence of stress amplitude and mean stress on life. The stress ratio was varied from R=−1 to 0.8. Both flat and cylindrical contacts were studied using a bridge‐type fretting fatigue test apparatus operating either in the partial slip or mixed fretting regimes. The fretting fatigue lives were correlated to a Walker equivalent stress relation. The influence of mean stress on fretting fatigue crack initiation, characterized by the value of the Walker exponent, is smaller compared with plain fatigue. The fretting fatigue knockdown factor based on the Walker equivalent stress is 4. Formation of fretting cracks is primarily associated with the tangential force amplitude at the contact interface. A simple fretting fatigue crack initiation metric that is based on the strength of the singular stress field at the edge of contact is evaluated. The metric has the advantage in that it is neither dependent on the coefficient of friction nor the location of the stick/slip boundary, both of which are often difficult to define with certainty a priori.

Mechanical creep as a life-limiting factor of radio frequency microswitches

One of the characteristic failure mechanisms of microelectromechanical switches is stiction. Measurements, made using an instrumented nanoindentor, indicate that the adhesion force between hemispherical and flat gold contacts increases logarithmically with the number of actuation cycles. Concurrently, the electrical conductance increases with actuation time and the contact area increases. These time-dependent behaviors are a result of creep of the gold contacts under load, which sets a design limit for the maximum life of a contact switch before stiction failure occurs.

Implantation and testing of subretinal film electrodes in domestic pigs

By definition, an electronic subretinal visual prosthesis requires the implantation of stimulation electrodes in the subretinal space of the eye. Polyimide film electrodes with flat contacts were implanted subretinally and used for electrical stimulation in acute experiments in anaesthetised domestic pigs. In two pigs, the film electrode was inserted through a sclerostomy into the vitreous cavity and, subsequently, via a retinotomy into the subretinal space around the posterior pole (ab interno approach). In three other pigs the sclera and pigment epithelium were opened for combined ab interno and transscleral positioning of the subretinal electrode. In all cases, perfluorocarbon liquid (PFCL) was used to establish a close contact between the film electrode and the outer retina. After cranial preparations of three pigs for epidural recording of visual cortex responses, retinal stimulation was performed in one pig with a film electrode implanted ab interno and in two pigs with film electrodes implanted by the ab interno and transscleral procedure. The five subretinal implantations were carried out successfully and each polyimide film electrode tip was positioned beneath the outer retina of the posterior pole. The retina was attached to the stimulation electrode in all cases. Epidural cortical responses to light and electrical stimulation were recorded in three experiments. Initial cortical responses to Ganzfeld light and to electrical stimuli occurred about 40 and 20 ms, respectively, after stimulation onset. The stimulation threshold was approximately 100 μA and, like the cortical response amplitudes, depended both on the correspondence between retinal stimulation and cortical recording sites and on the number of stimulation electrodes used simultaneously. Our results in a domestic pig model demonstrate that polyimide film electrodes can be implanted subretinally and tested by recording cortical responses to electrical stimulation. These findings suggest that the domestic pig could be an appropriate animal model for basic testing of subretinal implants.

Light Signaling in Scotopic Conditions in the Rabbit, Mouse and Rat Retina: A Physiological and Anatomical Study

In the dark, light signals are conventionally routed through the following circuit: rods synapse onto rod bipolar (RB) cells, which in turn contact AII amacrine cells. AII cells segregate the light signal into the on and off pathways by making electrical synapses with on cone bipolar (CB) cells and glycinergic inhibitory chemical synapses with off CB cells. These bipolar cells synapse onto their respective ganglion cells, which transfer on and off signals to the visual centers of the brain. Two alternative pathways have recently been postulated for the signal transfer in scotopic conditions: 1) electrical coupling between rods and cones, and 2) a circuit independent of cone photoreceptors, implying direct contacts between rods and off CB cells. Anatomical evidence supports the existence of both these circuits. To investigate the contribution of these alternative pathways to scotopic vision in the mammalian retina, we have performed patch-clamp recordings from ganglion cells in the dark-adapted retina of the rabbit, mouse, and rat. Approximately one-half of the ganglion cells in the rabbit retina received off signals through a circuit that was independent of RB cells. This was shown by their persistence in the presence of the glutamate agonist 2-amino-4-phosphonobutyric acid (APB), which blocks rod-->RB cell signaling. Consistent with this result, strychnine, a glycine receptor antagonist, was unable to abolish these off responses. In addition, we were able to show that some off cone bipolar dendrites terminate at rod spherules and make potential contacts. In the mouse retina, however, there seems to be a very low proportion of off signals carried by an APB-resistant pathway. No ganglion cells in the rat retina displayed APB- and strychnine-resistant responses. Our data support signaling through flat contacts between rods and off CB cells as the alternative route, but suggest that the significance of this pathway differs between species.

Molecular Conductance: Chemical Trends of Anchoring Groups

Combining density functional theory calculations for molecular electronic structure with a Green function method for electron transport, we calculate from first principles the molecular conductance of benzene connected to two Au leads through different anchoring atoms-S, Se, and Te. The relaxed atomic structure of the contact, different lead orientations, and different adsorption sites are fully considered. We find that the molecule-lead coupling, electron transfer, and conductance all depend strongly on the adsorption site, lead orientation, and local contact atomic configuration. For flat contacts the conductance decreases as the atomic number of the anchoring atom increases, regardless of the adsorption site, lead orientation, or bias. For small bias this chemical trend is, however, dependent on the contact atomic configuration: an additional Au atom at the contact with the (111) lead changes the best anchoring atom from S to Se, although for large bias the original chemical trend is recovered.

Uniqueness of solutions for constrained Elastica

We address the number of solutions in constrained Elastica, i.e. the number of forms and tensions possibly adopted by steady rods or sheets enclosed in a prescribed box. Our main result refers to sheets making contact with the compressing plates at their extremities only. For these so-called folds, we provide the first demonstration of uniqueness of solution. This result is obtained by combining direct methods that are focused on definite families of solutions and global methods that address the structure of the set of solutions in the parameter space. While the first methods are specific to Elastica, the latter are not and may be applied to other kinds of systems. We then address the origins of the multiplicity of solutions in more general configurations and find two of them: geometrical non-linearity; freedom in the distribution of the length of flat contacts. The former gives rise to two free-standing fold solutions beyond buckling; the latter yields multiple buckling thresholds and thus multiple elastic responses to compression. Altogether, these results improve the non-local analysis of Elastica and clarify the reasons for unique or multiple buckling thresholds in constrained configurations. Moreover, fold uniqueness appears very useful for saving computational times in the numerical quest for solutions, for detecting parasitic solutions in simulations, for establishing the robustness of the Euler’s model and for clarifying the role of friction. On a more general ground, our study provides non-local methods for determining the conditions for bifurcation in constrained systems involving a free energy.

Instrumentation to measure thermal contact resistance

Instrumentation was developed to measure the thermal contact resistance across metalliccontacts by varying the contact pressure in different environments. Experiments wereconducted on oxygen free, high conductivity (OFHC) copper cylindrical flat contacts andthe measured thermal contact resistance is in good agreement with the theoretical modelsreported in the literature. The thermal conductivity of OFHC copper and stainless steelwas measured at different temperatures and these values are in good agreement with theliterature values.

New results for the fretting-induced stress concentration on Hertzian and flat rounded contacts

Recent work on fretting fatigue has emphasized the role of stress concentration on fretting damage, while previous work had concentrated on empirical parameters to assess influence of fretting on fatigue life. In particular, analogies with fatigue in the presence of a crack or a notch have been noticed, suggesting that the stress field induced by frictional contact per se may explain the reduction of fatigue life due to fretting. In the paper, new analytical and numerical solutions are produced for the stress concentration induced in typical fretting contacts involving the Hertzian geometry or the flat punch with rounded corners in view of application to the dovetail joints. Normal and tangential load (in the Cattaneo–Mindlin sense) is considered with “moderate” or “large” bulk stresses.

Immunocytochemical description of five bipolar cell types of the mouse retina.

With the ever-growing number of transgenic mice being used in vision research, a precise knowledge of the cellular organization of the mouse retina is required. As with the cat, rabbit, rat, and primate retinae, as many as 10 cone bipolar types and one rod bipolar type can be expected to exist in the mouse retina; however, they still have to be defined. In the current study, several immunocytochemical markers were applied to sections of mouse retina, and the labeling of bipolar cells was studied using confocal microscopy and electron microscopy. By using antibodies against the neurokinin-3 receptor NK3R; the plasma membrane calcium ATPase1 (PMCA1); and the calcium (Ca)-binding proteins CaB1, CaB5, caldendrin, and recoverin, three different OFF-cone bipolar cells could be identified. One type of ON-cone bipolar cell was identified through its immunoreactivity for CaB5 and PMCA1. Rod bipolar cells, comparable in morphology to those of other mammalian retinae, expressed protein kinase Calpha and CaB5. It was also shown that putative OFF-cone bipolar cells receive light signals through flat contacts at the cone pedicle base, whereas ON-cone bipolar signaling involves invaginating contacts. The distribution of the kainate receptor subunit GluR5 was studied by confocal and electron microscopy. GluR5 was expressed at flat bipolar cell contacts; however, it appears to be involved with only certain types of OFF-cone bipolar cells. This suggests that different bipolar cell types receive their light signals through different sets of glutamate receptors.