Showing papers on "Contact area published in 2001"

Theory of rubber friction and contact mechanics

Abstract: When rubber slides on a hard, rough substrate, the surface asperities of the substrate exert oscillating forces on the rubber surface leading to energy “dissipation” via the internal friction of the rubber. I present a discussion of how the resulting friction force depends on the nature of the substrate surface roughness and on the sliding velocity. I consider in detail the case when the substrate surface has a self affine fractal structure. I also present a theory for the area of real contact, both for stationary and sliding bodies, with elastic or elastoplastic properties. The theoretical results are in good agreement with experimental observation.

Surface Step Effects on Nanoindentation

Abstract: Atomistic simulation is used to examine nanoindentation of a Au(111) crystal both near and far from a surface step. While the load needed to nucleate dislocations decreases significantly when indenting close to the step, the extent of the step's influence is not as great as seen experimentally. This behavior is explained by measuring the contact area from the simulation data. A new metric, the slip vector, shows material slip coinciding with the directions of a lowest unstable stacking fault barrier. The slip vector is used to calculate an atomic critical resolved shear stress, which is shown to be a good dislocation nucleation criterion.

Reduced area intersection between electrode and programming element

Abstract: A method comprising forming a sacrificial layer over less than the entire portion of a contact area on a substrate, the sacrificial layer having a thickness defining an edge over the contact area, forming a spacer layer over the spacer, the spacer layer conforming to the shape of the first sacrificial layer such that the spacer layer comprises an edge portion over the contact area adjacent the first sacrificial layer edge, removing the sacrificial layer, while retaining the edge portion of the spacer layer over the contact area, forming a dielectric layer over the contact area, removing the edge portion, and forming a programmable material to the contact area formerly occupied by the edge portion. An apparatus comprising a volume of programmable material, a conductor, and an electrode disposed between the volume of programmable material and the conductor, the electrode having a contact area at one end coupled to the volume of programmable material, wherein the contact area is less than the surface area at the one end.

Elastoplastic Contact between Randomly Rough Surfaces

Abstract: I have developed a theory of contact mechanics between randomly rough surfaces. The solids are assumed to deform elastically when the stress sigma is below the yield stress sigma(Y), and plastically when sigma reaches sigma(Y). I study the dependence of the (apparent) area of contact on the magnification. I show that in most cases the area of real contact A is proportional to the load. If the rough surface is self-affine fractal (Hurst exponent H) the whole way up to the lateral size L of the nominal contact area, then (assuming no plastic deformation) A approximately L(H).

Resilient contact structures formed and then attached to a substrate

Abstract: Contact structures exhibiting resilience or compliance for a variety of electronic components are formed by bonding a free end of a wire to a substrate, configuring the wire into a wire stem having a springable shape, severing the wire stem, and overcoating the wire stem with at least one layer of a material chosen primarily for its structural (resiliency, compliance) characteristics. A variety of techniques for configuring, severing, and overcoating the wire stem are disclosed. In an exemplary embodiment, a free end of a wire stem is bonded to a contact area on a substrate, the wire stem is configured to have a springable shape, the wire stem is severed to be free-standing by an electrical discharge, and the free-standing wire stem is overcoated by plating. A variety of materials for the wire stem (which serves as a falsework) and for the overcoat (which serves as a superstructure over the falsework) are disclosed. Various techniques are described for mounting the contact structures to a variety of electronic components (e.g., semiconductor wafers and dies, semiconductor packages, interposers, interconnect substrates, etc.), and various process sequences are described. The resilient contact structures described herein are ideal for making a “temporary” (probe) connections to an electronic component such as a semiconductor die, for burn-in and functional testing. The self-same resilient contact structures can be used for subsequent permanent mounting of the electronic component, such as by soldering to a printed circuit board (PCB). An irregular topography can be created on or imparted to the tip of the contact structure to enhance its ability to interconnect resiliently with another electronic component. Among the numerous advantages of the present invention is the great facility with which the tips of a plurality of contact structures can be made to be coplanar with one another. Other techniques and embodiments, such as wherein the falsework wirestem protrudes beyond an end of the superstructure, or is melted down, and wherein multiple free-standing resilient contact structures can be fabricated from loops, are described.

Shear strength of rock joints based on quantified surface description

Abstract: One of the primary objectives of this work is to better understand the frictional behavior of joints under shear loads, including the creation of damage zones. Discontinuities have an important influence on the deformational behavior of rock systems. The choice of a general criterion to determine the shear strength of rough rock joints is a general problem that has been investigated for many years. Numerous shear models have been proposed in the last decades to relate shear-strength to measurable joint parameters, but their limitations have to be recognized. The problem is how to measure and then to express the roughness with a number (e.g. JRC) or a mathematical expression in order to introduce the morphology of the joint into a shear strength criterion. In the frame of this work it has been pointed out that the geometry of roughness influences the size and distribution of contact areas during shearing. In order to locate and estimate the contact area during the shearing, it was argued that only the zones of the surface faced to the shear direction, and steeper than a threshold inclination are involved in the shearing. An empirical relation between the potential contact area and the minimal apparent dip inclination of the surface is proposed. The close agreement between this empirical description of the potential contact area, and experimental points permits to predict the real contact area involved in the phenomena. A new constitutive law, relating stress and displacements, is proposed to model the shear resistance of joints under constant normal load conditions. It is based on the empirical surface description, and on the results from more than fifty constant-normal-load direct-shear tests performed on both replicas of tensile joints, and induced tensile fractures for seven rock types. It is shown that this constitutive model is able to describe experimental shear tests realized in laboratory. Moreover, the parameters required in the model can be easily obtained through standard laboratory tests. The proposed model was also used to estimate the JRC value. The expression obtained to evaluate the joint roughness coefficient is capable of predicting the JRC. It was successfully compared with JRC values obtained by back analysis of shear tests. In the current research no attention was paid to investigate the influence of the scale on the shearing. The results have been validated only in the range of the samples tested in laboratory. Further studies are needed to explore the applicability of the proposed model in field conditions.

Polyethylene contact stresses, articular congruity, and knee alignment.

Abstract: Increased conformity at the tibiofemoral articulation increases contact area and reduces contact stresses in total knee arthroplasty. Malalignment, however, can increase polyethylene contact stresses. The effect of knee alignment and articular conformity on contact stresses was evaluated in a finite element model. The polyethylene insert and femoral component were modeled in high- and low-conformity conditions. An axial tibial load of 3000 N was applied across the tibiofemoral articulation at different knee positions ranging from 0° to 90° flexion, 0 to 10 mm anteroposterior translation, 0° to 10° axial rotation, and coronal plane angulation (liftoff). Increased conformity significantly reduced contact stresses in neutral alignment (by 44% at 0° flexion and 36% at 60° and 90° flexion). Liftoff significantly increased contact stresses in low- and high-conformity conditions, but to a lesser degree in the high-conformity condition. Malalignment in rotation was most detrimental especially with the high-conformity insert design. Overall, increasing articular conformity reduced stresses when the knee was well-aligned. However, malalignment in axial rotation was detrimental. Mobile-bearing knee designs with increased articular congruity may result in lower contact stresses, especially the rotating-bearing designs that theoretically minimize rotational malalignment.

Three-Dimensional Contact Analysis of Elastic-Plastic Layered Media With Fractal Surface Topographies

Abstract: Three-dimensional rough surfaces were generated using a modified two-variable Weierstrass-Mandelbrot function with fractal parameters determined from real surface images. The number and size of truncated asperities were assumed to follow power-law relations. A finite element model of a rigid sphere in normal contact with a semi-infinite elastic-plastic homogeneous medium was used to obtain a constitutive relation between the mean contact pressure, real contact area, and corresponding representative strain. The contact model was extended to layered media by modifying the constitutive equation of the homogeneous medium to include the effects of the mechanical properties of the layer and substrate materials and the layer thickness. Finite element simulations of an elastic-plastic layered medium indented by a rigid sphere validated the correctness of the modified contact model. Numerical results for the contact load and real contact area are presented for real surface topographies resembling those of magnetic recording heads and smooth rigid disks. The model yields insight into the evolution of elastic, elasticplastic, and fully plastic deformation at the contact interface in terms of the maximum local surface interference. The dependence of the contact load and real contact area on the fractal parameters and the carbon overcoat thickness is interpreted in light of simulation results obtained for a tri-pad picoslider in contact with a smooth thin-film hard disk.

Friction and fracture.

Abstract: Consider a block placed on a table and pushed sideways until it begins to slide. Amontons and Coulomb found that the force required to initiate sliding is proportional to the weight of the block (the constant of proportionality being the static coefficient of friction), but independent of the area of contact. This is commonly explained by asserting that, owing to the presence of asperities on the two surfaces, the actual area in physical contact is much smaller than it seems, and grows in proportion to the applied compressive force. Here we present an alternative picture of the static friction coefficient, which starts with an atomic description of surfaces in contact and then employs a multiscale analysis technique to describe how sliding occurs for large objects. We demonstrate the existence of self-healing cracks that have been postulated to solve geophysical paradoxes about heat generated by earthquakes, and we show that, when such cracks are present at the atomic scale, they result in solids that slip in accord with Coulomb's law of friction. We expect that this mechanism for friction will be found to operate at many length scales, and that our approach for connecting atomic and continuum descriptions will enable more realistic first-principles calculations of friction coefficients.

Smooth C1‐interpolations for two‐dimensional frictional contact problems

Abstract: Finite deformation contact problems are associated with large sliding in the contact area. Thus, in the discrete problem a slave node can slide over several master segments. Standard contact formulations of surfaces discretized by low order finite elements leads to sudden changes in the surface normal field. This can cause loss of convergence properties in the solution procedure and furthermore may initiate jumps in the velocity field in dynamic solutions. Furthermore non-smooth contact discretizations can lead to incorrect results in special cases where a good approximation of the contacting surfaces is needed. In this paper a smooth contact discretization is developed which circumvents most of the aformentioned problems. A smooth deformed surface with no slope discontinuities between segments is obtained by a C1-continuous interpolation of the master surface. Different forms of discretizations are possible. Among these are Bezier, Hermitian or other types of spline interpolations. In this paper we compare two formulations which can be used to obtain smooth normal and tangent fields for frictional contact of deformable bodies. The formulation is developed for two-dimensional applications and includes finite deformation behaviour. Examples show the performance of the new discretization technique for contact. Copyright © 2001 John Wiley & Sons, Ltd.

Scale effects on the attachment pads and friction forces in syrphid flies (Diptera, Syrphidae).

Abstract: To test the role of constructional and dimensional factors in the generation of friction force by systems of setose attachment pads, six species of syrphid fly (Platycheirus angustatus, Sphaerophoria scripta, Episyrphus balteatus, Eristalis tenax, Myathropa florea and Volucella pellucens) were studied using light and scanning electron microscopy. Flies were selected according to their various body mass and attachment pad dimensions. Such variables as pad area, setal density, the area of a single setal tip and body mass were individually measured. A centrifugal force tester, equipped with a fibre-optic sensor, was used to measure the friction forces of the pads on a smooth horizontal surface made of polyvinylchloride. Friction force, which is the resistance force of the insect mass against the sum of centrifugal and tangential forces, was greater in heavier insects such as Er. tenax, M. florea and V. pellucens. Although lighter species generated lower frictional forces, the acceleration required to detach an insect was greater in smaller species. The area of attachment pads, setal tip area and setal density differed significantly in the species studied, and the dependence of these variables on body mass was significant. The frictional properties of the material of the setal tips were not dependent on the dimensions of the fly species. Similar results were obtained for the frictional properties of the pulvillus as a whole. Thus, the properties of the secretion and the mechanical properties of the material of the setal tips are approximately constant among the species studied. It is concluded that differences in friction force must be related mainly to variations in the real contact area generated by the pad on the smooth surface. The real contact area can be estimated as the summed area of the broadened setal tips of the pad in contact with the surface. The real contact area depends on such morphological variables as setal density and the area of a single setal tip. Although individual variables vary among flies with different dimensions, they usually compensate such that smaller setal tip area is partially compensated for by higher setal density.

Silver nanoparticles deposited on dielectric surfaces

Abstract: Surface plasmon polaritons in nanoparticles were used as a sensitive indicator of structural and electronic properties of metallic nanoparticles deposited upon various dielectric substrates. Quantum size and cluster–substrate interactions were separated. The latter were modelled with the dynamic charge transfer effect. For calibration purposes, the free surfaces of the same clusters exposed to a UHV beam were also investigated. The particles were slightly deformed during deposition; their final shapes and, in particular, their contact areas were determined. The width of the plasmon excitation band was roughly doubled compared to that of the free particles, but proved to depend only slightly on the chemical nature of the substrates, in drastic contrast to the case of fully embedded particles. The analogy holds for the dephasing lifetimes. One reason for this is that the contact area varies strongly with the substrate material, while it is constant in systems of matrix-embedded particles.

Wear in Partial Slip Contact

Abstract: An analytical method that evaluates the evolution of stress and surface profile in fretting under the partial slip conditions is presented. The repeated slip occurring near the edges of contact generates wear that changes the contact geometry and contact stresses. The method is based on two scales of time: time for one cycle of the oscillating tangential force and time corresponding to the number of cycles. Archard's wear law is used to evaluate wear and gap variation within the slip zones during one cycle. The governing integral equations are reduced to calculate the contact pressure after each cycle. Evolution of the contact characteristics (contact pressure and shear stress, contact width, gap and slip functions) in fretting is calculated using a stepwise procedure. It is shown that the size of stick zone does not change in wear process of bodies with similar elastic properties under the constant amplitude load conditions, and that an asymptotic solution corresponding to the number of cycles approaching to infinity exists. Analytical expressions for the asymptotic contact pressure, shear and tensile stress, and the gap function are presented. It is proved that the asymptotic contact pressure and shear stress are singular at the ends of stick zone. Detailed results are given for two initial shapes of elastic indenter contacting with an elastic half-space: for the parabolic cylinder and for the indenter having a flat base with rounded edges.

Advanced Contact Mechanics–Road and Rail

Abstract: The development of contact theories and numerical formula for various applications is a field which expands rapidly. This publication focuses on the rolling contact problem both for tire-road and wheel-rail contact. For the tire-road application a central problem is the modeling of the composite structure of the tire under internal pressure and axle load. One actual contact problem is the rolling on soft soil, which is discussed as the main application. In the wheel-rail case the contact area is much smaller and much more emphasis has been laid on the treatment of material changes, wear and creep phenomena. These approaches are discussed in detail as well as a more recent finite element formulation following the arbitrary Lagrange-Eulerian concept. Ideas about damage mechanisms finish the article.

Artificial finger skin having ridges and distributed tactile sensors used for grasp force control

Abstract: An artificial elastic finger skin for robot fingers was developed for controlling the grasp force when the weight and friction coefficient of the grasped object are unknown. The elastic finger skin has ridges at the surface to divide the stick/slip area. It also has a pair of tactile sensors embedded per one ridge similar to human fingertips. The surface of the whole finger is curved so that the reaction force can be distributed. A finite element (FE) model of the elastic finger skin was developed to perform a dynamic contact analysis using the FE method in order to design the elastic finger skin. The elastic finger skin was then constructed. It was confirmed by calculation and experiment that the incipient slippage of the ridge that occurs near the edge of contact area can be detected. This result is useful for controlling the grasping force when the weight and friction coefficient between the elastic finger skin and grasping object are unknown.

Friction and wear of brake systems

Abstract: The contact area in brake systems shows characteristic structures. With respect to wear an equilibrium of flow of growing and destruction of hard patches is to be found on the contact surface. These patches modulate the friction coefficient of the brake system. The paper deals with this principal wear mechanism of brake pads which leads to a new type of differential equation of second order for the dynamic friction coefficient describing the stationary and transient friction behaviour of brake pads. Many known effects of friction in such systems are covered by the solutions of this new model.

Current-controlling electrode with adjustable contact area

Abstract: A medical electrode includes a conductive flexible member having a top side and a bottom side with a non-conductive flexible sheet covering the conductive flexible member top side A connector in contact with the conductive flexible member bottom side is provided for establishing electrical contact with an external electrical apparatus A conductive adhesive adhered to the conductive flexible member bottom side provides electrical conduction to a patient's skin

Adhesive Contact of Elastically Deformable Spheres: A Computational Study of Pull-Off Force and Contact Radius

Abstract: Elastic spheres in contact deform around the contact region, due to intermolecular interaction forces. The deformed contacting surfaces change the distance between interacting molecules that in turn alters the force of interaction. Thus, the contact behavior of elastic spheres constitutes a nonlinear mathematical problem that defies the traditional analytical methods for general solution. Efficient computational techniques have enabled a detailed study of adhesive contact behavior of elastically deformable spheres with self-consistent solutions of a nonlinear integral governing equation. The present work extends the previous computational analysis to the quantities of practical interests such as the pull-off force and the radius of contact area. Trends of variations in the pull-off force as physical properties change are examined. Computationally determined radial positions as stress condition indicators suggest that the concept of contact radius is not clearly defined in the literature and can be confusing. It seems that some contact mechanics models would be consistent with the definition of the edge of contact area as the radial position for the local surface stress to change from compression to tension, whereas others would rather assume the contact radius as the radial position for the local tensile stress to reach its peak. The substantial quantitative deviation of self-consistently computed contact radius from the DMT model prediction suggests that models based on the assumption of a well-defined contact area having a constant gap may not be appropriate when describing cases of small values of Tabor's parameter.