Showing papers on "Contact area published in 1998"

Portable information equipment and information storage medium

Abstract: PROBLEM TO BE SOLVED: To obtain an electronic book or a portable information equipment for realizing an operation input such as page turning by a convenient human interface and an information storage medium to be used for them. SOLUTION: This is an electronic book for outputting information to which a page number is applied as image information by page units. This device is provided with a finger input detecting part 10 for detecting the contact pressure, contact area, and contact position of a finger brought into contact with a display part, a finger input judging part 30 for judging page turning input, continuous page turning input, bookmark insertion, and bookmark insertion part reference input or the like based on the detected contact pressure, contact area, contact position, and moving direction of the finger, a page picture update controlling part 40 for controlling the update of the page picture, a bookmark processing part 50 for operating bookmark insertion and reference processing, and a picture generating g part 60 for generating a picture to be displayed at the display part. Then, at least one of the contact pressure and contact area of the finger is detected, and the presence or absence of the page turning input is judged based on at least one of them. Thus, it is possible to more accurately discriminate the page turning input from the other operation input compared with the case of the input of the page turning execution based on only the moving direction of the finger. Thus, much more input patterns can be formed only by the finger operation by using not only the moving direction of the finger but also the contact pressure and contact area of the finger as materials for judging the input.

Influences of pileup on the measurement of mechanical properties by load and depth sensing indentation techniques

Abstract: Finite element simulation of conical indentation of a wide variety of elastic-plastic materials has been used to investigate the influences of pileup on the accuracy with which hardness and elastic modulus can be measured by load and depth-sensing indentation techniques. The key parameter in the investigation is the contact area, which can be determined from the finite element results either by applying standard analysis procedures to the simulated indentation load-displacement data, as would be done in an experiment, or more directly, by examination of the contact profiles in the finite element mesh. Depending on the pileup behavior of the material, these two areas may be very different. When pileup is large, the areas deduced from analyses of the load-displacement curves underestimate the true contact areas by as much as 60%. This, in turn, leads to overestimations of the hardness and elastic modulus. The conditions under which the errors are significant are identified, and it is shown how parameters measured from the indentation load-displacement data can be used to identify when pileup is an important factor.

Formation and manipulation of a metallic wire of single gold atoms

Abstract: The continuing miniaturization of microelectronics raises the prospect of nanometre-scale devices with mechanical and electrical properties that are qualitatively different from those at larger dimensions. The investigation of these properties, and particularly the increasing influence of quantum effects on electron transport, has therefore attracted much interest. Quantum properties of the conductance can be observed when ‘breaking’ a metallic contact: as two metal electrodes in contact with each other are slowly retracted, the contact area undergoes structural rearrangements until it consists in its final stages of only a few bridging atoms1,2,3. Just before the abrupt transition to tunnelling occurs, the electrical conductance through a monovalent metal contact is always close to a value of 2e2/h (≈12.9 Ω−1), where e is the charge on an electron and h is Planck's constant4,5,6. This value corresponds to one quantum unit of conductance, thus indicating that the ‘neck’ of the contact consists of a single atom7. In contrast to previous observations of only single-atom necks, here we describe the breaking of atomic-scale gold contacts, which leads to the formation of gold chains one atom thick and at least four atoms long. Once we start to pull out a chain, the conductance never exceeds 2e2/h, confirming that it acts as a one-dimensional quantized nanowire. Given their high stability and the ability to support ballistic electron transport, these structures seem well suited for the investigation of atomic-scale electronics.

Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments

Abstract: The phenomena of pile-up and sink-in associated with nanoindentation have been found to have large effects on the measurements of the indentation modulus and hardness of copper. Pile-up (or sink-in) leads to contact areas that are greater than (or less than) the cross-sectional area of the indenter at a given depth. These effects lead to errors in the absolute measurement of mechanical properties by nanoindentation. To account for these effects, a new method of indenter tip shape calibration has been developed; it is based on measurements of contact compliance as well as direct SEM observations and measurements of the areas of large indentations. Application of this calibration technique to strain-hardened (pile-up) and annealed (sink-in) copper leads to a unique tip shape calibration for the diamond indenter itself, as well as to a material parameter, a, which characterizes the extent of pile-up or sink-in. Thus the shape of the indenter tip and nature of the material response are separated in this calibration method. Using this approach, it is possible to make accurate absolute measurements of hardness and indentation modulus by nanoindentation.

Contact analysis of elastic-plastic fractal surfaces

Abstract: Rough surfaces are characterized by fractal geometry using a modified two-variable Weierstrass–Mandelbrot function. The developed algorithm yields three-dimensional fractal surface topographies representative of engineering rough surfaces. This surface model is incorporated into an elastic-plastic contact mechanics analysis of two approaching rough surfaces. Closed form solutions for the elastic and plastic components of the total normal force and real contact area are derived in terms of fractal parameters, material properties, and mean surface separation distance. The effects of surface topography parameters and material properties on the total deformation force are investigated by comparing results from two- and three-dimensional contact analyses and elastic and elastic-perfectly plastic material behaviors. For normal contact of elastic-perfectly plastic silica surfaces and range of surface interference examined, the interfacial force is predominantly elastic and the real contact area is approximately ...

Scaling approach to conical indentation in elastic-plastic solids with work hardening

Abstract: We derive, using dimensional analysis and finite element calculations, several scaling relationships for conical indentation in elastic-plastic solids with work hardening. Using these scaling relationships, we examine the relationships between hardness, contact area, initial unloading slope, and mechanical properties of solids. The scaling relationships also provide new insights into the shape of indentation curves and form the basis for understanding indentation measurements, including nano- and micro-indentation techniques. They may also be helpful as a guide to numerical and finite element calculations of indentation problems.

Contact mechanics of rough surfaces in tribology: multiple asperity contact

Abstract: Contact modeling of two rough surfaces under normal approach and with relative motion is carried out to predict real area of contact and surface and subsurface stresses affecting friction and wear of an interface. When two macroscopically flat bodies with microroughness come in contact, the contact occurs at multiple asperities of arbitrary shapes, and varying sizes and heights. Deformation at the asperity contacts can be either elastic and/or elastic-plastic. If a thin liquid film is present at the interface, attractive meniscus forces may affect friction and wear. Historically, statistical models have been used to predict contact parameters, and these generally require many assumptions about asperity geometry and height distributions. With the advent of computer technology, numerical contact models of 3-D rough surfaces have been developed, particularly in the past decade, which can simulate digitized rough surfaces with no assumptions concerning the roughness distribution. In this article, a comprehensive review of modeling of multiple-asperity contacts in dry and wet conditions is presented. Contact models for homogeneous and layered, elastic and elastic-plastic solids with and without tangential loading are presented. The models reviewed in this paper fall into two groups: (a) analytical solutions for surfaces with well-defined height distributions and asperity geometry and (b) numerical solutions for real surfaces with asperities of arbitrary shape and varying size and height distributions. Implications of these models in friction and wear studies are discussed.

Flow in rock fractures : the local cubic law assumption reexamined

Abstract: We investigate the validity of applying the “local cubic law” (LCL) to flow in a fracture bounded by impermeable rock surfaces. A two-dimensional order-of-magnitude analysis of the Navier-Stokes equations yields three conditions for the applicability of LCL flow, as a leading-order approximation in a local fracture segment with parallel or nonparallel walls. These conditions demonstrate that the “cubic law” aperture should not be measured on a point-by-point basis but rather as an average over a certain length. Extending to the third dimension, in addition to defining apertures over segment lengths, we find that the geometry of the contact regions influences flow paths more significantly than might be expected from consideration of only the nominal area fraction of these contacts. Moreover, this latter effect is enhanced by the presence of non-LCL regions around these contacts. While contact ratios of 0.1–0.2 are usually assumed to have a negligible effect, our calculations suggest that contact ratios as low as 0.03–0.05 can be significant. Analysis of computer-generated fractures with self-affine walls demonstrates a nonlinear increase in contact area and a faster-than-cubic decrease in the overall hydraulic conductivity, with decreasing fracture aperture; these results are in accordance with existing experimental data on flow in fractures. Finally, our analysis of fractures with self-affine walls indicates that the aperture distribution is not lognormal or gamma as is frequently assumed but rather truncated-normal initially and increasingly skewed with fracture closure.

Contact mechanics of piezoelectric ultrasonic motors

Abstract: Piezoelectric ultrasonic motors are driven by tangential stresses in the interface between stator and rotor. These stresses are generated by the elliptical motion of the material points of the stator or rotor surface and depend on frictional processes in the contact area. The contact mechanics of piezoelectric ultrasonic motors determines the operational characteristics, like rotational speed and torque or transmitted mechanical power and efficiency. Wear properties and lifetime of piezoelectric ultrasonic motors are also determined by contact mechanics. The goal of the present paper is to summarize the state of the art in the understanding of some fundamental processes governing the contact mechanics of piezoelectric ultrasonic motors. After a short introduction, a survey of publications devoted to the subject will be given. Then, an attempt will be made to classify the mechanical models, which were developed in order to explain the contact mechanics of piezoelectric ultrasonic motors, according to the physical effects which have been taken into account in their derivation. Some results concerning the choice of proper contact materials, wear and lifetime of ultrasonic motors will be addressed in a separate section. Finally a summary and outlook will be given and open questions for future research will be formulated.

Axisymmetric adhesion tests of soft materials

Abstract: We describe a general, linearized fracture mechanics analysis for studying the adhesive properties of elastic, low modulus materials Several adhesion tests are described, but all involve an elastic material which is brought into contact with a rigid surface along an axis of radial symmetry Relationships between the load, displacement, and radius of the circular contact area between the two materials are described These relationships involve the elastic modulus of the compliant material, the energy release rate (or adhesion energy) and various parameters which characterize the geometry of interest The ratio of the contact radius to the thickness of the elastic material is shown to be a particularly important parameter After reviewing some general concepts relevant to the adhesion of soft polymeric materials, we describe the fracture mechanics analysis, and provide examples from our own work on the adhesion of elastomers, thermoreversible gels and pressure sensitive adhesives

Atomic Force Microscopy Study of an Ideally Hard Contact: The Diamond(111)/Tungsten Carbide Interface

Abstract: A comprehensive nanotribological study of a hydrogen-terminated diamond(111)/tungsten carbide interface has been performed using ultrahigh vacuum atomic force microscopy. Both contact conductance, which is proportional to contact area, and friction have been measured as a function of applied load. We demonstrate for the first time that the load dependence of the contact area in UHV for this extremely hard single asperity contact is described by the Derjaguin-M{umlt u}ller-Toporov continuum mechanics model. Furthermore, the frictional force is found to be directly proportional to the contact area. {copyright} {ital 1998} {ital The American Physical Society}

Amontons' law at the molecular level

Abstract: One of the fundamental postulates of friction is that at the microscopic or molecular level, the “real” area of contact is proportional to the load applied over the macroscopic or “apparent” area. This has both theoretical and experimental support and has formed the basis of many theoretical analyses, including an explanation of one of the most basic observations of everyday friction, i.e., that the friction force F is proportional to the load L or weight of the moving object (Amontons' law) where the ratio of F to L defines the coefficient of friction μ=F/L. We have carried out friction experiments between two molecularly smooth non-adhering surfaces under conditions where all the relevant macroscopic and microscopic parameters were directly measured. We find that even at the microscopic level the friction force is proportional to the net applied load and not to the real area of contact. One implication of this finding is that Amontons' law is also obeyed directly at the molecular level and does not emerge indirectly because of some fortuitous correlation between the net applied load and the local contact area or shear strength, as is commonly supposed. A physical model, based on intermolecular forces and thermodynamic considerations, is offered to explain why the friction force is proportional to the net applied load, and why the case of adhering surfaces - where the friction force is found to be proportional to the molecular contact area -is quite different from that of non-adhering surfaces.

The actual contact angle on a heterogeneous rough surface in three dimensions

Abstract: A general equation is presented for the actual contact angle on a solid surface in a three-dimensional setting. The solid surface may be rough or heterogeneous or both. The effects of the existence of line tension and its variation with the position of the contact line are also included. It is shown that when line tension can be ignored, the actual contact angle at each point on the solid surface always equals the intrinsic contact angle (which is given in this case by the Young equation). However, when line tension is significant, the actual contact angle deviates from the Young contact angle by a term proportional to the geodesic curvature of the contact line and a term depending on the directional derivative of the line tension. Various situations are presented and discussed. Of particular interest is the example of a drop on a sphere, for which it is shown that the actual contact angle equals the Young contact angle when the contact line coincides with the equator of the sphere.

A new principle in contact mechanics

Abstract: Two nonrotating elastic half-planes in quasi-static contact without coupling of the normal and tangential surface stresses are analyzed in this paper. It is proved that the tangential traction under constant normal forces and increasing tangential forces is equal to the difference between the actual normal pressure and the pressure for a smaller contact area, multiplied by the coefficient of friction. Every stick area corresponds to a contact area (or a configuration of multiple contact areas) that is smaller than the present contact area. In the same way as the contact area develops with increasing pressure, the stick area recedes with increasing tangential traction. General loading scenarios are solved by superposition of oblique increments under constant angles. As an example, this principle is applied to a rigid surface of the form A k x k , in contact on 0 ≤ x ≤ a and with a corner at x = 0, indenting an elastic half-plane.

Effects of 'sinking in' and 'piling up' on estimating the contact area under load in indentation

Abstract: The phenomena of the 'piling up' and 'sinking-in' of surface profiles in conical indentation in elastic-plastic solids with work hardening are studied using dimensional and finite-element analysis The degree of sinking in and piling up is shown to depend on the ratio of the initial yield strength Y to Young's modulus E and on the work-hardening exponent n The widely used procedure proposed by Oliver and Pharr for estimating contact depth is then evaluated systematically By comparing the contact depth obtained directly from finite-element calculations with that obtained from the initial unloading slope using the Oliver-Pharr procedure, the applicability of the procedure is discussed

Particle adsorption in evaporating droplets of polymer latex dispersions on hydrophilic and hydrophobic surfaces

Abstract: Stain patterns formed by drying up of droplets of polymer latex dispersion on hydrophilic and hydrophobic surfaces were examined in light of the mechanism of particle adsorption in evaporating droplets. On hydrophilic surfaces, the volume of droplets decreased with time, keeping the initial outline of contact area, and circular stain patterns were formed after the dry-up of droplets. By the microscopic observation of particles in the droplets, it was found that a large portion of the particles were forced to adsorb on the outline of the contact area where a microscopic thin water layer was formed because of hydrophilicity of the surface. On hydrophobic surfaces, on the other hand, the contact area of droplets decreased as evaporation proceeded, while no particle was adsorbed on the surface at the early stages. The particles in the droplets started to aggregate when the concentration of particles reached a critical value, and the aggregates adsorbed on the surface forming tiny spots after the dry-up. Time evolutions of contact angle, contact area and volume of the droplets were analyzed in light of differences in the adsorption mechanisms between hydrophilic and hydrophobic surfaces.

Adhesion, slip, cohesive zones and energy fluxes for elastic spheres in contact

Abstract: The energy fluxes upon shrinkage of the contact area are calculated for a pair of spheres in adhesion. Various notions of energy release rate are introduced and analyzed for correlating the external work parameters and the work of adhesion. Decomposition of the energy release rate into reversible and irreversible parts shows that the reversible part is the work of adhesion and it can be described by the cohesive response purely at the contact zone-edge. This result justifies the use of local zone-edge quantities for modeling the interaction of adhesion and friction. For specific quantitative analysis, adhesion is represented by the Dugdale model, uniform cohesive traction up to a limited separation, as an approximation to more exact inter-surface forces. Exact results are given for the entirely reversible energy release rate to the edge of the contact and the energy release rate to the cohesive zone. The latter is named the strain energy release rate and found to depend on the path in loading parameter space, while the reversible energy release rate is independent of the loading path. The solution for shear of the contact is given as well. Energy released reversibly to be converted into surface energy is identified in contrast to energy released due to slip which will be partially or totally dissipated as heat. The relevance of the results for friction is discussed and contrasted with their significance for the mixed mode fracture of a circular joint.

An Elliptic Elastic-Plastic Asperity Microcontact Model for Rough Surfaces

Abstract: An elastic-plastic microcontact model, that takes into account the directional nature of surface roughness, is proposed for elliptic contact spots between anisotropic rough surfaces. In addition, the plasticity index was modified to suit more general geometric contact shapes. This contact model, which expands the usefulness of the CEB model, is also utilized to determine the effect of effective radius ratio (γ) on microcontact behavior and to compare the results of this model and other models under different surface topographies. The results show that the elliptic contact model and circular contact model deviate considerably in regard to the separation (h), total real contact area (At ), plastic area (Ap ) and plasticity index (Ψ). The present model can be simplified to become other stochastic models.

Continuous measurements of load-penetration curves with spherical microindenters and the estimation of mechanical properties

Abstract: Elastic and plastic properties of metals and Young's modulus of ceramics are determined in the microindentation regime by continuous measurements of load versus depth of penetration with spherical indenters. Calibration procedures, usually applied in nanoindentation experiments, are not needed in the microregime where spherical indenters (rather than sharp indenters with microscopical spherical tips) can be manufactured. As indenters of larger diameters are used, the elastic response of the specimen can be probed during the loading stage of the indentation tests (and not only during unloading, as is the case with nanoindenters). Hence, an accurate determination of Young's modulus can be achieved without a prior knowledge of possible “piling up” or “sinking in” which may occur at the perimeter of the contact area. The contact response of materials is shown to undergo four distinct regions: (i) pre-Hertzian regime, (ii) Hertzian regime, (iii) small-scale plasticity, and (iv) large-scale plasticity. A general methodology for estimation of yield strength and hardening exponent of metals is proposed in the last regime.

Contact analysis of non-Gaussian random surfaces

Abstract: Surfaces produced by machining processes such as grinding, shaping and turning and some magnetic disk texturing processes such as sputtering and laser processing are frequently non-Gaussian...

Instrumented pendulum for impact characterization of whole fruit and vegetable specimens

Abstract: As part of an effort to measure impact damage-related physical properties, a precision 3-m (98-ft) instrumented pendulum was developed to record force and contact area profiles for normal impacts of whole fruit or vegetable specimens onto an essentially rigid, flat anvil The specimen is attached to four adjustable suspending lines (music wire and Kevlar™) to form a pendulum The anvil against which it strikes is fitted with a force transducer and with a contact area sensor of the authors’ design Two precisely spaced infrared beams (beams interrupted by sample) allowed approach and rebound velocities to be measured An accelerometer attached to the trailing end of the commodity measures deceleration during impact and free vibrations during rebound Impact profile data are typically sampled at 10 kHz per channel, sufficient to capture the required data while conserving data storage space Operating procedures include single impacts, constant-height multiple-impacts (CHMI) (for determining bruise resistance), increasing-height multiple-impacts (IHMI), and paired increasing-height multiple-impacts (PIHMI) (for determining bruise threshold in apples) These methods are ideally suited for studying impact failure in commodities exhibiting compression failure Those failing primarily in shear, such as potato tubers, can also be studied The design, calibration, and operating procedures are described

Image sensor with microlens material structure

Abstract: An optical device including a semiconductor-based substrate having a photosensitive circuit including a photosensitive area a portion of which is covered by color filter array material, a contact area surrounding the photosensitive area, and a microlens material overlying the portion of the photosensitive area and a portion of a contact area.

Female terminal with flexible contact area having inclined free edge portion

Abstract: A low inserting force terminal is provided. An elastic contact arm for a male terminal is formed inside the electrical contact unit, and the free edge portion of the elastic contact portion is slidable along the inner wall of the electrical contact unit. An inclined surface which is inclined in the sliding direction of the free edge portion is formed on the inner wall. The free edge portion is situated at the front edge of the inclined surface when the male terminal is in a non-inserted state. A contact surface for preventing excessive displacement of the elastic contact arm is formed at the rear edge of the inclined surface.