Showing papers on "Contact area published in 1985"

A solution method for planar and axisymmetric contact problems

Abstract: SUMMARY A solution procedure for the analysis of planar and axisymmetric contact problems involving sticking, frictional sliding and separation under large deformations is presented. The contact conditions are imposed using the total potential of the contact forces with the geometric compatibility conditions, which leads to contact system matrices and force vectors. Some key aspects of the procedure arc the contact matrices, the use of distributed tractions on the contact segments for deciding whether a node is sticking, sliding or releasing and the evaluation of the nodal point contact forces. The solutions to various sample problems are presented to demonstrate the applicability of the algorithm. Much progress has been made during recent years in the development of computational capabilities for general analysis of certain nonlinear effects in solids and structures. In each of these developments, quite naturally, the first step was the demonstration of some ideas and possibilities for the analyses under consideration, and then the research and development for reliable and general techniques was undertaken. The second step proved in many cases much more difficult, and in the case of capabilities for analysis of contact problems has yielded few general results. Although some of the first complex contact problems have been solved using the finite element method quite some time ago,'- and much interest exists in the research and solution of contact problems (see, for example, References 4-1 5), there is still a great deaiwf effort necessary for the development of a reliable, general and cost-effective algorithm for the practical analysis of such problems. This is largely due to the fact that the analysis of contact problems is computationally extremely difficult, even for the simplest constitutive relations used. Much of the difficulty lies in that the boundary conditions of the bodies under consideration are not known prior to the analysis, but they depend on the solution variables. The aim in our research is the development of a solution algorithm for analysis of general contact conditions which shall include the possibilities to analyse: contact between flexible-flexible and rigid--flexible bodies; sticking or sliding conditions (with or without friction); large relative motions between bodies; repeated contact and separation between the bodies. Since the large deformation motion of the individual bodies can in many cases be analysed already quite effectively,'6 an algorithm of the above nature will certainly enlarge, very

An Analysis of Particle Adhesion on Semiconductor Surfaces

Abstract: This paper constitutes an analysis of the forces of adhesion of small particles to surfaces, most specifically as applied to semiconductor surfaces. The primary forces of adhesion of small, less than 50 μm diam particles on a dry surface are van der Waals forces. These van der Waals forces of adhesion can increase as a function of time due to particle and/or surface deformation which increases the contact area; micron‐size particles can be held to surfaces by forces exceeding 100 dyn, which corresponds to pressures of 109 dyn/cm2 or more. Total forces of adhesion for micron‐size particles exceed the gravitational force on that particle by factors greater than 106. Electrostatic forces only become important and predominate for particles larger than 50 μm diam. Immersion of the adhered particle system can, in some cases, greatly reduce the total adhesion force, first by shielding of the electrostatic and van der Waals attractions, and also by adding double layer repulsion because of dipolar alignment of liquid molecules or dissolved ions at the surfaces. Double layer interactions may, however, also add to the attractive forces if dipoles align properly for attraction. An important consideration is the possibility that if the particles are not removed by the liquid immersion, then a liquid bridge can be formed by capillary action between the particle and surface upon removal from the liquid. This would add a very large capillary force to the total force of adhesion. This capillary force has been shown to remain, in some cases, even when the system is baked at above the liquid boiling point for more than 24h. Removal of these small particles from surfaces is in theory possible but is in practice extremely difficult. It is clear that emphasis should be placed on prevention of particle deposition rather than on counting on achieving subsequent removal.

The effectiveness of oxides in reducing sliding wear of alloys

Abstract: During like-on-like reciprocating sliding in air (amplitude 2.5 mm, load 1.5 kg, speed 500 double traversais per minute), the formation of oxides can have considerable influence on the friction and wear characteristics of high-temperature alloys, such as Jethete M152 and Rex 535. In particular, above a certain transition temperature, between 200 and 300°C for these alloys under these conditions, an adherent, smooth wear-protective oxide layer is developed on the load-bearing surfaces. At lower temperatures, oxide debris reduces the extent of metal-metal contact, thereby reducing the friction and wear rate, but does not eliminate it completely. The oxide debris is produced by two processes; one involves transient oxidation of the metal surfaces, removal of such oxide during each transversal, and reoxidation of the exposed metal; the other involves the formation, fracture, comminution, and oxidation of metal debris particles. At temperatures above the transition temperature, the oxide debris is compacted and comminuted between the sliding surfaces to develop the wear-protective oxide layer. This paper considers the reasons for the effectiveness of such oxides in terms of the influence of the hydrostatic pressures generated on plastic deformation of the very fine oxide particles or asperities in the surface. The resulting friction during sliding is less than during metal-metal contact because only limited asperity junction growth occurs before the asperities become sufficiently large and the hydrostatic pressures sufficiently reduced to allow fracture within the oxide-oxide junctions. The oxide-wear debris produced is recompacted into the surface, resulting in only very low wear rates. It has been shown that the number of asperity-asperity contacts during sliding of wear-protective oxide layers is relatively high, typically 5×103/mm2 of apparent contact area, while the mean surface flash temperature rise is low, typically 2°C. Consideration is given to some of the conditions that favor development of wear-protective oxide layers.

On grasping planar objects with two articulated fingers

Abstract: The grasps attainable by mechanical hands with two opposing articulated fingers are examined. Such grasps are called planar, since all forces lie in plane defined by the contact points and the center of mass of the object. Assuming that the contact interaction can be modeled by point contact with Coulomb friction, the equilibrium equations for the grasped object are obtained. Satisfaction of force and moment equilibrium leads to the development of a compatability condition that relates object shape, contact locations and surface roughness as characterized by the coefficient of static friction μ. The set of all possible equilibrium grasps is determined for some examples and the results are presented as curves in a friction angle space. This representation permits choosing a grasp that is optimum in accordance with an independently developed criterion such as minimum dependence on friction forces.

Computing the friction forces associated with a three-fingered grasp

Abstract: A procedure is presented for computing the friction forces required to satisfy static equilibrium, given a set of normal contact forces exerted by a three-fingered mechanical hand. The contact between the fingers and the object is modeled as "point contact with friction. "This means the fingertip is free to rotate about the point of contact, but sliding along its surface is resisted by a friction force. Comparing these friction forces to the maximum friction force, which can be sustained between the contacting surfaces, it must be determined whether the object slips from the grasp and further the instantaneous motion of the impending movement. Two examples are solved in detail to illustrate the procedure.

Method for handling semiconductor die and the like

Abstract: Apparatus for handling semiconductor chips and the like objects are disclosed which include the use of a flat flexible film that is supported on a flat porous texturized fabric sheet such as a woven or knit fabric having spaced fiber crossovers. Objects, are supported on the flat flexible film in intimate surface contact therewith for securely holding the same in position by interfacial forces therebetween. Adhesive may be included for increasing the interfacial force. To facilitate removal of objects from the film, the fabric is connected to a vacuum source for drawing portions of the flexible film over and between crossovers in the fabric whereby portions of the flexible sheet are withdrawn from the objects. The contact area and interfacial forces between the flexible sheet and objects is thereby reduced to enable removal of the objects from the sheet using conventional object handling techniques.

Computer Simulation of Elastic Rough Contacts

Abstract: A computer program is developed to analyze the contact of a rigid smooth plane and computer-simulated elastic rough surfaces. The simulated surfaces have isotropic Gaussian height distribution and bilinear autocorrelation function. Results of two cases are presented: (1) dry contact between a square elastic rough punch and a rigid smooth plane; (2) dry contact between an elastic rough half-space and a rigid smooth plane. Force-compliance relationship is compared with hat derived by Bush, Gibson, and Thomas. Real contact area ratio Ar is found to be approximately proportional to nominal contact pressure in the range 0.025 < Ar < 0.3. Presented at the 39th Annual Meeting in Chicago, Illinois May 7—10, 1984

An accurate method to extract specific contact resistivity using cross-bridge Kelvin resistors

Abstract: The cross-bridge Kelvin resistor structure is used to extract true interfacial specific contact resistivity (ρ c ). Two-dimensional (2-D) simulations demonstrate that the sublinear behavior of the measured contact resistance versus contact area on a log-log plot is due to current crowding around the contact which results from the contact window size being smaller than the diffusion width. The effect is more pronounced for low values of ρ c . Excellent agreement has been found between the simulations and measured data of contact resistances. An accurate value of ρ c has been extracted for the case of PtSi to n+polysilicon contacts.

A numerical-experimental analysis of the contact stress problem

Abstract: A general method is presented to evaluate the contact stresses and the contact area from the full field photoelastic data. The procedure utilizes the least squares technique in conjection w...

The role of surface forces in metal–metal contacts

Abstract: A real metal–metal contact involves the interaction between many small asperities on each surface. It is the way that these asperities deform and adhere that determines the more macroscopic properties of friction and wear. It is possible to investigate the interaction of a single asperity with another surface by contact experiments between a sharp metal point (1 μm radius) and a flat surface. This type of experiment also enables the interfacial adhesive energy to be directly measured. This parameter is important in thin film adhesion. In order to achieve true metal–metal contact, the experiments are performed on cleaned specimens in ultrahigh vacuum. The force required to separate the contact after a known load has been applied can be measured together wtih the area of contact (determined from electrical resistance). Results show that at very low applied loads the behavior is dominated by the action of surface forces which may themselves be strong enough to initiate plastic flow. There is also direct as w...

Experimental investigation of truck tire inflation pressure on pavement-tire contact area and pressure distribution. interim report

Abstract: This report contains the results of an experimental investigation into the gross contact areas and contact pressure distributions produced by statically loaded truck tires. The gross contact areas are determined using an automatic imaging system that computes the contact area from a digitized data base obtained from an inked tire print. Contact pressure distributions produced by statically loaded tires are determined using a pressure sensitive film technique.

Rapid thermal annealing of Al‐Si contacts

Abstract: Contact formation of Al on n+‐Si by rapid thermal annealing has been investigated. It was found that contact resistivity of the order of 6×10−7 Ω cm2 can be reproducibly achieved. The uniformity of the contact area morphology is much improved due to the limited Si migration into the Al metallization. Flat contact morphology can be obtained with a combined technique of ion mixing and rapid thermal annealing.

Bonding electrical conductors and bonded products

Abstract: Bonds between a contact area of a circuit of a semiconductor and a conductor are formed by applying a rotating tool to an opposed surface of the conductor or to an intervening material superposed on it. The conductor may be laminated to one or more layers of insulant material and when that material is for example polyester, the bond may be formed without prior removal of the insulant from between the contact area and the conductor; it is displaced by the effect of the tool. The areas and conductors may be in an array and the tool be brought across the members of the array in succession.

Dependence of Green Strength on Contact Area Between Powder Particles for Spherical Copper Powder Compacts

Abstract: Model 2 The geometrical considerations used here are, in principle, similar to those of Model 1, with respect to the contacting pairs of spheres considered in the densification process. Now, considering the two contacting spheres shown in Fig. 11 (see Appendix 1), the contact area will be increased necessary for evaluating the experimentally obtained data. The relative density of the powder compact can be experimentally determined and this can be related to the contact area between particles. Another aim of the present work was, therefore, to derive a simple geometrical equation describing the relationship between the relative density of the powder compact and the contact area. A model experiment was carried out on an ideal packing system to confirm the validity of this equation.

On the Contact Problem in Elastostatics

Abstract: Some aspects of the contact between elastic bodies are presented. Starting with the formulation of the contact problem we proceed to give algorithms for contact formation and frictional contact, with emphasis on rolling, which is the most general form of contact with friction. Numerical results are shown, and a comparison with experiments is made.

On the optimization of VLSI contacts

Abstract: The contact-resistance characteristic of silicon devices has been a subject of research and development since the early days of silicon integrated-circuit technology. The contact-chain losses suffered by very large scale integration (VLSI), however, have made the minimization of contact resistance a critical parameter due to the large number of contacts per circuit and due to the increase of contact resistance with decreasing contact size. This paper will present a brief review of the theory of contact resistance, the literature, measurement techniques, and of the transmission-line model (TLM) for analyzing contact-resistance data. Contact-resistance data pertaining to shallow high-conductivity contacts for VLSI will be presented as a function of the junction parameters (implant dose, etc.) and of the contact area for BF 2 and arsenic implants with aluminum-silicon metallization. Contact-resistance data for a sputtered molybdenum silicide contact barrier for boron and arsenic implants versus contact area will also be presented and compared to the aluminum-silicon control samples with a discussion regarding the uniformity of contacts to silicon.

2-D Simulations for accurate extraction of the specific contact resistivity from contact resistance data

Abstract: This paper presents a unified approach for the accurate extraction of specific contact resistivity (ρ c ) for ohmic contacts. Using 2-D simulations, which account for the current flow, or crowding around the contact window, we have analysed the resistance data obtained from the Cross Bridge Kelvin Resistor, the Contact End Resistor, and the Transmission Line Tap Resistor. For each particular structure, a universal set of curves is derived that allows accurate determination of ρ c , given the geometry of the structure. The values obtained for ρ c are independant of the test structure type, its geometry and the contact area. The data suggests that in the past researchers have overestimated ρ c , and that contact resistance will not limit device performance even with submicron design rules.

Magnetic behaviors of two spheres which contact each other with an area

Abstract: In the chain of spheres model proposed by Jacobs and Bean, spheres contact each other at a point. In order to see the change of the magnetic behaviors of the chain of spheres when spheres begin to contact each other with an area, we consider the chain of two spheres. Critical field Hcri for the irreversible rotation of the magnetization and coercive force Hc by both the parallel rotation and fanning mechanisms are calculated as a function of the contact area. Uniaxial magnetic anisotropy constant Ku by the parallel rotation mechanism is also calculated as a function of the contact area. Ku, Hcri, and Hc are found to increase, reach a maximum value, and decrease with an increase in contact area. The maximum values of Ku and Hcri by the parallel rotation mechanism are found to be 30% larger than the values of Ku and Hcri for the point contact. The maximum value of Hcri by the fanning mechanism is found to be 15% larger than the value of Hcri for the point contact.

Effect of space angle on constriction resistance and contact resistance for a point contact

Abstract: It can generally be considered that an actual contact makes an angle with the extension of the contact surface because the tip of a contact element is convex in shape (macroscopically) and has surface roughness (microscopically). The effect of this angle on constriction resistance and contact resistance for a point contact is analyzed theoretically by solving Laplace’s equation subject to boundary conditions determined by a modeled morphology of the contact. The analysis leads to the modified formulas for the constriction resistance and the contact resistance, which show that the effect cannot always be neglected and that the contact model with space angle is useful.

The Real Area of Contact in Polymeric Magnetic Media—I: Critical Assessment of Experimental Techniques

Abstract: A critical assessment of techniques used to measure the real area of contact has been conducted. The techniques that are found to be suitable to measure contact area between a polymeric magnetic medium and a mating hard surface are: electrical-contact resistance and two-beam optical interference. The limitation of the electrical-contact resistance is that both surfaces must be electrically conductive. This technique only provides semiquantitative information. The two-beam optical interference technique provides complete distribution of the asperity-contact areas. Limitations of this technique are that the mating member must be optically transparent and both surfaces must be smooth. A monochromatic light of wavelength 706 nm (red) and a glass slide of high refractive index (1.93) were found to be suitable for magnetic tapes under study. All measurement techniques suffer from overestimation of the real area of contact, especially in the case of smooth magnetic tapes. Calculations for overestimation of the r...

Mutual Overlap Coefficient and Wear Debris Motion in Dry Oscillating Friction and Wear Tests

Abstract: In oscillating dry friction and wear tests, mechanical parameters such as degrees of freedom and stroke amplitudes govern the formation of wear debris. A third body is formed by the wear debris within the contact. It is progressively eliminated from the contact area. The volume of wear debris lying outside the contact area corresponds to the total wear between the pin and the counterface. Wear is thus controlled by the elimination of wear debris outside the contact. The overlap of the pin and the friction track on the counterface thus controls the wear debris elimination. That overlap is characterized by the mutual overlap coefficient (MOC) which is defined as the ratio of the pin contact area to the counterface wear track. Wear debris formation and elimination was simulated with a pin made of a high-wear-rate material rubbing against an oscillating counterface. Widely different wear results and transfer film morphologies are obtained when the MOC varies between 0.66 and 0.99. Wear results are analyzed fo...