Actual Contact Area Research Articles

The effect of indenter shape on sub-micron indentation according to discrete dislocation plasticity

Two-dimensional discrete dislocation simulations of indentation in the sub-micron range are presented for wedge indenters with a sharp tip and for indenters with a circular tip. Plane strain calculations are carried out for single crystals that are initially free of mobile dislocations and with all dislocations nucleating from a specified distribution of internal sources. The hardness is expressed in terms of the indentation force divided by the actual contact area accounting for roughness of the surface in contact with the indenter. For wedge indenters the hardness is found to decrease with increasing indentation depth, while for indenters with a circular tip the hardness increases somewhat with increasing indentation depth. However, at a given indentation depth, the indentation hardness of circular indenters increases with decreasing tip radius. The difference in hardness evolution for the two tip shapes is mainly due to the manner in which the evolution of the contact area depends on indenter tip shape. The nominal hardness, i.e. that based on the geometric contact area neglecting material sink-in or pile-up and surface roughness, is found to follow the inverse square root size dependence predicted by Nix and Gao [1] and by Swadener et al [2], even though the plastic zone found in the simulations differs significantly in shape and size from that assumed in deriving the scaling laws.

An experimental evaluation of the constant β relating the contact stiffness to the contact area in nanoindentation

Measurements of mechanical properties by nanoindentation with triangular pyramidal indenters like the Berkovich rely heavily upon the relationship between the contact stiffness, S, the contact area, A, and the reduced elastic modulus, Er . This relationship is often written in the form S=2βEr (A/π)1/2, where β is a constant that depends on the geometry of the indenter. Although the most common values for β used in experimental measurements are 1.000 and 1.034, various theoretical analyses have yielded values as small as 1.00 or as large as 1.20, depending on the assumptions made to model the deformation. Here, the most appropriate value of β is explored by performing careful experiments in fused quartz with thin gold coatings applied to the surface to reveal the actual contact area when observed in the scanning electron microscope. Experiments were performed not only with the Berkovich indenter, but with five other three-sided pyramidal indenters with centreline-to-face angles ranging from 35.3° (cube corner) to 85.0°. The results are important in the accurate measurement of mechanical properties by nanoindentation

Tribological, thermal and mechanical coupling aspects of the dry sliding contact

An original experimental set-up, made of two coaxial rings in relative motion, a sapphire and steel, enabled temperature measurements on both sides of the third body at the friction interface. Hot spots have been identified and temperature gradient across the third body accurately measured. Infrared camera and thermocouples have shown to be an effective tool for this research. Investigations conducted using SEM enabled detailed analysis of friction interfaces of both components, the sapphire and steel rings. Two types of third body (layers) have been identified, the compact, smooth micro-plates—where the actual contact occurs, and granular—which seem to accumulate in depressions or against material obstacles. There are also clear indications that the hot spots and depressions on steel friction surface are directly related. These areas of contact seem to be ‘shrinking’ in height after the application and complete component cooling. The investigation of the third body phenomenon and its influence on interface temperatures has direct relation to the observations made in automotive disc brakes. A thermal numerical model, which was also developed, introduced the third body as a uniform layer with energy storage and conduction. The obtained thermal gradients seem to be accurate, when compared with measurements conducted. The results are also similar to those found in literature. In addition, when only a fraction (1/1000th and 1/2000th) of the total nominal friction surface was considered to be in the actual contact, experimental temperature results were exactly within the predicted range. This indicates that the actual contact area varies during application.

Properties of a newly developed concave nickel gasket for the ConFlat-type sealing system

Nickel gaskets for large-bored vacuum flange systems remain virtually nonexistent in practical use, despite strong demand for a gasket invulnerable to both oxidation and reduction atmospheres in vacuum application processes. Nickel gaskets would seem preferable in these processes, which are characterized by sensitivity to copper contamination and in which highly corrosive gases could wear away copper gaskets. In working to develop a nickel gasket for the ConFlat-type sealing system with a seal reliability and handling impression comparable to conventional copper gaskets, the authors found that nickel-plated copper gaskets could not attain secure sealing because the nickel layer was too hard to form a tight fit with the flange face. In earlier developmental stages, seven types of prototype nickel gaskets were produced and subjected to a tightening test. These prototype gaskets varied in their respective annealings and/or applied surface finishes. In the tightening test, deep penetration of the flange knife edge and a wide seal area were obtained on all the annealed prototypes, but their seal ability was nevertheless inferior to copper gaskets, even in the best case. Traced surface profiles of the tightened prototype gaskets with relatively roughly finished surfaces revealed that the original outlines of many protuberances and dimples remained, even after considerable seal pressure was applied on them. This observation suggests that the actual contact area between the gasket face and flange face was narrower than the apparent seal area, and too small to achieve secure sealing. Such poor accommodation of the flange surface was rarely observed on tightened gaskets with smoothly finished surfaces, although fine scratches remaining on the surface frequently functioned as leak paths after the tightening was completed. This insufficient fine deformation ability of the surface was not observed in commercially available copper gaskets. Results of tensile tests on prototype nickel gaskets versus commercially available copper gaskets made it clear that undesirable stiffness is an intrinsic characteristic of nickel gasket surfaces. This arises from the high hardening rate of the nickel material, and therefore cannot be improved by annealing alone. On further evaluation of the prototypes, the authors concluded that three factors are indispensable in order for nickel gaskets to be put into practical use: annealing to reduce hardness, a proper surface finish to obtain a tight fit on the sealing interface, and some sort of protection against scratching the gasket surface. This last requirement can be met by machining to reduce the sealing face region of the gasket surface. The final prototype nickel gasket, a concave version annealed and finished with fine lathing, showed basic sealing and flange knife edge damage characteristics comparable to copper gaskets, with superior seal stability at elevated temperature.

Contact Area Measurements Reveal Loading-History Dependence of Static Friction

We perform quantitative measurements of the actual area of contact, A, formed by two rough solids that are subjected to different normal loading protocols. We show that microscopic motion, induced by Poisson contraction or expansion, produces a strong memory dependence of on the loading history with a large corresponding influence on the system's frictional strength. These effects, together with accompanying transient dynamics, are independent of humidity, loading rates, and material contrast across the interface.

Study on the prediction technique of the wear amount of polyoxymethylene

AbstractThe influence of the sliding velocity and atmospheric temperature on the specific wear amount of polyoxymethylene was evaluated with the ring‐on‐ring apparatus. The specific wear amount showed the variation of S‐character type with maximum value, according to the change in the sliding velocity and the atmospheric temperature. When those results are plotted according to the sliding surface temperature, they have been found to be arranged as the same dependence. The specific wear amount of polyoxymethylene was assumed to be proportional to the product of actual contact area and reciprocal of the fracture energy. Then, the temperature dependency of the product of the fracture energy, calculated from stress–strain curve, and the actual contact area, calculated from Hertz's equation with elastic modulus, was able to explain the sliding surface temperature dependency of the specific wear amount well. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 4212–4218, 2006

An experimentally validated thermo-mechanical model for the prediction of thermal contact conductance

A predictive model for estimating thermal contact conductance between two nominally flat metallic rough surfaces has been developed and experimentally validated. The predictive model consists of two complementary parts, the first of which is a surface deformation analysis to calculate the actual area of contact for each contact spot, while the second accounts for the effects of constriction resistance and gas gap conductance between the contacting surfaces. A surface characterization technique is developed which generates an equivalent 3-D surface profile from multiple 2-D profiles and determines the unique wavelengths of importance for the surface deformation and constriction resistance models. For given surface profiles and material properties of two contacting surfaces, and a specified contact pressure, the surface characterization technique filters out non-essential wavelengths on the surface, after which the surface deformation analysis calculates the deformation and contact area of each contacting asperity by considering three different modes of deformation, namely, elastic, elastic–plastic, and plastic. The constriction resistance model is then used to calculate the constriction resistance for each contacting asperity based on the area of contact and radius of curvature of the asperity. The constriction resistance values for all the contacting asperities are then used to calculate the total thermal contact conductance. An experimental facility has also been constructed to measure thermal contact conductance of interfaces to verify the results of the predictive model. Good agreement has been found between the model predictions and experimental measurements, validating the modeling approach.

Effects of Contact on the Abrasiveness of a Thin Boron Carbide Coating

Boron carbide (B4C) has been studied under dry sliding conditions for use as a potential finite-life run-in coating. Such a coating has been found to polish its mating surface during dry sliding wear, thereby providing fatigue resistance to the coated part. Employing such run-in coatings requires a complete understanding of the changes that occur in the coating abrasiveness during the polishing process. Therefore, a thorough understanding of the changes in the contact conditions of such a system needs to be obtained. This study presents the role that contact plays in changes of the overall coating abrasiveness. By performing sliding wear experiments using various contact conditions, i.e. ball-on-disc, pin-on-disc and cone-on-disc, we directly investigated the effects of macro-scale contact conditions on the coating abrasiveness. It was found that the rate at which the coating abrasiveness decreased was independent of the macro-scale contact conditions. These findings were further validated by investigating the coating abrasiveness results that were obtained by performing spiral track wear experiments. Through the use of a three-dimensional thermomechanical asperity contact model, it was found that the coating abrasiveness was controlled by the actual micro-scale contact conditions. This study supports the classic Greenwood–Williamson model, which states that the number of micro-scale contacts and the total actual area of contact remains constant for a given load.

Three-dimensional dynamic hip contact area and pressure distribution during activities of daily living

Estimation of the hip joint contact area and pressure distribution during activities of daily living is important in predicting joint degeneration mechanism, prosthetic implant wear, providing biomechanical rationales for preoperative planning and postoperative rehabilitation. These biomechanical data were estimated utilizing a generic hip model, the Discrete Element Analysis technique, and the in vivo hip joint contact force data. The three-dimensional joint potential contact area was obtained from the anteroposterior radiograph of a subject and the actual joint contact area and pressure distribution in eight activities of daily living were calculated. During fast, normal, and slow walking, the peak pressure of moderate magnitude was located at the lateral roof of the acetabulum during mid-stance. In standing up and sitting down, and during knee bending, the peak pressures were located at the edge of the posterior horn and the magnitude of the peak pressure during sitting down was 2.8 times that of normal walking. The peak pressure was found at the lateral roof in climbing up stairs which was higher than that in going down stairs. These results can be used to rationalize rehabilitation protocols, functional restrictions after complex acetabular reconstructions, and prosthetic component wear and fatigue test set up. The same model and analysis can provide further insight to soft tissue loading and pathology such as labral injury. When the pressure distribution on the acetabulum is inverted onto the femoral head, prediction of subchondral bone collapse associated with avascular necrosis can be achieved with improved accuracy.

Spatial Analysis of 3′ Phosphoinositide Signaling in Living Fibroblasts, III: Influence of Cell Morphology and Morphological Polarity

Activation of phosphoinositide (PI) 3-kinase is a required signaling pathway in fibroblast migration directed by platelet-derived growth factor. The pattern of 3′ PI lipids in the plasma membrane, integrating local PI 3-kinase activity as well as 3′ PI diffusion and turnover, influences the spatiotemporal regulation of the cytoskeleton. In fibroblasts stimulated uniformly with platelet-derived growth factor, visualized using total internal reflection fluorescence microscopy, we consistently observed localized regions with significantly higher or lower 3′ PI levels than adjacent regions (hot and cold spots, respectively). A typical cell contained multiple hot spots, coinciding with apparent leading edge structures, and at most one cold spot at the rear. Using a framework for finite-element modeling with actual cell contact area geometries, we find that although the 3′ PI pattern is affected by irregular contact area shape, cell morphology alone cannot explain the presence of hot or cold spots. Our results and analysis instead suggest that these regions reflect different local 3′ PI dynamics, specifically through a combination of mechanisms: enhanced PI 3-kinase activity, reduced 3′ PI turnover, and possibly slow/constrained 3′ PI diffusion. The morphological polarity of the cell may thus bias 3′ PI signaling to promote persistent migration in fibroblasts.

Experimental investigation on dry frictional behavior of the two self-lubricating composites under heavy loading conditions

Two novel types of self-lubricating composites such as polytetrafluoroethylene (PTFE) composite and metal–plastic transverse section (SBP) composite were developed. The friction behavior of these composites, reciprocating sliding against stainless steel track in dry friction under heavy loading conditions, was investigated. Experimental results showed that the two self-lubricating composites exhibited low and stable coefficient of dry sliding friction of about 0.05. The time dependent of static friction of PTFE composite was strong, while that of SBP composite weak. Because the actual contact area of PTFE composite great increases with rest time, while that of SBP composite little increases resulting from supporting of thick metal backing under heavy loading conditions. This work is believed to be helpful for understanding of the time-dependence of dry sliding friction between different self-lubricating composites against stainless steel track under heavy loading conditions.

Finite element analysis of effect of electrode pitting in resistance spot welding of aluminium alloy

The effect of electrode pitting on the formation of the weld nugget in resistance spot welding of an aluminium alloy was investigated using the finite element method. Pitted electrodes were simulated by assuming a pre-drilled hole of varying diameter at the centre of the electrode tip surface. The results showed that a small pitting hole would not have a detrimental influence on the nugget size. The actual contact area at the electrode/sheet interface did not change significantly when the diameter of the pitting hole was increased. However, a large pitted area at the electrode tip surface resulted in a greatly increased contact area and hence reduced current density at the sheet/sheet interface, which in turn led to the formation of an undersized weld nugget. The numerical calculation of the nugget shape and dimensions agreed well with experimental observations.

Zr基バルクアモルファス合金の疑似体液中フレッティング疲労特性

Fretting fatigue properties were studied in air and in a simulated body fluid, PBS(−), using a commercial Zr-based amorphous alloy (7.6Ni-12.3Cu-3.5Al-76.6Zr in mass%). Fretting fatigue tests were carried out under load control using a sinusoidal wave with a stress ratio of 0.1, a frequency of 20 Hz in air and 2 Hz in PBS(−) and a contact pressure of 30 MPa for fretting. There was no difference between the stress-number of cycles to failure (S-N) curves of the plain fatigue test in air and in PBS(−), and the 107-cycle fatigue strength was approximately 150 MPa for both environments. The 107-cycle fretting fatigue strength in air was one-third as high as the plain fatigue strength, while the 2×106-cycle fretting fatigue strength in PBS(−) was approximately twice as high as that in air. Although the friction coefficient between the specimen surface and the fretting pad, which affects the fretting fatigue strength, was hardly different between air and PBS(−), SEM observations showed that the actual contact area of the fretting pad on the specimen surface tested in air was smaller than that tested in PBS(−). Thus, we considered that the decrease of the fretting fatigue strength in air was caused by the higher contact pressure of the pad in air than that in PBS(−). XPS analyses also showed that the specimens tested in air and in PBS(−) had the different compositions of the oxide films on their surfaces, suggesting that the difference in the composition of the oxide films affect the fretting damage and thus the fretting fatigue strength.

A multiscale finite-element method for solving rough-surface elastic-contact problems

A novel multiscale finite-element method to investigate the elastic contact of two-dimensional rough surfaces is presented. The aim of the method is to find the microscopic curve that describes the deformed shape of a solid with a smooth boundary surface in frictionless contact with a rigid rough surface. In addition, the real contact area is studied through the surface deformation. The contact traction on the contact surface and the maximum shear stress around the contact region are analyzed. This method is based on the variational inequality approach for solving the elastic frictionless contact problem. The strategy is to separate a small slice within the contact region and solve it as an independent system. Then the contact traction is obtained through iterations between the solution of the independent small slice and the solution of the total solid body. We observe a much higher pressure than the result of Hertz theory around the asperities. The main conclusions are (1)~the actual contact area and surface traction are dependent on the wavelength and amplitude of the surface roughness, (2) there is a much higher pressure around the asperities than predicted by Hertz theory, and (3) the location of maximum shear stress tends to be shifted toward the surface as compared with the case of smooth-surface contact. The method has the potential to be extended to solve three-dimensional rough contact problems.PACS Nos.: 03.40.D, 46.30.P, 62.20.P

Catalytic probe lithography: catalyst-functionalized scanning probes as nanopens for nanofabrication on self-assembled monolayers.

This article describes the use of scanning catalytic probe lithography for nanofabrication of patterns on self-assembled monolayers (SAMs) of reactive adsorbates. Catalytic writing was carried out by scanning over bis(omega-tert-butyldimethyl-siloxyundecyl)disulfide SAMs using 2-mercapto-5-benzimidazole sulfonic acid-functionalized gold-coated AFM tips. The acidic tips induced local hydrolysis of the silyl ether moieties in the contacted areas, and thus patterned surfaces were created. Diffusion effects arising from the use of an ink were excluded in these type of experiments, and therefore structures with well-defined shapes and sizes were produced. The smallest lines drawn by this technique were about 25 nm wide, corresponding to the actual contact area of the tip. Lateral force microscopy studies performed on different SAMs helped to clarify the nature and cause of the friction contrasts observed by AFM. Dendritic wedges with thiol functions inserted into the catalytically written areas, thus enhancing the height contrast. The created patterns open possibilities to build 3D nanostructures.

EFFECT OF ELECTRODE PITTING ON WELDING QUALITY IN RESISTANCE SPOT WELDING OF ALUMINIUM ALLOYS

The effect of electrode pitting on the welding quality in resistance spot welding (RSW) of aluminum alloy AA5182 is investigated using both finite element analysis and physical modeling methods. Results show that with the increasing of the pitted area at the electrode tip, the actual contact area at elec- trode/sheet interface does not change so much, while the con- tact area at sheet/sheet interface is increased significantly, therefore, the current density at the sheet/sheat interface is re- duced greatly, and the thickness and diameter of the nugget formed are both decreased. Dimensions and shapes of the nug- gets from physical modeling are in very good coincidence with numerical predictions. Only a donut shape nugget with very limited thickness is formed when the diameter of the pitting hole is 5.0 mm. These results reveal that the increasing of con- tact area at sheet/sheet interface by the increasing pitting hole diameter at the electrode tip is one of the major causes for worse and worse welding quality durin RSW of aluminum alloys.

An Experimental Evaluation of the Constant β Relating the Contact Stiffness to the Contact Area in Nanoindentation

ABSTRACTMeasurements of mechanical properties by nanoindentation with triangular pyramidal indenters like the Berkovich rely heavily upon the relationship between the contact stiffness, S, the contact area, A, and the reduced elastic modulus, Er. This relationship is often written in the form S = 2βEr(A/π)1/2, where β is a constant that depends on the geometry of the indenter. Although the most common values for β used in experimental measurements are 1.000 and 1.034, various theoretical analyses have yielded values as small as 1.00 or as large as 1.2, depending on the assumptions made to model the deformation. Here, we explore the most appropriate value of β by performing careful experiments in fused quartz with thin gold coatings applied to the surface to reveal the actual contact area when observed in the scanning electron microscope. Experiments were performed not only with the Berkovich indenter, but with five other three-sided pyramidal indenters with centerline-to-face angles ranging from 35.3° (cube corner) to 85°. Results are discussed as they apply to obtaining accurate measurements of mechanical properties by nanoindentation.

Dynamic strength of anisotropic conductive joints in flip chip on glass and flip chip on flex packages

The work presented in this paper focuses on the behavior of anisotropically conductive film (ACF) joint under the dynamic loading of flip chip on glass (COG) and flip chip on flexible (COF) substrate packages. Impact tests were performed to investigate the key factors that affect the adhesion strength. Scanning electron microscopy (SEM) was used to evaluate the fractography characteristics of the fracture. Impact strength increased with the bonding temperature, but after a certain temperature, it decreased. Good absorption and higher degree of curing at higher bonding temperature accounts for the increase of the adhesion strength, while too high temperature causes overcuring of ACF and degradation at ACF/substrate interface––thus decreases the adhesion strength. Higher extent of air bubbles was found at the ACF/substrate interface of the sample bonded at the higher temperature. These air bubbles reduce the actual contact area and hence reduce the impact strength. Although bonding pressure was not found to influence the impact strength significantly, it is still important for a reliable electrical interconnect. The behaviors of the conductive particles during impact loading were also studied. From the fracture mode study, it was found that impact load caused fracture to propagate in the ACF/substrate interface (for COG packages), and in the ACF matrix (for COF packages). Because of weak interaction of the ACF with the glass, COG showed poor impact adhesion.

Fundamentals of Surface Mechanics with Applications, Second Edition. Mechanical Engineering Series

Fundamentals of Surface Mechanics with Applications, Second Edition. Mechanical Engineering Series

A generalized analytical model for the elastic deformation of an adhesive contact between a sphere and a flat surface

A new method to calculate the elastic deformation of a sphere on a flat surface is presented. The model considers the influence of short-range as well as long-range attractive forces both inside and outside the actual contact area. In contrast to earlier models, this theory describes the nature of these deformations in the intermediate regime between the so-called JKR and DMT limits by simple analytic expressions. Equations for the calculation of the contact radius, the deformation, and the pressure distribution are given. In all equations, the critical force that might vary between the limiting values found in the DMT and the JKR model acts as transition parameter.