True Contact Research Articles

Asperity contact theories: Do they predict linearity between contact area and load?

During the last few years, the scientific community has been debating about which theory of contact between rough surfaces can be considered as the most accurate. The authors have been attracted by such a discussion and in this paper try to give their personal thought and contribution to this debate. We present a critical analysis of the principal contact theories of rough surfaces. We focus on the multiasperity contact models (which are all based on the original idea of Greenwood and Williamson (GW) [1966. Proc. R. Soc. London A 295, 300]), and also briefly discuss a relatively recent contact theory developed by Persson [2001. J. Chem. Phys. 115, 3840]. For small loads both asperity contact models and Persson's theory predict a linear relation between the area of true contact and the applied external load, but the two theories differ for the constant of proportionality. However, this is not the only difference between the two approaches. Indeed, we show that the fully calculated predictions of asperity contact models very rapidly deviates from the predicted linear relation already for very small and in many cases unrealistic vanishing applied loads and contact areas. Moreover, this deviation becomes more and more important as the PSD breadth parameter α (as defined by Nayak) increases. Therefore, the asymptotic linear relation of multiasperity contact theories turns out to be only an academic result. On the contrary, Persson's theory is not affected by α and shows a linear behavior between contact area and load up to 10–15% of the nominal contact area, i.e. for physical reasonable loads. The authors also prove that, at high separation, all multiasperity contact models, which take into account the influence of summit curvature variation as a function of summit height, necessarily converge to a (slightly) improved version of the GW model, which, therefore, remains one of the most important milestones in the field of contact mechanics of rough surfaces.

Nanoindentation-derived elastic modulus of an amorphous polymer and its sensitivity to load-hold period and unloading strain rate

An amorphous polymer was contacted by a Berkovich indenter using the same loading history but with four different unloading rates following a wide range of load-hold time periods. The strain-rate sensitivity index of the creeping solid was determined at each load-hold period based on two readily determinable parameters, which are the effective contact stiffness and strain rate at the onset of unloading. The measured strain-rate sensitivity index was found to increase with decreasing load-hold period, suggesting that the elastic moduli of the amorphous polymers determined by nanoindentation (together with the true contact area) depends significantly on the selection of the load-hold period. The rheological condition of the creeping solid under constant load changes substantially with time to affect the subsequent unloading recovery process. It is therefore advisable to control not only the unloading strain rate but also the load-hold period when testing time-dependent materials.

Analyzing friction and scratch tests without in situ observation

This paper presents an algorithm which allows one to estimate the elastic recovery in a scratch test without in situ observation of the true contact area between the tip and the surface. The algorithm is based on determination of the threshold normal forces at the end of elasticity and beginning of plasticity by measurement of the width of the residual groove left on the surface. The elastic recovery may then be estimated and hence the local friction and contact pressure. The estimated local friction lies between the experimental apparent friction and the true local friction derived from a flow line model and independent of the model. This analytical method is especially suitable for analysis of the scratching of polymer surfaces.

Wetting of pure aluminum and selected alloys on polycrystalline alumina and sapphire

Using a modification of the dispensed drop method to measure true contact angles of readily oxidizing metals and alloys, the wettability of polycrystalline alumina and A-plane sapphire by pure aluminum and selected aluminum alloys was investigated. The experiments were performed under high vacuum in a horizontal tube furnace. The experimental setup produces a sessile drop free of its natural surface oxide layer minimizing flight time of the drop, and maintaining a drop impingement on the substrate. The experiments showed that there is no significant difference in the wettability of alumina and sapphire by aluminum as well as Al–11.5Si, Al–1Mg and Al–7Cu. On both substrates, aluminum shows a strong increase in contact angle well into the non-wetting regime just above the melting point. The wetting behavior of Al–7Cu on both substrates is slightly but significantly reduced in comparison to pure aluminum. The contact angles of Al–1Mg and Al–11.5Si remain rather constant between the respective liquidus temperatures of the alloys and 800 °C with θ (Al–1Mg) < θ (Al–11.5Si). Only Al–7Cu above 730 °C achieves the contact angle interval of 70–86° suggested to be most beneficial in terms of aluminum foam stabilization.

Sliding-induced adhesion of stiff polymer microfibre arrays. I. Macroscale behaviour.

Gecko-inspired microfibre arrays with 42 million polypropylene fibres cm(-2) (each fibre with elastic modulus 1 GPa, length 20 microm and diameter 0.6 microm) were fabricated and tested under pure shear loading conditions, after removing a preload of less than 0.1 N cm(-2). After sliding to engage fibres, 2 cm2 patches developed up to 4N of shear force with an estimated contact region of 0.44 cm2. The control unfibrillated surface had no measurable shear force. For comparison, a natural setal patch tested under the same conditions on smooth glass showed approximately seven times greater shear per unit estimated contact region. Similar to gecko fibre arrays, the synthetic patch maintains contact and increases shear force with sliding. The high shear force observed (approx. 210 nN per fibre) suggests that fibres are in side contact, providing a larger true contact area than would be obtained by tip contact. Shear force increased over the course of repeated tests for synthetic patches, suggesting deformation of fibres into more favourable conformations.

A measurement study of a pressure transducer subjected to water drop impact

Numerous numerical methods exist that can be used to solve fluid/structure interactions during hydrodynamic impacts on deformable structures. In order to validate these methods, experimental references are needed and the use of pressure transducers appears to be quite sensible and natural. But the objectivity of such a pressure measurement may sometimes be questioned (bias due to the presence of the transducer itself, which has its own dynamic natural response). Such a systematic error is difficult to notice when structural tests are concerned, other uncertainties concerning the experimental configuration being possibly called for as an obvious explanation of any differences between test and simulation results. The purpose of the present paper is to propose a methodology of exploitation of dynamic tests responses, dedicated to the elimination of such measurement errors if needed, in order to get the true contact pressure that deformable structures have to support during hydrodynamic impacts. For that purpose, the dynamic calibration of a pressure transducer is performed using a shock tube, and a dynamic correction function is established, first theoretically, then practically. The obtained function is then applied on existing test results coming from water drop impacts onto the studied pressure transducer, in order to calculate the corresponding contact pressure on a flat panel, and to compare these latter data to different FE simulation solutions.

Compaction behavior of roller compacted ibuprofen

The effect of roller compaction pressure on the bulk compaction of roller compacted ibuprofen was investigated using instrumented rotary tablet press. Three different roller pressures were utilized to prepare granules and Heckel analysis, Walker analysis, compressibility, and tabletability were performed to derive densification, deformation, course of volume reduction and bonding phenomenon of different pressure roller compacted granules. Nominal single granule fracture strength was obtained by micro tensile testing. Heckel analysis indicated that granules prepared using lower pressure during roller compaction showed lower yield strength. The reduction in tabletability was observed for higher pressure roller compacted granules. The reduction in tabletability supports the results of granule size enlargement theory. Apart from the granule size enlargement theory, the available fines and relative fragmentation during compaction is responsible for higher bonding strength and provide larger areas for true particle contact at constant porosity for lower pressure roller compacted granules. Overall bulk compaction parameters indicated that granules prepared by lower roller compaction pressure were advantageous in terms of tabletability and densification. Overall results suggested that densification during roller compaction affects the particle level properties of specific surface area, nominal fracture strength, and compaction behavior.

Influence of Ga Content on Electrochemical Behavior of Mg-5 at%Hg Anode Materials

The effects of Ga content on the electrochemical behavior of Mg-5 at%Hg alloys which contain a small amount of Ga was investigated by the measurement of polarization curves and galvanostatic test. The microstructure of the alloys and the surface of the specimens corroded in galvanostatic test were observed by using scanning electron microscopy, energy spectrum analysis and X-ray diffraction analysis. It can be concluded that with the content of Ga increasing, the alloys come into Mg-Mg 3 Hg, Mg-Mg 7.2 (Hg, Ga) 2.8 and Mg-Mg 5 Ga 2 binary phase fields sequentially. The best electrochemical activity occur in the Mg-5 at%Hg -1 at%Ga alloy, with open circle potential -2.124V and mean potential -1.992 V. The corrosion resistance of the alloys is in the sequential order from big to small: Mg-5 at%Hg-5 at%Ga, Mg-5 at%Hg-22 at%Ga, Mg-5 at%Hg-1 at%Ga, Mg-5 at%Hg. The lowest corrosion current density is 0.418 mA·cm -2 . The activation mechanism of the magnesium alloy produced by Hg and Ga was concluded: the dissolution of Hg and Ga atoms leads to the back accumulation of liquid Hg and Ga, which makes a true metallic contact with a-Mg. Magnesium atoms diffuse through the liquid mercury and gallium to form magnesium amalgam and undergo severe oxidation at the amalgam/electrolyte interface. The reaction produces pure Hg and Ga again which continue the activation process.

Mechanical characterization of polymeric films using depth-sensing instrument: Correlation between viscoelastic-plastic properties and scratch resistance

The scratch behavior of polymer films deposited on PMMA substrate by three different coating techniques is investigated by scratch tests using a depth-sensing instrument. Using an improved measurement technique, we develop an advanced methodology based on a more appropriated model that includes an estimation of realistic stress and strain states during scratch tests. The scratch resistance is evaluated by comparing the average contact pressure for which the coating cracks, by taking into account the elastic–plastic behavior of the layer. The proposed model allows the determination of the true contact depth and the elastic recovery at the rear side of the elastic–plastic contact, and thus the true projected contact area between the moving tip and the polymeric surface. This determination depends first on a rheological factor estimated from standard load–displacement curves obtained by nanoindentation and then on the tip geometry. The viscoplacticity index and the activation volume of each type of coating are then determined by nanoscratch. The viscoplasticity index determined during an elastic–plastic contact and the activation volume related to the ductile–brittle transition are discussed as reliable criteria for determining which bilayer system (polymeric film on PMMA substrate) will truly exhibit better wear and scratch resistances in service.

Application of contact theory to metal-metal bonding of silicon wafers

A model is presented which relates the applied load and surface roughness to the integrity of metal-metal wafer-level thermocompression bonds. Using contact theory, the true contact area is calculated as a function of the applied load and surface roughness as characterized using atomic force microscopy. The relationship between the nominal and true contact areas quantifies the effects of applied load and surface roughness on the bond integrity of the bonded wafers as indicated by the dicing yield. Experiments on Cu–Cu bonds show that the true contact area provides a better indicator of bond integrity than either the nominal contact area or applied force, taken together or separately.

Surface energy measurements of coated titanium dioxide pigment

In this study surface energy measurements have been carried out on titanium dioxide pigments coated with different types of organic compounds. The organic coatings investigated were polymethylsiloxane and octyl triethoxy-silane. The level of coating applied was increased from 0.2 up to 1.5 wt%. Contact angles were measured using an advancing sessile drop method. To allow for the fact that measurements were made on pressed discs of particles rather than on a perfectly flat surface, a correction was applied to convert each measured contact angle to the true Young's contact angle. Surface energies were calculated from the corrected contact angles using the Owens and Wendt equation. From the values of surface energy it was possible to determine at what coating level the surface characteristics changed from hydrophilic to hydrophobic and hence when complete coverage had taken place. For both the siloxane and the silane coatings it was found that complete coating coverage occurred at an addition level of around 0.8 wt%. The surface energies of all the coated pigments were found to correlate well with their dispersion behaviour in liquid paraffin.

Use of secondary structural information and Cα-Cα distance restraints to model protein structures with MODELLER

Protein secondary structure predictions and amino acid long range contact map predictions from primary sequence of proteins have been explored to aid in modelling protein tertiary structures. In order to evaluate the usefulness of secondary structure and 3D-residue contact prediction methods to model protein structures we have used the known Q3 (alpha-helix,beta-strands and irregular turns/loops) secondary structure information, along with residue-residue contact information as restraints for MODELLER. We present here results of our modelling studies on 30 best resolved single domain protein structures of varied lengths. The results shows that it is very difficult to obtain useful models even with 100% accurate secondary structure predictions and accurate residue contact predictions for up to 30% of residues in a sequence. The best models that we obtained for proteins of lengths 37, 70, 118, 136 and 193 amino acid residues are of RMSDs 4.17, 5.27, 9.12, 7.89 and 9.69,respectively. The results show that one can obtain better models for the proteins which have high percent of alpha-helix content. This analysis further shows that MODELLER restrain optimization program can be useful only if we have truly homologous structure(s) as a template where it derives numerous restraints, almost identical to the templates used. This analysis also clearly indicates that even if we satisfy several true residue-residue contact distances, up to 30%of their sequence length with fully known secondary structural information, we end up predicting model structures much distant from their corresponding native structures.

Dynamics of Precursors to Frictional Sliding

We measure the spatial and temporal behavior of the true contact area A along a rough spatially extended interface between two blocks in frictional contact. Upon the application of shear the onset of motion is preceded by a discrete sequence of cracklike precursors, which are initiated at shear levels that are well below the threshold for static friction. These precursors arrest well before traversing the entire interface. They systematically increase in length with the applied shear force and significantly redistribute the true contact area along the interface. Thus, when frictional sliding occurs, the initially uniform contact area along the interface has already evolved to one that is highly nonuniform in space.

A Photometric Study of the Near Contact Binary UU Lyncis

The near-contact binary UU Lyn with an F3V-type primary was observed in 2005 and 2006. With the latest version of the Wilson-Devinney code, the photometric elements were computed. The results reveal that UU Lyn is a marginal contact system with a large temperature difference of about 1900 K between the primary and secondary components. All available eclipse times, including new ones, were used in the analysis. The results show that the orbital period of this system undergoes a continuous decrease at a rate of dP/dt = -1.84 x 10(-8) d yr(-1). With the period decrease, UU Lyn may evolve from the present short-period marginal contact system into a contact system with true thermal contact. This target might just be undergoing the cycles predicted by the theory of thermal relaxation oscillations (TRO). It is an interesting example resembling BL And, GW Tau, ZZ Aur, KQ Gem, CN And and AD Cnc, that lie in the key evolutionary stage.

Effects of Nanometer-Scale Surface Roughness and Applied Load on the Bond Strength and Contact Resistance of Cu-Cu Bonded 3D ICs

AbstractThe effects of total surface roughness of Cu bond layers and applied load during bonding on the bond strength and the contact resistance of the bonded interface were studied for three-dimensional (3D) devices. The 3D structures were fabricated by thermocompression bonding of two wafers, each fabricated with a Cu damascene process. The average bond strength of the samples was found to increase with increasing load, and with decreasing roughness. On the other hand, the average contact resistance increased as the total surface roughness of the bonded interface increased, as well as when the applied load decreased. The increase in bond strength (and also the dicing yield) is related to a smaller true contact area, which can be estimated using a model based on contact mechanics theory. The theory takes into account the roughness of the bonded surface, the applied load during bonding and the nominal bond area. A contact resistance model can also be used to estimate the contact resistance of bonded interfaces based on their true contact area. However, within each set of measurements, a significant spread about the average value of bond strength and contact resistance was observed, suggesting issues of contact and bonding non-uniformity of the wafers. Nonetheless, the contact resistance values given by the model were in good agreement with the minimum values observed in experiments, which may represent the ideal cases of bonding of rough surfaces. Our results show that the impact of surface roughness and applied load on the contact resistance of Cu-Cu thermocompression bonds can be quantified experimentally, and understood in the context of established theory for contact mechanics.

Optical indentation microscopy – a new family of instrumented indentation testing

A novel test system/analysis is proposed for determining the in situ true contact area during indentation loading/unloading by the use of an optically transparent indenter. A sapphire planoconvex lens as a spherical indenter or a diamond tetrahedral pyramid indenter is optically coupled with a microscope system equipped with a CCD video camera. This indentation microscope enables us to directly view the in situ contact impression, along with the measurement of the hysteresis curve of the indentation load-penetration depth relation. The in situ contact area can be readily determined from each frame of the video movie using an image analyzer that is synchronized with the indentation load. Accordingly, the mechanical properties including the true indentation stress–strain curve can be evaluated directly from these observable parameters without using any assumptions that have always been required for estimating the contact area in the conventional depth-sensing indentation apparatus.

Wear of a single asperity using Lateral Force Microscopy

This report describes an observation of alternating transitions between linear (Amontons) and non-linear friction-load behavior during Lateral Force Microscope experiments using a silicon tip sliding on a quartz surface. Initially, a transition from linear to non-linear behavior was attributed to nanoscale ‘running-in’ of the tip to form a single contact junction at the interface. Once this had occurred, a non-linear relationship between friction and applied load was observed during a number of loading and unloading cycles. For higher compressive loads, a further transition to a more linear friction-load behavior was attributed to nanoscale wear in the contact zone. Notably, when applied load was reduced below this ‘high-load’ transition point, the same non-linear friction-load behavior was again observed, but with a larger (friction per load) magnitude than seen previously. This cycle was repeated five times in these experiments, and each time, switching between non-linear and linear friction-load behavior occurred, along with a progressive increase in friction (per load) each time load was reduced below the transition point. The progressive increase in friction is attributed to an increased area of contact, caused by nanoscale wear at higher applied loads. An increase in tip size was confirmed by tip profiling before and after experiment. By progressively wearing the asperity at higher loads, the (interfacial or true) contact area, A, between the surfaces could be progressively increased, and as a result, a progressive increase in interfacial sliding friction, Ff, was obtained at lower loads (according to Ff = τA).

The activation of aluminium by mercury ions in non-aggressive media

The presence of Hg at concentration less than 300 ppm in Al base alloys causes their passivation breakdown. On alloys used as sacrificial anodes, it causes a major lowering (>0.3 V) in their operational potential in chloride media. Mercury as trace constituent in the natural gas stream causes severe damage to cryogenic heat exchangers. The present paper presents evidences of the mechanism by which mercury produces its pronounced effect in aqueous non-aggressive media. The work was carried out using pure (99.99%) aluminium and mercury (II) acetate solutions of different concentrations and pH. Open circuit potential–time responses were obtained. The surface effects were followed by means of scanning microscopy and EDAX/X-Ray analysis. The results demonstrate that immediately after immersion, the initial air-formed oxide film underwent a dynamic crack–healing process at flaws in the film, possible associated to grain boundaries. The subsequent healing process, if any, depends on the media composition. Thus, in this special case, Hg 2+ ions can be directly reduced on the bare aluminium, reaching a true metallic contact, and initiating surface diffusion. This enables the formation of an amalgam. Aluminium atoms diffuse through the liquid mercury and undergo oxidation at the amalgam/electrolyte interface. This process is responsible for the oxide detachment (by undermining) and the attack morphology (i.e., wide cavities). The presence of aggressive anions is not needed to initiate activation.

Friction and Contact Resistance through True Contact Interface

The main factor determining for both friction and contact resistance is the true contact area in the contact interface. Contact resistance depends on the size of the true contact area and contaminant films interposed between the contact areas of the interface. Moreover, friction force also depends on the true contact area. In particular, the formation of metallic junctions in the true contact area strongly effects the friction force. Therefore, since both electrical contact and friction force are related to the size of the true contact area, the contact resistance and friction force are considered to be interrelated through true contact areas. For electromechanical devices with sliding contacts such as connector and sliding switches, the contact resistance and friction are important characteristics. In order to obtain low contact resistance, contact load should be higher, but the friction force increases. These are opposite-side problems. In this study, as the contact resistance and friction occur in the same true contact area, the relationship between the contact resistance and friction was expressed in an equation. Moreover, this relationship was examined experimentally on a variety of contact surfaces under different surface conditions.

Advancing and Receding Motion of Droplets on Ultrahydrophobic Post Surfaces

We have fabricated a range of silicon post surfaces where post width and spacing have been systematically varied. As one subset, we have generated surfaces where the post spacings in x and y assume different values. On these surfaces, the dynamic contact angles become anisotropic. A fluoropolymer monolayer is photochemically attached to the microstructured silicon, leading to the appearance of ultrahydrophobic properties. On one side, the advancing contact angles on these surfaces are not affected by variations in the geometric parameters. This furthers the conclusion that, during the advancing motion, a true contact angle of 180 degrees is reached. On the other side, the receding angles are strongly influenced by the post size and spacing. We quantitatively analyze this dependence and relate variations in the receding angle to the shape and movement of the three-phase contact line. It is suggested that during the receding motion the meniscus successively dewets from one post at a time, with a step function running along the contact line until it has receded from a row of posts over its entire length.