Growth Of Contact Area Research Articles

Mathematical model of the human ankle joint

It has been suspected that the mechanical environment in which a particular joint functions has an effect on the initiation or progression of degenerative joint disease. The objective of this study is to define the mechanical environment of the ankle joint, specifically, the contact areas and pressure distributions, through the development and analysis of a simplified mathematical model. Since the state of pressure across articular surfaces during function is influenced by joint incongruity, cartilage thickness profile and the geometry of the opposing surfaces, these factors have been incorporated into the model formulation. Mathematical analysis of the model has resulted in pressure distributions in both the anterior-posterior and medial-lateral directions and contact area growth plots which correlate well with observed ankle contact patterns obtained from in vitro investigations. The significance of joint incongruity to these pressure distributions and to the relative immunity of the ankle joint to primary osteoarthritis is discussed.

The real area of contact between a rough and a flat surface

The shape, size, distribution and growth of individual micro-contact spots between a rough aluminium surface and a flat silver-steel surface pressed together under normal loads have been examined by the Nomarski interference technique. The contact pressure was varied from zero to one-third of the micro-hardness of the softer material. The smallest contact spots were approximately circular and measured 3 to 4 μm in diameter, but became elliptical as they grew in size. The maximum number of contact spots (~ 10 8 per m 2 of nominal contact area) was encountered at a dimensionless loading ( P M ) approximately equal to 2.5 × 10 −2. Two distinct modes of plastic deformation of surface asperities occurred. For low loads, the true contact area, A, was proportional to applied load, W, and the mean flow pressure at the interface equalled the Mallock hardness ( i.e. M 2 ), but at loadings exceeding 2.5 × 10 −2, A became proportional to W 0.67. For the latter region, the interaction of the zones of influence of the asperity bases led to an increasing resistance to further deformation. For the tested models (⋍0.8 mm in extent) the growth in total contact area occurred predominantly by increases in the areas of the individual micro-contact spots. A significant contribution due to the emergence of fresh contact spots was only exhibited at light loads, and never exceeded 28 %. of the increase for any increment in static load.

Apparatus for Environmental Friction-Adhesion Studies Using Ultrahigh Vacuum Techniques

An apparatus is described for the real-time analysis of sliding friction and normal force adhesion phenomena using ultrahigh vacuum techniques. Developed for the purpose of investigating the effects of surface cleaning, temperature, and deliberate gaseous contamination on the adhesion behavior of selected candidate materials for use in the NERVA nuclear rocket engine program, the system was designed to measure contact resistance by a four terminal ac (constant current-voltage drop) instrument calibrated in resistance. Using a torsion balance technique the relationship between the normal compressive load applied across crossed rod samples and the resultant contact resistance is used to ascertain the extent of contact area growth under anticipated service conditions. The apparatus can accommodate sample temperatures to 3000 K and maintain gaseous environments from pressures of 1 atm to 10−11 Torr. Contact resistance in the range 103–10−4 Ω, normal compressive loads from 1 mg to 600 g, and/or tangential loads to 155 g are displayed continuously in an analog fashion. Contact resistance data taken for a variety of metallic, intermetallic, and graphitic materials combinations have indicated the rate and extent of contact area growth to be expected during service and the effectiveness of gaseous lubricants in preventing adhesion. Typical data are presented for the materials combination 440C stainless steel vs 440C stainless steel.

Adhesion of Metallic Bodies Initiated by Physical Contact

Metallic adhesion produced by surfaces compression, discussing asperities plastic deformation and macrodeformation caused by contact area growth

Deformation of a plastic wedge by a rigid flat die under the action of a tangential force

A slip-line field has been constructed for the deformation of a rigid perfectly-plastic wedge compressed by a flat rigid die and subsequently sheared by a force acting tangentially to the face of the die. An associated velocity field is suggested. Consistency between the slip-line field, the velocity field and the changing profile of the wedge as deformation proceeds is closely, though not exactly, preserved. The progressive deformation has been found, using these fields, by an incremental graphical construction. The deformation and the growth of the area of contact between the wedge and the die face under the action of a constant normal force and increasing tangential force are found to agree well with experiment. The theoretical contact area growth supports Tabor's empirical expression for ‘junction growth’ in the build-up of static friction between metallic surfaces.

Electrical conduction in solids III. The contact of iron surfaces

Although the theoretical steady-state equilibrium relationship between potential and temperature in an electrically heated conductor has been established since the beginning of the century (Kohlrausch 1900) the important case in which equilibrium breaks down has until recently been overlooked. In part I (Bowden & Williamson 1958) this was discussed experimentally with reference to gold contacts; in part II (Greenwood & Williamson 1958) it wasshown theoretically that for suitable materials, equilibrium is only possible when the current is below a critical value. In the earlier experiments the metal contacts were free from contaminating films: this paper will describe the behaviour of iron surfaces which are contaminated by an oxide layer. It will be shown as before that conditions become unstable when the current is too large. Short pulses of current were passed through iron contacts. Currents below a critical size were found to have no effect; larger currents caused a growth of contact area and permanent decrease in contact resistance. When no contaminating films were present the product of the final contact resistance R 0 and the current I was constant. For iron contacts coated with varying amounts of oxide it was found that, instead of remaining constant, IR 0 increased steadily with the amount of contamination. The value observed for the cleanest contacts was close to the theoretical estimate for iron, while for badly contaminated ones it was two to three times as large. Experiments in which the length of the current pulse was varied demonstrate the dependence of the rate of heating on the contact area. Direct evidence for the unstable temperature rise is given by oscilloscope records of transient voltage across the contact during the passage of a current pulse. The observations are compared with a new theoretical estimate of the rate of temperature development in non-equilibrium conditions.