Frictional energy dissipation in contact of nominally flat rough surfaces under harmonically varying loads

If the nominal contact tractions at an interface are everywhere below the Coulomb friction limit throughout a cycle of oscillatory loading, the introduction of surface roughness will generally cause local microslip between the contacting asperities and hence some frictional dissipation. This dissipation is important both as a source of structural damping and as an indicator of potential fretting damage. Here we use a strategy based on the Ciavarella-Jäger superposition and a recent solution of the general problem of the contact of two half spaces under oscillatory loading to derive expressions for the dissipation per cycle which depend only on the normal incremental stiffness of the contact, the external forces and the local coefficient of friction. The results show that the dissipation depends significantly on the relative phase between the oscillations in normal and tangential load—a factor which has been largely ignored in previous investigations. In particular, for given load amplitudes, the dissipation is significantly larger when the loads are out of phase. We also establish that for small amplitudes the dissipation varies with the cube of the load amplitude and is linearly proportional to the second derivative of the elastic compliance function for all contact geometries, including those involving surface roughness. It follows that experimental observations of less than cubic dependence on load amplitude cannot be explained by reference to roughness alone, or by any other geometric effect in the contact of half spaces.     

Physics-based modeling for partial slip behavior of spherical contacts

A physics-based modeling approach for partial slip behavior of a spherical contact is proposed. In this approach, elastic and elastic–plastic normal preload and preload-dependent friction coefficient models are integrated into the Cattaneo–Mindlin partial slip solution. Partial slip responses to cyclic tangential loading (fretting loops) obtained by this approach are favorably compared with experiments and finite element results from the literature. In addition to load-deformation curves, tangential stiffness of the contact and energy dissipation per fretting cycle predictions of the models are also provided. Finally, the critical assumptions of elastically similar bodies, smooth contact surface and negligible adhesion, and limitations of this physics-based modeling approach are discussed.     

Experimental simulation of capillary effect on rough flat surfaces

The movement of the liquid column inside the slit was utilized to experimentally simulate the characteristics of the capillary force per unit length for different rough flat surfaces. The movement of the liquid column was achieved by continuously changing the slit interval. The maximum climb height and contact angle of the liquid column were observed during this process to study the relationship between capillary force and contact surface roughness. Based on the assumption that the microstructures on the rough surfaces are of the same form and continuously and uniformly distributed, it is shown that the capillary force per unit length under homogeneous wetting is independent of the roughness. For heterogeneous wetting, the capillary force per unit length is positively correlated with the roughness. The results also indicate that the appearance of “contact line pinning” is caused by insufficient capillary force along the direction of liquid column movement.     

Experimental simulation of capillary effect on rough flat surfaces

The movement of the liquid column inside the slit was utilized to experimentally simulate the character-istics of the capillary force per unit length for differ...     

End effects of nominally two-dimensional thin flat plates

Differences in the structure and dynamics of nominally two-dimensional turbulent wakes are investigated experimentally for a thin flat plate, normal to a uniform flow, with two different end conditions: with and without end plates. Both cases are characterized by Karman-like vortex shedding with broadband low frequency unsteadiness. Both wakes evidence a low frequency flapping motion in addition to the slowly drifting base flow common to cylinder wakes. For the case without end plates, an interaction between the drift motion and the vortex formation process is associated with a much stronger modulation of the quasiperiodic vortex shedding amplitude when compared to the case with end plates where a flapping motion is more strongly expressed. These dynamics underlie structural differences in the mean wake and Reynolds stress fields.     

Finite element modeling of elasto-plastic contact between rough surfaces

This paper presents a finite element calculation of frictionless, non-adhesive, contact between a rigid plane and an elasto-plastic solid with a self-affine fractal surface. The calculations are conducted within an explicit dynamic Lagrangian framework. The elasto-plastic response of the material is described by a J₂ isotropic plasticity law. Parametric studies are used to establish general relations between contact properties and key material parameters. In all cases, the contact area A rises linearly with the applied load. The rate of increase grows as the yield stress σ_y decreases, scaling as a power of σ_y over the range typical of real materials. Results for A from different plasticity laws and surface morphologies can all be described by a simple scaling formula. Plasticity produces qualitative changes in the distributions of local pressures in the contact and of the size of connected contact regions. The probability of large local pressures is decreased, while large clusters become more likely. Loading-unloading cycles are considered and the total plastic work is found to be nearly constant over a wide range of yield stresses.     

Experimental investigation of thermal contact conductance for nominally flat metallic contact

A unique experimental set-up was fabricated to carry out axial heat flow steady state experiments for the assessment of thermal contact conductance (TCC) at the interface of two materials. Three different materials (copper, brass and stainless steel) were selected for the experiments considering their mechanical and thermal properties. Heat transfer experiments were performed in vacuum environment (0.045 torr) to find out solid spot contact conductance for nominally flat surfaces with different surface roughness (1–5 μm) for each specimen under several load conditions (0.6–15 MPa). A precise estimation of TCC for the interface of sets of similar materials was one of the most important results of this research. The effects of the surface roughness, the material properties and the load conditions (nominal interface pressure) have been studied and documented. Furthermore, the experimental results of solid spot contact conductance were compared with four theoretical models, showing their limitations to make a precise estimation of the TCC in the range of the used parameters.     

Quasicontinuum multiscale modeling of the effect of rough surface on nanoindentation behavior

Roughness of surface has as an important influence on identifying the mechanical behavior and performance of crystalline metals. In this study, nanoindentation simulations are conducted by the two dimensional quasicontinuum method to determine the load–penetration response and the critical load associated with the onset of plasticity in rough surfaces of a face-centered cubic single crystal copper. The arithmetic roughness index, ranging between 2 and 13 Å, is used to specify the roughness of surface. Results of indentation with different roughnesses are in good agreement with previous studies for the indenter size of 10–140 Å. The resultant load–penetration scattering, which stems from the roughness, indicates different dislocation nucleation steps, different subsequent dislocations intervals and varying stiffness values of samples. It can be concluded that the surface roughness has a significant effect on the first dislocation emission because of the indenter position and surface interactions beneath it. Moreover, the critical penetration depth for the first dislocation emission increases by the increase of the contact area between the indenter and surface.

     

Elastic contact between nominally plane surfaces in the presence of roughness and adhesion

The solution of the problem of interaction with regard to the forces of adhesive (molecular) attraction of two nominally plane half-spaces one of which is elastic and the surface of the other has a regular relief is presented. The surface mutual approach dependence on the applied nominal pressure and the effective specific work of adhesion are analyzed for various parameters of adhesive interaction and micro-geometry of the surfaces.     

On angular-spectrum representations for scattering by infinite rough surfaces

A plane acoustic wave insonifies an infinite rough surface. The reflected field is written as an angular-spectrum representation (plane-wave expansion), with an unknown amplitude function A. It is pointed out that A must be considered as a generalized function, and not as a continuous function. Various decompositions of A are suggested and analysed. Energy considerations lead to relations between the coefficients in these decompositions, generalizing some known results for scattering by periodic surfaces (gratings). It is shown that the reflected field must include at least one propagating plane wave.     

A comparison of approximate theories for scattering from rough surfaces

Scattering from a perfectly conducting rough interface is developed in terms of a generalized angular spectrum of plane waves which includes both upward and downward traveling waves. This spectral formulation is used to examine the interrelationships between three classical approximate techniques in rough surface scattering, i.e., physical optics, boundary perturbation, and extinction theorem. These methods are also traced to conventional deterministic scattering analysis techniques. In particular, physical optics is related to the Magnetic Field Integral Equation, boundary perturbation is shown to result from the Electric Field Integral Equation subsequent to invoking the Rayleigh Hypothesis, and the extinction theorem is equivalent to the Extended Boundary Condition Method. The capabilities and limitations of these rough surface approximate techniques are developed using the angular spectrum approach, and they are discussed in detail.     

A slip-line plasticity analysis of sliding friction of rough surfaces exhibiting self-affine (fractal) behavior

A plasticity analysis of sliding friction of rough (fractal) surfaces sliding against smooth surfaces was developed based on a slip-line model of a rigid spherical asperity (wear particle) plowing and cutting through a soft semi-infinite medium. Solutions of the fraction of fully plastic asperity microcontacts responsible for the evolution of friction and energy dissipation were obtained in terms of the total normal load (global interference), interfacial adhesion characteristics, topography (fractal) parameters of the hard surface, and elastic–plastic material properties of the soft surface. This was accomplished by incorporating the slip-line model of a single microcontact into a friction analysis of sliding surfaces demonstrating multi-scale roughness. Numerical results provide insight into the effects of global interference (normal load), fractal parameters (surface roughness) of the hard surface, interfacial shear strength (adhesion), and material properties of the soft surface on plastic deformation at the microcontact level, global coefficient of friction, and frictional energy dissipated during sliding.     

Unloading an elastic-plastic contact of rough surfaces

A statistical model for the unloading of elastic-plastic contact of rough surfaces is presented for a single load-unload cycle. The hystereses of load-separation and load real contact area behavior are analyzed for a wide range of surface roughness and loading conditions. The residual topography of the unloaded rough surfaces is also analyzed and the new distribution functions of asperity heights and summit radii of curvature along with a corresponding GW residual plasticity index are presented. A new modified plasticity index (MPI) is suggested which considers the energy dissipation due to unrecovered plastic deformations. This MPI varies from zero for purely elastic contacts to unity for purely plastic contacts and hence, can better define the level of plasticity of contacting rough surfaces compared to the original GW plasticity index.     

Thermal contact conductance of nominaly flat surfaces

The variation of thermal conductance of contact has been investigated as a function of apparent contact pressure experimentally. Experimental data has been obtained for steel, brass, copper and aluminum test pieces having different surface roughness over a wide range of contact pressures. Experimental results are compared with the theoretical predictions of an existing theory. Comparison revealed good agreement of trend with the experimental data, however, numerical values vary widely. Theory can predict the experimental results within an over-all error of less than 35%. An erratum to this article can be found at     

Speckle technique for dynamic drop profile measurement on rough surfaces

A technique has been developed for measuring three-dimensional instantaneous drop profiles on rough surfaces. The surface is illuminated using a laser and images are captured of the resulting speckle pattern with and without the drop in place. The analysis consists of finding the contact line, measuring the deformation of the speckle field caused by refraction of light at the drop surface, then reconstructing the drop using simulated annealing optimization to find the drop shape whose shift vector field best matches the one measured. An error analysis of the technique was performed using a Monte Carlo technique and comparisons to sideview drop images for a large sample of drops. Mean contact angle measurement error was found to be −1.6° with a 1 − σ error bound of −6.9°, +2.0°.     

Anticlastic behavior of flat plates

The purpose of this paper is to show that the readings from strain gages can be used effectively to compute small transverse deflections in a rectangular plate and, further, show that the theory developed by Lamb for the rectangular-plate problem agrees with experiment. A numerical procedure is developed, based on the trapezoidal rule, which determines the transverse deflections from the readings of strain gages mounted to the top and bottom surface of a rectangular plate subjected to large longitudinal curvatures. It is shown using the strain-gage technique that experiment agrees with Lamb's theory forb ² /Rt ratios up to 50.