Rolling contact problem involving surface roughness

Rolling contact problems for two elastic rollers are investigated. The surface micro-roughness is taken into account. For modelling of boundary roughness a new model is proposed. The problem is solved by the boundary integral method. Presented results show the effect of the roughness on the shearing traction and on the creepforce–creep relation.     

Effects of oxidation and surface roughness on contact angle

Contact angle is known to be a parameter that effects boiling. This study was undertaken to measure contact angle of high and low surface tension fluids on copper and aluminum surfaces.Data were taken for polished, oxidized, and rough surfaces. A simple, yet fairly accurate method of measuring the static equilibrium contact angle of a solid/liquid interface is presented. The principles of a line light source and tilting plate were modified and then combined in the design of this apparatus. The angles obtained and their variation with the solid surface properties were in good agreement with previously published data. The contact angle of distilled water o of the organic fluids and refrigerants tested were in the range of 2–5°. Roughness and oxidation reduce the contact angle. If the depth of the roughness is less than 0.5 μm contact angle. The apparatus is fairly simple in construction, is inexpensive, and has good reproductibity. The measured angles were then compared to those measured with the sessile drop method.     

A mechanical model for the adhesive contact with local sliding induced by a tangential force

Adhesion has been demonstrated to play an important role in contact and friction between objects at small scales. While various models have been established for adhesive contact under normal forces, studies on the adhesive contact under tangential force have been far fewer, which if any, are mostly confined to the non-slipping situations. In the present work, a model has been proposed for adhesive contact with local sliding under tangential forces. Herein, the onset of local sliding in adhesive contact has been addressed by assuming the nucleation of dislocations. By analogy with the emission of dislocations at a crack tip, the critical tangential force for the onset of sliding has been determined, and its effect on the evolution of contact size has also been studied. Comparison with relevant experiments has verified the validity of the present model.     

Micro-plasticity of surface steps under adhesive contact: Part II—Multiple-dislocation mediated contact hardening

The study of micro-plastic behavior of rough surface contacts is the critical link towards a fundamental understanding of contact, friction, adhesion, and surface failures at small length scales. In the companion paper (Yu, H.H., Shrotriya, P., Gao, Y.F., Kim, K.-S., 2007. Micro-plasticity of surface steps under adhesive contact. Part I. Surface yielding controlled by single-dislocation nucleation. J. Mech. Phys. Solids 55, 489–516), we have studied the onset of surface yielding due to single-dislocation nucleation from a stepped surface under adhesive contact. Here we analyze the contact hardening behavior due to multiple dislocations in a two-dimensional dislocation model. Continuum micro-mechanical analyses are used to derive the configurational force on the dislocation, while a modified Rice–Thomson criterion is used to model dislocation nucleation. Dislocations nucleated from the surface step are stabilized and pile up as a result of the balance between the resolved driving force and the non-zero lattice resistance in the solid. The dislocation pileup will exert a strong back stress to prevent further dislocation nucleation and thus lead to the contact hardening behavior, the degree of which depends on the slip-plane orientation. Particularly, we find that dislocation interactions between two slip planes can make the contact loading order-of-magnitude easy to nucleate multiple dislocations, which is thus named “latent softening”. A mechanistic explanation shows that the latent softening is closely related to the stress-concentration mode mixity at the surface step. Dislocation nucleation will modify the geometric characteristics of the surface step, so that the contact-induced stress state near the step, as described by the mode mixity, changes, which influences the subsequent dislocation nucleation. Our calculations show that the dislocation pileup on one slip plane can even cause the spontaneous dislocation nucleation on the other slip plane without further increase of the contact load. Furthermore, it is found that rough surface contacts at small length scale can lead to the dislocation segregation and the formation of a surface tensile sub-layer. The discrete-dislocation model presented here and in the companion paper provides novel insights in bridging the atomistic simulations and continuum plastic flow analysis of surface asperity contact.     

Micro-plasticity of surface steps under adhesive contact: Part I—Surface yielding controlled by single-dislocation nucleation

Mechanics of nano- and meso-scale contacts of rough surfaces is of fundamental importance in understanding deformation and failure mechanisms of a solid surface, and in engineering fabrication and reliability of small surface structures. We present a micro-mechanical dislocation model of contact-induced deformation of a surface step or ledge, as a unit process model to construct a meso-scale model of plastic deformations near and at a rough surface. This paper (Part I) considers onset of contact-induced surface yielding controlled by single-dislocation nucleation from a surface step. The Stroh formalism of anisotropic elasticity and conservation integrals are used to evaluate the driving force on the dislocation. The driving force together with a dislocation nucleation criterion is used to construct a contact-strength map of a surface step in terms of contact pressure, step height, surface adhesion and lattice resistance. Atomistic simulations of atomic surface-step indentation on a gold (1 0 0) surface have been also carried out with the embedded atom method. As predicted by the continuum dislocation model, the atomistic simulations also indicate that surface adhesion plays a significant role in dislocation nucleation processes. Instabilities due to adhesion and dislocation nucleation are evident. The atomistic simulation is used to calibrate the continuum dislocation nucleation criterion, while the continuum dislocation modeling captures the dislocation energetics in the inhomogeneous stress field of the surface-step under contact loading. Results show that dislocations in certain slip planes can be easily nucleated but will stay in equilibrium positions very close to the surface step, while dislocations in some other slip planes easily move away from the surface into the bulk. This phenomenon is called contact-induced near-surface dislocation segregation. As a consequence, we predict the existence of a thin tensile-stress sub-layer adjacent to the surface within the boundary layer of near-surface plastic deformation. In the companion paper (Part II), we analyze the surface hardening behavior caused by multiple dislocations.     

Mechanics of adhesive contact at the nanoscale: The effect of surface stress

At small length scales, the adhesion and surface effect are of great significance, both of which play important roles in the contact between two elastic solids. In this study, the classical Johnson–Kendall–Roberts (JKR) adhesive contact theory is generalized to the nanoscale at which the surface effect is considered. The influence of the surface stress on the JKR adhesive contact is investigated by employing the non-classical Boussinesq fundamental solutions. It is found that, compared with the classical theory, the pull-off force increases while the critical contact radius decreases as a result of the surface effect. Numerical results show that a relative error of 10% can be introduced in the pull-off force when the indenter radius is less than 20 nm. A detailed theoretical analysis of this interesting phenomenon is presented based on dimensional analysis, and two scaling laws for the adhesive contact at the nanoscale are constructed. These two new scaling laws reveal that the pull-off force is relevant to the elastic properties of the bulk materials, which is different from the classical adhesive contact theory. The present work is promising for the engineering applications in micro-electro-mechanical systems (MEMS) and nano-intelligent devices.     

Large-scale spanwise periodicity in a turbulent boundary layer induced by highly ordered and directional surface roughness

The effect of converging–diverging riblet-type surface roughness (riblets arranged in a ‘herringbone’ pattern) are investigated experimentally in a zero pressure gradient turbulent boundary layer. For this initial parametric investigation three different parameters of the surface roughness are analysed in detail; the converging–diverging riblet yaw angle α, the streamwise fetch or development length over the rough surface F_x and the viscous-scaled riblet height h⁺. It is observed that this highly directional surface roughness pattern induces a large-scale spanwise periodicity onto the boundary layer, resulting in a pronounced spanwise modification of the boundary layer thickness. Hot-wire measurements reveal that above the diverging region, the local mean velocity increases while the turbulent intensity decreases, resulting in a thinner overall boundary layer thickness in these locations. The opposite situation occurs over the converging region, where the local mean velocity is decreased and the turbulent intensity increases, producing a locally thicker boundary layer. Increasing the converging–diverging angle or the viscous-scaled riblet height results in stronger spanwise perturbations. For the strongest convergent–divergent angle, the spanwise variation of the boundary layer thickness between the diverging and converging region is almost a factor of two. Such a large variation is remarkable considering that the riblet height is only 1% of the unperturbed boundary layer thickness. Increasing the fetch seems to cause the perturbations to grow further from the surface, while the overall strength of the induced high and low speed regions remain relatively unaltered. Further analysis of the pre-multiplied energy spectra suggests that the surface roughness has modified or redistributed the largest scale energetic structures.     

Modeling the macroscopic behavior of two-phase nonlinear composites by infinite-rank laminates

A new approach is proposed for estimating the macroscopic behavior of two-phase nonlinear composites with random, particulate microstructures. The central idea is to model composites by sequentially laminated constructions of infinite rank whose macroscopic behavior can be determined exactly. The resulting estimates incorporate microstructural information up to the two-point correlation functions, and require the solution to a Hamilton–Jacobi equation with the inclusion concentration and the macroscopic fields playing the role of ‘time’ and ‘spatial’ variables, respectively. Because they are realizable, by construction, these estimates are guaranteed to be convex, to satisfy all pertinent bounds, to exhibit no duality gap, and to be exact to second order in the heterogeneity contrast. Sample results are provided for two- and three-dimensional power-law composites, and are compared with other homogenization estimates, as well as with numerical simulations available from the literature. The estimates are found to give physically sensible predictions for all the cases considered, even for extreme values of the nonlinearity and heterogeneity contrast. Interestingly, in the case of isotropic porous materials under hydrostatic loadings, the estimates agree exactly with standard Gurson-type models for viscoplastic porous media.     

On the macroscopic dynamics induced by a model wave-particle collision operator

The macroscopic dynamics of a kinetic equation involving a model wave-particle collision operator of plasma physics is investigated. The Chapman-Enskog asymptotics is first considered in the framework of a hydrodynamic scaling. The obtained macroscopic model still involves a kinetic variable, the particle energy in the rest frame of the fluid, but shares similarities with the compressible Navier-Stokes equation of gas dynamics. Then a diffusive scaling is examined under the hypothesis of small perturbations of a global equilibrium. In this case, the macroscopic model couples the usual incompressible Navier-Stokes with a diffusion equation for the energy distribution function of the particles, constrained by an extended version of the Boussinesq relation. In both cases, the effect of a Lorentz force term is developed, in the perspective of plasma physical modelling. Received June 16, 1997     

Disturbances of a three-dimensional boundary layer generated by surface roughness

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 129–134, September–October, 1989.     

泡沫铝弹性接触静力学行为的多尺度模拟

对泡沫铝的宏、细观组织结构,基于MC方法建立与材料制备工艺相应的数值模型,作为多尺度模拟的前提.通过计算模拟和统计分析大量数值试样的力学性能,得到了不同制备工艺制得的泡沫铝的弹性模量的分散性特点.借鉴代表性体积单元方法(RVE)和完全多格方法(FMG)的思想,采用基于"巨原子"模型的多尺度关联方法,并以简化的物理势场描述巨原子问的关系,设计了原子-巨原子-有限元多尺度算法.通过算例探讨了与理想刚性平面接触时,泡沫铝接触表面的应力集中情况.     

Evolution of vortex structure in boundary layer transition induced by roughness elements

The particle image velocimetry (PIV) and hydrogen-bubble visualization technique are used to investigate the flat-plate boundary layer transition induced by an array of roughness elements. The streamwise evolutions of the mean and fluctuation velocity are analyzed, and the critical Reynolds number Re _k,c is determined between 339 and 443 under current experimental setup. The hairpin vortices shed from supercritical roughness elements are visualized by swirling strength, in which two pairs of counter-rotating vortices can be observed: one vortex pair is the manifestation of the neck of the hairpin vortices shed from the top of the roughness; the other vortex pair, which originates from the lower part of the roughness, comes from the streamwise vortices that are constantly perturbed by the hairpin vortex shedding.     

Analysis of the adhesive contact of confined layers by using a Green's function approach

The authors develop a numerical procedure to analyze the adhesive contact between a soft elastic layer and a rough rigid substrate. The solution of the problem, which belongs to the class of the free boundary problems, is obtained by calculating the Green's function which links the pressure distribution to the normal displacements at the interface. The problem is then formulated in the form of a Fredholm integral equation of the first kind with a logarithmic kernel, and the boundaries of the contact area are calculated by requiring that the energy of the system is stationary. The methodology is relatively simple and easy to implement in a numerical code. It has been utilized to analyze the adhesive properties of a confined layer in contact with a wavy rigid substrate as a function of thickness, applied stress or penetration. It is shown that reducing the thickness of the slab reduces the effective energy of adhesion, i.e. the work needed to separate the bodies, but nevertheless increases the adherence force between the slab and the substrate. However, thinning the slab also increases the confinement of the system and therefore increases the negative hydrostatic pressure in the layer. This, in turn, may produce cavitation. When this happens the rupture of the adhesive bond does not occur through interfacial crack propagation but, by the growth of new interfacial voids or cavities.     

Stress analysis of a layered elastic solid in contact with a rough surface exhibiting fractal behavior

A contact stress analysis is presented for a layered elastic half-space in contact with a rough surface exhibiting self-affine (fractal) behavior. Relationships for the mean contact pressure versus representative strain and the real half-contact width versus elastic properties of the layer and the substrate, asperity radius, layer thickness, and truncated half-contact width were derived from finite element simulations of a layered medium compressed elastically by a rigid cylindrical asperity. These relationships were incorporated in a numerical algorithm that was used to obtain the contact pressure distributions and stresses generated by the asperity contacts formed at the interface of the layered medium and the fractal surface. Analytical solutions illustrate the significance of the elastic material properties, layer thickness, and surface topography (roughness) on global parameters such as normal load and real contact area. Results for the contact pressure distribution and the surface and subsurface stresses provide insight into the initiation of yielding and the tendency for cracking in the layered medium. It is shown that cracking at the surface and the layer/substrate interface is more likely to occur in the case of a stiff layer, whereas surface cracking is more prominent for a relatively compliant layer.     

Flow instability in the laminar boundary layer separation zone created by a small roughness element

The development of disturbances of the laminar flow in the separation zone behind a surface projection in the boundary layer on a flat plate has been experimentally investigated. The linear instability characteristics of the separated flow are determined and the interaction between the oscillations growing in the separation zone and the average flow is studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 16–22, January–February, 1990.     

Flows induced by power-law stretching surface motion modulated by transverse or orthogonal surface shear

Boundary-layer solutions to Banks' problem for the flow induced by power-law stretching of a plate are obtained for two generalizations that include arbitrary transverse plate shearing motion. In one extension an arbitrary transverse shearing motion is the product of the power-law stretching. In the other extension the streamwise stretching coordinate is added to an arbitrary transverse shearing and together raised to the power of stretching. In addition we find that Banks' power law stretching may be accompanied by orthogonal power-law shear. In all cases, the original boundary-value problem of Banks [1] is recovered. Results are illustrated with velocity profiles both at the plate and at fixed height in the fluid above the plate.     

The effects of surface roughness geometry of flow undergoing Poiseuille flow by molecular dynamics simulation

Numerical simulation of Poiseuille flow of liquid Argon in a rough nano-channel using the non-equilibrium molecular dynamics simulation is performed. Density and velocity profiles across the channel are investigated in which roughness is implemented only on the lower wall. The Lennard–Jones potential is used to model the interactions between all particles. The effects of surface roughness geometry, gap between roughness elements (or roughness periodicity), surface roughness height and surface attraction energy on the behavior of the flow undergoing Poiseuille flow are presented. Results show that surface shape and roughness height have a decisive role on the flow behaviors. In fact, by increasing the roughness ratio (height to base ratio), the slip velocity and the maximum velocity in the channel cross section are reduced, and the density fluctuations near the wall increases. Results also show that the maximum density near the wall for a rough surface is less than a smooth wall. Moreover, the simulation results show that the effect of triangle roughness surface on the flow behavior is more than the cylindrical ones.     

Supersonic boundary layer transition induced by roughness on the attachment line of a yawed cylinder

The effect of a single two-dimensional irregularity and sandy roughness on boundary layer transition in supersonic flow over a yawed cylinder (M = 6)-has been experimentally investigated. The characteristic flow regimes beyond the roughness are identified, and their limits are determined as a function of the Reynolds number and the ratio of the height of the roughness to the characteristic thickness of the boundary layer. A qualitative comparison is made with the flow regimes induced by roughness on the attachment line in incompressible flow over a cylinder [1–3]. The thermal indicator coating method is used to measure the heat fluxes along the attachment line and a comparison is made with calculations carried out in accordance with the methods of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 28–35, November–December, 1991.The authors are grateful to A. F. Kiselev for helping to calculate the heat flux in the turbulent boundary layer.