Wavy Contact Research Articles

On the interplay between roughness and viscoelasticity in adhesive hysteresis

Viscoelasticity and roughness are among the possible causes of the adhesive hysteresis displayed by soft contacts. Viscoelasticity causes an increased effective work of adhesion due to stiffening of the contact, while roughness is responsible for elastic instabilities. Herein, we explore the interplay between viscoelasticity and roughness by simulating in two dimensions the retraction of a rigid cylinder, with wavy surface profile, from a viscoelastic half-space. The wave amplitude and length are varied to induce instabilities in the load–to–area response, while the retraction velocity is increased to promote viscoelasticity. Results show that, in the regime where viscoelasticity is confined to the edges of the wavy contact, the contributions of viscoelasticity and waviness to adhesive hysteresis are nearly independent and additive. At low retraction rates, the instabilities in the load-area curve typical of rough elastic contacts are suppressed by viscoelasticity: the contact stiffens to promote a stable decrease of the contact area with load. This occurs with a minimal change in work of adhesion. However, when the instantaneous limit is met at high retraction rates, mechanical instabilities appear.

Transient Elastohydrodynamic Lubrication of Rough Contact Surface for Intermittent Motion

The current study aims to study the characteristics of transient elastohydrodynamic lubrication of smooth and rough surface contacts subjected to intermittent motion for different inactive periods of motion and deceleration/acceleration periods to fulfill an identified need for such conjunction. In this case, the non-steady Reynolds’ equation, the film thickness equation with elastic deformation and taking into account the influence of surface roughness, and the load balance equation are simultaneously solved using the Newton-Raphson with Gauss-Seidel iterations method to determine the film profile and pressure distribution at various time steps. Surface contact of sinusoidal waves is presented with different amplitudes and wavelengths. The results indicated that surface waviness causes random oscillations in pressure and film profiles at different time steps. The greater the amplitude of the waviness, the more pressure and film profile variations occur. The magnitude of the pressure and film profile fluctuations becomes little noticeable as the wavelength of a wavy surface rises. The findings of this investigation also revealed that increasing the inactive duration for wavy surfaces results in zero minimum film thickness and surface contact. Squeezing action is ineffective in conveying loading capacity in this circumstance. The central and maximum pressure heights increase during the stop time interval as stop time increases. The centre film thickness increases at the end of the deceleration phase when the deceleration/acceleration period is reduced, but the minimum film thickness is unaffected. In fact, the minimum film thickness tends to be zero at the end of the deceleration phase, regardless of the deceleration/acceleration period. The central and maximum pressure increase during the stop time interval with the decrease of the deceleration/acceleration period. The difference between the results for smooth and wavy surface contacts is the appearance of fluctuations in film and pressure profiles, as well as the reduction of the film thickness and increase in pressure for the wavy surface when compared to contact with a smooth surface.

Laser-assisted conduction joining of carbon fiber reinforced sheet molding compound to dual-phase steel by a polycarbonate interlayer

This study was performed to investigate the feasibilities, characteristics and mechanisms of laser bonding heterogeneous joints from thermoset carbon fiber reinforced sheet molding compound (SMC) and dual-phase steel (DP590) with the aid of an intermediate polycarbonate (PC) mid-layer. The single lap-joint showed that the load at failure reached up to 3.31 kN (i.e. 4.9 MPa for shear strength). Morphological analysis of four fracture modes as well as mechanical characterization of the heterogeneous joints were carried out to understand the effect of laser line energy on the joint quality including defects and strength. By analyzing the relationship between the area percentage of four fracture modes and ultimate shear force (USF) of the joints with various line energies, the contribution of each fracture mode to the joint strength was determined and discussed. In addition, cross-sectional analysis indicates that bubble expansion caused by SMC substrate degradation results in carbon fibers being squeezed into molten PC, which increases the bonding area by creating wavy contacts and generates a mechanical interlock at the SMC/PC interface.

Estimation of Process Damping Coefficient Using Dynamic Cutting Force Model

A model of process damping in milling was developed in this study. The process damping is a critical parameter to increase the stable cutting region at low cutting speed to avoid chatter. The previous studies conducted experiments to estimate the process damping. Nevertheless, it is time and cost consuming. A model of dynamic cutting force was employed in this study. The plowing force generated by the flank-wave contact is considered as the main source of process damping to dissipate vibratory energy during cutting. In addition to the material properties and plowing force, the effects of chatter amplitude and wavelength, which result in the various indentation conditions and affect the coefficient of process damping, were also considered. The consideration of wavy contact surface and indentation area in this model allows quick determination of cutting stability conditions with high accuracy. The process damping coefficient estimated by the proposed model successfully represented the effect of the tool wear on chatter because of the change of tool geometry. Experiments were conducted to verify the new model.

Sintering shape distortions controlled by interface roughness in powder composites

The co-sintering of laminar composites is modeled by means of finite element simulations. The densification of an alumina/ceria-stabilized tetragonal zirconia polycrystal bilayer is optimized by substituting the conventional flat interface morphology with a wavy contact surface. The presence of such roughness significantly decreases the undesired macroscopic distortions characterizing multi-material sintering. Various configurations of the wavy interface are numerically reconstructed. The introduction of rough interfaces generates beneficial stress redistribution and constraint relaxation effects, thus reducing the bending of the composite. The obtained results are in good agreement with previously conducted experiments and provide new guidelines to prevent flaw generation.

Analytical solution of the dynamic contact problem of anisotropic materials indented with a rigid wavy surface

This article establishes a dynamic wavy contact model of anisotropic materials subject to a rigid indenter, which moves at a constant speed. There is a gap between the indenter and the substrate prior to deformation. The Galilean transformation is introduced to make the equations of motion tractable. Applying the generalized Almansi’s theorem, general solutions for anisotropic governing equations are given for three root cases by using potential theory. The stated problem is reduced to dual series equations, which are solved exactly. Displacement and stress are given in the infinite series forms. Numerical tests have been done to examine the convergence of the infinite series. It is found that maximum magnitudes of the stress can be relieved by adjusting the relative velocity and the elastic constant ratio.

Modeling of Roughness Contact in Piezoelectric/Piezomagnetic Bimaterial Using Potentials

For convenient characterization of the roughness of the interface between two different piezoelectric/piezomagnetic materials (PPMs), a wavy contact model is developed. Eight potential functions are proposed, which makes the considered mixed boundary values problems mathematically tractable. Important physical objectives, such as the unknown contact region and surface normal stress, are presented explicitly. Results in a special case, full contact, are offered. Figures are plotted to show the effects of the piezoelectric phase volume fraction and the external loading on the interactions between two different PPMs. Numerical test reveals that enhancing the piezoelectric phase volume fraction produces a wider contact region.

Dynamic spreading on pillar-arrayed surfaces: Viscous resistance versus molecular friction

The dynamic spreading of a liquid droplet on micropillar-arrayed surfaces is experimentally investigated. A theoretical model is proposed to include energy dissipations raised from both the viscous resistance at mesoscale and the molecular friction at microscale in the triple-phase region. The scaling laws and spreading shape of the droplet change with the variation of the liquid viscosity because of the competition between these two mechanisms of energy dissipations at the moving contact line. The Laplace pressures at the interior corner and at the wavy contact line are the answers to the excess driving energy and the superwetting on pillar-arrayed surfaces. The formation and evolution of the bulk and the fringe are also analyzed in detail. Our results may help to understand the wetting dynamics on microtextured surfaces and assist the future design of engineered surfaces in practical applications.

APPLICATION OF DUAL SERIES EQUATIONS TO WAVY CONTACT BETWEEN PIEZOELECTRIC MATERIALS AND AN ELASTIC SOLID

In this paper, the wavy contact between piezoelectric materials and an isotropic solid is considered. The Papkovich–Neuber potentials for the isotropic solid and three harmonic functions for piezoelectric materials are also presented. The stated problem is reduced to a pair of dual series equations and then recast as an integral equation of the Abel type. Employing the product relation for trigonometric functions and the Mehler integral yields an exact solution of the reduced Abel type integral equation. The relationship between contact length and the level of loading, and the distribution of the surface normal stress are given in terms of elementary functions. The derived results agree well with the previous ones for the purely elastic solid. It is found that a critical loading exists for the disturbance. For limiting cases, such as the low level of loading case and full contact case, corresponding contact behaviors are presented. Numerical analyses are done to reveal the influence of the level of loading on the contact behaviors.

Deformation component of friction force in a wavy elastic contact subjected to wear

The problem of frictional interaction between a wavy punch subjected to wear and an elastic strip is discussed. The contact of the punch and strip is assumed to cover the whole its lengths (complete contact). An analytic solution of the problem is presented, based on which the formula for the deformation component of the friction force is derived. Analysis of this formula enables us to represent visually certain features of the deformation component of the friction force, particularly in relation to its behavior in time.

Controlling Inplane Orientation of a Monolayer Colloidal Crystal by Meniscus Pinning

We demonstrate the usage of meniscus pinning by surface relief boundaries to control in-plane orientation of monolayer colloidal crystals without the interruption of grain disorientation. By optimizing the pinning boundary and withdrawal speed, a well controlled linear meniscus contact line offers unidirectional growth of a colloidal crystal-densely packed crystal direction ⟨11⟩ and ⟨10⟩ parallel to linear edge-giving rise to a single domain crystal with only twins and vacancies present as residual defects. The pinning effect works by eliminating the wavy contact line induced by fingering instability which is commonly found in liquid wetting film. It is found that surfactants and colloidal particles play significant roles to enhance edge pinning, increasing the distance traveled by receding bulk meniscus (during substrate withdrawal) before liquid depinning or rupturing.

Effect of Non-Steady State Loading on Rolling-Sliding Contact Stress

The stresses, strains, and deformations produced by repeated, two-dimensional non-steady state rolling-sliding contact were analyzed using an elastic-plastic finite element model. An advanced cyclic plasticity model was used. The non-steady state rolling contact was restricted to a harmonic variation of the normal Herztian contact pressure. Repeated rolling and sliding were simulated by multiple translations of a set of varying normal and tangential surface tractions across an elastic-plastic semi-infinite half space. The non-steady state loading considered results in a wavy contact surface profile. The surface displacements and wave depth of the wavy deformation increase with increasing rolling passes, but the increases in wave depth per rolling pass (ratchetting rate) decay. The residual stresses and strains near the wave trough of the residual wavy deformation are higher than those near the wave crest. The results are in agreement with the experimental observations. The tangential force has a greater influence on the residual strains than on the residual stresses.

Adhesion at the Wavy Contact Interface Between Two Elastic Bodies

The plane strain elastic contact of two bodies with a wavy contact interface is investigated. The effect of adhesion is accounted for by using the Maugis model. This periodic mixed boundary value problem is solved using integral transform techniques. Results are obtained for the extent of the contact region as a function of the dimensionless applied pressure and for various values of the dimensionless adhesive stress and peak-to-valley height. These contact length versus applied pressure curves are characterized by discontinuities and hysteresis. A finite contact region exists at zero load, with further loading causing one or more jumps into a complete contact configuration. Unloading is also characterized by one or more jumps before pull-off occurs suddenly with a finite contact length and tensile pressure loading.

Tribological Behavior of Aligned Single-Walled Carbon Nanotubes

An abnormal friction law refers to the case where the friction force does not increase monotonically with the normal pressure. We investigate the possibility of abnormal tribological behavior for two surfaces coated with aligned single-walled carbon nanotubes (SWCNTs). Detailed molecular dynamics simulations for aligned SWCNTs predict modulated variation between the kinetic friction force and the applied pressure. The interacting SWCNTs float with respect to each other at about the equilibrium separation of van der Waals interaction, and the wavy contact profile breaks the symmetry of the contacting cross-section. Cases treated by molecular dynamics simulation include two aligned (10,10) SWCNTs with periodic end conditions, and a stack of three aligned (10,10) SWCNTs with free end boundary conditions. A continuum theory based on the wall deflection under finite deformation, in combination with an adhesion criterion similar to the JKR theory, on the other hand, predicts a declining law between the frictional force and the pressure. The correlation of the data obtained through the atomistic and the continuum approaches relies on a deeper understanding on the friction process among SWCNTs.

Vibration and Stability of Frictional Sliding of Two Elastic Bodies With a Wavy Contact Interface

Abstract The stability of steady sliding, with Amontons-Coulomb friction, of two elastic bodies with a rough contact interface is analyzed. The bodies are modeled as elastic half-spaces, one of which has a periodic wavy surface. The steady-state solution yields a periodic set of contact and separation zones, but the stability analysis requires consideration of dynamic effects. By considering a spatial Fourier decomposition of the vibration modes, the dynamic problem is reduced to a singular integral equation for determining the eigenvectors (modes) and eigenvalues (frequencies). A pure imaginary root for an eigenvalue corresponds to a standing wave confined to the interface, while a positive/negative real part of the eigenvalue indicates instability/dissipation. A complex eigenvector indicates a complex mode of vibration. Two types of modes are considered—periodic symmetric modes with period equal to the surface waviness period and periodic antisymmetric modes with the period equal to twice the surface waviness. The singular integral equation is solved by reducing it to a system of linear algebraic equations using a Jacobi polynomial series and a collocation method. For the limit of zero friction it can be demonstrated analytically that the problem is self-adjoint and the eigenvalues, if they exist, are pure imaginary (no energy dissipation). These roots are found for a wide range of material properties and ratios of separation to contact zones lengths. For the limiting case of complete contact, the solution found corresponds to a superposition of two slip waves (generalized Rayleigh waves) traveling in opposite directions and forming a standing wave. With increasing separation zone length, the vibration frequency decreases from the slip wave frequency to the smaller surface wave frequency of the two bodies. With a nonzero separation zone, solutions can exist for material combinations which do not allow slip waves. For nonzero friction and sliding velocities, unstable solutions are found. The degree of instability is proportional to the product of the friction coefficient and the sliding velocity. These instabilities may contribute to the formation of friction-induced vibrations at high sliding speeds.

Experimental Study of Filler Insertion Effect on Mean Thermal Contact Conductance

A series of experiments have been performed to investigate the filler insertion effect on the temperature drop at the wavy contact interface ΔT and the mean thermal contact conductance hm, f. Representative behavior of ΔT against the mean nominal contact pressure pm is clarified, and the effect of an interval of time on ΔT is shown for the silicone filler with thickness δfo=2mm. The silicone elastomer is proved effective to increase hm, f despite its low thermal conductivity. Further, it is shown that hm, f of 0.5mm thick silicone filler becomes two to three times higher than that of bare contact under the unloading process. However, it is also shown that hm, f decreases with increasing δfo, therefore filler insertion with improper thickness results in a reverse effect on increase in hm, f. As for metallic filler insertion using an aluminum or a copper foil, only a little improvement in hm, f is obtained in spite of its high thermal conductivity.

Boulder‐gravel hummocks and wavy basal till contacts: products of subglacial meltwater flow beneath the Saginaw Lobe, south‐central Michigan, USA

Hummocky terrain composed of boulder gravel and a wavy contact between stratified till and sand are described and explained as products of subglacial meltwater activity beneath the Saginaw Lobe of the Laurentide Ice Sheet in south‐central Michigan. Exposures and geophysical investigations of hummocky terrain in a tunnel channel reveal that hummocks (˜100m diameter) are glaciofluvial bedforms with a supraglacial melt‐out till or till flow veneer. The hummocky terrain is interpreted as a subglacial glaciofluvial landscape rather than one of stagnant ice processes commonly assumed for hummocky landscapes. Sandy bedforms at another site are in‐phase with a wavy contact at the base of a stratified till exposed for 50m along the margin of a tunnel channel. The 0.4m thick stratified till is overlain by up to 5m of compact, pebble‐rich, sandy subglacial melt‐out till. The contact between the till and sand has a wave form with a 0.5m amplitude and 3‐5m wavelength. Bedding within the stratified till, sandy bedforms and melt‐out till are mostly in‐phase with each other. Clasts from the overlying stratified till penetrate and deform the underlying sand recording recoupling of the ice to its bed. Ice ripples cut into the base of river ice have a similar morphology and are considered analogs for cavities cut into the base of the glacier and subsequently filled with sand. Subglacial meltwater activity was not coeval at each study site, indicating that subglacial meltwater played important roles in the evolution of the subglacial environment beneath the Saginaw Lobe at different times.

Steady-State Frictional Sliding of Two Elastic Bodies With a Wavy Contact Interface

Dry frictional sliding of two elastic bodies, one of which has a periodic wavy surface, is considered. Such a model represents the frictional sliding of two nominally flat surfaces, one of which has periodically spaced asperities. The dependence of the true contact area on loading is analyzed by using the plane strain theory of elasticity. Fourier series and integral transform techniques are applied to reduce the problem to an integral equation which is solved using a series of Jacobi polynomials. For steady-state dynamic frictional sliding with given values of the friction coefficient, materials constants, and sliding velocity, the dependence of the contact zone length on the remotely applied tractions is determined. The results indicate a decrease of the minimum applied traction required to close the gap between the bodies, with an increase of the friction coefficient and/or the sliding velocity. A resonance exists as the sliding velocity approaches the Rayleigh wave speed of the flat body. [S0742-4787(00)01403-X]

各種接触担体と水生植物の組み合わせによる生活排水汚濁水路浄化施設の処理特性

For the purification of urban river water polluted with grey water, a new method applying various kinds of contact materials and aquatic plant as nutrient absorber was invented and its purification capabilities were experimentally made clear. Actual purification plant, whose working volume was 26.4m3, was consisted of contact oxidation tanks and aquatic plant cultivation tank. Oxidation tanks were composed of wavy contact material and porous concrete block. Water lettuce (Pistia stratiotes) was cultivated in an aquatic plant cultivation tank. This purification plant was continuously operated under TOC loading rate of 50-170g/m3/d. TOC was removed at the efficiencies of about 40% and SS and anionic surfactants were effectively removed. Cultivation of water lettuce was succeeded by using the effluent from contact oxidation tank. 30kg (wet weight) of water lettuce were harvested from aquatic plant cultivation tank whose cultivation area was only 2.16m2. Purification of polluted river water using contact materials and aquatic plant was experimentally proved to have a high application potential.

Evolution of the continuous interface between gases of different density during the passage of a shock wave

The evolution of the interface between gases of different density following the passage of a shock wave has been experimentally investigated. It is shown that replacing the discontinuous change of density on the wavy contact discontinuity by a continuous change in a layer of finite thickness leads to a reduction in the amplitude growth rate in the initial stage of development of Richtmyer—Meshkov instability. The experimentally determined values of the amplitude growth rate reduction factor are satisfactorily described by a model to be found in the literature.