Multi-asperity Model Research Articles

On the contact between elasto-plastic media with self-affine fractal roughness

Modeling the elasto-plastic contact between rough interfaces may require high computational effort as real surfaces present broad roughness spectra. In this work, we propose an efficient multi-asperity model where each asperity follows Jackson and Green’s equations and both coupling and coalescence of contact spots are considered. In agreement with previous studies, the contact area A is found to rise linearly with the applied load. Moreover, under the assumption of yield stress independent of the asperity size, no differences are found with respect to the elastic contact solution for nanometric root mean square (rms) roughness amplitudes hrms. On the contrary, for micrometric hrms, the slope of the area-load relation is observed to increase when reducing the yield strength σY. We have also investigated the effect of increasing the rms roughness gradient of the surface hrms′ by adding fine-scale wavelengths to the roughness spectrum. Due to plastic deformations, the contact area A is found to be independent of the high-frequency cut-off of the roughness spectrum as it converges when increasing the number of roughness scales.

A concise treatise on model-based enhancements of cohesive powder properties via dry particle coating

• Advances in model-guided dry coating of cohesive powder flow enhancement presented. • Chen-NJCEP model explains the mechanism of dry coating induced flow enhancements. • Models offered for the guest amount and type, and granular Bond number estimation. • Dry coating led to drastically enhance flow, packing, agglomeration, dissolution. • Agglomeration, indicator of flowability, dramatically reduced with dry coating. This paper presents a review of our key advances in model-guided dry coating-based enhancements of poor flow and packing of fine cohesive powders. The existing van der Waals force-based particle-contact models are reviewed to elucidate the main mechanism of flow enhancement through silica dry coating. Our multi-asperity model explains the effect of the amount of silica, insufficient flowability enhancements through conventional blending, and the predominant effect of particle surface roughness on cohesion reduction. Models are presented for the determination of the amount and type of guest particles, and estimation of the granular Bond number, used for cohesion nondimensionalization, based on particle size, particle density, asperity size, surface area coverage, and dispersive surface energy. Selection of the processing conditions for LabRAM, a benchmarking device, is presented followed by key examples of enhancements of flow, packing, agglomeration, and dissolution through the dry coating. Powder agglomeration is shown as a screening indicator of powder flowability. The mixing synergy is identified as a cause for enhanced blend flowability with a minor dry coated constituent at silica < 0.01%. The analysis and outcomes presented in this paper are intended to demonstrate the importance of dry coating as an essential tool for industry practitioners.

A Predictive Model for Galling Phenomenon and Its Applicability for Deep Drawing Processes

Abstract Galling is a recurring phenomenon in deep drawing processes which requires frequent maintenance of tools to improve the product surface quality. Adhesive transfer of softer material on the hard tool surface results in sharp features which causes surface roughening of the tools and deterioration of deep drawn products. In this article, an adhesive wear model based on a deterministic approach is developed to predict the galling behavior in a deep drawing process. The model uses the surface topography, material properties and contact conditions to predict the surface roughening of tool surfaces under perfectly plastic conditions. The adhesive transfer of material is considered by the growth of the asperities based on its geometry for the increase in height and radial direction by preserving the original shape and volume consistency. The results of the multi-asperity models show the growth of the transfer layer and its effects due to load, sliding cycle, sliding distance, and affinity of the materials. The results show the influence of the above-said parameters and its applicability for deep drawing process conditions. The simulated results show an 85% level of confidence in comparison with the experiments from literature for the prediction of the surface evolution due to the galling mechanism.

Contact analysis of measured surfaces based on modified interacting and coalescing Hertzian asperities (ICHA) model with oblique contact asperities

The contact mechanism for joint surfaces is important for predicting the loading process and dynamic properties of precision machinery products. A multiasperity model considering the lateral interaction and coalescence of contact regions with oblique asperity contact, the interacting and coalescing Hertzian asperities (ICHA) model, is introduced in this work. Contact angle [Formula: see text] and radius of curvature [Formula: see text] are vital parameters that are directly calculated based on grid points measured from the milling and grinding surfaces. Numerical simulations of [Formula: see text] and [Formula: see text] were analysed. The results show that the proposed model is more effective at improving the contact area versus force relationship than various asperity models for low and middle contact forces. [Formula: see text] and [Formula: see text] follow a Gaussian distribution. Because of the existence of coalescence, they decrease with increasing contact force. Furthermore, the [Formula: see text] and [Formula: see text] in the startup phase are crucial data that can be used to judge the effects of oblique asperity contact. They are greatly influenced by fractal dimension [Formula: see text] and fractal roughness G. From the comparisons with the surfaces generated by Weierstrass-Mandelbrot function, it is suggested that to obtain an accurate contact prediction in the loading process, oblique contact is as important as lateral interaction and coalescence.

Comparative analysis of leakage calculations for metallic seals of ball-seat valves using the multi-asperity model and the magnification-based model

The leakage characteristics of metallic seals have a significant influence on valve performance. The contact status along the sealing zone greatly affects sealing properties, but is still not fully understood in current studies. There are mainly two different models for the seal’s contact mechanics: the multi-asperity model and the magnification-based model. This paper conducted a comparative analysis of leakage calculations for metallic seals of ball-seat valves based on the above two contact models. The test rig for measuring leakage values at different pressures has been constructed. The simulation with/without considering plastic effects is presented and verified by the experiment. The results indicate that the magnification-based model, with the consideration of plastic effects, can provide a better coincidence with experimental results.

Research on the effect of structured water on growth of lettuce plants and rhizosphere microbiota

Contact analysis without adhesion is still a challenging issue, mainly owing to the multiscale and self-fractal characteristics of rough surfaces. One of the most widely used theories for analyzing contact behavior of rough surfaces is the asperity-based Hertz contact models initiated by Greenwood and Williamson. Due to its single-scaled nature, however, G-W models generally output less accurate predictions when indentation is deep. This article aims for proposing a new theoretical model that effectively formulates the contact status of rough surfaces throughout the entire compression process. This is achieved by integrating the idea of magnification, or evolving resolution into the G-W model, and a magnification-based multi-asperity model is thus established where the multiscale nature of rough surface is taken into account properly. In the derived model, the originally complex contact problem is decomposed into a family of sub-problems each defined on a morphologically simpler contact islands, and a number of explicit formulations from existing multi-asperity models can thus be used. The present model not only effectively reproduces the results of G-W models for short indentation distance, but is also shown that when indentation is sufficiently deep, the present model smoothly transits to the regime of elastic interaction between smooth surfaces governed by Hookean-law formulation. Compared to other G-W type models, the proposed framework has also shown its strength in the computation of actual contact area. The proposed model is then compared with existing molecular dynamics simulation and experimental results for validation.

A magnification-based multi-asperity (MBMA) model of rough contact without adhesion

Contact analysis without adhesion is still a challenging issue, mainly owing to the multiscale and self-fractal characteristics of rough surfaces. One of the most widely used theories for analyzing contact behavior of rough surfaces is the asperity-based Hertz contact models initiated by Greenwood and Williamson. Due to its single-scaled nature, however, G-W models generally output less accurate predictions when indentation is deep. This article aims for proposing a new theoretical model that effectively formulates the contact status of rough surfaces throughout the entire compression process. This is achieved by integrating the idea of magnification, or evolving resolution into the G-W model, and a magnification-based multi-asperity model is thus established where the multiscale nature of rough surface is taken into account properly. In the derived model, the originally complex contact problem is decomposed into a family of sub-problems each defined on a morphologically simpler contact islands, and a number of explicit formulations from existing multi-asperity models can thus be used. The present model not only effectively reproduces the results of G-W models for short indentation distance, but is also shown that when indentation is sufficiently deep, the present model smoothly transits to the regime of elastic interaction between smooth surfaces governed by Hookean-law formulation. Compared to other G-W type models, the proposed framework has also shown its strength in the computation of actual contact area. The proposed model is then compared with existing molecular dynamics simulation and experimental results for validation.

Contact of rough surfaces: Modeling adhesion in advanced multiasperity models

Surface roughness affects several tribological phenomena and in particular adhesion. For many years, multiasperity models have been the most used in the study of rough contacts notwithstanding their evident limitations. In this work, we propose a fair assessment of improved asperity models with adhesion modeled according to the Derjaguin, Muller and Toporov theory, which assumes attractive forces do not deform the surface profiles. Results are given for three enhanced asperity models: the discrete Greenwood and Williamson model, where the effective heights and curvatures of the surface asperities are used rather than a statistical description; the interacting Hertzian asperities model, where the elastic coupling effects are included; the interacting and coalescing Hertzian asperities model, where the coalescence of contact spots is also conveniently considered. A comparison with advanced contact mechanics theories shows that only the interacting and coalescing Hertzian asperities model correctly captures the physics of the problem at all roughness scales.

The Elastic Contact of Rough Spheres Investigated Using a Deterministic Multi-Asperity Model

In this paper, we use a deterministic multi-asperity model to investigate the elastic contact of rough spheres. Synthetic rough surfaces with controllable spectra were used to identify individual asperities, their locations and curvatures. The deterministic analysis enables to capture both particular deformation modes of individual rough surfaces and also statistical deformation regimes, which involve averaging over a big number of roughness realizations. Two regimes of contact area growth were identified: the Hertzian regime at light loads at the scale of a single asperity, and the linear regime at higher loads involving multiple contacting asperities. The transition between the regimes occurs at the load which depends on the second and the fourth spectral moments. It is shown that at light indentation the radius of circumference delimiting the contact area is always considerably larger than Hertzian contact radius. Therefore, it suggests that there is no scale separation in contact problems at light loads. In particular, the geometrical shape cannot be considered separately from the surface roughness at least for approaching greater than one standard roughness deviation.

Elastic Contact Mechanics of Randomly Rough Surfaces: An Assessment of Advanced Asperity Models and Persson’s Theory

In this work, we discuss important improvements of asperity models. Specifically, we assess the predictive capabilities of a recently developed multiasperity model, which differs from the original Greenwood and Williamson model by (i) including the coupling between the elastic fields generated by each contact spot, and (ii) taking into account the coalescence among the contact areas, occurring during the loading process. Interaction of the elastic field is captured by summing the contributions, which are analytically known, of the elastic displacements in a given point of the surface due to each Hertzian-like contact spot. The coalescence is instead considered by defining an equivalent contact spot in such a way to guarantee conservation of contact area during coalescence. To evaluate the accuracy of the model, a comparison with fully numerical ‘exact’ calculations and Persson’s contact mechanics theory of elastic rough surfaces is proposed. Results in terms of contact area versus load and separation versus load show that the three approaches give almost the same predictions, while traditional asperity models neglecting coalescence and elastic coupling between contact regions are unable to correctly capture the contact behavior. Finally, very good results are also obtained when dealing with the probability distribution of interfacial stresses and gaps.

Granular bond number model to predict the flow of fine flour powders using particle properties

In order to improve the fundamental understanding of fine flour flow behavior, which is essential for the success of sieving and other particulate size based separation processes, this study investigates the relationship between particle properties and the flow function coefficient, a metric used to assess the flow performance. The granular Bond number quantified from the inter-particle cohesion force using the multi-asperity model correlates well with the flow function coefficient. The lower values of standard error of prediction (0.04–0.10) for flow function coefficient of size segregated wheat flours and (0.03–0.19) flour blends indicate that the developed model agreed well with the experimental measurements. It was established that, the variations in the surface chemical composition of flour particles have a significant impact on the flow behavior of fine flours. The flow function coefficients of blends of size segregated flours can be predicted from ternary diagrams developed based on the model, and these predictions matched well with the experimental measurements. The model developed in this study will be useful to increase the throughput during size separation of wheat flours and also to assess the flow behavior of wheat flour blends.

Using the Multiasperity Models to Investigate the Effect of Cylindrical Micro/Nanoparticle Roughness on the Critical Manipulation Forces

In this paper, the process of moving rough cylindrical bacteria micro/nanoparticles on a smooth substrate by means of an atomic force microscope's (AFM) probe has been investigated. For this purpose, three common adhesion models of Rumpf, Rabinovich, and Cooper have been further developed in the form of multiasperity contact models and with regards to the cylindrical geometry of bacteria nanoparticles. The number of asperities in contact and also the areas of contact between nanoparticle/substrate and nanoparticle/AFM probe tip have been calculated. Then, a dynamic model for simulating rough cylindrical nanoparticles displacement on a smooth substrate has been presented and adhesive forces obtained from the aforementioned three models have been employed in this model to determine the critical force and time values for onset of rolling and sliding of particles on the substrate. Then, the effect of geometrical and roughness parameters on critical forces has been investigated. The simulation results have shown that critical forces required for pushing a rough particle are less than a smooth one. Also, the simulation results indicated that with increasing particle radius, the critical sliding force increases while the critical rolling force diminishes. For the results to be more realistic, simulations have been performed based on the roughness and geometrical parameters extracted from topographical images of bacteria micro/nanoparticles. For this purpose, two different bacteria samples were obtained and after preparing them, the topographic images of these samples were acquired by means of the AFM. Then, the roughness and geometrical parameters of these particles were extracted from the topographic images and using these parameters the manipulation process was simulated for these particles. The simulation results indicate that the maximum difference between Rumpf and Rabinovich models is 8%, so these model results are in a good agreement. Finally, the models developed in this research were validated by comparing the results with the findings of a research on gold nanoparticles.

Prediction of powder flow performance using a multi-component granular Bond number

In order to improve fundamental understanding of powder flow behavior which is essential to the success of many pharmaceutical processes, this study investigates the relationship between particle-scale interactions dominated by the cohesive van der Waals force and the flow function coefficient. This study finds that the granular Bond number, defined as the ratio of the inter-particle cohesion force to particle weight, correlates well to the flow function coefficient, a metric used to assess powder flow performance and defined as the ratio of consolidation stress to unconfined yield strength. The inter-particle cohesion force was calculated by the so-called multi-asperity model which is a modification of the well-known Rumpf equation. As a major novelty, a granular Bond number is defined for multi-component mixtures (i.e. powder blends) and used to predict the flow function coefficient of binary, ternary, and quinary mixtures of a model API, acetaminophen, and two common pharmaceutical excipients, microcrystalline cellulose and pregelatinized starch. Surface modification via dry-coating was also used to alter the inter-particle force and more thoroughly investigate the effect of particle interactions on powder flow performance. Since the multi-component granular Bond number takes into account particle properties and particle interactions of all components in the powder blend, this novel approach shows good predictability for powder mixtures. Although the flow function coefficient alone is not a stringent prediction of powder flow, the modeling effort put forth in this study can be used to better guide formulation development.

Investigating the effect of surface roughness on the critical sliding and rolling forces of cylindrical nanoparticles based on the multi-asperity contact models

This paper has investigated the dynamic behavior of a cylindrically shaped DNA nanoparticle during its displacement on a rough substrate by an atomic force microscope. Due to the cylindrical geometry of the DNA nanoparticle, two multi-asperity models have been considered for the adhesion between nanoparticle and rough substrate. The two selected models for the contact between smooth and rough surfaces have been further developed for cylindrical geometries. One of these models is analytical and based on uniform asperities and the other one is based on random asperities. Also, in each of these models, the real area of contact between particle and rough substrate has been calculated based on the number of asperities in contact. Then, a 3D dynamic model for the manipulation of cylindrical nanoparticle on rough substrate has been developed and simulated. The maximum difference between the results obtained from the two multi-asperity models is <5 %, indicating a good agreement between the two models. The comparison of critical forces indicates that the critical force necessary for moving a particle is smaller for rough substrates than for smooth substrates and larger compared to the critical force obtained from the Rabinovich model, which is single-asperity model. Finally, the surface roughness parameters were estimated from the topographic images, and the manipulation process was simulated for these substrates by developing the relevant equations. The obtained results indicated that the critical force for a substrate with a higher root-mean-square roughness is smaller and particles can be moved easier on such a substrate.

Improvements to a scale-dependent model for contact and friction

In this investigation three effects are included in a recently developed scale-dependent multi-asperity model of elastic contact and friction. First, a Weibull distribution of asperity heights is used, which allows the skew and kurtosis to be varied, but not independently of each other. Second, the effect of non-constant radii of curvature of the asperity summits, with the curvature varying with asperity height, is examined. Finally, the influence of noncontacting asperities on the normal force and hence on contact and friction is included. It is noted that the contact and friction model used (Adams et al 2003 ASME J. Tribol. 125 700–8) includes the effects of adhesion and scale-dependent friction. It is demonstrated that positive/negative skew decreases/increases both the friction coefficient and its dependence on the normal load. The results also indicate that for radii of curvature that increase/decrease with height, the friction coefficient increases/decreases as does its dependence on load.

A Scale-Dependent Model for Multi-Asperity Contact and Friction

As loading forces decrease in applications such as MEMS and NEMS devices, the size of the asperity contacts which comprise the real contact area tend to decrease into the nano scale regime. This reduction in size of the contacts is only partially offset by the nominally increased smoothness of these contacting surfaces. Because the friction force depends on the real area of contact, it is important to understand how the material and topographical properties of surfaces contribute to friction forces at this nano scale. In this investigation, the single asperity nano contact model of Hurtado and Kim is incorporated into a multi-asperity model for contact and friction which includes the effect of asperity adhesion forces using the Maugis-Dugdale model. The model spans the range from nano-scale to micro-scale to macro-scale contacts. Three key dimensionless parameters have been identified which represent combinations of surface roughness measures, Burgers vector length, surface energy, and elastic properties. Results are given for the friction coefficient versus normal force, the normal and friction forces versus separation, and the pull-off force for various values of these key parameters.

Linear elastic contact of the Weierstrass profile

A contact problem is considered in which an elastic half–plane is pressed against a rigid fractally rough surface, whose profile is defined by a Weierstrass series. It is shown that no applied mean pressure is sufficiently large to ensure full contact and indeed there are not even any contact areas of finite dimension — the contact area consists of a set of fractal character for all values of the geometric and loading parameters. A solution for the partial contact of a sinusoidal surface is used to develop a relation between the contact pressure distribution at scale n − 1 and that at scale n . Recursive numerical integration of this relation yields the contact area as a function of scale. An analytical solution to the same problem appropriate at large n is constructed following a technique due to Archard. This is found to give a very good approximation to the numerical results even at small n , except for cases where the dimensionless applied load is large. The contact area is found to decrease continuously with n , tending to a power–law behaviour at large n which corresponds to a limiting fractal dimension of (2 − D ), where D is the fractal dimension of the surface profile. However, it is not a ‘simple’ fractal, in the sense that it deviates from the power–law form at low n , at which there is also a dependence on the applied load. Contact segment lengths become smaller at small scales, but an appropriately normalized size distribution tends to a limiting function at large n . † The authors dedicate this paper to the memory of Dr J. F. Archard, 1918–1989.

Spherical indentation of elastic–plastic solids

The finite–element method is used to perform an accurate numerical study of the normal indentation of an elastic–plastic half–space by a rigid sphere. The effects of elasticity and strain–hardening rate of the half–space are explored, and the role of friction is assessed by analysing the limiting cases of frictionless contact and sticking friction. Indentation maps are constructed with axes of contact radius a (normalized by the indenter radius R and the yield strain of the half–space. Competing regimes of deformation mode are determined and are plotted on the indentation map: (i) elastic Hertzian contact; (ii) elastic–plastic deformation; (iii) plastic similarity regime; (iv) finite–deformation elastic contact; and (v) finite–deformation plastic contact. The locations of the boundaries between deformation regimes change only slightly with the degree of strain–hardening rate and of interfacial friction. It is found that the domain of validity of the rigid–strain–hardening similarity solution is rather restricted: it is relevant only for solids with a yield strain of less than 2 x 10 −4 and a / R

Tribology of diamond-like carbon films from generic fabrication routes investigated by lateral force microscopy

The tribological characteristics of diamond-like carbon (DLC) films have been studied by lateral force microscopy (LFM). Specimens from two fabrication routes, ion-beam assisted deposition and chemical vapour deposition, have been investigated. Thick (micrometres) and thin (a few nanometres) films from both routes have been considered, as have the service environments of ambient air and vacuum. Lateral force data were calculated from `friction loops', obtained as functions of load, surface topography, scan speed and service environment. An identical methodology and LFM probe were used throughout the series of measurements in order to ensure internal consistency, and the validity of the methodology was checked against measurements on epitaxially grown Si. A linear dependence was observed between lateral force and force loading up to ca , in accord with a multi-asperity model, thus allowing determination of coefficients of friction that ranged from 0.05 to 0.15. The results showed that adhesive interactions contributed up to to the overall dynamic load. Meniscus interaction played a minor role in comparison to that from tribo-generated electrostatic forces. The experiments show that LFM methodologies have value and relevance to the science and technology of tribology, especially when the required spatial resolution cannot be obtained with the traditional macroscopic techniques.

Contact Resistance on Surfaces with Nonuniform Contaminant Films

A probe has been designed for making point-by-point mapping measurements of contact resistance over large surface areas. The probe, which operates in the low force range of 5 mg to 5 g, permits simultaneous measurement of both contact resistance as a function of load and the integral of contact resistance versus force. To accomplish this a magnetically damped torsion bar mounted pendulum/sample holder is electromagnetically driven against a smooth spherical probe tip mounted directly on a force transducer which, in turn, is mounted on an x-y precision translation stage. The associated instrument package includes a variable sweep rate electromagnetic drive, high-frequency rejecting load and contact voltage amplifiers (the latter being an ultrastable differential amplifier), a voltage-to-frequency converter, a scaler, and an x-y recorder. The probe has been used to explore spatial variations in contact resistance due to a nonuniform fiuoropolymer film on a gold substrate. The data show a large statistical variability, which is simply analyzed by assuming normally distributed surface asperities and applying this assumption to the accepted model for multi-asperity electrical contact. This procedure leads to a prediction that the square of the conductance will follow a Gaussian distribution. Contact resistances that were obtained in the course of this work as a function of force are shown to be consistent with the multi-asperity model, Data are presented which agree well with the statistical model. This insight into the statistical variability of contact resistance data is useful in that it suggests a successful data smoothing technique that presents a reasonable appearing line map of the effective contact resistance due to a nonuniform film. It is demonstrated that data smoothed in this fashion can be favorably compared to the degree of surface contamination as determined with a scanning electron microscope.