Continuum Contact Mechanics Research Articles

Mechanistic model for quantifying the effect of impact force on mechanochemical reactivity.

Conventional mechanochemical synthetic tools, such as ball mills, offer no methodology to quantitatively link macroscale reaction parameters, such as shaking frequency or milling ball radius, to fundamental drivers of reactivity, namely the force vectors applied to the reactive molecules. As a result, although mechanochemistry has proven to be a valuable method to make a wide variety of products, the results are seldom reproduceable between reactors, difficult to rationally optimize, and hard to ascribe to a specific reaction pathway. Here we have developed a controlled force reactor, which is a mechanochemical ball mill reactor with integrated force measurement and control during each impact. We relate two macroscale reactor parameters-impact force and impact time-to thermodynamic and kinetic transition state theories of mechanochemistry utilizing continuum contact mechanics principles. We demonstrate force controlled particle fracture of NaCl to characterize particle size evolution during reactions, and force controlled reaction between anhydrous copper(II) chloride and (1, 10) phenanthroline. During the fracture of NaCl, we monitor the evolution of particle size as a function of impact force and find that particles quickly reach a particle size of ∼100 μm largely independent of impact force, and reach steady state 10-100× faster than reaction kinetics of typical mechanochemical reactions. We monitor the copper(II) chloride reactivity by measuring color change during reaction. Applying our transition state theory developed here to the reaction curves of copper(II) chloride and (1, 10) phenanthroline at multiple impact forces results in an activation energy barrier of 0.61 ± 0.07 eV, distinctly higher than barriers for hydrated metal salts and organic ligands and distinctly lower than the direct cleavage of the CuCl bond, indicating that the reaction may be mediated by the higher affinity of Fe in the stainless steel vessel to Cl. We further show that the results in the controlled force reactor match rudimentary estimations of impact force within a commercial ball mill reactor Retsch MM400. These results demonstrate the ability to quantitatively link macroscale reactor parameters to reaction properties, motivating further work to make mechanochemical synthesis quantitative, predictable, and fundamentally insightful.

Thermal activation Eyring energy approach to characterise the dependence of nanoscale friction on the surface roughness

Atomic Force Microscope (AFM) is used to characterise the frictional response of surfaces with varying roughness parameters in dry and in the presence of fully formulated lubricants. The surface roughness has shown to affect nanoscale friction. The characteristics involved the investigation of roughness, small-scale adhesive forces and nanoscale friction using AFM in lateral force mode. The fluid-cell Lateral Force Microscopy (LFM) results were used to model thermal activation Eyring energy components in conjunction with the relevant continuum contact mechanics model. The paper shows that a combination of LFM, for dry and fluid-cell LFM and thermal activation Eyring energy barrier approach is a useful tool to explain the effect of surface roughness on nanoscale friction.

Pressure-dependent bulk compressibility of a porous granular material modeled by improved contact mechanics and micromechanical approaches: Effects of surface roughness of grains

The change of the mechanical properties of granular materials with pressure is an important topic associated with many industrial applications. In this paper we investigate the influence of hydrostatic pressure (Pe) on the effective bulk compressibility (Ceff) of a granular material by applying two modified theoretical approaches that are based on contact mechanics and micromechanics, respectively. For a granular material composed of rough grains, an extended contact model is developed to elucidate the effect of roughness of grain surfaces on bulk compressibility. At relatively low pressures, the model predicts that the decrease of bulk compressibility with pressure may be described by a power law with an exponent of -1/2 (i.e., Ceff ∝Pe−1/2), but deviates at intermediate pressures. At elevated pressures beyond full contact, bulk compressibility remains almost unchanged, which may be roughly evaluated by continuum contact mechanics. As an alternative explanation of pressure-dependent bulk compressibility, we suggest a micromechanical model that accounts for effects of different types of pore space present in granular materials. Narrow and compliant inter-granular cracks are approximated by three-dimensional oblate spheroidal cracks with rough surfaces, whereas the equant and stiff pores surrounded by three and four neighboring grains are modeled as tubular pores with cross sections of three and four cusp-like corners, respectively. In this model, bulk compressibility is strongly reduced with increasing pressure by progressive closure of rough-walled cracks. At pressures exceeding crack closure pressure, deformation of the remaining equant pores is largely insensitive to pressure, with almost no further change in bulk compressibility. To validate these models, we performed hydrostatic compression tests on Bentheim sandstone (a granular rock consisting of quartz with high porosity) under a wide range of pressure. The relation between observed microstructures and measured pressure-dependent bulk compressibility is well explained by both suggested models.

Performance of Poly Alpha Olefin Nanolubricant

The viscosity and tribological behavior of nanofluids formed by dispersed nano-diamond particles within Poly-Alpha-Olefin (PAO6) lubricant is studied at different concentrations. The variation of coefficient of friction with nanoparticle concentration is measured using pin-on-disc tribometry under boundary, mixed, and hydrodynamic regimes of lubrication. A multi-scale multi-physics thermo-mixed lubrication model is developed to provide fundamental understanding of the measured tribometric results. The analytical approach combines continuum contact mechanics, thermal-mixed lubrication comprising the interaction of rough surfaces, as well as a thermal network heat transfer model. In particular, Einstein’s viscosity model for dispersed hard particles together with Vogel’s viscosity-temperature dependence model for fluid viscosity containing nanoparticles represent new contributions to knowledge. This integrated numerical-experimental study of nanofluid thermal and tribological assessment has not hitherto been reported in literature. It is shown that improved heat transfer capability of nanofluids is particularly effective in the reduction of friction under a mixed regime of lubrication.

Multiscale Friction in Lubricant-Surface Systems for High-Performance Transmissions Under Mild Wear

The lubricant-surface system is complex in nature and can significantly affect the frictional performance of high-performance transmission systems. The complexity stems from the coupled mechanical and chemical phenomena that occur at the interfacial tooth conjunctions. A combined analytical and precision experimental approach is presented to analyse the salient parameters of the lubricant-surface system. A multiscale procedure comprising topographical measurement, pin-on-disc tribometry, atomic force microscopy in lateral force mode, X-ray photo-electron spectroscopy and continuum contact mechanics analysis under mixed non-Newtonian thermo-elastohydrodynamics is used to describe the formation of a tribo-film, as well as wear and frictional characteristics of the lubricant-surface system. The contribution of chemisorbed and physisorbed bonded tribo-film on the boundary coefficient of friction is ascertained at different physical scales. Therefore, the paper presents a novel multiscale analysis, promoting improved understanding of the complex interactions between mechanisms of friction, wear and surface chemistry.

Asperity level tribological investigation of automotive bore material and coatings

Choosing in-cylinder surfaces is complex. A well-chosen surface has low friction and wear. Conversely, poor oversight often leads to premature failure through wear and scuffing. Typically cylinder bore surfaces are selected experientially. This paper demonstrates the use of Atomic Force Microscopy in LFM mode, characterising typical cylinder bore materials and coatings. The approach uses integrated LFM with continuum contact mechanics. It evaluates the real contact area and effective elastic modulus of the surface, including the effect of any reactive surface film. Surface energy and shear strength, as well as the coefficient of friction in nanoscale interactions are also determined. These properties are measured for 6 cylinder bore materials, including for composite Nickel-Silicon Carbide and DLC, used for high performance engines.

Analysis of the adhesion effect in RF-MEMS switches using atomic force microscope

The main scope of this paper is to investigate the adhesion effect on the mechanical response of MEMS components from RF switch application by using an atomic force microscope (AFM). The occurrence and strength of adhesion effects in MEMS devices depend on a variety of environmental, geometrical and operational parameters (temperature, relative humidity, contact area, surface energies of contact materials, surface roughness and shape of contact surfaces) — so-called adhesion parameters should be taken into account when investigating the reliability of MEMS devices with respect to adhesion-induced failures. After, the temperature influence on adhesion is experimentally analyzed considering commonly used MEMS materials to fabricate RF switches. The adhesion force is the main factor with influence on stiction. In fact, stiction is the adhesion occurring between the contact surfaces due to surface forces including van der Waals, capillary forces, Casmir forces, and electrostatic forces. First, the adhesion between AFM tip and the materials under interest is investigated using the spectroscopy in point of an atomic force microscope. Different coated AFM tip is considered for tests. The AFM spectroscopy-in-point curve gives the direct measurement of tip-sample interaction force as a function of the gap between the tip and sample. The adhesion between tip and sample is characterized by so-called pull-off or pull-out force. The pull-off force is related in current continuum contact mechanics model to the work of adhesion. Using a thermal controller stage the temperature of investigated materials is changed from 0°C to 80°C. The mechanical properties variation of MEMS materials as a function of temperature is monitored and the temperature influence on adhesion is analyzed. The influence of the surface roughness on the adhesion forces between AFM tip and samples is determined. Different roughness (Ra) of investigated polysilicon samples is varied in the range of ∼5–15 nm. The adhesion force between Si 3 N 4 and these surfaces increases from 0.94nN to 12.72nN if the roughness decreases from 12nm to 7nm. In order to compare the influence of cantilever type of adhesion testing was done on several samples of the gold using two kinds of cantilevers. As the roughness decreases, the adhesion force increases, respectively. A high value of adhesion force is determined for the contact between gold AFM tip and gold sample comparatively with the contact between Si 3 N 4 AFM tip and gold material. This difference is based on the surface energy of materials. After material testing, flexible MEMS component used in RF switches is investigated in order to determine the adhesion force between him and the substrate. The contact areas between an AFM tip and substrate is an important parameter for analyzing the adhesion effect. The results from laboratory indicate that the adhesive force increases if the surface roughness decreases because the contact area increases, respectively. The adhesion between microcantilever and substrate is obtained based on experimental tests of 11.675μN.

Simulated Adhesion between Realistic Hydrocarbon Materials: Effects of Composition, Roughness, and Contact Point

The work of adhesion is an interfacial materials property that is often extracted from atomic force microscope (AFM) measurements of the pull-off force for tips in contact with flat substrates. Such measurements rely on the use of continuum contact mechanics models, which ignore the atomic structure and contain other assumptions that can be challenging to justify from experiments alone. In this work, molecular dynamics is used to examine work of adhesion values obtained from simulations that mimic such AFM experiments and to examine variables that influence the calculated work of adhesion. Ultrastrong carbon-based materials, which are relevant to high-performance AFM and nano- and micromanufacturing applications, are considered. The three tips used in the simulations were composed of amorphous carbon terminated with hydrogen (a-C-H), and ultrananocrystalline diamond with and without hydrogen (UNCD-H and UNCD, respectively). The model substrate materials used were amorphous carbon with hydrogen termination (a-C-H) and without hydrogen (a-C); ultrananocrystalline diamond with (UNCD-H) and without hydrogen (UNCD); and the (111) face of single crystal diamond with (C(111)-H) and without a monolayer of hydrogen (C(111)). The a-C-H tip was found to have the lowest work of adhesion on all substrates examined, followed by the UNCD-H and then the UNCD tips. This trend is attributable to a combination of roughness on both the tip and sample, the degree of alignment of tip and substrate atoms, and the surface termination. Continuum estimates of the pull-off forces were approximately 2-5 times larger than the MD value for all but one tip-sample pair.

Multiscale model of elastic nanocontacts

A multiscale scheme for adhesive elastic contact is proposed to evaluate the interaction mechanisms between two solids. The constitutive law, internal to each body, is described by classical continuum mechanics. The model introduces the atomic structure in the region of contact to evaluate the contact conditions at the coarse scale. Simulations of normal loading and sliding were used to compare quantities such as contact radius, stresses and frictional forces with that from Molecular Dynamics. The radius of contact obtained from the non-adhesive cases show that the model falls in between continuum contact mechanics and molecular dynamics. Stresses resulting from a normal loading are within a few percents of the discrete model for regions further than 15σ from the contact interface. The frictional characteristics exhibit essential stick–slip phenomenon and compare favourably with the Molecular Dynamics results. The integration of the non-linearities of the material at the coarse scale and the account of the out of phase motions of atoms within the coarse scale mesh are necessary to improve the solution in regions subject to more severe stresses.

Specific adhesion of a soft elastic body on a wavy surface

This paper aims at developing a stochastic-elastic model of a soft elastic body adhering on a wavy surface via a patch of molecular bonds. The elastic deformation of the system is modeled by using continuum contact mechanics, while the stochastic behavior of adhesive bonds is modeled by using Bell's type of exponential bond association/dissociation rates. It is found that for sufficiently small adhesion patch size or stress concentration index, the adhesion strength is insensitive to the wavelength but decreases with the amplitude of surface undulation, and that for large adhesion patch size or stress concentration index, there exist optimal values of the surface wavelength and amplitude for maximum adhesion strength.

Study on Contact Characteristic of Nanoscale Asperities by Using Molecular Dynamics Simulations

The nanoscale contacts, which play a key role in nanotechnology and micro-/nanoelectromechanical systems, are fundamentally important for a wide range of problems including adhesion, contact formation, friction and wear, etc. Because continuum contact mechanics has limitations when it is applied at length of nanoscale, molecular dynamics (MD) simulations, which can investigate internal physical mechanisms of nanostructures by atomic motions in detail, become one of the most promising approaches for investigating mechanical behaviors of contacts in nanoscale. First, contacts between rigid cylindrical probes with different radii and an elastic half-space substrate are studied by using MD simulations with the assistance of the classical Lennard-Jones potential. For contacts without adhesion, the relationship between the applied force and the contact half-width is analyzed. The von Mises stress distributions are then discussed. For contacts with adhesion, the phenomena of the jump-to-contact, the break-off contact, and the hysteresis are observed. The pressure distributions and the von Mises stress contours in the contact region agree with the existing solutions. Second, the effects of the surface topography on adhesive contacts are studied by using MD simulations with the embedded atom method potential. The adhesive contact mechanical characteristic of a series of asperities with different shapes, different sizes, and different numbers on contacting surfaces are discovered and compared. The results show that the surface topography is one of the major factors, which may influence the contact behaviors between the interfaces of nanoscale components.

Contact Mechanics of UV/Ozone-Treated PDMS by AFM and JKR Testing: Mechanical Performance from Nano- to Micrometer Length Scales

The Young’s modulus of cross-linked poly(dimethylsiloxane) (PDMS) surface was quantitatively investigated as a function of UV/ozone treatment time across different length scales. An AFM was used to probe PDMS surface mechanical properties at the nanometer length scale. The Young’s modulus of each sample was estimated with continuum contact mechanics theory (Sneddon method) using AFM data by employing the hyperboloid tip shape model. A custom-built ATD device (JKR method) was also used which allowed us to simultaneously monitor the load, the contact area, and the relative displacement between (a) a lens (made either of PDMS elastomer or of Si3N4) and (b) surface-treated PDMS films upon loading and unloading on the micrometer to submillimeter length scales. The modulus of PDMS increased with increasing treatment time as observed by AFM as well as by ATD, which we explained by the gradual formation of a silica-like layer. For all specimens tested, the modulus values obtained were highest from AFM, lower from ATD, and lowest from bulk tensile experiments for the same UV/ozone dose. These results demonstrate the effect of the probed length scale of the tests used to assess mechanical performance

An atomic interaction‐based continuum model for computational multiscale contact mechanics

AbstractA computational multiscale contact mechanics model is presented which describes the interaction between deformable solids based on the interaction of individual atoms or molecules. The contact model is formulated in the framework of large deformation continuum mechanics and combines the approaches of molecular modelling [1] and continuum contact mechanics [2]. In the following a brief overview of the contact model is given. Further details can be found in [3], [4] and [5]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Friction Study of a Ni Nanodot-patterned Surface

Nanoscale frictional behavior of a Ni nanodot-patterned surface (NDPS) was studied using a TriboIndenter by employing a diamond tip with a 1 μm nominal radius of curvature. The Ni NDPS was fabricated by thermal evaporation of Ni through a porous anodized aluminum oxide (AAO) template onto a Si substrate. Surface morphology and the deformation of the NDPS were characterized by scanning electron microscopy (SEM) and atomic force microscopy (AFM), before and after friction/scratch testing. SEM images after scratching clearly showed that, similar to what was assumed at the macroscale, the frictional force is proportional to the real area of contact at the nanoscale. It was found that adhesion played a major role in the frictional performance, when the normal load was less than 20 μN and plastic deformation was the dominant contributor to the frictional force, when the normal load was between 60 μN and 125 μN. Surprisingly, a continuum contact mechanics model was found to be applicable to the nanoscale contact between the tip and the inhomogeneous Ni NDPS at low loads. The coefficient of friction (COF) was also found to depend on the size of the tip and was four times the COF between a 100 μm tip and the Ni NDPS. Finally, the critical shear strength of the Ni nanodots/Si substrate interface was estimated to be about 1.24 GPa.

Cellulose Thin Films: Degree of Cellulose Ordering and Its Influence on Adhesion

Adhesion measurements have been performed with thin cellulose films using continuum contact mechanics with application of the JKR theory. Three different cellulose surfaces were prepared, one crystalline and two surfaces with a lower degree of crystalline order. Adhesion between two cross-linked poly(dimethylsiloxane) (PDMS) caps, as well as the adhesion between PDMS and the various cellulose surfaces, was measured. The work of adhesion (from loading) was found to be similar for all three surfaces, and from contact angle measurement with methylene iodide it was concluded that dispersive interactions dominate. However, the adhesion hysteresis differed significantly, being larger for a less ordered cellulose surface and decreasing with increasing degree of crystalline order. This is suggested to be due to the surface groups' ability to orient themselves and participate in specific or nonspecific interactions, where a surface with a lower degree of crystalline order has a higher possibility for reorientation of the surface groups. The mobility of cellulose chains increases with water uptake, resulting in stronger adhesive joints. These films will hence allow for determination of the contributions of hydrogen bonding and inter-diffusion on the adhesion, determined from the unloading data, as the thermodynamic work of adhesion was found to be independent of the cellulose surface used.

A contact mechanics model for quasi‐continua

AbstractA computational multiscale contact mechanics model is proposed to describe the interaction between deformable solids based on the interaction of individual atoms or molecules belonging to the solids. The contact model, formulated in the framework of large deformation continuum mechanics, is derived from coarsening the molecular dynamics (MD) description of a large assembly of individual atoms, and it thus bears some of the characteristics of the underlying atomic structure. The multiscale contact model distinguishes between atoms interacting within a small neighbourhood within the solids and atoms interacting over large distances between remote regions of the solids. The former furnishes a constitutive relation for the continuum, like the Cauchy–Born Rule, while the latter is used to model the interaction between distinct bodies. The proposed contact model is formulated as a variational weak form and implemented within an updated Lagrangian finite element method. It is shown that, as the problem size increases, the description of the model can be simplified to yield more efficient computational algorithms. In this respect, the proposed multiscale formulation leads to a smooth transition from MD to continuum contact mechanics. The general behaviour of the contact model is studied, and some numerical examples are given. Copyright © 2007 John Wiley & Sons, Ltd.

Ni nanodot-patterned surfaces for adhesion and friction reduction

Surface nano-patterning with Ni nanodot arrays was investigated for adhesion and friction reduction of contacting interfaces. Self-assembled anodized aluminum oxide (AAO) templates in conjunction with thermal evaporation was used to fabricate nano-patterned surfaces with ordered Ni nanodot arrays on Si substrates. Surface morphology of the Ni nanodot-patterned surfaces (NDPSs) was characterized by scanning electron microscopy (SEM). Adhesion and friction studies on a Ni NDPS and a baseline smooth Si(100) surface were conducted using a TriboIndenter employing a diamond tip with 100 μm nominal radius of curvature. The results show that the ordered Ni nanodot-patterning reduced the adhesion forces and coefficients of friction up to 92 and 83%, respectively, compared to those of the smooth silicon surface. Surprisingly, the nanoscale multi-asperity contact between the diamond tip and inhomogeneous Ni NDPSs under low loads follows a continuum contact mechanics model.

Contact of single asperities with varying adhesion: Comparing continuum mechanics to atomistic simulations

Atomistic simulations are used to test the equations of continuum contact mechanics in nanometer scale contacts. Nominally spherical tips, made by bending crystals or cutting crystalline or amorphous solids, are pressed into a flat, elastic substrate. The normal displacement, contact radius, stress distribution, friction, and lateral stiffness are examined as a function of load and adhesion. The atomic scale roughness present on any tip made of discrete atoms is shown to have profound effects on the results. Contact areas, local stresses, and the work of adhesion change by factors of 2 to 4, and the friction and lateral stiffness vary by orders of magnitude. The microscopic factors responsible for these changes are discussed. The results are also used to test methods for analyzing experimental data with continuum theory to determine information, such as contact area, that cannot be measured directly in nanometer scale contacts. Even when the data appear to be fit by continuum theory, extracted quantities can differ substantially from their true values.

The breakdown of continuum models for mechanical contacts

Forces acting within the area of atomic contact between surfaces play a central role in friction and adhesion. Such forces are traditionally calculated using continuum contact mechanics, which is known to break down as the contact radius approaches atomic dimensions. Yet contact mechanics is being applied at ever smaller lengths, driven by interest in shrinking devices to nanometre scales, creating nanostructured materials with optimized mechanical properties, and understanding the molecular origins of macroscopic friction and adhesion. Here we use molecular simulations to test the limits of contact mechanics under ideal conditions. Our findings indicate that atomic discreteness within the bulk of the solids does not have a significant effect, but that the atomic-scale surface roughness that is always produced by discrete atoms leads to dramatic deviations from continuum theory. Contact areas and stresses may be changed by a factor of two, whereas friction and lateral contact stiffness change by an order of magnitude. These variations are likely to affect continuum predictions for many macroscopic rough surfaces, where studies show that the total contact area is broken up into many separate regions with very small mean radius.

Accounting for the JKR–DMT transition in adhesion and friction measurements with atomic force microscopy

Over the last 15 years, researchers have applied theories of continuum contact mechanics to nanotribology measurements to determine fundamental parameters and processes at play in nanometer-scale contacts. In this paper we discuss work using the atomic force microscope to determine nanoscale adhesion and friction properties between solids. Our focus is on the role that continuum contact mechanics plays in analyzing these measurements. In particular, we show how the JKR-to-DMT transition is taken into account, as well as limitations involved in using these models of contact in the presence of adhesion.