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Journal membership for December 2023 : Current tendencies in modeling of asperity-level put on

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J.-F. Molinari 1, S. Z. Wattel 1, L. Ma 2, and R. Aghababaei 2

1 Computational Stable Mechanics Laboratory, Institute of Civil Engineering, Institute of Supplies, École Polytechnique Fédérale de Lausanne (EPFL), CH 1015 Lausanne, Switzerland

2 Floor Mechanics and Tribology Group, Division of Mechanical and Manufacturing Engineering, Aarhus College, 8000 Aarhus C, Denmark

 https://imechanica.org/files/Sacha_Wattel.jpg

1 Introduction

Ernest Rabinowicz’s phrases, spoken 20 years in the past in his groundbreaking textbook on the friction and put on of supplies [1], proceed to resonate right now: ’Though put on is a crucial matter, it has by no means obtained the eye it deserves.’ Rabinowicz’s work laid the muse for modern tribology analysis [2]. Put on, characterised because the elimination and deformation of fabric on a floor as a result of mechanical motion of one other floor, carries vital penalties for the economic system, sustainability, and poses well being hazards by means of the emission of small particles. Based on some estimates [1, 3], the financial impression is substantial, accounting for roughly 5% of the Gross Nationwide Product (GNP).

Regardless of its paramount significance, scientists and engineers typically shrink back from put on evaluation as a result of intricate nature of the underlying processes. Put on is commonly perceived as a ”soiled” matter, and with good purpose. It manifests in varied varieties, every with its personal intricacies, arising from complicated chemical and bodily processes. These processes unfold at completely different phases, making a time-dependent phenomenon influenced by key parameters reminiscent of sliding velocity, ambient or native temperature, mechanical masses, and chemical reactions within the presence of international atoms or humidity.

Determine 1: Publication statistics within the Put on journal, displaying a negligible contribution of numerical research over previous a long time [4]. Blue bars present the entire variety of annual publications on the topic. Crimson bars present the variety of publications that studied the topic utilizing a numerical device, together with the finite-element method, the discrete-particle technique, and the molecular-dynamics method. Statistics are obtained from the Scopus web site.

The overview paper by Vakis et al. [5] supplies a broad perspective on the complexity of tribology issues. This complexity has led to quite a few remoted research specializing in particular put on mechanisms or processes. The proliferation of empirical put on fashions in engineering has resulted in an abundance of mannequin variables and match coefficients [6], making an attempt to seize the intricacies of experimental information.

Tribology faces a elementary problem as a result of multitude of interconnected scales. Surfaces exhibit roughness with asperities occurring at varied wavelengths. Solely a small fraction of those asperities come into contact, and a fair smaller fraction produces put on particles. The explanations behind why, how, and when this happens aren’t absolutely understood. The particles progressively alter the floor profile and interacts with each other, both being evacuated from the contact interface or gripping it, resulting in extreme put on. On account of this problem of scales, contributions of numerical research in put on analysis over the previous a long time sum as much as lower than 1% (see Fig. 1). But, thrilling alternatives exist for modeling, which we try to debate right here.

Whereas analyzing a single asperity contact could not unveil all the story, it arguably represents probably the most elementary stage to grasp put on processes. This weblog entry seeks to encapsulate the authors’ perspective on this quickly evolving matter. Acknowledging its inherent bias, the purpose is to spark controversies and discussions that contribute to a vibrant blogosphere on the mechanics of the method.

The following part delves into the authors’ endeavors in modeling adhesive put on on the asperity stage. Part 3 navigates the transition to abrasive put on, whereas Part 4 explores alternatives for upscaling asperity-level mechanisms to the meso-scale, with the aspiration of establishing predictive fashions. Lastly, though the first focus of this weblog entry is on modeling efforts, it might be remiss to not point out just a few latest advances on the experimental entrance.

2 Atomistic simulations of adhesive put on

Our dialogue focuses particularly on asperity-level put on mechanisms, the place a big overlap happens between contacting junctions. This leads to both extreme plastic deformation or the formation of particles. There may be after all a big physique of labor in nanotribology that investigates nanoscale mechanisms, reminiscent of atom by atom attrition, that we miss of the dialogue [7–9].

We begin by inspecting Molecular Dynamics (MD) simulations carried out by Aghababaei, Warner, and Molinari [10]. Their work, for the primary time, revealed the adhesive put on course of described by Rabinowicz [1] and mentioned in a perspective paper [2]. Fig. 2 succinctly summarizes the primary discovering, a ductile to brittle transition at a essential materials size scale. Contact asperities forming junctions beneath this scale bear plastic deformation, whereas bigger junctions result in crack formation, leading to particles that detaches from the contact interface. This materials size scale determines the minimal particles particle measurement, essential in understanding the onset of damage and in addition fantastic particle air air pollution. The minimal particles particle measurement is decided by Griffith’s argument, addressing whether or not the saved elastic vitality within the sheared contact junction is ample to create new crack surfaces. The ensuing size scale d* is proportional to the floor vitality γ (for very brittle supplies), the shear modulus G and inversely proportional to the sq. of the shear power τ:

 

with λ a geometrical issue of the order of unity.

Though Rabinowicz initially proposed an identical energetic argument [2] for the discharge of trapped particles, the simulations of Aghababaei et al. not solely verify the existence of a minimal particles measurement but additionally reveal that small contact junctions bear plastic deformation, constantly smoothing floor roughness throughout sliding. Ductile processes due to this fact scale back roughness, finally forming junctions massive sufficient to lead to particles formation at a later stage. This competitors between ductile and brittle occasions is a key commentary and results in roughness reaching a gentle state.

Whereas MD simulations are resource-intensive and constrained in time and house, Milanese et al. [11] demonstrated that after particles creation, the floor roughness resembles a self-affine fractal. These 2D simulations, illustrating roughness creation, have been not too long ago prolonged to 3D utilizing a supercomputer [12, 13]. A vital level is that to disclose brittle occasions and create roughness, the simulation area should exceed the essential junction measurement. MD simulations that neglect this size scale solely show a flattening of the contact floor, as seen by Spijker [14], the place tough aluminum samples have been modeled with an EAM potential in a simulation field of 32nm, which is clearly inadequate to symbolize fracture processes in aluminium. Equally, the MD simulations in [15, 16] aren’t carried out at scales that may reveal brittle mechanisms.

Aghababaei et al. simulations have opened up a number of views, indicating that frictional work is a wonderful predictor of particles particle measurement for contact junctions close to the essential measurement [17], whereas serving as an higher certain for bigger junctions [18]. Brink prolonged early simulations that used easy Morse potentials to extra practical potentials for ceramics, uncovering a 3rd mechanism—slip for surfaces with lowered adhesion [19].

Naturally, these fashions may be utilized to supplies with hardness distinction, exploring the transition to abrasive put on—an space we delve into within the subsequent part.

 

Determine 2: A ductile to brittle transition controls the particles formation course of. a) Aghababaei, Warner and Molinari have proven that adhesive put on is managed by the geometry of asperities that collide and materials properties [10]. b) Contact junctions smaller than a cloth size scale d* deform plastically throughout sliding. c) Contact junctions bigger than d* consequence within the formation of a indifferent particles. These outcomes have been initially obtained with easy and fairly brittle Morse potentials, that allowed MD simulations to span the parameter house at a low computational price.      

 

3 Atomistic simulations of abrasive put on

Within the realm of abrasive put on, MD simulations have gained appreciable consideration. On this part, we primarily overview the MD simulations of two-body abrasive put on on the single asperity stage.

Beginning within the Eighties with the event of Atomic Power Microscopy (AFM) [20], tribology has taken a flip in the direction of bringing about atomic insights into single-asperity abrasive put on [21]. Kato et al. [22] established an abrasive put on mode map, distinguishing the chopping, wedge-forming, and plowing modes. In recent times, many researchers have used MD simulations to review parameters that management abrasive put on and corresponding materials elimination mechanisms. Fang et al. [23, 24] undertook a scientific exploration of how loading circumstances, reminiscent of utilized load, dwell time, temperature, and geometry affect the wear and tear responses throughout nanoscratching [25–27].

The interaction of adhesive interactions between the abrasive piece and substrate emerges as an necessary think about materials elimination charge and mechanism [28]. Hu et al. [29] investigated the results of adhesive power and cargo on materials switch throughout nanoscale sliding, discovering that adhesion and abrasion contribute to materials switch, with their relative significance relying on load and work of adhesion. It was additionally proven [30, 31] that the upper the adhesive power, the bigger the plastic deformation and materials switch. However, low adhesive power results in materials detachment with out vital subsurface deformation.

Li and Aghababaei [32, 33] studied the impact of abrasion and adhesion on materials elimination through controlling scratching depth and adhesive power. As proven in Fig. 3, this research confirmed the existence of a essential adhesive power, dictating the transition between the atom-by-atom elimination and the fragment elimination regimes. It may be seen that the bigger the scratching depth, the smaller the essential adhesive power at which the transition within the materials elimination mechanism happens. It was additionally proven that the wear and tear coefficient will increase with adhesion power and scratching depth and finally saturates to a continuing worth. The saturation noticed is linked to the shift from atomic attrition put on to plasticity-induced put on. This confirms the potential of acquiring a put on coefficient impartial of depth and adhesion when plastic deformation governs abrasive put on.

 

Determine 3: Picture taken from [32] that investigates how abrasion and adhesion affect the fabric elimination mechanisms throughout abrasive put on. There’s a essential adhesive power, indicating the transition between (i) atom-by-atom elimination and (ii) fragment elimination regimes. The essential adhesive power is a operate of scratching depth.

Crystalline supplies exhibit anisotropy on the micro- and nano-scale because of completely different crystallographic orientations. This may occasionally affect the floor morphology [34, 35] and scratching forces [36]. Intensive MD simulations have been carried out to review the anisotropic scratch response of single crystal Cu [37–39], Ni [40, 41], and Au [42, 43]. Additionally, researchers investigated the deformation mechanism and tribological properties of nanolayered overcoats by means of single-asperity abrasive put on fashions. Worth et al. [44] carried out MD simulations to review the impression of coating design parameters, reminiscent of layer thickness and composition, on the adhesion of ultra-thin multi-layer DLC coatings to the substrate. Their findings reveal that an intermediate DLC layer with a decrease sp3 fraction than the outermost DLC coating layer protects the substrate from plastic deformation below exterior loading. The layering morphology of assorted multilayer coatings was studied utilizing MD simulations, strategically aimed toward optimizing abrasive put on efficiency [45–47].

4 Upscaling

MD simulations implicitly account for a lot of complicated mechanisms reminiscent of contact, plasticity, injury or fracture, which make them of nice use for the numerical investigation of tribology. Nonetheless, a big downside is their excessive computational price, limiting their applicability to modeling large-sized asperities or surfaces comprising many asperities. Within the following, strategies to cope with each of those challenges are introduced.

4.1 Single asperity past the nanometer

 

4.1.1 Coarse-graining strategies

To deal with the computational price situation, coarse-graining strategies have been not too long ago proposed. Pham-Ba and Molinari [48] suggest a Discrete-Factor Mannequin (DEM) the place every particle represents many atoms. The interplay potential between particles options an elastic department when two particles are in compressive contact and a cohesive department when they’re pulled away, aiming to emulate the adhesive contact and fracture conduct of atomistic simulations. The potential may be tuned to match desired macroscale properties reminiscent of Younger’s modulus or floor vitality. This mannequin is ready to seize the brittle to ductile transition of single asperity whereas lowering the computation necessities by a number of orders of magnitude. Nevertheless, because the particles are non-breaking, a pure measurement limitation seems: the particle ought to keep beneath d* if one needs to maintain the dimensions of particles shaped in line with the essential junction measurement mannequin. To upscale additional, Mollon introduces one other DEM framework utilizing each deformable particles and cohesion [49]. Certainly, cohesion has been discovered to be a mandatory ingredient to have the ability to seize the rolling conduct of third our bodies. With these fashions, [50, 51], a wealthy set of third-body conduct was uncovered, together with a mixed-mode conduct, combining traits of the rolling third physique conduct and of shear bands. These modes are illustrated in Fig. 4, and have been proven to be a essential issue within the origin of friction forces.

It is very important word that each fashions differ essentially from standard DEM formulations, as their interplay legal guidelines aren’t designed to symbolize a particular granular materials. Slightly, parameters are tuned to match homogenized materials properties, positioning these fashions as surrogate representations of damageable steady media.

Current efforts [52, 53] developed a concurrent multiscale technique, coupling the continuum finite-element area with discrete coarse-grained atomistic potentials [10]. On this multiscale framework, complexities like massive deformation, crack nucleation, and propagation are simulated within the atomistic area, whereas far-field boundary circumstances are modeled within the continuum area. It’s proven that the strategy can precisely predict crack formation whereas lowering the computation price considerably.

These strategies open analysis alternatives by enabling micromechanical simulations at a bigger scale.

 

Determine 4: (a) Instance of a combined regime, showcasing the technology of damage particles, their aggregation, and subsequent reattachment to the sliding our bodies. The hole between the our bodies stays constantly sized. The colours denote the preliminary vertical place of the particles. (b) Instance of a shear band state of affairs. No discernible hole is noticed between the 2 our bodies, and the particles exhibit vertical migration. (c) Instance of the formation of huge put on particles, growing in measurement till they match the scale of all the system. Reproduced from [51].  

 

 

4.1.2 Continuum strategies

Whereas continuum fashions may wrestle to seize the massive deformations and particles formation mechanisms seen at a tribological interface, they endure much less from scaling points. A number of latest works [54–56] modeled asperity collision with a phase-field method for fracture. By adjusting the fabric ductility and mannequin geometry, they get better the three behaviors mentioned above: slipping with out vital injury, injury to the asperity’s tip, or crack nucleation on the base of the asperity [56]. As soon as once more, the essential size scale d* proves helpful in predicting the predominant conduct. Micromechanics of asperity fracture below static and cyclic loading circumstances have additionally been investigated in recent times [57–60], offering a foundation for growing put on fashions for brittle solids.

A latest investigation of abrasion with size-dependent crystal plasticity by Zhu and Aghababaei [61] indicated that crystallographic anisotropy leads to orientation and scratching direction-dependent put on quantity and thus coefficient, see Fig. 5. Alternatively, it’s proven {that a} distinctive put on coefficient may be obtained for crystalline supplies when one makes use of the scratching hardness in Archard’s put on regulation. Moreover, it’s proven [62] that the diploma and nature of size-dependency within the scratch hardness worth and pile-up magnitude differ considerably and oppositely with the scratch course. For example, whereas the [001] course exhibits the very best diploma of measurement impact in scratch hardness, it presents the bottom pile-up measurement impact.

 

Determine 5: Comparability of floor topographies of damage groves on (001)-oriented single crystalline copper (a.) obtained from experiments and simulations after scratching in (b.) 0° and (c.) 22.5°, measured based mostly on [100] crystalline course. (d.) presents the entire put on quantity obtained from scratching simulations and experiments for various scratch instructions on [001], [101], and [111] crystalline copper surfaces.

On one other word, Milanese and Molinari [63] carried out an analytical and numerical research of the mechanics of a rolling particle. The aim of this investigation was to elucidate the commentary {that a} particle, whereas rolling between two surfaces within the presence of considerable adhesion, tends to extend in measurement, resembling the build-up of a snowman. It was proven that, on the junction of the particle and the majority, cracks ideally develop into the majority somewhat than into the particle, leading to chips adhering to the particle.

4.2 Going past the one asperity

Whereas single asperity contact constitutes probably the most elementary mechanism, nearly all of sliding contacts of curiosity contain many micro-contacts. These micro-contacts could or could not work together, affecting the general conduct. Furthermore, the fractal, self-affine, nature of most pure and man-made surfaces signifies that what’s outlined as a single asperity can rely upon the dimensions of commentary. Thus, it’s essential to increase the understanding gained of the one asperity mechanics – the microscale – to the multi-asperities contact – the mesoscale. Right here, we current latest findings on the interplay of asperities and discover how these insights could contribute to advancing the comprehension of macroscale put on legal guidelines.

4.2.1 Asperity interactions

Interactions between neighboring asperities play a vital function in tribological phenomena. When broadly spaced, asperities react individually, however because the spacing decreases, their sub-surface stress fields begin to overlap, inflicting them to react collectively. Aghababei, Brink and Molinari [64] carried out a parametric research utilizing MD simulations of double asperity-to-asperity collision with various spacing. When the spacing was massive in comparison with the asperity diameter, the 2 contacts behaved independently. Nevertheless, because the spacing approached the asperity measurement, each asperity indifferent collectively, as if appearing as a single bigger asperity, leading to a proportionally greater put on quantity. Son et al. studied the elastic stress discipline generated by the asperity collision for each the two-dimensional [65] and three-dimensional case [66]. Supplementing the analytical outcomes with MD simulations, maps predicting the anticipated conduct are derived. Primarily based on spacing and asperity measurement relative to d*, it could possibly be decided whether or not plastic, impartial or mixed conduct would happen within the simulations.

Asperity interplay could clarify the transition from delicate to extreme put on when the traditional load is elevated [64]. Because the load will increase, contact patches develop bigger and new distinct patches seem. Whereas the rise in actual contact space is kind of linear with the load, the patches can begin to work together, which leads to put on particles bigger than the dimensions of particular person patches and thus an excellent linear scaling of the wear and tear charge with load.

4.2.2 Examination of engineering put on legal guidelines

Archard’s put on regulation is broadly utilized in engineering functions. It states that put on is proportional to the sliding distance and regular drive, and inversely proportional to the hardness. A put on coefficient, basically a becoming coefficient, which may take worth anyplace between 108 to 101, accounts for the impact of different parameters and should be, as of now, decided empirically. One of many nice challenges of tribology is to find out how this put on coefficient could possibly be derived from first rules.

Systematic investigation of asperity stage adhesive put on [18, 67, 68] highlighted {that a} linear adhesive put on regulation (i.e. Archard’s relation) may be recovered on the single-asperity stage provided that the fabric elimination is dominated by plastic deformation, confirming the longstanding Archard’s theoretical speculation. Alternatively, the relation breaks down when cleavage fracture or thermally activated atomic detachment governs the lack of materials on the asperity stage. Moreover, it’s proven that [69] within the presence of weak adhesion, sliding is dominated by frictional slipping (i.e., dislocations glide within the contact aircraft), the place occasional atomic cluster detachments and a sublinear put on relation are anticipated. Alternatively, a linear relationship between the amount of indifferent materials and the frictional work may be obtained when bulk plasticity dominates materials elimination on the asperity tip. Beneath this situation, high-shear stresses on the contact set off the migration of misfit dislocations into the asperity bulk, inflicting extreme plastic deformation through dislocation-mediated interface migration. This consequence highlights that the state of stresses at contact governs the method of fabric elimination and put on relations on the asperity stage. Moreover, it’s proven [70] that on the nanoscale, the wear and tear coefficient will increase by the adhesion power and scratching depth and finally saturates to a continuing worth. The saturation is related to the transition from atomic attrition put on mode to plasticity-induced put on.

 

Determine 6: Schematic of the wear and tear fashions. (a) Tough-on-rough elastoplastic contact drawback, which is solved as a inflexible tough on elastoplastic flat contact following Johnson’s assumption [71]. The yellow areas correspond to the contact patches. (b) The preliminary mannequin proposed by Frérot et al. [72] Contact patches in purple type particles. Rising the hardness (conserving all different mannequin parameters fixed) results in a bigger fraction of microcontacts being purple, in opposition to Archard’s regulation. (c) The improved mannequin of Brink et al. [73], which takes the sliding course of under consideration and reconciles mannequin’s prediction with Archard. Reproduced from [73].

Insights from single asperity mechanics and asperities interactions may be utilized to the outcomes of BEM (Boundary Factor Methodology) simulations of rough-on-rough contact to deliver some parts of reply to the query of the origin of the wear and tear coefficient. BEM simulations permit the environment friendly modeling of the elastoplastic contact drawback between two self-affine tough surfaces [74, 75]. From these simulations, the contact patches may be recovered.

An preliminary thought [72] was to take the elastic contact map as-is and assume that any contact patch bigger than d* would contribute to the wear and tear quantity. Popov and Pohrt [76] ran an identical research utilizing elasto-plastic BEM simulations and predicted particle detachment with the ratio of elastic saved vitality to adhesion vitality, as for the formulation of d*. Brink et al. added an necessary factor, that’s the historical past of the sliding [73]. As the 2 surfaces slide towards one another, new contact patches seem and develop in measurement earlier than disappearing once more. Then, it’s assumed that every contact patch will result in the creation of a put on particle when its measurement reaches d* after which be ”deactivated” (i.e. can not type one other put on particle), as illustrated in Fig. 6. On this case, growing the hardness and thus lowering d* results in the creation of smaller put on particles and thus a smaller put on charge. Thus, by taking into consideration the sliding motion, the mannequin and Archard’s put on regulation are reconciled. This mannequin, which accommodates no match parameter, yield qualitatively good tendencies however would wish additional refinement and experimental information to match to to be able to attain quantitative energy.

5 Outlook on experiments

To enhance the understanding gathered from numerical simulations, systematic put on experiments at small scales are essential. They permit validation and refinement of numerical simulations, providing a holistic perspective on put on modeling from nano to engineering scales. Such experiments provide invaluable insights into the basic mechanisms governing adhesive and abrasive put on on the nanoscale stage. In keeping with the prediction of the essential junction measurement mannequin, proposed by Aghababaei et. al., asperity stage put on experiments pictured two distinct put on mechanisms: plastic smoothening [77–81] and asperity fracture [82, 83].

By using exact management and measurement capabilities, researchers have explored the interactions between particular person asperities [77] and surfaces [84, 85]. Leriche et. al [84], proposed an novel experimental approach enabling the detection of damage volumes as small as 0.016μm3 over contact areas massive sufficient to supply insights on interactions between asperities. Leriche et. al [85] confirmed that Si3N4 wears by means of both atomic attrition or ductile elimination enhanced by subsurface injury, relying on the magnitude of the native Si3N4-on-Si contact stress. Surprisingly, they noticed that Si3N4 put on within the pre-sliding put on experiments didn’t scale with the vitality dissipated by means of friction, suggesting that contact formation and adhesive put on performed an necessary function within the put on course of. Current advances in X-ray and computed tomography additionally allow finding out the contact mechanics between non-transparent surfaces [86]. It’s apparent that in-situ put on experiments throughout various scales develop into important, as these experiments present real-time information that validate numerical simulations and advance our elementary comprehension of damage mechanisms.

6 Concluding remarks

We conclude this weblog entry by reemphasizing the essential significance of tribology in business and for a sustainable economic system. The view of the authors’ is that there’s a substantial place for development in Science in tribology. Laptop simulations and nanoscale experimental measurements of damage processes have opened new alternatives for predictive put on fashions. Definitely, we’ve got forgotten many related references within the abstract above. We hope this entry will generate a vigorous dialogue to enrich our biased and incomplete record of references.

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