From the Climate Change to the Atomic Scale Friction: Contact Mechanics Workshop Summary

This is a summary of International Workshop: Contact Mechanics and Friction – Foundations and Applications that was organized by Professor Popov and his group at TU Berlin on 13-17 October 2019. The workshop held this year was a special one since this year it was the 60th anniversary of Professor Popov. Valentin Leonidovich Popov is a well recognized tribologist and physicist who has enriched the fields of tribology and contact mechanics with many great research articles and books, future generation talent nurture. I will cite Professor Ciavarella here (from the special issue of Facta Universitatis):
I can say that I admire of Prof. Popov two things: one is the ability to go to the essentials of (tribological) problems, reaching solutions of engineering interest with the cleanest and simplest formulation, not using redundant mathematics to impress the reader (this having also a positive effect in teaching and in educating students at all levels). And the other is to have built a group of collaborators who apparently simply adore him, and this shows he is able to obtain from them the maximum collaboration also without redundant pressure.
– Michele Ciavarella –
It is the second time I attend this yearly workshop, which already has a long history. It started in 2004 and is organized by Professor Popov and his colleagues at Technical University of Berlin. In 2017 I attended the workshop the first time and it was devoted to the adhesion effects in contact mechanics, but this time the variety of topics was broader: from the climate change and earthquakes to the atomic scale friction and contact mechanics of living cells, from modeling, to experiments. There were many great presentations, but I can only highlight a few here. The full program of the workshop can be found here.

Friction impact on the climate change

The talk by Professor Jacqueline Krim from North Carolina State University was devoted to electrotunable control of friction with nanoparticles at solid-liquid interfaces. As it was shown during the presentation, by applying the voltage and varying the amount and type of nanoparticles, the friction at interfaces can be controlled. In her group, a Quartz Crystal Microbalance and atomic level simulations are used to explore the behavior of various nanoparticles in tribological contacts. The details on the applications and mechanisms of electortunable friction can be found in the recent work of the group – Controlling Friction With External Electric or Magnetic Fields: 25 Examples.

An important topic discussed by Professor Krim was related to the impact of friction on the economy and climate change. According to the presented estimates, potential financial savings from implementing currently available technologies in the field of tribology are up to 1.4% of US Gross National Product, and most of the savings are related to friction reduction (see the figure above). Besides a clear economical impact, friction may also have a great impact on the climate change as stated by Professor Krim. An estimate of the friction contribution to the average temperature rise reveals that ~0.25C of the total ~3C of the average temperature increase until 2100 year, as well as ~3.2 Gt CO2 emissions may be linked to friction losses in various mechanical systems. At the same time, Professor Krim argues, most of the savings on friction would be possible if existing insights from tribology science were implemented in current technology. A manuscript with details of this study is in preparation (J. Krim, Nanotribology, Basic Science and Applications, in preparation).

The New Advances of Superlubricity

A talk by Professor Jianbin Luo from Tsinghua University was devoted to superlubricity – the state of vanishingly small friction (what is small? See the figure on the left). This is the dream of many tribologists and green activists (even if they don’t know about it yet). The term was first introduced by Professor Hirano in the 1990 who carefully considered the details of the friction at the atomic scale. Professor Hirano theoretically predicted the existence of a physical state where friction can nearly vanish in case if the sliding interface is made of surfaces that are atomically flat, rigid, incommensurate (non-matching) and clean. Under these conditions the lateral force experienced by the atoms at the sliding interface would be canceled out resulting in negligible net friction force. Later researchers experimentally confirmed existence of the superlubricity state in the contact of Diamond Like Carbon and graphene, graphene and gold, and other dry contacts. And a bit more recently the superlubricity state was observed in lubricated sliding interfaces, such as gold-teflon contact lubricated by cyclohexane, quartz glass contact lubricated by biological liquid obtained from mucilage of Brasenia schreberi and others. Consequently, superlubricity is classified as solid superlubricity and liquid superlubricity depending on the lubricants present at the interfaces. Despite significant progress in the topic, there is still luck of understanding in the mechanisms leading to superlubricity, as well as challenges with increasing the ‘range of action’ (e.g., in contact pressures) to the range encountered in engineering applications, such as in bearings for example.

Liquid superlubricity has several advantages: it is easier achieved at the macroscale, less sensitive to the surface roughness and the surrounding atmosphere. The group of Professor Luo specializes in the area of superlubricity with an emphasis to the liquid superlubricity. By studying various superlubric systems, Professor Luo developed a model of the liquid superlubricity, see the figure below. According to the model, there are 3 effects that lead to the superlubricity in lubricated contacts: formation of an electric double layer, hydrodynamic effect and the hydration effect. The electric double layer generates a repulsion force between the surfaces and consequently reduces friction.  The hydrodynamic effect is associated with a shearing of low shear resistance liquid, such as hydrated water layer (but not free water, which might actually ruin the superlubricity). And finally, the hydration effect is related to a short-range repulsive interaction that acts between polar surfaces separated by a thin layer of polar liquid. Professor Luo gave a great summary of the liquid superlubricity mechanisms which are now much better understood. It was also shown that of now, the superlubricity occurs in a narrow range of external parameters (such as pressure, humidity, etc.) and the main goal for the research community is to find ways to stretch the range so that the superlubricity can be achieved in engineering applications.

A recent review of the liquid superlubricity can be found in the article: Macroscale Superlubricity Achieved With Various Liquid Molecules: A Review, Xiangyu Ge, Jinjin Li and Jianbin Luo, https://doi.org/10.3389/fmech.2019.00002.

The Friction and the Earthquakes

Let’s take a look at the bigger picture of things, say at the scale of our beloved planet Earth. The subsurface of Earth is actually a very active place which involves the motion of tectonic plates. This activity leads to the hazardous consequences sometimes, such as earthquakes and volcanic eruptions. Approximately 50,000 earthquakes occur annually around the world and 100 are large enough to create substantial damage if their centre is located near populated areas. Extremely large earthquakes occur once per year on average. Earthquakes are responsible for the deaths of millions of individuals over the Earth’s history. That’s why researchers try to explain and predict the behavior and motion of the earthquakes. It appears that friction plays a major role in these processes and the talk of Professor Jay Fineberg from The Hebrew University of Jerusalem was devoted to this problem. The group of Professor Fineberg studies the ‘laboratory earthquakes’ – laboratory scale experiments of space-time dynamics of the onset of the friction sliding. According to their findings, the onset of sliding is governed by the rupture fronts, which can be quantitatively described by the brittle fracture theory (further details here). ”Friction is fracture” – that is the main message of Professor Fineberg.

The group of Professor Fineberg looks at the real contact area evolution during the onset of sliding using the method of total internal reflection, see figure below. The light is shining into the contact, while an extremely fast camera records the transmitted light. The intensity of the transmitted light is proportional to the real contact area. Using such a set up, the evolution of the contact area can be traced with a great detail in time during the sliding, but what is the most important also prior to sliding.

Based on these experiments Professor Fineberg concludes that the motion (slip) initiates locally, and that the gross sliding of the bodies starts only after a crack-like rupture front propagates through the whole contact. Figure below shows a typical result of the measurements. Figure (a) shows the stick-slip friction force signal measurement, while Figures (b) and (c) the real contact area measurement in time corresponding to the onset of sliding. The onset of motion is characterized by a rapid drop in the friction force measurement and a rapid reduction of the real contact area A (see Figure (b)). Figure (c) presents a typical example of a propagating rupture, where  CR is the Rayleigh wave speed (the asymptotic velocity of singular shear cracks). In these example, the rupture nucleates at , accelerates in the positive x direction, and leaves a significantly reduced A.

With these results Professor Fineberg and his collaborators went further and employed the Linear Fracture Elastic Mechanics (LFEM) theory to describe not only the propagation of the cracks, but also the arrest of the cracks. In the LEFM framework, crack arrest takes place if the energy flux to the tip of a propagating crack is insufficient to overcome the energy needed to fracture. Using this simple theory, the researchers successfully predicted both, the dynamics of crack propagation and the length of the crack propagation and validated the theory in the experiments. These results are relevant for any frictional interface, however, they are especially important to explain the mechanisms of an earthquake propagation and arrest. Hopefully, this theory will help not only to predict friction in engineering contacts, but also in predicting/preventing the consequences of the earthquakes in future.

Further details of the theory presented by Professor J. Fineberg can be found in a recent review article: Brittle Fracture Theory Describes the Onset of Frictional Motion, Ilya Svetlizky, Elsa Bayart, and Jay Fineberg, https://doi.org/10.1146/annurev-conmatphys-031218-013327.

Modeling contact of elastic solids using GFMD

Professor Martin Muser devoted his talk to the Green’s Function Molecular Dynamic (GFMD) approach of solving contact problems, its recent developments and application to model soft matter.

GFMD is a boundary-value method that allows to solve an elastic contact problem within the framework of Molecular Dynamics, meaning that the surface displacements are propagated according to Newton’s equations of motion. This method was tested during the contact mechanics challenge and along with the Boundary Element – Fast Fourier Transform (BEM-FFT) approach was proven to be the most accurate among the existing contact models. According to Professor Muser, the advantages of GFMD are in its flexibility and the ability to consider relatively large systems, from 4096 × 4096 surface atoms on single CPUs to systems on supercomputers.

One drawback of the traditional GFMD approach is its slow convergence rate (as compared to BEM-FFT). This is due to the use of Molecular Dynamics framework, namely the time-step integration of Newton’s equations. Recently, however, two techniques were introduced into GFMD to improve its convergence rate: fast internal-relaxation engine (FIRE) and mass-weighted GFMD (the details here). These techniques allowed to improve the convergence rates significantly as shown in the figure on the left.

GFMD can also be employed to explore the impact of thermal effects on the contact. Since the atoms at the interface fluctuate, they have an impact on the stress distribution in the contact. This effect is typically neglected in the contact mechanics models, but with GFMD it can be explored. As shown in the figure below, the impact on stress distribution can be considerable. Results of this work will be published shortly.

Tribology at the molecular level

A talk of Professor Daniele Dini from Imperial College London was devoted to the tribology topics across the scales, from a single atom to the continuum scale (see the figure to the left). Additives, Lubricants and Contact Mechanics: Insights from molecular and multi-scale simulations was the title of the talk and it was an overview of the work performed by the tribology group at Imperial College London.

At the continuum level the group of Professor Dini works on the improvement of tribological performance and efficiency of an internal combustion engine and particularly of the contact of the cylinder liner and piston rings. This contact takes up for around 4% of the overall fuel consumption. The friction reduction is planned to be achieved using Laser Surface Texturing. A specially designed test rig simultaneously measures friction force and film thickness in a reciprocating contact. A mathematical model involves the generalized Reynolds equation, Elrod’s algorithm to model cavitation and the EHL effects. Together with the model, an optimum texture is sought of to minimize the energy losses.

At the molecular level, one of the areas researched at Imperial College is the application of non-equilibrium molecular dynamics simulations to investigate the mechanochemical behavior of lubricant additive molecules and friction modifiers. Classical molecular dynamics simulations are employed to obtain the stresses acting on additive molecules under shear motion. First-principles modelling allows to accurately model lubricant reactivity under the action of normal and shear forces in tribological contacts. The new and more effective additives need to be designed in future and the proposed approach can be used to help such design quests.

And finally, a modeling approach linking the atomic and continuum scales was discussed. Currently, these scales remain mainly separated, each focusing on specialized applications. At the macro level, continuum models describe the lubrication processes rather well. At the smaller scales, however, continuum models can not describe many phenomena coming from the atomic nature of matter and may fail to capture essential physical effects. Molecular modeling techniques in such cases can be employed.

The group of Professor Dini works on the development of a multi-scale approach that connects the nano and macro-scales. Hybrid methods, as they are called, linking atomistic simulations and continuum computational fluid dynamics, combine the strengths of both universes. This work has resulted in development of an open source multi-scale simulation tool, which links the atomistic simualtion tool  – LAMMPS and the Continuum Fluid Dynamic simulation tool – OpenFOAM. The tool is available for use and I believe will greatly benefit the simulation capabilities of tribological community. The tool is available at www.cpl-library.org.

Friction at the adhesive contacts

Tribology is the science of friction, wear and lubrication. The first systematic study of friction is attributed to Leonardo Da Vinci (1452-1519), however in the current state of the art of tribology, predicting coefficient of friction in many cases is still not possible. Moreover, as discussed by Professor Valentin Popov in his recent article, in many cases it is not even clear what is the main contributor to the friction. There are many possible contributors: contact interactions, adsorbed layers, tribochemical reactions, adhesion among many others. In his talk during the workshop, Professor Popov discussed the origin of friction in adhesive contacts.

Friction is a loss of energy. In case of sliding of rough metal surfaces, the energy is usually lost in permanent deformation via ploughing as proposed by Bowden and Tabor in 1950s. In case of rubber, gels and other soft materials, the energy is lost due to viscoelasticity. But what happens, when smooth hard amorphous solids slide against each other without plastic deformation? Theoretically, this could be a perfect zero friction case, if there would be no adhesion. But adhesion makes the contact to dissipate the energy according to Professor Popov. To prove this theory, several experiments and simulations were performed in the group at TU Berlin and at least qualitative similarity between the theory and numerical simulations were observed.

At first, the sliding of a rough sphere on a flat was simulated using the recently developed adhesion contact model. In the simulation video shown below, the contact area evolution during sliding is shown. As it can be seen from the video, the sliding process is not continuous, but consists of local attachment and detachment events. This attachment and detachment events are actually the cause of the energy dissipation. Each of the attachment-detachment cycles dissipates energy, just like in the pull-off force experiments performed by Atomic Force Microscopes, for example.

A very similar behavior can be observed in the video taken during the experiments (see below). In this video at first a rough sphere is pressed against a flat and then the sliding starts. The sliding continues at a very slow speed, which allows to see the variation of contact area with a great detail. The sliding consists of local attachment and detachment events. And they are responsible for the friction.

Hopefully, with the development of this theory the friction coefficient prediction will be made possible in the contact between smooth hard amorphous solids, as encountered in microelectormechanical systems, silicon wafer contacts and others.