Home Page of Professor Q. Jane Wang

Tribological Interface

The figure here is an “enlarged view” of a typical tribological interface. Friction and wear are interfacial problems. On the other hand, it is a tribochemical reactor, an energy exchanger.

Referenced to suggestions by Prof. H. S Cheng, GROLM (geometry, roughness, operation, lubricant, material), the interface consists of five essential interfacial elements, which are, (1) solid materials (from the bulk to surface), (2) fluid materials (formulated and/or contaminated), (3) multiscale geometry, surface topography/roughness (machined or textured), (4) surface functionality (treatment, tribochemistry, and tribophysical), and (5) operating and controlling conditions. They are mutually intervened and interactive in the states of thermodynamic, tribophysical, and tribochemical variations of themselves and the interface. Knowing that each interfacial elementary aspect itself involves many choices and great details, for example, the wide ranges of solid materials and coatings, as well as surface textures, the design of an optimal combination of the five essential aspects to accomplish a particular goal for friction and wear control is a great challenge.

Related Publications

1. Wang, Q. and Zhu, D., Dec. 2019, Interfacial Mechanics, Theories and Methods for Contact and Lubrication, CRC Press, ISBN: 978-1-4398-1510-6, 978-1-1387-4890-3 Boca Raton, London, New York.
2. Zhu, D. and Wang, Q., 2011, “Elastohydrodynamic Lubrication (EHL): A Gateway to Interfacial Mechanics – Review and Prospect,” Journal of Tribology, Vol. 133, 041001-1-14. https://doi.org/10.1115/1.4004457.

Texture, Topography, and Roughness: Friction Anisotropy and Lubrication Enhancement

Friction anisotropy was explored from the differences in contact area, surface stiffness, stiction length, and energy barrier from the continuum mechanics prospective and in the stick-slip phenomena at the atomic level.  Friction characteristics change with the orientation of surface grooves, with extreme friction values in the parallel and perpendicular directions. Similar friction anisotropy trends were observed from all materials studied. The contact area, surface contact stiffness, stiction length and energy barrier in two directions all affect the friction anisotropy. The contribution from each is closely related to the relative pattern size. Stick-slip dominates friction for surfaces with narrow grooves, while energy barrier is the leading factor, which causes the trend transition, for surfaces with wider grooves. A mechanism for adhesion prevention was identified and applied to surface anti-seizure design.

Textures of U, R, W, T shapes and their variances in a number of distribution patterns have been numerically created to store lubricant, and, if designed properly, they help wet surfaces and enhance lubrication. Mechanisms for lubrication enhancement have been quantified as micro-wedges and micro-steps, the effects shape fabrication errors analyzed, and the influence of machined roughness evaluated. Depending on the type, the shapes allow a 10-20%  error tolerance, and depending on the ratio of the shape and roughness, a certain roughness of the machined surfaces can be acceptable to make textures. 

On the other hand, roughness strongly affects lubrication when it is in the same order of magnitude as the film thickness. A longitudinal pattern of surface interaction prefers a longitudinal asperity orientation to enhance lubrication in the mixed-lubrication regime, while a transverse pattern prefers a transverse asperity orientation to do so. The effects of surface roughness on lubrication is scaled to the size of the gap (or the lubricant film thickness), and surface textures for reducing lubricated friction are matched with the dimensions of the interface.  

Related publications

1. Wang, Q. and Zhu, D., 2005, “Virtual Texturing: Modeling the Performance of Lubricated Contacts of Engineered Surfaces,” ASME Journal of Tribology, Vol. 127, pp. 722-728. https://doi.org/10.1115/1.2000273.
2. Ren, N, Nanbu, T., Yasuda, Y., Zhu, D., and Wang, Q., 2007, “Micro Textures in Concentrated Conformal-Contact Lubrication: Effect of Distribution Patterns,” Tribology Letters, Vol. 28, pp 275-285. https://link.springer.com/article/10.1007/s11249-007-9271-4
3. Nanbu, T., Ren, N., Yasuda, Y., Zhu, D., and Wang, Q., 2008, “Micro Textures in Concentrated Conformal-Contact Lubrication: Effects of Texture Bottom Shape and Surface Relative Motion,” Tribology Letters, Vol. 29, 241 – 252. https://link.springer.com/article/10.1007/s11249-008-9302-9
4. He, B., Chen, W. W., and Wang, Q., 2008, “Surface Texture Effect on Friction of A Micro-Textured Poly(dimethylsiloxane) (PDMS),” Tribology Letters, Vol. 31, pp 187-197. https://link.springer.com/article/10.1007/s11249-008-9351-0.
5. Zhu, D., Nanbu, N., Ren, N., Yasuda, Y., and Wang, Q, 2010, “Model-Based Virtual Surface Texturing for Concentrated Conformal-Contact Lubrication,” Proceedings of the Institution of Mechanical Engineers, Part J, Journal of Engineering Tribology, Vol. 224, pp. 686-696. https://doi.org/10.1243/13506501JET739
6. Yu, C. and Wang, Q., 2012, “Friction Anisotropy with Respect to Topographic Orientation,” Scientific Reports, Vol. 2, 988, pp. 1-6. doi:10.1038/srep00988.
7. Zhu, D. and Wang, Q., 2013, “Effect of Roughness Orientation on the EHL Film Thickness,” Journal of Tribology, 135 (3), 031501-1-9. doi:10.1115/1.4023250. http://tribology.asmedigitalcollection.asme.org/article.aspx?articleid=1674124
8. Yu, C, Yu, H., Liu, G., Chen, W., He, B., and Wang, Q., 2014, Understanding Topographic-Dependence of Friction with Micro- and Nano Grooved Surfaces,” Tribology Letters. Vol. 53, pp 145-156. http://link.springer.com/article/10.1007%2Fs11249-013-0252-5
9. Ling, T., D., Liu, P., Xiong, S., Grzina, D., Cao, J., Wang, Q., Xia, Z., Talwar, R., 2013, “Surface Texturing of Drill Bits for Adhesion Reduction and Tool Life Enhancement,” Tribology Letters, Vol. 52, PP. 113-122. http://link.springer.com/article/10.1007%2Fs11249-013-0198-7
10. Gu, T., Wang, Q., Xiong, S., Liu, Z., Gangopadhyay, A., and Lu, Z., 2019, “Profile Design for Misaligned Journal Bearings Subjected to Transient Mixed-Lubrication,” Journal of Tribology. 141(7): 071701, https://doi.org/10.1115/1.4043506
11. Gu, T., Wang, Q., Gangopadhyay, A., and Liu, Z., 2020, “Journal Bearing Surface Topography Design Based on Transient Lubrication Analysis,” Journal of Tribology. DOI: 1115/1.4046289, https://doi.org/10.1115/1.4046289.
12. Khan, M. A, Wang, Q., Fernandez, J., Li, Z., and Liu, Y., 2021 “Friction at Ring-Liner Interface Analyzed with a Systematic Surface Characterization,” Tribology Transactions, Vol. 64(6), pp. 1064-1078, https://doi.org/10.1080/10402004.2021.1964663.
13. Liu, Z., Gu, T., Pickens, D., Nishino, T., and Wang, Q., 2021, “Housing Profile Design for Improved Apex Seal Lubrication Using a Finite-Length Roller EHL Model,” Journal of Tribology, Vol. 143 (8), 082301, https://doi.org/10.1115/1.4048998.

Lubrication Transition and Basis for Surface Design Principles

Mixed lubrication is a mode of lubrication in which both hydrodynamic lubricant film and rough surface asperity contact coexist; it transits to fill-film lubrication if asperity contact disappears but becomes boundary lubrication and dry contact if hydrodynamics disappears. When the film thickness/roughness ratio is greater than 0.6 ~1.2, little or no asperity contact is found in either experimental results or numerical solutions. If the ratio is around 0.05~0.1, there may still be a considerable portion of load, e.g. greater than 10~15%, supported by micro lubricant hydrodynamics. It appears that mixed lubrication spans largely for the film thickness/roughness ratio up to 0.6~1.2, based on numerical simulation results, which is in a reasonably good agreement with experimental observations found in the literature. Roughness and its orientation strongly affect mixed lubrication.  Understanding the nature of lubrication transition from full film to boundary/asperity contact leads to the principles for surface design for lubrication enhancement and friction reduction: 1) roughness orientation should be in agreement with the contact orientation, 2) lubrication film is enhanced if the faster-moving surface is rougher, 3) however, when surface pitting fatigue is a concern, slower moving rough surface experiences more stress cycles, and its mating surface should be designed with smoother with longer waviness. It is important to optimally balance these requirements. Together with the principle of texture-promoted adhesion prevention, surface geometry design may lead to up to 10~60% friction reduction or more and one order of magnitude contact fatigue life enhancement. These have been used in Boeing, Eaton, Ford, GM, Nissan, Mazda.

Related Publications

1. Wang, Q. and Zhu, D., Dec. 2019, Interfacial Mechanics, Theories and Methods for Contact and Lubrication, CRC Press, ISBN: 978-1-4398-1510-6, 978-1-1387-4890-3 Boca Raton, London, New York.
2. Zhu, D. and Wang, Q., 2013, “Effect of Roughness Orientation on the EHL Film Thickness,” Journal of Tribology, 135 (3), 031501-1-9. doi:10.1115/1.4023250.
3. Yu, C. and Wang, Q., 2012, “Friction Anisotropy with Respect to Topographic Orientation,” Scientific Reports, Vol. 2, 988, pp. 1-6. doi:10.1038/srep00988
4. Zhu, D., Ren, N., and Wang, Q., 2009, “Pitting Life Prediction Based on 3-D Line Contact Mixed EHL Analysis and Subsurface von Mises Stress Calculation,” Journal of Tribology, Vol. 131/ 041501-1.
5. Nanbu, T., Ren, N., Yasuda, Y., Zhu, D., and Wang, Q., 2008, “Micro Textures in Concentrated Conformal-Contact Lubrication: Effects of Texture Bottom Shape and Surface Relative Motion,” Tribology Letters, Vol. 29, 241 – 252. https://link.springer.com/article/10.1007/s11249-008-9302-9
6. Zhu, D. and Wang, Q., 2013, “Effect of Roughness Orientation on the EHL Film Thickness,” Journal of Tribology, 135 (3), 031501-1-9. doi:10.1115/1.4023250. http://tribology.asmedigitalcollection.asme.org/article.aspx?articleid=1674124

Heterocyclic Alkyl-Cyclens to Lower Friction

New molecular heterocyclic friction modifiers,  nicknamed the “flower pots” by Professor Wang and co-workers, made by the chemists of the research team, exhibit excellent friction and wear reduction in the boundary lubrication regime. Work is done to explores the mechanisms by which friction reduction occurs with heterocyclic alkyl-cyclen friction-modifiers molecules. It is found that these chelating molecules adsorb onto (oxidized) steel surfaces far more tenaciously than conventional friction modifiers such as simple alkylamines. Molecular dynamics simulations argue that the surface coverage of these heterocyclic friction-modifiers molecules remains close to 100% even at 200 °C. The thermal stability permits the friction modifiers to firmly anchor on the surface, allowing the hydrocarbon chains of the molecules to interact and trap base oil molecules.  Altogether, the enhanced surface adsorption, prolonged surface residence, reduced desorption rate, and entanglement of the alkyl-cyclen’s alkyl chains with base oil molecules are the essential mechanisms supporting the excellent boundary-lubrication performance of the new alkyl-cyclen heterocyclic friction modifiers.

Related Publications

1. He, X., Lu, J., Desanker, M., Invergo, A., Lohr, T., Ren, N., Lockwood, F., Marks, T. J., Chung, Y.-W., and Wang, Q., 2018, “Boundary Lubrication Mechanisms for High-Performance Friction Modifiers,” ACS Applied Materials & Interfaces, Vol. 10 (46), pp 40203–40211. DOI: 10.1021/acsami.8b11075.
2. Desanker, M., He, X., Lu, J., Johnson, B. A., Liu, L., Delferro, M, Ren N., Lockwood, F., Greco, A., Erdemir A., Marks, T. J., Wang, Q., and Chung, Y.-W., 2018, “High-Performance Heterocyclic Friction Modifiers for Boundary Lubrication” Tribology Letters, 60:50, https://link.springer.com/article/10.1007/s11249-018-0996-zDOI: 10.1007/s11249-018-0996-z.
3. Marks, T. J., Delferro, M., Wang, Q., Chung, Y. W., Bazzi, H. S., Seyam, A.B., Desanker, M., Johnson, B., Jin, D., applied 2016,15/013,878, granted 2017, Lubricant Additives, US Patent No. 9,777,021 B2.

Mechanisms and Nature of In-Situ Carbon Films

A low-friction, wear-protective carbon-containing tribofilms can be self-generated and replenishable by additives. Such carbon-containing films are formed under modest sliding conditions in a lubricant consisting of cyclopropanecarboxylic acid (CPCa) or alike as an additive dissolved in a polyalphaolefin base oil. These tribofilms show  Raman D and G signatures. In this research,  the film materials were made via a tribo-process and a thermal process. Time evolution of the molecules shows  C-fragments, followed by a polymerization process.  Experimental characterization results, via 1) heating the film and examine the D, G peaks, 2) using a solvent to soak the product and examine these peak again, and reactive molecular dynamics simulations demonstrate that these films are high molecular-weight hydrocarbons acting as anti-friction tribo-polymers.

Related Publications

1. Johnson, B., Wu, H., Desanker, M., Pickens, D., Chung, Y.W., and Wang, Q., 2018, “Direct Formation of Lubricious and Wear-Protective Carbon Films from Phosphorus- and Sulfur-Free Oil-Soluble Additives,” Tribology Letters, Vol. 66: 2. doi.org/10.1007/s11249-017-0945-2.
2. Wu^*, H., Khan^*, A. M., Johnson, B., Sasikumar, K., Chung, Y-W., and Wang, Q., 2019, “Formation and Nature of Carbon-Containing Tribofilms,” ACS Applied Materials & Interfaces, Vol. 11 (17), pp. 16139-16146, https://pubs.acs.org/doi/10.1021/acsami.8b22496
3. Khan^*, A. M., Wu^*, H., Ma, Q., Chung, Y. W., and Wang Q., 2020, “Relating Tribological Performance and Tribofilm Formation to the Adsorption Strength of Surface-Active Precursors,” Tribology Letters, Vol. 68, Article No. 6, https://doi.org/10.1007/s11249-019-1249-5.
4. Ma*, Q., Khan*, A., Wang, Q., and Chung, Y. W., 2020, “Dependence of Tribological Performance and Tribopolymerization on the Surface Binding Strength of Selected Cycloalkane-Carboxylic Acid Additives,” Tribology Letters. Vol. 68, paper 68, https://doi.org/10.1007/s11249-020-01329-2.

Universal Wear Law of Abrasion and Wear Performance Map

Finding a wear law that is valid over a wide range of conditions and materials would have enormous practical value. This collaborative work has developed a wear model, based on a simple relationship describing the evolution of the abrasive wear rate of steel sliding against boron carbide-coated coupons and  accounting for its kinetics. A wear mapping shows that this wear equation accurately describes the evolution of abrasive wear rates for a number of additional material pairs and contact conditions that were tested, as well as for all of the material pairs for which literature data could be found. The only material parameters are the initial abrasiveness and the initial rate at which the abrasiveness changes with number of cycles. No other wear law so simple, accurate and widely applicable is known. 

Related Publications

1. Siniawski, M., Harris, S., and Wang, Q., 2007, “A Universal Wear Law for Abrasion,” Wear, Vol. 262, pp. 883-888.
2. Siniawski, M., Harris, S., and Wang, Q., 2005, “Effects of Contact on the Abrasiveness of a Thin Boron Carbide Coating,” Tribology Letters, Vol. 20, pp. 21-30.
3. Siniawski, M., Wang, Q., Harris, S. J., Chung, Y-W., and Freyman, C., 2004, “Effects of Thickness and Roughness Variations on the Abrasiveness of a Thin Boron Carbide Coating,” Tribology Letters, Vol. 17, pp. 931-937.

Contact Failure Initiation Map for Multilayered Materials

Contact failure initiation in multilayered materials can be modeled with the multi-layer coating mechanics developed in her group. Here shows an example of failure initiation mapping for trilayer materials consisting of a functional outer layer on a substrate containing one intermediate layer, which are widely used in data processing devices, biomedical components, and mechanical elements. The analytical frequency response functions derived in her group  for the contact of multilayer materials (see Computational Mechanotribology) leads to the novel deterministic modeling of frictionless and frictional contact involving a trilayer material system designed with various thickness and elastic property combinations. Displacements and stresses for point contacts are calculated effectively by employing the discrete-convolution and fast Fourier transform method based on the influence coefficients obtained from the analytical frequency response functions. The maximum von Mises stress and its location, which are critical information for understanding the material contact status, are thoroughly investigated for a wide range of trilayer materials. The results provide an informative guideline for the design of multilayer coatings without contact failure.

Related Publications

1. Yu, C, Wang, Z., Liu, G., Keer, L. M., and Wang, Q., 2016, “Maximum von Mises Stress and Its Location in Trilayer Materials in Contact,” Journal of Tribology, 138, 041402 doi:10.1115/1.4032888
2. Wang, Q. and Zhu, D., Dec. 2019, Interfacial Mechanics, Theories and Methods for Contact and Lubrication, CRC Press, ISBN: 978-1-4398-1510-6, 978-1-1387-4890-3 Boca Raton, London, New York.

Rolling and Sliding Contact Fatigue of Surfaces

Fatigue of surfaces under contact and rolling, sliding, or combined rolling and sliding, is a serious life-threatening problems of mechanical systems. Professor Wang’s group and collaborators have developed methods to simulate, test, and modeling issues related to rolling/sliding contact fatigue problems, considering the effects of rough surfaces, material heat treatments, coatings, and inclusions/inhomogeneities.  The modeling of rolling/sliding contact fatigue problems is based on her mixed-lubrication models and computational contact micromechanics.  The research of rolling-contact fatigue of case-hardened steels reveals that the non-dimensional case slope and the distance S between the yield strength profile and stress distribution curve have a significant influence on the RCF lives of case-hardened steels. For the materials whose hardness, as well as the yield strengths, can be expressed by a straight-line variation with depth, their RCF lives can be inversely correlated to a slope-related parameter.

 The team has also developed a rough-surface asperity stress-counting method in gear rolling-sliding pitting prediction considering the sliding-speed effect, and this concept will be in the new AGMA 925 standard as the rate of asperity contact.  The results assisted Eaton, Nissan and Timken engineers in choosing surface finish methods for higher drivetrain efficiency and durability. One order of magnitude of contact fatigue life improvement was accomplished.

These theories and methods have supported her group on the development of industrial application software sets for component R&D, now used in Eaton, GM, Timken, either in company-wide design platforms or as standing-alone design/analysis software. The model-based analysis and tests of case-hardened steels helped the development of BRP’s new generation of Evinrude E-TEC engines, which was globally launched in 2014.

Related Publications

1. Xie, L. Palmer, D., Otto, F., Wang, Z., and Wang, Q., 2015, “Effect of Surface Hardening Technique and Case Depth on Rolling Contact Fatigue Behavior of Alloy Steels,” Tribology Transactions, Vol. 58, pp. 215-224. https://doi.org/10.1080/10402004.2014.960957.
2. Li, D., Zhang, M., Xie, L., Wang, Z., Zhou, Z., Zhao, N., Palmer, D., and Wang, Q., 2020, “Contact Yield Initiation and Its Influence on RCF of Case Hardened Steels,” Journal of Tribology, 142(12): 121501, https://doi.org/10.1115/1.4047581
3. Greco, A., Martini, A., Liu, Y., Lin, C., and Wang, Q., 2010, “Rolling Contact Fatigue Performance of Vibro-Mechanical Textured Surfaces,” Tribology Transactions, Vol. 53, pp. 610-620. https://doi.org/10.1080/10402000903518861.
4. Epstein, E., Keer, L. M., Wang, Q., Cheng, H. S., and Zhu, D., 2003, “Effect of Surface Topography on Contact Fatigue in Mixed Lubrication,” Tribology Transactions, Vol.46, pp.506-513. https://doi.org/10.1080/10402000308982657.
5. Zhu, D., Ren, N., and Wang, Q., 2009, “Pitting Life Prediction Based on 3-D Line Contact Mixed EHL Analysis and Subsurface von Mises Stress Calculation,” Journal of Tribology, Vol. 131/ 041501-1. https://doi.org/10.1115/1.3195040.

Partial Slip, Creep, and Friction Transition

The relative motion between two surfaces under a normal load is impeded by friction. Interfacial junctions are formed between surfaces of asperity tips, and sliding inception occurs when shear tractions in the entire contact area reach the shear strength and the junction materials are about to be separated.  A numerical contact modeling system has been developed to study the transition from static to kinetic friction, or from partial slip to full junction slip, in rough-surface elastoplastic contact. Static friction coefficients are predicted for various material pairs in contact. The static friction coefficient is lower for the contact of materials with larger difference in properties.  The interface involving a surface of a larger RMS roughness renders a smaller static friction coefficient, but the effect of surface roughness becomes less obvious under a heavier normal load. 

Related Publications

1. Chen, W., W. and Wang, Q., 2009, “A Numerical Static Friction Model for Spherical Contacts of Rough Surfaces, Influence of Load, Material, and Roughness,” Journal of Tribology, Vol. 131, 021402-1-8. https://doi.org/10.1115/1.3063814.
2. Wang, Q. and Zhu, D., Dec. 2019, Interfacial Mechanics, Theories and Methods for Contact and Lubrication, CRC Press, ISBN: 978-1-4398-1510-6, 978-1-1387-4890-3 Boca Raton, London, New York. https://www.crcpress.com/Interfacial-Mechanics-Theories-and-Methods-for-Contact-and-Lubrication/Wang-Zhu/p/book/9781439815106

Extended Hertz Theories for Coated Surfaces

This group of work extends the Hertzian formulae for contact radius (or half width) of the contact zone, the maximum contact pressure, and the contact approach to material systems with a layer of coating, in terms of the applied load, equivalent radius, and an extended equivalent modulus. According to the form of an analytically known frequency response function, the extended equivalent modulus due to the presence of the coating is a function of Young’s moduli and Poisson’s ratios of the coating and the substrate, the coating thickness, and a set of equivalence parameters obtained through substantial numerical simulation. Both cylindrical and spherical coating contact problems have been solved and parameters determined.  

Related Publications

1. Liu, S., Wang, Q., and, Liu, G., 2000, “A Versatile Method of Discrete Convolution and FFT (DC-FFT) for Contact Analyses,” Wear, Vol. 243, pp. 101-111.
2. Liu, S. and Wang, Q., 2001, “A Three-Dimensional Thermomechanical Model of Contact between Non-Conforming Rough Surfaces,” ASME Journal of Tribology, Vol. 123, pp. 17-26.
3. Liu, S. and Wang, Q., 2002, “Studying Contact Stress Fields Caused by Surface Tractions with a Discrete Convolution and Fast Fourier Transform Algorithm,” ASME Journal of Tribology, Vol. 124, pp. 36-45.
4. Liu, S., Peyronnel, A., Wang, Q., and Keer, L. M., 2005, “An Extension of the Hertz Theory for 2D Coated Components,” Tribology Letters, vol. 18, pp-505-511.
5. Liu, S., Peyronnel, A., Wang, Q, and Keer, L. M., 2005, “An Extension of the Hertz Theory for Three-Dimensional Coated Bodies,” Tribology Letters, vol. 18, pp. 303-314.
6. Liu, S. and Wang, Q, 2007, “Determination of Young’s Modulus and Poisson’s Ratio for Coatings,” Surface and Coatings Technology, Vol. 201, pp. 6470-6477.

Stribeck Curves and Stribeck Surface

The Stribeck curve is an overall view of friction variation in the entire range of lubrication, plotted as a function of the Hersey number (viscosity x speed/average pressure). Friction in the mixed lubrication regime is the summation of the friction due to viscous shear and that due to asperity contact and sliding specified in the boundary lubrication.  However, load directly influences deformation, and the latter contributes to film thickness.  For journal-bearing mixed elastohydrodynamic lubrication interfaces, the same Hersey number can be constructed with different combinations of speed and load; different deformations, or different film thickness, may occur under the same Hersey number.  This calls for a three- dimensional Stribeck surface.  In addition, the shape of Stribeck Curves for EHL is affected by roughness and surface topography orientation. 

Related Publications

1. Wang, Y., Lin, C., Wang, Q., and Shi, F., 2006, “Development of a Set of Stribeck Curves for Conformal Contacts of Rough Surfaces,” Tribology Transactions, Vol. 49, pp. 526-535.
2. Wang, Y. and Wang, Q., 2013, “Stribeck Curves,” Encyclopedia of Tribology, Springer, ISBN 978-0-387-92898-2, pp. 3365-3370.
3. Wang, Q. and Zhu, D., Dec. 2019, Interfacial Mechanics, Theories and Methods for Contact and Lubrication, CRC Press, ISBN: 978-1-4398-1510-6, 978-1-1387-4890-3 Boca Raton, London, New York. https://www.crcpress.com/Interfacial-Mechanics-Theories-and-Methods-for-Contact-and-Lubrication/Wang-Zhu/p/book/9781439815106