Research Papers: Friction and Wear

Efficient Steady-State Computation for Wear of Multimaterial Composites

[+] Author and Article Information
Florian Feppon

Centre de Mathématiques Appliquées,
École polytechnique,
Route de Saclay,
Palaiseau 91128, France
e-mail: florian.feppon@polytechnique.edu

Mark A. Sidebottom

Department of Mechanical
Engineering and Mechanics,
Lehigh University,
Bethlehem, PA 18015

Georgios Michailidis

SIMaP-Université de Grenoble, INPG,
1130 rue de la Piscine,
St. Martin d'Hères 38402, France

Brandon A. Krick

Assistant Professor
Department of Mechanical
Engineering and Mechanics,
Lehigh University,
Bethlehem, PA 18015

Natasha Vermaak

Assistant Professor
Department of Mechanical
Engineering and Mechanics,
Lehigh University,
Bethlehem, PA 18015

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received July 8, 2015; final manuscript received October 16, 2015; published online February 18, 2016. Assoc. Editor: Min Zou.

J. Tribol 138(3), 031602 (Feb 18, 2016) (10 pages) Paper No: TRIB-15-1247; doi: 10.1115/1.4031993 History: Received July 08, 2015; Revised October 16, 2015

Traditionally, iterative schemes have been used to predict evolving material profiles under abrasive wear. In this work, more efficient continuous formulations are presented for predicting the wear of tribological systems. Following previous work, the formulation is based on a two parameter elastic Pasternak foundation model. It is considered as a simplified framework to analyze the wear of multimaterial surfaces. It is shown that the evolving wear profile is also the solution of a parabolic partial differential equation (PDE). The wearing profile is proven to converge to a steady-state that propagates with constant wear rate. A relationship between this velocity and the inverse rule of mixtures or harmonic mean for composites is derived. For cases where only the final steady-state profile is of interest, it is shown that the steady-state profile can be accurately and directly determined by solving a simple elliptic differential system—thus avoiding iterative schemes altogether. Stability analysis is performed to identify conditions under which an iterative scheme can provide accurate predictions and several comparisons between iterative and the proposed formulation are made. Prospects of the new continuous wear formulation and steady-state characterization are discussed for advanced optimization, design, manufacturing, and control applications.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Archard, J. F. , and Hirst, W. , 1956, “ The Wear of Metals Under Unlubricated Conditions,” Proc. R. Soc. London, Ser. A., 236(1206), pp. 397–410. [CrossRef]
Archard, J. F. , 1953, “ Contact and Rubbing of Flat Surfaces,” J. Appl. Phys., 24(8), pp. 981–988. [CrossRef]
Hatchett, C. , 1803, “ Experiments and Observations on the Various Alloys, on the Specific Gravity, and on the Comparative Wear of Gold,” Philos. Trans. R. Soc. London, 93, pp. 43–194. [CrossRef]
Põdra, P. , and Andersson, S. , 1997, “ Wear Simulation With the Winkler Surface Model,” Wear, 207(1), pp. 79–85. [CrossRef]
Põdra, P. , and Andersson, S. , 1999, “ Finite Element Analysis Wear Simulation of a Conical Spinning Contact Considering Surface Topography,” Wear, 224(1), pp. 13–21. [CrossRef]
Podra, P. , and Andersson, S. , 1999, “ Simulating Sliding Wear With Finite Element Method,” Tribol. Int., 32(2), pp. 71–81. [CrossRef]
Kim, N. H. , Won, D. , Burris, D. , Holtkamp, B. , Gessel, G. R. , Swanson, P. , and Sawyer, W. G. , 2005, “ Finite Element Analysis and Experiments of Metal/Metal Wear in Oscillatory Contacts,” Wear, 258(11), pp. 1787–1793. [CrossRef]
Mukras, S. , Kim, N. H. , Mauntler, N. A. , Schmitz, T. L. , and Sawyer, W. G. , 2010, “ Analysis of Planar Multibody Systems With Revolute Joint Wear,” Wear, 268(5), pp. 643–652. [CrossRef]
Mukras, S. , Kim, N. H. , Sawyer, W. G. , Jackson, D. B. , and Bergquist, L. W. , 2009, “ Numerical Integration Schemes and Parallel Computation for Wear Prediction Using Finite Element Method,” Wear, 266(7), pp. 822–831. [CrossRef]
Lengiewicz, J. , and Stupkiewicz, S. , 2013, “ Efficient Model of Evolution of Wear in Quasi-Steady-State Sliding Contacts,” Wear, 303(1), pp. 611–621. [CrossRef]
Fregly, B. J. , Sawyer, W. G. , Harman, M. K. , and Banks, S. A. , 2005, “ Computational Wear Prediction of a Total Knee Replacement From In Vivo Kinematics,” J. Biomech., 38(2), pp. 305–314. [CrossRef] [PubMed]
Chongyi, C. , Chengguo, W. , and Ying, J. , 2010, “ Study on Numerical Method to Predict Wheel/Rail Profile Evolution Due to Wear,” Wear, 269(3), pp. 167–173. [CrossRef]
Telliskivi, T. , 2004, “ Simulation of Wear in a Rolling–Sliding Contact by a Semi-Winkler Model and the Archard's Wear Law,” Wear, 256(7), pp. 817–831. [CrossRef]
Sawyer, W. G. , Argibay, N. , Burris, D. L. , and Krick, B. A. , 2014, “ Mechanistic Studies in Friction and Wear of Bulk Materials,” Annu. Rev. Mater. Res., 44(1), pp. 395–427. [CrossRef]
Sierra Suarez, J. A. , and Higgs, C. F., III , 2015, “ A Contact Mechanics Formulation for Predicting Dishing and Erosion CMP Defects in Integrated Circuits,” Tribol. Lett., 59(2), pp. 1–12. [CrossRef]
Ashby, M. F. , and Lim, S. C. , 1990, “ Wear-Mechanism Maps,” Scr. Metall. Mater., 24(5), pp. 805–810. [CrossRef]
Williams, J. A. , 1999, “ Wear Modeling: Analytical, Computational and Mapping: A Continuum Mechanics Approach,” Wear, 225, pp. 1–17. [CrossRef]
Dickrell, D. J. , Dooner, D. B. , and Sawyer, W. G. , 2003, “ The Evolution of Geometry for a Wearing Circular Cam: Analytical and Computer Simulation With Comparison to Experiment,” ASME J. Tribol., 125(1), pp. 187–192. [CrossRef]
Blanchet, T. A. , 1997, “ The Interaction of Wear and Dynamics of a Simple Mechanism,” ASME J. Tribol., 119(3), pp. 597–599. [CrossRef]
Dickrell, D. J. , and Sawyer, W. G. , 2004, “ Evolution of Wear in a Two-Dimensional Bushing,” Tribol. Trans., 47(2), pp. 257–262. [CrossRef]
Sawyer, W. G. , 2001, “ Wear Predictions for a Simple-Cam Including the Coupled Evolution of Wear and Load,” Lubr. Eng, 57(9), pp. 31–36.
Ling, F. F. , Lai, W. M. , and Lucca, D. A. , 2012, Fundamentals of Surface Mechanics: With Applications, Springer Science & Business Media, New York.
Ling, F. F. , and Pu, S. , 1964, “ Probable Interface Temperatures of Solids in Sliding Contact,” Wear, 7(1), pp. 23–34. [CrossRef]
Ling, F. F. , 1959, “ A Quasi-Iterative Method for Computing Interface Temperature Distributions,” Z. Angew. Math. Phys., 10(5), pp. 461–474. [CrossRef]
Kennedy, F. E. , and Ling, F. F. , 1974, “ A Thermal, Thermoelastic, and Wear Simulation of a High-Energy Sliding Contact Problem,” ASME J. Tribol., 96(3), pp. 497–505.
Batra, S. K. , and Ling, F. F. , 1967, “ On Deformation Friction and Interface Shear Stress in Viscoelastic–Elastic Layered System Under a Moving Load,” ASLE Trans., 10(3), pp. 294–301. [CrossRef]
Han, S. W. , and Blanchet, T. A. , 1997, “ Experimental Evaluation of a Steady-State Model for the Wear of Particle-Filled Polymer Composite Materials,” ASME J. Tribol., 119(4), pp. 694–699. [CrossRef]
Rowe, K. G. , Erickson, G. M. , Sawyer, W. G. , and Krick, B. A. , 2014, “ Evolution in Surfaces: Interaction of Topography With Contact Pressure During Wear of Composites Including Dinosaur Dentition,” Tribol. Lett., 54(3), pp. 249–255. [CrossRef]
Sawyer, W. G. , 2004, “ Surface Shape and Contact Pressure Evolution in Two Component Surfaces: Application to Copper Chemical Mechanical Polishing,” Tribol. Lett., 17(2), pp. 139–145. [CrossRef]
Lee, G. Y. , Dharan, C. K. H. , and Ritchie, R. O. , 2002, “ A Physically-Based Abrasive Wear Model for Composite Materials,” Wear, 252(3), pp. 322–331. [CrossRef]
Blau, P. J. , 2006, “ On the Nature of Running-In,” Tribol. Int., 38(11), pp. 1007–1012.
Archard, J. F. , and Hirst, W. , 1957, “ An Examination of a Mild Wear Process,” Proc. R. Soc. London A, 238(1215), pp. 515–528. [CrossRef]
Viafara, C. C. , Castro, M. I. , Velez, J. M. , and Toro, A. , 2005, “ Unlubricated Sliding Wear of Pearlitic and Bainitic Steels,” Wear, 259(1), pp. 405–411. [CrossRef]
Queener, C. A. , Smith, T. C. , and Mitchell, W. L. , 1965, “ Transient Wear of Machine Parts,” Wear, 8(5), pp. 391–400. [CrossRef]
Rodríguez-Tembleque, L. , Abascal, R. , and Aliabadi, M. H. , 2010, “ A Boundary Element Formulation for Wear Modeling on 3D Contact and Rolling–Contact Problems,” Int. J. Solids Struct., 47(18–19), pp. 2600–2612. [CrossRef]
Erickson, G. M. , Krick, B. A. , Hamilton, M. , Bourne, G. R. , Norell, M. A. , Lilleodden, E. , and Sawyer, W. G. , 2012, “ Complex Dental Structure and Wear Biomechanics in Hadrosaurid Dinosaurs,” Science, 338(6103), pp. 98–101. [CrossRef] [PubMed]
Erickson, G. M. , Sidebottom, M. A. , Kay, D. I. , Turner, K. T. , Ip, N. , Norell, M. A. , Sawyer, W. G. , and Krick, B. A. , 2015, “ Wear Biomechanics in the Slicing Dentition of the Giant Horned Dinosaur Triceratops,” Sci. Adv., 1(5), p. e1500055. [CrossRef] [PubMed]
Sidebottom, M. A. , Feppon, F. , Vermaak, N. , and Krick, B. A. , “ Modeling Wear of Multi-Material Composite Wear Surfaces,” ASME J. Tribol. (in press).
Yastrebov, V. A. , 2013, Numerical Methods in Contact Mechanics, ISTE, Wiley, Hoboken, NJ.
Jang, I. , Burris, D. L. , Dickrell, P. L. , Barry, P. R. , Santos, C. , Perry, S. S. , Phillpot, S. R. , Sinnott, S. B. , and Sawyer, W. G. , 2007, “ Sliding Orientation Effects on the Tribological Properties of Polytetrafluoroethylene,” J. Appl. Phys., 102(12), p. 123509. [CrossRef]
Mosey, N. J. , Müser, M. H. , and Woo, T. K. , 2005, “ Molecular Mechanisms for the Functionality of Lubricant Additives,” Science, 307(5715), pp. 1612–1615. [CrossRef] [PubMed]
Mo, Y. , Turner, K. T. , and Szlufarska, I. , 2009, “ Friction Laws at the Nanoscale,” Nature, 457(7233), pp. 1116–1119. [CrossRef] [PubMed]
Pastewka, L. , Moser, S. , Gumbsch, P. , and Moseler, M. , 2011, “ Anisotropic Mechanical Amorphization Drives Wear in Diamond,” Nat. Mater., 10(1), pp. 34–38. [CrossRef] [PubMed]
Dong, Y. , Li, Q. , and Martini, A. , 2013, “ Molecular Dynamics Simulation of Atomic Friction: A Review and Guide,” J. Vac. Sci. Technol. A, 31(3), p. 030801. [CrossRef]
Jackson, R. L. , Ghaednia, H. , Lee, H. , Rostami, A. , and Wang, X. , 2013, Contact Mechanics, Springer Science & Business Media, New York.
Carpick, R. W. , Ogletree, D. F. , and Salmeron, M. , 1999, “ A General Equation for Fitting Contact Area and Friction versus Load Measurements,” J. Colloid Interface Sci., 211(2), pp. 395–400. [CrossRef] [PubMed]
Kerr, A. D. , 1964, “ Elastic and Viscoelastic Foundation Models,” ASME J. Appl. Mech., 31(3), pp. 491–498. [CrossRef]
Kerr, A. D. , 1965, “ A Study of a New Foundation Model,” Acta Mech., 1(2), pp. 135–147. [CrossRef]
Pasternak, P. L. , 1954, “ On a New Method of Analysis of an Elastic Foundation by Means of Two Foundation Constants,” Gosudarstvennoe Izdatel'stvo Litearturi po Stroitel'stvu i Arkhitekture, Moscow, USSR (in Russian).
Allaire, G. , 2007, “ Numerical Analysis and Optimization. An Introduction to Mathematical Modelling and Numerical Simulation,” Numerical Mathematics and Scientific Computation, Vol. 87, Oxford University Press, Oxford, UK.
Johansson, L. , 1994, “ Numerical Simulation of Contact Pressure Evolution in Fretting,” ASME J. Tribol., 116(2), pp. 247–254. [CrossRef]
Bendsoe, M. P. , and Sigmund, O. , 2003, Topology Optimization: Theory, Methods and Applications, Springer, Berlin.
Allaire, G. , 2002, “ Shape Optimization by the Homogenization Method,” Applied Mathematical Sciences, Vol. 146, Springer Verlag, New York.
Eschenauer, H. A. , and Olhoff, N. , 2001, “ Topology Optimization of Continuum Structures: A Review,” ASME Appl. Mech. Rev., 54(4), pp. 331–390. [CrossRef]
Wang, M. Y. , and Wang, X. , 2005, “ A Level-Set Based Variational Method for Design and Optimization of Heterogeneous Objects,” Comput. Aided Des., 37(3), pp. 321–337. [CrossRef]
Kang, B.-S. , Park, G.-J. , and Arora, J. S. , 2006, “ A Review of Optimization of Structures Subjected to Transient Loads,” Struct. Multidiscip. Optim., 31(2), pp. 81–95. [CrossRef]
Allaire, G. , Dapogny, C. , Delgado, G. , and Michailidis, G. , 2014, “ Multi-Phase Structural Optimization Via a Level Set Method,” COCV, 20(2), pp. 576–611. [CrossRef]
Flodin, A. , and Andersson, S. , 1997, “ Simulation of Mild Wear in Spur Gears,” Wear, 207(1), pp. 16–23. [CrossRef]
Allaire, G. , Jouve, F. , and Toader, A.-M. , 2004, “ Structural Optimization Using Sensitivity Analysis and a Level-Set Method,” J. Comput. Phys., 194(1), pp. 363–393. [CrossRef]
Willing, R. , and Kim, I. , 2009, “ Three Dimensional Shape Optimization of Total Knee Replacements for Reduced Wear,” Struct. Multidiscip. Optim., 38(4), pp. 405–414. [CrossRef]
Markine, V. L. , Shevtsov, I. Y. , and Esveld, C. , 2007, “ An Inverse Shape Design Method for Railway Wheel Profiles,” Struct. Multidiscip. Optim., 33(3), pp. 243–253. [CrossRef]
Vermaak, N. , Michailidis, G. , Parry, G. , Estevez, R. , Allaire, G. , and Bréchet, Y. , 2014, “ Material Interface Effects on the Topology Optimization of Multi-Phase Structures Using a Level Set Method,” Struct. Multidiscip. Optim., 50(4), pp. 623–644. [CrossRef]
Axen, N. , and Jacobson, S. , 1994, “ A Model for the Abrasive Wear Resistance of Multiphase Materials,” Wear, 174(1), pp. 187–199. [CrossRef]
Hovis, S. K. , Talia, J. E. , and Scattergood, R. O. , 1986, “ Erosion in Multiphase Systems,” Wear, 108(2), pp. 139–155. [CrossRef]
Hecht, F. , 2012, “ New Development in FREEFEM++,” J. Numer. Math., 20(3–4), pp. 251–266.
Mugler, D. H. , and Scott, R. A. , 1988, “ Fast Fourier Transform Method for Partial Differential Equations, Case Study: The 2-D Diffusion Equation,” Comput. Math. Appl., 16(3), pp. 221–228. [CrossRef]
Duhamel, P. , and Vetterli, M. , 1990, “ Fast Fourier Transforms: A Tutorial Review and a State of the Art,” Signal Process., 19(4), pp. 259–299. [CrossRef]
Enterprises, S. , 2012, scilab: Free and Open Source Software for Numerical Computation.


Grahic Jump Location
Fig. 1

Representation of the wear model coupling the evolution of contact pressure and the surface topography. (a) Nonuniform wear in heterogeneous materials. In this example, the wear rate of material B, Kb, would be less than that of material A. (b) Schematic of elastic foundation model relating pressure and topography.

Grahic Jump Location
Fig. 2

Schematic of the computational domain, Ω. The domain is occupied by two materials (A, B) with the wear coefficient rates Ka > Kb.

Grahic Jump Location
Fig. 3

(a) An in-plane distribution of materials (see Sec. 5, H = L). For this distribution, the wear profile is computed and plotted along the dotted-dashed line in (a) with two CFL values: CFL = 2.5 (b) and CFL = 0.45 (c). A CFL constant greater than one is subject to potential numerical instability issues. Note the difference in scale between (b) and (c).

Grahic Jump Location
Fig. 4

(a) A first example in-plane distribution of materials with (H = L) and (b) a schematic of the corresponding 3D steady-state profile computed by solving Eq. (20). The material with wear coefficient, Kb, is indicated in black. (c) Along the dotted-dashed line in (a), comparisons are shown of the evolving worn profile (dashed line, z, Eq. (13)) and the steady-state (solid-line, z̃, Eq. (22)) profile at several iterations of the finite-difference scheme (Eq. (13)).

Grahic Jump Location
Fig. 5

(a) A second example in-plane distribution of materials (H = L) with (b) a schematic of the 3D steady-state profile computed by solving Eq. (20). The material with wear coefficient, Kb, is indicated in black. (c) Along the dotted-dashed line in (a), comparisons are shown of the evolving worn profile (dashed line, z, Eq. (13)) and the steady-state (solid-line, z̃, Eq. (22)) profile at several iterations of the finite-difference scheme (Eq. (13)).



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In