Skip to main content

Multi-scale Contact Approach Considering Material Heterogeneity and Wear

Abstract

A multi-scale contact method that can deal with tribological problems in a broad context is proposed. It is based on a numerical homogenization technique which allows to take into account a heterogeneous material and the generation of wear under contact conditions. Globally and locally, a finite element method is used. More precisely, at the micro scale, a behavior is computed from the microstructure and then injected into the macro model through contact stiffnesses. The approach being completely integrated between the macro and micro scales, a relocalization of the contact forces on the microstructure allows wear generation at the scale of the heterogeneities. An example is given in this paper where with respect to a reference case, the proposed method proves to be faster and as consistent.

Graphic Abstract

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Data Availability

Not applicable.

Code Availability

Not applicable.

References

  1. 1.

    Vakis, A., Yastrebov, V., Scheibert, J., Nicola, L., Dini, D., Minfray, C., Almqvist, A., Paggi, M., Lee, S., Limbert, G., et al.: Modeling and simulation in tribology across scales: an overview. Tribol. Int. 125, 169–199 (2018)

    Article  Google Scholar 

  2. 2.

    Berthier, Y.: Maurice Godet’s Third Body. Tribology Series, vol. 31, pp. 21–30. Elsevier, Amsterdam (1996)

    Google Scholar 

  3. 3.

    Dhir, D.K.: Thermo-mechanical performance of automotive disc brakes. Mater. Today 5(1), 1864–1871 (2018)

    Google Scholar 

  4. 4.

    Dufrénoy, P., Weichert, D.: A thermomechanical model for the analysis of disc brake fracture mechanisms. J. Thermal Stress. 26(8), 815–828 (2003)

    Article  Google Scholar 

  5. 5.

    Kao, T., Richmond, J., Douarre, A.: Brake disc hot spotting and thermal judder: an experimental and finite element study. Int. J. Vehicle Des. 23(3–4), 276–296 (2000)

    Article  Google Scholar 

  6. 6.

    Baba, H., Wada, T., Takagi, T.: Study on reduction of brake squeal caused by in-plane vibration on rotor. Tech. Rep, SAE Technical Paper (2001)

  7. 7.

    Liles, G.D.: Analysis of disc brake squeal using finite element methods. Tech. Rep, SAE Technical Paper (1989)

  8. 8.

    Massi, F., Baillet, L., Giannini, O., Sestieri, A.: Brake squeal: linear and nonlinear numerical approaches. Mech. Syst. Signal Process. 21(6), 2374–2393 (2007)

    Article  Google Scholar 

  9. 9.

    Greenwood, J., Williamson, J.P.: Contact of nominally flat surfaces. Proc. R. Soc. Lond. Ser. A 295, 300–319 (1966)

    CAS  Article  Google Scholar 

  10. 10.

    Bush, A., Gibson, R., Thomas, T.: The elastic contact of a rough surface. Wear 35(1), 87–111 (1975)

    Article  Google Scholar 

  11. 11.

    Ciavarella, M., Delfine, V., Demelio, G.: A “Re-vitalized’’ Greenwood and Williamson model of elastic contact between fractal surfaces. J. Mech. Phys. Solids 54, 2569–2591 (2006)

    CAS  Article  Google Scholar 

  12. 12.

    Nayak, P.R.: Random process model of rough surfaces. J. Lubr. Technol. 93(3), 398–407 (1971)

    Article  Google Scholar 

  13. 13.

    Persson, B.N.: Theory of rubber friction and contact mechanics. J. Chem. Phys. 115(8), 3840–3861 (2001)

    CAS  Article  Google Scholar 

  14. 14.

    Hertz, H.: Über die berührung fester elastischer körper und über die härte-verhandlungen des vereins zur beförderung des gewerbefleißes (1882)

  15. 15.

    Ciavarella, M., Papangelo, A., Barber, J.: Effect of wear on the evolution of contact pressure at a bimaterial sliding interface. Tribol. Lett. 68(1), 1–7 (2020)

    Article  Google Scholar 

  16. 16.

    Pei, L., Hyun, S., Molinari, J., Robbins, M.O.: Finite element modeling of elasto-plastic contact between rough surfaces. J. Mech. Phys. Solids 53(11), 2385–2409 (2005)

    CAS  Article  Google Scholar 

  17. 17.

    Bandeira, A.A., Wriggers, P., de Mattos Pimenta, P.: Numerical derivation of contact mechanics interface laws using a finite element approach for large 3d deformation. Int. J. Numer. Methods Eng. 59(2), 173–195 (2004)

    Article  Google Scholar 

  18. 18.

    De Lorenzis, L., Wriggers, P.: Computational homogenization of rubber friction on rough rigid surfaces. Comput. Mater. Sci. 77, 264–280 (2013)

    Article  Google Scholar 

  19. 19.

    Zavarise, G., Wriggers, P., Stein, E., Schrefler, B.: Real contact mechanisms and finite element formulation-a coupled thermomechanical approach. Int. J. Numer. Methods Eng. 35(4), 767–785 (1992)

    Article  Google Scholar 

  20. 20.

    Waddad, Y., Magnier, V., Dufrénoy, P., De Saxcé, G.: A multiscale method for frictionless contact mechanics of rough surfaces. Tribol. Int. 96, 109–121 (2016)

    Article  Google Scholar 

  21. 21.

    Dufrenoy, P., Magnier, V., Waddad, Y., Brunel, J.F., De Saxce, G.: A multiscale model of a disc brake including material and surface heterogeneities. SAE Int. J. Passeng. Cars Mech. Syst. 9, 1136–1143 (2016)

    Article  Google Scholar 

  22. 22.

    Chan, D., Stachowiak, G.: Review of automotive brake friction materials. Proc. Inst. Mech. Eng. Part D 218(9), 953–966 (2004)

    Article  Google Scholar 

  23. 23.

    Magnier, V., Brunel, J.F., Dufrénoy, P.: Impact of contact stiffness heterogeneities on friction-induced vibration. Int. J. Solids Struct. 51(9), 1662–1669 (2014)

    Article  Google Scholar 

  24. 24.

    Okada, H., Fukui, Y., Kumazawa, N.: Homogenization method for heterogeneous material based on boundary element method. Comput. Struct. 79(20–21), 1987–2007 (2001)

    Article  Google Scholar 

  25. 25.

    Qin, Q.H., Yang, Q.S.: Macro-micro Theory on Multi-field Coupling Behavior of Heterogeneous Materials. Springer, New York (2008)

    Google Scholar 

  26. 26.

    Leroux, J., Fulleringer, B., Nelias, D.: Contact analysis in presence of spherical inhomogeneities within a half-space. Int. J. Solids Struct. 47(22–23), 3034–3049 (2010)

    Article  Google Scholar 

  27. 27.

    Hoan-Pham, Q., Ha-Minh, C., Long-Chu, T., Kanit, T., Imad, A.: Analysis of the transverse compressive behavior of Kevlar fibers using microscopic scale approach. Int. J. Mech. Sci. 164, 105149 (2019)

    Article  Google Scholar 

  28. 28.

    Pham, Q.H., Ha-Minh, C., Chu, T.L., Kanit, T., Imad, A.: On microscopic and homogenized macroscopic analysis of one Kevlar® km2 yarn under transverse compressive loading. Mech. Res. Commun. 104, 103496 (2020)

    Article  Google Scholar 

  29. 29.

    Temizer, I., Wriggers, P.: On the computation of the macroscopic tangent for multiscale volumetric homogenization problems. Comput. Methods Appl. Mech. Eng. 198(3–4), 495–510 (2008)

    Article  Google Scholar 

  30. 30.

    Archard, J.: Contact and rubbing of flat surfaces. J. Appl. Phys. 24(8), 981–988 (1953)

    Article  Google Scholar 

  31. 31.

    Abu Bakar, A., Ouyang, H., James, S., Li, L.: Finite element analysis of wear and its effect on squeal generation. Proc. Inst. Mech. Eng. Part D 222(7), 1153–1165 (2008)

    Article  Google Scholar 

  32. 32.

    Arfa, E., Magnier, V., Dufrénoy, P., de Saxcé, G.: Contact modelling of highly heterogeneous friction material for braking applications. Mech. Ind. 21(5), 507 (2020)

    Article  Google Scholar 

  33. 33.

    Duboc, M.: Etude multi-échelle du crissement: dispositif expérimental et éléments de compréhension. Ph.D. thesis, Lille 1 (2013)

  34. 34.

    Waddad, Y., Magnier, V., Dufrénoy, P., De Saxcé, G.: Multiscale thermomechanical modeling of frictional contact problems considering wear-application to a pin-on-disc system. Wear 426, 1399–1409 (2019)

    Article  Google Scholar 

  35. 35.

    Dhieb, H., Buijnsters, J.G., Eddoumy, F., Celis, J.P.: Surface damage of unidirectional carbon fiber reinforced epoxy composites under reciprocating sliding in ambient air. Compos. Sci. Technol. 71(15), 1769–1776 (2011)

    CAS  Article  Google Scholar 

  36. 36.

    Sellami, A., Hentati, N., Kchaou, M., Chowdhury, M.A., Elleuch, R.: Effect of size and shape of copper alloys particles on the mechanical and tribological behavior of friction materials. Mech. Ind. 21(6), 613 (2020)

    CAS  Article  Google Scholar 

  37. 37.

    Aghababaei, R., Warner, D.H., Molinari, J.F.: Critical length scale controls adhesive wear mechanisms. Nat. Commun. 7(1), 1–8 (2016)

    Article  Google Scholar 

  38. 38.

    Milanese, E., Brink, T., Aghababaei, R., Molinari, J.F.: Role of interfacial adhesion on minimum wear particle size and roughness evolution. Phys. Rev. E 102(4), 043001 (2020)

    CAS  Article  Google Scholar 

Download references

Acknowledgements

The present research work has been supported by the ELSAT project, the Hauts-de-France Region, the European Union, the Regional Delegation for Research and Technology, the Ministry of Higher Education and Research and the National Center for Scientific Research. The authors gratefully acknowledge these institutions for their support.

Funding

Research supported by institutions listed in Acknowledgements section.

Author information

Affiliations

Authors

Contributions

Not applicable.

Corresponding author

Correspondence to E. Arfa.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Consent to Participate

Not applicable.

Consent for Publication

I, corresponding author, and all the contributed authors give our consent for publication, for the present work, to Tribology Letters journal.

Ethical Approval

Not applicable.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Arfa, E., Magnier, V., Dufrénoy, P. et al. Multi-scale Contact Approach Considering Material Heterogeneity and Wear. Tribol Lett 69, 135 (2021). https://doi.org/10.1007/s11249-021-01507-w

Download citation

Keywords

  • Multi-scale contact
  • Heterogeneous material
  • Wear