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Hysteresis in an Adhesive Contact upon a Change in the Indenter Direction of Motion: an Experiment and Phenomenological Model

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Abstract

A phenomenological model is proposed for describing the hysteretic behavior in an adhesive contact between a soft elastomer and a hard indenter upon a change in the indenter direction of motion. The model takes into account the increase in the contact strength with increasing contact time. Dependences of the elastic force and the contact radius on the indentation depth are obtained. It is shown that the adhesive strength of the contact increases with the indentation depth. An experiment on intrusion of a spherical steel indenter into a rubber sheet of a fixed thickness is performed. It is shown that the experimental and theoretical results coincide qualitatively.

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Notes

  1. In this article, we describe the experiment with an indenter of radius R = 22 mm, while in our earlier similar experiment [25], the indenter radius was R = 40 mm. Because of the larger indenter radius in the experiment described in [25], the value of Fmin = –5.24 mN averaged over six experiments was realized at the indentation stage. With account for the indenter radius, this gives the value of γeff, 1 = 0.031 J/m2, which is close to the value obtained in the present study.

REFERENCES

  1. S. Gorb, Adhesion and Friction in Biological Systems (Springer, Netherlands, 2012).

    Google Scholar 

  2. M. Ciavarella, J. Joe, A. Papangelo, and J. R. Barber, J. R. Soc., Interface 16 (151), 20180738 (2019). https://doi.org/10.1098/rsif.2018.0738

    Article  Google Scholar 

  3. P. Schmitt, D. Eberlein, C. Ebert, M. Tranitz, I. Eitner, and H. Wirth, Energy Procedia 38, 380 (2013). https://doi.org/10.1016/j.egypro.2013.07.293

    Article  Google Scholar 

  4. A. I. Dmitriev, A. Y. Nikonov, and W. Österle, Lubricants 4 (3), 24 (2016). https://doi.org/10.3390/lubricants4030024

    Article  Google Scholar 

  5. G. Carbone, E. Pierro, and S. N. Gorb, Soft Matter 7 (12), 5545 (2011). https://doi.org/10.1039/C0SM01482F

    Article  ADS  Google Scholar 

  6. K. L. Johnson, K. Kendall, and A. D. Roberts, Proc. R. Soc. London, Ser. A 324 (1558), 301 (1971). https://doi.org/10.1098/rspa.1971.0141

    Article  ADS  Google Scholar 

  7. B. V. Derjaguin, V. M. Muller, and Y. P. Toporov, J. Colloid Interface Sci. 53 (2), 314 (1975). https://doi.org/10.1016/0021-9797(75)90018-1

    Article  ADS  Google Scholar 

  8. D. Maugis, J. Colloid Interface Sci. 150 (1), 243 (1992). https://doi.org/10.1016/0021-9797(92)90285-T

    Article  ADS  Google Scholar 

  9. E. Popova and V. L. Popov, Phys. Mesomech. 21 (1), 1 (2018). https://doi.org/10.1134/S1029959918010010

    Article  Google Scholar 

  10. J. Joe, J. R. Barber, and M. D. Thouless, Front. Mech. Eng. 6, 31 (2020). https://doi.org/10.3389/fmech.2020.00031

    Article  Google Scholar 

  11. W. Deng and H. Kesari, Sci. Rep. 9, 1639 (2019). https://doi.org/10.1038/s41598-018-38212-z

    Article  ADS  Google Scholar 

  12. L. Pastewka and M. O. Robbins, Proc. Natl. Acad. Sci. U.S.A. 111 (9), 3298 (2014). https://doi.org/10.1073/pnas.1320846111

    Article  ADS  Google Scholar 

  13. R. W. Style, C. Hyland, R. Boltyanskiy, J. S. Wettlaufer, and E.R. Dufresne, Nat. Commun. 4, 2728 (2013). https://doi.org/10.1038/ncomms3728

    Article  ADS  Google Scholar 

  14. S. Karpitschka, L. van Wijngaarden, and J. H. Snoeijer, Soft Matter 12 (19), 4463 (2016). https://doi.org/10.1039/C5SM03079J

    Article  ADS  Google Scholar 

  15. J. Long, G. Wang, X. Feng, and S. Yu, Int. J. Solids Struct. 84, 133 (2016). https://doi.org/10.1016/j.ijsolstr.2016.01.021

    Article  Google Scholar 

  16. A. Papangelo, J. Scheibert, R. Sahli, G. Pallares, and M. Ciavarella, Phys. Rev. E 99 (5), 053005 (2019). https://doi.org/10.1103/PhysRevE.99.053005

    Article  ADS  Google Scholar 

  17. J. Scheibert, R. Sahli, and M. Peyrard, Front. Mech. Eng. 6, 18 (2020). https://doi.org/10.3389/fmech.2020.00018

    Article  Google Scholar 

  18. B. Lorentz and A. Albers, Tribol. Int. 59, 259 (2013). https://doi.org/10.1016/j.triboint.2012.08.023

    Article  Google Scholar 

  19. A. I. Dmitriev, A. Y. Nikonov, and W. Österle, Lubricants 6 (2), 43 (2018). https://doi.org/10.3390/lubricants6020043

    Article  Google Scholar 

  20. J. F. Waters and P. R. Guduru, Proc. R. Soc., Ser. A 466 (2117), 1303 (2010). https://doi.org/10.1098/rspa.2009.0461

  21. J. F. Waters and P. R. Guduru, Proc. R. Soc., Ser. A 467 (2132), 2209 (2011). https://doi.org/10.1098/rspa.2010.0617

  22. J. F. Waters, J. Kalow, H. Gao, and P. R. Guduru, J. Adhesion 88 (2), 134 (2012). https://doi.org/10.1080/00218464.2012.648061

    Article  Google Scholar 

  23. J. F. Waters, H. J. Gao, and P. R. Guduru, J. Adhesion 87 (3), 194 (2011). https://doi.org/10.1080/00218464.2011.557325

    Article  Google Scholar 

  24. I. A. Lyashenko and V. L. Popov, AIP Conf. Proc. 2167 (1), 020201 (2019). https://doi.org/10.1063/1.5132068

    Article  Google Scholar 

  25. I. A. Lyashenko and V. L. Popov, Tech. Phys. 65 (10), 1695 (2020). https://doi.org/10.1134/S1063784220100126

    Article  Google Scholar 

  26. I. Argatov, Facta Univ., Ser. Mech. Eng. 17 (2), 181 (2019). https://doi.org/10.22190/FUME190330024A

    Article  Google Scholar 

  27. V. L. Popov, M. Heß, and E. Willert, Handbook of Contact Mechanics: Exact Solutions of Axisymmetric Contact Problems (Springer, Berlin, 2019). https://doi.org/10.1007/978-3-662-58709-6

  28. M. Heß, Über die exakte Abbildung ausgewählter dreidimensionaler Kontakte auf Systeme mit niedrigerer räumlicher Dimension (Cuvillier, Berlin, 2011). ISBN: 978-3869558233

    Google Scholar 

  29. I. A. Lyashenko and Z. M. Liashenko, Ukr. J. Phys. 65 (3), 205 (2020). https://doi.org/10.15407/ujpe65.3.205

    Article  Google Scholar 

  30. Z. Liu, H. Lu, Y. Zheng, D. Tao, Y. Meng, and Y. Tian, Sci. Rep. 8, 6147 (2018). https://doi.org/10.1038/s41598-018-24587-6

    Article  ADS  Google Scholar 

  31. V. L. Popov, AIP Conf. Proc. 2167 (1), 020286 (2019). https://doi.org/10.1063/1.5132153

    Article  Google Scholar 

  32. S. Dalvi, A. Gujrati, S. R. Khanal, L. Pastewka, A. Dhinojwala, and T. D. B. Jacobs, Proc. Natl. Acad. Sci. U.S.A. 116 (51), 25484 (2019). https://doi.org/10.1073/pnas.1913126116

    Article  ADS  Google Scholar 

  33. Q. Li, R. Pohrt, and V. L. Popov, Front. Mech. Eng. 5, 7 (2019). https://doi.org/10.3389/fmech.2019.00007

    Article  Google Scholar 

  34. H. Kesari, J. C. Doll, B. L. Pruitt, W. Cai, and A. L. Lew, Philos. Mag. Lett. 90 (12), 891 (2010). https://doi.org/10.1080/09500839.2010.521204

    Article  ADS  Google Scholar 

  35. I. A. Lyashenko and V. L. Popov, Tech. Phys. Lett. 46 (11), 1092 (2020). https://doi.org/10.1134/S1063785020110097

    Article  ADS  Google Scholar 

  36. https://www.k-tanac.co.jp/crystalnone

  37. Q. Li, R. Pohrt, I. A. Lyashenko, and V. L. Popov, Proc. Inst. Mech. Eng., Part J 234 (1), 73 (2020). https://doi.org/10.1177/1350650119854250

    Article  Google Scholar 

  38. J. A. Greenwood, Tribol. Lett. 65, 159 (2017). https://doi.org/10.1007/s11249-017-0938-1

    Article  Google Scholar 

  39. I. A. Lyashenko and R. Pohrt, Front. Mech. Eng. 6, 49 (2020). https://doi.org/10.3389/fmech.2020.00049

    Article  Google Scholar 

  40. A. Papangelo, Facta Univ., Ser. Mech. Eng. 16, 19 (2018). https://doi.org/10.22190/FUME180102008P

    Article  Google Scholar 

  41. H. Hertz, J. Reine Angew. Math. 92, 156 (1882). https://doi.org/10.1515/crll.1882.92.156

    Article  MathSciNet  Google Scholar 

  42. V. R. Regel’, A. I. Slutsker, and E. E. Tomashevskii, Kinetic Nature of the Strength of Solids (Nauka, Moscow, 1974) [in Russian].

    Google Scholar 

  43. V. A. Petrov, A. Ya. Bashkarev, and V. I. Vettegren’, Physical Foundations of Prediction of the Durability of Structural Materials (Politekhnika, St. Petersburg, 1993) [in Russian].

    Google Scholar 

  44. V. L. Popov, Preprints No. 2020030131 (2020). https://doi.org/10.20944/preprints202003.0131.v1

  45. I. Argatov, M. Heß, and V. L. Popov, J. Appl. Math. Mech. 98 (4), 622 (2018). https://doi.org/10.1002/zamm.201700213

    Article  Google Scholar 

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Funding

This study was supported by the Deutsche Forschungsgemeinschaft, project RO 810-55-1.

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Authors and Affiliations

  1. Technische Universität Berlin, 10623, Berlin, Germany

    I. A. Lyashenko & V. L. Popov

  2. Sumy State University, 40007, Sumy, Ukraine

    I. A. Lyashenko

  3. Tomsk National Research State University, 634050, Tomsk, Russia

    V. L. Popov

  4. Institute of Strength Physics and Materials Science, Siberian Branch, Russian Academy of Sciences, 634055, Tomsk, Russia

    V. L. Popov

Authors
  1. I. A. Lyashenko
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Correspondence to I. A. Lyashenko.

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Translated by N. Wadhwa

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Lyashenko, I.A., Popov, V.L. Hysteresis in an Adhesive Contact upon a Change in the Indenter Direction of Motion: an Experiment and Phenomenological Model. Tech. Phys. 66, 611–629 (2021). https://doi.org/10.1134/S1063784221040113

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