- PII
- S30346428S1026351925010065-1
- DOI
- 10.7868/S3034642825010065
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume / Issue number 1
- Pages
- 116-135
- Abstract
- A theoretical and experimental method is poroposed for identification of mechanical properties of the surface layers of highly elastic materials by the results of their dynamic indentation for small depths (nanoDMA). The method is based on an approximate solution of the contact problem for a rigid ball in contact with a deformable specimen, the contact being loaded by an oscillating normal force. The specimen is modeled by a linear viscoelastic half-space with the relaxation kernel presented as a sum of exponential terms. The method allows one to determine sets of parameters defining the relaxation and creep functions of a material in a time interval corresponding to the experimental range of frequencies, as well as to calculate the dynamic storage and loss moduli for each frequency. The application of the method is shown by an example of the analysis of the mechanical properties of surface layers for two types of frost-resistant rubber (butadiene-nitrile and isoprene) depending on the degree of wear of their surfaces. It is established that the wear of surfaces of the rubbers under investigation leads to an increase of the surface layers stiffness and to a decrease in their relaxation properties; these changes are more pronounced for rubber based on nitrile butadiene than for that based on isoprene.
- Keywords
- наноДМА резина циклическое индентирование спектр релаксации экспоненциальное ядро релаксации экспоненциальное ядро ползучести вязкоупругость
- Date of publication
- 20.01.2026
- Year of publication
- 2026
- Number of purchasers
- 0
- Views
- 16
References
- 1. Ферри Дж. Вязкоупругие свойства полимеров. Пер. с англ. М.: Изд-во иностр. лит., 1963. 536 с.
- 2. Горячева И.Г. Маховская Ю.Ю., Морозов А.В., Степанов Ф.И. Трение эластомеров. Моделирование и эксперимент. М.-Ижевск: Институт компьютерных исследований, 2017. 204 с.
- 3. Oliver W.C., Pharr G.M. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments // J. Mater. Res. 1992. V. 7. № 6. P. 1564–1583. https://doi.org/10.1557/JMR.1992.1564
- 4. Asif S.A.S., Wahl K.J., Colton R.J. Nanoindentation and contact stiffness measurement using force modulation with a capacitive load-displacement transducer // Rev. Sci. Instrum. 1999. V. 70. № 5. P. 2408–2413. https://doi.org/10.1063/1.1149769
- 5. Herbert E.G., Oliver W.C., Pharr G.M. Nanoindentation and the dynamic characterization of viscoelastic solids // J. Phys. D Appl. Phys. 2008. V. 41. № 7. P. 074021. https://doi.org/10.1088/0022-3727/41/7/074021
- 6. Pharr G.M., Oliver W.C., Brotzen F.R. On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation // J. Mater. Res. 1992. V. 7. № 3. P. 613–617. https://doi.org/10.1557/JMR.1992.0613
- 7. Igarashi T. et al. Nanorheological mapping of rubbers by atomic force microscopy // Macromolecules. 2013. V. 46. № 5. P. 1916–1922. https://doi.org/10.1021/ma302616a
- 8. Pittenger B. et al. Nanoscale DMA with the atomic force microscope: a new method for measuring viscoelastic properties of nanostructured polymer materials // JOM. 2019. V. 71. № 10. P. 3390–3398. https://doi.org/10.1007/s11837-019-03698-z
- 9. Huang G., Wang B., Lu H. Measurements of viscoelastic functions of polymers in the frequency-domain using nanoindentation // Mech. Time-Depend Mater. 2004. V. 8. № 4. P. 345–364. https://doi.org/10.1007/s11043-004-0440-7
- 10. Cheng Y.-T., Ni W., Cheng C.-M. Nonlinear analysis of oscillatory indentation in elastic and viscoelastic solids // Phys. Rev. Lett. 2006. V. 97. № 7. P. 075506. https://doi.org/10.1103/PhysRevLett.97.075506
- 11. Nikfarjam M. et al. Imaging of viscoelastic soft matter with small indentation using higher eigenmodes in single-eigenmode amplitude-modulation atomic force microscopy // Beilstein J. Nanotechnology. 2018. V. 9. P. 1116–1122. https://doi.org/10.3762/bjnano.9.103
- 12. Greenwood J.A. Contact between an axisymmetric indenter and a viscoelastic half-space // Int. J. Mech. Sci. 2010. V. 52. № 6. P. 829–835. https://doi.org/10.1016/j.ijmecsci.2010.01.010
- 13. Wayne Chen W. et al. Semi-analytical viscoelastic contact modeling of polymer-based materials // J. Tribol. 2011. V. 133. № 4. 041404. https://doi.org/10.1115/1.4004928
- 14. Работнов Ю.Н. Ползучесть элементов конструкций. М.: Наука, 1966. 752 с.
- 15. Джонсон К. Механика контактного взаимодействия. М.: Мир, 1989. 510 с.
- 16. Кристенсен Р. Введение в теорию вязкоупругости. Пер. с англ. М.И. Рейтмана / Под ред. Г.С. Шапиро. М.: Мир, 1974. 338 с.
- 17. Снеддон И. Преобразование Фурье. М.: Иностр. лит, 1955. 668 с.
- 18. Haiat G., Phan Huy M.C., Barthel E. The adhesive contact of viscoelastic spheres // J. Mech. Phys. Solids. 2003. V. 51. № 1. P. 69–99. https://doi.org/10.1016/S0022-5096 (02)00059-5
- 19. Argatov I.I., Popov V.L. Rebound indentation problem for a viscoelastic half‐space and axisymmetric indenter — Solution by the method of dimensionality reduction // ZAMM – Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. 2016. V. 96. № 8. P. 956–967. https://doi.org/10.1002/zamm.201500144
- 20. Morozov A.V., Bukovskiy P.O. Method of constructing a 3D friction map for a rubber tire tread sliding over a rough surface // J. Frict. Wear. 2018. V. 39. № 2. P. 129–136. https://doi.org/10.3103/S1068366618020113
- 21. Morozov A.V., Makhovskaya Y.Y., Kravchuk K.S. Influence of adhesive properties and surface texture of laminated plywood on rubber friction // J. Frict. Wear. 2021. V. 42. № 4. P. 281–289. https://doi.org/10.3103/S1068366621040085
- 22. Baumgaertel M., Winter H.H. Determination of discrete relaxation and retardation time spectra from dynamic mechanical data // Rheol Acta. 1989. V. 28. № 6. P. 511–519. https://doi.org/10.1007/BF01332922
- 23. Grosch K.A. The relation between the friction and visco-elastic properties of rubber // Proc. R. Soc. Lond. A Math. Phys. Sci. 1963. V. 274. № 1356. P. 21–39. https://doi.org/10.1098/rspa.1963.0112
