Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Vatulyan A. O., Lyapin A. A., Kossovich E. L. Studying of Elastoplastic Properties of Coal Specimens Using Indentation Technique. Izv. Sarat. Univ. Math. Mech. Inform., 2018, vol. 18, iss. 4, pp. 412-420. DOI: 10.18500/1816-9791-2018-18-4-412-420

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Studying of Elastoplastic Properties of Coal Specimens Using Indentation Technique

Vatulyan Alexandr Ovanesovitsch, Southern Federal University
Lyapin Alexander A., Southern Federal University
Kossovich Elena Leonidovna, Saratov State University

A numerical study on elsatoplastic properties in problem of coals specimen nanoindentation by Berkovich pyramid is presented. The stress-strain state of specimen during indentation is calculated using finite element method including complex elastoplastic behaviour on the basis of Drucker-Prager model. The effective axisymmetrical indenter of cone shape is introduced and used for the simulation. The influence of basic geometrical and material parameters of the solid model on the indentation curve is studied. In addition, some new form of indentation curve approximation is proposed. For all the results calculated, the sets of approximation parameters are given. Using modern nanoindentation equipment the number of real experiments were performed and comparison with the mathematical model is presented.

  1. Meyer E. Untersuchen über Härteprüfung und Härte. Zeitschrift des Vereins deutschen Ingenieure, 1908, vol. 52, pp. 645–654.
  2. Chang A. C., Liu B. H. Modified flat-punch model for hyperelastic polymeric and biological materials in nanoindentation. Mechanics of Materials, 2018, vol. 118, pp. 17–21. DOI: https://doi.org/10.1016/j.mechmat.2017.12.010
  3. Zhankun Sun, Fuguo Li, Jun Cao, Xinkai Ma, Jinghui Li. Study on concavity-convexity transition of loading curve for spherical indentation. Mechanics of Materials, 2017, vol. 114, pp. 107–118. DOI: https://doi.org/10.1016/j.mechmat.2017.07.006
  4. 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, vol. 7, iss. 6, pp. 1564–1583. DOI: https://doi.org/10.1557/JMR.1992.1564
  5. Das B. The effect of load on Vicker’s indentation hardness of coal. International Journal of Rock Mechanics and Mining. Sciences & Geomechanics Abstracts, 1972, vol. 9, iss. 6, pp. 783–788. DOI: https://doi.org/10.1016/0148-9062(72)90036-8
  6. Kossovich E., Epshtein S., Dobryakova N., Minin M., Gavrilova D. Mechanical properties of thin films of coals by nanoindentation. In: Karev V., Klimov D., Pokazeev K. (eds.) PM-MEEP 2017: Physical and Mathematical Modeling of Earth and Environment Processes. Springer Geology. Springer, Cham, 2018, pp. 45–50. DOI: https://doi.org/10.1007/978-3319-77788-7_6
  7. Kossovich E. L., Epshtein S. A., Shkuratnik V. L., Minin M. G. Perspectives and problems of modern depth-sensing indentation techniques application for diagnostics of coals mechanical properties. Gornyi Zhurnal, 2017, no. 12, pp. 25–30 (in Russian). DOI: https://doi.org/10.17580/gzh.2017.12.05
  8. Kossovich E., Dobryakova N., Epshtein S., Belov D. Mechanical properties of coal microcomponents under continuous indentation. Journal of Mining Science, 2016, vol. 52, iss. 5, pp. 906–912. DOI: https://doi.org/10.1134/S1062739116041382
  9. Drucker D. C., Prager W. Soil mechanics and plastic analysis or limit design. Quarterlyof Applied Mathematics, 1952, vol. 10, no. 2, pp. 157–165.
  10. Hernot X., Bartier O., Mauvoisin G., Collin J.-M. A universal formulation for indentation whatever the indenter geometry. Mechanics of Materials, 2015, vol. 81, pp. 101–109. DOI: https://doi.org/10.1016/j.mechmat.2014.11.006
  11. Shim S., Oliver W., Pharr G. A critical examination of the berkovich vs. conical indentation based on 3d finite element calculation. MRS Proceedings, 2004, vol. 841, R9.5. DOI: https://doi.org/10.1557/PROC-841-R9.5
  12. Oliver W. C., Pharr G. M. Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 2004, vol. 19, iss. 1, pp. 3–20. DOI: https://doi.org/10.1557/jmr.2004.19.1.3
  13. Vatul’yan A. O., Kossovich E. L., Plotnikov D. K. Some specific characteristics of indentation of cracked layered structures. Mechanics of Solids, 2017, vol. 52, iss. 4, pp. 429–434. DOI: https://doi.org/10.3103/S0025654417040094
  14. Gadelrab K. R., Bonilla F. A., Chiesa M. Densification modeling of fused silica under nanoindentation. Journal of Non-Crystalline Solids, 2012, vol. 358, iss. 2, pp. 392–398. DOI: https://doi.org/10.1016/j.jnoncrysol.2011.10.011
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