Dependences of Mechanical Properties of Ceramics with Bimodal Pore Size Distribution on the Porosity at Various Scale Levels

  • A. Yu. SmolinEmail author
  • G. M. Eremina
  • S. Yu. Korostelev

Peculiarities in the dependences of the elastic and strength properties of ceramics with a hierarchically organized pore structure on the porosity are revealed. To exclude the influence of other microstructural factors, such as, for example, grain size, the study was carried out on the basis of multilevel computer modeling using movable cellular automata and a probabilistic approach. A special computer model of the mechanical behavior of porous ceramics with a bimodal pore size distribution has been developed. At the lower level of the model, small isolated pores are explicitly taken into account and series of calculations are carried out for the representative samples with individual pore arrangement in space. The values of the elastic and strength characteristics of these samples obtained as a result of Weibull analysis serve as effective properties of the porous material matrix at the mesoscale. At the mesoscale, large pores of both equiaxial and elongated shapes are considered explicitly. At the macrolevel, the heterogeneity of the material is described implicitly by setting to the automata the unique elastic and strength properties obtained from the Weibull analysis of the calculation results obtained at the mesoscale.


ceramics porous structure fracture multilevel modeling the method of movable cellular automata 


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  1. 1.
    Solid Mechanics and its Applications, eds. M. Kachanov and I. Sevostianov, 193, Springer (2013).Google Scholar
  2. 2.
    A. V. Manoylov, F. M. Borodich, and H. P. Evans, Proc. R. Soc. A, 469, 20120689 (2013). Scholar
  3. 3.
    K. A. Acton, S. C. Baxter, B. Bahmani, et al., Comput. Methods Appl. Mech. Eng., 336, 135–155 (2018). 1016/j.cma.2018.02.025 0045-7825.Google Scholar
  4. 4.
    I. Yu. Smolin, P. V. Makarov, A. S. Kulkov, et al., Phys. Mesomech., 21, 297–304 (2018). Scholar
  5. 5.
    V. A. Mikushina, I. Yu. Smolin, and Yu. N. Sidorenko, Inorg. Mater. Appl. Res., 10, 66–69 (2019). Scholar
  6. 6.
    S. G. Psakhie, D. D. Moiseyenko, I. Yu. Smolin, et al., Comp. Mater. Sci., 16, 333–343 (1999).CrossRefGoogle Scholar
  7. 7.
    A. I. Dmitriev, A.Yu. Smolin, V. L. Popov, and S. G. Psakhie, Phys. Mesomech., 12, Iss. 1–2, 11–19 (2009).CrossRefGoogle Scholar
  8. 8.
    A. Yu. Smolin, E. V. Shilko, S. V. Astafurov, et al., Defence Technology, 14, 643–656 (2018). Scholar
  9. 9.
    D. Aniszewska, Theor. Appl. Fract. Mech., 62, 34–39 (2012). Scholar
  10. 10.
    J. Czopor, D. Aniszewska, and M. Rybaczuk, Comput. Mater. Sci., 51, 151–155 (2012). Scholar
  11. 11.
    A. Yu. Smolin, I. Yu. Smolin, and I. Yu. Smolina, AIP Conf. Proc., 1893, 030127-1 (2017). Scholar
  12. 12.
    N. V. Roman, Multilevel Modeling of Deformation and Fracture of Brittle Porous Materials by the Method of Movable Cellular Automata [in Russian], Thesis Cand. Phys.-Math. Sciences, Tomsk State University, Tomsk (2012).Google Scholar
  13. 13.
    S. Kulkov, S. Buyakova, and L. Gömze, Építőanyag-JSBCM, 66, No. 1, 1–6 (2014). Scholar
  14. 14.
    E. S. Kalatur, S. P. Buyakova, S. N. Kulkov, et al., Építőanyag-JSBCM, 66, No. 2, 31–34, (2014). Scholar
  15. 15.
    I. Zhukov, V. Promakhov, S. Buyakova, and S. Kulkov, Adv. Environment. Biol., 8, Iss. 13, 447–450 (2014). Scholar
  16. 16.
    Ig. S. Konovalenko, A.Yu. Smolin, and S. G. Psakhie, Frattura ed Integrità Strutturale, 24, 75–80 (2013). 10.3221/IGF-ESIS.24.07.Google Scholar
  17. 17.
    A. Yu. Smolin, I. Yu. Smolin, and I. Yu. Smolina, Procedia Structural Integrity, 2, 661–668 (2016). Scholar
  18. 18.
    R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, Access mode
  19. 19.
    Project Abernethy. Implementation of functions supporting reliability analysis methods presented in “The New Weibull Handbook” by R. B. Abernethy, Access mode

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • A. Yu. Smolin
    • 1
    • 2
    Email author
  • G. M. Eremina
    • 1
    • 2
  • S. Yu. Korostelev
    • 1
  1. 1.Institute of Strength Physics and Materials Science of the Siberian Branch of the Russian Academy of SciencesTomskRussia
  2. 2.National Research Tomsk State UniversityTomskRussia

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