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V. V. Struzhanov, S. S. Volkov, T. A. Volkova


DOI: 10.17804/2410-9908.2016.3.021-030

The proposed model represents a micro-heterogeneous medium with random properties of elastic-brittle microstructure elements and with fractures forming during the deformation of structurally heterogeneous materials. The probability of stress exceeding the ultimate strength in one element determines the probability of the failure of this element and the relative damage at the micro level. The suggested methodology for the calculation of damage is based on the use of a single parameter, specifically, the distribution density of the ultimate strengths of structural elements. Defining the increment step for the macro strain axis, we draw segments of the stress-strain curve taking into account the changed properties on each interval. The influence of damage on the stress-strain curve is observed. Uniaxial stress-strain diagram calculation for the exponential distribution of ultimate microstructure strengths in a model material is studied using the proposed methodology.

Keywords: random properties, microstructure damage, ultimate strength, stress-strain curve


  1. Sih G.C. Fracture mechanics in retrospect in contrast to multiscaling in prospect. In: Proceedings of the 17-th National Conference of Italian Group of Fracture, A. Finelli, L. Nobile, eds., Bologna, June 16–18, 2004, pp. 15–37.
  2. Szuromi Ph. Microstructural Engineering of Materials. Science, 1997, vol. 277, no. 5330, pp. 1183. DOI: 10.1126/science.277.5330.1183.
  3. Olson G.B. Computational Design of Hierarchically Structured Materials. Science, 1997, vol. 77, pp. 1237–1242. DOI: 10.1126/science.277.5330.1237.
  4. Kornev V.M., Kurguzov V.D. Multiparametric sufficient criterion of quasi-brittle fracture for complicated stress state. Engineering Fracture Mechanics, 2008, vol. 75, iss. 5, pp. 1099–1113. DOI: 10.1016/j.engfracmech.2007.04.023.
  5. Taylor D. The theory of critical distances. Engineering Fracture Mechanics, 2008, vol. 75, pp. 1696–1705. DOI: 10.1016/j.engfracmech.2007.04.007.
  6. Trusov P.V., Volegov P.S., Yanz A.Yu. Two-Scale Models of Polycrystals: Evaluation of Validity of Ilyushin’s Isotropy Postulate at Large Displacement Gradients. Physical Mesomechanics, vol. 19, iss. 1, pp. 21–34. DOI: 10.1134/S1029959916010033.
  7. Volkov S.D., Stavrov V.P. Statisticheskaya mekhanika kompozitnykh materialov [Statistical Mechanics of Composite Materials]. Minsk, Belorus. Gos. Univ. Publ, 1978. (In Russian).
  8. Volkov S.D. Statistical Strength Theory. Series: Russian Monographs and Texts on Advanced Mathematics and Physics, vol. XI. New York, Gordon and Breach, 1962.
  9. Vildeman V.E., Sokolkin Yu.V., Tashkinov A.A. Mekhanika neuprugogo deformirovaniya i razrusheniya kompozitsionnykh materialov [Mechanics of Non-Elastic Deformation and Fracture of Composite Materials]. Moscow, Nauka Publ., 1997. (In Russian).
  10. Volkova T.A., Volkov S.S. Microstructure damage related to deformation properties of grain composites. Theoretical and Applied Fracture Mechanics, 2008, vol. 49, iss. 3, pp. 242–250. DOI: 10.1016/j.tafmec.2008.02.004.
  11. Volkova T.A., Volkov S.S. Microstructure damage related to stress- strain curve for grain composites. Theoretical and Applied Fracture Mechanics, 2009, vol. 52, iss. 2, pp. 83–90. DOI: 10.1016/j.tafmec.2009.08.007.
  12. Zaitsev A.V. Second-order moment functions for the random structure of unidirectionally reinforced fibrous composites. In: Vestnik UGTU-UPI. Mekhanika microneodnorodnykh materialov i razrushenie [Herald of UGTU-UPI. Mechanics of Micro-Heterogeneous Materials and Fracture]. Ekaterinburg, GOU VPO UGTU-UPI Publ., 2006, no. 11 (82), pp. 161–167. (In Russian).
  13. Surikova N.S., Panin V.E., Derevyagina L.S., Lutfullin R.Ya., Manzhina E.V., Kruglov A.A., Sarkeeva A.A. Micromechanisms of Deformation and Fracture in a VT6 Titanium Laminate under Impact Load. Phys. Mesomech., 2015, vol. 18, iss. 3, pp. 250–260. DOI: 10.1134/S1029959915030091.
  14. Schastlivtsev V.M., Tabatchikova T.I., Yakovleva I.L., Klyueva S.Yu., Kruglova A.A., Khlusova E.I., Orlov V.V. Microstructure and properties of low-carbon weld steel after thermomechanical strengthening. The Physics of Metals and Metallography, 2012, vol. 113, iss. 5, pp. 480–488. DOI: 10.1134/S0031918X12050067.
  15. Yokobori T. An Interdisciplinary Approach to Fracture and Strength of Solids. Groningen, Wolters-Noordhoff Scientific Ltd, 1968.
  16. Tamuzs V.P., Kuksenko V.S. Micromekhanika rasrushenia polimernykh materialov [Microme chanics of Fracture of Polymeric Materials]. Riga, Zinatne Publ., 1978, 296 p. (In Russian).
  17. Struzhanov V.V., Bashurov V.V., Tartashnik K.A. On one approach to the modeling of elas tic-brittle material properties. In: Vestnik UGTU-UPI. Mekhanika microneodnorodnykh materialov i razrushenie [Herald of UGTU-UPI. Mechanics of Micro-Heterogeneous Materials and Fracture]. Ekaterinburg, GOU VPO UGTU-UPI Publ., 2004, no. 22 (52), pp. 99–109. (In Russian).
  18. Privalova V.V., Struzhanov V.V. Some regularities in the behavior of elastic-brittle material under cyclic tension. Uchenye zapiski Komsomolskogo-na-Amure gosudarstvennogo tekhnich eskogo universiteta. Ser. Nauki o prirode i tekhnike, 2012, no. I–1 (9), pp. 94–99. (In Russian).
  19. Encyclopedia of Physics. Flügge S., ed. Mechanics of Solids I, vol. VI a/1, S. Truesdell, ed. Berlin–Heidelberg–New York, Springer-Verlag, 1973.
  20. Fridman Ya.B. Mekhanicheskie svoistva metallov [Mechanical Properties of Metals. Part 1. Deformation and Fracture]. M., Mashinostroenie Publ., 1974, 472 p. (In Russian).
  21. Volkov S.S. Mekhanika anizotropnykh kompozitov [Mechanics of Anisotropic Composites]. Ekaterinburg, UrO RAN Publ., 2010, 85 p. (In Russian).


Article reference

Struzhanov V. V., Volkov S. S., Volkova T. A. Devolopment of Microstructure Damage in Structurally Heterogeneous Materials under Deformation // Diagnostics, Resource and Mechanics of materials and structures. - 2016. - Iss. 3. - P. 21-30. -
DOI: 10.17804/2410-9908.2016.3.021-030. -
URL: http://eng.dream-journal.org/issues/2016-3/2016-3_83.html
(accessed: 06/22/2024).


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