Investigation of Influence of the Factor of Anisotropy on Regularity of Change of Volume in Microstructure Elements

V. Iu. Marina$^{1}$, V. I. Marina$^{2}$

$^{1}$Ministry of Education of the Republic of Moldova, 1 Velikogo Natsional’nogo Sobraniya Sqr., MD-2033 Kishinev, Moldova
$^{2}$Technical University of Moldova, 168 Shtefan chel Mare Blvd., MD-2004 Kishinev, Moldova

Received: 31.08.2016. Download: PDF

The regularities of fluctuations of spherical stress tensors in cubic-lattice crystals are investigated depending on their orientation in polycrystalline single-phase materials. As shown, the interactions between the crystals in conglomerate of polycrystals lead to local bulk stresses/strains appearance even at pure macroscopic shear. The interval of changing spherical stress/strain tensors is comparable with macroscopic module of deviator of stresses/strains tensor and depends on anisotropy coefficient of crystals. Based on established laws, it is possible to explain some experimental thermomechanical effects, for example, energy dissipation, which is connected with concept of internal friction. According to this model, the conditions of destructions of polycrystalline materials can be described for general load using, at local level, simple strength criteria—maximal normal stress/strain.

Key words: structure, stress tensor, deformation, anisotropy, single crystal, polycrystals.



PACS: 02.70.Dh, 46.50.+a, 62.20.D-,, 81.40Jj, 81.40.Np

Citation: V. Iu. Marina and V. I. Marina, Investigation of Influence of the Factor of Anisotropy on Regularity of Change of Volume in Microstructure Elements, Metallofiz. Noveishie Tekhnol., 39, No. 3: 387—399 (2017) (in Russian)

  1. W. Voight, Lehrbuch der Kristallphysik (Berlin: Teubner: 1928).
  2. A. Reuss, Z. Angev. Math. und Mech., 9, No. 1: 49 (1929).
  3. V. V. Novozhilov and Yu. I. Kadashevich, Mikronapryazheniya v Konstruktsionnykh Materialakh [Microstresses in Constructional Materials] (Leningrad: Mashinostroenie: 1990) (in Russian).
  4. E. Kroner, Zeitschrift für Physik, 151: 504 (1958). Crossref
  5. V. I. Marina, Mnogoelementnaya Model' Sredy, Opisyvayushchaya Peremennye Slozhnye Neizotermicheskie Protsessy Nagruzheniya [A Multi-Element Model of the Medium Described Variable Complex Non-Isothermal Loading Processes] (Thesis of Disser. … for Dr. Phys.-Math. Sci.) (Kyiv: Institute of Mechanics, N.A.S. of Ukraine: 1991) (in Russian).
  6. V. I. Marina, Prikladnaya Mekhanika, No. 6: 9 (1997) (in Russian).
  7. V. Marina, Metallurgy and New Materials Researches, 11, No. 3: 50 (1994).
  8. Z. Khill, Prikladnaya Matematika i Mekhanika, 35, Iss. 1: 31 (1971) (in Russian).
  9. V. I. Marina, Izvestiya Akademii Nauk Respubliki Moldova. Matematika, No. 2: 16 (1998) (in Russian).
  10. M. Onami, S. Ivasimudzu, and K. Genka, Vvedenie v Mikromekhaniku [Introduction to Micromechanics] (Moscow: Metallurgiya: 1987) (in Russian).