Izvestiya vuzov. Yadernaya Energetika

The peer-reviewed scientific and technology journal. ISSN: 0204-3327

Determination of third-order elastic moduli to measure stressed-strained states in metal structural components of nuclear power plants

3/23/2018 2018 - #01 Nuclear power plants

Minin S.I.

DOI: https://doi.org/10.26583/npe.2018.1.02

UDC: 534.6.08

The article presents theoretically derived third-order elastic moduli. Data on the values of the third-order elastic moduli are required for measuring stressed-strained states [1] in metal structural components of NPPs. The values of the second-order elastic moduli obtained by different methods are found in the reference books [2, 3]. The third-order elastic moduli were obtained only by an acoustic method and there is a large scatter of numerical data, reaching several orders of magnitude [4 – 8]. The accuracy in determining stressed states by acoustic methods depends on the adequacy of an ultrasonic wave propagation velocity model and the accuracy in determining ultrasonic velocities. Therefore, it is necessary to develop methods for determining third-order elastic moduli without using acoustic methods. The author presents such a method based on experimental data on all-round compression, using a differential equation connecting the stress tensor with the strain tensor. The third order elastic constants were determined by the equations for the all-round, uniaxial and biaxial compression-tension. To determine the third-order elastic moduli in alloys used in nuclear power engineering, it is necessary to have data on the all-round compression of these materials [9 – 13]. Then, using the above procedure, it is possible to determine the values of these moduli. The experimentally obtained values of stresses with a negligible error coincide with the values of stresses calculated from the formulas.

References

  1. Murnaghan F.D. Finite deformation of an elastic solid. J. Willey and Sons. N.Y., 1951, 140 р.
  2. Grigoriev I.S., Meylikhova E.Z. A physical quantity. Reference. Moscow. Energoatomizdat Publ., 1991, 1232 р. (in Russian).
  3. Sorokin V.G., Gervazieva M.N. Steel and alloys. Marochnik. Moscow. Intermet Engineering Publ., 2001, 608 p. (in Russian).
  4. Landau L.D., Lifshits E.M. Theory of elasticity. Moscow. Nauka Publ., 1987. 248 p. (in Russian).
  5. Novozhilov V.V. Foundations of nonlinear theory of elasticity. Moscow. Gostekhizdat Publ., 1948, 212 p. (in Russian).
  6. Novozhilov V.V. Theory of elasticity. Leningrad. Sudpromgiz Publ., 1958. 370 p. (in Russian).
  7. Guz’ A.N., Makhort F.G., Gushcha O.I. Introduction to acoustoelasticity. Kiev. Naukova Dumka Publ., 1977. 151 p. (in Russian).
  8. Hughes D.S., Kelly J.L. Second-order elastic deformation of solids. Phys. Rev. 1953, v. 92, no. 5, pp. 1145-1149.
  9. Savin G.N. The propagation of elastic waves in a solid body in the case of a nonlinear elastic model of a continuous medium. Prikladnaya mekhanika. 1970, v. VI, iss. 2, pp. 38-42 (in Russian).
  10. Smith R., Stern and Stephens R.W. Third-order elastic moduli of polycrystalline metals from ultrasonics velocity measurements. J. Acoust. Soc. Am., 1966, v. 40, no. 5, pp. 1002-1008/U.
  11. Sekoyan C.C. On the calculation of elasticity constants of the third order according to the results of ultra-rozwojowych measurements. Akusticheskij zhurnal. 1970, v. 16, no. 3, pp. 453-457 (in Russian).
  12. Crecraft D.J.Ultrasonic Wave Velocities in Stressend Nickel Steel. Nature, 1962, v. 195, no. 4847, pp.1193-1194.
  13. Hughes D.S. and Maurette M. Dynamic Moduli of Iron, Aluminum, and Fused Quarz. Journal of Applied Physics, 1956, v. 27, no. 10, pp. 1184-1186.
  14. Bobrenko V.M., Vangheli M.S., Kutsenko A.N. Acoustic control methods of material’s stress of machinery elements. Kishinev. Shtiintsa Publ., 1981. 148 p. (in Russian).
  15. Nikitina N.E. The effect of material anisotropy on the accuracy of the voltage measurement method of customproperty. Defektoskopiya. 1996, no. 4, pp. 77-85 (in Russian).
  16. Nikitina N.Ye., Ostrovsky L.A. An ultrasonic method for measuring stresses in engineering materials. Ultrasonics, 1998, v. 35, pp. 605-610.
  17. Nikitina N.E. Determination of plane stress state of structural materials using bulk elastic waves. Defektoskopiya. 1999, no. 1, pp. 48-54 (in Russian).
  18. Nikitina N.E. Acoustoelasticity. Experience of practical application. N. Novgorod. TALAM Publ., 2005. 208 p. (in Russian).
  19. Nikitina N.E. Kamyshev, A.V., Smirnov V.A. Borschivs’kyi A.V., Sharygin Yu.M. Determination of axial and circumferential stresses in the wall of a closed pipe ultrasonic method based on the phenomenon of customproperty. Defektoskopiya. 2006, no. 3, pp. 49-54 (in Russian).
  20. Nikitina N.E. Kamyshev, A.V., Kazachek S.V. The use of the phenomenon of customroot in the study of the stressed state of process pipelines. Defektoskopiya. 2009, no. 12, pp. 52-59 (in Russian).
  21. Nikitina N.E. Kozachek S.V. Advantages of the acoustoelasticity method for non-destructive control of mechanical stresses in the machine parts. Vestnik nauchno-tekhnicheskogo razvitiya. 2010, v. 32, no. 4, pp. 18-28 (in Russian).
  22. Trofimov A.I., Minin S.I., Trofimov M.A., Usanov D.A., Vasylkovsky D.V. , Kosyrev K.A. Ultrasonic testing method of residual stress in metal structures of nuclear power plants based on the effect of acoustoelasticity. Proc. of the International Scientific-Technical Conference «Strength of Materials and Structural Elements». Kiev. Sept. 28-30, 2010, pp. 137-138 (in Russian).

elastic moduli tension acoustoelasticity equations early diagnosis

Link for citing the article: Minin S.I. Determination of third-order elastic moduli to measure stressed-strained states in metal structural components of nuclear power plants. Izvestiya vuzov. Yadernaya Energetika. 2018, no. 1, pp. 15-22; DOI: https://doi.org/10.26583/npe.2018.1.02 (in Russian).

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