Funct. Mater. 2021; 28 (3): 542-548.

doi:https://doi.org/10.15407/fm28.03.542

Anisotropy of elastic modules of the planes of a hexagonal crystal and damage of titanium sheets

N.A.Volchok1, Ya.D.Klubis1, A.P.Nachev2, A.F.Tarasov1, G.Gershtein2

1K.D.Ushinsky South Ukrainian National Pedagogical University, 26 Staroportofrankovskaya Str, 65020 Odessa, Ukraine
2G.F.Leibniz Institute of Materials Science of Hannover University, 30823 Garbsen, Germany

Abstract: 

A Fourier analysis of the anisotropy of the elastic properties of the crystallographic planes of hexagonal crystals, given by their angle of inclination to the isotropic plane of the basis (0001), is carried out. It was found that the anisotropy of Young's modulus of titanium for all planes is monotonic with a minimum in [101Bar0] and a maximum in [101Bar0] + π/2. For the zirconium and magnesium crystallographic planes forming an angle α0 with the (0001) plane, the values of E take the minimum in the direction [101Bar0] + π/4, and the maximum - in [101Bar0] + π/2. We used the dynamic method to study the anisotropy of E for annealed and tensile-deformed titanium samples cut from sheets at different angles to the rolling direction (RD) and estimated the level of integral damage (D) of deformed samples (strips) relative to undeformed ones. The anisotropy of D is similar to the anisotropy of E; it is approximated by a Fourier series with harmonic amplitudes A0 = 1.38, A2 = -0.99, A4 = -0.2 %. Prevailing influence of A2 in the anisotropy of D indicates damage as a property of the second tensor dimension. This is expressed in the characteristic shape of pores in the form of ellipsoids, which are observed on microstructures.

Keywords: 
hexagonal crystal, Young and shear moduli, Fourier analysis, titanium, zirconium, magnesium, damage, pores.

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References: 
1.H. Bunge, Verlag, Berlin, Seiten Geb, 330, (1969)
 
2. G. Wasserman, I. Grevin, Metallurgy, Moscow, 654, (1959) [in Russian].
 
3. N. A. Volchok, D. A. Dyachok, Z.A. Briukhanova, E.V. Dyshlov, Functional Materials, 27, 1, 170, (2020).
 
4. J.F Nye, Physical Properties of Crystals. Clarendon Press, Oxford, XVII, 329, (1985).
 
5. J, Lemaitre, Course on Damage Mechanics, Berlin,Verlag, 210, (1992).
https://doi.org/10.1007/978-3-662-02761-5
 
6. G. Schulze, Metallphysik, Berlin, Akademie, Verlag, 458, (1967).
 
7. Y.D. Vishnyakov, A.A. Babareko, S.A. Vladimirov, I.V. Egiz, Nauka, Moscow 344, (1979) [in Russian].
 
8. A. A. Bryukhanov, N. A. Volchok, T. S. Sovkova, FiTVD, 1, 123, (2010).
 
9. A. A. Bryukhanov, N. A. Volchok, T. S. Sovkova, Mater. Sci., 4, 9 (2010).
 
10.A. A. Bryukhanov, N. A. Volchok, T. S. Sovkova, Tekhnologiya metallov, 12, 14, (2010).
 
11. Standard Test Method for Dynamic Modulus, Shear Modulus, Poisson's Ratio by Impulse Excitation of Vibration, ASTM International, E187609, p..
 
12. Spectra PLUS 5.0.23, www.spectraplus.com, Pioneer Hill Software LLC, 24460 Mason Road NW, Poulsbo, WA 98370 USA.
 

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