Determination of the shear constants of the cubic crystals

S.A. Muslov1, A Korneev2, N. Zaytseva3
1A.I. Evdokimov MSMSU
2Moscow State University of Medicine and Dentistry named A. I. Evdokimov
31. Moscow State University of Medicine and Dentistry named A. I. Evdokimov
As a result of the research, formulas for calculating shear elastic constants of cubic crystals, based on the resonant frequency of torsional vibrations of samples c44 and C' with square and rectangular cross-section in the method of the composite piezoelectric vibrator was obtained. Despite the fact that the resonance method does not need a large single crystals, the calculation formulas for the samples most simple to manufacture prismatic either incomplete or completely unknown. For example, there is data on the calculation of the c44 and C' of the natural frequencies of torsional vibrations of the rods only circular cross-section. An exception is the ultrasonic pulse method for measuring the elastic constants, but it requires to measure single-crystal samples of sufficiently large size. The calculation is reduced to finding the proper expressions for rotating mechanical torque, which is more or less complex function of the cross-section and the elastic constants of the sample material. At the same time it takes into account the amendment to the warping of the cross-section of anisotropic samples under torsion. Then calculates the natural frequencies of torsional vibration samples of square and rectangular cross-section and the corresponding shear elastic constants. As an example, the calculation of shear considered constant C' on the basis of the pitch frequency of torsional vibrations of square cross-section sample of nickel-titanium NiTi.
Received: 04 December 2015   Accepted: 09 February 2016
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