PSI - Issue 32

M.O. Levi et al. / Procedia Structural Integrity 32 (2021) 306–312 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

311

6

0.005

0.01

 Vf/Vs

 V mode 1

 V mode 2

mfs 2 mfs 4 mfs 6 mfs 10

 Vf/Vs

mfs 2 mfs 4 mfs 6 mfs 10

0.004

0.008

0.003

0.006

0.002

0.004



0.001

0.002



0

0

a)

b)

0

2

4

6

8

10

3.5

5

6.5

8

9.5

0.01

 V mode 3

 Vf/Vs

0.008

0.006

0.004

0.002

mfs 2 mfs 6

mfs 4 mfs 10



0

c)

6.8

7.8

8.8

9.8

Fig. 2. Difference of phase velocities for the first three modes of SH wave relative to Vf/Vs (1.6): a) first mode; b) second mode; c) third mode.

Table 2. Material properties for MgO.

44 c (GPa)

66 c (GPa)

11  (C

33  (C

2 /Nm 2 )

2 /Nm 2 )

 (kg/m 3 )

0 

0 

MgO

155

100.5

3576

Figure 1 show a general view of dimensionless phase velocities in mediumfor misfit strain value 1.6. In our case, 3 wave modes are placed in the investigated frequency range. Figure 2 shows difference between phase velocities for misfit strain 1.6 and other values for the first three modes. The effect of the misfit deformation on the first wave mode is most significant in the frequency domain  3.5, and with increasing frequency, the difference between misfit deformations decreases. In the frequency range  <0.8, the effect of misfit deformation is an order of magnitude less than in the rest of the investigated frequency range. In the general case, the region close to the R – phase changes the constants more significantly than in the rest of the misfit strain region, this can be seen from the difference between the misfit strain values 1.6 and 4, as well as between 4 and 10, and here the misfit strain change from 4 to 10 has a smaller influence is less than change from 2 to 4. The peak of the effect of misfit deformation for the second mode is observed at a frequency of 4.2, for the third mode at a frequency of 7.7.Similar to the first mode, with increasing frequency, the effect of misfit deformation also decreases for second and third modes. Acknowledgements The work was performed as a part of the implementation of the state assignment of the Southern Scientific Center of the Russian Academy of Sciences (SSC-RAS), project 01201354242 with partial financial support from the Russian Foundation for Basic Research (RFBR), grants 19-08-01051, 19-01-00719, 19-48-230042.