PSI - Issue 80

Miroslav Hrstka et al. / Procedia Structural Integrity 80 (2026) 471–492 M. Hrstka et al./ Structural Integrity Procedia 00 (2025) 000 – 000

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criterion positive in this range, cf. Fig. 9. σ 22 is greater than 0 in the whole range thus making the contribution to the switching criterion positive , cf. Fig. 9. When the thermal misfit strains are not included, the stress component σ 11 >0 in the whole interval of θ and its contribution to the switching criterion is always negative . σ 22 is also greater than 0, but about of 15% smaller. The electric field plays a significant role in the switching criterion. The E 1 component does not differ much whether or not misfit strains are considered, however the E 2 component differs significantly between the two cases, see Fig. 10. While with the thermal misfit strains included is the E 2 component negative in the whole range, thus providing a positive contribution to the switching criterion, in the case when the thermal misfit strains are not included is the E 2 component negative only in the range 0 < θ < π /2 and having the absolute value more as 3 times lower. The electrical part of the switching criterion is thus the main source of the large increase in the switching zone for the initial poling direction 0° under conditions of thermal misfit strains. However, it should be emphasized that despite the large increase in the switching zone in the presence of thermal misfit strains for an initial polarization of 0°, the size of the switching zone is still an or der of magnitude smaller than the size of the switching zone for an initial polarization of 90°. The explanation of the increase in the size of the switching zone for polarization 90 ° due to thermal misfit strain can be done in a similar vein as for the initial polarization 0 ° . However, since the differences between the mechanical and electrical quantities in this case are not as significant as in the previous case, see Fig. 11 and 12, the increase in the switching zone due to thermal misfit strain is less pronounced.

Fig. 11. Comparison of stress components σ 11 , σ 22 in case of the initial poling direction 9 0° for thermal misfit strains included ( ΔT = –160 °C ) and thermal misfit strains not included ( ΔT = 0 °C )

Fig. 12. Comparison of electric field components in case of the initial poling direction 9 0° for thermal misfit strains included ( ΔT = –160 °C ) and thermal misfit strains not included ( ΔT = 0 °C )