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

487 17

Fig. 6. The stress components, displacements, electric displacement components and electric potential of a PZT-5H/SiO 2 interface crack on the circular path r = 0.001mm, ω 1 = 180 °, ω 2 = – 180 °, poling direction α 1 = 0°, loaded by σ 2 appl = 20 MPa and ΔT = –160 °C.

Table 2. The conventional stress intensity factors K I , K II , K IV calculated for both initial poling directions

α 1 = 90° ΔT = 0 °C

α 1 = 90° ΔT = –160 °C

α 1 = 0° ΔT = 0 °C

α 1 = 0° ΔT = –160 °C

Stress intensity factor

K I [MPa m K II [MPa m K IV [ μC m

1/2 ] 1/2 ]

3.44 -0.27 0.40

4.34 1.18 1.18

3.49 -0.73 -1.25

4.32 0.83 -0.55

1/2 ]

Notice, that for both considered initial poling directions α 1 =0 °, 90° is the change of spontaneous strain Δε 12 = 0. The switching zone predicted from the criterion (42) by employing the linear asymptotic field in Eq. (17) with evaluated GSIFs H i is shown for two selected initial poling directions in Fig. 7 and Fig. 8. For comparison, the switching zone is displayed for both the temperature change ΔT = –160 °C and ΔT = 0 °C. The orientation of the switching angle i.e. 90°or –90°, depends on the criterion (42), priority is given to the orientation for which the criterion (42) is met first. Most surprising is the extraordinary increase in the size of the switching zone by more than one order of magnitude for the initial poling direction 0 ° when thermal misfit strains are included, cf. Fig. 7.

Fig. 7. Domain switching zone for an interface crack loaded by σ 2 appl = 20 MPa for the initial poling direction 0° with respect to the interface. For comparison, the switching zone is displayed both for temperature change ΔT = –160 °C and ΔT = 0 °C ; on the right-hand side the detailed view is shown