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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Fig. 5 and 6 demonstrate the correctness of the formula (39) for the GSIFs evaluation. The asymptotic solution with the computed GSIFs for stress components, displacements, electric displacement components and electric potential of a PZT-5H/SiO 2 interface crack is compared with the full-field solution obtained by FEM on a very fine mesh along the circular path r = 0.001mm, proving thus an excellent agreement. Also contributions of individual terms in Eq. (30) and (31) are presented and reveal that the terms proportional to the GSIF H 3 almost do not affect the mechanical and electrical fields in PZT-5H, but strongly influence the electric potential in SiO 2 substrate. Notice, that the initial poling direction in PZT-5H is considered to be parallel with the interface and perpendicular to it, respectively. The conventional stress intensity factors K I , K II , K IV calculated from Eq.(46) are also given in Tab. 2 for both initial poling directions and, for comparison, two variants are presented: (i) thermal misfit strains are considered, (ii) thermal misfit strains are not considered. The reference length was chosen as l = 1 mm. It is seen in Tab. 2 that thermal misfit strains significantly change the SIF K II and the electric K IV intensity factor. Observe that the electric K IV intensity factor is nonzero in both variants even though the loading is purely mechanical one which is significantly different from the case of a crack in a homogeneous material, where K IV vanishes for purely mechanical loading. The switching criterion (42) was employed in the vicinity of the crack tip. The changes in the spontaneous strain and the spontaneous polarization during switching are considered as given in Eqs. (43) and the magnitudes of the spontaneous polarization, spontaneous strain, and the coercive electric field are given in Tab. 1.