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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4. Concluding remarks The presented work studied effect of initial misfit strains emerging from temperature loading of a bi-material notch composed of piezoelectric layer PZT-5H and non-piezoelectric substrate SiO 2 . The work followed up author's previous research where robustness and settings of the algorithm were tested. The radius of the integration path encircling the crack tip was set to r=1 mm, so as the radius of the circle of the domain integral containing temperature strains. As the gradient of complex potential of the auxiliary strains is large in the close vicinity of the crack tip, the integration over finite elements was realized by incorporating 7-point Gauss quadrature to achieve acceptable accuracy. The mesh sensitivity study was not performed as these aspects has been tested in the previous author's works. It has been shown that the temperature change generating initial thermal strains has significant impact to the domain switching zone shapes. The effect is stronger for the piezoelectric material poled in the x 1 axis, even though the domain switching zone was smaller than for poling in x 2 direction. Since the formation of the switching zone significantly affects the shielding or anti-shielding of the crack tip, leading to an increase or decrease in the apparent fracture toughness, it is obvious that the thermal misfit strain arising from the cooling from the poling temperature of the piezoceramic layer on the substrate will have a significant indirect impact on the resulting apparent toughness of the investigated bimaterial structure. Therefore, the next step is to solve the boundary value problem with the prescribed spontaneous strain and polarization within the switching domain using FEM and to employ the computed electroelastic field in the Betti’s recipr ocal principle with the aim to calculate the new local GSIF tip i H according to Eq. (44). The results of the calculations will be presented at the conference. Acknowledgements The authors acknowledge the supports by Horizon Europe via the project HORIZON-WIDERA-2021-ACCESS 03, SEP-210806308 and by the project "Mechanical Engineering of Biological and Bio-inspired Systems", funded as project No. CZ.02.01.01/00/22_008/0004634 by Programme Johannes Amos Commenius, call Excellent Research.

Appendix A The transformation matrices in Eq. (4) are defined as:

               

                

2

2

cos sin

sin cos

0 0 0 0 1 0 0 cos

0 0 0

2cos sin 2cos sin





 

2

2

−





 

0 0 0

0 0 0

0 0 0

K

= 

(A1)

sin

−





0 sin cos 



2

2

cos sin cos sin 0 0    

0 cos

sin

−

−





cos sin 0 sin cos 0 0 0 1    

   

    

Ω

=  −

i  Z in Eq.(16) is defined as follows:

The complex function