PSI - Issue 6

Sviatoslav M. Lobanov et al. / Procedia Structural Integrity 6 (2017) 90–94 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

93

4

120 6

(6)

180 c G G G G G G      71 90 109 60 2 2 2 c c c c c

5

On the other hand, as there are three phases it might be supposed that there should be three indifferent P α parameters for each phase. The physical meaning of P α is that in case of 100% fraction of one phase the ferroelectric saturation of polarization would be reached on the level of P α . This parameter can be identified from experimental hysteresis curve for material not depending of phase composition. Thus due to geometrical reasons there might be presented the following relations between P α for phases:

tetr

3

om rh b

orth

2

(7)







P

P

P P 







4

4

Thus, using (6) and (7) the overall number of model parameters was reduced from 14 to 4, which are G c , P α , n, m . 3. Results and discussion The hysteresises loops for described polycrystalic specimen of 20;0.5 BNKT-KNN-BKT, marked yellow on fig. 1, under cyclic electric loading with maximum magnitude of E max =4; 6; 8 MV/m were obtained and compared with experimental data (see fig.3). The parameters used in simulation are included in tables 1 and 2.

Fig. 3. Comparison of experimental and model data for cyclic electric loading with amplitude of 4;6;8 MV/m.

As seen on fig. 3 parameters tuning in the present model can give quite an accurate hysteresis behavior prediction for a wide range of loading amplitudes. The parameters study gives following results. Even though, changing of any parameter affects the whole form of hysteresis, the coercetive field, the remanent polarization and polarization maximum, there are main trends that depend on each of parameters. Thus, P α works as scaling coefficient for vertical axis, while G c works alike in horizontal direction, n mostly affects E c and velocity of saturation, while m changes the angle of hysteresis curve in the beginning of reloading. The sensitivity of the proposed model to phase composition changing was studied and compared with experimental data presented by Seifert (2010). Even though, the model depicts monotonic response of hysteresis parameters from phase volume fractions change, it cannot work out the huge impact of 1% changing which is showed in experiment within the x;y pairs from fig. 1.