PSI - Issue 6

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

94

5

Table 1. Material constants (linear behavior) .

Table 2. Model parameters (nonlinear behavior).

G c , MV C/m 3

d 33 , m/V d 31 , m/V d 15 , m/V k 33 , F/m E 1 , N/m

1.57e-010

7.5e7

2

P α , C/m

8e-011

0.21

n

1.94e-010 2.51e-008 9.26e+010

1.2 1.0

m

2

ν 12

0.304

The possible and believed solution for phase fraction sensibility problem is implementing this model to finite element program PANTOCRATOR (Semenov, 2003). This will increase the accuracy of predictions by this model due to taking in account domains interactions. For the case of two-phase composition it was already made (Lobanov et al., 2016) and gave satisfying results. The inadequacy of the simplest schemes of homogenization (Reuss or Voigt averaging) and the importance of using finite element homogenization for studying extremal properties near MPB has been shown earlier (Neumeister and Balke, 2011).

Acknowledgements

This work was supported by the Russian Foundation for Basic Research under the grant № 16-08-00845.

References Huber J.E., Fleck N.A., 2001. Multi-axial electrical switching of a ferroelectric: theory versus experiment, J. Mech. Phys. Solids, 49, 785 – 811. Huber J.E., Fleck N.A., Landis C.M., McMeeking R.M., 1999. A constitutive model for ferroelectric polycrystals, Journal of the Mechanics and Physics of Solids, 36, 1663-1697 Liskowsky A.C., Semenov A.S., Balke H., McMeeking R.M., 2005. Finite element modeling of the ferroelectroelastic material behavior in consideration of domain wall motions. In: R.M. McMeeking, M. Kamlah, S. Seelecke and D. Viehland (Ed.). Coupled Nonlinear Phenomena – Modeling and Simulation for Smart, Ferroic and Multiferroic Materials, Proc. MRS Spring Meeting, Vol. 881E, CC4.2. Lobanov S.M., Semenov A.S., 2016. Finite-element modeling of nonlinear behavior of lead-free ferroelectric materials with different fraction rhombohedric and tetragonal phases, Proceedings of conference “Week of Science SPBPU 2016”, SPBSPU, 89 -91. (In Russian) Neumeister P., Balke H., 2011. Micromechanical modelling of the remanent properties of morphotropic PZT, J. of the Mech. and Physics of Solids. Vol. 59, p. 1794-1807. Pathak A., McMeeking R.M., 2008. Three-dimensional finite element simulations of ferroelectric polycrystals under electrical and mechanical loading, J. Mech. Phys. Solids. Vol. 56, p. 663-683. Rödel J., Jo W., Seifert K., Anton E., Granzow T., 2009. Perspective on the Development of Lead-free Piezoceramics, J. Am. Ceram. Soc., 92(6), 1153 – 1177. Seifert K. Lead-Free Piezoelectric Ceramics // TU Darmstadt, 2010. Semenov A.S., 2003. PANTOCRATOR – finite element program for solving nonlinear mechanical problems, Proceedings of the Vth Int. Conf. "Scientific and technical problems of prediction of reliability and durability of structures and methods for their solution”, SPBSPU, 466 -480. (In Russian) Semenov A.S., 2008. Computational methods in plasticity theory, SPBSPU, Saint-Petersburg. (In Russian) Semenov AS, Balke H., Melnikov B.E., 2011. Simulation of polycrystalline piezokeramics by means of finite-element homogenization. Marine Intelligent Technologies, №3 , 109-115. (In Russian)