PSI - Issue 6

Pudeleva Olga et al. / Procedia Structural Integrity 6 (2017) 309–315 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

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Fig.2. Effective saturation strain level as a function of the remanent strain invariant ratio for tetragonal, rhombohedral and mixed variants.

6. Conclusions

Multivariant computational studies were carried out with taking into account the presence of tetragonal and rhombohedral phases within the single crystals in order to determine the free energy parameters of the phenomenological model of ferroelectroelastic material by the method of finite element homogenization. For each type of lattice, the dependences of the saturation strain on the form of the stress state for various distributions of the orientations of single crystals in a polycrystal were established, and analytical dependences of the saturation strain on the form of the stress state were obtained. The mail result of this study is that an increase of portion of rhombohedral single crystals in a polycrystal leads to an increase of the value of the residual strain under different regimes of multiaxial loading. Zhukov, S.A., 2009. O piezokeramike i perspektivah ee primenenija. The World of Technics and Technologics №5, pp.56-60. Ivashov, I.V., Semenov, A.S., 2014. Vlijanie granichnyh uslovij na beregah treshhiny na process razrushenija polikristallicheskoj p'ezokeramiki. Magazine of Civil Engineering, №7(51), pp.5-15 Huber, J.E., Fleck, N.A., Landis, C.M., McMeeking, R.M., 1999. A constitutive model for ferroelectric polycrystals. J. Mech. Phys. Solids, Vol. 47, pp.1663 – 1697. Huber JE, Fleck NA. Multi-axial electrical switching of a ferroelectric: theory versus experiment. J. Mech. Phys. Solids 2001; 49:785 – 811. Landis, C. M., 2003. On the Strain Saturation Conditions for Polycrystalline Ferroelastic Materials. J. of App. Mechanics, 70(4), pp.470-478. 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, Proceedings of the 2005 MRS Spring Meeting, Vol. 881E. 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, pp.663-683. Semenov, A.S., Balke, H., Melnikov, B.E., 2011. Modelirovanie polikristallicheskoj piezokeramiki metodom konechno-jelementnoj gomogenizacii. Marine Intellectual Technologies №3, pp.109-115. Neumeister, P., Balke, H., 2011. Micromechanical modelling of the remanent properties of morphotropic PZT // J. of the Mech. and Physics of Solids, Vol. 59, pp.1794-1807. Landis, C.M., 2002. A new finite-element formulation for electromechanical boundary value problems. International Journal for Numerical Methods in Engineering, 55, pp.613-628. Semenov, A.S., Liskowsky, A.C., Balke, H., 2010. Return mapping algorithms and consistent tangent operators in ferroelectroelasticity. International Journal for Numerical Methods in Engineering, 81, pp.1298 – 1340. References