Simulations of domain evolution in morphotropic ferroelectric ceramics under electromechanical loading using an optimization-based model

Abstract

In this paper, an optimization-based computational model is proposed to study the nonlinear performance and domain texture evolution in morphotropic ferroelectric ceramics composed of numerous random oriented grains, each of which contains fourteen types of domains (six are tetragonal and eight are rhombohedral). Field induced phase transformations between the tetragonal and rhombohedral domains are permissible; thus, both the in-phase and inter-phase domain switching can occur in this model. The charge screening effect in real ceramics is taken into account and thus the electric depolarization field caused by incompatible polarization vanishes. The mechanical constraint from the neighboring grains, however, cannot be neglected and is considered using the Eshelby inclusion approach. Under any prescribed electromechanical loading, the volume fraction of each domain in a grain is obtained by minimizing the sum of the potential energy and switching the related dissipation energy of the whole grain using the sequential quadratic programming optimization algorithm. Similar to the phase field model, this model also does not require the imposition of any a priori domain-switching criterion. The computational efficiency of this model is fairly high and it is feasible to study 3-D cases using numerous grains. The domain texture evolution process can also be calculated step by step and shown using the pole figures of the polar axis. Simulation results on the morphotropic lead titanate zirconate ceramics under uniaxial electromechanical loading show that with the increase of the uniaxial compression, both the D-E hysteresis loops and the butterfly curves becomes more flat and the electric coercive field becomes less distinct, which is in good agreement with existing experimental results. The calculated domain-texture evolution process indicates that when the compression is large enough, the domains have been constrained with their polar axis aligned in those planes nearly perpendicular to the compressive direction and almost cannot switch under moderate electric loading, thus leading to the more flat D-E hysteresis loops and butterfly curves.