Phase field simulations of polarization switching-induced toughening in ferroelectric ceramics

Wang, Jie; Zhang, Tong‐Yi

doi:10.1016/j.actamat.2006.11.041

Cited by 89 publications

(50 citation statements)

References 29 publications

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“…The results reported by Li and Landis (2011) indicate positive energy release rates for a sharp crack with a modified form of impermeable boundary conditions under purely electrical loading, which is in agreement with the weakening effect of negative electric fields observed in our simulations. However, we have found a disagreement with the results of Wang and Zhang (2007). For permeable conditions, this paper reports that a positive electric field reduces the apparent fracture toughness, while a negative electric field enhances it.…”

Section: Propagating Cracks In Ferroelectricscontrasting

confidence: 55%

Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions

Abdollahi

Arias

2012

Journal of the Mechanics and Physics of Solids

136

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a b s t r a c tWe present a family of phase field models for fracture in piezoelectric and ferroelectric materials. These models couple a variational formulation of brittle fracture with, respectively, (1) the linear theory of piezoelectricity, and (2) a Ginzburg Landau model of the ferroelectric microstructure to address the full complexity of the fracture phenomenon in these materials. In these models, both the cracks and the ferroelectric domain walls are represented in a diffuse way by phase fields. The main challenge addressed here is encoding various electromechanical crack models (introduced as crack face boundary conditions in sharp models) into the phase field framework. The proposed models are verified through comparisons with the corresponding sharp crack models. We also perform two dimensional finite element simulations to demonstrate the effect of the different crack face conditions, the electromechanical loading and the media filling the crack gap on the crack propagation and the microstructure evolution. Salient features of the results are compared with experiments.

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Section: Propagating Cracks In Ferroelectricscontrasting

confidence: 55%

Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions

Abdollahi

Arias

2012

Journal of the Mechanics and Physics of Solids

136

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“…It is a robust and versatile method for studying interfacial problems of a wide spectrum of physical phenomena, such as the flexoelectric coupling [31,32] and fracturing [33,34] in ferroelectric solids. At present, there are several different versions of phase-field approach for ferroelectric materials in the literature [35][36][37][38][39][40][41]. Here we will adopt the framework established in Su and Landis [37] to carry out the analysis.…”

Section: Introductionmentioning

confidence: 99%

Intrinsic versus extrinsic effects of the grain boundary on the properties of ferroelectric nanoceramics

Kang

Wang

et al. 2017

Phys. Rev. B

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As the grain size decreases to the nanometer range, the characteristics of the ferroelectric nanoceramic can be ultimately determined by the competition between two effects: the intrinsic effect that is associated with the local properties of the grain boundary and the extrinsic effect that arises from the dynamics of domain structure which is highly influenced by the depolarization field caused by the grain boundary. In this work we investigate such a competition with a phase-field simulation based on the time-dependent Ginzburg-Landau (TDGL) kinetic equation.The study is performed on poled/unpoled nanoceramics under high-and low-amplitude bipolar alternating electric field with selected grain size and loading frequency. Our calculations for poled BaTiO 3 at 100 Hz show that, for the grain size from 170 to 50 nm, its properties are dominated by the extrinsic effect, and from 50 to 10 nm, they are dominated by the intrinsic one. As the grain size decreases, the dielectric and piezoelectric constants at the remnant state continuously rise in the extrinsic-dominated region and then drop sharply in the intrinsic-dominated region. Our frequency calculations from 10 to 2,500 Hz at the grain size of 100 nm indicate that the high-frequency behavior is very similar to that of the small grain-size, intrinsic-dominated one, whereas the low-frequency behavior is closely related to that of the large grain-size, extrinsic-dominated part, with the demarcation line occurring around 400 Hz. For the un-poled ceramics under small signal loading, the intrinsic effect is dominant over the entire range of grain size and frequency.

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“…The third group of theoretical approaches is based on phase-field or timedependent Devonshire-Ginzburg-Landau (TDGL) models, which have been developed to explicitly describe the formation and evolution of individual ferroelectric domains in the framework of continuum mechanics [20,102,107,110,132,135,144]. These models have allowed researchers to study the nucleation and growth of domains near crack tips and the influence on the stress field [136], the mechanical and electromechanical J−integrals [64,65,108,122,125,133], and nonlinear behavior of ferroelectrics [37]. For completeness, we mention that cohesive theories aimed at fracture in ferroelectric materials have also been proposed [10,32].…”

Section: Introductionmentioning

confidence: 99%

Phase-Field Modeling of Fracture in Ferroelectric Materials

Abdollahi

Arias

2014

Arch Computat Methods Eng

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This paper presents a family of phase-field models for the coupled simulation of the microstructure formation and evolution, and the nucleation and propagation of cracks in single and polycrystalline ferroelectric materials. The first objective is to introduce a phase-field model for ferroelectric single crystals. The model naturally couples two existing energetic phasefield approaches for brittle fracture and ferroelectric domain formation and evolution. Simulations show the interactions between the microstructure and the crack under mechanical and electromechanical loadings. Another objective of this paper is to encode different crack face boundary conditions into the phase-field framework since these conditions strongly affect the fracture behavior of ferroelectrics. The smeared imposition of these conditions are discussed and the results are compared with that of sharp crack models to validate the proposed approaches. Simulations show the effects of different conditions and electromechanical loadings on the crack propagation. In a third step, the model is modified by introducing a crack non-interpenetration condition in the variational approach to fracture accounting for the asymmetric behavior in tension and compression. The modified model makes it possible to explain anisotropic crack growth in ferroelectrics under the Vickers indentation loading. This model is also employed for the fracture analysis of multilayer ferroelectric actuators, which shows the potential of the model for future applications. The coupled phase-field model is also extended to polycrystals by introducing realistic polycrystalline microstructures in the model.

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Phase field simulations of polarization switching-induced toughening in ferroelectric ceramics

Cited by 89 publications

References 29 publications

Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions

Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions

Intrinsic versus extrinsic effects of the grain boundary on the properties of ferroelectric nanoceramics

Phase-Field Modeling of Fracture in Ferroelectric Materials

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