A phenomenological cohesive model of ferroelectric fatigue

Arias, Irene; Serebrinsky, Santiago; Ortiz, Michael

doi:10.1016/j.actamat.2005.10.035

Cited by 61 publications

(38 citation statements)

References 52 publications

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“…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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Section: Introductionmentioning

confidence: 99%

Phase-Field Modeling of Fracture in Ferroelectric Materials

Abdollahi

Arias

2014

Arch Computat Methods Eng

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“…The mechanism of microcracks on electric fatigue was previously reported by Arias et al, 89 Nuffer et al, 90 and Lupascu and Rodel. 27 The discontinuities of mechanical displacement and electric potential, 89 as well as the concentration of defects at the microcracks, 27,91 could pin the movement of domain walls.…”

Section: Pmn-pt Single Crystal With a Predominantly R Phasementioning

confidence: 78%

“…27 The discontinuities of mechanical displacement and electric potential, 89 as well as the concentration of defects at the microcracks, 27,91 could pin the movement of domain walls. Therefore, microcracks act as the trapping sites that pin the electric dipoles.…”

Section: Pmn-pt Single Crystal With a Predominantly R Phasementioning

confidence: 99%

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Phase fragility and mechatronic reliability for Pb(Mg_1/3Nb_2/3)O₃–PbTiO₃ ferroelectric single crystals — A review

Fang

Yang

2014

J. Adv. Dielect.

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Single crystals of (1 À x)Pb(Mg 1=3 Nb 2=3 ÞO 3 -xPbTiO 3 (PMN-xPT) near their morphotropic phase boundaries (MPBs) are under extensive investigations for their extraordinary high dielectric and piezoelectric behavior. Applications of those single crystals facilitated the breakthrough in ultrasonic transducer materials and devices. Ferroelectric materials are known to be fragile which often leads to various reliability failures in applications involving electric loadings. In a mechanical sense, the failure modes concern the fracture under an intensive electric field, and the fatigue crack propagation under an alternating electric field. In an electrical sense, the failure is exhibited by degenerated hysteresis loop by shrinking the remnant polarization and expanding the coercive field. All these modes degrade the performance for ferroelectric devices. As a departure from the tetragonal (TÞ ferroelectric materials, exemplified by BaTiO 3 and Pb(ZrTi)O 3 , the domain structures of PMN-PT around the MPB are versatile and intricate, depending sensitively on the composition variation, orientation and previous loading history. In this review, the attention is mainly focused on three aspects. First, the phase fragility and multiphase coexistence are presented for both [100]-and [101]-oriented PMN-PT single crystals. Second, investigations on electric field-induced fatigue crack propagation are described, along with the orientation effect on the crack propagation behavior. Third, the inverse effects of the phase transition and fatigue crack growth on the polarization behavior, or the interaction between the mechanical and electrical degradations will be elucidated. The review aims for better understanding the underlying mechanism for the ultrahigh performance of the PMN-PT single crystals, to bridge the studies of ferroelectric materials from the mechanical and electrical senses, as well as to evaluate the reliability of PMN-PT single crystals under device applications.

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“…There are many thermodynamically motivated material models for grains, often taking switching phenomena into account [4][5][6][7]. Concerning ferroelectric interfaces, an analytical proposion for a cycle-by-cycle treatment of fatigue, introducing an effective quantity [8], has been made [9].…”

Section: Introductionmentioning

confidence: 99%

Investigation of microcracks in ferroelectric materials by application of a grain‐boundary‐motivated cohesive law

Utzinger

Menzel

Steinmann³

2007

Proc Appl Math and Mech

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Ferroelectric materials exhibit a huge potential for engineering applications -ranging from electrical actuators (inverse piezoelectric effect) to sensor technology (direct piezoelectric effect). To give an example, lead zirconate titanate (PZT) is a typical perovskite ion crystal possessing ferroelectric properties. In this contribution, we are particularly interested in the modelling of microcracking effects in ferroelectric materials.In view of Finite-Element-based simulations, the geometry of a natural grain structure, as observed on the so-called micro-level, is represented by an appropriate mesh. While the response on the grains themselves is approximated by coupled continuum elements, grain boundaries are numerically incorporated via so-called cohesive-type elements. For the sake of simplicity, switching effects in the bulk material will be neglected. The behaviour of the grain boundaries is modelled by means of cohesive-type laws. Identifying grain boundaries as potential failure zones leading to microcracking, cohesive-type elements consequently offer a great potential for numerical simulations. As an advantage, in the case of failure they do not a priori result in ill-conditioned systems of equations as compared with the application of standard continuum elements to localised deformations. Finally, representative constitutive relations for both the bulk material and the grain boundaries, enable two-dimensional studies of low-cycle-fatigue motivated benchmark boundary value problems.

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A phenomenological cohesive model of ferroelectric fatigue

Cited by 61 publications

References 52 publications

Phase-Field Modeling of Fracture in Ferroelectric Materials

Phase-Field Modeling of Fracture in Ferroelectric Materials

Phase fragility and mechatronic reliability for Pb(Mg_1/3Nb_2/3)O₃–PbTiO₃ ferroelectric single crystals — A review

Investigation of microcracks in ferroelectric materials by application of a grain‐boundary‐motivated cohesive law

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A phenomenological cohesive model of ferroelectric fatigue

Cited by 61 publications

References 52 publications

Phase-Field Modeling of Fracture in Ferroelectric Materials

Phase-Field Modeling of Fracture in Ferroelectric Materials

Phase fragility and mechatronic reliability for Pb(Mg1/3Nb2/3)O3–PbTiO3 ferroelectric single crystals — A review

Investigation of microcracks in ferroelectric materials by application of a grain‐boundary‐motivated cohesive law

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Phase fragility and mechatronic reliability for Pb(Mg_1/3Nb_2/3)O₃–PbTiO₃ ferroelectric single crystals — A review