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• Three-dimensional simulation of crack propagation in ferroelectric polycrystals: Effect of combined toughening mechanisms

  A. Abdollahi, I. Arias

  Acta Materialia (2014). Vol. 65, pp. 106-117 (Preprint)

  
  

  Abstract

  We simulate the fracture processes of ferroelectric polycrystals in three dimensions using a phase-field model. In this model, the grain boundaries, cracks and ferroelectric domain walls are represented in a diffuse way by three phase-fields. We thereby avoid the difficulty of tracking the interfaces in three dimensions. The resulting model can capture complex interactions between the crack and the polycrystalline and ferroelectric domain microstructures. The simulation results show the effect of the microstructures on the fracture response of the material. Crack deflection, crack bridging, crack branching and ferroelastic domain switching are observed to act as the main fracture toughening mechanisms in ferroelectric polycrystals. Our fully 3-D simulations illustrate how the combination of these mechanisms enhances the fracture toughness of the material, and pave the way for further systematic studies, including fracture homogenization.

  Abstract
  We simulate the fracture processes of ferroelectric polycrystals in three dimensions using a phase-field model. In this model, the grain boundaries, cracks and ferroelectric [...]

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• Conducting crack propagation driven by electric fields in ferroelectric ceramics

  A. Abdollahi, I. Arias

  Acta Materialia (2013). Vol. 61 (19), pp. 7087-7097 (Preprint)

  
  

  Abstract

  Ferroelectric ceramics are susceptible to fracture under high electric fields, which are commonly generated in the vicinity of electrodes or conducting layers. In the present work, we extend a phase-field model of fracture in ferroelectric single crystals to the simulation of the propagation of conducting cracks under purely electrical loading. This is done by introducing the electrical enthalpy of a diffuse conducting layer into the phase-field formulation. Simulation results show oblique crack propagation and crack branching from a conducting notch, forming a tree-like crack pattern in a ferroelectric sample under positive and negative electric fields. Microstructure evolution indicates the formation of tail-to-tail and head-to-head 90° domains, which results in charge accumulation around the crack. The charge accumulation, in turn, induces a high electric field and hence a high electrostatic energy, further driving the conducting crack. Salient features of the results are compared with experiments.

  Abstract
  Ferroelectric ceramics are susceptible to fracture under high electric fields, which are commonly generated in the vicinity of electrodes or conducting layers. In the present [...]

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

  I. Arias, A. Abdollahi

  Journal of the Mechanics and Physics of Solids (2012). Vol. 60 (12), pp. 2100-2126

  
  

  Abstract

  We 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.

  Abstract
  We present a family of phase-field models for fracture in piezoelectric and ferroelectric materials. These models couple a variational formulation of brittle fracture with, [...]

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• Crack initiation patterns at electrode edges in multilayer ferroelectric actuators

  A. Abdollahi, I. Arias

  Smart materials and structures (2012). Vol. 21 (9), pp. 094011

  
  

  Abstract

  In multilayer ferroelectric actuators, electrode edges are the main source of fracture due to the generation of non-uniform electric fields in their vicinity. The electric fields, in turn, induce incompatible strain fields and hence concentrated stresses, which may cause the ceramic to crack. In this paper, the crack initiation from the electrode edges is simulated using a phase-field model. This model is based on variational formulations of brittle crack propagation and domain evolution in ferroelectric materials. The simulation results show different crack initiation patterns depending on the bonding conditions between the ceramic and electrode layers. Three extreme conditions are considered, which are fully cofired, partially cofired, and separated layers. The crack initiation patterns can be either delimitation along the electrode–ceramic interface or oblique cracking from the electrode into the material. The calculations suggest a mechanism explaining the experimentally observed crack branches near the electrode edges. The effects of the ceramic layer thickness and length of the internal electrode on the crack initiation are also evaluated.

  Abstract
  In multilayer ferroelectric actuators, electrode edges are the main source of fracture due to the generation of non-uniform electric fields in their vicinity. The electric [...]

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• Numerical simulation of intergranular and transgranular crack propagation in ferroelectric polycrystals

  A. Abdollahi, I. Arias

  International Journal of Fracture (2012). Vol. 174 (1), pp. 3-15

  
  

  Abstract

  We present a phase-field model to simulate intergranular and transgranular crack propagation in ferroelectric polycrystals. The proposed model couples three phase-fields describing (1) the polycrystalline structure, (2) the location of the cracks, and (3) the ferroelectric domain microstructure. Different polycrystalline microstructures are obtained from computer simulations of grain growth. Then, a phase-field model for fracture in ferroelectric single-crystals is extended to polycrystals by incorporating the differential fracture toughness of the bulk and the grain boundaries, and the different crystal orientations of the grains. Our simulation results show intergranular crack propagation in fine-grain microstructures, while transgranular crack propagation is observed in coarse grains. Crack deflection is shown as the main toughening mechanism in the fine-grain structure. Due to the ferroelectric domain switching mechanism, noticeable fracture toughness enhancement is also obtained for transgranular crack propagation. These observations agree with experiment.

  Abstract
  We present a phase-field model to simulate intergranular and transgranular crack propagation in ferroelectric polycrystals. The proposed model couples three phase-fields describing [...]

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• Phase-field modeling of the coupled microstructure and fracture evolution in ferroelectric single crystals

  A. Abdollahi, I. Arias

  Acta Materialia (2011). Vol. 59 (12), pp. 4733-4746

  
  

  Abstract

  We propose a phase-field model for the coupled simulation of microstructure formation and evolution, and the nucleation and propagation of cracks in single-crystal ferroelectric materials. The model naturally couples two existing energetic phase-field approaches for brittle fracture and ferroelectric domain formation and evolution. The finite-element implementation of the theory in two dimensions (plane-polarization and plane-strain) is described. We perform, to the best of our knowledge, the first crack propagation calculations of ferroelectric single crystals, simultaneously allowing general microstructures to develop. Previously, the microstructure calculations were performed at fixed crack configurations or under the assumption of small-scale switching. Our simulations show that this assumption breaks down as soon as the crack-tip field interacts with the boundaries of the test sample (or, in general, obstacles such as defects or grain boundaries). Then, the microstructure induced by the presence of the crack propagates beyond its vicinity, leading to the formation of twins. Interactions between the twins and the crack are investigated under mechanical and electromechanical loadings, both for permeable and impermeable cracks, with an emphasis on fracture toughening due to domain switching, and compared with experiments

  Abstract
  We propose a phase-field model for the coupled simulation of microstructure formation and evolution, and the nucleation and propagation of cracks in single-crystal ferroelectric [...]

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• Phase-field simulation of anisotropic crack propagation in ferroelectric single crystals: effect of microstructure on the fracture process

  A. Abdollahi, I. Arias

  Modeling and simulation in materials science and engineering (2011). Vol. 19 (7), pp. 1-13

  
  

  Abstract

  Crack propagation during the indentation test of a ferroelectric single crystal is simulated using a phase- eld model. This model is based on variational formulations of brittle crack propagation and domain evolution in ferroelectric materials. Due to the high compressive stresses near the indenter contact faces, a modi ed regularized formulation of the variational brittle fracture is coupled with the material model to prevent crack formation and interpenetration in the compressed regions. The simulation results show that the radial cracks perpendicular to the poling direction of the material propagate faster than the parallel ones, which is in agreement with experimental observations. This anisotropy in the crack propagation is due to interactions between the material microstructure and the radial cracks, as captured by the phase- eld simulation. Crack propagation during the indentation test of a ferroelectric single crystal is simulated using a phase-eld model. This model is based on variational formulations of brittle crack propagation and domain evolution in ferroelectric materials. Due to the high compressive stresses near the indenter contact faces, a modied regularized formulation of the variational brittle fracture is coupled with the material model to prevent crack formation and interpenetration in the compressed regions. The simulation results show that the radial cracks perpendicular to the poling direction of the material propagate faster than the parallel ones, which is in agreement with experimental observations. This anisotropy in the crack propagation is due to interactions between the material microstructure and the radial cracks, as captured by the phase-eld simulation.

  Abstract
  Crack propagation during the indentation test of a ferroelectric single crystal is simulated using a phase- eld model. This model is based on variational formulations of brittle [...]

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• Experimental validation of large-scale simulations of dynamic fracture along weak planes

  V. Chalivendra, S. Hong, I. Arias, J. Knap, A. Rosakis, M. Ortiz

  Int. J. Impact Engineering (2009). Vol. 36 (7), pp. 888-898

  
  

  Abstract

  A well-controlled and minimal experimental scheme for dynamic fracture along weak planes is specifically designed for the validation of large-scale simulations using cohesive finite elements. The role of the experiments in the integrated approach is two-fold. On the one hand, careful measurements provide accurate boundary conditions and material parameters for a complete setup of the simulations without free parameters. On the other hand, quantitative performance metrics are provided by the experiments, which are compared a posteriori with the results of the simulations. A modified Hopkinson bar setup in association with notch-face loading is used to obtain controlled loading of the fracture specimens. An inverse problem of cohesive zone modeling is performed to obtain accurate mode-I cohesive zone laws from experimentally measured deformation fields. The speckle interferometry technique is employed to obtain the experimentally measured deformation field. Dynamic photoelasticity in conjunction with high-speed photography is used to capture experimental records of crack propagation. The comparison shows that both the experiments and the numerical simulations result in very similar crack initiation times and produce crack tip velocities which differ by less than 6%. The results also confirm that the detailed shape of the non-linear cohesive zone law has no significant influence on the numerical results.

  Abstract
  A well-controlled and minimal experimental scheme for dynamic fracture along weak planes is specifically designed for the validation of large-scale simulations using cohesive [...]

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• Numerical modelling and experimental validation of dynamic fracture events along weak planes

  I. Arias, J. Knap, J. Chalivendra, S. Hong, M. Ortiz, A. Rosakis

  Comput. Methods Appl. Mech. Engrg., (2007). Vol. 196 (37-40), pp. 3833-3840

  
  

  Abstract

  The conceptual simplicity and the ability of cohesive finite element models to describe complex fracture phenomena makes them often the approach of choice to study dynamic fracture. These models have proven to reproduce some experimental features, but to this point, no systematic study has validated their predictive ability; the difficulty in producing a sufficiently complete experimental record, and the intensive computational requirements needed to obtain converged simulations are possible causes. Here, we present a systematic integrated numerical–experimental approach to the verification and validation (V&V) of simulations of dynamic fracture along weak planes. We describe the intertwined computational and the experimental sides of the work, present the V&V results, and extract general conclusions about this kind of integrative approach.

  Abstract
  The conceptual simplicity and the ability of cohesive finite element models to describe complex fracture phenomena makes them often the approach of choice to study dynamic [...]

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• A phenomenological cohesive model of ferroelectric fatigue

  I. Arias, S. Serebrinsky, M. Ortiz

  Acta Materialia (2006). Vol. 54 (4), pp. 975-984

  
  

  Abstract

  We develop a phenomenological model of electro-mechanical ferroelectric fatigue based on a ferroelectric cohesive law that couples mechanical displacement and electric-potential discontinuity to mechanical tractions and surface-charge density. The ferroelectric cohesive law exhibits a monotonic envelope and loading–unloading hysteresis. The model is applicable whenever the changes in properties leading to fatigue are localized in one or more planar-like regions, modeled by the cohesive surfaces. We validate the model against experimental data for a simple test configuration consisting of an infinite slab acted upon by an oscillatory voltage differential across the slab and otherwise stress free. The model captures salient features of the experimental record including: the existence of a threshold nominal field for the onset of fatigue; the dependence of the threshold on the applied-field frequency; the dependence of fatigue life on the amplitude of the nominal field; and the dependence of the coercive field on the size of the component, or size effect. Our results, although not conclusive, indicate that planar-like regions affected by cycling may lead to the observed fatigue in tetragonal PZT.

  Abstract
  We develop a phenomenological model of electro-mechanical ferroelectric fatigue based on a ferroelectric cohesive law that couples mechanical displacement and electric-potential [...]

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