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Fracture simulation of ferroelectrics based on the phase field continuum and a damage variable

Xu, Bai-Xiang and Schrade, David and Gross, Dietmar and Mueller, Ralf (2010):
Fracture simulation of ferroelectrics based on the phase field continuum and a damage variable.
In: International Journal of Fracture, 166 (1-2), pp. 163-172, ISSN 0376-9429,
[Online-Edition: http://dx.doi.org/10.1007/s10704-010-9520-7],
[Article]

Abstract

Domain switching in the vicinity of a crack tip is known as one of the major aspects of local nonlinear behavior of ferroelectrics, and it plays an important role in the fracture behavior. In the present paper, a fracture model based on a phase field continuum and a damage variable is presented to study the fracture behavior of ferroelectrics and its interaction with the domain structures. In this model the energy of fracture is regularized by the damage variable. When the damage variable equals one, it represents undamaged material. In this case, the energy reduces to the phase field potential with the spontaneous polarization being an order parameter, and the system of equations becomes the same as that of a conventional phase field continuum. When the damage variable becomes zero, it represents a crack region, and the potential becomes the energy density stored in the crack medium. The evolution of the damage variable is governed by a Ginzburg-Landau type equation. In this way, the fracture model can simulate the fracture behavior such as crack growth, kinking and formation, with no a priori assumption on fracture criteria and predefined crack paths. The model is implemented in a 2D Finite Element Method in combination with implicit time integration and non-linear Newton iteration. As example, the fracture model is used to simulate the fracture of an edge crack in a ferroelectric single crystal under mechanical mode-I loading. In the simulation crack propagation, kinking and formation are observed. In particular, the results show the interaction between the domain structure evolution and the crack propagation.

Item Type: Article
Erschienen: 2010
Creators: Xu, Bai-Xiang and Schrade, David and Gross, Dietmar and Mueller, Ralf
Title: Fracture simulation of ferroelectrics based on the phase field continuum and a damage variable
Language: English
Abstract:

Domain switching in the vicinity of a crack tip is known as one of the major aspects of local nonlinear behavior of ferroelectrics, and it plays an important role in the fracture behavior. In the present paper, a fracture model based on a phase field continuum and a damage variable is presented to study the fracture behavior of ferroelectrics and its interaction with the domain structures. In this model the energy of fracture is regularized by the damage variable. When the damage variable equals one, it represents undamaged material. In this case, the energy reduces to the phase field potential with the spontaneous polarization being an order parameter, and the system of equations becomes the same as that of a conventional phase field continuum. When the damage variable becomes zero, it represents a crack region, and the potential becomes the energy density stored in the crack medium. The evolution of the damage variable is governed by a Ginzburg-Landau type equation. In this way, the fracture model can simulate the fracture behavior such as crack growth, kinking and formation, with no a priori assumption on fracture criteria and predefined crack paths. The model is implemented in a 2D Finite Element Method in combination with implicit time integration and non-linear Newton iteration. As example, the fracture model is used to simulate the fracture of an edge crack in a ferroelectric single crystal under mechanical mode-I loading. In the simulation crack propagation, kinking and formation are observed. In particular, the results show the interaction between the domain structure evolution and the crack propagation.

Journal or Publication Title: International Journal of Fracture
Volume: 166
Number: 1-2
Uncontrolled Keywords: Phase field simulation - Ferroelectric domain structure - Continuum fracture model - Crack propagation
Divisions: 11 Department of Materials and Earth Sciences
11 Department of Materials and Earth Sciences > Material Science
Zentrale Einrichtungen
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 595: Electrical fatigue
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 595: Electrical fatigue > C - Modelling
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 595: Electrical fatigue > C - Modelling > Subproject C3: Microscopic investigations into defect agglomeration and its effect on the mobility of domain walls
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres
DFG-Collaborative Research Centres (incl. Transregio)
Date Deposited: 27 Sep 2011 11:45
Official URL: http://dx.doi.org/10.1007/s10704-010-9520-7
Additional Information:

SFB 595 C3

Identification Number: doi:10.1007/s10704-010-9520-7
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