Nucleation and growth of domains near crack tips in single crystal ferroelectrics

Journal of the Mechanics and Physics of Solids

2012

140

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.

Section: Propagating Cracks In Ferroelectricssupporting

confidence: 81%

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

Abdollahi

Journal of the Mechanics and Physics of Solids

2012

140

“…Interactions between the microstructure, grain boundaries, localized stress and electric fields near the crack tips lead to the complexity of fracture phenomena in ferroelectric polycrystals. Several approaches have been proposed to study the fracture in ferroelectric materials, including phenomenological constitutive models (Landis 2003;Sheng and Landis 2007;Wang and Landis 2006), models investigating the local phase transformations near the crack tip Yang 1997, 1999;Yang and Zhu 1998), phasefield models for computing the mechanical and electromechanical J -integrals (Song et al 2007; Zhang 2007, 2008;Li and Landis 2011;Li and Kuna 2011), and more recently, a phase-field model accurately accounting for the stray fields (Yang and Dayal 2011). See also (DeSimone et al 2001) for a related approach in ferromagnetics.…”

Section: Introductionmentioning

confidence: 98%

Numerical simulation of intergranular and transgranular crack propagation in ferroelectric polycrystals

Abdollahi

2012

Int J Fract

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.

“…These microstructural models have specifically been applied to fracture, in all cases with a fixed crack. The nucleation and growth of domains near crack tips have been studied under applied electromechanical loadings, and the influence on the stress field and the mechanical and electromechanical J−integrals have been reported [27][28][29]. For completeness, we mention that cohesive theories aimed at fracture in ferroelectric materials have been proposed [30,31].…”

Section: Introductionmentioning

confidence: 99%

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

Abdollahi¹,

Modelling Simul. Mater. Sci. Eng.

2011

Abstract. Crack propagation during the indentation test of a ferroelectric single crystal is simulated using a phase-field 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 modified 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-field simulation.