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

Polarization switching-induced shielding or anti-shielding of an electrically permeable crack in a mono-domain ferroelectric material with the original polarization direction perpendicular to the crack is simulated by a phase field model based on the time-dependent Ginzburg–Landau equation. The domain wall energy and the long-range mechanical and electrical interactions between polarizations are taken into account. The phase field simulations exhibit a wing-shape-switched zone backwards from the crack tip. The polarization switching-induced internal stresses shield the crack tip from applied mechanical loads. A local J-integral is numerically calculated and used as a failure criterion to illustrate the polarization switching-toughening. The result indicates that an applied uniform electric field parallel to the original polarization direction reduces the apparent fracture toughness, while an applied uniform electric field anti-parallel to the original polarization direction enhances it.     

Coupled motion of asymmetrical tilt grain boundaries: Molecular dynamics and phase field crystal simulations

Previous simulation and experimental studies have shown that some grain boundaries (GBs) can couple to applied shear stresses and be moved by them, producing shear deformation of the lattice traversed by their motion. While this coupling effect has been well confirmed for symmetrical tilt GBs, little is known about the coupling ability of asymmetrical boundaries. In this work we apply a combination of molecular dynamics and phase field crystal simulations to investigate stress-driven motion of asymmetrical GBs between cubic crystals over the entire range of inclination angles. Our main findings are that the coupling effect exists for most of the asymmetrical GBs and that the coupling factor exhibits a non-trivial dependence on both the misorientation and inclination angles. This dependence is characterized by a discontinuous change of sign of the coupling factor, which reflects a transition between two different coupling modes over a narrow range of angles. Importantly, the magnitude of the coupling factor becomes large or divergent within this transition region, thereby giving rise to a sliding-like behavior. Our results are interpreted in terms of a diagram presenting the domains of existence of the two coupling modes and the transition region between them in the plane of misorientation and inclination angles. The simulations reveal some of the dislocation mechanisms responsible for the motion of asymmetrical tilt GBs. The results of this study compare favorably with existing experimental measurements and provide a theoretical ground for the design of future experiments.     

Phase transitions and domain structures of ferroelectric nanoparticles: Phase field model incorporating strong elastic and dielectric inhomogeneity

An efficient numerical algorithm based on a Fourier spectral iterative perturbation method is proposed to accurately compute the electrostatic fields in three-dimensional (3D) microstructures with arbitrary dielectric inhomogeneity and anisotropy. The method can be conveniently implemented in phase field modeling of microstructure evolution in systems with inhomogeneous dielectric constants as well as inhomogeneous polarization and charge distributions. It is employed to determine the temperature–shape (aspect ratio) phase diagram, domain structures, and domain switching of PbTiO₃ nanoparticles using phase field simulations. It is shown that the Curie temperature is enhanced for nanowires and nanorods and reduced for nanodots. The critical sizes below which the ferroelectricity disappears for the nanowire and thin film are estimated to be around 1.4 nm. Vortex domain structures are found in nanorods, nanodots, and nanodisks. Results are in general agreement with existing experimental observations and first principle calculations.     

Effect of grain orientation and grain size on ferroelectric domain switching and evolution: Phase field simulations

Phase field simulations were conducted in order to understand the effect of grain orientation, grain boundary and grain size on ferroelectric domain switching, stress distribution and evolution behavior under an applied electric field. Tetragonal ferroelectric domains were considered. Hysteresis loops were obtained for a single crystal, a bi-crystal and a polycrystal and the differences in their coercive fields were examined. It was found that the magnitude of the coercive field was closely related to the domain structures at the maximum electric field. Nucleation of new domains at a grain boundary led to local high stress. The effect of a reduced ferroelectric transition temperature at the grain boundary on the polarization distribution, domain structure and switching was studied.     

The influence of grain boundaries and texture on ferroelectric domain hysteresis

As ferroelectric device dimensions continue to shrink, the increasing ratio of boundary to bulk necessitates a thorough understanding of interfacial properties. Accordingly, the local piezoelectric hysteresis of a polycrystalline lead zirconate titanate thin film is quantitatively measured and compared to the separately measured grain orientation and the corresponding predicted residual stress and charge. The piezoelectric response is determined using a variation of atomic-force microscopy known as piezo-force microscopy, with which nearly 20 hysteresis measurements were acquired spanning four grain boundaries and five grains. The grain orientation in this region was determined by scanning-electron microscope using electron-backscattered diffraction.     

Anti-phase boundaries and magnetic domain structures in Ni2MnGa-type Heusler alloys

The microstructure and magnetic domain structure of austenitic Heusler Ni₂MnGa are investigated as a function of heat treatment to study the interplay of anti-phase boundaries and magnetic domain walls. Conventional electron microscopy observations on arc-melted polycrystalline samples show that anti-phase boundaries in this system are invisible for standard two-beam imaging conditions, due to the large extinction distance of the Heusler superlattice reflections. Lorentz Fresnel and Foucault observations on quenched samples reveal a wavy magnetic domain morphology, reminiscent of curved anti-phase boundaries. A close inspection of the domain images indicates that the anti-phase boundaries have a magnetization state different from that of the matrix. Fresnel image simulations for a simple magnetization model are in good agreement with the observations. Magnetic coercivity measurements show a decrease in coercivity with annealing, which correlates with the microscopy observations of reduced anti-phase boundary density for annealed samples.     

Nanoscale phase field microelasticity theory of dislocations: model and 3D simulations

The first Phase Field model of evolution of a multi-dislocation system in elastically anisotropic crystal under applied stress is formulated. The model is a modification and extension of our Phase Field Microelasticity approach to the theory of coherent phase transformations. The long-range strain-induced interaction of individual dislocations is calculated exactly and is explicitly incorporated in the Phase Field formalism. It also automatically takes into account the effects of “short-range interactions”, such as multiplication and annihilation of dislocations and a formation of various metastable microstructures involving dislocations and defects. The proposed 3-dimensional Phase Field model of dislocations does not impose a priori constraints on possible dislocation structures or their evolution paths. Examples of simulation of the FCC 3D system under applied stress are considered.     

Phase field crystal simulations of nanocrystalline grain growth in two dimensions

We study two-dimensional grain growth at the nanoscale using the phase field crystal (PFC) model. Our results show that for circular grains with large misorientations the grain area decreases linearly with time, in good agreement with classical grain growth theory. For circular grains with small initial misorientations, grain rotation occurs as a result of the coupled motion between the normal motion of the grain boundary and the tangential motion of the adjacent grains. Despite this rotation and its effect on the grain boundary energy, the grain area decreases linearly with time. In addition, for intermediate initial grain misorientations, we find a repeating faceting-defaceting transition during grain shrinkage and a different relationship between the grain area and time, which suggests a different grain growth mechanism than that for small and large misorientations. For a circular grain embedded between a bicrystal with a symmetric tilt boundary, we find that the evolution of the embedded grain closely depends on dislocation reactions at triple junctions.     

Phase field modeling of the tetragonal-to-monoclinic phase transformation in zirconia

The allotropic phase transformation in zirconia from the tetragonal to monoclinic double lattices is known to occur by a martensitic twinning mechanism which shows a complex dependence on temperature, stress and environment. This paper is concerned with the development of a phase field model which accounts for the main metallurgical mechanisms governing this martensitic transition. The symmetry reduction and orientation relationship between the parent and product phases were simulated using several non-conserved order parameters representing different transformation paths. Inhomogeneous and anisotropic elastic properties were considered to determine the resultant elastic stresses. Governing equations of the tetragonal-to-monoclinic transformation were solved in a finite element framework under a variety of initial and boundary conditions. It was shown that applying different initial conditions, such as seed embryo or random, did not change the twinning patterns or the final volume fractions of the parent and product phases after the relaxation period. On the other hand, enforcing different boundary conditions resulted in completely different twinning patterns and phase volume fractions. The model was able to predict both the “V” shape morphology of twinning and the surface stress relief with “gable roof” patterns, which were observed by transmission electron microscopy and atomic force microscopy to be characteristic of the tetragonal-to-monoclinic transition.     

低体积分数相析出过程的相场模拟

通过构建局域自由能函数,并考虑晶界对析出过程的影响,建立了低体积分数相析出过程的相场模型,模拟了溶质体积分数为2%的体系中第二相在晶界和晶内析出及其演变过程.结果表明,在相同相场步条件下,晶粒空间矢量平方和的幂指数项(∑(η)2)μ决定了第二相在晶界和晶内的析出比例;晶内析出相的比例随μ值的减小而增加;析出相尺寸的大小取决于浓度场梯度能系数к(ζ)值的高低;μ=1或较大к(ζ)时,析出相全部集中于晶界上.     

Role of grain orientation distribution in the ferroelectric and ferroelastic domain switching of ferroelectric polycrystals

The non-linear electromechanical behavior of ferroelectric polycrystals stems from polarization/domain switching, which are affected by the grain boundaries and grain orientations. The effects of grain orientation distribution on the domain switching and non-linear behavior of a two-dimensional ferroelectric polycrystal subjected to an electric or/and mechanical load are investigated by computer simulations with a real-space phase-field model. Phase-field simulations indicate that the macroscopic coercive field, remanent polarization and remanent strain in the polycrystal with a random distribution of grain orientation are correspondingly smaller than those in the polycrystal with a uniform distribution of grain orientation. However, the polycrystal with randomly distributed grain has a larger strain variation with the electric field than the polycrystal with uniformly distributed grains, which suggests that the random polycrystal has a better piezoelectric property than the uniform one. The different macroscopic non-linear behaviors of the ferroelectric polycrystals are attributed to different microscopic domain switching processes. For the polycrystal with randomly distributed grains, the domain switching takes place from the regions near the large angle grain boundaries, while new domains nucleate from the cross sections between the grain boundaries and the material surface in the polycrystal with uniform grain orientation.     

Multiphase Ni–Cr–Al diffusion couples: A comparison of phase field simulations with experimental data

Microstructures in γ+β/γ diffusion couples made of Ni–Cr–Al alloys were investigated numerically in two dimensions using a phase field model. With experimental thermodynamic and mobility data from the literature as inputs, the model was used to predict the evolution of the precipitate morphology, the dissolution of the two-phase γ+β regions and the diffusion paths as functions of alloy composition The dissolution rates and diffusion paths obtained from the simulations were in general agreement with experimental data, although quantitative differences were found. Differences in the dissolution rates and diffusion paths could be directly related to differences in the predicted phase diagram and the phase diagram reported in the experimental study.     

Investigation of boundaries and structures in dissimilar metal welds

Abstract

Cracking, or disbonding, along the fusion boundary in dissimilar metal welds has been a persistent problem, particularly in applications where austenitic alloys are clad on to structural steels for corrosion protection. Many failures in dissimilar metal welds occur as a result of cracking along a boundary that runs parallel to the fusion boundary in the adjacent weld metal. A preliminary investigation was undertaken to determine the nature and evolution of boundaries and structure in dissimilar metal welds using a simple ternary system composed of a pure iron substrate and a 70Ni–30Cu (Monel) filler metal. Changes in base metal dilution were found to alter the evolution of boundaries and structures near the fusion boundary dramatically. Optical metallography and electron microanalysis reveal that the resulting weld microstructures and boundaries are similar to those observed in engineering materials used for cladding and corrosion resistant overlay. Transmission electron diffraction analysis revealed orientation relationships between adjacent base metal and weld metal grains at the fusion boundary to be different from the cube on cube relationship normally observed in similar metal welds. A model is proposed describing the evolution of the boundary most susceptible to cracking in dissimilar welds.     

Atomistic simulations of interactions between screw dislocation and twin boundaries in zirconium

Molecular statics was employed to simulate interaction between screw dislocation and twin boundaries (TB) in hexagonal close-packed zirconium. In the moving TB model, the interaction of a moving $\left\{10\overline{1}2\right\}$ TB with a static $1/3〈11\overline{2}0〉\left\{10\overline{1}0\right\}$ screw dislocation was investigated. Twinning dislocation (TD) nucleation and movement play an important role in the interaction. The screw dislocation passes through the moving TB and changes to a basal one with a wide core. In the moving dislocation model, a moving $1/3〈11\overline{2}0〉\left\{10\overline{1}0\right\}$ dislocation passes through the TB, converting into a basal one containing two partial dislocations and an extremely short stacking fault. If the TB changes to the $\left\{10\overline{1}1\right\}$ one, the moving $1/3〈11\overline{2}0〉\left\{10\overline{1}0\right\}$ prismatic screw dislocation can be absorbed by the static TB and dissociated into two TDs on the TB. Along with the stress–strain relationship, results reveal the complicated mechanisms of interactions between the dislocation and TBs.     

Phase field simulation of liquid-solid-eutectoid multiple phase transformations of a Fe-C binary alloy

A new continuous multi-phase transformation field model was established for liquid-solid-eutectoid transformation.Taking Fe-C alloy as an example,the model was used to simulate the evolution of the micro-morphology of the liquid-solid phase transition,and the effects of temperature,solute and free energy on the nucleation of pearlite after the liquid-solid phase transition were analyzed.The micro-morphology of pearlite was simulated.The simulation results show that the austenite structure has hereditary effect on the pearlite,the morphology of pearlite structure was similar to that of the parent austenite.The eutectoid structure at the front of pearlite grows toward the interior of austenite grains in a bifurcation manner and in the spherical coronal shape.In addition,the growth rate of pearlite was related to the shape of concave-convex interface at the nucleation site,and the growth rate at the convex interface was faster than that at the concave interface.     

双模晶体相场研究六方四方相变过程晶界和位错演化

对于晶粒,晶界,应力和位错的交互作用的深入理解有助于优化材料组织和提升材料性能。本文采用双模晶体相场法研究六方相向正方相的转变。分别针对倾侧角为0°,15°,30°,和 45°,晶粒取向差为6°的六方相体系做了系统研究。六方晶粒长大、溶合、并形成共格晶界,位错组沿六方晶界均匀分布,并有两种取向。正方相在位错组处形核,并且其取向取决于位错组取向。每一种倾侧角的体系种均形成两个取向正方相的变体。针对倾侧角为0 °,15°,30°,和 45°的六方相体系生成的四方相相变体之间的取向差分别为30°, 30°, 10°, 和5°。不同取向的正方相晶粒长大熟化的方式有差异,位于有利取向的晶粒将会优先生长占据主导地位。以共格晶界形式长大的晶粒,晶界处有位错组生成以松弛晶粒长大的应力集中。     

空位扩散诱导点缺陷环与富Cu相的相互作用

辐照诱导产生的点缺陷会加速核电站材料微观组织的演变,在很大程度上影响反应堆的寿命。本文基于相场法的四元连续相场模型,耦合了空位和间隙原子,利用该模型模拟了Fe-15at.%Cu-1at.%Ni-1at.%Mn合金在空位扩散机制下的相分离,研究了点缺陷与富Cu相的相互作用机理。结果表明,空位和间隙原子会促进富Cu相的长大和粗化,点缺陷初始浓度的升高会促进相分离,加快析出相的失稳分解速率,并且升高温度会延缓Cu原子和空位环的生长和粗化,点缺陷也可以增加一定的屈服强度,为探究空位扩散机制影响抗辐照材料性能方面提供了新的思路。     

The influence of friction models on finite element simulations of machining

In the analysis of orthogonal cutting process using finite element (FE) simulations, predictions are greatly influenced by two major factors; a) flow stress characteristics of work material at cutting regimes and b) friction characteristics mainly at the tool-chip interface. The uncertainty of work material flow stress upon FE simulations may be low when there is a constitutive model for work material that is obtained empirically from high-strain rate and temperature deformation tests. However, the difficulty arises when one needs to implement accurate friction models for cutting simulations using a particular FE formulation. In this study, an updated Lagrangian finite element formulation is used to simulate continuous chip formation process in orthogonal cutting of low carbon free-cutting steel. Experimentally measured stress distributions on the tool rake face are utilized in developing several different friction models. The effects of tool-chip interfacial friction models on the FE simulations are investigated. The comparison results depict that the friction modeling at the tool-chip interface has significant influence on the FE simulations of machining. Specifically, variable friction models that are developed from the experimentally measured normal and frictional stresses at the tool rake face resulted in most favorable predictions. Predictions presented in this work also justify that the FE simulation technique used for orthogonal cutting process can be an accurate and viable analysis as long as flow stress behavior of the work material is valid at the machining regimes and the friction characteristics at the tool-chip interface is modeled properly.