Anisotropic Grain Boundary Energy Research Articles

Microstructure evolution in 439 stainless steels under tensile: phase field simulation and experiment

A combination of phase-field simulations and experimental validation is utilized to examine the effect of annealing tension on the microstructure evolution of 439 ferrite stainless steel (FSS). The study reveals the competing mechanisms of texture under tensile stress. Furthermore, a phase field model that incorporates anisotropic grain boundary (GB) energy and elastic energy is established. The microstructure of 439 FSS is created using a 3D reconstruction strategy based on the 2D electron backscatter diffraction characterization proposed in this work. Elastic constants are calibrated using actual alloy data and determined through molecular dynamics simulations. Finally, simulations of the grain coarsening process in 439 FSS are successfully achieved, considering both tensile stress and anisotropic GB energy effects. The results reveal that the presence of low-angle GBs deviates from Hillert model predictions in terms of grain size distribution and slows down the average grain size evolution over time. A significant deviation in the grain size distribution, compared to Hillert predictions, is observed in the textured system under tensile stress. The results of growth kinetics indicate that tensile stress promotes grain growth more than GB energy anisotropy retards microstructure evolution. Both experiment and simulation results consistently demonstrate that grains with <111>//ND orientation experience a better growth proficiency compared to grains of other orientations under tensile stress. This investigation offers fresh insights into managing the ferritic microstructure of FSS to enhance its formability capabilities.

Investigation of the influence of misorientation-dependent anisotropy on the microstructure evolution under magnetic field: A multi-phase-field study

The influence of magnetic field-driven grain growth in a polycrystalline microstructure is studied via the multi-phase-field approach with the assumptions of isotropic and anisotropic grain boundary (GB) energy. Simulations are carried out using a two-dimensional representative volume element of titanium polycrystalline with the hexagonal crystal structure. The GB energy is a function of the misorientation angle by Read-Shockley equation and is independent of the GB inclination. The simulation results illustrate that the grain growth kinetics and final texture influentially depend on the initial texture when considering the misorientation-dependent anisotropy of GB energy. If the Euler angle φ 2 is randomly distributed for all of the grains, the simulation results are similar for isotropic and anisotropic GB energies. Whereas the simulation results for anisotropic GB energy are significantly different from the isotropic case by considering φ 2 = 0 for all grains. The elongation of grains, the aggregation of grains with analogous orientations, and deceleration of texture evolution and grain growth kinetics are its most important features. Also, the impact of magnetic field intensity is examined and, it is illustrated that the difference in simulation results for isotropic and anisotropic GB energies decreases with increasing the magnetic field intensity.

Grain growth behavior of ferroelectric ceramics under anisotropic grain boundary energy conditions simulated by the phase field method

The grain growth behavior of ferroelectric ceramics is different from that under the condition of an isotropic grain boundary energy, owing to the existence of many high-energy grain boundaries. A simple phase-field model based on the anisotropy of the grain boundary energy was developed to simulate the microstructure evolution of ferroelectric ceramics. The effects of the anisotropy of the grain boundary energy on the grain growth behavior and formation of characteristic regions were investigated using the phase-field method. The experimental data confirmed the simulation results. It was observed that the rapid migration of high-energy grain boundaries and slow migration of low-energy grain boundaries resulted in the appearance of both, small grains with edge numbers greater than six and numerous strip grains. The grain microstructures showed a specific orientation distribution in the 2-D cross section. The anisotropy of grain boundary energy can regulate the grain orientation distribution. This work provides a basis for microstructure control and the stable preparation of high-performance ferroelectric ceramics.

Real-Time Capturing of Microscale Events Controlling the Sintering of Lead-Free Piezoelectric Potassium-Sodium Niobate.

Sintering is a very important process in materials science and technological applications. Despite breakthroughs in achieving optimized piezoelectric properties, fundamentals of K0.5 Na0.5 NbO3 (KNN) sintering are not yet fully understood, facing densification versus grain growth competition. At present, microscale events during KNN sintering under reducing atmospheres are real-time monitored using a High Temperature-Environmental Scanning Electron Microscope. A two contacting KNN particles model satisfying the Kingery and Berg's bulk diffusion model is reported. Dynamic events like individual grain growth and grain elimination process are explored through a postanalysis of recorded image series. The diffusion coefficient for oxygen vacancies of 10-8 cm2 s-1 and average boundary mobility of 10-9 cm4 J-1 s-1 are reported for the KNN ceramics. Moreover, the local pore shrinkage is consistent with the Kingery and François's concept of pore stability except that pore curvatures are not all concave, convex or flat due to anisotropic grain-boundary energies. The global grain growth kinetics are described using parabolic and/or cubic laws. The effect of atmospheres and microstructure evolution on the intrinsic and extrinsic contributions to the dielectric response using Rayleigh's law is also explored. These results bring a new breath for KNN sintering studies in order to adapt the sintering process.

A molecular dynamics survey of grain boundary energy in uranium dioxide and cerium dioxide

AbstractUranium dioxide (UO2) is the primary fuel material that is used in current nuclear reactors. As one of the most fundamental material parameters, grain boundary (GB) energy strongly influences many fuel properties, and the influences depend on the characters and properties of individual GBs. Using molecular dynamics simulations, a high throughput survey of GB energy in UO2 was carried out for the purpose of elucidating the roles of GB geometry such as misorientation and inclination, as well as the bonding nature of UO2, in affecting GB energy. GB energies in CeO2 were calculated as well for comparison with UO2 to investigate the generality of GB energy anisotropy in fluorite phase oxides. The results show significant GB energy anisotropy in both UO2 and CeO2 that is associated with the cubic symmetry of the fluorite structure. More interestingly, the GB anisotropy is found to be dependent not only on the crystal structure but also the ionic bonding. As such, the GB energy anisotropy in fluorite oxides has significant differences compared with that in fcc metals. The data obtained and the increased knowledge on GB anisotropy will facilitate GB engineering for nuclear fuels with improved properties.

Comparative Study and Limits of Different Level-Set Formulations for the Modeling of Anisotropic Grain Growth.

In this study, four different finite element level-set (FE-LS) formulations are compared for the modeling of grain growth in the context of polycrystalline structures and, moreover, two of them are presented for the first time using anisotropic grain boundary (GB) energy and mobility. Mean values and distributions are compared using the four formulations. First, we present the strong and weak formulations for the different models and the crystallographic parameters used at the mesoscopic scale. Second, some Grim Reaper analytical cases are presented and compared with the simulation results, and the evolutions of individual multiple junctions are followed. Additionally, large-scale simulations are presented. Anisotropic GB energy and mobility are respectively defined as functions of the mis-orientation/inclination and disorientation. The evolution of the disorientation distribution function (DDF) is computed, and its evolution is in accordance with prior works. We found that the formulation called “Anisotropic” is the more physical one, but it could be replaced at the mesoscopic scale by an isotropic formulation for simple microstructures presenting an initial Mackenzie-type DDF.

Competitive grain growth behavior in laminated ceramic composites: An insight from numerical simulation

The properties of the laminated ceramic composites are known not only determined by the macro-laminated composite structure, but also highly dependent on their micro-polycrystalline structure. With the aim to investigate the competitive grain growth behavior during polycrystalline microstructure formation in laminated ceramic composites, a phase-field simulation for anisotropic grain growth is carried out in this study, and the effect of anisotropy in grain boundary energy on the grain coarsening and deformation near the interfaces is meticulously studied. Simulation results indicate that the polycrystalline microstructure is highly influenced by the competitive grain growth kinetics, and an oriented columnar grain layer is newly-formed near the interface. This abnormal grain growth phenomenon in the binary polycrystalline interface is attributed to the different grain boundary migrations in two layers, thereby leading to the interface migration in the laminated polycrystalline microstructures with an intermediate layer, which is consistent with experimental observations. Therefore, specifying the characteristics of the laminated polycrystalline microstructures could be an efficient way to improve the structure and performance design ability in laminated ceramics.

Effect of grain boundary energy anisotropy on grain growth in ZK60 alloy using a 3D phase-field modeling* *Project supported by the National Key Research and Development Program of China (Grant No. 2016YFB0701204), the 111 Project, China (Grant No. B20029), the Fundamental Research Funds for the Central Universities, China (Grant Nos. N2002017 and N2007011), the National Natural Science Foundation of China

A three-dimensional (3D) multiple phase field model, which takes into account the grain boundary (GB) energy anisotropy caused by texture, is established based on real grain orientations and Read–Shockley model. The model is applied to the grain growth process of polycrystalline Mg (ZK60) alloy to investigate the evolution characteristics in different systems with varying proportions of low-angle grain boundary (LAGB) caused by different texture levels. It is found that the GB energy anisotropy can cause the grain growth kinetics to change, namely, higher texture levels (also means higher LAGB proportion) result in lower kinetics, and vice versa. The simulation results also show that the topological characteristics, such as LAGB proportion and distribution of grain size, undergo different evolution characteristics in different systems, and a more serious grain size fluctuation can be caused by a higher texture level. The mechanism is mainly the slower evolution of textured grains in their accumulation area and the faster coarsening rate of non-textured grains. Therefore, weakening the texture level is an effective way for implementing a desired homogenized microstructure in ZK60 Mg alloy. The rules revealed by the simulation results should be of great significance for revealing how the GB anisotropy affects the evolution of polycrystalline during the grain growth after recrystallization and offer the ideas for processing the alloy and optimizing the microstructure.

Three-dimensional phase field modelling of twin nucleation during directional solidification of multi-crystalline silicon

The development of grain structures during directional solidification of multi-crystalline silicon (mc-Si) plays a crucial role in the materials quality for silicon solar cells. Three dimensional (3D) modelling of the grain boundary (GB) interaction and evolution based on phase fields by considering anisotropic GB energy and mobility for mc-Si has been developed recently. Here, we further consider twin nucleation at the tri-junction groove for the simulation. To compare with the experimental results, the initial seed orientations are described by the Euler angles. With the previous developed twinning model at the three-grain tri-junction and the T matrix for twinning, the simulated grain orientation and the resulted GB types are consistent with the experiments.

Phase field modeling of stressed grain growth: Effect of inclination and misorientation dependence of grain boundary energy

The effect of anisotropic grain boundary energy on the kinetics of stressed grain growth is investigated by two-dimensional phase field simulations. The simulations are performed for a two-dimensional representative volume element of polycrystalline copper with elastic cubic symmetry under both uniaxial elongation and shear loading with elastic strains in the order of a few thousandths. The Read-Shockley relation for the misorientation–dependence and the cubic symmetry for the inclination–dependence of grain boundary energy are assumed. The simulation results have generally shown that the misorientation–dependent anisotropy, compared to the inclination–dependent anisotropy, significantly affects the evolution of microstructure and texture during stressed grain growth. Particularly, the misorientation–dependent anisotropy of grain boundary energy results in (i) the elongated morphology of grains in the evolved microstructure; (ii) the aggregation of grains with similar orientations in the evolved microstructure; (iii) the strengthening of lower–misorientation angle grain boundary segments; and hence (iv) decelerating the overall rate of stressed grain growth and texture evolution and (v) decelerating stress relaxation under constant–strain loading. These results are based on the assumption that the isotropic grain boundary energy is equal to the high angle grain boundary energy of the misorientation–dependent grain boundary energy and the inclination–dependent grain boundary energy varies sinusoidally around the isotropic grain boundary energy.

Three dimensional modelling of grain boundary interaction and evolution during directional solidification of multi-crystalline silicon

The development of grain structures during directional solidification of multi-crystalline silicon (mc-Si) plays a crucial role in the materials quality for silicon solar cells. Three dimensional (3D) modelling of the grain boundary (GB) interaction and evolution based on phase fields by considering anisotropic GB energy and mobility for mc-Si is carried out for the first time to elucidate the process. The energy and mobility of GBs are allowed to depend on misorientation and the GB plane. To examine the correctness of our method, the known the coincident site lattice (CSL) combinations such as (∑a+∑b→∑a×b) or (∑a+∑b→∑a/b) are verified. We frther discuss how to use the GB normal to characterize a ∑3 twin GB into a tilt or a twist one, and show the interaction between tilt and twist ∑3 twin GBs. Two experimental scenarios are considered for comparison and the results are in good agreement with the experiments as well as the theoretical predictions.

Multi-phase-field study of the effects of anisotropic grain-boundary properties on polycrystalline grain growth

Numerical studies of the effects of anisotropic (misorientation-dependent) grain-boundary energy and mobility on polycrystalline grain growth have been carried out for decades. However, conclusive knowledge has yet to be obtained even for the simplest two-dimensional case, which is mainly due to limitations in the computational accuracy of the grain-growth models and computer resources that have been employed to date. Our study attempts to address these problems by utilizing a higher-order multi-phase-field (MPF) model, which was developed to accurately simulate grain growth with anisotropic grain-boundary properties. In addition, we also employ general-purpose computing on graphics processing units to accelerate MPF grain-growth simulations. Through a series of simulations of anisotropic grain growth, we succeeded in confirming that both the anisotropies in grain-boundary energy and mobility affect the morphology formed during grain growth. On the other hand, we found the grain growth kinetics in anisotropic systems to follow parabolic law similar to isotropic growth, but only after an initial transient period.

Extended higher-order multi-phase-field model for three-dimensional anisotropic-grain-growth simulations

Based on the multi-phase-field (MPF) model reported by Steinbach et al., we constructed a higher-order MPF model in a previous study that contains a higher-order term and an additional kinetic parameter to represent the properties of triple junctions (TJs); this model was observed to be suitable for the simulation of 2D grain growth with anisotropic grain-boundary (GB) energy and mobility, which are strongly dependent on the misorientation angle (Δθ). In the current study, we attempt to improve the accuracy of 3D MPF simulations of anisotropic grain growth by extending this higher-order MPF model such that it accounts for the properties of quadruple junctions as well as those of TJs. In addition, using the extended higher-order MPF model, a series of grain-growth simulations are performed for a 3D columnar structure while considering the anisotropic GB properties, through which the accuracy of the model is examined in detail. The results confirm that the extended higher-order MPF model enables the anisotropic GB properties to be handled accurately for wider-ranging Δθ than in previous models.

Validation of a novel higher-order multi-phase-field model for grain-growth simulations using anisotropic grain-boundary properties

The multi-phase-field (MPF) model proposed by Steinbach et al. has several advantages when it comes to numerically simulating the grain growth, recrystallization, and multiple phase transitions. In this study, in order to improve the accuracy of MPF simulations using the anisotropic grain-boundary energy and mobility, which depend strongly on the misorientation angles, we account for the triple-junction properties in the MPF model. Further, two-dimensional simulations of grain-boundary migrations in three-grain systems as well as simulations of abnormal grain growth in a polycrystalline system are performed using the proposed model, in order to confirm its validity. The results show that the proposed model allows for the introduction of the anisotropic energy and mobility with high accuracy for a wider range of misorientations, in contrast to the conventional model.

Motion of Grain Boundaries: Experiments on Bicrystals

Recent research on grain boundary migration is reviewed. Novel in-situ measuring techniques based on orientation contrast imaging and the experimental results obtained on specially grown bicrystals are presented. Particularly, the investigated faceting and migration behavior of low angle grain boundaries under the curvature force in aluminum bicrystals was addressed. In contrast to the pure tilt boundaries, which remained straight/flat and immobile during annealing at elevated temperatures, mixed tilt-twist boundaries readily assumed a curved shape and steadily moved under the capillary force. Computational analysis revealed that this behavior is due to the inclinational anisotropy of grain boundary energy, which in turn depends on boundary geometry. The migration of planar grain boundaries induced by a magnetic field was measured in bismuth and zinc bicrystals. Various structurally different boundaries were investigated. The results revealed that grain boundary mobility essentially depends on the misorientation angle and the inclination of the boundary plane. Stress driven boundary migration in aluminium bicrystals was observed to be coupled to a tangential translation of the grains. The activation enthalpy of high angle boundary migration was found to vary non-monotonously with misorientation angle, whereas for low angle boundaries the migration activation enthalpy was virtually the same. The motion of the mixed tilt-twist boundaries under stress was observed to be accompanied by both the translation of adjacent grains parallel to the boundary plane and their rotation around the boundary plane normal.

Grain boundary motion and grain rotation in aluminum bicrystals: recent experiments and simulations

The results of experimental and computational efforts over recent years to study the motion of geometrically different grain boundaries and grain rotation under various driving forces are briefly reviewed. Novel in-situ measuring techniques based on orientation contrast imaging and applied simulation techniques are described. The experimental results obtained on specially grown aluminum bicrystals are presented and discussed. Particularly, the faceting and migration behavior of low angle grain boundaries under the curvature force is addressed. In contrast to the pure tilt boundaries, which remained flat/faceted and immobile during annealing at elevated temperatures, mixed tilt-twist boundaries readily assumed a curved shape and steadily moved under the capillary force. Computational analysis revealed that this behavior is due to the inclinational anisotropy of grain boundary energy, which in turn depends on boundary geometry. The shape evolution and shrinkage kinetics of cylindrical grains with different tilt and mixed boundaries were studied by molecular dynamics simulations. The mobility of low angle <100> boundaries with misorientation angles higher than 10°, obtained by both the experiments and simulations, was found not to differ from that of the high angle boundaries, but decreases essentially with further decrease of misorientation. The shape evolution of the embedded grains in simulations was found to relate directly to results of the energy computations. Further simulation results revealed that the shrinkage of grains with pure tilt boundaries is accompanied by grain rotation. In contrast, grains with the tilt-twist boundaries composed of dislocations with the mixed edge-screw character do not rotate during their shrinkage. Stress driven boundary migration in aluminium bicrystals was observed to be coupled to a tangential translation of the grains. The activation enthalpy of high angle boundary migration was found to vary non-monotonically with misorientation angle, whereas for low angle boundaries the migration activation enthalpy was virtually the same. The motion of the mixed tilt-twist boundaries under stress was observed to be accompanied by both the translation of adjacent grains parallel to the boundary plane and their rotation around the boundary plane normal.

The origin and enhancement of [formula omitted][formula omitted] texture during heat treatment of rolled AZ31B magnesium alloys

Electron backscatter diffraction data from warm-rolled AZ31B, a commercial Mg alloy, are used as microstructural input into a Monte Carlo Potts grain growth model. It is shown that the {0001}〈111¯0〉 texture, recently discovered to strongly evolve during grain growth annealing, is the result of a grain size advantage that emerges during recrystallization; where grains closer to the {0001}〈112¯0〉 orientation are larger on average than competing {0001}〈101¯0〉 oriented grains. As a consequence, there is no need to invoke anisotropy in grain boundary energy or mobility to quantitatively model the relationship between grain growth and texture. The observed textural evolution shows a surprising similarity to that of hexagonally close packed Zr alloys despite underlying differences in the deformation mechanisms between the two alloy systems. Crystal plasticity simulations, however, reveal that the faint underlying {0001}〈101¯0〉 deformation texture in this Mg alloy is due to prismatic slip activity during rolling.

Computation of Five-Dimensional Grain Boundary Energy

A broken-bond type computational method has been developed for the calculation of the five-dimensional grain boundary energy. The model allows quick quantification of the unrelaxed five-dimensionally specified grain boundary energy in arbitrary orientations. It has been validated on some face-centred cubic metals. The stereo projections of grain boundary energy of ∑3, ∑5, ∑7, ∑9, ∑11, ∑17b and ∑31a have been studied. The results of Ni closely resemble experimentally determined grain boundary energy distribution figures, suggesting that the overall anisotropy of grain boundary energy can be reasonably approximated by the present simple model. Owing to the overlooking of relaxation matter, the absolute values of energy calculated in present model are found to be higher than molecular dynamic-based results by a consistent magnitude, which is 1 J/m2 for Ni. The coverage of present method forms a bridge between atomistic and meso-scale simulations regarding polycrystalline microstructure.

A two-dimensional study of coupled grain boundary motion using the level set method

The coupled motion of a closed non-circular grain boundary (GB) in a bicrystal, with both isotropic and anisotropic GB energies, is studied using the level set method. The kinetic relations, obtained within the framework of linear irreversible thermodynamics, govern the overall dynamics, including normal motion (migration) of the GB, viscous sliding along the GB and tangential motion of the grains which is geometrically coupled with the migration. The shape accommodation necessary to maintain coherency of relatively rotating and non-deforming grains is accomplished by allowing for diffusion along the GB. We solve the governing equations for the coupled motion in order to determine the shape and the misorientation evolution of an isolated GB under various constitutive assumptions. First, assuming both GB energy and kinetic coefficients to be isotropic, we study the interplay between kinetic coefficients for initially circular, near-circular and non-circular GBs, as well as the impact of stress and initial conditions on the GB dynamics. Next, we study the influence of anisotropy in the GB energy, mobility and geometric coupling for various combinations of parameters and initial conditions. Allowing for geometric coupling can in fact lead to shapes distinctly different to those that are usually predicted on the basis of migration alone. Our numerical scheme provides a general framework in which to study these and other related problems of GB motion.

Effect of Grain Boundary Energy Anisotropy on Faceting and Migration of Low Angle Grain Boundaries

The faceting and migration behavior of low angle &lt;100&gt; grain boundaries in high purity aluminum bicrystals was investigated. In-situ technique based on orientation contrast imaging was applied. In contrast to the pure tilt boundaries, which remained straight/flat and immobile during annealing at elevated temperatures, mixed tilt-twist boundaries readily assumed a curved shape and steadily moved under the capillary force. Computational analysis revealed that this behavior is due to the inclinational anisotropy of grain boundary energy, which in turn depends on boundary geometry – the energy of pure tilt low angle &lt;100&gt; boundaries is anisotropic, whereas that of mixed tilt-twist boundaries isotropic with respect to boundary inclination.