Grain Growth Model Research Articles

Phase field modelling of stressed grain growth: Analytical study and the effect of microstructural length scale

We establish the correlation between the diffuse interface and sharp interface descriptions for stressed grain boundary migration by presenting analytical solutions for stressed migration of a circular grain boundary in a bicrystalline phase field domain. The validity and accuracy of the phase field model is investigated by comparing the phase field simulation results against analytical solutions. The phase field model can reproduce precise boundary kinetics and stress evolution provided that a thermodynamically consistent theory and proper expressions for model parameters in terms of physical material properties are employed. Quantitative phase field simulations are then employed to investigate the effect of microstructural length scale on microstructure and texture evolution by stressed grain growth in an elastically deformed polycrystalline aggregate. The simulation results reveal a transitional behaviour from normal to abnormal grain growth by increasing the microstructural length scale.

Growing dust grains in protoplanetary discs – II. The radial-drift barrier problem

We aim to study the migration of growing dust grains in protoplanetary discs, where growth and migration are tightly coupled. This includes the crucial issue of the radial-drift barrier for growing dust grains. We therefore extend the study performed in Paper I, considering models for grain growth and grain dynamics where both the migration and growth rate depend on the grain size and the location in the disc. The parameter space of disc profiles and growth models is exhaustively explored. In doing so, interpretations for the grain motion found in numerical simulations are also provided. We find that a large number of cases is required to characterise entirely the grains radial motion, providing a large number of possible outcomes. Some of them lead dust particles to be accreted onto the central star and some of them don't. We find then that q<1 is required for discs to retain their growing particles, where q is the exponent of the radial temperature profile T(R) proportional to R^-q. Additionally, the initial dust-to gas ratio has to exceed a critical value for grains to pile up efficiently, thus avoiding being accreted onto the central star. Discs are also found to retain efficiently small dust grains regenerated by fragmentation. We show how those results are sensitive to the turbulent model considered. Even though some physical processes have been neglected, this study allows to sketch a scenario in which grains can survive the radial-drift barrier in protoplanetary discs as they grow.

The effects of soaking time on the grain growth, dielectric and ferroelectric properties of BaTi0.95Zr0.05O3 ceramics prepared by microwave sintering

Dense ceramics of BaTi1−xZrxO3 with x = 0.05 have been prepared by microwave sintering, and the powders were synthetized by conventional hydrothermal method. Microwave sintering was conducted at 1260–1300 °C for different soaking times (0.5 h, 1 h, 1.5 h and 2 h) in air and the hydrothermal processing was conducted at 180 °C for 10 h. The effects of soaking time on the grain growth, dielectric and ferroelectric properties were investigated. The XRD analysis revealed that the synthesized compound was formed with no secondary phases. The ceramics showed a maximum density at soaking time = 1 h 30 min and the SEM micrographs indicated the grain growth of ceramics with increasing soaking time. The model of grain growth was also investigated. The dielectric constant as a function of temperature showed a maximum value in permittivity at soaking time = 1 h 30 min on increasing the soaking time. The Pr decreased from 10.27 μC/cm2 to 8.44 μC/cm2 with increasing soaking time, which can be observed in the P–E loops.

The interrelated effect of activation energy and grain boundary energy on grain growth in nanocrystalline materials

Abstract The interrelated effect of activation energy and grain boundary energy on grain growth and thermal stabilization in nanocrystalline materials was investigated. Departing from Borisov's equation and Kirchheim's grain boundary energy model, an activation energy model was derived incorporating solute segregation and grain growth. An integrated thermokinetic model for nanoscale grain growth was then developed by incorporating the coupled effects of activation energy and grain boundary energy. By application of the model to nanoscale grain growth of dense nanocrystalline gadolinia-doped ceria, a good agreement between the model predictions and the experimental results was obtained. It is shown that the interrelated effect of increased activation energy and decreased grain boundary energy induced thermal stability in the nanocrystalline materials.

Phase Field Model for Grain Growth with Second-Phase Particles of Stick Shape

The phase field method was applied to study the effect of second-phase particles (SPP) with different geometric orientations and shapes on grain growth. The results show that, in the grain growth process, most of the spherical second-phase particles located at triple junctions, while the stick SPPs located at the grain boundaries along the grain boundary. The second-phase particles are of the strong pinning effect on grain boundary and the limiting grain radius can be expressed by Zener relations. In the condition of the second-phase particles area fraction and size remaining the same, the stick SPPs are of more effective pinning on grain growth than that for spherical SPPs, and the orientation of disk second-phase particles is also an influence factor for pinning effect. Stick second-phase particles with multiple orientations can make a better pining effect than those with only one orientation.

3D modelling of ferrite and austenite grain coarsening using real-valued cellular automata based on transition function

A new extended technique for 3D modelling of normal grain growth in low carbon steels is presented in this paper. This technique is based on real-valued cellular automata with the use of a local transition function that allows it to be applied to materials with both fcc and bcc lattices with the grain growth being easily simulated in ferrite as well as in austenite cases. The simulated data were calibrated with four sets of experimental data for isothermal grain coarsening in austenite, alpha- and delta-ferrites. The obtained results cogently demonstrate that there is a good agreement between simulated and experimental data across a wide range of temperatures. The new model developed in this paper, allows for the identification of two different mechanisms of grain growth in austenite. It is also shown in this paper that the newly presented approach can be used to extract additional parameters from the grain growth process, such as grain boundary velocity, mobility and driving force, which are hardly accessible even via real-time experiments.

Orientation Selectivity of Secondary Recrystallization in Grain-Oriented Silicon Steel

It has been observed that grain size of Goss secondary grain has a strong correlation with deviation angle from the exact Goss orientation and sharper Goss grain has larger grain diameter. This orientation selectivity of secondary recrystallization has been investigated with the statistical model of grain growth in which inhibitor and texture are taken into account. The model assumes that sharper Goss grain has a higher frequency of CSL boundaries to the matrix grains and thus has lower statistical grain boundary energy and suffers lower pinning force from the inhibitor. The analysis showed that this model successfully explains orientation selectivity and depicts the effect of inhibitor and texture.

Coupled Grain Growth and Precipitation Modeling in Multi-Phase Systems

In this work, we utilize recent software for precipitation kinetics simulation and couple it with models for grain growth. Basis of our studies is the thermo-kinetic software MatCalc, which has been designed for simulation of the evolution of precipitates in general multi-component multi-phase alloy systems. Grain growth approaches of different complexity are incorporated into the precipitation kinetics framework, investigated with respect to their coupling behavior with precipitation and precipitate dissolution and, finally, benchmarked on typical grain growth problems of industrial practice. The example presented in this work comprises austenite grain growth studies accompanying TiN and NbC precipitation/dissolution during austenitization of a Ti/Nb microalloyed steel. It is demonstrated that the present approach represents a versatile tool for analysis of simultaneous grain growth and precipitation in industrially important alloy systems.

Boundary Structure-Dependent Grain Growth Behavior in Polycrystals: Model and Principle

This paper reviews our recent investigations on grain growth in ceramics. Grain growth behavior has been found to be governed by the grain boundary structure: normal growth with a stationary relative grain size distribution for rough boundaries and non-normal (nonstationary) growth for faceted boundaries. Based on the concept of nonlinear migration of faceted boundaries, the mixed control model of grain growth is introduced and the principle of microstructural evolution is deduced. This principle states that various types of grain growth behavior are predicted as a result of the coupling effect between the maximum driving force for growth and the critical driving force for appreciable migration of the boundary. A wealth of experimental results supports the theoretical predictions of grain growth behavior, showing the generality of the suggested principle of microstructural evolution. Application of this principle is also demonstrated for the fabrication of single crystals as well as polycrystals with desired microstructures.

Austenite Grain Size Evolution in Railway Wheel During Multi-Stage Forging Processes

The knowledge of microstructure evolution of railway wheel during hot forming process is the prerequisite of improving mechanical properties of the final product. In order to investigate the austenite grain size evolution of railway wheel during multi-stage forging process, mathematical models of recrystallization and austenite grain growth were derived firstly by hot compression tests for railway wheel steel CL50D, which then were integrated with a thermal-mechanical finite element model by the developed subroutines. The information about kinetics of recrystallization and grain size distribution during the forging process was obtained by simulation. The predicted results were validated by experiments in an industrial scale, and the average error between the predicted grain sizes and the measured ones is about 5%. The result shows that, under the current railway wheel forging process, the grain size distribution after final forging is inhomogeneous extremely. There is a narrow coarse grain zone between the external part and center of the hub caused by Static recrystallization after final forging. With cooling of 60 s after final forging, the grain size is about 85 μm for the areas near the web surface and 175 μm for center areas of the hub and rim.

Constitutive modeling of stress-driven grain growth in nanocrystalline metals

In this work, we present a variational multiscale model for grain growth in face-centered cubic nanocrystalline (nc) metals. In particular, grain-growth-induced stress softening and the resulting relaxation phenomena are addressed. The behavior of the polycrystal is described by a conventional Taylor-type averaging scheme in which the grains are treated as two-phase composites consisting of a grain interior phase and a grain boundary-affected zone. Furthermore, a grain-growth law that captures the experimentally observed characteristics of the grain coarsening phenomena is proposed. To this end, the grain size is not taken as constant and varies according to the proposed stress-driven growth law. Several parametric studies are conducted to emphasize the influence of the grain-growth rule on the overall macroscopic response. Finally, the model is shown to provide a good description of the experimentally observed grain-growth-induced relaxation in nc-copper.

Simulations of anisotropic grain growth: Efficient algorithms and misorientation distributions

An accurate and efficient algorithm, closely related to the level set method, is presented for the simulation of Mullins’s model of grain growth with arbitrarily prescribed surface energies. The implicit representation of interfaces allows for seamless transitions through topological changes. Well-resolved large-scale simulations are presented, beginning with over 650,000 grains in two dimensions and 64,000 grains in three dimensions. The evolution of the misorientation distribution function (MDF) is computed, starting from random and fiber crystallographic textures with Read–Shockley surface energies. Prior work had established that with random texture the MDF shows little change as the grain network coarsened whereas with fiber texture the MDF concentrates near zero misorientation. The lack of concentration about zero of the MDF in the random texture case has not been satisfactorily explained previously since this concentration would decrease the energy of the system. In this study, very-large-scale simulations confirm these previous studies. However, computations with a larger cut-off for the Read–Shockley energies and an affine surface energy show a greater tendency for the MDF to concentrate near small misorientations. This suggests that the reason the previous studies had observed little change in the MDF is kinetic in nature. In addition, patterns of similarly oriented grains are observed to form as the MDF concentrates.

Predictive Model for Austenite Grain Growth during Reheating of Alloy Steels

Predictive Model for Austenite Grain Growth during Reheating of Alloy Steels

Understanding the effect of inert support on the reactivity stabilization for synthetic calcium based sorbents

The decay of sorbent reactivity in multiple carbonation/calcination cycles is a critical problem for calcium looping. By introducing inert support materials into CaO particles, the cyclic reactivity of calcium based sorbent could be drastically improved. However, there is a lack of understanding of the interaction between the CaO grain and the support material; thus, much of studies of synthesizing calcium based sorbents are by trial-and-error. In order to understand the possible mechanism of synthetic calcium based sorbent, the widely accepted Zener pinning theory in the field of metallurgy was used here to describe the inhibition of CaO grain sintering due to the addition of inert support. A simple model of CaO grain growth for synthetic calcium-based sorbents was developed to analyze the effect of inert support on the stabilization of cyclic reactivity of CaO. The mechanism of sintering resistant in the synthetic calcium-based sorbents was the pinning force exerted by the dispersed support particles. The inhibition effect of inert support on CaO grain growth is related with the grain migration due to surface energy (γ), support size (r) and volume fraction (f), and the interaction (Finteract) between the support and CaO. The model was validated with the published data and can predict reasonably the experimental results, and the relative importance of some elementary steps was discussed. This study will provide a theoretical understanding for the further development and reactivity improvement of synthetic calcium-based sorbents.

Accelerated Potts model for grain growth – Application to an IF steel

A modification of the Potts model for grain growth is presented. We add to the site energy a grain size factor that favors growth of large grains and whose magnitude has been optimized with respect to various aspects. The motivation for such a modification as well as the consequences in term of calculation speed are presented. The capabilities of this modified model are checked by comparing several characteristics of the microstructures obtained after various grain growth simulations with experimental data obtained for an IF steel. One large EBSD map, made at the end of the primary recrystallization, is used directly as the initial image for the calculations. A second EBSD map, obtained after grain growth (with a mean diameter of the grains about twice the initial value) was used for comparisons between the simulations and the experiment. The grain size distribution, the grain boundary character distribution and the crystallographic texture are reproduced rather well with this modified model using a moderate grain size factor effect. Also the speedup of the calculation is quite significant.

Second order accuracy in phase field modeling of normal grain growth

The first and second order accuracy of phase field modeling of normal grain growth is investigated using asymptotic analysis. It is found that the model can achieve first order accuracy but fails to gain second order accuracy. The deviation in second order accuracy is proportional to the inverse of interface thickness so that phase field simulation approaches the sharp interface prediction as interface thickness increases. This result is confirmed by comparison of phase field simulation and analytical solutions, and it well explains the effect of interface thickness on phase field simulation of grain growth observed in previous work.

Modeling of Grain Growth in One and Two Phase Materials by 2D Cellular Automata

Modeling of Grain Growth in One and Two Phase Materials by 2D Cellular Automata

CAN THE GROWTH OF DUST GRAINS IN LOW-METALLICITY STAR-FORMING CLOUDS AFFECT THE FORMATION OF METAL-POOR LOW-MASS STARS?

The discovery of a low-mass star with such low metallicity as < 4.5x10^{-5} Z_sun reveals the critical role of dust in the formation of extremely metal-poor stars. In this paper we explore the effect of the growth of dust grains through accretion of gaseous refractory elements in very low-metallicity pre-stellar cores on the cloud fragmentation induced by the dust emission cooling. Employing a simple model of grain growth in a gravitationally collapsing gas, we show that Fe and Si grains can grow efficiently at hydrogen densities of ~10^{10}-10^{14} cm^{-3} in the clouds with metal abundances of -5 <~ [Fe, Si/H] <~ -3. The critical metal number abundances, above which the grain growth could induce the fragmentation of the gas clouds, are estimated to be A_{crit} ~ 10^{-9}-10^{-8}, unless the initial grain radius is too large (>~ 1 um) or the sticking probability is too small (<~ 0.01). We find that even if the initial dust-to-gas mass ratio is well below the minimum value required for the dust-induced fragmentation, the grain growth increases the dust mass high enough to cause the gas fragmentation into sub-solar mass clumps. We suggest that as long as the critical metal abundance is satisfied, the grain growth could play an important role in the formation of low-mass stars with metallicity as low as 10^{-5} Z_sun.

Determination of fracture toughness of AZ31 Mg alloy using the cohesive finite element method

The objective of this study is to develop a micromechanical approach for determining the fracture toughness. A phase-field model for grain growth is employed to generate microstructures with varying attributes and the cohesive finite element method is employed to quantify the interaction between a propagating crack and microstructures of an AZ31 Mg alloy. Simulations show that fracture toughness increases as the average grain size decreases and that the local crack tip environment significantly affects the fracture behavior. Dramatically different dependences of fracture toughness on overall strain rate are seen when two different types of cohesive laws are employed.

Limited grain growth and chemical ordering during high-temperature sintering of PtNiCo nanoparticle aggregates

High-temperature sintering of ternary PtxNi100−x−yCoy (x = 28–44%, y = 40–54%) nanoparticles of interest in catalysis was studied in situ and in real-time with synchrotron-based x-ray diffraction. For the first time we were able to experimentally capture the early stage of the thermal treatment, and found the nanoparticles to undergo an unusual two-step coalescence process that involves transient growth and restructuring of the nanoparticles. The coalescence process is accompanied by lattice contraction, likely due to composition evolution towards a random alloy. In the late stage of sintering, evidence was found for self-limited grain growth and L10 chemical ordering. The order–disorder transition temperature was found to be around 800 °C in all four ternary alloy compositions studied. Fitting of the experimental data with the model for grain growth with size-dependent impediment leads to an activation energy for mass transport of about 100 kJ mol−1, and may be used as a predictive tool to estimate particle size as a function of heat treatment temperature and duration.