Analysis of higher-order corrections to the interface kinetics in the multiphase field method

We use geometrical arguments based on grain boundary symmetries to introduce crystalline interfacial energies for interfaces in polycrystalline thin films with a cubic lattice. These crystalline energies are incorporated into a multi-phase field model. Our aim is to apply the multi-phase field method to describe the evolution of faceted grain boundary triple junctions in epitaxially growing microstructures. In particular, we are interested in symmetry properties of triple junctions in tricrystalline thin films. Symmetries of triple junctions in tricrystalline films have been studied in experiments by Dahmen and Thangaraj.6,25 In accordance with their experiments, we find in numerical simulations that any two neighboring triple junctions belong to different symmetry classes. We introduce a local equilibrium condition at triple junctions which can be interpreted as a crystalline version of Young's law. The local equilibrium condition at triple junctions is purely determined by the grain boundary energies. In particular no triple junction energies are necessary to explain which triple junctions are possible. All triple junctions observed in the experiments as well as in the simulations fulfil the crystalline version of Young's law. Our approach is also capable of describing grain boundary motion in general polycrystalline thin films.

An ordered active parameter tracking method for efficient multiphase field simulations

In this work, molecular dynamics (MD) simulations have been used to study the heterogeneous nucleation occurring at grain boundaries (GBs) during the austenite (FCC) phase to ferrite (BCC) phase transformation in a pure Fe polycrystalline system. The critical nucleus properties (including size, shape, and activation energy) determined by classical nucleation theory are compared with those obtained by using a combination of the multi-phase field method (MPFM) and the nudged elastic band (NEB) method. For nucleation events that exhibit low-energy facets completely embedded within the parent FCC phase, there is a good agreement between the MD and the MPFM result with respect to the critical nucleus size, shape, and nucleation energy barrier. For systems where the emerging nucleus contains facets that cross the GB plane, the MPFM-NEB, when compared to MD, yields a better prediction than the classical approach for the nucleus morphology. New observations from the MPFM-NEB method indicate that the critical nucleus shape may change with volume and therefore depends on the nucleation driving force (undercooling).

We proposed a microstructure-based multiscale simulation framework using various commercial simulation software and applied it to analyze the hot rolling of duplex stainless steel. According to the Integrated Computational Material Engineering (ICME) concept, we established a procedure to bridge various simulation software from nano- to macroscopic length scales. Using our framework, first, microstructure evolutions by multiphase field (MPF) simulations coupled with the Calculation of Phase Diagrams (CALPHAD) database were performed. In our application, we simulated the columnar and equiaxed solidification during the continuous casting of duplex stainless steel. In the MPF simulations, the temperature field in the slab was calculated by heat conduction analysis using a finite element method (FEM). Then, the macroscopic elastic and plastic mechanical properties of the microstructure obtained by the MPF simulations were estimated by the virtual material test using a nonlinear FEM based on the homogenization method. Because the elastic constants of single δ-ferrite and γ phases in the microstructure are necessary for the virtual material test, they were calculated by molecular dynamics and first principle calculations. Furthermore, the plastic stress–strain properties of the single phases were estimated on the basis of the results of nano-indentation and uniaxial tensile tests. Subsequently, the hot rolling of the slab was simulated using an elastoplastic FEM with the mechanical properties obtained by the virtual material test. Finally, the static recrystallization in the rolled slab was again simulated by the MPF method.

Icing and ice accumulation on blades or cooling apertures in aero-engines along with other mechanical systems present significant hazards to operating efficiency and structural integrity. Porous structures enhance fluid flow and modify thermal conductivity. Therefore, this study examines droplet spreading and heat transfer on subcooled porous surfaces, modelling the interactions between droplets and porous structures based on the multiphase flow-phase field method coupled with a heat transfer module. The model's accuracy and reliability were validated by comparing experimental results with numerical simulations. The dynamics of droplets on porous surfaces are examined in detail, focusing on the influence of Weber number, while emphasizing its effect on the coupled heat transfer during impact on subcooled porous structures. It is found that increasing the Weber number markedly enhances droplet dynamics, resulting in a larger spreading factor and an increased tendency for icing, accompanied by pronounced secondary heat transfer effects, which modify the local heat flux distribution during the impact and solidification processes. When the Weber number increases from 60 to 160, the peak heat flux is observed to increase by approximately 90%. In addition, the reduction in surface wettability leads to distinct penetration and heat transfer modes of the droplet. Specifically, the peak heat flux is lowered by roughly 3% compared with the normal wettability conditions, and no pronounced secondary heat transfer behavior is observed. These results provide theoretical insights into droplet icing behavior and support the development of more effective anti-icing strategies.

Multiphase-field modelling of anisotropic elasticity at finite deformation in Eulerian space

The reduction pretreatment (RP) process is an effective method to improve billet quality, and the deformation recrystallization plays an important role in the process. Exploring the RP process parameters, a dynamic recrystallization model of GCr15 steel was established by the phase-field method and physical simulation. The recrystallization kinetics and flow stress curves during hot compression were simulated by using this mode. The effects of deformation parameters and initial grain size on the dynamic recrystallization were investigated. Moreover, by using the results obtained by Finite element method (FEM), dynamic recrystallization during the RP process was investigated though this model. It was found that increasing the deformation temperature, deformation rate and decreasing the initial grain size can promote the dynamic recrystallization kinetics. Large Zener-Hollomon parameters can enhance recrystallized grain refinement, while the recrystallized grain size was not affected by the initial grain size. During the RP process, when the reduction is insufficient (10%), partial recrystallization occurs in the billet. With the increase of reduction from 10% to 16%, the area of complete recrystallization increases gradually. When the reduction is the same, the recrystallization in the billet center increases with the decrease of casting speed. When the reduction is 10%, partial recrystallization occurs in the billet center at a casting speed of 0.7 m min−1, and fully recrystallization occurs in the billet center with a casting speed of 0.5 m min−1. Thus, when the reduction is difficult to increase further, the recrystallization in the billet center can be improved by decreasing the casting speed.

The multi-phase field method and CALPHAD (calculation of phase diagram) are applied to the study of the equiaxed solidifications in the Al-Ti-B and Al-Si-Ti-B systems by coupled with thermodynamic and diffusion databases. In these calculations, recalescence phenomenon is considered on the basis of the latent heat, and a plot of the seed density-radius distribution is obtained by calibration with experimental data. The calculated solidified-grain sizes are in quantitative agreement with the experimental measurements for various hypoperitectic compositions.

In this paper, the grain-refining effect of Al-Nb-B refiner in wrought Al alloys and corresponding refining mechanism was investigated using phase-field simulation and experiment methods. Through experimental statistics and data correction, the seed radius introduced by Al-Nb-B refiner into Al alloy melt and the corresponding quantitative density distribution data were obtained, and a seed density model (SDM) model has been established. On this basis, a multi-phase field method (MPFM) combined with the calculation of phase diagram (CALPHAD) has been employed to simulate the α-Al grain evolution of Al-Mg-Si alloy during the solidification process with the help of thermodynamic database. Experimental studies showed that the addition of 0.03 wt% Nb (Adding by Al-1.93Nb-0.22B master alloy) significantly reduced the grain size from 956.4 μm to about 219.4 μm, and the grain size slowly decreased to 192.3 μm by continuing to add refiner to 0.09 wt% Nb. Meanwhile, the simulation results demonstrated that after the addition of refiners, dendrite morphology transformed from the relatively developed dendrites with secondary and tertiary dendrites to a fine and uniform equiaxed shape. Simulation and experimental studies showed quantitative agreement. In addition, the results also prove that the addition of Al-Nb-B refiner can provide high-quality and stable heterogeneous nucleation particles.

An analytical study of the static state of multi-junctions in a multi-phase field model

Multiphasic analysis of gas production kinetics for in vitro fermentation of ruminant feeds

Analysis of Solidification Microstructure in Additive Manufacturing by Multi-Phase Field Method

The effect of microstructural morphologies on solidification microsegregation and residual liquid distribution was investigated in Fe-Cr-Ni-C alloy, which forms the basis for austenitic stainless steel with fully γ solidification mode by using the multi-phase field (MPF) method. When the cellular dendrite growth direction became inclined, the growth of the secondary arm became remarkable in the branching part and liquid droplets were formed irregularly around the grain boundary region. A liquid film was formed in the blocking part of inclined cellular growth, where stress concentration occurred continuously. This liquid film can influence solidification cracking susceptibility. Stress concentration occurred discontinuously in the branching part. The effect of varying the interface energy during solidification on the residual liquid morphology was not large, even when 2σL-γ≪σγ-γ, where σL-γ is the interface energy of liquid/γ and σγ-γ is the interface energy of γ/γ.

Light. Volume 2. Laser Light Dynamics. By H. Haken. (Amsterdam, New York, Oxford: North-Holland, 1985.) [Pp. xxiii + 336 + subject index.] Price Dfl. 125·00/US $46.25 hard cover. Electronic Structure and Electronic Transitions in Layered Materials. Edited by V. Grasso. (Dordrecht, Boston, Lancaster: D. Reidel, 1986.) [Pp. ix + 491 + author and subject index.] Price Dfl.225.00 hard cover. The Physics and Fabrication of Microstructures and Microdevices. Edited by M. J. Kelly and C. Weisbuch. (Berlin, Heidelberg, New York: Springer-Verlag, 1986.) [Pp. xi + 460.1 Price DM 99·00 hard cover. Unitary Transformations in Solid State Physics. By M. Wagner. (Amsterdam, Oxford, New York: North-Holland, 1986.) [Pp. xvi + 341 + author and subject index.] Price Dfl.225.00 hard cover. Differential Manifolds and Theoretical Physics. By W. D. Curtis and F. R. Miller. (Orlando, San Diego and New York: Academic Press, 1985.) [Pp. xiii + 388 + subject index.] Price £69·00 hard cover. Coherent States. Applications in Physics and Mathematical Physics. By J. R. Klauder and B. Skagerstam. (Singapore: World Scientific, 1985.) [Pp. xvii + 911.] Price £6670 soft cover. (69 reprints from various journals + introduction.) International Tables for Crystallography. Edited by T. Hahn. (Dordrecht, Boston, Lancaster: D. Reidel, 1985.) [Pp. viii +119.1 Price £9·00 soft cover. (Brief Teaching Edition of Volume A—Space-Group Symmetry.) Multiple Time Scales. Edited by J. U. Brackbill and B. I. Cohen. (Orlando, San Diego, New York: Academic Press, 1985.) [Pp. xiii + 436 + subject index.] Price ·65.00 hard cover. (Thirteen reviews of applications in physics.) Silicon-on-Insulator: Its Technology and Applications. Edited by S. Furukawa. (Dordrecht, Boston, London: D. Reidel; and Tokyo: KTK Scientific Publishers, 1985.) [Pp. vii + 295 + author index.] Price £49·95 hard cover. (20 papers presented at the seminar on ‘Solid Phase Epitaxy and Interface Kinetics’ held in Oiso, Japan, June, 1983.) Layered Structures and Interface Kinetics: Their Technology and Applications. Edited by S. Furukawa. (Dordrecht, Boston, London: D. Reidel; and Tokyo: KTK Scientific Publishers, 1985.) [Pp. viii + 367 + author index.] Price £60·95 hard cover. (22 papers presented at the seminar on ‘Solid Phase Epitaxy and Interface Kinetics’ held in Oiso, Japan, June, 1983.) Superlattices and Microstructures. Volume 1. Number 1. Edited by J. D. Dow. (Orlando, London, New York: Academic Press, 1985.) [Pp. 96.] soft cover. (New interdisciplinary journal devoted to the physics, chemistry, materials science and electrical engineering of submicron structures not only in semiconductors but also in materials with metallic, insulating and superconducting properties.) Solid Clues. Quantum Physics, Molecular Biology, and the Future of Science. By G. Feinberg. (London: Heinemann, 1985.) [Pp. i + 278 + subject index.] Price £12·95 hard cover. Laser Spectroscopy of Solids. Second Printing. Edited by W. M. Yen and P. M. Selzer. (Berlin, Heidelberg, New York: Springer-Verlag, 1986.) [Pp. xiv + 311 + subject index.] Price DM79 soft cover (See Phil. Mag. B, 44, 185 for review.)

Modelling the influence of microstructural morphology and triple junctions on hydrogen transport in nanopolycrystalline nickel