Primary arm array during directional solidification of a single-crystal binary alloy: Large-scale phase-field study

AbstractPrimary arm arrays formed during the directional solidification of a single-crystal binary alloy were investigated by performing large-scale phase-field simulations using the GPU supercomputer TSUBAME2.5 at Tokyo Institute of Technology. The primary arm array and spacing were investigated by Voronoi decomposition and Delaunay triangulation, respectively. It was concluded that a hexagonal array was dominant for both the dendrite and cell structures and that penta–hepta defects, which are typical defects in hexagonal patterns, were formed. The primary arms continuously moved such that the number of hexagons increased, and the distribution of primary arm spacing became uniform over time even after the number of primary arms was constant. The order of array was highest in the growth condition of the dendrite close to the cell-to-dendrite transition region. In addition, we proposed a realistic and accurate evaluation method of primary arm array by removing small sides from the Voronoi polygons

Numerical testing of quantitative phase-field models with different polynomials for isothermal solidification in binary alloys

Quantitative phase-field models have been developed as feasible computational tools for solving the free-boundary problem in solidification processes. These models are constructed with some polynomials of the phase-field variable that describe variations of the physical quantities inside the diffuse interface. The accuracy of the simulation depends on the choice of the polynomials and such dependence is indispensable for high-performance computing and valuable for extending the range of applications of the model to several physical systems. However, little is known about the dependence of the accuracy on the choice of the polynomials. In this study, numerical testing is carried out for quantitative phase-field models with extensive sets of polynomials (24 different models) for isothermal solidification in binary alloys. It is demonstrated in two-dimensional simulations of dendritic growth that a specific set of polynomials must be employed to achieve high accuracy in the models with double-well and double-obstacle potentials. Both types of model with the best set of polynomials yield almost the same numerical accuracy. (C) 2017 Elsevier Inc. All rights reserved

Variational formulation of a quantitative phase-field model for nonisothermal solidification in a multicomponent alloy

A variational formulation of a quantitative phase-field model is presented for nonisothermal solidification in a multicomponent alloy with two-sided asymmetric diffusion. The essential ingredient of this formulation is that the diffusion fluxes for conserved variables in both the liquid and solid are separately derived from functional derivatives of the total entropy and then these fluxes are related to each other on the basis of the local equilibrium conditions. In the present formulation, the cross-coupling terms between the phase-field and conserved variables naturally arise in the phase-field equation and diffusion equations, one of which corresponds to the antitrapping current, the phenomenological correction term in early nonvariational models. In addition, this formulation results in diffusivities of tensor form inside the interface. Asymptotic analysis demonstrates that this model can exactly reproduce the free-boundary problem in the thin-interface limit. The present model is widely applicable because approximations and simplifications are not formally introduced into the bulk's free energy densities and because off-diagonal elements of the diffusivity matrix are explicitly taken into account. Furthermore, we propose a nonvariational form of the present model to achieve high numerical performance. A numerical test of the nonvariational model is carried out for nonisothermal solidification in a binary alloy. It shows fast convergence of the results with decreasing interface thickness

Solidification in a Supercomputer: From Crystal Nuclei to Dendrite Assemblages

Thanks to the recent progress in high-performance computational environments, the range of applications of computational metallurgy is expanding rapidly. In this paper, cutting-edge simulations of solidification from atomic to microstructural levels performed on a graphics processing unit (GPU) architecture are introduced with a brief introduction to advances in computational studies on solidification. In particular, million-atom molecular dynamics simulations captured the spontaneous evolution of anisotropy in a solid nucleus in an undercooled melt and homogeneous nucleation without any inducing factor, which is followed by grain growth. At the microstructural level, the quantitative phase-field model has been gaining importance as a powerful tool for predicting solidification microstructures. In this paper, the convergence behavior of simulation results obtained with this model is discussed, in detail. Such convergence ensures the reliability of results of phase-field simulations. Using the quantitative phase-field model, the competitive growth of dendrite assemblages during the directional solidification of a binary alloy bicrystal at the millimeter scale is examined by performing two-and three-dimensional large-scale simulations by multi-GPU computation on the supercomputer, TSUBAME2.5. This cutting-edge approach using a GPU supercomputer is opening a new phase in computational metallurgy

Variational formulation and numerical accuracy of a quantitative phase-field model for binary alloy solidification with two-sided diffusion

We present the variational formulation of a quantitative phase-field model for isothermal low-speed solidification in a binary dilute alloy with diffusion in the solid. In the present formulation, cross-coupling terms between the phase field and composition field, including the so-called antitrapping current, naturally arise in the time evolution equations. One of the essential ingredients in the present formulation is the utilization of tensor diffusivity instead of scalar diffusivity. In an asymptotic analysis, it is shown that the correct mapping between the present variational model and a free-boundary problem for alloy solidification with an arbitrary value of solid diffusivity is successfully achieved in the thin-interface limit due to the cross-coupling terms and tensor diffusivity. Furthermore, we investigate the numerical performance of the variational model and also its nonvariational versions by carrying out two-dimensional simulations of free dendritic growth. The nonvariational model with tensor diffusivity shows excellent convergence of results with respect to the interface thickness

Atomistic Simulation of the Interaction Between Point Defects and Twin Boundary

While nanotwinned metals have been proven to show excellent mechanical properties, they are generally anticipated to be less effective in the alleviation of radiation damage. However, recent in situ studies have indicated that some nanotwinned metals exhibit unprecedented radiation tolerance, and the unexpected self‐healing of twin boundaries in response to radiation was observed. To reveal the underlying atomic mechanisms, we performed long‐time molecular dynamics simulations to study the dynamic interaction between twin boundary and some typical radiation‐induced point defects, including vacancy cluster and self‐interstitial atoms. The defective structures of coherent twin boundary which contains incoherent twin segment or self‐interstitial atoms are considered, and these structure features are found to effectively improve the ability of twin boundary to act as a sink for point defects

Uniquely selected primary dendrite arm spacing during competitive growth of columnar grains in Al-Cu alloy

The steady-state value of primary dendrite arm spacing (PDAS) in the columnar dendrites growing between the converging and diverging grain boundaries is investigated by means of quantitative phase-field simulations. The simulations show that there is a unique value of PDAS under a given solidification condition in the system with grain boundaries. This is in contrast to existence of allowable range of PDAS under a given solidification in a system without the grain boundaries, i.e., an infinitely large columnar grain investigated in many early works. Such a unique value of PDAS depends on the pulling speed and inclination angle of the crystal, but not on the initial condition; that is, it is independent of the history of solidification condition. The dependences of the unique value on the pulling speed and inclination angle qualitatively agree with the theoretical models