Tomohiro Takaki

Peta-scale phase-field simulation for dendritic solidification on the TSUBAME 2.0 supercomputer

The mechanical properties of metal materials largely depend on their intrinsic internal microstructures. To develop engineering materials with the expected properties, predicting patterns in solidified metals would be indispensable. The phase-field simulation is the most powerful method known to simulate the micro-scale dendritic growth during solidification in a binary alloy. To evaluate the realistic description of solidification, however, phase-field simulation requires computing a large number of complex nonlinear terms over a fine-grained grid. Due to such heavy computational demand, previous work on simulating three-dimensional solidification with phase-field methods was successful only in describing simple shapes. Our new simulation techniques achieved scales unprecedentedly large, sufficient for handling complex dendritic structures required in material science. Our simulations on the GPU-rich TSUBAME 2.0 super- computer at the Tokyo Institute of Technology have demonstrated good weak scaling and achieved 1.017 PFlops in single precision for our largest configuration, using 4,000 CPUs along with 16,000 CPU cores.

Homogeneous nucleation and microstructure evolution in million-atom molecular dynamics simulation.

Homogeneous nucleation from an undercooled iron melt is investigated by the statistical sampling of million-atom molecular dynamics (MD) simulations performed on a graphics processing unit (GPU). Fifty independent instances of isothermal MD calculations with one million atoms in a quasi-two-dimensional cell over a nanosecond reveal that the nucleation rate and the incubation time of nucleation as functions of temperature have characteristic shapes with a nose at the critical temperature. This indicates that thermally activated homogeneous nucleation occurs spontaneously in MD simulations without any inducing factor, whereas most previous studies have employed factors such as pressure, surface effect, and continuous cooling to induce nucleation. Moreover, further calculations over ten nanoseconds capture the microstructure evolution on the order of tens of nanometers from the atomistic viewpoint and the grain growth exponent is directly estimated. Our novel approach based on the concept of “melting pots in a supercomputer” is opening a new phase in computational metallurgy with the aid of rapid advances in computational environments.

A phase-field-lattice Boltzmann method for modeling motion and growth of a dendrite for binary alloy solidification in the presence of melt convection

Abstract In this study, a combination of the lattice Boltzmann method (LBM) and the phase-field method (PFM) is used for modeling simultaneous growth and motion of a dendrite during solidification. PFM is used as a numerical tool to simulate the morphological changes of the solid phase, and the fluid flow of the liquid phase is described by using LBM. The no-slip boundary condition at the liquid–solid interface is satisfied by adding a diffusive-forcing term in the LBM formulation. The equations of motion are solved for tracking the translational and rotational motion of the solid phase. The proposed method is easily implemented on a single Cartesian grid and is suitable for parallel computation. Two-dimensional benchmark computations show that the no-slip boundary condition and the shape preservation condition are satisfied in this method. Then, the present method is applied to the calculation of dendritic growth of a binary alloy under melt convection. Initially, the solid is stationary, and then, the solid moves freely due to the influence of fluid flow. Simultaneous growth and motion are effectively simulated. As a result, it is found that motion and melt convection enhance dendritic growth along the flow direction.

Heterogeneity in homogeneous nucleation from billion-atom molecular dynamics simulation of solidification of pure metal

Can completely homogeneous nucleation occur? Large scale molecular dynamics simulations performed on a graphics-processing-unit rich supercomputer can shed light on this long-standing issue. Here, a billion-atom molecular dynamics simulation of homogeneous nucleation from an undercooled iron melt reveals that some satellite-like small grains surrounding previously formed large grains exist in the middle of the nucleation process, which are not distributed uniformly. At the same time, grains with a twin boundary are formed by heterogeneous nucleation from the surface of the previously formed grains. The local heterogeneity in the distribution of grains is caused by the local accumulation of the icosahedral structure in the undercooled melt near the previously formed grains. This insight is mainly attributable to the multi-graphics processing unit parallel computation combined with the rapid progress in high-performance computational environments.Nucleation is a fundamental physical process, however it is a long-standing issue whether completely homogeneous nucleation can occur. Here the authors reveal, via a billion-atom molecular dynamics simulation, that local heterogeneity exists during homogeneous nucleation in an undercooled iron melt.

Finite element simulation of bolt-up process of pipe flange connections with spiral wound gasket

It is well known that a large amount of scatter in bolt preloads is observed when boltingup a pipe flange connection, especially in the case of using a spiral wound gasket. In thisstudy, a numerical approach is proposed, which can simulate the bolt-up process of a pipeflange connection with a spiral wound gasket inserted. The numerical approach is de-signed so as to predict the scatter in bolt preloads and achieve uniform bolt preloads atthe completion of pipe flange assembly. To attain the foregoing purposes, the stress-strainrelationship of a spiral wound gasket, which shows highly nonlinear behavior, is identifiedwith a sixth-degree polynomial during loading and with an exponential equation duringunloading and reloading. Numerical analyses are conducted by three-dimensional FEM,in which a gasket is modeled as groups of nonlinear one-dimensional elements.@DOI: 10.1115/1.1613304#

Elastic Plastic Finite Element Analysis of Bolted Joint During Tightening Process

Mechanical behavior of bolted joints during the tightening process with torque control is analyzed by FEM as elastic plastic contact problems. Three-dimensional analysis was conducted employing two-dimensional model with each node having three degrees of freedom that attains high computation efficiency. Such important factors as development of plastic zones, variations of load distributions along engaged threads, the relationships between axial bolt stress and nut rotation angle were analyzed in order to provide an effective guideline when tightening critical structures with high bolt preloads. It was also shown that the proposed numerical method can be applied to evaluate the tightening process by plastic region tightening used extensively in recent years. The validity of the numerical method is demonstrated by comparing the calculated bolt elongation with that obtained from experiment.

Finite element simulation of bolt-up process of pipe flange connections

Achieving uniform bolt preload is difficult when tightening a pipe flange with a number of bolts. Several bolt-tightening strategies have been proposed so far for achieving uniform bolt preloads. It seems, however, that effective guidelines for tightening pipe flange connections have not been established. In this study, a numerical approach is presented for estimating the scatter in bolt preloads and achieving the uniform bolt preloads when tightening each bolt one by one in an arbitrary order. Numerical analyses are conducted using three-dimensional FEM as an elastic contact problem. The analytical objects are pipe flanges specified in JIS B 2238 with an aluminum gasket inserted. The validity of the numerical procedures proposed here is ascertained by experiment.

GPU phase-field lattice Boltzmann simulations of growth and motion of a binary alloy dendrite

A GPU code has been developed for a phase-field lattice Boltzmann (PFLB) method, which can simulate the dendritic growth with motion of solids in a dilute binary alloy melt. The GPU accelerated PFLB method has been implemented using CUDA C. The equiaxed dendritic growth in a shear flow and settling condition have been simulated by the developed GPU code. It has been confirmed that the PFLB simulations were efficiently accelerated by introducing the GPU computation. The characteristic dendrite morphologies which depend on the melt flow and the motion of the dendrite could also be confirmed by the simulations.

Ultra-large-scale phase-field simulation study of ideal grain growth

Grain growth, a competitive growth of crystal grains accompanied by curvature-driven boundary migration, is one of the most fundamental phenomena in the context of metallurgy and other scientific disciplines. However, the true picture of grain growth is still controversial, even for the simplest (or ‘ideal’) case. This problem can be addressed only by large-scale numerical simulation. Here, we analyze ideal grain growth via ultra-large-scale phase-field simulations on a supercomputer for elucidating the corresponding authentic statistical behaviors. The performed simulations are more than ten times larger in time and space than the ones previously considered as the largest; this computational scale gives a strong indication of the achievement of true steady-state growth with statistically sufficient number of grains. Moreover, we provide a comprehensive theoretical description of ideal grain growth behaviors correctly quantified by the present simulations. Our findings provide conclusive knowledge on ideal grain growth, establishing a platform for studying more realistic growth processes.Grain growth: Simulations elucidate statistical behaviorGrain growth under ideal conditions is simulated by phase-field simulations in ultra-large time and space scales to elucidate the statistical behaviors. A team led by Tomohiro Takaki at Kyoto Institute of Technology in Japan performed large scale phase-field simulations to study ideal grain growth behavior. The time and space scales used in the simulations are more than ten times larger than those in previous reports, enabling them to reach a true steady-state with a statistically significant number of grains. A comprehensive theoretical description was derived to understand the ideal grain growth behavior based on the simulations. The knowledge provided by these findings may offer a model to understand the effects of complicated factors present in real materials and thus establish a platform to study more realistic grain growth phenomena in the future.

GPU-accelerated 3D phase-field simulations of dendrite competitive growth during directional solidification of binary alloy

Phase-field method has emerged as the most powerful numerical scheme to simulate dendrite growth. However, most phase-field simulations of dendrite growth performed so far are limited to two-dimension or single dendrite in three-dimension because of the large computational cost involved. To express actual solidification microstructures, multiple dendrites with different preferred growth directions should be computed at the same time. In this study, in order to enable large-scale phase-field dendrite growth simulations, we developed a phase-field code using multiple graphics processing units in which a quantitative phase-field method for binary alloy solidification and moving frame algorithm for directional solidification were employed. First, we performed strong and weak scaling tests for the developed parallel code. Then, dendrite competitive growth simulations in three-dimensional binary alloy bicrystal were performed and the dendrite interactions in three-dimensional space were investigated.