Phase-field Simulation Of Microstructure Evolution Research Articles

Physics-embedded graph network for accelerating phase-field simulation of microstructure evolution in additive manufacturing

The phase-field (PF) method is a physics-based computational approach for simulating interfacial morphology. It has been used to model powder melting, rapid solidification, and grain structure evolution in metal additive manufacturing (AM). However, traditional direct numerical simulation (DNS) of the PF method is computationally expensive due to sufficiently small mesh size. Here, a physics-embedded graph network (PEGN) is proposed to leverage an elegant graph representation of the grain structure and embed the classic PF theory into the graph network. By reformulating the classic PF problem as an unsupervised machine learning task on a graph network, PEGN efficiently solves temperature field, liquid/solid phase fraction, and grain orientation variables to minimize a physics-based loss/energy function. The approach is at least 50 times faster than DNS in both CPU and GPU implementation while still capturing key physical features. Hence, PEGN allows to simulate large-scale multi-layer and multi-track AM build effectively.

Phase-Field Simulation of Microstructure Evolution of Inconel 718 Alloy by Laser Powder Bed Fusion Solidification and Homogenization Heat Treatment

Phase-Field Simulation of Microstructure Evolution of Inconel 718 Alloy by Laser Powder Bed Fusion Solidification and Homogenization Heat Treatment

Tusas: A fully implicit parallel approach for coupled phase-field equations

We develop a fully-coupled, fully-implicit approach for phase-field modeling of solidification in metals and alloys. Predictive simulation of solidification in pure metals and metal alloys remains a significant challenge in the field of materials science, as microstructure formation during the solidification process plays a critical role in the properties and performance of the solid material. Our simulation approach consists of a finite element spatial discretization of the fully-coupled nonlinear system of partial differential equations at the microscale, which is treated implicitly in time with a preconditioned Jacobian-free Newton-Krylov method. The approach is algorithmically scalable as well as efficient due to an effective preconditioning strategy based on algebraic multigrid and block factorization. We implement this approach in the open-source Tusas framework, which is a general, flexible tool developed in C++ for solving coupled systems of nonlinear partial differential equations. The performance of our approach is analyzed in terms of algorithmic scalability and efficiency, while the computational performance of Tusas is presented in terms of parallel scalability and efficiency on emerging heterogeneous architectures. We demonstrate that modern algorithms, discretizations, and computational science, and heterogeneous hardware provide a robust route for predictive phase-field simulation of microstructure evolution during additive manufacturing.

Phase-field simulation of microstructure evolution during friction stir welding of 304 stainless steel

Dynamic recrystallization (DRX) is the most significant metallurgical phenomenon during friction stir welding (FSW) and friction stir processing (FSP). In order to simulate the microstructure evolution during FSW, the phase-field method was applied. For this purpose, the growth and shrinkage of a nucleus in the matrix of a grain using the DRX mechanism models was simulated using the phase-field method. In order to have suitable parameters for microstructure modeling, the finite element method (FEM) was used for numerical simulation of the FSW process, including thermal, computational fluid dynamics (CFD) and mechanical simulations. The phase-field simulation of DRX microstructure evolution was performed based on the FEM results. The simulation results were validated by being compared to the experimental findings reported by other researches. It was found that the rotating speed plays a significant role in the formation of the final microstructure in the process. Grain size distribution is nearly interdependent of the nucleation rate, growth and therefore, recrystallized fraction areas. Grain boundary fraction was also predicted by post-processing of the simulation results. It was also found that the rotating speed affecting the nucleation and growth rate significantly affected the grain boundary fraction in FSW process.

Phase-field simulation of microstructure evolution in electron beam additive manufacturing.

Electron beam additive manufacturing (EBAM) is an emerging additive manufacturing technology with extremely high energy beam. The rapid solidification in the molten pool is of interest but not fully understood. In EBAM, with both large thermal gradient and cooling rate, the microstructure evolution during solidification is difficult to be described. The quantitative multi-phase-field model provides an effective way to reveal the dynamic evolution of dendrites in the molten pool of EBAM. In this study, the thermal profile is interpolated from the macroscale simulation at each time-step, to couple the realistic thermal evolution in the molten pool. The microstructure evolution and competitive growth have been investigated in details. Simulations of dendrite arrays with the same orientation showed how the growth velocity and the primary spacing of columnar dendrites depend on thermal gradient and cooling rate. The results are in agreement with theoretical models qualitatively. Moreover, the Gaussian nucleation model was introduced so as to give a better prediction of the microstructure in EBAM.

3D non-isothermal phase-field simulation of microstructure evolution during selective laser sintering

During selective laser sintering (SLS), the microstructure evolution and local temperature variation interact mutually. Application of conventional isothermal sintering model is thereby insufficient to describe SLS. In this work, we construct our model from entropy level, and derive the non-isothermal kinetics for order parameters along with the heat transfer equation coupled with microstructure evolution. Influences from partial melting and laser-powder interaction are also addressed. We then perform 3D finite element non-isothermal phase-field simulations of the SLS single scan. To confront the high computation cost, we propose a novel algorithm analogy to minimum coloring problem and manage to simulate a system of 200 grains with grain tracking algorithm using as low as 8 non-conserved order parameters. Specifically, applying the model to SLS of the stainless steel 316L powder, we identify the influences of laser power and scan speed on microstructural features, including the porosity, surface morphology, temperature profile, grain geometry, and densification. We further validate the first-order kinetics of the transient porosity during densification, and demonstrate the applicability of the developed model in predicting the linkage of densification factor to the specific energy input during SLS.

A Trial to Design γ/γ′ Bond Coat in Ni–Al–Cr Mode TBCs Aided by Phase-Field Simulation

Phase-field modeling coupled with calculation of phase diagram (CALPHAD) database was utilized to perform a series of two-dimensional phase-field simulations of microstructure evolution in the γ + γ′/γ + γ′ Ni–Al–Cr mode bond coat/substrate systems. With the aid of phase-field simulated microstructure evolution, the relationship between the interdiffusion microstructure and the cohesiveness/aluminum protective property with different alloy compositions and bond coat thicknesses was fully discussed. A semi-quantitative tie-line selection criteria for alloy composition of the bond coat/substrate system with the identical elements, i.e., that the equilibrium Al concentrations of γ′ and γ phases in the bond coat should be similar to those in substrate, while the phase fraction of γ′ in the bond coat tends to be higher than that in the substrate, was then proposed to reduce the formation of polycrystalline structure and thermal shock from the temperature gradient.

Unit-cell design for two-dimensional phase-field simulation of microstructure evolution in single-crystal Ni-based superalloys during solidification

Phase-field simulation serves as an effective tool for quantitative characterization of microstructure evolution in single-crystal Ni-based superalloys during solidification nowadays. The classic unit cell is either limited to γ dendrites along <001> crystal orientation or too ideal to cover complex morphologies for γ dendrites. An attempt to design the unit cell for two-dimensional (2-D) phase-field simulations of microstructure evolution in single-crystal Ni-based superalloys during solidification was thus performed by using the MICRESS (MICRostructure Evolution Simulation Software) in the framework of the multi-phase-field (MPF) model, and demonstrated in a commercial TMS-113 superalloy. The coupling to CALPHAD (CALculation of PHAse Diagram) thermodynamic database was realized via the TQ interface and the experimental diffusion coefficients were utilized in the simulation. Firstly, the classic unit cell with a single γ dendrite along <001> crystal orientation was employed for the phase-field simulation in order to reproduce the microstructure features. Then, such simple unit cell was extended into the cases with two other different crystal orientations, i.e., <011> and <111>. Thirdly, for <001> crystal orientations, the effect of γ dendritic orientations and unit cell sizes on microstructure and microsegregation was comprehensively studied, from which a new unit cell with multiple γ dendrites was proposed. The phase-field simulation with the newly proposed unit cell was further performed in the TMS-113 superalloy, and the microstructure features including the competitive growth of γ dendrites, microsegregation of different solutes and distribution of γ′ grains, can be nicely reproduced.

Phase-field simulations of microstructure evolution during physical vapor deposition of single-phase thin films

Physical vapor deposition (PVD) simulations are performed using a phase-field model to study microstructure evolution in single-phase polycrystalline materials as a function of deposition conditions. Specifically, this work focuses on the influence of (i) polycrystalline substrate microstructure with low-angle and high-angle grain boundaries (GBs), (ii) incident vapor flux rate, and (iii) model parameters controlling grain evolution dynamics. Simulation results show that low-angle and high-angle GBs in the substrate promote the formation of low-angle and high-angle GBs within the deposited thin film, in qualitative agreement with experimental reports. Changing the vapor flux rate has a significant influence on the deposited microstructure. A relatively low flux rate is found to provide a thin film with no subsurface porosity, smoothed surface roughness, and a mixture of grain sizes. With an increased vapor flux rate, uniformly distributed surface columnar features are observed with subsurface porosity. The GBs migrate during growth to align with these surface features. At the largest flux rate studied, a dendritic style microstructure is formed where the GBs tend to align with and grow along the regions of low phase density within the thin film. Finally, a parametric study is performed on the phase-field model grain evolution parameters to elucidate their role on grain boundary thickness, internal grain variations and grain rotation during simulated PVD.

Ti-Nb-O系合金における組織形成と力学応答のフェーズフィールドシミュレーション

Ti-Nb-O系合金における組織形成と力学応答のフェーズフィールドシミュレーション

Phase-field simulation of microstructure evolution of Ti–6Al–4V in electron beam additive manufacturing process

Electron beam additive manufacturing (EBAM) is a relatively new technology to produce metallic parts in a layer by layer fashion by melting and fusing the metallic powders. Ti–6Al–4V is one of the most used industrial alloys used for aerospace and biomedical application. EBAM is a rapid solidification process and the properties of the build material depend on the solidification behavior as well as the microstructure of the build material. Thus, the prediction of part microstructures during the process may be an important factor for process optimization. In this study, a phase field model is developed for microstructure evolution of Ti–6Al–4V powder in EBAM process. FORTRAN code is used to solve the phase field equations, which incorporates the temperature gradient and solidification velocity as the simulation parameters. The effect of temperature gradient and the beam scan speed on microstructure is investigated through simulation. The simulation results are compared with the analytical model and experimental findings by measuring the spacing evolution under the solidification condition

P102] Phase-field simulation of microstructure evolution and microsegregation in Al-4.5Cu-0.5Mg-1.0Si (wt.%) alloy during solidification

P102] Phase-field simulation of microstructure evolution and microsegregation in Al-4.5Cu-0.5Mg-1.0Si (wt.%) alloy during solidification

Phase-Field Simulation of Microstructure Evolution in Industrial A2214 Alloy During Solidification

By linking to the thermodynamic and atomic mobility databases in Al alloys well established in our research group, the microstructure evolution in industrial A2214 alloy (Al-4.5Cu-0.5Mg-1.0Si, in wt pct) during solidification process was studied by means of two-dimensional phase-field simulation via MICRostructure Evolution Simulation Software in the framework of the multi-phase-field formalism. The thermophysical parameters including interfacial energies and interfacial mobilities were carefully chosen for reproducing the experimental features. The solidification sequence due to the present phase-field simulation conforms to both equilibrium calculation and Scheil simulation. The predicted microstructure reproduces the experimental data very well. These facts indicate that a quantitative phase-field simulation was achieved in the present work. Moreover, the mechanisms of characteristic patterns and microstructure formation were revealed with the aid of the phase-field simulation. In addition, the effect of cooling rate on the secondary dendrite arm spacing and microsegregation was also investigated through comprehensive comparison with the experimental data.

Design of the Precipitation Process for Ni-Al Alloys with Optimal Mechanical Properties: A Phase-Field Study

An attempt to design the heat treatment schedule for binary Ni-Al alloys with optimal mechanical properties was made in the present work. A series of quantitative three-dimensional (3-D) phase-field simulations of microstructure evolution in Ni-Al alloys during the precipitation process were first performed using MICRESS (MICRostructure Evolution Simulation Software) package developed in the formalism of the multi-phase field model. The coupling to CALPHAD (CALculation of PHAse Diagram) thermodynamic and atomic mobility databases was realized via TQ interface. Moreover, the temperature-dependent lattice misfits and elastic constants were utilized for simulation. The effect of the alloy composition and aging temperature on microstructure evolution was extensively studied with the aid of statistical analysis. After that, an evaluation function was proposed for evaluating the optimal heat treatment schedule by choosing the phase fraction, grain size, and shape factor of γ′ precipitate as the evaluation indicators. Based on 50 groups of phase-field-simulated and experimental microstructure information, as well as the proposed evaluation function, the optimal alloy composition, aging temperature, and aging time for binary Ni-Al alloy with optimal mechanical properties were finally chosen. The successful application in the present Ni-Al alloys indicates that it is possible to design the optimal alloy composition and heat treatment for other binary and even multicomponent alloys with optimal mechanical properties based on the evaluation function and the sufficient microstructure information. Additionally, the combination of the present method and the key experiments can definitely accelerate the material design and improve the efficiency and accuracy.

Mg合金のGPゾーン硬化に対するフェーズフィールド組織特性解析

Mg合金のGPゾーン硬化に対するフェーズフィールド組織特性解析

GPU-accelerated phase-field simulation of dendritic solidification in a binary alloy

The phase-field simulation for dendritic solidification of a binary alloy has been accelerated by using a graphic processing unit (GPU). To perform the phase-field simulation of the alloy solidification on GPU, a program code was developed with computer unified device architecture (CUDA). In this paper, the implementation technique of the phase-field model on GPU is presented. Also, we evaluated the acceleration performance of the three-dimensional solidification simulation by using a single NVIDIA TESLA C1060 GPU and the developed program code. The results showed that the GPU calculation for 5763 computational grids achieved the performance of 170 GFLOPS by utilizing the shared memory as a software-managed cache. Furthermore, it can be demonstrated that the computation with the GPU is 100 times faster than that with a single CPU core. From the obtained results, we confirmed the feasibility of realizing a real-time full three-dimensional phase-field simulation of microstructure evolution on a personal desktop computer.

Phase-field simulation of microstructure evolution during the initial stage of rapid solidification of alloys

Microstructure evolution during the rapid solidification of Fe-C alloys is simulated using the phase-field model for binary alloys with thin interface limit parameters. The heat transfer equation is solved simultaneously to study the heat flow and the effect of latent heat generation on the microstructure. The calculations have been carried out using a double grid method and parallel computing technique. The competitive growth of growing cells was reproduced, and the cellular/dendritic transition was also observed. Since there is a negative thermal gradient in front of the leading tip, growth can be regarded as unidirectional free dendrite growth. The microstructure changes depending on the preferred growth orientation and the secondary arms start developing only on one side with the increase of the tilted angle. With the two-dimensional heat diffusion effect, negative thermal gradient appears on both the solid and liquid side of the leading tip.