Multicomponent Phase-field Model Research Articles

Phase-field approach assisted solution heat treatment efficient design for novel multicomponent Co-based superalloys

Fast homogenization without incipient melting is the key to designing solution heat treatment (SHT) process for single crystal superalloys. In this paper, a multicomponent phase-field model coupled with solidus temperature is developed for dynamically tracking incipient melting temperature, TIM, of alloy during SHT. The simulation process runs completely automatically only by inputting the composition information of as-cast specimen. Based on the obtained TIM-time profile, the holding temperature and the time of SHT are determined. Applying this approach to Co–30Ni–11Al–4W–1Ta–4Ti–5Cr single crystal specimen, a gradual increased TIM from 1247 °C to 1293 °C within 72,000 s is obtained, and thus a stepwise SHT process with a short time of less than 20 h is designed. The experimental verification shows that after SHT, the segregation coefficient of the slowest diffusing element W decreased from more than 2 to 1.065, the content of harmful secondary phase has decreased to below 0.1%, and no incipient melting occurs.

A phase field methodology for simulating the microstructure evolution during laser powder bed fusion in-situ alloying process

A recently-developed [1] multi-component phase field model has been utilized to investigate microstructure evolution during in-situ alloying of a blended elemental Ti-1Al-8V-5Fe alloy powder via the Laser Powder Bed Fusion process. The process of in-situ alloying, where elemental powder is used instead of pre-alloyed powder, was studied by performing two simulations having: (1) a uniform initial composition, and (2) a spatially varying initial composition to represent different powder particles. Specifically, the grain morphology, solute distribution, competitive growth and nucleation under the two different scenarios were simulated and compared. To assist the microstructure simulations, a macro-scale finite element model was developed to simulate the heat transfer during LPBF process. The thermal history data calculated by the finite element model was provided to the phase field model in order to simulate transient dendritic growth behaviour. The results show that a set of evenly-spaced columnar dendrites form in the uniform initial composition case, whereas when the initial composition is spatially varying, non-uniform dendrites having elongated shape can develop. It is also shown that competitive growth between dendrites is influenced by nucleation. For the spatially varying initial composition case, the results indicate that full alloying is difficult to achieve during the LPBF printing process; this incomplete alloying greatly influences the dendrite morphology and solute distribution.

Phase-field investigation on the peritectic transition in Fe-C system

We adopt a thermodynamically consistent multi-phase, multi-component phase-field model to investigate the morphological evolution of peritectic transition in carbon steel though 2-D and 3-D simulations. By using phase-field method, we rationalize the peritectic solidification in both 2-D and 3-D simulations under different liquid supersaturations as well as on the δ particle with distinct microstructures. Through the comparison between 2-D and 3-D simulation results, we clarify the reason for the different growth rate of γ phase in two and three dimensions. In 3-D simulation, we observe the unequal growth rate of γ phase in radial and axis directions. In addition, a novel measurement method is proposed to determine the dynamic contact angle. We anticipate that the simulation results can be applied to interpret the isothermal peritectic transition with a liquid supersaturation in alloys.

Phase-Field Investigation on the Peritectic Transition in Fe-C System

We adopt a thermodynamically consistent multi-phase, multi-component phase-field model to investigate the morphological evolution of peritectic transition in carbon steel though 2-D and 3-D simulations. By using phase-field method, we rationalize the peritectic solidification in both 2-D and 3-D simulations under different liquid supersaturations as well as on the δ particle with distinct microstructures. Through the comparison between 2-D and 3-D simulation results, we clarify the reason for the different growth rate of γ phase in two and three dimensions. In 3-D simulation, we observe the unequal growth rate of γ phase in radial and axis directions. In addition, a novel measurement method is proposed to determine the dynamic contact angle. We anticipate that the simulation results can be applied to interpret the isothermal peritectic transition with a liquid supersaturation in alloys.

Grand-potential based phase-field model for systems with interstitial sites

Existing grand-potential based multicomponent phase-field model is extended to handle systems with interstitial sublattice. This is achieved by treating the concentration of alloying elements in site-fraction. Correspondingly, the chemical species are distinguished based on their lattice positions, and their mode of diffusion, interstitial or substitutional, is appropriately realised. An approach to incorporate quantitative driving-force, through parabolic approximation of CALPHAD data, is introduced. By modelling austenite decomposition in ternary Fe–C–Mn, albeit in a representative microstructure, the ability of the current formalism to handle phases with interstitial components, and to distinguish interstitial diffusion from substitutional in grand-potential framework is elucidated. Furthermore, phase transformation under paraequilibrium is modelled to demonstrate the limitation of adopting mole-fraction based formulation to treat multicomponent systems.

Experimental and modelling studies for solidification of undercooled Ni-Fe-Si alloys.

We present experimental results, analytical calculations and phase-field simulations for undercooled Ni-Fe-Si alloy system. Undercooling experiments are performed using flux encapsulation along with in situ measurement of recalescence speed using a high-speed camera followed by microstructural characterization. Dendrite growth calculations are performed using a modified Boettinger, Coriell and Trivedi theory to incorporate constitutional undercooling due to multiple segregating elements and a modified kinetic undercooling term. Phase-field simulations are performed using a multi-component phase-field model to generate dendrites in this alloy. High growth velocities are observed and the analytical calculations are in good agreement with experiments. The microstructure evolution from the phase-field simulations indicates that there is a difference in solute segregation during growth of dendrites. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.

Microstructure Evolution of Binary and Multicomponent Manganese Steels During Selective Laser Melting: Phase-Field Modeling and Experimental Validation

In additive manufacturing processes, solidification velocities are extremely high in comparison to ordinary directional solidification. Therefore, the dependencies of the primary dendrite arm spacing (PDAS) on the process parameters deviate from the dependencies predicted by standard analytical methods. In this work, we investigate the microstructure evolution and element distribution in Fe-18.9Mn and Fe-18.5Mn-Al-C alloys solidified during the selective laser melting process. A quantitative multicomponent phase-field model verified by Green-function calculations (Karma, Rappel: Phys. Rev. E, 1998, 57, 4323) and the convergence analysis is used. The resulting non-standard dependencies of the PDAS on the process parameters in a wide range of solidification velocities are compared with analytical calculations. It is shown that the numerical values of the PDAS are similar to the values predicted by the Kurz–Fisher method for the low and intermediate solidification velocities and are smaller for the solidification velocities higher than 0.03 m/s. The PDAS and the Mn distribution in a Fe-18.5Mn-Al-C alloy are compared to the experimental results and a very good agreement is found.

GPU-accelerated three-dimensional large-scale simulation of dendrite growth for Ti6Al4V alloy based on multi-component phase-field model

Ti6Al4V is one of the most widely used ternary alloys in additive manufacturing. Its mechanical properties are highly determined by the prior β phase. However, simulation of the ternary alloy solidified microstructure is limited for the lack of available methods. In this study, we carried out two-dimensional (2D) and three-dimensional (3D) simulations based on a new multi-component (MC) phase-field (PF) model by extending Karma’s binary PF theory. The correctness and accuracy of the MC model are validated by the Gibbs-Thomson relation at dendrite tip. With the equipment multiple GPUs, the highest speedup ratio more than 150 is obtained compared with serial programming running on one of the top CPUs and simulations with billion nodes can be completed within acceptable time. Using this model as benchmark, previous Ti6Al4V dendrite evolution using pseudo-binary PF model is investigated and found magnifying the driving force and growth artificially. 3D large-scale directional solidification simulations also shed light on dendrite merging which leads coarse primary dendrites. We believe that the GPU-accelerated MC PF framework provides an accurate and efficient insight in understanding the solidifying evolution for Ti6Al4V.

A method of integrating CALPHAD data into phase-field models using an approximated minimiser applied to intermetallic layer growth in the Al-Mg system

This article describes an approach to combine single phase thermodynamic potentials into a multiphase composite potential suitable for integration in a multicomponent phase-field model. The composite potential avoids implicit interfacial energy contributions by starting from a grand potential formulation. The method is made explicit by expanding the minimiser resulting from the Legendre transform between grand and Helmholtz potentials about a known equilibrium state. The resulting composite function is explicit, reproduces the equilibrium states exactly, and is smooth such that it can be differentiated to provide the driving forces for mass transport and phase change in a thermodynamically self-consistent manner. The model is demonstrated by simulating a sequence of phase transformations for intermetallic growth in Al-Mg interdiffusion for advanced nuclear research reactor fuel.

Phase-Field Modeling of Sigma-Phase Precipitation in 25Cr7Ni4Mo Duplex Stainless Steel

Phase-field modeling is used to simulate the formation of sigma phase in a model alloy mimicking a commercial super duplex stainless steel (SDSS) alloy, in order to study precipitation and growth of sigma phase under linear continuous cooling. The so-called Warren–Boettinger–McFadden (WBM) model is used to build the basis of the multiphase and multicomponent phase-field model. The thermodynamic inconsistency at the multiple junctions associated with the multiphase formulation of the WBM model is resolved by means of a numerical Cut-off algorithm. To make realistic simulations, all the kinetic and the thermodynamic quantities are derived from the CALPHAD databases at each numerical time step, using Thermo-Calc and TQ-Interface. The credibility of the phase-field model is verified by comparing the results from the phase-field simulations with the corresponding DICTRA simulations and also with the empirical data. 2D phase-field simulations are performed for three different cooling rates in two different initial microstructures. A simple model for the nucleation of sigma phase is also implemented in the first case. Simulation results show that the precipitation of sigma phase is characterized by the accumulation of Cr and Mo at the austenite-ferrite and the ferrite-ferrite boundaries. Moreover, it is observed that a slow cooling rate promotes the growth of sigma phase, while a higher cooling rate restricts it, eventually preserving the duplex structure in the SDSS alloy. Results from the phase-field simulations are also compared quantitatively with the experiments, performed on a commercial 2507 SDSS alloy. It is found that overall, the predicted morphological features of the transformation and the composition profiles show good conformity with the empirical data.

A phase-field model for interphase precipitation in V-micro-alloyed structural steels

A multi-component phase field model was developed based on CALPHAD method and directly coupled with the CALPHAD thermodynamic database using a four-sublattice model. Interphase carbide precipitation at the γ/α interface is simulated and the predictions are tested against reported experimental results for a medium carbon, vanadium micro-alloyed steel during an isothermal γ→α+MC transformation at 973K. The model is found to be able to accurately predict: interphase precipitate composition, morphology and size of the precipitates. Furthermore, the tip-to-tip pairing of interphase precipitates in γ/α interphase boundaries is elucidated and found to be attributable to the minimisation of interfacial energy.

Preliminary investigation of using a multi-component phase field model to evaluate microstructure of asphalt binders

Asphalt mixtures are engineered and designed by treating the mixture as a two-component composite of the binder and mineral aggregate. Typically, asphalt binder is regarded as a homogeneous ‘glue’ that binds the mineral aggregates. However, there is a strong body of evidence in the literature spanning over five decades that indicates that the asphalt binder can be modelled as a colloid with a distinct microstructure. The introduction of advanced microscopic techniques such as Atomic Force Microscopy has generated a renewed interest in being able to better understand the relationship between the chemical makeup of the asphalt binder, its microstructure and engineering properties. The objective of this paper is to present a preliminary phase field model that was used to model the evolution of microstructure of a mixture comprising four fractions with different polarities, analogous to that of the asphalt binder. This work extends the concepts developed in previous research studies to explain the evolution of damage and self-healing at a micrometre length scale in asphalt binders. Although the model and parameters presented in this paper are not a definitive description of the microstructure evolution in asphalt binders, results show that with additional work on rigorous parameter estimation this methodology can be used as a reasonable approach to better understand the relationship between binder composition and microstructure evolution.

Multicomponent phase-field model for extremely large partition coefficients

We develop a multicomponent phase-field model specially formulated to robustly simulate concentration variations from molar to atomic magnitudes across an interface, i.e., partition coefficients in excess of 10±23 such as may be the case with species which are predominant in one phase and insoluble in the other. Substitutional interdiffusion on a normal lattice and concurrent interstitial diffusion are included. The composition in the interface follows the approach of Kim, Kim, and Suzuki [Phys. Rev. E 60, 7186 (1999)] and is compared to that of Wheeler, Boettinger, and McFadden [Phys. Rev. A 45, 7424 (1992)] in the context of large partitioning. The model successfully reproduces analytical solutions for binary diffusion couples and solute trapping for the demonstrated cases of extremely large partitioning.

Growth morphologies in peritectic solidification of Fe–C: A phase-field study

We use a thermodynamically consistent multi-phase, multi-component phase-field model, where the evolution equations for the different fields are derived from an entropy functional, for simulating peritectic growth structures in two and three dimensions. Different solidification morphologies are obtained in the computations and the characteristic properties of the growth forms are discussed. The phase-field method allows for a prediction of the surface energies in the three-phase system δ-ferrite, γ-austenite and liquid based on comparison between experimentally observed and simulated structures. Additionally an investigation of possible nucleation sites in evolving domains is presented and its dependence on the solid–solid surface energy is examined.

A metallic glass composite: Phase-field simulations and experimental analysis of microstructure evolution

The growth process of a crystalline dendritic solid phase from an undercooled melt in the metallic glass composite Zr Ti Nb Ni Cu Be is analyzed by experimental investigations and by adaptive finite element simulations based on a multicomponent phase-field model. The phase transition: L ( liquid ) → S ( dendrite ) + M ( matrix ) can be described by considering a pseudo-ternary system of late transition metals A = (Zr, Ti, Nb), of early transition metals B = (Ni, Cu) and of the component C = (Be). Scanning and transmission electron microscopy are employed to experimentally determine structural properties of the two-phase system and to provide concentration distributions of the components across the dendrite/matrix interface. The computed and experimentally observed microstructures, length scales and chemical compositions are in good agreement.

Transient eutectic solidification in In–Bi–Sn: Two-dimensional experiments and numerical simulation

A technique widely used for the in situ observation of microstructure formation in transparent organic systems was applied to metallic alloys with low melting temperature. In the ternary eutectic alloy system In–Bi–Sn, we observed by light microscopy steady state and transient eutectic microstructure formation during unidirectional solidification in thin (5–10 μm) glass capillaries. Starting from an equilibrated planar single-phase front in a slightly off-eutectic alloy we studied the dynamic processes like nucleation of univariant, and finally invariant ternary eutectic when the liquid transforms into three distinct solid phases. Numerical microstructure simulation was performed by applying a general multiphase and multi-component phase field model which couples directly to the complete thermodynamic dataset of the In–Bi–Sn alloy system. Via comparison of the experimental to the simulated data some thermo-physical values like diffusion coefficients and critical undercooling for nucleation have been evaluated.

Dendritic to Globular Morphology Transition in Ternary Alloy Solidification

The evolution of solidification microstructures in ternary metallic alloys is investigated by adaptive finite element simulations of a general multicomponent phase-field model. A morphological transition from dendritic to globular growth is found by varying the alloy composition at a fixed undercooling. The dependence of the growth velocity and of the impurity segregation in the solid phase on the composition is analyzed and indicates a smooth type of transition between the dendritic and globular growth structures.