Microscopic Phase-field Model Research Articles

Multiscale modelling of microstructure evolution, and local solidification behaviours of the AlSi10Mg build component in laser powder bed fusion process

Laser powder bed fusion (L-PBF) process is an additive manufacturing process, in which rapid heating and cooling takes place. The microstructure and the solidification behaviour of L-PBF components have significant impacts on their mechanical properties. The solidification takes place in a very short duration which is difficult to capture experimentally, therefore the finite-element (FE) simulation is the best feasible solution. In this paper, to study the evolution of the AlSi10Mg alloy’s microstructure during the L-PBF process, a model composed of macroscopic finite element (FE) model and microscopic phase field (PF) model was built. This model is suitable to predict a more realistic thermal behaviour involving the possible physical phenomena and the thermal behaviour for various heat inputs was calculated. The PF model was then updated with these results in order to simulate the chemical compositions’ concentration field and solidified microstructure. According to the simulation’s results, the primary dendrite arm spacing (PDAS) is significantly influenced by the laser line energy. To validate the FE model along with the Phase field (PF) model, the results were compared with the analytical and experimental findings; and the FE model and PF results exhibited good agreement with the experimental results. Additionally, the solute distribution analysis demonstrated that during the solidification process, micro-segregation developed and the process parameters affected the micro-segregation. Finally, the specimens were subjected to metallographic and element distribution analyses using an energy-dispersive spectrometer (EDS) to compare the results with those from the PF simulation and establish the relationship between the process parameters.

Microstructure and Solute Concentration Analysis of Epitaxial Growth during Wire and Arc Additive Manufacturing of Aluminum Alloy

Microstructure and solute distribution have a significant impact on the mechanical properties of wire and arc additive manufacturing (WAAM) deposits. In this study, a multiscale model, consisting of a macroscopic finite element (FE) model and a microscopic phase field (PF) model, was used to predict the 2319 Al alloy microstructure evolution with epitaxial growth. Temperature fields, and the corresponding temperature gradient under the selected process parameters, were calculated by the FE model. Based on the results of macroscopic thermal simulation on the WAAM process, a PF model with a misorientation angle was employed to simulate the microstructure and competitive behaviors under the effect of epitaxial growth of grains. The dendrites with high misorientation angles experienced competitive growth and tended to be eliminated in the solidification process. The inclined dendrites are commonly hindered by other grains in front of the dendrite tip. Moreover, the solute enrichment near the solid/liquid interface reduced the driving force of solidification. The inclined angle of dendrites increased with the misorientation angle, and the solute distributions near the interface had similar patterns, but various concentrations, with different misorientation angles. Finally, metallographic experiments were conducted on the WAAM specimen to validate the morphology and size of the dendrites, and electron backscattered diffraction was used to indicate the preferred orientation of grains near the fusion line, proving the existence of epitaxial growth.

Dependency of grain boundary dislocation network configuration on generalized stacking fault energy surface in FCC metals

We use a microscopic phase-field (MPF) model, incorporating the generalized stacking fault energy (GSFE) surfaces (i.e., the γ-surface) as inputs, to investigate systematically the evolution of dislocation network configurations at low-angle pure twist grain boundaries (GBs) in six face-centered cubic (FCC) metals (Ag, Cu, Rh, Ir, Pd and Pt) that have different GSFE surfaces. The equilibrium configurations of GB dislocation networks are obtained via the interplay between the crystalline energy and the elastic strain energy during the energy minimization process. It was found that for {111} twist GBs, though the geometrically necessary dislocations (GNDs) of the screw type are observed, they can be either full or partial ones depending on the GSFE surfaces of the above metal systems. The areas of the staking faults regions formed between partial dislocations are quantitatively characterized as a function of the magnitude of the stacking fault energy, the elastic modulus and the GB misorientation angle. A fast-acting model for predicting the geometric characteristics of the GB dislocation networks is developed based directly on the material properties and GB misorientation, which is validated by its applications to another two metal systems (Au and Ni) with the same GB.

Microscopic Phase-Field Simulation of γ′ Precipitation in Ni-Based Binary Alloys Coupled with CALPHAD Method

In the present work, the first (1st) and second (2nd) nearest-neighbor interaction energies are calculated by coupling the microscopic phase-field kinetic model with the calculation of phase diagrams (CALPHAD) method. The morphological evolution of the γ′ precipitate and the variation of its atomic ordering parameter for Ni–X (X = Al, Fe, Mn, Pt, or Si) alloys during aging are studied. The simulation results predict different occupation preferences for solute and solvent atoms in the γ′ phase, i.e., solute atoms are inclined to occupy the corner sites and solvent atoms tend to occupy the face sites. In order to understand the precipitation process of the γ′ phase systematically, the ordering and clustering behaviors of solute atoms are analyzed.

Mathematical modelling of permeability reduction in porous media caused by CO2 hydrate formation using microscopic phase-field model simulations

Mathematical modelling of permeability reduction in porous media caused by CO2 hydrate formation using microscopic phase-field model simulations

Modelling and experimental observation of the deposition geometry and microstructure evolution of aluminum alloy fabricated by wire-arc additive manufacturing

In this paper, a model composed of a macroscopic finite element (FE) model coupled with a microscopic phase field (PF) model was constructed to investigate the Al alloy microstructure evolution during wire arc additive manufacturing (WAAM). First, the relationships between single layer process parameters and the resulting deposition geometries (width and height) were investigated. A three-dimensional FE model was built to calculate the thermal distribution and temperature gradient under different process parameters. These results were then fed into a PF model to obtain the microstructure corresponding to each set of process parameters. A bridge was constructed by this method, starting from the WAAM process parameters and yielding the microstructure throughout solidification. The simulated results showed that the primary dendrite arm spacing (PDAS) decreased slightly with current increases, but the substrate moving speed had a more obvious impact on PDAS, which rose significantly with increased substrate speed. Finally, metallographic examination and energy dispersive spectroscopy tests were conducted on specimens fabricated by WAAM with different process parameters, to verify the simulated PF results. The simulated morphology and size of dendrites were in good agreement with experimental results.

Stress-dependence of dislocation dissociation, nucleation and annihilation in elastically anisotropic Cu

Dislocation dynamics under external stresses are an important manifestation of plastic behaviors of materials. In this study, based on the work of Shen et al. (2014), an improved microscopic phase field (MPF) model incorporating gradient energy term into the energy functional is developed to thoroughly investigate the stress dependence of whole dislocation evolution processes, including dislocation dissociation, nucleation, and annihilation in Cu with prominent elastic anisotropy. Necessary physical parameters such as elastic constants, lattice energy and gradient energy coefficients are all determined by atomistic molecular statics (MS) simulations. The residue theorem is utilized to accurately solve the anisotropic stress kernels as pre-factors characterizing the long-range elastic interaction produced by edge and screw components of mixed dislocations in anisotropic Cu. The Peierls stress of screw dislocations and stacking fault width under applied stress are evaluated by the MPF model and compared with those assessed by the semi-discrete variational Peierls-Nabarro (SVPN) model and MS simulations. The MPF model is then applied to screw dislocation dipoles and dislocation loops to examine possible dislocation evolution paths under different stress states. Through systematic simulations, we find the dislocation evolution regimes are closely related with the applied stress, and can be distinguished by three important critical stresses, i.e., critical stress, singular stress, and nucleation stress. Specifically, when the applied stress is less than the critical stress, the dislocation loops always collapse in the end, and do not depend on the final states of Shockley partials, which may exist or have annihilated. Furthermore, when the applied stress exceeds the nucleation stress, partial dislocations will spontaneously nucleate within stacking fault (SF) area, followed by a series of dislocation reactions until partial dislocations bρ1 and bρ3 are left in the end. Besides, the shear stress components perpendicular to the Escaig stress in slip plane are found to suppress the nucleation of partial dislocations in SF area.

Multiscale modelling of microstructure, micro-segregation, and local mechanical properties of Al-Cu alloys in wire and arc additive manufacturing

Abstract Wire and Arc Additive Manufacturing (WAAM) is a combination of welding and AM technologies and uses an electric arc as the heat source to melt welding wire. The mechanical properties of WAAM components are greatly dependent on the solidification behavior and microstructure. In this paper, a model composed of a macroscopic finite element (FE) model combined with a microscopic phase field (PF) model was constructed to investigate the Al alloy microstructure evolution during WAAM. First, the FE model was implemented to calculate the temperature gradient and solidification speed under different processing parameters. These results were then fed into the PF model to simulate the microstructure and concentration field of chemical compositions. The simulated results indicate that the moving speed of the substrate has a pronounced impact on the primary dendrite arm spacing (PDAS), which grew significantly as the moving speed increased, while the PDAS decreased slightly upon increasing the electric current. Furthermore, the solute distribution analysis showed that micro-segregation formed during the solidification process, and that current and substrate speed had evident impact on the micro-segregation ratio. Finally, metallographic experiments, energy-dispersive spectrometer analysis for element distribution, and miniature tensile tests were conducted on the specimens to validate the PF simulated results and obtain the relationship between process parameters and mechanical properties.

Atomic-scale characterization of the site occupancies in the B2 FeAl phase: Effects of Ni addition, temperature and lattice misfit

A microscopic phase-field model is constructed to study the influences of Ni addition, temperature and lattice misfit on the site occupancies in complex B2 FeAl–Ni intermetallic phase. The tendencies of six site occupancies are explored through tracing the atomic site occupation probability. The results reveal that six site occupancies are monotone functions of Ni concentration, temperature and the lattice misfit, respectively. For the antisite behavior of Fe (AlFe), Al (FeAl) and the substitution behavior of Ni (AlNi, FeNi), the ranks of four defect occupancies are identical under three factors. The transformation rate and ordering degree of the complex FeAl–Ni are dependent of three factors. The mechanism of configuration of six site occupancies is revealed from the energy analysis. The results are in accordance with experimental and theoretical data and provide theoretical support to the questioned validity of the lattice misfit effect on the ordering behavior in intermetallics.

Precipitation Sequence of Middle Al Concentration Alloy Using the Inversion Algorithm and Microscopic Phase Field Model

Precipitation Sequence of Middle Al Concentration Alloy Using the Inversion Algorithm and Microscopic Phase Field Model

Predicting grain boundary structure and energy in BCC metals by integrated atomistic and phase-field modeling

We predict structure and energy of low-angle (11¯0) pure twist grain boundaries (GBs) in five BCC transition metals (β-titanium, molybdenum, niobium, tungsten, and tantalum) using a combination of atomistic and microscopic phase-field (MPF) modeling. The MPF model takes as inputs solely the generalized stacking fault energy surfaces (i.e., the γ-surface) and elastic constants obtained from the atomistic simulations. Being an energy-based method, the MPF model lifts the degeneracy of the geometric models in predicting GB structures. For example, the multiple indefinite solutions offered by the Frank-Bilby equation are shown to converge to exactly the same equilibrium structure. It predicts a transition of the equilibrium GB structure from a pure screw hexagonal network (Mo and W) to mixed hexagonal networks (Nb and Ta) to a rhombus network (β-Ti) of dislocations. Parametric simulation studies and detailed analyses of the underlying dislocation reactions that are responsible for the formation of the rhombus and hexagonal structures reveal a close correlation between material properties (including the elastic anisotropic ratio and the local curvature on the γ-surface) and the GB structure and energy in BCC metals. This integrated approach allows one to explore, through high throughput calculations, the potential to tailor the structure and energy of special GBs in BCC metals by alloying.

Microscopic Phase-field Simulation for the Influence of Aging Process on the Precipitation Process of Ni75Al15Ti10 Alloy

The precipitation process of Ni75Al15Ti10 alloy was simulated by a microscopic phase-field kinetics model. The microscopic morphology evolution was studied, which indicates that the precipitation process can be divided into two stages: the first is the transformation from L10 phase to L12 phase, and the second is the formation of the stoichiometric L12 phase. The effect of single aging temperature on the microstructure, atomic occupation probability and atomic diffusion was investigated. The result shows that the shape of γ′ precipitates transforms from irregular shape to regular cuboid and the degree of orientation growth increases with increasing aging temperature. But the higher the aging temperature, the lower the occupation probability and the order degree. Meanwhile, the path of diffusion of Al atom is from the interface of the γ′ phase to the internal, and the diffusion of Ti atom is the opposite. Furthermore, we studied the dual aging to improve occupation probability of γ′ precipitates and to discuss their influence on the γ′ phase. Dual aging can not only obtain a stable γ′ phase with regular shape, but also increase the occupation probability of Al and Ti and inhibit the formation of anti-site defects.

Inversion Calculation of the Interatomic Potentials for Ni0.75AlxMo0.25–x Alloy Employing Microscopic Phase-Field Model

Based on microscopic phase field theory, the interatomic potentials of Ni3Al (L1(2) structure) and Ni3Mo (DO22 structure) was calculated employing the inversion calculation method, and their dependence on temperature and concentration are also studied. The inversion calculation results demonstrate that the first nearest neighbor interatomic potentials (WNi-Al and WNi-Mo) increase linearly with the temperature increasing continuously. WNi-Al increases but WNi-Mo decreases linearly with the continuous increase of Al concentration, and vice versa. Substituting the inversion calculated WNi-Al and WNi-Mo at 973 K into the microscopic phase-field kinetics model, the atomic temporal evolution pictures of phase transformation process are similar to the results obtained by empirical interatomic potentials. In addition, the precipitated gamma' phase has a higher ordered degree, which is more consistent with the actual microstructure evolution of phase transformation process than the calculated results reported in previous studies using empirical interatomic potentials.

Quantitative determination of anti-structured defects applied to alloys of a wide chemical range**Project supported by the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2016JQ5014), the Fundamental Research Funds for the Central Universities, China (Grant No. 3102014JCQ01024), the Research Fund of the State Key Laboratory of Solidification Processing (NWPU), China (Grant No. 114-QP-2014), the Specialized Research

Anti-structured defects bridge atom migration among heterogeneous sublattices facilitating diffusion but could also result in the collapse of ordered structure. Component distribution Ni75AlxV25−x alloys are investigated using a microscopic phase field model to illuminate relations between anti-structured defects and composition, precipitate order, precipitate type, and phase stability. The Ni75AlxV25−x alloys undergo single Ni3V (stage I), dual Ni3Al and Ni3V (stage II with Ni3V prior; and stage III with Ni3Al prior), and single Ni3Al (stage IV) with enhanced aluminum level. For Ni3V phase, anti-structured defects (VNi1, NiV, except VNi2) and substitution defects (AlNi1, AlNi2, AlV) exhibit a positive correlation to aluminum in stage I, the positive trend becomes to negative correlation or smooth during stage II. For Ni3Al phase, anti-structured defects (AlNi, NiAl) and substitution defects (VNi, VAl) have a positive correlation to aluminum in stage II, but NiAl goes down since stage III and lasts to stage IV. VNi and VAl fluctuate when Ni3Al precipitates prior, but go down drastically in stage IV. Precipitate type conversion of single Ni3V/dual (Ni3V+Ni3Al) affects Ni3V defects, while dual (Ni3V+Ni3Al)/single Ni3Al has little effect on Ni3Al defects. Precipitate order swap occurred in the dual phase region affects on Ni3Al defects but not on Ni3V.

Microscopic Phase-Field Simulation for the Influence of Interatomic Potential on the Precipitation Process of Ni75Al14Mo11 Alloy

The process of γ′ phase precipitating from Ni75Al14Mo11 is studied by a computational simulation technique based on microscopic phase-field kinetics model. We studied the phase transformation with the purpose of clarifying the influence of the nearest interatomic potential V Ni–Al (the nearest interatomic potential) on the precipitation process of γ′ phase. The result demonstrates that there are two kinds of ordered phases, respective L10 and L12 in the early stage, and L10 phase transforms into L12 phase subsequently. For L12 phase, Ni atoms mainly occupy α site (face center positions), while Al and Mo atoms occupy β sites (the vertex positions). When V Ni–Al is increased by 10 MeV, the occupation probability of Ni atoms on α sites and Al atoms on β sites are enhanced. Enhanced V Ni–Al facilitates clustering and ordering of Al atom, which promotes the formation of the γ′ phase. At last, the simulation result was discussed by employing the thermodynamic stability.

Simulation of pre-precipitation in Ni75Al14Mo11 alloy by microscopic phase-field model

The early precipitation process of Ni75Al14Mo11 alloy was simulated by microscopic phase-field model at different temperatures. The microstructure of the alloy, the precipitation time of L10 structure and occupation probability of the three kinds of atoms were investigated. It is indicated that the non-stoichiometric L10 (I/II) phases are found in the precipitation process. With the temperature increasing, the appearance time of L10 is brought forward. The L10 (II) structure always precipitates earlier than the L10 (I) structure. Compared with lower temperature, higher temperature brings the formation time of L10 phase forward and makes L10 phase have a higher order degree. But lower temperature shortens the process time of the L10 phase to the L12 phase. Al and Mo atoms tend to occupy γ site, Ni atom tends to occupy α and β sites. At the same temperature, Al atom has stronger occupation ability than Mo atom in the same site. Ni, Al and Mo collectively form the composited L12 structure.

Site occupation evolution of alloying elements in Ni3V phase during phase transformation in Ni75Al4.2V20.8

Based on the microscopic phase-field model, the correlation between site occupation evolution of alloying elements in Ni3V-DO22 phase and growth of Ni3Al-L12 phase was studied during the phase transformation of Ni75Al4.2V20.8. The results demonstrate that the growth of L12 phase can be divided into two stages: at the early stage, the composition of alloying elements in DO22 phase almost remains unchanged; at the late stage, the compositions of Ni and Al decrease while V increases in DO22 phase. Part of alloying elements for L12 phase growth are supplied from the site occupation evolution of alloying elements on three kinds of sublattices in DO22 phase. Ni is mainly supplied from V sublattice, and part of Al is supplied from Niı and V sites at the centre of DO22 phase. The excessive V from the decreasing DO22 phase migrates into the centre of DO22 phase and mainly occupies V and NiII sites. It is the site occupation evolution of antisite atoms and ternary additions in DO22 phase that controls the growth rate of L12 phase at the late stage.

Phase-field study on competition precipitation process of Ni-Al-V alloy

With microscopic phase-field kinetic model, atomic-scale computer simulation program for the precipitation sequence and microstructure evolution of the ordered intermetallic compound γ' and θ in ternary Ni75AlxV25–x alloy were studied. The simulation results show that Al concentration has important effects on the precipitation sequence. When Al concentration in Ni75AlxV25–x alloy is low, θ(Ni3V) ordered phase will be firstly precipitated, followed by γ'(Ni3Al) ordered phase. With Al concentration increasing, θ and γ' ordered phases are simultaneously precipitated. With Al concentration further increasing, γ' ordered phase is firstly precipitated, followed by θ ordered phase. There is a competition relationship between θ and γ' ordered phases during growth and coarsening process. No matter which first precipitates, θ ordered phase always occupies advantage in the competition process of coarsening, thus, the microstructure with preferred orientation is formed.

Predicting structure and energy of dislocations and grain boundaries

A microscopic phase field (MPF) model is formulated to describe quantitatively the core structure and energy of dislocations using ab initio data as input. Based on phase field microelasticity theory implemented in the slip plane using Green’s function to describe the long-range elastic interaction, the MPF model is a three-dimensional generalization of the Peierls model. Using the same generalized stacking fault energy as input, the core structure and energy predicted for straight dislocations by the MPF model show complete agreement with those predicted by the Peierls model. The ability of the MPF model to treat dislocations of arbitrary configurations is demonstrated by calculating the structure and energy of a twist grain boundary in aluminum. After discrete lattice sampling a la Nabarro, the grain boundary energy manifests Read–Shockley behavior for low-angle boundaries as well as deep cusps for high-angle special boundaries, indicating a “Peierls torque friction” effect for grain boundaries that has the same physical origin as the Peierls lattice friction for dislocation cores.

Microscopic Phase Field Study on the Kinetics of Order-Disorder Transition of APDBs Formed between DO<sub>22</sub> Phases during Stress Aging

Kinetics of order-disorder transition at antiphase domain boundary (APDB) formed between DO22 (Ni3V) phases during stress aging was investigated using microscopic phase field model. The results demonstrated that whether order-disorder transition happens or not depends on the atomic structure of the APDB. Accompanied with the depletion of V and enrichment of Ni and Al, order-disorder transition happened at the APDB (001)//(002). Whereas at the APDB {100}·1⁄2[100], which remains ordered with temporal evolution, Ni and Al enrich and V depletes. Composition evolution of APDB with order-disorder transition favors the nucleation of the L12 and disordered phase. Some of the grains grew bigger while the others disappeared, accompanying the formation of disordered phase layer during order-disorder transition of APDBs, and the order-disorder transition of APDBs can be considered as accompanying process of coarsening of ordered domain phases and growth of disordered phases.