Multiphase Field Simulation Research Articles

Rate theory coupling multi-phase-field simulation for neutron irradiation nanophase and vacancy evolution

Radiation damage is a critical problem for the alloys serving under irradiation circumstances where the numerous defects is induced by the cascade collision of radiation particles, the microstructure and mechanical properties will be damaged by the irradiation. By combination of rate theory (RT) and multi-phase-field (MPF) model, the influences of neutron irradiation dose rate (DR) and irradiation temperature are studied on the radiation-enhanced precipitation, vacancies and interstitial atoms in Fe-35Cr-10Al (at.%) alloys. The RT coupled with phase-field simulations capture the radiation induced nanoscale precipitates, clustering of vacancies and interstitial atoms. With the increase of DR, the diffusion of solute atoms is accelerated for the generation of vacancies and interstitial atoms, and the growth and coarsening rate of α′ phase is quickened. The DR affects the distribution of elements between α/α′ phases, high DR promotes the Fe and Al to partition into α phase, Cr into α′ phase in the formation of α′ phase. Therefore, in the steady-state coarsening stage, the high DR leads to the α′ phase to reach the equilibrium composition earlier. As the increase of neutron irradiation temperature, the separation and coarsening rate of α′ phase are accelerated. The simulation morphology and quantitative characteristics are consistent with the experimental results. The coupling of RT and MPF simulation in alloys with point defects and nanophase under neutron irradiation put forward the study tactics and theory understanding for radiation-enhanced multiple microstructure evolutions.

Solute segregation in a rapidly solidified Hastelloy-X Ni-based superalloy during laser powder bed fusion investigated by phase-field and computational thermal-fluid dynamics simulations

Solute segregation significantly affects material properties and is a critical issue in the laser powder-bed fusion (LPBF) additive manufacturing (AM) of Ni-based superalloys. To the best of our knowledge, this is the first study to demonstrate a computational thermal-fluid dynamics (CtFD) simulation coupled multi-phase-field (MPF) simulation with a multicomponent-composition model of Ni-based superalloy to predict solute segregation under solidification conditions in LPBF. The MPF simulation of the Hastelloy-X superalloy reproduced the experimentally observed submicron-sized cell structure. Significant solute segregations were formed within interdendritic regions during solidification at high cooling rates of up to 1.6 × 106 K s−1, a characteristic feature of LPBF. Solute segregation caused a decrease in the solidus temperature (TS), with a reduction of up to 38.4 K, which increases the risk of liquation cracks during LPBF. In addition, the segregation triggers the formation of carbide phases, which increases the susceptibility to ductility dip cracking. Conversely, we found that the decrease in TS is suppressed at the melt-pool boundary regions, where re-remelting occurs during the stacking of the layer above. Controlling the re-remelting behavior is deemed to be crucial for designing crack-free alloys. Thus, we demonstrated that solute segregation at the various interfacial regions of Ni-based multicomponent alloys can be predicted by the conventional MPF simulation. The design of crack-free Ni-based superalloys can be expedited by MPF simulations of a broad range of element combinations and their concentrations in multicomponent Ni-based superalloys.

Evolution of microstructural heterogeneities in additively manufactured low-alloy steel

Understanding the complex phase transformations during additive manufacturing (AM) of low-alloy multi-phase steels is a necessary task to discover the mechanisms that lead to formation of AM-specific, heterogeneous microstructures. In the present study, investigations were carried out to gain fundamental insights on microstructure evolution of low-alloy steels during AM and upon post-AM heat-treatments. To this end, a low-alloy steel, with a composition similar to DP600 dual-phase (DP) steel, was processed by laser powder bed fusion (L-PBF). Subsequently, two post-L-PBF heat-treatments were applied to obtain ferritic-martensitic DP microstructures. The first heat-treatment consisted of austenitization followed by isothermal holding in ferrite (α)/austenite (γ) region (AIH), whereas the second comprised of inter-critical annealing (IC) in α/γ region. The as-built state exhibited a tempered martensitic microstructure with a weak (almost random) crystallographic texture in combination with compositional and morphological heterogeneities. Combination of multiphase-field simulation and multi-scale microstructure characterization revealed that the formation of compositional and morphological heterogeneities in as-built state was governed by consecutive liquid-solid (delta-ferrite (δ) → γ) and solid-solid (γ ↔ martensite (α΄)) phase-transformations. For both post-L-PBF heat-treatments, Mn-segregation bands that formed during L-PBF led to heterogeneous α΄ distribution after annealing. Electron microprobe analysis (EPMA) measurements revealed that the local Mn and C distributions were closely related to the spatial distribution of α and α΄. The AIH heat-treatment resulted in annihilation of morphological heterogeneities, namely coarse- and fine-grained clusters. The absence of austenitization in IC heat-treatment resulted in distribution of ferritic-martensitic DP microstructure in coarse- and fine-grained clusters that inherited the L-PBF specific grain morphology distribution. Lastly, the IC state showed overall best mechanical properties due to the conservation of the heterogenous clustered microstructure, which potentially aided to simultaneously obtain high tensile strength (890.9 MPa) and relatively high ductility (20.5 %).

Optimization of Pore Formation Process of Lotus Aluminum by Phase Field Simulation

Abstract We have used multi-phase field simulation to mimic the actual process of lotus aluminum production, i.e., unidirectional solidification of aluminum in a hydrogen atmosphere. We used PD control and PID control, conventional methods of feedback control, to control the pore width precisely in the simulation. The pore width was shown to decrease slowly in PID control due to the slow feedback of I-control, and PD control was shown to produce stable long pores, although the pore width became larger than the target pore width. The initial hydrogen concentration in the liquid, which was controlled by atmospheric hydrogen pressure, had a significant effect on the pore growth; the higher the hydrogen concentration, the thicker the pore width and vice versa. It was also clarified that the pore width and the elongation length of the pore took various values depending on the combination of PD parameters even if the same target value was set.

Multiphase field simulation of dynamic recrystallization during friction stir welding of AZ31 magnesium alloy

Multiphase field simulation of dynamic recrystallization during friction stir welding of AZ31 magnesium alloy

Effect of Rapid Heating and Cooling Conditions on Microstructure Formation in Powder Bed Fusion of Al-Si Hypoeutectic Alloy: A Phase-Field Study.

Al alloy parts fabricated by powder bed fusion (PBF) have attracted much attention because of the degrees of freedom in both shapes and mechanical properties. We previously reported that the Si regions in Al-Si alloy that remain after the rapid remelting process in PBF act as intrinsic heterogeneous nucleation sites during the subsequent resolidification. This suggests that the Si particles are crucial for a novel grain refinement strategy. To provide guidelines for grain refinement, the effects of solidification, remelting, and resolidification conditions on microstructures were investigated by multiphase-field simulation. We revealed that the resolidification microstructure is determined by the size and number of Si regions in the initial solidification microstructures and by the threshold size for the nucleation site, depending on the remelting and resolidification conditions. Furthermore, the most refined microstructure with the average grain size of 4.8 µm is predicted to be formed under conditions with a large temperature gradient of Gsol = 106 K/m in the initial solidification, a high heating rate of HR = 105 K/s in the remelting process, and a fast solidification rate of Rresol = 10−1 m/s in the resolidification process. Each of these conditions is necessary to be considered to control the microstructures of Al-Si alloys fabricated via PBF.

Multi phase-field simulation study on microstructural grain development during inductive-based friction surfacing of aluminium

The computational solution is considered an effective tool for the analysis and a good understanding of the complex microstructural development that occurs during friction surfacing. In this article, ABACUS software was used to create a 3D-FE model of friction surfaced layering of AA 6063 aluminium on EN8 carbon steel, and the heat and strain rate collected throughout the operation were utilised for a computational investigation of microstructural recrystallization and grain development. The Multi-phase Field model (MFM) and constructive material model (CMM) were used for the prediction of the grain development during the process. A decrease in the incubation period from 0.839 sec to 0.578 sec was seen before recrystallization, after a temperature rises from 100°C to 300°C for substrate preheating. Validation of the reliability model obtained from the computational study was done using the image received from electron backscattered diffraction (EBSD) for grain size development and distribution. An appropriate assessment has been made between computational and experimental images which shows the maximum error of less than 10%. The development of grain structure during recrystallization was impacted extensively for increasing the coating strength, which was seen as inversely proportional to the average coating's grain diameter.

Multi-phase field simulation of competitive grain growth for directional solidification

The multi-phase field model of grain competitive growth during directional solidification of alloy is established. Solving multi-phase field models for thin interface layer thickness conditions, the grain boundary evolution and grain elimination during the competitive growth of SCN-0.24-wt% camphor model alloy bi-crystals are investigated. The effects of different crystal orientations and pulling velocities on grain boundary microstructure evolution are quantitatively analyzed. The obtained results are shown below. In the competitive growth of convergent bi-crystals, when favorably oriented dendrites are in the same direction as the heat flow and the pulling speed is too large, the orientation angle of the bi-crystal from small to large size is the normal elimination phenomenon of the favorably oriented dendrite, blocking the unfavorably oriented dendrite, and the grain boundary is along the growth direction of the favorably oriented dendrite. When the pulling speed becomes small, the grain boundary shows the anomalous elimination phenomenon of the unfavorably oriented dendrite, eliminating the favorably oriented dendrite. In the process of competitive growth of divergent bi-crystal, when the growth direction of favorably oriented dendrites is the same as the heat flow direction and the orientation angle of unfavorably oriented grains is small, the frequency of new spindles of favorably oriented grains is significantly higher than that of unfavorably oriented grains, and as the orientation angle of unfavorably oriented dendrites becomes larger, the unfavorably oriented grains are more likely to have stable secondary dendritic arms, which in turn develop new primary dendritic arms to occupy the liquid phase grain boundary space, but the grain boundary direction is still parallel to favorably oriented dendrites. In addition, the tertiary dendritic arms on the developed secondary dendritic arms may also be blocked by the surrounding lateral branches from further developing into nascent main axes, this blocking of the tertiary dendritic arms has a random nature, which can have aninfluence on the generation of nascent primary main axes in the grain boundaries.

Multiphase-field simulation of grain coalescence behavior and its effects on solidification cracking susceptibility during welding of Al-Cu alloys

Solidification cracking (SC) is highly related to the grain coalescence behavior during welding of aluminum alloys. In this study, the grain coalescence behavior and its effects on solidification cracking susceptibility (SCS) were investigated using the multiphase-field approach. Why SCS is high at a certain value of Cu concentration and why SC often occurs at high misorientation angles are revealed. Firstly, nominal compositions of Cu affect the morphology of microstructure during solidification. The crystals morphology is cellular at the low concentration, while the crystals are dendritic at the high concentration in the columnar grain region. The SCS of cellular grains is higher than dendrites due to the high volume fraction of solid when the grains/subgrains bridge. Under the action of tensile stress, the scarce residual liquid phase cannot backfill in time. Secondly, high misorientation angles make grain boundary energy in the solid–solid interface (σSS) is high. It is found that σSS suppresses the grain coalescence and increases the SCS of alloys. This leads the emergence of SC at high misorientation angles during welding. In this study, the coalescence behavior of grains during solidification is visually presented by simulation and the coherency point at the last-stage solidification is achieved accurately.

On Ti6Al4V Microsegregation in Electron Beam Additive Manufacturing with Multiphase-Field Simulation Coupled with Thermodynamic Data

On Ti6Al4V Microsegregation in Electron Beam Additive Manufacturing with Multiphase-Field Simulation Coupled with Thermodynamic Data

フェーズフィールド法による Ni 基超合金付加製造における凝固偏析予測

フェーズフィールド法による Ni 基超合金付加製造における凝固偏析予測

Quantitative phase-field simulation of the entire solidification process in one hypereutectic Al–Si alloy considering the effect of latent heat

The multi-phase-field (MPF) model coupled with reliable CALPHAD thermodynamic/atomic mobility descriptions, appropriate faceted anisotropy and key experimental validation is employed to perform the quantitative simulation of the microstructure evolution of the hypereutectic Al-16 ​wt%Si alloy during solidification. By considering the effect of latent heat released during the eutectic phase transformation in the simulation, the appropriate entire solidification sequence is obtained. All the characteristics in the as-cast microstructure can be nicely reproduced, including the primary (Si) encircled by the second primary (Al) halo, and the coupled eutectic grains appearing at the Liquid/(Al) interface rather than Liquid/(Si) interface. Moreover, three types of growth patterns of eutectic (Si) with different lengths are distinguished according to the distance between primary (Si) and the nucleation position of eutectic (Si). Furthermore, the evaluated ratios of width to length for 50 eutectic (Si) grains due to the MPF simulation are in good agreement with the experimental data. The quantitative phase-field simulation of the entire solidification process of the hypereutectic Al-16 ​wt%Si alloy in the present work is anticipated to pave the way for revealing the grain refinement mechanism in hypereutectic Al–Si alloys in the future studies.

Multiphase-field simulation of the solution heat treatment process in a Ni-based superalloy

New generation of nickel based single crystal superalloy requires complex solution heat treatment (SHT) procedures to improve its high temperature performance. However, the designation of SHT is difficult due to severe segregation, significant fraction of eutectic, and undesired incipient melting. The multiphase-field simulation coupled with thermodynamic calculation was used to investigate microstructure evolution and element distribution from solidification to SHT process in a superalloy. The simulated solidified microstructure was used as input for subsequent SHT simulation. And the simulation results were verified by experimental measurements in terms of the γ/γ' eutectic fraction and microsegregation pattern in the as-cast state and during each step of SHT. Based on the simulated microstructure and concentration, the incipient melting temperature was obtained by thermodynamic calculation. The results show that the region with lowest melting temperature is located at the boundary between γ dendrite and interdendritic bulk γ' phase, which is last solidification region. And incipient melting temperature gradually increases during SHT. Besides, the variation of γ' phase fraction under different holding temperatures was simulated, and calculated γ' reduction rate increases significantly with the temperature. The current work has demonstrated the ability of multiphase-field simulation and thermodynamic calculation in designing SHT procedures for complex superalloys.

Multiphase-field simulation of austenite reversion in medium-Mn steels

Medium-Mn steels have attracted immense attention for automotive applications owing to their outstanding combination of high strength and superior ductility. This steel class is generally characterized by an ultrafine-grained duplex microstructure consisting of ferrite and a large amount of austenite. Such a unique microstructure is processed by intercritical annealing, where austenite reversion occurs in a fine martensitic matrix. In the present study, austenite reversion in a medium-Mn alloy was simulated by the multiphase-field approach using the commercial software MICRESS® coupled with the thermodynamic database TCFE8 and the kinetic database MOBFE2. In particular, a faceted anisotropy model was incorporated to replicate the lamellar morphology of reversed austenite. The simulated microstructural morphology and phase transformation kinetics (indicated by the amount of phase) concurred well with experimental observations by scanning electron microscopy and in situ synchrotron high-energy X-ray diffraction, respectively.

A comprehensive analysis of three-dimensional normal grain growth of pure iron via multi-phase field simulation

A three-dimensional (3D) multi-phase field model was established to simulate normal grain growth in pure iron. The advanced visualization technology was used to extract the related data for individual grains, which can clearly display the grain morphology with distinct grain boundary surface as well as the space distribution of neighboring grains?Based on the simulation results, the grain growth kinetics model was described, which is in conformity with Burke and Turnbull?s parabolic law. The phenomenon of a ?Hillert regime? in 3D grain growth and the topological transformation mechanism were investigated. The grain size distributions under different time evolution showed a good agreement with the Hillert distribution. The details of grain growth, especially grain size distribution and volume growth rate, were analyzed. The models of von Neumann-Mullins and Hilgensfeldt for predicting the volumetric growth rate were compared. The volumetric growth rate was approximately zero when the number of grain sides was close to 13.7. The multi-phase field simulation can be used to analyze the dynamic evolution of the topological relationship of grains and reveal the general law of normal grain growth quantitatively.

3D - Multi Phase-Field Simulation of Stress, Strain, and Concentration Field Due to Al 3X (X = Sc, Zr, Er) Particle Growth in Al Matrix

3D - Multi Phase-Field Simulation of Stress, Strain, and Concentration Field Due to Al ₃X (X = Sc, Zr, Er) Particle Growth in Al Matrix

Multi-phase field simulation of multi-grain peritectic transition in multiple phase transformation

Taking Fe-C binary alloy as an example, based on the multi-phase field model, the nucleation and growth of δ phase, peritectic reaction, peritectic transformation, and the growth of subsequent austenite are simulated. Effects of the nucleation site of austenite on the peritectic reaction rate and the starting time of the peritectic transformation were studied. The simulation results show that the γ phase, as a shell, surrounds the δ phase and grows rapidly when the peritectic reaction occurs between the dendritic δ grains, and a layer of γ phase shell is formed around δ phase after the peritectic reaction. After the δ phase is surrounded by γ phase completely, the membrane shell separates the L phase from the δ phase, so that the phase transfers from peritectic reaction to peritectic transformation. During the peritectic transformation, since the solute diffusion coefficient of the liquid phase is much greater than that of the solid phase, the average growth rate of austenite in the liquid phase is visibly higher than that of the δ phase. The peritectic reaction rate is related to the curvature of the nucleation site of the γ phase on the δ phase grains. The peritectic reaction rate at the large curvatures is faster than that at small curvatures.

Combining multi-phase field simulation with neural network analysis to unravel thermomigration accelerated growth behavior of Cu6Sn5 IMC at cold side Cu–Sn interface

In Pb-free solder alloys used in solder balls of diameter of 50 µm or smaller, larger proportion of Cu6Sn5 intermetallics formation is a major reliability concern, and this is aggravated in presence of external thermal gradient. A complete understanding of the mechanism for intermetallics compound (IMC) growth under thermomigration is essential for devising solder materials resistant to degradation under thermal gradient. This work integrates neural network analysis with multi-phase field method to quantify the mechanism of thermomigration at the cold side of a solder-substrate system. At hot side temperature of 523.15 K, 1D multi-phase field model is built for a combined driving force of bulk diffusion and thermomigration, and is solved using finite element method (FEM). The free energy density function for the thermomigration driving force is introduced, and coupled with the functions for bulk and interfacial free energy density of each phase. Data of heats of transport, temperature difference and growth rate constant of IMC are obtained from multiple FEM simulations, and the FEM-generated dataset is employed in the neural network. The machine learning predicted growth rate constant is tallied with experimental value, and heat of transport of Cu in IMC phase (QCuimc) is determined from the inverse method. The obtained value of optimized QCuimc is +35.10 kJ/mol. 2D IMC grain growth simulations are performed with hot-side at 523.15 K and the cold side lowered to 523.0817 K and 522.0 K respectively, thereby revealing that the accelerated grain growth for larger temperature difference is noticed within the first 20 s of the simulations.

Multiscale solidification simulation of Sr-modified Al-Si-Mg alloy in die casting

Thermomechanical casting simulations incorporating solidification models are widely applied to improve the dimensional accuracy of casting components. The solidification path is commonly described based on Scheil-Gulliver assumptions which however fail to describe the effect of Strontium in Sr-modified Al-Si-Mg casting alloys. Strontium, even in small amounts, strongly affects the solidification morphology of the Al-Si eutectic together with its growth undercooling and hence the fraction solid–temperature relation during later stages of solidification. In order to address this problem, a dedicated micro-macro simulation approach is proposed here. The macroscopic thermomechanical casting simulation is linked with a spatially resolved multi-phase field simulation of the microstructure. Due to the fine fibrous morphology of the Si eutectic, a two-level homogenization scheme was applied to derive the effective mechanical properties of the Al alloy during its solidification. The proposed multiscale simulation and homogenization approach was applied to a permanent mould casting using an axisymmetric bowl cast from A356 for experimental validation.

Micrometer-scale molecular dynamics simulation of microstructure formation linked with multi-phase-field simulation in same space scale

The micrometer-scale polycrystalline microstructure is directly obtained from a 10 billion atom molecular dynamics (MD) simulation of the nucleation and growth of crystals from an undercooled melt, which is performed on a graphics processing unit-rich supercomputer. The grain size distribution in the as-grown microstructure obtained from the MD simulation largely deviates from that resulting from steady-state growth in ideal grain growth, whereas the distribution of the disorientation angle between grains in contact with each other basically agrees with a random distribution. The atomistic configuration of the polycrystalline microstructure is then converted into a phase-field profile (diffuse interface description) of a phase-field model (PFM) and the subsequent grain growth is examined by multi-phase-field (MPF) simulation. A significant achievement in this study is direct mapping of the atomistic configuration into the phase-field profile used in the MPF simulation since only representative parameters for larger-scale model (e.g. interatomic potentials for MD and interfacial parameters for PFM) are extracted from a smaller‐scale simulation in conventional multi-scale modeling. Our new achievement supported by high-performance supercomputing can be regarded as an evolution of multi-scale modeling, which we call inter-scale modeling to differentiate it from conventional multi-scale modeling.