A phase-field model including magnetic field induced dendrite fragmentation was established and applied to the cases with different initial crystal nuclear positions for AA5754 aluminum alloy electromagnetic laser bea...A phase-field model including magnetic field induced dendrite fragmentation was established and applied to the cases with different initial crystal nuclear positions for AA5754 aluminum alloy electromagnetic laser beam welding.Compare the calculated results that include dendrite fragmentation caused by the thermal electromagnetic Lorentz force with the results that consider only the thermal electromagnetic Lorentz force,without fragmentation,at the characteristic time instants.Both in the early and late stages,the small fragmentation at the dendrite tip promotes the number of higher-order branches and their growth,especially in the direction perpendicular to the solidification.The later stage fragmentation has the possibility of breaking one grain into several,which verifies the possibility of grain refinement caused by dendrite fragmentation.The fracture surface caused by fragmentation also makes more solid-liquid interfaces and their growth.In addition,the cases with different initial nuclear positions were compared.The grain growth in the low-temperature zone can be inhibited by the equiaxed grains'fragmentation at the high-temperature area(179.8μm^(2) and 14.7% start at the center,115.4μm^(2) and 9.4% start at the high-temperature corner,134.3μm^(2) and 10.9%start at the low-temperature corner),which is another kind of grain refinement by the dendrite fragmentation.This kind of inhibition effect on grain growth in the low-temperature region will be enhanced with the increasing time interval between the two crystal nuclei’appearance(179.8μm^(2) and 14.7%when virtual grains appear at t=4.3803 s and t=4.3803 s,134.3μm^(2) and 10.9%at t=4.0977 s and t=3.9564 s,and 115.4μm^(2) and 9.4%at t=3.8151 s and t=3.5325 s).展开更多
Lithium metal batteries(LMBs)represent a promising solution for next-generation energy storage due to their high energy density,but the growth of lithium dendrites presents significant challenges to their performance ...Lithium metal batteries(LMBs)represent a promising solution for next-generation energy storage due to their high energy density,but the growth of lithium dendrites presents significant challenges to their performance and safety.This review provides a comprehensive overview of the mechanisms behind lithium dendrite formation and the role of in situ/operando observation and phase field simulation in understanding and mitigating this issue,The key driving factors of dendrite growth,such as lithium-ion flux heterogeneity,surface defects,and localized stress,are explored through advanced experimental techniques,which enable real-time visualization of dendrite nucleation and growth dynamics.Complementarily,phase field simulations provide insights into subsurface and temporal evolution of dendrites by modeling thermodynamic and kinetic processes,while machine learning techniques optimize simulation accuracy through data-driven parameter refinement.The integration of experimental observations with simulation models holds great potential in improving understanding and predictive capabilities.Despite ongoing progress,challenges remain in resolving technical limitations in observation techniques,improving computational efficiency,and fostering interdisciplinary collaboration.This review highlights the synergy between experimental and computational strategies in advancing the development of LMBs and calls for continued research to overcome existing hurdles and unlock the full potential of lithium metal anodes.展开更多
Shale reservoirs have abundant bedding structures,which deeply alter the mechanical properties of rocks,and thus affect the reservoir stimulation performance.Previous research mostly focuses on the effects of parallel...Shale reservoirs have abundant bedding structures,which deeply alter the mechanical properties of rocks,and thus affect the reservoir stimulation performance.Previous research mostly focuses on the effects of parallel bedding on fracture propagation,while the mechanical properties and mechanisms of fracture propagation remain unclear for rocks with complex wavy bedding(e.g.China’s continentalorigin Gulong shale).Herein,a mixed phase-field fracture model of the wavy-bedding shale was applied,based on the local tension-compression decomposition phase field method(PFM)and geometric structure generation algorithm for the bedding with controllable morphological features.The parametric analysis of fracture propagation behaviors in the case of abundant complex bedding structures showed that with wavy bedding,the vertical fracture propagation rate is far higher than the horizontal propagation rate.Moreover,the development of branch fractures is suppressed during the fracturing process of the wavy-bedding sample,and the stimulated volume is limited,which is different from the characteristic of parallel bedding that promotes horizontal fracture initiation and propagation.The results showed that larger amplitudes,higher frequencies,higher inclination angles,and larger strengths of wavy bedding all promote the formation of vertical penetrating fractures and suppress the growth of branch fractures.Under such circumstances,it is hard to create a well-connected fracture network after fracturing.This research may provide a theoretical basis for understanding fracture behaviors in rocks with such complex wavy bedding.展开更多
The two-phase flow in porous media is affected by multiple factors.In the present study,a two-dimensional numerical model of porous media was developed using the actual pore structure of the core sample.The phase fiel...The two-phase flow in porous media is affected by multiple factors.In the present study,a two-dimensional numerical model of porous media was developed using the actual pore structure of the core sample.The phase field method was utilized to simulate the impact of displacement velocity,the water-gas viscosity ratio,and the density ratio on the flow behavior of two-phase fluids in porous media.The effectiveness of displacement was evaluated by analyzing CO_(2)saturation levels.The results indicate that the saturation of CO_(2)in porous media increased as the displacement velocity increased.When the displacement velocity exceeded 0.01 m/s,there was a corresponding increase in CO_(2)saturation.Conversely,when the displacement velocity was below this threshold,the impact on CO_(2)saturation was minimal.An“inflection point,”M3,was present in the viscosity ratio.When the viscosity of CO_(2)is less than 8.937×10^(-5)Pa·s(viscosity ratio below M3),variations in the viscosity of CO_(2)had little impact on its saturation.Conversely,when the viscosity of CO_(2)exceeded 8.937×10^(-5)Pa·s(viscosity ratio greater than M3),saturation increased with an increase in the viscosity ratio.In terms of the density ratio,the saturation of CO_(2)increased monotonically with an increase in the density ratio.Similarly,increasing density ratios resulted in a monotonic increase in CO_(2)saturation,though this trend was less pronounced in numerical simulations.Analysis results of displacement within dead-end pores using pressure and velocity diagrams reveal eddy currents as contributing factors.Finally,the impact of pore throat structure on the formation of dominant channels was examined.展开更多
The influence of supercooled melt forced lamina flow on microsegregation was investigated. The concentration distribution at solid-liquid boundary of binary alloy Ni-Cu was simulated using phase field model coupled wi...The influence of supercooled melt forced lamina flow on microsegregation was investigated. The concentration distribution at solid-liquid boundary of binary alloy Ni-Cu was simulated using phase field model coupled with flow field. The microsegregation, concentration maximum value, boundary thickness of concentration near upstream dendrite and normal to flow dendrite, and downstream dendrite were studied quantitatively in the case of forced lamia flow. The simulation results show that solute field and flow field interact complexly. Compared with melt without flow, in front of upstream dendrite tip, the concentration boundary thickness is the lowest and the concentration maximum value is the smallest for melt with flow. However, in front of downstream dendrite tip, the results are just the opposite. The zone of poor Cu in upstream dendrite where is the most severely microsegregation and shrinkage cavity is wider and the concentration is lower for melt with flow than that without flow.展开更多
By utilizing phase field method combined with analysis on free energy and interatomic potentials, pre-precipitation phase formation and transformation process of Ni0.75Al0.05Fe0.2 alloy in early precipitation stage du...By utilizing phase field method combined with analysis on free energy and interatomic potentials, pre-precipitation phase formation and transformation process of Ni0.75Al0.05Fe0.2 alloy in early precipitation stage during the ageing process under 1 000 K were studied. And free energy, microstructures, compositions and volume fractions of pre-precipitation phase and equilibrium phase were analyzed. The simulation results indicate that nonstoichiometric Llo pre-precipitation phase formed first, and then would gradually transform into L12 equilibrium phase. It is discovered that the phase transformation process was closely related to free energy and interatomic potentials. Additionally, it is revealed that free energy of Llo pre-precipitation phase was higher and interatomic potential was smaller than that of L12 equilibrium phase. Therefore, it is concluded that Llo phase was unstable, and phase transformation would occur to L12 which was more stable.展开更多
Lithium metal batteries are the most promising choices for next-generation high-energy–density batteries. However, there is little mechanism understanding on lithium dendrite growth during lithium plating and the dea...Lithium metal batteries are the most promising choices for next-generation high-energy–density batteries. However, there is little mechanism understanding on lithium dendrite growth during lithium plating and the dead lithium(the main component of inactive lithium) formation during lithium stripping. This work proposed a phase field model to describe the lithium stripping process with dead lithium formation.The coupling of galvanostatic conditions enables the phase field method to accurately match experimental results. The factors influencing the dead lithium formation on the increasing discharge polarization are revealed. Besides, the simulation of the battery polarization curve, the capacity loss peak, and the Coulomb efficiency is realized. This contribution affords an insightful understanding on dead lithium formation with phase field methods, which can contribute general principles on rational design of lithium metal batteries.展开更多
A numerical simulation based on a regularized phase field model is developed to describe faceted dendrite growth morphology. The effects of mesh grid, anisotropy, supersaturation and fold symmetry on dendrite growth m...A numerical simulation based on a regularized phase field model is developed to describe faceted dendrite growth morphology. The effects of mesh grid, anisotropy, supersaturation and fold symmetry on dendrite growth morphology were investigated, respectively. These results indicate that the nucleus grows into a hexagonal symmetry faceted dendrite. When the mesh grid is above 640×640, the size has no much effect on the shape. With the increase in the anisotropy value, the tip velocities of faceted dendrite increase and reach a balance value, and then decrease gradually. With the increase in the supersaturation value, crystal evolves from circle to the developed faceted dendrite morphology. Based on the Wulff theory and faceted symmetry morphology diagram, the proposed model was proved to be effective, and it can be generalized to arbitrary crystal symmetries.展开更多
The formation of non-dendritic structures in the primary phase of an aluminum alloy solidified using low superheat pouring with a shearing field(LSPSF) machine was investigated by numerical simulation.The growth and m...The formation of non-dendritic structures in the primary phase of an aluminum alloy solidified using low superheat pouring with a shearing field(LSPSF) machine was investigated by numerical simulation.The growth and motion of a dendrite during solidification was simulated by a combination of the lattice Boltzmann method and the phase field method.The simulation results indicated that enough shear flow helped homogenize the concentration fields,rotate crystals and altere microstructures from dendritic to non-dendritic.The interaction of grains was also discussed.A fragmentation criterion was established based on partial remelting of dendrite arms;fragmentation was enhanced by a strong shear flow and larger inclined angles.The simulation results were verified experimentally.展开更多
Numerical simulation based on a new regularized phase field model was presented to simulate the dendritic shape of a non-isothermal alloy with strong anisotropy in a forced flow. The simulation results show that a cry...Numerical simulation based on a new regularized phase field model was presented to simulate the dendritic shape of a non-isothermal alloy with strong anisotropy in a forced flow. The simulation results show that a crystal nucleus grows into a symmetric dendrite in a free flow and into an asymmetry dendrite in a forced flow. As the forced flow velocity is increased, both of the promoting effect on the upstream arm and the inhibiting effects on the downstream and perpendicular arms are intensified, and the perpendicular arm tilts to the upstream direction. With increasing the anisotropy value to 0.14, all of the dendrite arms tip velocities are gradually stabilized and finally reach their relative saturation values. In addition, the effects of an undercooling parameter and a forced compound flow on the faceted dendrite growth were also investigated.展开更多
The phase-field model coupled with a flow field was used to simulate the solidification of pure materials by the finite difference method. The effects of initial crystal radius, the space step and the interface thickn...The phase-field model coupled with a flow field was used to simulate the solidification of pure materials by the finite difference method. The effects of initial crystal radius, the space step and the interface thickness on the dendrite growth were studied. Results indicate that the grain grows into an equiaxial dendrite during free flow and into a typical branched structure under forced flow. The radius of an initial crystal can affect the growth of side-branches but not the stability of the dendrite＇s tip when an appropriate value is assigned to it. With an increase in space steps, side-branches appear at the upstream of the longitudinal principal branch and they grow rapidly. With an increase in the interface thickness, the trunk of the longitudinal upstream and lateral principal branches grow longer and become more slender while the number of secondary branches increases.展开更多
Currently,in the era of big data and 5G communication technology,electromigration has become a serious reliability issue for the miniaturized solder joints used in microelectronic devices.Since the effective charge nu...Currently,in the era of big data and 5G communication technology,electromigration has become a serious reliability issue for the miniaturized solder joints used in microelectronic devices.Since the effective charge number(Z*)is considered as the driving force for electromigration,the lack of accurate experimental values for Z* poses severe challenges for the simulation-aided design of electronic materials.In this work,a data-driven framework is developed to predict the Z* values of Cu and Sn species at the anode based LIQUID,Cu_(6)Sn_(5) intermetallic compound(IMC)and FCC phases for the binary Cu-Sn system undergoing electromigration at 523.15 K.The growth rate constants(kem)of the anode IMC at several magnitudes of applied low current density(j=1×10^6 to 10×10^6A/m^2)are extracted from simulations based on a 1D multi-phase field model.A neural network employing Z* and j as input features,whereas utilizing these computed kemdata as the expected output is trained.The results of the neural network analysis are optimized with experimental growth rate constants to estimate the effective charge numbers.For a negligible increase in temperature at low j values,effective charge numbers of all phases are found to increase with current density and the increase is much more pronounced for the IMC phase.The predicted values of effective charge numbers Z* are then utilized in a 2D simulation to observe the anode IMC grain growth and electrical resistance changes in the multi-phase system.As the work consists of the aspects of experiments,theory,computation,and machine learning,it can be called the four paradigms approach for the study of electromigration in Pb-free solder.Such a combination of multiple paradigms of materials design can be problem-solving for any future research scenario that is marked by uncertainties regarding the determination of material properties.展开更多
The formation and growth of Kirkendall voids in a binary alloy system during deformation process were investigated byphase field crystal model.The simulation results show that Kirkendall voids nucleate preferentially ...The formation and growth of Kirkendall voids in a binary alloy system during deformation process were investigated byphase field crystal model.The simulation results show that Kirkendall voids nucleate preferentially at the interface,and the averagesize of the voids increases with both the time and strain rate.There is an obvious coalescence of the voids at a large strain rate whenthe deformation is applied along the interface under both constant and cyclic strain rate conditions.For the cyclic strain rate appliedalong the interface,the growth exponent of Kirkendall voids increases with increasing the strain rate when the strain rate is largerthan1.0×10-6,while it increases initially and then decreases when the strain rate is smaller than9.0×10?7.The growth exponent ofKirkendall voids increases initially and then decreases gradually with increasing the length of cyclic period under a square-waveform constant strain rate.展开更多
The phase field method has been mainly used to simulate the growth of a single crystal in the past. But polycrystalline materials predominate in engineering. In this work, a phase field model for multigrain solidifica...The phase field method has been mainly used to simulate the growth of a single crystal in the past. But polycrystalline materials predominate in engineering. In this work, a phase field model for multigrain solidification is developed, which takes into account the random crystallographic orientations of crystallites and preserves the rotational invariance of the free energy. The morphological evolution of equiaxial multigrain solidification is predicted and the effect of composition on transformation kinetics is studied. The numerical results indicate that due to the soft impingement of grains the Avrami exponent varies with the initial melt composition and the solidification fraction.展开更多
The phase field method for fracture integrates the Griffith theory and damage mechanics approach to predict crack initiation and propagation within one framework.It replaced the discrete representation of crack by dif...The phase field method for fracture integrates the Griffith theory and damage mechanics approach to predict crack initiation and propagation within one framework.It replaced the discrete representation of crack by diffusive damage and solved it based on a minimization of the global energy storage functional.As a result,no crack tracking topology is needed,and complex crack shapes can be captures without user intervention.However,it is also reported to have an inconsistency between the predicted fracture toughness and the material strength.Recently,a novel energetic degradation function was proposed in literature to handle this issue.This research does some further modifications to the global energy storage functional so that Newton's method can be directly used to solve the energy minimization.With the new energy form,direct implementation of the length-scale independent phase field method into finite element packages like LS-DYNA becomes possible.This paper presents the framework and details of implementing the length-scale independent phase field method into LS-DYNA through a user-defined element and material subroutine.Several numerical examples are presented to compare with the experiment crack shape.Most importantly,this paper is one of the first ones to quantitatively predict accurate force response compared to experiments.These examples verify the accuracy of the new energy form and implementation.展开更多
High-temperature oxidation is an important property to evaluate thermal protection materials. However, since oxidation is a complex process involving microstructure evolution, its quantitative analysis has always been...High-temperature oxidation is an important property to evaluate thermal protection materials. However, since oxidation is a complex process involving microstructure evolution, its quantitative analysis has always been a challenge. In this work, a phase field method （PFM） based on the thermodynamics theory is developed to simulate the oxidation behavior and oxidation induced growth stress. It involves microstructure evolution and solves the problem of quantitatively computational analysis for the oxidation behavior and growth stress. Employing this method, the diffusion process, oxidation performance, and stress evolution axe predicted for Fe-Cr-A1-Y alloys. The numerical results agree well with the experimental data. The linear relationship between the maximum growth stress and the environment oxygen concentration is found. PFM provides a powerful tool to investigate high-temperature oxidation in complex environments.展开更多
Based on the bulk free energy density and the degenerate mobility constructed by the quartic double-well potential function,a phase field model is established to simulate the evolution of intragranular microvoids due ...Based on the bulk free energy density and the degenerate mobility constructed by the quartic double-well potential function,a phase field model is established to simulate the evolution of intragranular microvoids due to surface diffusion in a stress field.The corresponding phase field governing equations are derived.The evolution of elliptical microvoids with different stressesΛ,aspect ratiosβand linewidths hˉis calculated using the mesh adaptation finite element method and the reliability of the procedure is verified.The results show that there exist critical values of the stressΛc,the aspect ratioβc and the linewidth hˉc of intragranular microvoids under equivalent biaxial tensile stress.When Λ≥Λ_(c),β≥β_(c) or h≤h_(c),the elliptical microvoids are instable with an extending crack tip.WhenΛ<Λ_(c),β<β_(c) or hˉ>h_(c),the elliptical microvoids gradually cylindricalize and remain a stable shape.The instability time decreases with increasing the stress or the aspect ratio,while increases with increasing the linewidth.In addition,for the interconnects containing two elliptical voids not far apart,the stress will promote the merging of the voids.展开更多
Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in a metallic system. In this paper, the equiaxed dendrite evolution during the solidification of a pu...Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in a metallic system. In this paper, the equiaxed dendrite evolution during the solidification of a pure material was numerically simulated using the phase field model. The equiaxed dendrite growth in a two-dimensional square domain of undercooled melt (nickel) with four-fold anisotropy was simulated. The phase field model equations was solved using the explicit finite difference method on a uniform mesh. The formation of various equiaxed dendrite patterns was shown by a series of simulations, and the effect of anisotropy on equiaxed dendrite morphology was investigated.展开更多
A series of material parameters are derived from atomistic simulations and implemented into a phase field（PF） model to simulate void evolution in body-centered cubic（bcc） iron subjected to different irradiation do...A series of material parameters are derived from atomistic simulations and implemented into a phase field（PF） model to simulate void evolution in body-centered cubic（bcc） iron subjected to different irradiation doses at different temperatures.The simulation results show good agreement with experimental observations — the porosity as a function of temperature varies in a bell-shaped manner and the void density monotonically decreases with increasing temperatures; both porosity and void density increase with increasing irradiation dose at the same temperature. Analysis reveals that the evolution of void number and size is determined by the interplay among the production, diffusion and recombination of vacancy and interstitial.展开更多
A numerical simulation scheme is proposed to analyze domain tessellation and pattern formation on a spherical surface using the phase-field method. A multi-phase-field model is adopted to represent domain growth, and ...A numerical simulation scheme is proposed to analyze domain tessellation and pattern formation on a spherical surface using the phase-field method. A multi-phase-field model is adopted to represent domain growth, and the finite-difference method (FDM) is used for numerical integration. The lattice points for the FDM are distributed regularly on a spherical surface so that a mostly regular triangular domain division is realized. First, a conventional diffusion process is simulated using this lattice to confirm its validity. The multi-phase-field equation is then applied, and pattern formation processes under various initial conditions are simulated. Unlike pattern formation on a flat plane, where the regular hexagonal domains are always stable, certain different patterns are generated. Specifically, characteristic stable patterns are obtained when the number of domains, n, is 6, 8, or 12;for instance, a regular pentagonal domain division pattern is generated for n = 12, which corresponds to a regular dodecahedron.展开更多
基金supported by the Alexander von Humboldt Foundation,and Deutsche Forschungsgemeinschaft(DFG,German Research Foundation,Project No.506270597 and No.466939224).
文摘A phase-field model including magnetic field induced dendrite fragmentation was established and applied to the cases with different initial crystal nuclear positions for AA5754 aluminum alloy electromagnetic laser beam welding.Compare the calculated results that include dendrite fragmentation caused by the thermal electromagnetic Lorentz force with the results that consider only the thermal electromagnetic Lorentz force,without fragmentation,at the characteristic time instants.Both in the early and late stages,the small fragmentation at the dendrite tip promotes the number of higher-order branches and their growth,especially in the direction perpendicular to the solidification.The later stage fragmentation has the possibility of breaking one grain into several,which verifies the possibility of grain refinement caused by dendrite fragmentation.The fracture surface caused by fragmentation also makes more solid-liquid interfaces and their growth.In addition,the cases with different initial nuclear positions were compared.The grain growth in the low-temperature zone can be inhibited by the equiaxed grains'fragmentation at the high-temperature area(179.8μm^(2) and 14.7% start at the center,115.4μm^(2) and 9.4% start at the high-temperature corner,134.3μm^(2) and 10.9%start at the low-temperature corner),which is another kind of grain refinement by the dendrite fragmentation.This kind of inhibition effect on grain growth in the low-temperature region will be enhanced with the increasing time interval between the two crystal nuclei’appearance(179.8μm^(2) and 14.7%when virtual grains appear at t=4.3803 s and t=4.3803 s,134.3μm^(2) and 10.9%at t=4.0977 s and t=3.9564 s,and 115.4μm^(2) and 9.4%at t=3.8151 s and t=3.5325 s).
基金the financial support of the National Natural Science Foundation of China(Nos.12172206 and 11972218)。
文摘Lithium metal batteries(LMBs)represent a promising solution for next-generation energy storage due to their high energy density,but the growth of lithium dendrites presents significant challenges to their performance and safety.This review provides a comprehensive overview of the mechanisms behind lithium dendrite formation and the role of in situ/operando observation and phase field simulation in understanding and mitigating this issue,The key driving factors of dendrite growth,such as lithium-ion flux heterogeneity,surface defects,and localized stress,are explored through advanced experimental techniques,which enable real-time visualization of dendrite nucleation and growth dynamics.Complementarily,phase field simulations provide insights into subsurface and temporal evolution of dendrites by modeling thermodynamic and kinetic processes,while machine learning techniques optimize simulation accuracy through data-driven parameter refinement.The integration of experimental observations with simulation models holds great potential in improving understanding and predictive capabilities.Despite ongoing progress,challenges remain in resolving technical limitations in observation techniques,improving computational efficiency,and fostering interdisciplinary collaboration.This review highlights the synergy between experimental and computational strategies in advancing the development of LMBs and calls for continued research to overcome existing hurdles and unlock the full potential of lithium metal anodes.
基金supported by the Technology Project of CNPC(Grant No.2023ZZ08)the National Natural Science Foundation of China(Grant No.52274058)the USTC Research Funds of the Double First-Class Initiative(Grant No.YD2090002025).
文摘Shale reservoirs have abundant bedding structures,which deeply alter the mechanical properties of rocks,and thus affect the reservoir stimulation performance.Previous research mostly focuses on the effects of parallel bedding on fracture propagation,while the mechanical properties and mechanisms of fracture propagation remain unclear for rocks with complex wavy bedding(e.g.China’s continentalorigin Gulong shale).Herein,a mixed phase-field fracture model of the wavy-bedding shale was applied,based on the local tension-compression decomposition phase field method(PFM)and geometric structure generation algorithm for the bedding with controllable morphological features.The parametric analysis of fracture propagation behaviors in the case of abundant complex bedding structures showed that with wavy bedding,the vertical fracture propagation rate is far higher than the horizontal propagation rate.Moreover,the development of branch fractures is suppressed during the fracturing process of the wavy-bedding sample,and the stimulated volume is limited,which is different from the characteristic of parallel bedding that promotes horizontal fracture initiation and propagation.The results showed that larger amplitudes,higher frequencies,higher inclination angles,and larger strengths of wavy bedding all promote the formation of vertical penetrating fractures and suppress the growth of branch fractures.Under such circumstances,it is hard to create a well-connected fracture network after fracturing.This research may provide a theoretical basis for understanding fracture behaviors in rocks with such complex wavy bedding.
基金National Science Foundation of China,Grant/Award Number:5227090113Shenzhen Science and Technology Program,Grant/Award Numbers:KCXFZ20230731093901003,KCXFZ20211020163816023The Project of Hetao Shenzhen-Hong Kong Science and Technology Innovation Cooperation Zone,Grant/Award Number:HZQB-KCZYB-2020083。
文摘The two-phase flow in porous media is affected by multiple factors.In the present study,a two-dimensional numerical model of porous media was developed using the actual pore structure of the core sample.The phase field method was utilized to simulate the impact of displacement velocity,the water-gas viscosity ratio,and the density ratio on the flow behavior of two-phase fluids in porous media.The effectiveness of displacement was evaluated by analyzing CO_(2)saturation levels.The results indicate that the saturation of CO_(2)in porous media increased as the displacement velocity increased.When the displacement velocity exceeded 0.01 m/s,there was a corresponding increase in CO_(2)saturation.Conversely,when the displacement velocity was below this threshold,the impact on CO_(2)saturation was minimal.An“inflection point,”M3,was present in the viscosity ratio.When the viscosity of CO_(2)is less than 8.937×10^(-5)Pa·s(viscosity ratio below M3),variations in the viscosity of CO_(2)had little impact on its saturation.Conversely,when the viscosity of CO_(2)exceeded 8.937×10^(-5)Pa·s(viscosity ratio greater than M3),saturation increased with an increase in the viscosity ratio.In terms of the density ratio,the saturation of CO_(2)increased monotonically with an increase in the density ratio.Similarly,increasing density ratios resulted in a monotonic increase in CO_(2)saturation,though this trend was less pronounced in numerical simulations.Analysis results of displacement within dead-end pores using pressure and velocity diagrams reveal eddy currents as contributing factors.Finally,the impact of pore throat structure on the formation of dominant channels was examined.
基金Project (10964004) supported by the National Natural Science Foundation of ChinaProject (20070731001) supported by Research Fund for the Doctoral Program of ChinaProject (096RJZA104) supported by the Natural Science Foundation of Gansu Province,China
文摘The influence of supercooled melt forced lamina flow on microsegregation was investigated. The concentration distribution at solid-liquid boundary of binary alloy Ni-Cu was simulated using phase field model coupled with flow field. The microsegregation, concentration maximum value, boundary thickness of concentration near upstream dendrite and normal to flow dendrite, and downstream dendrite were studied quantitatively in the case of forced lamia flow. The simulation results show that solute field and flow field interact complexly. Compared with melt without flow, in front of upstream dendrite tip, the concentration boundary thickness is the lowest and the concentration maximum value is the smallest for melt with flow. However, in front of downstream dendrite tip, the results are just the opposite. The zone of poor Cu in upstream dendrite where is the most severely microsegregation and shrinkage cavity is wider and the concentration is lower for melt with flow than that without flow.
基金Projects(10902086, 50941020, 50875217) supported by the National Natural Science Foundation of China Projects(JC201005) supported by Basic Research Fund of Northwestern Polytechnical University, China Project supported by Graduate Starting Seed Fund and Doctoral Foundation of Northwestern Polytechnical University, China
文摘By utilizing phase field method combined with analysis on free energy and interatomic potentials, pre-precipitation phase formation and transformation process of Ni0.75Al0.05Fe0.2 alloy in early precipitation stage during the ageing process under 1 000 K were studied. And free energy, microstructures, compositions and volume fractions of pre-precipitation phase and equilibrium phase were analyzed. The simulation results indicate that nonstoichiometric Llo pre-precipitation phase formed first, and then would gradually transform into L12 equilibrium phase. It is discovered that the phase transformation process was closely related to free energy and interatomic potentials. Additionally, it is revealed that free energy of Llo pre-precipitation phase was higher and interatomic potential was smaller than that of L12 equilibrium phase. Therefore, it is concluded that Llo phase was unstable, and phase transformation would occur to L12 which was more stable.
基金supported by the National Natural Scientific Foundation of China(22109011)the China Postdoctoral Science Foundation(BX20200047,2021M690380)。
文摘Lithium metal batteries are the most promising choices for next-generation high-energy–density batteries. However, there is little mechanism understanding on lithium dendrite growth during lithium plating and the dead lithium(the main component of inactive lithium) formation during lithium stripping. This work proposed a phase field model to describe the lithium stripping process with dead lithium formation.The coupling of galvanostatic conditions enables the phase field method to accurately match experimental results. The factors influencing the dead lithium formation on the increasing discharge polarization are revealed. Besides, the simulation of the battery polarization curve, the capacity loss peak, and the Coulomb efficiency is realized. This contribution affords an insightful understanding on dead lithium formation with phase field methods, which can contribute general principles on rational design of lithium metal batteries.
基金Projects(11102164,11304243)supported by the National Natural Science Foundation of ChinaProject(2014JQ1039)supported by the Natural Science Foundation of Shannxi Province,China+1 种基金Project(3102016ZY027)supported by the Fundamental Research Funds for the Central Universities of ChinaProject(13GH014602)supported by the Program of New Staff and Research Area Project of NWPU,China
文摘A numerical simulation based on a regularized phase field model is developed to describe faceted dendrite growth morphology. The effects of mesh grid, anisotropy, supersaturation and fold symmetry on dendrite growth morphology were investigated, respectively. These results indicate that the nucleus grows into a hexagonal symmetry faceted dendrite. When the mesh grid is above 640×640, the size has no much effect on the shape. With the increase in the anisotropy value, the tip velocities of faceted dendrite increase and reach a balance value, and then decrease gradually. With the increase in the supersaturation value, crystal evolves from circle to the developed faceted dendrite morphology. Based on the Wulff theory and faceted symmetry morphology diagram, the proposed model was proved to be effective, and it can be generalized to arbitrary crystal symmetries.
基金Project(51674144)supported by the National Natural Science Foundation of ChinaProject(KJLD14016)supported by the Luodi Research Plan of Jiangxi Educational Department,China+1 种基金Projects(20122BAB206021,20133ACB21003)supported by the Natural Science Foundation of Jiangxi Province,ChinaProject(20122BCB23001)supported by the Young Scientists Cultivating Program of Jiangxi Province,China
文摘The formation of non-dendritic structures in the primary phase of an aluminum alloy solidified using low superheat pouring with a shearing field(LSPSF) machine was investigated by numerical simulation.The growth and motion of a dendrite during solidification was simulated by a combination of the lattice Boltzmann method and the phase field method.The simulation results indicated that enough shear flow helped homogenize the concentration fields,rotate crystals and altere microstructures from dendritic to non-dendritic.The interaction of grains was also discussed.A fragmentation criterion was established based on partial remelting of dendrite arms;fragmentation was enhanced by a strong shear flow and larger inclined angles.The simulation results were verified experimentally.
基金Project(11102164)supported by the National Natural Science Foundation of ChinaProject(G9KY101502)supported by NPU Foundation for Fundamental Research,China
文摘Numerical simulation based on a new regularized phase field model was presented to simulate the dendritic shape of a non-isothermal alloy with strong anisotropy in a forced flow. The simulation results show that a crystal nucleus grows into a symmetric dendrite in a free flow and into an asymmetry dendrite in a forced flow. As the forced flow velocity is increased, both of the promoting effect on the upstream arm and the inhibiting effects on the downstream and perpendicular arms are intensified, and the perpendicular arm tilts to the upstream direction. With increasing the anisotropy value to 0.14, all of the dendrite arms tip velocities are gradually stabilized and finally reach their relative saturation values. In addition, the effects of an undercooling parameter and a forced compound flow on the faceted dendrite growth were also investigated.
基金supported by a Program of the Lanzhou Science and Technology Bureau (No.2009-1-9)the Doctoral Fund of Lanzhou University of Technology(No.SB01200606)
文摘The phase-field model coupled with a flow field was used to simulate the solidification of pure materials by the finite difference method. The effects of initial crystal radius, the space step and the interface thickness on the dendrite growth were studied. Results indicate that the grain grows into an equiaxial dendrite during free flow and into a typical branched structure under forced flow. The radius of an initial crystal can affect the growth of side-branches but not the stability of the dendrite＇s tip when an appropriate value is assigned to it. With an increase in space steps, side-branches appear at the upstream of the longitudinal principal branch and they grow rapidly. With an increase in the interface thickness, the trunk of the longitudinal upstream and lateral principal branches grow longer and become more slender while the number of secondary branches increases.
基金financially supported by the KU Leuven Research Fund(C14/17/075)the National Natural Science Foundation of China(No.51871040)the European Research Council(ERC)under the European Union’s Horizon 2020 research and innovation program(INTERDIFFUSION,No.714754)。
文摘Currently,in the era of big data and 5G communication technology,electromigration has become a serious reliability issue for the miniaturized solder joints used in microelectronic devices.Since the effective charge number(Z*)is considered as the driving force for electromigration,the lack of accurate experimental values for Z* poses severe challenges for the simulation-aided design of electronic materials.In this work,a data-driven framework is developed to predict the Z* values of Cu and Sn species at the anode based LIQUID,Cu_(6)Sn_(5) intermetallic compound(IMC)and FCC phases for the binary Cu-Sn system undergoing electromigration at 523.15 K.The growth rate constants(kem)of the anode IMC at several magnitudes of applied low current density(j=1×10^6 to 10×10^6A/m^2)are extracted from simulations based on a 1D multi-phase field model.A neural network employing Z* and j as input features,whereas utilizing these computed kemdata as the expected output is trained.The results of the neural network analysis are optimized with experimental growth rate constants to estimate the effective charge numbers.For a negligible increase in temperature at low j values,effective charge numbers of all phases are found to increase with current density and the increase is much more pronounced for the IMC phase.The predicted values of effective charge numbers Z* are then utilized in a 2D simulation to observe the anode IMC grain growth and electrical resistance changes in the multi-phase system.As the work consists of the aspects of experiments,theory,computation,and machine learning,it can be called the four paradigms approach for the study of electromigration in Pb-free solder.Such a combination of multiple paradigms of materials design can be problem-solving for any future research scenario that is marked by uncertainties regarding the determination of material properties.
基金Projects(51275178,51405162,51205135) supported by the National Natural Science Foundation of ChinaProjects(20110172110003,20130172120055) supported by the Doctoral Program of Higher Education of China
文摘The formation and growth of Kirkendall voids in a binary alloy system during deformation process were investigated byphase field crystal model.The simulation results show that Kirkendall voids nucleate preferentially at the interface,and the averagesize of the voids increases with both the time and strain rate.There is an obvious coalescence of the voids at a large strain rate whenthe deformation is applied along the interface under both constant and cyclic strain rate conditions.For the cyclic strain rate appliedalong the interface,the growth exponent of Kirkendall voids increases with increasing the strain rate when the strain rate is largerthan1.0×10-6,while it increases initially and then decreases when the strain rate is smaller than9.0×10?7.The growth exponent ofKirkendall voids increases initially and then decreases gradually with increasing the length of cyclic period under a square-waveform constant strain rate.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 50395103 and 50271057）.
文摘The phase field method has been mainly used to simulate the growth of a single crystal in the past. But polycrystalline materials predominate in engineering. In this work, a phase field model for multigrain solidification is developed, which takes into account the random crystallographic orientations of crystallites and preserves the rotational invariance of the free energy. The morphological evolution of equiaxial multigrain solidification is predicted and the effect of composition on transformation kinetics is studied. The numerical results indicate that due to the soft impingement of grains the Avrami exponent varies with the initial melt composition and the solidification fraction.
文摘The phase field method for fracture integrates the Griffith theory and damage mechanics approach to predict crack initiation and propagation within one framework.It replaced the discrete representation of crack by diffusive damage and solved it based on a minimization of the global energy storage functional.As a result,no crack tracking topology is needed,and complex crack shapes can be captures without user intervention.However,it is also reported to have an inconsistency between the predicted fracture toughness and the material strength.Recently,a novel energetic degradation function was proposed in literature to handle this issue.This research does some further modifications to the global energy storage functional so that Newton's method can be directly used to solve the energy minimization.With the new energy form,direct implementation of the length-scale independent phase field method into finite element packages like LS-DYNA becomes possible.This paper presents the framework and details of implementing the length-scale independent phase field method into LS-DYNA through a user-defined element and material subroutine.Several numerical examples are presented to compare with the experiment crack shape.Most importantly,this paper is one of the first ones to quantitatively predict accurate force response compared to experiments.These examples verify the accuracy of the new energy form and implementation.
基金Project supported by the National Natural Science Foundation of China (Nos. 90505015 and10702035)
文摘High-temperature oxidation is an important property to evaluate thermal protection materials. However, since oxidation is a complex process involving microstructure evolution, its quantitative analysis has always been a challenge. In this work, a phase field method （PFM） based on the thermodynamics theory is developed to simulate the oxidation behavior and oxidation induced growth stress. It involves microstructure evolution and solves the problem of quantitatively computational analysis for the oxidation behavior and growth stress. Employing this method, the diffusion process, oxidation performance, and stress evolution axe predicted for Fe-Cr-A1-Y alloys. The numerical results agree well with the experimental data. The linear relationship between the maximum growth stress and the environment oxygen concentration is found. PFM provides a powerful tool to investigate high-temperature oxidation in complex environments.
基金supported by the Natural Science Foundation of Jiangsu Province of China (No. BK20141407)the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘Based on the bulk free energy density and the degenerate mobility constructed by the quartic double-well potential function,a phase field model is established to simulate the evolution of intragranular microvoids due to surface diffusion in a stress field.The corresponding phase field governing equations are derived.The evolution of elliptical microvoids with different stressesΛ,aspect ratiosβand linewidths hˉis calculated using the mesh adaptation finite element method and the reliability of the procedure is verified.The results show that there exist critical values of the stressΛc,the aspect ratioβc and the linewidth hˉc of intragranular microvoids under equivalent biaxial tensile stress.When Λ≥Λ_(c),β≥β_(c) or h≤h_(c),the elliptical microvoids are instable with an extending crack tip.WhenΛ<Λ_(c),β<β_(c) or hˉ>h_(c),the elliptical microvoids gradually cylindricalize and remain a stable shape.The instability time decreases with increasing the stress or the aspect ratio,while increases with increasing the linewidth.In addition,for the interconnects containing two elliptical voids not far apart,the stress will promote the merging of the voids.
文摘Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in a metallic system. In this paper, the equiaxed dendrite evolution during the solidification of a pure material was numerically simulated using the phase field model. The equiaxed dendrite growth in a two-dimensional square domain of undercooled melt (nickel) with four-fold anisotropy was simulated. The phase field model equations was solved using the explicit finite difference method on a uniform mesh. The formation of various equiaxed dendrite patterns was shown by a series of simulations, and the effect of anisotropy on equiaxed dendrite morphology was investigated.
基金Project supported by the National Magnetic Confinement Fusion Energy Research Project of China(Grant No.2015GB118001)the Fundamental Research Funds for the Central Universities,China(Grant No.DUT16RC(3)052)+1 种基金the National Basic Research Program of China(Grant No.2012CB619402)the NETL Project(Grant No.DE-FE0027776)
文摘A series of material parameters are derived from atomistic simulations and implemented into a phase field（PF） model to simulate void evolution in body-centered cubic（bcc） iron subjected to different irradiation doses at different temperatures.The simulation results show good agreement with experimental observations — the porosity as a function of temperature varies in a bell-shaped manner and the void density monotonically decreases with increasing temperatures; both porosity and void density increase with increasing irradiation dose at the same temperature. Analysis reveals that the evolution of void number and size is determined by the interplay among the production, diffusion and recombination of vacancy and interstitial.
文摘A numerical simulation scheme is proposed to analyze domain tessellation and pattern formation on a spherical surface using the phase-field method. A multi-phase-field model is adopted to represent domain growth, and the finite-difference method (FDM) is used for numerical integration. The lattice points for the FDM are distributed regularly on a spherical surface so that a mostly regular triangular domain division is realized. First, a conventional diffusion process is simulated using this lattice to confirm its validity. The multi-phase-field equation is then applied, and pattern formation processes under various initial conditions are simulated. Unlike pattern formation on a flat plane, where the regular hexagonal domains are always stable, certain different patterns are generated. Specifically, characteristic stable patterns are obtained when the number of domains, n, is 6, 8, or 12;for instance, a regular pentagonal domain division pattern is generated for n = 12, which corresponds to a regular dodecahedron.
