γʹvolume fraction(fv)plays a critical role in the mechanical properties of Ni-based single-crystal superalloys.A creep phase-field model is utilized to simulate the microstructure evolution and creep performance duri...γʹvolume fraction(fv)plays a critical role in the mechanical properties of Ni-based single-crystal superalloys.A creep phase-field model is utilized to simulate the microstructure evolution and creep performance during creep under different fv conditions.The influence mechanism of fv on creep properties is investigated based on the analysis of evolutions of internal stress and strain fields.As fv increases,the morphology ofγʹrafts changes from discontinuous to continuous,while the morphological change ofγchannels is opposite,the inclination ofγchannels from the[010]direction to(011)directions during tertiary creep first decreases and then increases,the creep life first increases and then decreases,and the main distribution of creep damage shifts fromγʹtoγʹ/γinterfaces andγchannels.The longest creep life under fv of 0.65 can be attributed to the stableγʹraft structure,the lowest stress and strain inγchannels,and the slowest damage accumulation.展开更多
The effect of undercooling DT and the interface energy anisotropy parameter e4 on the shape of the equiaxed dendritic tip has been investigated by using a quantitative phase-field model for solidification of binary al...The effect of undercooling DT and the interface energy anisotropy parameter e4 on the shape of the equiaxed dendritic tip has been investigated by using a quantitative phase-field model for solidification of binary alloys.It was found that the tip radius r increases and the tip shape amplitude coefficient A4 decreases with the increase of the fitting range for all cases.The dendrite tip shape selection parameter sdecreases and then stabilizes with the increase of the fitting range,and sincreases with the increase of e4.The relationship between sand e4 follows a power-law function sµea 4,and a is independent of DT but dependent on the fitting range.Numerical results demonstrate that the predicted sis consistent with the curve of microscopic solvability theory(MST)for e4<0.02,and sobtained from our phase-field simulations is sensitive to the undercooling when e4 is fixed.展开更多
Sintering,a well-established technique in powder metallurgy,plays a critical role in the processing of high melting point materials.A comprehensive understanding of structural changes during the sintering process is e...Sintering,a well-established technique in powder metallurgy,plays a critical role in the processing of high melting point materials.A comprehensive understanding of structural changes during the sintering process is essential for effective product assessment.The phase-field method stands out for its unique ability to simulate these structural transformations.Despite its widespread application,there is a notable absence of literature reviews focused on its usage in sintering simulations.Therefore,this paper addresses this gap by reviewing the latest advancements in phase-field sintering models,covering approaches based on energy,grand potential,and entropy increase.The characteristics of various models are extensively discussed,with a specific emphasis on energy-based models incorporating considerations such as interface energy anisotropy,tensor-form diffusion mechanisms,and various forms of rigid particle motion during sintering.Furthermore,the paper offers a concise summary of phase-field sintering models that integrate with other physical fields,including stress/strain fields,viscous flow,temperature field,and external electric fields.In conclusion,the paper provides a succinct overview of the entire content and delineates potential avenues for future research.展开更多
Hydride precipitation in zirconium cladding materials can damage their integrity and durability.Service temperature and material defects have a significant effect on the dynamic growth of hydrides.In this study,we hav...Hydride precipitation in zirconium cladding materials can damage their integrity and durability.Service temperature and material defects have a significant effect on the dynamic growth of hydrides.In this study,we have developed a phasefield model based on the assumption of elastic behaviour within a specific temperature range(613 K-653 K).This model allows us to study the influence of temperature and interfacial effects on the morphology,stress,and average growth rate of zirconium hydride.The results suggest that changes in temperature and interfacial energy influence the length-to-thickness ratio and average growth rate of the hydride morphology.The ultimate determinant of hydride orientation is the loss of interfacial coherency,primarily induced by interfacial dislocation defects and quantifiable by the mismatch degree q.An escalation in interfacial coherency loss leads to a transition of hydride growth from horizontal to vertical,accompanied by the onset of redirection behaviour.Interestingly,redirection occurs at a critical mismatch level,denoted as qc,and remains unaffected by variations in temperature and interfacial energy.However,this redirection leads to an increase in the maximum stress,which may influence the direction of hydride crack propagation.This research highlights the importance of interfacial coherency and provides valuable insights into the morphology and growth kinetics of hydrides in zirconium alloys.展开更多
In this work,a three-dimensional crystal-plasticity-based phase-field model considering three kinds of inelastic deformation mechanisms,i.e.,martensitic transformation,dislocation slip in austenite,and dislocation sli...In this work,a three-dimensional crystal-plasticity-based phase-field model considering three kinds of inelastic deformation mechanisms,i.e.,martensitic transformation,dislocation slip in austenite,and dislocation slip in martensite,is established to simulate the stress-assisted two-way shape memory effect(SATWSME)of NiTi single crystals and its cyclic degradation.The simulation results show that the ability of the SATWSME of NiTi single crystal increases as increasing the constant stress in the range discussed in this work(10–100 MPa),which is due to the increase of reoriented martensite formed in the cooling process due to the enhanced variant-selection capability of increased constant stress.The martensitic transformation and its reverse in the cyclic process reflecting the SATWSME show more and more obvious localization characteristics,resulting in the accumulation of significantly heterogeneous plastic deformation(mainly caused by the dislocation slip in austenite),which leads to the cyclic degradation of SATWSME.The simulation results and the conclusions drawn from this work are helpful for further understanding the mechanism of functional cyclic degradation of NiTi alloys.展开更多
The effect of supercooled melt forced laminar flow at low Reynolds Number on dendritic growth perpendicular to melt flow direction was investigated with the phase-field method by incorporating melt convection and ther...The effect of supercooled melt forced laminar flow at low Reynolds Number on dendritic growth perpendicular to melt flow direction was investigated with the phase-field method by incorporating melt convection and thermal noise under non-isothermal condition. By taking the dendritic growth of high pure succinonitrile （SCN） supercooled melt as an example, side-branching shape difference of melts with flow and without flow was analyzed. Relationships among supercooled melt inflow velocity, deflexion angle of dendritic arm and dendritic tip growth velocity were studied. Results show that the melt inflow velocity has few effects on the dendritic tip growth velocity. A formula of relationship between the velocity of the melt in front of primary dendritic tip and the dendritic growth time was deduced, and the calculated result was in quantitative agreement with the simulation result.展开更多
Dendrite growth in lithium-ion batteries may bring thermal run-away especially at high current densities,which remains the major bottleneck to implement safe and fast charging for portable electronic devices or electr...Dendrite growth in lithium-ion batteries may bring thermal run-away especially at high current densities,which remains the major bottleneck to implement safe and fast charging for portable electronic devices or electronical vehicles.Designing dendrite inhibition separators with proper pore size is considered to be one of the most promising strategies to guarantee the battery safety.However,due to the impossible observation of lithium-ion distribution under separator by experiments,the underlying dendrite inhibition mechanism is still not fully understood.Here,we apply the phase-field model,which takes the separator phase into account to construct the electrochemical system total free energy,to study the ion re-distribution behavior of porous separator and understand the pore size inhibition effect on lithium dendrite.The numerical results indicate that separator with smaller pore size is beneficial to smoother electrodeposition,since the lithium-ion concentration on the electrode surface is more uniform under denser separator pores,when their sizes is larger than the critical nucleus.The proposed model could capture the physicochemical process of electrodeposition under multiphase structures,so it could also be used to explore dendrite growth under composite electrodes and composite solid electrolytes.展开更多
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-...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.展开更多
The random distribution problem of dendrite preferred growth direction was settled by random grid method.This method was used to study the influence of forced laminar flow effect on multiple grains during solidificati...The random distribution problem of dendrite preferred growth direction was settled by random grid method.This method was used to study the influence of forced laminar flow effect on multiple grains during solidification.Taking high pure succinonitrile （SCN） undercooled melt as an example,the forced laminar flow effect on multiple grains was studied by phase-field model of single grain which coupled with flow equations at non-isothermal condition.The simulation results show that the random grid method can reasonably settle the problem of random distribution and is more effective.When the solid fraction is relatively low,melt particles flow around the downstream side of dendrite,and the flow velocity between two dendrite arms becomes high.At the stage of solidification time less than 1800Δt,every dendrite grows freely;the upstream dendrites are stronger than the downstream ones.The higher the melt flow rate,the higher the solid fraction.However,when the solid fraction is relatively high,the dendrite arm intertwins and only a little residual melt which is not encapsulated can flow;the solid fraction will gradually tend to equal to solid fraction of melt without flow.展开更多
A phase-field model is modified to investigate the grain growth and texture evolution in AZ31 magnesium alloy during stressing at elevated temperatures. The order parameters are defined to represent a physical variabl...A phase-field model is modified to investigate the grain growth and texture evolution in AZ31 magnesium alloy during stressing at elevated temperatures. The order parameters are defined to represent a physical variable of grain orientation in terms of three angles in spatial coordinates so that the grain volume of different order parameters can be used to indicate the texture of the alloy. The stiffness tensors for different grains are different because of elastic anisotropy of the magnesium lattice. The tensor is defined by transforming the standard stiffness tensor according to the angle between the （0001） plane of a grain and the direction of applied stress. Therefore, different grains contribute to different amounts of work under applied stress. The simulation results are well-explained by using the limited experimental data available, and the texture results are in good agreement with the experimental observations. The simulation results reveal that the applied stress strongly influences AZ31 alloy grain growth and that the grain-growth rate increases with the applied stress increasing, particularly when the stress is less than 400 MPa. A parameter （△d） is introduced to characterize the degree of grain-size variation due to abnormal grain growth; the △d increases with applied stress increasing and becomes considerably large only when the stress is greater than 800 MPa. Moreover, the applied stress also results in an intensive texture of the 〈0001〉 axis parallel to the direction of compressive stress in AZ31 alloy after growing at elevated temperatures, only when the applied stress is greater than 500 MPa.展开更多
Using general multi-phase-field model,detailed microstructures corresponding to different initial lamellar sets were simulated in a binary eutectic alloy with an asymmetric phase diagram.The simulation results show th...Using general multi-phase-field model,detailed microstructures corresponding to different initial lamellar sets were simulated in a binary eutectic alloy with an asymmetric phase diagram.The simulation results show that regular or unstable oscillating lamellar structures depend on the initial lamellar widths of two solid phases.A lamellar morphology map associating with the initial widths has been derived,which is capable of showing the condition of forming various lamella structures.For instance,a regular lamella was formed with fast solidification while large lamella resulted from disorder growth with low interfacial velocity. The investigated interface velocities indicate that with fast solidification to form regular lamella,a disorder growth manner or a large lamellar spacing causes a low interface velocity.These results are in good agreement with those proposed by Jackson-Hunt model.展开更多
Nanotwinned polycrystals exhibit an excellent strength-ductility combination due to nanoscale twins and grains. However, nanotwin-assisted grain coarsening under mechanical loading reported in recent experiments may r...Nanotwinned polycrystals exhibit an excellent strength-ductility combination due to nanoscale twins and grains. However, nanotwin-assisted grain coarsening under mechanical loading reported in recent experiments may result in strength drop based on the Hall-Petch law. In this paper, a phase-field model is developed to investigate the effect of coupled evolutions of twin and grain boundaries on nanotwin-assisted grain growth. The simulation result demonstrates that there are three pathways for coupled motions of twin and grain boundaries in a bicrystal under the applied loading, dependent on the amplitude of applied loading and misorientation of the bicrystal. It reveals that a large misorientation angle and a large applied stress promote the twinning-driven grain boundary migration. The resultant twin-assisted grain coarsening is confirmed in the simulations for the microstructural evolutions in twinned and un-twinned polycrystals under a high applied stress.展开更多
A multi-phase-field model is implemented to investigate the peritectic solidification of Fe-C alloy. The nucleation mode of austenite is based on the local driving force, and two different thicknesses of the primary a...A multi-phase-field model is implemented to investigate the peritectic solidification of Fe-C alloy. The nucleation mode of austenite is based on the local driving force, and two different thicknesses of the primary austenite on the surface of the ferrite equiaxed crystal grain are used as the initial conditions. The simulation shows the multiple interactions of ferrite, austenite, and liquid phases, and the effects of carbon diffusion, which presents the non-equilibrium dynamic process during Fe-C peritectic solidification at the mesoscopic scale. This work not only reveals the influence of the austenite nucleation position, but also clarifies the formation mechanism of liquid phase channels and molten pools. Therefore, the present study contributes to the understanding of the micro-morphology and micro-segregation evolution mechanisms of Fe-C alloy during peritectic solidification.展开更多
On the basis of the microscopic phase-field dynamic model and the microelasticity theory, the characteristics of the coarsening behavior of γ＇ phase in Ni-Al alloys have been systematically studied in a certain volu...On the basis of the microscopic phase-field dynamic model and the microelasticity theory, the characteristics of the coarsening behavior of γ＇ phase in Ni-Al alloys have been systematically studied in a certain volume fraction of the precipitates. It was found that the initial irregular shape, randomly distributed γ＇ phase, gradually transformed into cuboidal shape, regularly aligned along the [100] and [010] directions, and a highly preferential selected microstructure was formed during the later stage of precipitation. The volume fraction of the precipitates produced some effects on the precipitate morphology but did not produce an obvious effect on the regularities of precipitate distribution. The coarsening rate constant from the cubic growth law decreased as a function of volume fraction for small volume fractions, remained constant for intermediate volume fractions, and increased as a function of volume fraction for large volume fractions. During the coherent coarsening process, four ＂splitting＂ patterns between γ＇ phases, which belonged to different antiphase domains, were produced via particle aggregation, such as an L-shaped pattern, a doublet, a triplet, and a quartet.展开更多
With the microscopic phase-field dynamic model, the effects of temperature and concentration on the nucleation incubation time of Ni75AlxV25-x alloy were studied and the relation between the incubation time and precip...With the microscopic phase-field dynamic model, the effects of temperature and concentration on the nucleation incubation time of Ni75AlxV25-x alloy were studied and the relation between the incubation time and precipitation mechanism was investigated by using the atomic occupation probability picture and average order parameter curve. The simulation results demonstrate that there exists the incubation time for different precipitation mechanisms~ such as non-classical nucleation, the mixed style of non-classical nucleation and spinodal decomposition, and spinodal ordering; and the incubation time shortens in turn for the three kinds of mechanisms. With the increase of Al content of Ni75AlxV25-x alloy, the incubation time of Llz phases shortens continuously and that of DOzz phases is prolonged. The effects of temperature on the incubation time of Llz and DOzz phases are accordant, i.e. the incuba- tion time is greatly prolonged with the temperature rising.展开更多
The early precipitation ofγ’-Co3(Al,W)phase affects the spatial distribution and kinetic evolution of precipitates for the morphology transmission effect,but the nucleation and concomitant growth are not studied sti...The early precipitation ofγ’-Co3(Al,W)phase affects the spatial distribution and kinetic evolution of precipitates for the morphology transmission effect,but the nucleation and concomitant growth are not studied still by aging experiments due to the expeditious precipitation ofγ’phase in Co-Al-W alloy.By using the phase-field simulation with sublattice free energy,the early-stage kinetics evolution ofγ’-Co3(Al,W)phase in a medium supersaturation Co-9 Al-8 W(at.%)alloy aged from 1023 K to 1173 K is investigated.The influences of aging temperature on the evolution of morphology and composition ofγ’phase,and the kinetics of nucleation and growth to coarsening are clarified.It is found that the rates of composition evolution of W inγphase are two or three times that ofγ’phase,and the W compositions inγandγ’phases show a linear relationship with time t–1/3,which means that the coarsening takes place earlier at high temperature.In addition,the equilibrium partitioning ratios indicate Al and W partition into theγ’phase and the ratios decrease with elevated temperature.The compositional variations across theγ/γ’phase interfaces suggest that low aging temperature makes the stoichiometric ratio closer to 3:1.Moreover,the precipitation evolutions from early nucleation to growth and coarsening in Co-Al-W alloy are distinguished,and the rate constants of square and cube of average particles radius increase with temperature.In later growth stage,the relationship of the square of average particles radius and time is obeyed,while the steady-state coarsening stage follows the cube law.The time exponents of particles number density at the coarsening stage are close to–1 of Kuehmann-Voorhees(KV)theory.The study demonstrates that the early-stage evolution ofγ’phase which is undiscovered in the experiment can be captured by the phase-field simulation,and the resultant kinetics laws agree well with the experimental and theoretical results.展开更多
Phase field method was used to simulate the effect of grains orientation angle θ_(11) and azimuth θ_A of non-preferentially growing dendrites on the secondary dendrites of preferentially growing dendrites. In the si...Phase field method was used to simulate the effect of grains orientation angle θ_(11) and azimuth θ_A of non-preferentially growing dendrites on the secondary dendrites of preferentially growing dendrites. In the simulation process, two single-factor influence experiments were designed for columnar crystal structures. The simulation results showed that, when θ_(11) < 45o and θ_A < 45o, as θ_(11) was enlarged, the growth direction of the secondary dendrites on the preferentially growing dendrites at the converging grain boundary(GB) presented an increasing inclination to that of preferentially growing dendrites; with increasing θ_A, the growth direction of the secondary dendrites on the preferentially growing dendrites at the converging GB exhibited greater deflection,and the secondary dendrites grew with branches; the secondary dendrites on the preferentially growing dendrites at diverging GBs grew along a direction vertical to the growth direction of the preferentially growing dendrites.When θ_A = 45o and θ_(11) = 45o, the secondary dendrites grew in a direction vertical to the growth direction of preferentially growing dendrites. The morphologies of the dendrites obtained through simulation can also be found in metallographs of practical solidification experiments. This implies that the effect of a grain's orientation angle and azimuth of non-preferentially growing dendrites on the secondary dendrites of preferentially growing dendrites does exist and frequently appears in the practical solidification process.展开更多
The influence of temperature on the precipitation mechanism and sequence of L 12 and D022 phases during the early precipitation process of a Ni-15.Sat%Cr-14at%Al alloy was simulated based on the microscopic phase-fiel...The influence of temperature on the precipitation mechanism and sequence of L 12 and D022 phases during the early precipitation process of a Ni-15.Sat%Cr-14at%Al alloy was simulated based on the microscopic phase-field model. In the range from 873 to 1373 K, the precipitation mechanism transformed from spinodal decomposition to non-classic nucleation and growth; the incubation period prolonged gradually with increasing temperature. The volume fraction of L12 phases increased and that of D022 phases decreased. D022 phases disappeared at 1373 K, and finally single-phase L12 phases were formed.展开更多
Simulation of the microstructure evolution during solidifi cation is greatly benefi cial to the control of solidifi cation microstructures. A phase-fi eld method based on the full threaded tree(FTT) for the simulation...Simulation of the microstructure evolution during solidifi cation is greatly benefi cial to the control of solidifi cation microstructures. A phase-fi eld method based on the full threaded tree(FTT) for the simulation of casting solidifi cation microstructure was proposed in this paper, and the structure of the full threaded tree and the mesh refi nement method was discussed. During dendritic growth in solidifi cation, the mesh for simulation is adaptively refi ned at the liquid-solid interface, and coarsened in other areas. The numerical results of a threedimension dendrite growth indicate that the phase-fi eld method based on FTT is suitable for microstructure simulation. Most importantly, the FTT method can increase the spatial and temporal resolutions beyond the limits imposed by the available hardware compared with the conventional uniform mesh. At the simulation time of 0.03 s in this study, the computer memory used for computation is no more than 10 MB with the FTT method, while it is about 50 MB with the uniform mesh method. In addition, the proposed FTT method is more effi cient in computation time when compared with the uniform mesh method. It would take about 20 h for the uniform mesh method, while only 2 h for the FTT method for computation when the solidifi cation time is 0.17 s in this study.展开更多
Lithium dendrite growth due to uneven electrodeposition usually leads to the potential hazard of internal short circuit and shorter lifetime of lithium-based batteries. Extensive efforts have been devoted to explore t...Lithium dendrite growth due to uneven electrodeposition usually leads to the potential hazard of internal short circuit and shorter lifetime of lithium-based batteries. Extensive efforts have been devoted to explore the effects of single or two factors on dendrite growth, involving the diffusion coefficient, exchange current density, electrolyte concentration, temperature, and applied voltage. However, these factors interrelate during battery operation, signifying that a understanding of how they jointly influence the electrodeposition is of paramount importance for the effective suppression of dendrites. Here, we incorporate the dependent relationships among key factors into the phase-field model to capture their synergistic effects on electrodeposition. All the simulations are implemented in our self-written MATLAB code under a unified modeling framework. Following this, five groups of experimentally common dendrite patterns are reproduced and the corresponding electrodeposition driving forces are identified. Unexpectedly, we find that with the decrease of the ratio of exchange current density(or applied voltage) to diffusion coefficient, the electrodeposition morphology changes from needle-like dendrites to columnar dendrites and to uniform deposition. The present phase-field simulation tends to depict the practical electrodeposition process, providing important insights into synergistic regulation to suppress dendrite growth.展开更多
基金the supports provided by the National Natural Science Foundation of China(Nos.52301171,52031012,51971174)the National Science and Technology Major Project,China(Nos.2019-VI-0020-0135)+1 种基金the Key Research and Development Program of Shaanxi Province,China(No.2020ZDLGY13-02)the Research Fund of the State Key Laboratory of Solidification Processing(NPU),China(No.2022-TZ-01)。
文摘γʹvolume fraction(fv)plays a critical role in the mechanical properties of Ni-based single-crystal superalloys.A creep phase-field model is utilized to simulate the microstructure evolution and creep performance during creep under different fv conditions.The influence mechanism of fv on creep properties is investigated based on the analysis of evolutions of internal stress and strain fields.As fv increases,the morphology ofγʹrafts changes from discontinuous to continuous,while the morphological change ofγchannels is opposite,the inclination ofγchannels from the[010]direction to(011)directions during tertiary creep first decreases and then increases,the creep life first increases and then decreases,and the main distribution of creep damage shifts fromγʹtoγʹ/γinterfaces andγchannels.The longest creep life under fv of 0.65 can be attributed to the stableγʹraft structure,the lowest stress and strain inγchannels,and the slowest damage accumulation.
基金the National Key Research and De-velopment Program of China(Grant No.2021YFB3502600)Shenzhen Science and Technology Program(Grant No.JCYJ20220530161813029).
文摘The effect of undercooling DT and the interface energy anisotropy parameter e4 on the shape of the equiaxed dendritic tip has been investigated by using a quantitative phase-field model for solidification of binary alloys.It was found that the tip radius r increases and the tip shape amplitude coefficient A4 decreases with the increase of the fitting range for all cases.The dendrite tip shape selection parameter sdecreases and then stabilizes with the increase of the fitting range,and sincreases with the increase of e4.The relationship between sand e4 follows a power-law function sµea 4,and a is independent of DT but dependent on the fitting range.Numerical results demonstrate that the predicted sis consistent with the curve of microscopic solvability theory(MST)for e4<0.02,and sobtained from our phase-field simulations is sensitive to the undercooling when e4 is fixed.
基金supported by the National Science and TechnologyMajor Project,China(No.J2019-IV-0014-0082)the National Key Research and Development Program of China(No.2022YFB4600700)+1 种基金the National Overseas Youth Talents Program,China,the Research Fund of State Key Laboratory of Mechanics and Control for Aerospace Structures,China(No.MCMS-I-0422K01)a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions,China.
文摘Sintering,a well-established technique in powder metallurgy,plays a critical role in the processing of high melting point materials.A comprehensive understanding of structural changes during the sintering process is essential for effective product assessment.The phase-field method stands out for its unique ability to simulate these structural transformations.Despite its widespread application,there is a notable absence of literature reviews focused on its usage in sintering simulations.Therefore,this paper addresses this gap by reviewing the latest advancements in phase-field sintering models,covering approaches based on energy,grand potential,and entropy increase.The characteristics of various models are extensively discussed,with a specific emphasis on energy-based models incorporating considerations such as interface energy anisotropy,tensor-form diffusion mechanisms,and various forms of rigid particle motion during sintering.Furthermore,the paper offers a concise summary of phase-field sintering models that integrate with other physical fields,including stress/strain fields,viscous flow,temperature field,and external electric fields.In conclusion,the paper provides a succinct overview of the entire content and delineates potential avenues for future research.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.U2230401,U1930401,and 12004048)the National Key Research and Development Program of China (Grant No.2021YFB3501503)+1 种基金the Science Challenge Project (Grant No.TZ2018002)the Foundation of LCP。
文摘Hydride precipitation in zirconium cladding materials can damage their integrity and durability.Service temperature and material defects have a significant effect on the dynamic growth of hydrides.In this study,we have developed a phasefield model based on the assumption of elastic behaviour within a specific temperature range(613 K-653 K).This model allows us to study the influence of temperature and interfacial effects on the morphology,stress,and average growth rate of zirconium hydride.The results suggest that changes in temperature and interfacial energy influence the length-to-thickness ratio and average growth rate of the hydride morphology.The ultimate determinant of hydride orientation is the loss of interfacial coherency,primarily induced by interfacial dislocation defects and quantifiable by the mismatch degree q.An escalation in interfacial coherency loss leads to a transition of hydride growth from horizontal to vertical,accompanied by the onset of redirection behaviour.Interestingly,redirection occurs at a critical mismatch level,denoted as qc,and remains unaffected by variations in temperature and interfacial energy.However,this redirection leads to an increase in the maximum stress,which may influence the direction of hydride crack propagation.This research highlights the importance of interfacial coherency and provides valuable insights into the morphology and growth kinetics of hydrides in zirconium alloys.
基金The National Natural Science Foundation of China(12202294,12022208,and 12322203)the Project funded by China Postdoctoral Science Foundation(2022M712243)the Fundamental Research Funds for the Central Universities(2023SCU12098)are acknowledged.
文摘In this work,a three-dimensional crystal-plasticity-based phase-field model considering three kinds of inelastic deformation mechanisms,i.e.,martensitic transformation,dislocation slip in austenite,and dislocation slip in martensite,is established to simulate the stress-assisted two-way shape memory effect(SATWSME)of NiTi single crystals and its cyclic degradation.The simulation results show that the ability of the SATWSME of NiTi single crystal increases as increasing the constant stress in the range discussed in this work(10–100 MPa),which is due to the increase of reoriented martensite formed in the cooling process due to the enhanced variant-selection capability of increased constant stress.The martensitic transformation and its reverse in the cyclic process reflecting the SATWSME show more and more obvious localization characteristics,resulting in the accumulation of significantly heterogeneous plastic deformation(mainly caused by the dislocation slip in austenite),which leads to the cyclic degradation of SATWSME.The simulation results and the conclusions drawn from this work are helpful for further understanding the mechanism of functional cyclic degradation of NiTi alloys.
基金Project (10964004) supported by the National Natural Science Foundation of ChinaProject (096RJZA104) supported by the Natural Science Foundation of Gansu Province, China
文摘The effect of supercooled melt forced laminar flow at low Reynolds Number on dendritic growth perpendicular to melt flow direction was investigated with the phase-field method by incorporating melt convection and thermal noise under non-isothermal condition. By taking the dendritic growth of high pure succinonitrile （SCN） supercooled melt as an example, side-branching shape difference of melts with flow and without flow was analyzed. Relationships among supercooled melt inflow velocity, deflexion angle of dendritic arm and dendritic tip growth velocity were studied. Results show that the melt inflow velocity has few effects on the dendritic tip growth velocity. A formula of relationship between the velocity of the melt in front of primary dendritic tip and the dendritic growth time was deduced, and the calculated result was in quantitative agreement with the simulation result.
基金the National Natural Science Foundation of China(Nos.52102280,U2030206,11874254,51622207)Shanghai Pujiang Program(No.2019PJD016)+2 种基金Foundation of China Academy of Engineering Physics-Key Laboratory of Neutron Physics(No.2019BB07)Scientific Research Project of Zhijiang Laboratory(No.2021PE0AC02)funding from King Abdullah University of Science and Technology(KAUST)。
文摘Dendrite growth in lithium-ion batteries may bring thermal run-away especially at high current densities,which remains the major bottleneck to implement safe and fast charging for portable electronic devices or electronical vehicles.Designing dendrite inhibition separators with proper pore size is considered to be one of the most promising strategies to guarantee the battery safety.However,due to the impossible observation of lithium-ion distribution under separator by experiments,the underlying dendrite inhibition mechanism is still not fully understood.Here,we apply the phase-field model,which takes the separator phase into account to construct the electrochemical system total free energy,to study the ion re-distribution behavior of porous separator and understand the pore size inhibition effect on lithium dendrite.The numerical results indicate that separator with smaller pore size is beneficial to smoother electrodeposition,since the lithium-ion concentration on the electrode surface is more uniform under denser separator pores,when their sizes is larger than the critical nucleus.The proposed model could capture the physicochemical process of electrodeposition under multiphase structures,so it could also be used to explore dendrite growth under composite electrodes and composite solid electrolytes.
基金The authors gratefully acknowledge the financial support of the Deutsche Forschungsgemeinschaft(DFG)within the Collaborative Research Center(SFB)761‘Steel-ab initio:Quantum mechanics guided design of new Fe-based materials’and the project BL402/49-1.H.W.Luo is thankful for the financial supports from the National Natural Science Foundation of China(Nos.51861135302 and 51831002).Dr.Bernd Böttger at ACCESS e.V.is acknowledged for the helpful discussions.The synchrotron high-energy X-ray diffraction measurements were carried out at the Powder Diffraction and Total Scattering Beamline P02.1 of PETRA III at DESY(No.I-20181007),a member of the Helmholtz Association(HGF),which is gratefully acknowledged.Dr.Martin Etter at DESY is acknowledged for his support of acquiring HEXRD data.
文摘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.
基金Project(10964004) supported by the National Natural Science Foundation of ChinaProject(20070731001) supported by Research Fund for the Doctoral Program of China+1 种基金 Project(096RJZA104) supported by the Natural Science Foundation of Gansu Province,ChinaProject(SB14200801) supported by the Doctoral Fund of Lanzhou University of Technology,China
文摘The random distribution problem of dendrite preferred growth direction was settled by random grid method.This method was used to study the influence of forced laminar flow effect on multiple grains during solidification.Taking high pure succinonitrile （SCN） undercooled melt as an example,the forced laminar flow effect on multiple grains was studied by phase-field model of single grain which coupled with flow equations at non-isothermal condition.The simulation results show that the random grid method can reasonably settle the problem of random distribution and is more effective.When the solid fraction is relatively low,melt particles flow around the downstream side of dendrite,and the flow velocity between two dendrite arms becomes high.At the stage of solidification time less than 1800Δt,every dendrite grows freely;the upstream dendrites are stronger than the downstream ones.The higher the melt flow rate,the higher the solid fraction.However,when the solid fraction is relatively high,the dendrite arm intertwins and only a little residual melt which is not encapsulated can flow;the solid fraction will gradually tend to equal to solid fraction of melt without flow.
基金Project supported by the National Key Research Development Program of China(Grant No.2016YFB0701204)the National Natural Science Foundation of China(Grant Nos.U1302272 and 51571055)
文摘A phase-field model is modified to investigate the grain growth and texture evolution in AZ31 magnesium alloy during stressing at elevated temperatures. The order parameters are defined to represent a physical variable of grain orientation in terms of three angles in spatial coordinates so that the grain volume of different order parameters can be used to indicate the texture of the alloy. The stiffness tensors for different grains are different because of elastic anisotropy of the magnesium lattice. The tensor is defined by transforming the standard stiffness tensor according to the angle between the （0001） plane of a grain and the direction of applied stress. Therefore, different grains contribute to different amounts of work under applied stress. The simulation results are well-explained by using the limited experimental data available, and the texture results are in good agreement with the experimental observations. The simulation results reveal that the applied stress strongly influences AZ31 alloy grain growth and that the grain-growth rate increases with the applied stress increasing, particularly when the stress is less than 400 MPa. A parameter （△d） is introduced to characterize the degree of grain-size variation due to abnormal grain growth; the △d increases with applied stress increasing and becomes considerably large only when the stress is greater than 800 MPa. Moreover, the applied stress also results in an intensive texture of the 〈0001〉 axis parallel to the direction of compressive stress in AZ31 alloy after growing at elevated temperatures, only when the applied stress is greater than 500 MPa.
基金Projects(50771041,50801019)supported by the National Natural Science Foundation of ChinaProject(20080430909)supported by China Postdoctoral Science FoundationProject(HITQNJS.2008.018)supported by Development Program for Outstanding Young Teachers in Harbin Institute of Technology,China
文摘Using general multi-phase-field model,detailed microstructures corresponding to different initial lamellar sets were simulated in a binary eutectic alloy with an asymmetric phase diagram.The simulation results show that regular or unstable oscillating lamellar structures depend on the initial lamellar widths of two solid phases.A lamellar morphology map associating with the initial widths has been derived,which is capable of showing the condition of forming various lamella structures.For instance,a regular lamella was formed with fast solidification while large lamella resulted from disorder growth with low interfacial velocity. The investigated interface velocities indicate that with fast solidification to form regular lamella,a disorder growth manner or a large lamellar spacing causes a low interface velocity.These results are in good agreement with those proposed by Jackson-Hunt model.
基金Project supported by the National Natural Science Foundation of China(No.11672285)the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDB22040502)+1 种基金the Collaborative Innovation Center of Suzhou Nano Science and Technologythe Fundamental Research Funds for the Central Universities
文摘Nanotwinned polycrystals exhibit an excellent strength-ductility combination due to nanoscale twins and grains. However, nanotwin-assisted grain coarsening under mechanical loading reported in recent experiments may result in strength drop based on the Hall-Petch law. In this paper, a phase-field model is developed to investigate the effect of coupled evolutions of twin and grain boundaries on nanotwin-assisted grain growth. The simulation result demonstrates that there are three pathways for coupled motions of twin and grain boundaries in a bicrystal under the applied loading, dependent on the amplitude of applied loading and misorientation of the bicrystal. It reveals that a large misorientation angle and a large applied stress promote the twinning-driven grain boundary migration. The resultant twin-assisted grain coarsening is confirmed in the simulations for the microstructural evolutions in twinned and un-twinned polycrystals under a high applied stress.
基金Project supported by the Science Challenge Project,China(Grant No.TZZT2019-D1-03)the National Natural Science Foundation of China(Grant No.51972028)the National Key Research and Development Program of China(Grant No.2019YFA0307900)。
文摘A multi-phase-field model is implemented to investigate the peritectic solidification of Fe-C alloy. The nucleation mode of austenite is based on the local driving force, and two different thicknesses of the primary austenite on the surface of the ferrite equiaxed crystal grain are used as the initial conditions. The simulation shows the multiple interactions of ferrite, austenite, and liquid phases, and the effects of carbon diffusion, which presents the non-equilibrium dynamic process during Fe-C peritectic solidification at the mesoscopic scale. This work not only reveals the influence of the austenite nucleation position, but also clarifies the formation mechanism of liquid phase channels and molten pools. Therefore, the present study contributes to the understanding of the micro-morphology and micro-segregation evolution mechanisms of Fe-C alloy during peritectic solidification.
基金This work was financially supported by the National Natural Science Foundation of China (No.50671084)China Postdoctoral Science Foundation (No.20070420218).
文摘On the basis of the microscopic phase-field dynamic model and the microelasticity theory, the characteristics of the coarsening behavior of γ＇ phase in Ni-Al alloys have been systematically studied in a certain volume fraction of the precipitates. It was found that the initial irregular shape, randomly distributed γ＇ phase, gradually transformed into cuboidal shape, regularly aligned along the [100] and [010] directions, and a highly preferential selected microstructure was formed during the later stage of precipitation. The volume fraction of the precipitates produced some effects on the precipitate morphology but did not produce an obvious effect on the regularities of precipitate distribution. The coarsening rate constant from the cubic growth law decreased as a function of volume fraction for small volume fractions, remained constant for intermediate volume fractions, and increased as a function of volume fraction for large volume fractions. During the coherent coarsening process, four ＂splitting＂ patterns between γ＇ phases, which belonged to different antiphase domains, were produced via particle aggregation, such as an L-shaped pattern, a doublet, a triplet, and a quartet.
文摘With the microscopic phase-field dynamic model, the effects of temperature and concentration on the nucleation incubation time of Ni75AlxV25-x alloy were studied and the relation between the incubation time and precipitation mechanism was investigated by using the atomic occupation probability picture and average order parameter curve. The simulation results demonstrate that there exists the incubation time for different precipitation mechanisms~ such as non-classical nucleation, the mixed style of non-classical nucleation and spinodal decomposition, and spinodal ordering; and the incubation time shortens in turn for the three kinds of mechanisms. With the increase of Al content of Ni75AlxV25-x alloy, the incubation time of Llz phases shortens continuously and that of DOzz phases is prolonged. The effects of temperature on the incubation time of Llz and DOzz phases are accordant, i.e. the incuba- tion time is greatly prolonged with the temperature rising.
基金financially supported by the National Natural Science Foundation of China(No.51571122)the Fundamental Research Funds for the Central Universities(No.30916015107)。
文摘The early precipitation ofγ’-Co3(Al,W)phase affects the spatial distribution and kinetic evolution of precipitates for the morphology transmission effect,but the nucleation and concomitant growth are not studied still by aging experiments due to the expeditious precipitation ofγ’phase in Co-Al-W alloy.By using the phase-field simulation with sublattice free energy,the early-stage kinetics evolution ofγ’-Co3(Al,W)phase in a medium supersaturation Co-9 Al-8 W(at.%)alloy aged from 1023 K to 1173 K is investigated.The influences of aging temperature on the evolution of morphology and composition ofγ’phase,and the kinetics of nucleation and growth to coarsening are clarified.It is found that the rates of composition evolution of W inγphase are two or three times that ofγ’phase,and the W compositions inγandγ’phases show a linear relationship with time t–1/3,which means that the coarsening takes place earlier at high temperature.In addition,the equilibrium partitioning ratios indicate Al and W partition into theγ’phase and the ratios decrease with elevated temperature.The compositional variations across theγ/γ’phase interfaces suggest that low aging temperature makes the stoichiometric ratio closer to 3:1.Moreover,the precipitation evolutions from early nucleation to growth and coarsening in Co-Al-W alloy are distinguished,and the rate constants of square and cube of average particles radius increase with temperature.In later growth stage,the relationship of the square of average particles radius and time is obeyed,while the steady-state coarsening stage follows the cube law.The time exponents of particles number density at the coarsening stage are close to–1 of Kuehmann-Voorhees(KV)theory.The study demonstrates that the early-stage evolution ofγ’phase which is undiscovered in the experiment can be captured by the phase-field simulation,and the resultant kinetics laws agree well with the experimental and theoretical results.
基金supported by the National Natural Science Foundation of China(Grant Nos.:11504149,11364024,and 51661020)
文摘Phase field method was used to simulate the effect of grains orientation angle θ_(11) and azimuth θ_A of non-preferentially growing dendrites on the secondary dendrites of preferentially growing dendrites. In the simulation process, two single-factor influence experiments were designed for columnar crystal structures. The simulation results showed that, when θ_(11) < 45o and θ_A < 45o, as θ_(11) was enlarged, the growth direction of the secondary dendrites on the preferentially growing dendrites at the converging grain boundary(GB) presented an increasing inclination to that of preferentially growing dendrites; with increasing θ_A, the growth direction of the secondary dendrites on the preferentially growing dendrites at the converging GB exhibited greater deflection,and the secondary dendrites grew with branches; the secondary dendrites on the preferentially growing dendrites at diverging GBs grew along a direction vertical to the growth direction of the preferentially growing dendrites.When θ_A = 45o and θ_(11) = 45o, the secondary dendrites grew in a direction vertical to the growth direction of preferentially growing dendrites. The morphologies of the dendrites obtained through simulation can also be found in metallographs of practical solidification experiments. This implies that the effect of a grain's orientation angle and azimuth of non-preferentially growing dendrites on the secondary dendrites of preferentially growing dendrites does exist and frequently appears in the practical solidification process.
基金This work was financially supported by the National Natural Science Foundation of China (No.50071046) and the National High-Tech Research and Development Program of China (No.2002AA331051).
文摘The influence of temperature on the precipitation mechanism and sequence of L 12 and D022 phases during the early precipitation process of a Ni-15.Sat%Cr-14at%Al alloy was simulated based on the microscopic phase-field model. In the range from 873 to 1373 K, the precipitation mechanism transformed from spinodal decomposition to non-classic nucleation and growth; the incubation period prolonged gradually with increasing temperature. The volume fraction of L12 phases increased and that of D022 phases decreased. D022 phases disappeared at 1373 K, and finally single-phase L12 phases were formed.
基金financially supported by Program for New Century Excellent Talents in University(No.NCET-090396)the Foundation for Innovative Research Groups of the Natural Science Foundation of Hubei Province,China(2010CDA067)State Major Science and Technology Special Project Foundation for High-end Numerical Machine and Basic Manufacturing Equipment(2011ZX04014-052,2012ZX04012-011)
文摘Simulation of the microstructure evolution during solidifi cation is greatly benefi cial to the control of solidifi cation microstructures. A phase-fi eld method based on the full threaded tree(FTT) for the simulation of casting solidifi cation microstructure was proposed in this paper, and the structure of the full threaded tree and the mesh refi nement method was discussed. During dendritic growth in solidifi cation, the mesh for simulation is adaptively refi ned at the liquid-solid interface, and coarsened in other areas. The numerical results of a threedimension dendrite growth indicate that the phase-fi eld method based on FTT is suitable for microstructure simulation. Most importantly, the FTT method can increase the spatial and temporal resolutions beyond the limits imposed by the available hardware compared with the conventional uniform mesh. At the simulation time of 0.03 s in this study, the computer memory used for computation is no more than 10 MB with the FTT method, while it is about 50 MB with the uniform mesh method. In addition, the proposed FTT method is more effi cient in computation time when compared with the uniform mesh method. It would take about 20 h for the uniform mesh method, while only 2 h for the FTT method for computation when the solidifi cation time is 0.17 s in this study.
基金supported by the National Natural Science Foundation of China (Nos. 52102280, U2030206, 11874254, 51622207)Shanghai Pujiang Program (No. 2019PJD016)+2 种基金Foundation of China Academy of Engineering Physics-Key Laboratory of Neutron Physics (No. 2019BB07)Scientific Research Project of Zhijiang Laboratory (No. 2021PE0AC02)supported by funding from King Abdullah University of Science and Technology (KAUST)。
文摘Lithium dendrite growth due to uneven electrodeposition usually leads to the potential hazard of internal short circuit and shorter lifetime of lithium-based batteries. Extensive efforts have been devoted to explore the effects of single or two factors on dendrite growth, involving the diffusion coefficient, exchange current density, electrolyte concentration, temperature, and applied voltage. However, these factors interrelate during battery operation, signifying that a understanding of how they jointly influence the electrodeposition is of paramount importance for the effective suppression of dendrites. Here, we incorporate the dependent relationships among key factors into the phase-field model to capture their synergistic effects on electrodeposition. All the simulations are implemented in our self-written MATLAB code under a unified modeling framework. Following this, five groups of experimentally common dendrite patterns are reproduced and the corresponding electrodeposition driving forces are identified. Unexpectedly, we find that with the decrease of the ratio of exchange current density(or applied voltage) to diffusion coefficient, the electrodeposition morphology changes from needle-like dendrites to columnar dendrites and to uniform deposition. The present phase-field simulation tends to depict the practical electrodeposition process, providing important insights into synergistic regulation to suppress dendrite growth.
