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
The anisotropy of the structure and properties caused by the strong epitaxial growth of grains during laser powder bed fusion(L-PBF)significantly affects the mechanical performance of Inconel 718 alloy components such...The anisotropy of the structure and properties caused by the strong epitaxial growth of grains during laser powder bed fusion(L-PBF)significantly affects the mechanical performance of Inconel 718 alloy components such as turbine disks.The defects(lack-of-fusion Lo F)in components processed via L-PBF are detrimental to the strength of the alloy.The purpose of this study is to investigate the effect of laser scanning parameters on the epitaxial grain growth and LoF formation in order to obtain the parameter space in which the microstructure is refined and LoF defect is suppressed.The temperature field of the molten pool and the epitaxial grain growth are simulated using a multiscale model combining the finite element method with the phase-field method.The LoF model is proposed to predict the formation of LoF defects resulting from insufficient melting during L-PBF.Defect mitigation and grain-structure control during L-PBF can be realized simultaneously in the model.The simulation shows the input laser energy density for the as-deposited structure with fine grains and without LoF defects varied from 55.0–62.5 J·mm^(-3)when the interlayer rotation angle was 0°–90°.The optimized process parameters(laser power of 280 W,scanning speed of 1160 mm·s^(-1),and rotation angle of 67°)were computationally screened.In these conditions,the average grain size was 7.0μm,and the ultimate tensile strength and yield strength at room temperature were(1111±3)MPa and(820±7)MPa,respectively,which is 8.8%and10.5%higher than those of reported.The results indicating the proposed multiscale computational approach for predicting grain growth and Lo F defects could allow simultaneous grain-structure control and defect mitigation during L-PBF.展开更多
Parameter calculation and result storage, as two necessary steps in phase-field simulation play an important role in ensuring the accuracy of simulation results. A strategy of parameter calculation and result storage ...Parameter calculation and result storage, as two necessary steps in phase-field simulation play an important role in ensuring the accuracy of simulation results. A strategy of parameter calculation and result storage is presented for phase-field simulation in α-Mg dendrite growth of Mg-5-wt% Zn alloy under isothermal solidification. Based on the phase diagram and empirical formulas, key parameters of the phase-field model, such as equilibrium partition coefficient k, liquidus slope m, solutal diffusion coefficient in liquid Dl, and solutal diffusion coefficient in solid Ds, can be obtained.Both structured grid method and structured point method can be used to store simulation results, but using the latter method will reduce about 60% storage space and 37.5% storage time compared with the former. Finally, convergent simulation results of α-Mg dendrite growth are obtained and they are in good agreement with the experimental results about optical micrograph, which verify the accuracy of parameters and stability of storage method.展开更多
Previous studies ofδhydride in zirconium alloys have mainly assumed an isotropic interface.In practice,the difference in crystal structure at the interface between the matrix phase and the precipitate phase results i...Previous studies ofδhydride in zirconium alloys have mainly assumed an isotropic interface.In practice,the difference in crystal structure at the interface between the matrix phase and the precipitate phase results in an anisotropic interface.With the purpose of probing the real evolution ofδhydrides,this paper couples an anisotropy function in the interfacial energy and interfacial mobility.The influence of anisotropic interfacial energy and interfacial mobility on the morphology ofδhydride precipitation was investigated using the phase-field method.The results show that the isotropy hydride precipitates a slate-like morphology,and the anisotropicδhydride precipitates at the semi-coherent and non-coherent interfaces exhibited parallelogram-like and needle-like,which is consistent with the actual experimental morphology.Compared with the coherent interface,the semi-coherent or non-coherent interface adjusts the lattice mismatch,resulting in lower gradient energy that is more consistent with the true interfacial state.Simultaneously,an important chain of relationships is proposed,in the range of I_(x)<I_(y)<1.5I_(x)(I_(y)<I_(x) or I_(y)>1.5I_(x)),with the increase of the anisotropic mobility I_(y) in the y-axis,the gradient energy increases(decreases),the tendency of the non-coherent(semi-coherent)relationship at the interface,and the precipitation rate of hydride decreases(increases).Furthermore,the inhomogeneous stress distribution around the hydride leads to a localized enrichment of the hydrogen concentration,producing a hydride tip.The study of interfacial anisotropy is informative for future studies ofδhydride precipitation orientation and properties.展开更多
Using the advanced algorithm combining parallel computing,adaptive mesh re-griding and multigrid methods,quantitative 3D phase-field simulations of non-isothermal solidification of binary alloy were carried out.The 3D...Using the advanced algorithm combining parallel computing,adaptive mesh re-griding and multigrid methods,quantitative 3D phase-field simulations of non-isothermal solidification of binary alloy were carried out.The 3D phase-field simulation results were compared with the analytical LKT(Lipton,Kurz and Trivedi)theory.For comparison,the simulation and analytical results for 2D cases were also given.The 3D phase-field simulation results support the transport portion of the LKT theory.However,the tip radius and tip velocity predicted by the simulations are not in good agreement with the LKT theory over the whole range of undercooling.The stability parameter calculated from phase-field simulations varies significantly with the Peclet number,indicating that the stability criterion,which assumes that the stability parameter is constant,is invalid.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
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
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
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
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
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
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
The simulations of Cr atom substitution character during the formation of L12 and DO22 phases in Ni-Cr-Al alloy were performed at 873 K based on microscopic phase-field model. It is found that the substitution of Cr i...The simulations of Cr atom substitution character during the formation of L12 and DO22 phases in Ni-Cr-Al alloy were performed at 873 K based on microscopic phase-field model. It is found that the substitution of Cr is affected by Cr and Al contents and limits of occupation probabilities of Cr atom in L12 phase are present. The precipitate is single L12 phase when the component is less than the limit, Cr atoms substitute the Al sublattices in Ll2 phase, and both of atoms Al and Cr occupy the β-sites and complex phases Ni3（Al1-xCrx） are formed; Cr atoms enter Ni sites when Al and Cr contents exceed the limit, and substitute β-sites or both of α- and β-sites. The DO22 phase is formed at the boundary of Ll2 phase.展开更多
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supported by the National Key Research and Development Program of China(No.2021YFB 3700701)the National Natural Science Foundation of China(Nos.52090041,52022011)+1 种基金the National Major Science and Technology Projects of China(No.J2019-VI-00090123)the Key-area Research and Development Program of Guangdong Province(No.2019b010943001)。
文摘The anisotropy of the structure and properties caused by the strong epitaxial growth of grains during laser powder bed fusion(L-PBF)significantly affects the mechanical performance of Inconel 718 alloy components such as turbine disks.The defects(lack-of-fusion Lo F)in components processed via L-PBF are detrimental to the strength of the alloy.The purpose of this study is to investigate the effect of laser scanning parameters on the epitaxial grain growth and LoF formation in order to obtain the parameter space in which the microstructure is refined and LoF defect is suppressed.The temperature field of the molten pool and the epitaxial grain growth are simulated using a multiscale model combining the finite element method with the phase-field method.The LoF model is proposed to predict the formation of LoF defects resulting from insufficient melting during L-PBF.Defect mitigation and grain-structure control during L-PBF can be realized simultaneously in the model.The simulation shows the input laser energy density for the as-deposited structure with fine grains and without LoF defects varied from 55.0–62.5 J·mm^(-3)when the interlayer rotation angle was 0°–90°.The optimized process parameters(laser power of 280 W,scanning speed of 1160 mm·s^(-1),and rotation angle of 67°)were computationally screened.In these conditions,the average grain size was 7.0μm,and the ultimate tensile strength and yield strength at room temperature were(1111±3)MPa and(820±7)MPa,respectively,which is 8.8%and10.5%higher than those of reported.The results indicating the proposed multiscale computational approach for predicting grain growth and Lo F defects could allow simultaneous grain-structure control and defect mitigation during L-PBF.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 52074246, 52275390, 52205429, and 52201146)the National Defense Basic Scientific Research Program of China (Grant Nos. JCKY2020408B002 and WDZC2022-12)+1 种基金the Science and Technology Major Project of Shanxi Province, China (Grant Nos. 20191102008 and 20191102007)the Guiding Local Science and Technology Development Projects by the Central Government, China (Grant Nos. YDZJSX2022A025 and YDZJSX2021A027)。
文摘Parameter calculation and result storage, as two necessary steps in phase-field simulation play an important role in ensuring the accuracy of simulation results. A strategy of parameter calculation and result storage is presented for phase-field simulation in α-Mg dendrite growth of Mg-5-wt% Zn alloy under isothermal solidification. Based on the phase diagram and empirical formulas, key parameters of the phase-field model, such as equilibrium partition coefficient k, liquidus slope m, solutal diffusion coefficient in liquid Dl, and solutal diffusion coefficient in solid Ds, can be obtained.Both structured grid method and structured point method can be used to store simulation results, but using the latter method will reduce about 60% storage space and 37.5% storage time compared with the former. Finally, convergent simulation results of α-Mg dendrite growth are obtained and they are in good agreement with the experimental results about optical micrograph, which verify the accuracy of parameters and stability of storage method.
基金support from the National Natural Science Foundation of China(Nos.52375394,52074246,52275390,52205429,52201146)National Defense Basic Scientific Research Program of China(JCKY2020408B002,WDZC2022-12)+2 种基金Key Research and Development Program of Shanxi Province(202102050201011,202202050201014)Science and Technology Major Project of Shanxi Province(20191102008,20191102007)Guiding Local Science and Technology Development Projects by the Central Government(YDZJSX2022A025,YDZJSX2021A027).
文摘Previous studies ofδhydride in zirconium alloys have mainly assumed an isotropic interface.In practice,the difference in crystal structure at the interface between the matrix phase and the precipitate phase results in an anisotropic interface.With the purpose of probing the real evolution ofδhydrides,this paper couples an anisotropy function in the interfacial energy and interfacial mobility.The influence of anisotropic interfacial energy and interfacial mobility on the morphology ofδhydride precipitation was investigated using the phase-field method.The results show that the isotropy hydride precipitates a slate-like morphology,and the anisotropicδhydride precipitates at the semi-coherent and non-coherent interfaces exhibited parallelogram-like and needle-like,which is consistent with the actual experimental morphology.Compared with the coherent interface,the semi-coherent or non-coherent interface adjusts the lattice mismatch,resulting in lower gradient energy that is more consistent with the true interfacial state.Simultaneously,an important chain of relationships is proposed,in the range of I_(x)<I_(y)<1.5I_(x)(I_(y)<I_(x) or I_(y)>1.5I_(x)),with the increase of the anisotropic mobility I_(y) in the y-axis,the gradient energy increases(decreases),the tendency of the non-coherent(semi-coherent)relationship at the interface,and the precipitation rate of hydride decreases(increases).Furthermore,the inhomogeneous stress distribution around the hydride leads to a localized enrichment of the hydrogen concentration,producing a hydride tip.The study of interfacial anisotropy is informative for future studies ofδhydride precipitation orientation and properties.
文摘Using the advanced algorithm combining parallel computing,adaptive mesh re-griding and multigrid methods,quantitative 3D phase-field simulations of non-isothermal solidification of binary alloy were carried out.The 3D phase-field simulation results were compared with the analytical LKT(Lipton,Kurz and Trivedi)theory.For comparison,the simulation and analytical results for 2D cases were also given.The 3D phase-field simulation results support the transport portion of the LKT theory.However,the tip radius and tip velocity predicted by the simulations are not in good agreement with the LKT theory over the whole range of undercooling.The stability parameter calculated from phase-field simulations varies significantly with the Peclet number,indicating that the stability criterion,which assumes that the stability parameter is constant,is invalid.
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 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Project(50071046) supported by the National Natural Science Foundation of China
文摘The simulations of Cr atom substitution character during the formation of L12 and DO22 phases in Ni-Cr-Al alloy were performed at 873 K based on microscopic phase-field model. It is found that the substitution of Cr is affected by Cr and Al contents and limits of occupation probabilities of Cr atom in L12 phase are present. The precipitate is single L12 phase when the component is less than the limit, Cr atoms substitute the Al sublattices in Ll2 phase, and both of atoms Al and Cr occupy the β-sites and complex phases Ni3（Al1-xCrx） are formed; Cr atoms enter Ni sites when Al and Cr contents exceed the limit, and substitute β-sites or both of α- and β-sites. The DO22 phase is formed at the boundary of Ll2 phase.
