It is well known that coarse-grained super-elastic NiTi shape memory alloys(SMAs)exhibit localized rather than homogeneous martensite transformation(MT),which,however,can be strongly influenced by either internal size...It is well known that coarse-grained super-elastic NiTi shape memory alloys(SMAs)exhibit localized rather than homogeneous martensite transformation(MT),which,however,can be strongly influenced by either internal size(grain size,GS)or the external size(geometric size).The coupled effect of GS and geometric size on the functional properties has not been clearly understood yet.In this work,the super-elasticity,one-way,and stress-assisted two-way shape memory effects of the polycrystalline NiTi SMAs with different aspect ratios(length/width for the gauge section)and different GSs are investigated based on the phase field method.The coupled effect of the aspect ratio and GS on the functional properties is adequately revealed.The simulated results indicate that when the aspect ratio is lower than about 4:1,the stress biaxiality and stress heterogeneity in the gauge section of the sample become more and more obvious with decreasing the aspect ratio,which can significantly influence the microstructure evolution in the process involving external stress.Therefore,the corresponding functional property is strongly dependent on the aspect ratio.With decreasing the GS and the aspect ratio(to be lower than 4:1),both the aspect ratio and GS can affect the MT or martensite reorientation in each grain and the interaction among grains.Thus,due to the strong internal constraint(i.e.,the constraint of grain boundary)and the external constraint(i.e.,the constraint of geometric boundary),the capabilities of the functional properties of NiTi SMAs are gradually weakened and highly dependent on these two factors.展开更多
As the demand for advanced material design and performance prediction continues to grow,traditional phase-field models are increasingly challenged by limitations in computational efficiency and predictive accuracy,par...As the demand for advanced material design and performance prediction continues to grow,traditional phase-field models are increasingly challenged by limitations in computational efficiency and predictive accuracy,particularly when addressing high-dimensional and complex data in multicomponent systems.To overcome these challenges,this study proposes an innovative model,LSGWO-BP,which integrates an improved Grey Wolf Optimizer(GWO)with a backpropagation neural network(BP)to enhance the accuracy and efficiency of quasi-phase equilibrium predictions within the KKS phase-field framework.Three mapping enhancement strategies were investigated–Circle-Root,Tent-Cosine,and Logistic-Sine mappings-with the Logistic mapping further improved via Sine perturbation to boost global search capability and convergence speed in large-scale,complex data scenarios.Evaluation results demonstrate that the LSGWO-BP model significantly outperforms conventional machine learning approaches in predicting quasi-phase equilibrium,achieving a 14%–28%reduction in mean absolute error(MAE).Substantial improvements were also observed in mean squared error,root mean squared error,and mean absolute percentage error,alongside a 7%–33%increase in the coefficient of determination(R2).Furthermore,the model exhibits strong potential for microstructural simulation applications.Overall,the study confirms the effectiveness of the LSGWO-BP model in materials science,especially in enhancing phase-field modeling efficiency and enabling accurate,intelligent prediction for multicomponent alloy systems,thereby offering robust support for microstructure prediction and control.展开更多
Ab st ra ct Nanocrystalline materials exhibit unique properties due to their extremely high grain boundary(GB) density.However,this high-density characteristic induces grain coarsening at elevated temperatures,thereby...Ab st ra ct Nanocrystalline materials exhibit unique properties due to their extremely high grain boundary(GB) density.However,this high-density characteristic induces grain coarsening at elevated temperatures,thereby limiting the widespread application of nanocrystalline materials.Recent experimental observations revealed that GB segregation and second-phase pinning effectively hinder GB migration,thereby improving the stability of nanocry stalline materials.In this study,a mouified phase-field model that integrates mismatch strain,solute segregation and precipitation was developed to evaluate the influence of lattice misfit on the thermal stability of nanocrystalline alloys.The simulation results indicated that introducing a suitable mismatch strain can effectively enhance the microstructural stability of nanocrystalline alloys.By synergizing precipitation with an appropriate lattice misfit,the formation of second-phase particles in the bulk grains can be suppressed,thereby facilitating solute segregation/precipitation at the GBs.This concentrated solute segregation and precipitation at the GBs effectively hinders grain migration,thereby preventing grain coarsening.These findings provide a new perspective on the design and regulation of nanocrystalline alloys with enhanced thermal stability.展开更多
In contrast to conventional transformers, power electronic transformers, as an integral component of new energy power system, are often subjected to high-frequency and transient electrical stresses, leading to heighte...In contrast to conventional transformers, power electronic transformers, as an integral component of new energy power system, are often subjected to high-frequency and transient electrical stresses, leading to heightened concerns regarding insulation failures. Meanwhile, the underlying mechanism behind discharge breakdown failure and nanofiller enhancement under high-frequency electrical stress remains unclear. An electric-thermal coupled discharge breakdown phase field model was constructed to study the evolution of the breakdown path in polyimide nanocomposite insulation subjected to high-frequency stress. The investigation focused on analyzing the effect of various factors, including frequency, temperature, and nanofiller shape, on the breakdown path of Polyimide(PI) composites. Additionally, it elucidated the enhancement mechanism of nano-modified composite insulation at the mesoscopic scale. The results indicated that with increasing frequency and temperature, the discharge breakdown path demonstrates accelerated development, accompanied by a gradual dominance of Joule heat energy. This enhancement is attributed to the dispersed electric field distribution and the hindering effect of the nanosheets. The research findings offer a theoretical foundation and methodological framework to inform the optimal design and performance management of new insulating materials utilized in high-frequency power equipment.展开更多
The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifur...The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifurcation analysis to explore the mathematical solution structure of phase field models.Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions.To elucidate the idea,we apply this analytical approach to three representative phase field equations:the Allen-Cahn equation,the Cahn-Hilliard equation,and the Allen-Cahn-Ohta-Kawasaki system.The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.展开更多
A thermodynamic consistent phase field model is developed to describe the sintering process with multiphase powders. In this model, the interface region is assumed to be a mixture of different phases with the same che...A thermodynamic consistent phase field model is developed to describe the sintering process with multiphase powders. In this model, the interface region is assumed to be a mixture of different phases with the same chemical potential, but with different compositions. The interface diffusion and boundary diffusion are also considered in the model. As an example, the model is applied to the sintering process with Fe-Cu powders. The free energy of each phase is described by the well-developed thermodynamic models, together with the published optimized parameters. The microstructure and solute distribution during the sintering process can both be obtained quantitively.展开更多
Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in metallic systems. In this study, the growth process of multiple dendrites in AI-2-mole-%-Si binary ...Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in metallic systems. In this study, the growth process of multiple dendrites in AI-2-mole-%-Si binary alloy under isothermal solidification was simulated using phase field model. The simulation results showed the impingement of arbitrarily oriented crystals and the competitive growth among the grains during solidification. With the increase of growing time, the grains begin to coalesce and impinge the adjacent grains. When the dendrites start to impinge, the dendrite growth is obviously inhibited.展开更多
Single dendrite and multi-dendrite growth for Al-2 mol pct Si alloy during isothermal solidification are simulated by phase field method. In the case of single equiaxed dendrite growth, the secondary and the necking p...Single dendrite and multi-dendrite growth for Al-2 mol pct Si alloy during isothermal solidification are simulated by phase field method. In the case of single equiaxed dendrite growth, the secondary and the necking phenomenon can be observed. For multi-dendrite growth, there exists the competitive growth among the dendrites during solidification. As solidification proceeds, growing and coarsening of the primary arms occurs, together with the branching and coarsening of the secondary arms. When the diffusion fields of dendrite tips come into contact with those of the branches growing from the neighboring dendrites, the dendrites stop growing and being to ripen and thicken.展开更多
Fracture is a very common failure mode of the composite materials,which seriously affects the reliability and service-life of composite materials.Therefore,the study of the fracture behavior of the composite materials...Fracture is a very common failure mode of the composite materials,which seriously affects the reliability and service-life of composite materials.Therefore,the study of the fracture behavior of the composite materials is of great significance and necessity,which demands an accurate and efficient numerical tool in general cases because of the complexity of the arising boundary-value or initial-boundary value problems.In this paper,a phase field model is adopted and applied for the numerical simulation of the crack nucleation and propagation in brittle linear elastic two-phase perforated/particulate composites under a quasi-static tensile loading.The phase field model can well describe the initiation,propagation and coalescence of the cracks without assuming the existence and the geometry of the initial cracks in advance.Its numerical implementation is realized within the framework of the finite element method(FEM).The accuracy and the efficiency of the present phase field model are verified by the available reference results in literature.In the numerical examples,we first study and discuss the influences of the hole/particle size on the crack propagation trajectory and the force-displacement curve.Then,the effects of the hole/particle shape on the crack initiation and propagation are investigated.Furthermore,numerical examples are presented and discussed to show the influences of the hole/particle location on the crack initiation and propagation characteristics.It will be demonstrated that the present phase field model is an efficient tool for the numerical simulation of the crack initiation and propagation problems in brittle two-phase composite materials,and the corresponding results may play an important role in predicting and preventing possible hazardous crack initiation and propagation in engineering applications.展开更多
Microscopic stress distribution in a metallic material which has complex microstructure is simulated using a phase field model.The fundamental equations which take into account the coupling effects among phase transfo...Microscopic stress distribution in a metallic material which has complex microstructure is simulated using a phase field model.The fundamental equations which take into account the coupling effects among phase transformation,temperature and stress/strain are used,while thermal effects are neglected to focus on the volumetric change due to phase transformation in this paper.A two-dimensional square region is considered,and the evolution of microscopic stress and the resultant residual stress distribution are calculated using the finite element method.As the phase transformation progresses and grains grow larger,stress is generated around the growing interface.When a grain collides with another one,specifically large stress is observed.Residual stress is finally distributed in the microstructure formed,and apparently large stresses are retained along the grain boundaries. Subsequently,dependency of the stress distribution on microstructure pattern is investigated.First,variously sized square grains are tested,and it reveals that the maximum stress tends to decrease as the grain size becomes smaller.Next,the shapes of the grains are varied.As a result,the stress distribution is remarkably affected,while the maximum stress value does not change so much.More complicated grain arrangement is finally tested with eight or nine grain models.Then,it is revealed as a common feature that large stress is generated along the grain boundaries and that the stress distribution is dependent on the grain arrangement.展开更多
The ring-banded spherulite is a special morphology of polymer crystals and has attracted considerable attention over recent decades. In this study, a new phase field model with polymer characteristics is established t...The ring-banded spherulite is a special morphology of polymer crystals and has attracted considerable attention over recent decades. In this study, a new phase field model with polymer characteristics is established to investigate the emergence and formation mechanism of the ring-banded spherulites of crystalline polymers. The model consists of a nonconserved phase field representing the phase transition and a temperature field describing the diffusion of the released latent heat. The corresponding model parameters can be obtained from experimentally accessible material parameters.Two-dimensional calculations are carried out for the ring-banded spherulitic growth of polyethylene film under a series of crystallization temperatures. The results of these calculations demonstrate that the formation of ring-banded spherulites can be triggered by the self-generated thermal field. Moreover, some temperature-dependent characteristics of the ring-banded spherulites observed in experiments are reproduced by simulations, which may help to study the effects of crystallization temperature on the ring-banded structures.展开更多
All the quantitative phase field models try to get rid of the artificial factors of solutal drag, interface diffusion and interface stretch in the diffuse interface. These artificial non-equilibrium effects due to the...All the quantitative phase field models try to get rid of the artificial factors of solutal drag, interface diffusion and interface stretch in the diffuse interface. These artificial non-equilibrium effects due to the introducing of diffuse interface are analysed based on the thermodynamic status across the diffuse interface in the quantitative phase field model of binary alloys. Results indicate that the non-equilibrium effects are related to the negative driving force in the local region of solid side across the diffuse interface. The negative driving force results from the fact that the phase field model is derived from equilibrium condition but used to simulate the non-equilibrium solidification process. The interface thickness dependence of the non-equilibrium effects and its restriction on the large scale simulation are also discussed.展开更多
In phase field fracture models the value of the order parameter distin- guishes between broken and undamaged material. At crack faces the order param- eter interpolates smoothly between these two states of the materia...In phase field fracture models the value of the order parameter distin- guishes between broken and undamaged material. At crack faces the order param- eter interpolates smoothly between these two states of the material, which can be regarded as phases. The crack evolution follows implicitly from the time inte- gration of an evolution equation of the order parameter, which is coupled to the mechanical field equations. Among other phenomena phase field fracture mod- els are able to reproduce crack nucleation in initially sound materials. For a 1D setting it has been shown that crack nucleation is triggered by the loss of stability of the unfractured, spatially homogeneous solution, and that the stability point depends on the size of the considered structure. This work numerically investi- gates to which extend size effects are reproduced by the 2D phase field model. Exemplarily, a finite element study of the hole size effect is performed and the simulation results are compared to exnerimental data.展开更多
Thixocasting requires manufacturing of billets with non-dendritic microstructure.Aluminum alloy A356 billets were produced by rheocasting in a mould placed inside a linear electromagnetic stirrer.Subsequent heat treat...Thixocasting requires manufacturing of billets with non-dendritic microstructure.Aluminum alloy A356 billets were produced by rheocasting in a mould placed inside a linear electromagnetic stirrer.Subsequent heat treatment was used to produce a transition from rosette to globular microstructure.The current and the duration of stirring were explored as control parameters.Simultaneous induction heating of the billet during stirring was quantified using experimentally determined thermal profiles.The effect of processing parameters on the dendrite fragmentation was discussed.Corresponding computational modeling of the process was performed using phase-field modeling of alloy solidification in order to gain insight into the process of morphological changes of a solid during this process.A non-isothermal alloy solidification model was used for simulations.The morphological evolution under such imposed thermal cycles was simulated and compared with experimentally determined one.Suitable scaling using the thermosolutal diffusion distances was used to overcome computational difficulties in quantitative comparison at system scale.The results were interpreted in the light of existing theories of microstructure refinement and globularisation.展开更多
A cellular automaton （CA）-finite element （FE） model and a phase field （PF）-FE model were used to simulate equiaxed dendritic growth during the solidification of hexagonal metals. In the CA-FE model, the conserva...A cellular automaton （CA）-finite element （FE） model and a phase field （PF）-FE model were used to simulate equiaxed dendritic growth during the solidification of hexagonal metals. In the CA-FE model, the conservation equations of mass and energy were solved in order to calculate the temperature field, solute concentration, and the dendritic growth morphology. CA-FE simulation results showed reasonable agreement with the previously reported experimental data on secondary dendrite arm spacing （SDAS） vs cooling rate. In the PF model, a PF variable was used to distinguish solid and liquid phases similar to the conventional PF models for solidification of pure materials. Another PF variable was considered to determine the evolution of solute concentration. Validation of both models was performed by comparing the simulation results with the analytical model developed by Lipton-Glicksman-Kurz （LGK）, showing quantitatively good agreement in the tip growth velocity at a given melt undercooling. Application to magnesium alloy AZ91 （approximated with the binary Mg-8.9 wt% AI） illustrates the difficulty of modeling dendrite growth in hexagonal systems using CA-FE regarding mesh-induced anisotropy and a better performance of PF-FE in modeling multiple arbitrarily-oriented dendrites growth.展开更多
In this paper,a numerical investigation about the metal transfer of GMAW is investigated based on the phase field model.Be different of most published work,we take the thermocapillary effect and mixture energy into th...In this paper,a numerical investigation about the metal transfer of GMAW is investigated based on the phase field model.Be different of most published work,we take the thermocapillary effect and mixture energy into the process of phase transfer and interface change which is different from volume of fluid( VOF) method.We discretize the whole model with a continuous finite element method and we also apply a penalty formulation to the continuity condition enhancing the stability of the pressure.Metal transfer of GMAW with constant and pulse current is computed as numerical examples which agrees well with the data of high-speed photography.The result shows that the computing process of the phase field model is stability and it has a higher precision in predicting the diameter of droplet.展开更多
Liquid permeability of the mushy zone is important for porosity formation during the solidification process. In order to investigate the permeability of the mushy zone, an integrated model was developed by combining t...Liquid permeability of the mushy zone is important for porosity formation during the solidification process. In order to investigate the permeability of the mushy zone, an integrated model was developed by combining the phase field model and computational fluid dynamics (CFD) model. The three-dimensional multigrain dendrite morphology was obtained by using the phase field model. Subsequently, the computer-aided design (CAD) geometry and mesh were generated based on calculated dendrite morphologies. Finally, the permeability of the dendritic mushy zone was obtained by solving the Navier-Stokes and continuity equations in ANSYS Fluent software. As an example, the dendritic mushy zone permeability of Al-4.5wt%Cu alloy and its relationship with the solid fractions were studied in detail. The predicted permeability data can be input to the solidification model on a greater length scale for macro segregation and porosity simulations.展开更多
A multi-phase-field model has been developed to simulate the microstructure evolution and kinetics of the austenite static recrystallization（SRX） in a C–Mn steel. In this model, the bulk free energy that coupling t...A multi-phase-field model has been developed to simulate the microstructure evolution and kinetics of the austenite static recrystallization（SRX） in a C–Mn steel. In this model, the bulk free energy that coupling the deformation stored energy with a special interpolation function is incorporated. Both the deformed grain topology and the deformation stored energy have been included in order to investigate the influence of pre-deformation on the subsequent austenite SRX at different hot deformation levels. Diverse scenarios of microstructure evolution show different deformation-dependent recrystallized grain sizes. The transformation kinetics is then discussed by analyzing the overall SRX fraction and the average interface velocity on the recrystallization front.展开更多
The morphology of Ni_(4)Ti_(3) precipitates is important in tuning the martensitic transformation(MT)behavior and mechanical properties of nitinol.Constrained ageing is effective in engineering the morphology of Ni_(4...The morphology of Ni_(4)Ti_(3) precipitates is important in tuning the martensitic transformation(MT)behavior and mechanical properties of nitinol.Constrained ageing is effective in engineering the morphology of Ni_(4)Ti_(3) precipitates due to the variant selection effect of external load which is still lacking.In this work,maps of variant selection effect of external load applied along all crystallographic directions are obtained by using a combination of theoretical analyses and phase field simulations.It is found that maps produced by uniaxial tension and uniaxial compression are quite different.The number and types of Ni_(4)Ti_(3) variants preferred by external load vary as the loading direction changes.Moreover,factors influencing the strength of variant selection effect are discovered.This work provides insights on understanding the Ni_(4)Ti_(3) precipitation process and sheds light on the engineering of morphology of Ni_(4)Ti_(3) precipitates for desired mechanical and functional properties.展开更多
A model has been established to simulate the realistic spatio-temporal microstructure evolution in recrystallization of a magnesium alloy using the phase field approach. A set of rules have been proposed to decide the...A model has been established to simulate the realistic spatio-temporal microstructure evolution in recrystallization of a magnesium alloy using the phase field approach. A set of rules have been proposed to decide the real physical value of all parameters in the model. The thermodynamic software THERMOCALC is applied to determine the local chemical free energy and strain energy, which is added to the free energy density of grains before recrystallization. The Arrhenius formula is used to describe boundary mobility and the activity energy is suggested with a value of zinc segregation energy at the boundary. However, the mobility constant in the formula was found out by fitting to a group of grain size measurements during recrystallization of the alloy. The boundary range is suggested to decide the gradient parameters in addition of fitting to the experimental boundary energy value. These parameter values can be regarded as a database for other similar simulations and the fitting rules can also be applied to build up databases for any other alloy systems. The simulated results show a good agreement with reported experimental measurement of the alloy at the temperatures from 300 to 400℃ for up to 100 min but not at 250℃. This implies a mechanism variation in activity energy of the boundary mobility in the alloy at low temperature.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos.12202294 and 12022208)the Project funded by China Postdoctoral Science Foundation (Grant No.2022M712243)the Fundamental Research Funds for the Central Universities (Grant No.2023SCU12098).
文摘It is well known that coarse-grained super-elastic NiTi shape memory alloys(SMAs)exhibit localized rather than homogeneous martensite transformation(MT),which,however,can be strongly influenced by either internal size(grain size,GS)or the external size(geometric size).The coupled effect of GS and geometric size on the functional properties has not been clearly understood yet.In this work,the super-elasticity,one-way,and stress-assisted two-way shape memory effects of the polycrystalline NiTi SMAs with different aspect ratios(length/width for the gauge section)and different GSs are investigated based on the phase field method.The coupled effect of the aspect ratio and GS on the functional properties is adequately revealed.The simulated results indicate that when the aspect ratio is lower than about 4:1,the stress biaxiality and stress heterogeneity in the gauge section of the sample become more and more obvious with decreasing the aspect ratio,which can significantly influence the microstructure evolution in the process involving external stress.Therefore,the corresponding functional property is strongly dependent on the aspect ratio.With decreasing the GS and the aspect ratio(to be lower than 4:1),both the aspect ratio and GS can affect the MT or martensite reorientation in each grain and the interaction among grains.Thus,due to the strong internal constraint(i.e.,the constraint of grain boundary)and the external constraint(i.e.,the constraint of geometric boundary),the capabilities of the functional properties of NiTi SMAs are gradually weakened and highly dependent on these two factors.
基金supported by the National Natural Science Foundation of China(Grant Nos.52161002,51661020 and 11364024)。
文摘As the demand for advanced material design and performance prediction continues to grow,traditional phase-field models are increasingly challenged by limitations in computational efficiency and predictive accuracy,particularly when addressing high-dimensional and complex data in multicomponent systems.To overcome these challenges,this study proposes an innovative model,LSGWO-BP,which integrates an improved Grey Wolf Optimizer(GWO)with a backpropagation neural network(BP)to enhance the accuracy and efficiency of quasi-phase equilibrium predictions within the KKS phase-field framework.Three mapping enhancement strategies were investigated–Circle-Root,Tent-Cosine,and Logistic-Sine mappings-with the Logistic mapping further improved via Sine perturbation to boost global search capability and convergence speed in large-scale,complex data scenarios.Evaluation results demonstrate that the LSGWO-BP model significantly outperforms conventional machine learning approaches in predicting quasi-phase equilibrium,achieving a 14%–28%reduction in mean absolute error(MAE).Substantial improvements were also observed in mean squared error,root mean squared error,and mean absolute percentage error,alongside a 7%–33%increase in the coefficient of determination(R2).Furthermore,the model exhibits strong potential for microstructural simulation applications.Overall,the study confirms the effectiveness of the LSGWO-BP model in materials science,especially in enhancing phase-field modeling efficiency and enabling accurate,intelligent prediction for multicomponent alloy systems,thereby offering robust support for microstructure prediction and control.
基金financially supported by the National Natural Science Foundation of China (Nos.52122408, 51901013,51971018,52101188,52225103,52071023 and U20B2025)the Funds for Creative Research Groups of NSFC (No.51921001)the financial support from the Fundamental Research Funds for the Central Universities (University of Science and Technology Beijing,Nos.FRF-TP-2021-04C1 and 06500135)。
文摘Ab st ra ct Nanocrystalline materials exhibit unique properties due to their extremely high grain boundary(GB) density.However,this high-density characteristic induces grain coarsening at elevated temperatures,thereby limiting the widespread application of nanocrystalline materials.Recent experimental observations revealed that GB segregation and second-phase pinning effectively hinder GB migration,thereby improving the stability of nanocry stalline materials.In this study,a mouified phase-field model that integrates mismatch strain,solute segregation and precipitation was developed to evaluate the influence of lattice misfit on the thermal stability of nanocrystalline alloys.The simulation results indicated that introducing a suitable mismatch strain can effectively enhance the microstructural stability of nanocrystalline alloys.By synergizing precipitation with an appropriate lattice misfit,the formation of second-phase particles in the bulk grains can be suppressed,thereby facilitating solute segregation/precipitation at the GBs.This concentrated solute segregation and precipitation at the GBs effectively hinders grain migration,thereby preventing grain coarsening.These findings provide a new perspective on the design and regulation of nanocrystalline alloys with enhanced thermal stability.
基金supported in part by the National Key R&D Program of China (No.2021YFB2601404)Beijing Natural Science Foundation (No.3232053)National Natural Science Foundation of China (Nos.51929701 and 52127812)。
文摘In contrast to conventional transformers, power electronic transformers, as an integral component of new energy power system, are often subjected to high-frequency and transient electrical stresses, leading to heightened concerns regarding insulation failures. Meanwhile, the underlying mechanism behind discharge breakdown failure and nanofiller enhancement under high-frequency electrical stress remains unclear. An electric-thermal coupled discharge breakdown phase field model was constructed to study the evolution of the breakdown path in polyimide nanocomposite insulation subjected to high-frequency stress. The investigation focused on analyzing the effect of various factors, including frequency, temperature, and nanofiller shape, on the breakdown path of Polyimide(PI) composites. Additionally, it elucidated the enhancement mechanism of nano-modified composite insulation at the mesoscopic scale. The results indicated that with increasing frequency and temperature, the discharge breakdown path demonstrates accelerated development, accompanied by a gradual dominance of Joule heat energy. This enhancement is attributed to the dispersed electric field distribution and the hindering effect of the nanosheets. The research findings offer a theoretical foundation and methodological framework to inform the optimal design and performance management of new insulating materials utilized in high-frequency power equipment.
基金supported as part of the Computational Materials Sciences Program funded by the U.S.Department of Energy,Office of Science,Basic Energy Sciences,under Award No.DE-SC0020145Y.Z.would like to acknowledge support for his effort by the Simons Foundation through Grant No.357963 and NSF grant DMS-2142500.
文摘The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifurcation analysis to explore the mathematical solution structure of phase field models.Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions.To elucidate the idea,we apply this analytical approach to three representative phase field equations:the Allen-Cahn equation,the Cahn-Hilliard equation,and the Allen-Cahn-Ohta-Kawasaki system.The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.
基金Project(2011CB606306)supported by the National Basic Research Program of ChinaProject(51101014)supported by the National Natural Science Foundation of ChinaProject(SKLSP201214)supported by the State Key Laboratory of Solidification Processing in Northwestern Polytechnical University,China
文摘A thermodynamic consistent phase field model is developed to describe the sintering process with multiphase powders. In this model, the interface region is assumed to be a mixture of different phases with the same chemical potential, but with different compositions. The interface diffusion and boundary diffusion are also considered in the model. As an example, the model is applied to the sintering process with Fe-Cu powders. The free energy of each phase is described by the well-developed thermodynamic models, together with the published optimized parameters. The microstructure and solute distribution during the sintering process can both be obtained quantitively.
基金supported by the Doctor Foundational Research Project in Shenyang Ligong University(Serial Number:0010).
文摘Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in metallic systems. In this study, the growth process of multiple dendrites in AI-2-mole-%-Si binary alloy under isothermal solidification was simulated using phase field model. The simulation results showed the impingement of arbitrarily oriented crystals and the competitive growth among the grains during solidification. With the increase of growing time, the grains begin to coalesce and impinge the adjacent grains. When the dendrites start to impinge, the dendrite growth is obviously inhibited.
基金financially supported by the Educational Department of Liaoning Province (No.20060744)the Shenyang Nurturing Young Scientific Technological Talents Items (No.1081230-1-00)
文摘Single dendrite and multi-dendrite growth for Al-2 mol pct Si alloy during isothermal solidification are simulated by phase field method. In the case of single equiaxed dendrite growth, the secondary and the necking phenomenon can be observed. For multi-dendrite growth, there exists the competitive growth among the dendrites during solidification. As solidification proceeds, growing and coarsening of the primary arms occurs, together with the branching and coarsening of the secondary arms. When the diffusion fields of dendrite tips come into contact with those of the branches growing from the neighboring dendrites, the dendrites stop growing and being to ripen and thicken.
基金the National Natural Science Foundation of China(Grants U1333201 and U1833116)。
文摘Fracture is a very common failure mode of the composite materials,which seriously affects the reliability and service-life of composite materials.Therefore,the study of the fracture behavior of the composite materials is of great significance and necessity,which demands an accurate and efficient numerical tool in general cases because of the complexity of the arising boundary-value or initial-boundary value problems.In this paper,a phase field model is adopted and applied for the numerical simulation of the crack nucleation and propagation in brittle linear elastic two-phase perforated/particulate composites under a quasi-static tensile loading.The phase field model can well describe the initiation,propagation and coalescence of the cracks without assuming the existence and the geometry of the initial cracks in advance.Its numerical implementation is realized within the framework of the finite element method(FEM).The accuracy and the efficiency of the present phase field model are verified by the available reference results in literature.In the numerical examples,we first study and discuss the influences of the hole/particle size on the crack propagation trajectory and the force-displacement curve.Then,the effects of the hole/particle shape on the crack initiation and propagation are investigated.Furthermore,numerical examples are presented and discussed to show the influences of the hole/particle location on the crack initiation and propagation characteristics.It will be demonstrated that the present phase field model is an efficient tool for the numerical simulation of the crack initiation and propagation problems in brittle two-phase composite materials,and the corresponding results may play an important role in predicting and preventing possible hazardous crack initiation and propagation in engineering applications.
文摘Microscopic stress distribution in a metallic material which has complex microstructure is simulated using a phase field model.The fundamental equations which take into account the coupling effects among phase transformation,temperature and stress/strain are used,while thermal effects are neglected to focus on the volumetric change due to phase transformation in this paper.A two-dimensional square region is considered,and the evolution of microscopic stress and the resultant residual stress distribution are calculated using the finite element method.As the phase transformation progresses and grains grow larger,stress is generated around the growing interface.When a grain collides with another one,specifically large stress is observed.Residual stress is finally distributed in the microstructure formed,and apparently large stresses are retained along the grain boundaries. Subsequently,dependency of the stress distribution on microstructure pattern is investigated.First,variously sized square grains are tested,and it reveals that the maximum stress tends to decrease as the grain size becomes smaller.Next,the shapes of the grains are varied.As a result,the stress distribution is remarkably affected,while the maximum stress value does not change so much.More complicated grain arrangement is finally tested with eight or nine grain models.Then,it is revealed as a common feature that large stress is generated along the grain boundaries and that the stress distribution is dependent on the grain arrangement.
基金Project supported by the National Key Basic Research Program of China(Grant No.2012CB025903)the National Natural Science Foundation of China(Grant No.11402210)+1 种基金the Northwestern Polytechnical University Foundation for Fundamental Research(Grant No.JCY20130141)the Ministry of Education Fund for Doctoral Students Newcomer Awards of China
文摘The ring-banded spherulite is a special morphology of polymer crystals and has attracted considerable attention over recent decades. In this study, a new phase field model with polymer characteristics is established to investigate the emergence and formation mechanism of the ring-banded spherulites of crystalline polymers. The model consists of a nonconserved phase field representing the phase transition and a temperature field describing the diffusion of the released latent heat. The corresponding model parameters can be obtained from experimentally accessible material parameters.Two-dimensional calculations are carried out for the ring-banded spherulitic growth of polyethylene film under a series of crystallization temperatures. The results of these calculations demonstrate that the formation of ring-banded spherulites can be triggered by the self-generated thermal field. Moreover, some temperature-dependent characteristics of the ring-banded spherulites observed in experiments are reproduced by simulations, which may help to study the effects of crystallization temperature on the ring-banded structures.
基金supported by the fund of the State Key Laboratory of Solidification Processing in NWPU,China (Grants Nos. 17-TZ-2007,03-TP-2008,and 24-TZ-2009)the Doctorate Foundation of Northwestern Polytechnical University
文摘All the quantitative phase field models try to get rid of the artificial factors of solutal drag, interface diffusion and interface stretch in the diffuse interface. These artificial non-equilibrium effects due to the introducing of diffuse interface are analysed based on the thermodynamic status across the diffuse interface in the quantitative phase field model of binary alloys. Results indicate that the non-equilibrium effects are related to the negative driving force in the local region of solid side across the diffuse interface. The negative driving force results from the fact that the phase field model is derived from equilibrium condition but used to simulate the non-equilibrium solidification process. The interface thickness dependence of the non-equilibrium effects and its restriction on the large scale simulation are also discussed.
文摘In phase field fracture models the value of the order parameter distin- guishes between broken and undamaged material. At crack faces the order param- eter interpolates smoothly between these two states of the material, which can be regarded as phases. The crack evolution follows implicitly from the time inte- gration of an evolution equation of the order parameter, which is coupled to the mechanical field equations. Among other phenomena phase field fracture mod- els are able to reproduce crack nucleation in initially sound materials. For a 1D setting it has been shown that crack nucleation is triggered by the loss of stability of the unfractured, spatially homogeneous solution, and that the stability point depends on the size of the considered structure. This work numerically investi- gates to which extend size effects are reproduced by the 2D phase field model. Exemplarily, a finite element study of the hole size effect is performed and the simulation results are compared to exnerimental data.
文摘Thixocasting requires manufacturing of billets with non-dendritic microstructure.Aluminum alloy A356 billets were produced by rheocasting in a mould placed inside a linear electromagnetic stirrer.Subsequent heat treatment was used to produce a transition from rosette to globular microstructure.The current and the duration of stirring were explored as control parameters.Simultaneous induction heating of the billet during stirring was quantified using experimentally determined thermal profiles.The effect of processing parameters on the dendrite fragmentation was discussed.Corresponding computational modeling of the process was performed using phase-field modeling of alloy solidification in order to gain insight into the process of morphological changes of a solid during this process.A non-isothermal alloy solidification model was used for simulations.The morphological evolution under such imposed thermal cycles was simulated and compared with experimentally determined one.Suitable scaling using the thermosolutal diffusion distances was used to overcome computational difficulties in quantitative comparison at system scale.The results were interpreted in the light of existing theories of microstructure refinement and globularisation.
基金supported by the National Science Foundation(USA) through Grant No.CBET-0931801the Department of Energy(USA)through cooperative agreement No.DE-FC-26-06NT42755
文摘A cellular automaton （CA）-finite element （FE） model and a phase field （PF）-FE model were used to simulate equiaxed dendritic growth during the solidification of hexagonal metals. In the CA-FE model, the conservation equations of mass and energy were solved in order to calculate the temperature field, solute concentration, and the dendritic growth morphology. CA-FE simulation results showed reasonable agreement with the previously reported experimental data on secondary dendrite arm spacing （SDAS） vs cooling rate. In the PF model, a PF variable was used to distinguish solid and liquid phases similar to the conventional PF models for solidification of pure materials. Another PF variable was considered to determine the evolution of solute concentration. Validation of both models was performed by comparing the simulation results with the analytical model developed by Lipton-Glicksman-Kurz （LGK）, showing quantitatively good agreement in the tip growth velocity at a given melt undercooling. Application to magnesium alloy AZ91 （approximated with the binary Mg-8.9 wt% AI） illustrates the difficulty of modeling dendrite growth in hexagonal systems using CA-FE regarding mesh-induced anisotropy and a better performance of PF-FE in modeling multiple arbitrarily-oriented dendrites growth.
文摘In this paper,a numerical investigation about the metal transfer of GMAW is investigated based on the phase field model.Be different of most published work,we take the thermocapillary effect and mixture energy into the process of phase transfer and interface change which is different from volume of fluid( VOF) method.We discretize the whole model with a continuous finite element method and we also apply a penalty formulation to the continuity condition enhancing the stability of the pressure.Metal transfer of GMAW with constant and pulse current is computed as numerical examples which agrees well with the data of high-speed photography.The result shows that the computing process of the phase field model is stability and it has a higher precision in predicting the diameter of droplet.
基金financially supported by the National Key Research and Development Program of China(No.2016YFB0700503)National Natural Science Foundation of China(No.51701013)Beijing Laboratory of Metallic Materials and Processing for Modern Transportation
文摘Liquid permeability of the mushy zone is important for porosity formation during the solidification process. In order to investigate the permeability of the mushy zone, an integrated model was developed by combining the phase field model and computational fluid dynamics (CFD) model. The three-dimensional multigrain dendrite morphology was obtained by using the phase field model. Subsequently, the computer-aided design (CAD) geometry and mesh were generated based on calculated dendrite morphologies. Finally, the permeability of the dendritic mushy zone was obtained by solving the Navier-Stokes and continuity equations in ANSYS Fluent software. As an example, the dendritic mushy zone permeability of Al-4.5wt%Cu alloy and its relationship with the solid fractions were studied in detail. The predicted permeability data can be input to the solidification model on a greater length scale for macro segregation and porosity simulations.
基金financially supported by the National Science Foundation of China (Grant No. 51371169) and (Grant No. 51401214)
文摘A multi-phase-field model has been developed to simulate the microstructure evolution and kinetics of the austenite static recrystallization（SRX） in a C–Mn steel. In this model, the bulk free energy that coupling the deformation stored energy with a special interpolation function is incorporated. Both the deformed grain topology and the deformation stored energy have been included in order to investigate the influence of pre-deformation on the subsequent austenite SRX at different hot deformation levels. Diverse scenarios of microstructure evolution show different deformation-dependent recrystallized grain sizes. The transformation kinetics is then discussed by analyzing the overall SRX fraction and the average interface velocity on the recrystallization front.
基金supported by the National Natural Science Foundation of China(Grant No.12372152)the Qilu Young Talent Program of Shandong University,Zhejiang Lab Open Research Project(Grant No.K2022PE0AB05)+1 种基金Shandong Provincial Natural Science Foundation(Grant No.ZR2023MA058)Guangdong Basic and Applied Basic Research Foundation(Grant No.2023A1515011819).
文摘The morphology of Ni_(4)Ti_(3) precipitates is important in tuning the martensitic transformation(MT)behavior and mechanical properties of nitinol.Constrained ageing is effective in engineering the morphology of Ni_(4)Ti_(3) precipitates due to the variant selection effect of external load which is still lacking.In this work,maps of variant selection effect of external load applied along all crystallographic directions are obtained by using a combination of theoretical analyses and phase field simulations.It is found that maps produced by uniaxial tension and uniaxial compression are quite different.The number and types of Ni_(4)Ti_(3) variants preferred by external load vary as the loading direction changes.Moreover,factors influencing the strength of variant selection effect are discovered.This work provides insights on understanding the Ni_(4)Ti_(3) precipitation process and sheds light on the engineering of morphology of Ni_(4)Ti_(3) precipitates for desired mechanical and functional properties.
基金the National Natural Science Foundation of China for the financial support under the grant Nos.50771028 and 50471024Education Ministry of China for an outstanding teacher research fund to this study.
文摘A model has been established to simulate the realistic spatio-temporal microstructure evolution in recrystallization of a magnesium alloy using the phase field approach. A set of rules have been proposed to decide the real physical value of all parameters in the model. The thermodynamic software THERMOCALC is applied to determine the local chemical free energy and strain energy, which is added to the free energy density of grains before recrystallization. The Arrhenius formula is used to describe boundary mobility and the activity energy is suggested with a value of zinc segregation energy at the boundary. However, the mobility constant in the formula was found out by fitting to a group of grain size measurements during recrystallization of the alloy. The boundary range is suggested to decide the gradient parameters in addition of fitting to the experimental boundary energy value. These parameter values can be regarded as a database for other similar simulations and the fitting rules can also be applied to build up databases for any other alloy systems. The simulated results show a good agreement with reported experimental measurement of the alloy at the temperatures from 300 to 400℃ for up to 100 min but not at 250℃. This implies a mechanism variation in activity energy of the boundary mobility in the alloy at low temperature.
