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
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
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
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
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
This paper applies a phase field model for polycrystalline solidification in binary alloys to simulate the formation and growth of the columnar dendritic array under the isothermal and constant cooling conditions. The...This paper applies a phase field model for polycrystalline solidification in binary alloys to simulate the formation and growth of the columnar dendritic array under the isothermal and constant cooling conditions. The solidification process and microsegregation in the mushy zone are analysed in detail. It is shown that under the isothermal condition solidification will stop after the formation of the mushy zone, but dendritic coarsening will progress continuously, which results in the decrease of the total interface area. Under the constant cooling condition the mushy zone will solidify and coarsen simultaneously. For the constant cooling solidification, microsegregation predicted by a modified Brody- Flemings model is compared with the simulation results. It is found that the Fourier number which characterizes microsegregation is different for regions with different microstructures. Dendritic coarsening and the larger area of interface should account for the enhanced Fourier number in the region with well developed second dendritic arms.展开更多
A new phase field method for two-dimensional simulations of binary alloy solidification was studied. A model basing on solute conservative in every unit was developed for solving the solute diffusion equation during s...A new phase field method for two-dimensional simulations of binary alloy solidification was studied. A model basing on solute conservative in every unit was developed for solving the solute diffusion equation during solidification. Two-dimensional computations were performed for ideal solutions and Ni-Cu dendritic growth into an isothermal and highly supersaturated liquid phase.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
The deconfinement phase transition with external magnetic field is investigated in the Friedberg-Lee model. We expand the potentiM around the two locM minima of the first-order deconfinement phase transition and extra...The deconfinement phase transition with external magnetic field is investigated in the Friedberg-Lee model. We expand the potentiM around the two locM minima of the first-order deconfinement phase transition and extract the ground state of the system in the frame of functional renormalization group. By solving the flow equations we find that the magnetic field displays a catalysis effect and it becomes more difficult to break through the confinement.展开更多
We present a thermodynamically consistent model for diblock copolymer melts coupled with an electric field derived using the Onsager linear response theory.We compare the model with the thermodynamically inconsistent ...We present a thermodynamically consistent model for diblock copolymer melts coupled with an electric field derived using the Onsager linear response theory.We compare the model with the thermodynamically inconsistent one previously used for the coupled system to highlight their differences in describing transient dynamics.展开更多
Direct metal laser sintering (DMLS) has evolvedas a popular technique in additive manufacturing, whichproduces metallic parts layer-by-layer by the application oflaser power. DMLS is a rapid manufacturing process, a...Direct metal laser sintering (DMLS) has evolvedas a popular technique in additive manufacturing, whichproduces metallic parts layer-by-layer by the application oflaser power. DMLS is a rapid manufacturing process, andthe properties of the build material depend on the sinteringmechanism as well as the microstructure of the buildmaterial. Thus, the prediction of part microstructures dur-ing the process may be a key factor for process optimiza-tion. In addition, the process parameters play a crucial rolein the microstructure evolution, and need to be controlledeffectively. In this study, the microstructure evolution ofA1-Si-10Mg alloy in DMLS process is studied with the helpof the phase field modeling. A MATLAB code is used tosolve the phase field equations, where the simulationparameters include temperature gradient, laser power andscan speed. From the simulation result, it is found that thetemperature gradient plays a significant role in the evolu-tion of microstructure with different process parameters. Ina single-seed simulation, the growth of the dendriticstructure increases with the increase in the temperaturegradient. When considering multiple seeds, the increasingin temperature gradients leads to the formation of finerdendrites; however, with increasing time, the dendrites joinand grain growth are seen to be controlled at the interface.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
Lithium(Li)metal anodes promise an ultrahigh theoretical energy density and low redox potential,thus being the critical energy material for next-generation batteries.Unfortunately,the formation of Li dendrites in Li m...Lithium(Li)metal anodes promise an ultrahigh theoretical energy density and low redox potential,thus being the critical energy material for next-generation batteries.Unfortunately,the formation of Li dendrites in Li metal anodes remarkably hinders the practical applications of Li metal anodes.Herein,the dynamic evolution of discrete Li dendrites and aggregated Li dendrites with increasing current densities is visualized by in-situ optical microscopy in conjunction with ex-situ scanning electron microscopy.As revealed by the phase field simulations,the formation of aggregated Li dendrites under high current density is attributed to the locally concentrated electric field rather than the depletion of Li ions.More specifically,the locally concentrated electric field stems from the spatial inhomogeneity on the Li metal surface and will be further enhanced with increasing current densities.Adjusting the above two factors with the help of the constructed phase field model is able to regulate the electrodeposited morphology from aggregated Li dendrites to discrete Li dendrites,and ultimately columnar Li morphology.The methodology and mechanistic understanding established herein give a significant step toward the practical applications of Li metal anodes.展开更多
A phase field model is developed to simulate the grain evolution of 17-4PH steel during cyclic heat treatment (CHT). Our simulations successfully reproduce the grain morphologies of every CHT. In the process of ever...A phase field model is developed to simulate the grain evolution of 17-4PH steel during cyclic heat treatment (CHT). Our simulations successfully reproduce the grain morphologies of every CHT. In the process of every CHT, phase transformation recrystallization happens. The recrystallized grains appear mainly on the original grain boundaries. The average grain size of 13.2 μm obtained by 1040 ℃×1 h solution treatment for this experimental steel can be refined to 2.2 μm after five CHT's. Furthermore, the effects of phenomenological parameters in our model are discussed.展开更多
Domain switching around electrically permeable and impermeable cracks in ferro-electric single crystals subjected to a mechanical load is investigated by using a phase field model.It is found that the electrical bound...Domain switching around electrically permeable and impermeable cracks in ferro-electric single crystals subjected to a mechanical load is investigated by using a phase field model.It is found that the electrical boundary conditions have little effect on the polarization distribution without any external load when the initial polarization is parallel to the crack,which is totally different from previous studies where the initial polarization is perpendicular to the crack.How-ever,the simulation results show that the electrical boundary conditions have great influence on the polarization distribution as well as the domain switching behavior when a mechanical load is applied.The critical mechanical load of domain switching with a permeable crack is much smaller than that in the case of an impermeable crack.展开更多
The phase field crystal (PFC) model is used to simulate the premelting dislocation movement of the symmetric tilt grain boundary (STGB) under strain action when the system temperature is at far from the melting po...The phase field crystal (PFC) model is used to simulate the premelting dislocation movement of the symmetric tilt grain boundary (STGB) under strain action when the system temperature is at far from the melting point and close to the melting point, respectively. The results show a local premelting occurs surrounding the dislocations as the premelting temperature is approached to from below temperature. The premelting dislocations of the STGB can glide under strain action, and the premelting region is a companion for dislocation gliding. The process of STGB decay is very similar at the two high temperature conditions. As premelting presents, it diminishes the gliding resistance for the dislocations and leads to a faster movement of dislocations, and also brings about more energy reduction of the system during the decay process of STGB. In spite of applying strain to these premelting samples in whole decay processes of STGB, the premelting dislocation region does not obviously develop and extend. This indicates that the external strain action does not promote the premelting at the high temperature, and cannot induce more premelting dislocation, which can be owed to the premelting phase around the dislocation exhibit fluid-like properties and to the premelting dislocation easily gliding and relaxing the strain energy; this is in agreement with the results of experiments and molecular dynamics.展开更多
A quantitative phase field method of multi-component diffusion-controlled phase transformations coupled with the Kim-Kim-Suzuki model was applied to study the effect of initial particle size distribution (PSD) in 3D...A quantitative phase field method of multi-component diffusion-controlled phase transformations coupled with the Kim-Kim-Suzuki model was applied to study the effect of initial particle size distribution (PSD) in 3D and space distribution in 2D on dissolution of α particles in Ti-6Al-4V alloy below β transus temperature in real time and length scale. The thermodynamic and mobility data were obtained from Thermo-Calc and DICTRA softwares, respectively. The results show that the volume fractions of α particles decay with time as: f =feq + (f0 -feq) exp(-Ktn) for four cases of PSD. The sequence of dissolution kinetics from fast to slow is: uniform PSD, normal PSD, lognormal PSD and bimodal PSD. The space distribution is found to be a major factor affecting the dissolution kinetics and the microstructures. When the distance of the particles is less than critical value, the dissolution rates reduce with the decrease in distance. The Al and V concentration fields around the particles appear more obvious soft impingement.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
In this paper,we study linearly first and second order in time,uniquely solvable and unconditionally energy stable numerical schemes to approximate the phase field model of solid-state dewetting problems based on the ...In this paper,we study linearly first and second order in time,uniquely solvable and unconditionally energy stable numerical schemes to approximate the phase field model of solid-state dewetting problems based on the novel"scalar auxiliary variable"(SAV)approach,a new developed efficient and accurate method for a large class of gradient flows.The schemes are based on the first order Euler method and the second order backward differential formulas(BDF2)for time discretization,and finite element methods for space discretization.The proposed schemes are proved to be unconditionally stable and the discrete equations are uniquely solvable for all time steps.Various numerical experiments are presented to validate the stability and accuracy of the proposed schemes.展开更多
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 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.
基金supported by the National Natural Science Foundation of China (Grant No 50401013)Doctorate Foundation of Northwestern Polytechnical University,China
文摘This paper applies a phase field model for polycrystalline solidification in binary alloys to simulate the formation and growth of the columnar dendritic array under the isothermal and constant cooling conditions. The solidification process and microsegregation in the mushy zone are analysed in detail. It is shown that under the isothermal condition solidification will stop after the formation of the mushy zone, but dendritic coarsening will progress continuously, which results in the decrease of the total interface area. Under the constant cooling condition the mushy zone will solidify and coarsen simultaneously. For the constant cooling solidification, microsegregation predicted by a modified Brody- Flemings model is compared with the simulation results. It is found that the Fourier number which characterizes microsegregation is different for regions with different microstructures. Dendritic coarsening and the larger area of interface should account for the enhanced Fourier number in the region with well developed second dendritic arms.
基金the National Natural Science Foundation of China financially(Grant No.10176009)
文摘A new phase field method for two-dimensional simulations of binary alloy solidification was studied. A model basing on solute conservative in every unit was developed for solving the solute diffusion equation during solidification. Two-dimensional computations were performed for ideal solutions and Ni-Cu dendritic growth into an isothermal and highly supersaturated liquid phase.
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.
基金Supported by the National Natural Science Foundation of China under Grant No 11405122the China Postdoctoral Science Foundation under Grant No 2014M550483
文摘The deconfinement phase transition with external magnetic field is investigated in the Friedberg-Lee model. We expand the potentiM around the two locM minima of the first-order deconfinement phase transition and extract the ground state of the system in the frame of functional renormalization group. By solving the flow equations we find that the magnetic field displays a catalysis effect and it becomes more difficult to break through the confinement.
基金partially supported by the National Natural Science Foundation of China(Grant Nos.11971051 and U1930402)partially supported by National Science Foundation grants(award DMS-1815921,1954532 and OIA-1655740)a GEAR award from SC EPSCoR/IDeA Program。
文摘We present a thermodynamically consistent model for diblock copolymer melts coupled with an electric field derived using the Onsager linear response theory.We compare the model with the thermodynamically inconsistent one previously used for the coupled system to highlight their differences in describing transient dynamics.
文摘Direct metal laser sintering (DMLS) has evolvedas a popular technique in additive manufacturing, whichproduces metallic parts layer-by-layer by the application oflaser power. DMLS is a rapid manufacturing process, andthe properties of the build material depend on the sinteringmechanism as well as the microstructure of the buildmaterial. Thus, the prediction of part microstructures dur-ing the process may be a key factor for process optimiza-tion. In addition, the process parameters play a crucial rolein the microstructure evolution, and need to be controlledeffectively. In this study, the microstructure evolution ofA1-Si-10Mg alloy in DMLS process is studied with the helpof the phase field modeling. A MATLAB code is used tosolve the phase field equations, where the simulationparameters include temperature gradient, laser power andscan speed. From the simulation result, it is found that thetemperature gradient plays a significant role in the evolu-tion of microstructure with different process parameters. Ina single-seed simulation, the growth of the dendriticstructure increases with the increase in the temperaturegradient. When considering multiple seeds, the increasingin temperature gradients leads to the formation of finerdendrites; however, with increasing time, the dendrites joinand grain growth are seen to be controlled at the interface.
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.
基金supported by the National Natural Science Foundation of China(22061132002,U1801257,and 21825501)Russell Sage Foundation project(21-43-00006)+2 种基金the National Key Research and Development Program(2016YFA0200102 and 2016YFA0202500)Beijing Municipal Natural Science Foundation(Z20J00043)the Tsinghua University Initiative Scientific Research Program。
文摘Lithium(Li)metal anodes promise an ultrahigh theoretical energy density and low redox potential,thus being the critical energy material for next-generation batteries.Unfortunately,the formation of Li dendrites in Li metal anodes remarkably hinders the practical applications of Li metal anodes.Herein,the dynamic evolution of discrete Li dendrites and aggregated Li dendrites with increasing current densities is visualized by in-situ optical microscopy in conjunction with ex-situ scanning electron microscopy.As revealed by the phase field simulations,the formation of aggregated Li dendrites under high current density is attributed to the locally concentrated electric field rather than the depletion of Li ions.More specifically,the locally concentrated electric field stems from the spatial inhomogeneity on the Li metal surface and will be further enhanced with increasing current densities.Adjusting the above two factors with the help of the constructed phase field model is able to regulate the electrodeposited morphology from aggregated Li dendrites to discrete Li dendrites,and ultimately columnar Li morphology.The methodology and mechanistic understanding established herein give a significant step toward the practical applications of Li metal anodes.
基金supported by National Natural Science Foundation of China(No.51071061)NSAF(No.11176011)
文摘A phase field model is developed to simulate the grain evolution of 17-4PH steel during cyclic heat treatment (CHT). Our simulations successfully reproduce the grain morphologies of every CHT. In the process of every CHT, phase transformation recrystallization happens. The recrystallized grains appear mainly on the original grain boundaries. The average grain size of 13.2 μm obtained by 1040 ℃×1 h solution treatment for this experimental steel can be refined to 2.2 μm after five CHT's. Furthermore, the effects of phenomenological parameters in our model are discussed.
基金supported by the National Natural Science Foundation of China (Nos. 10832009,11002123 and 11090333)the Zhejiang Provincial Natural Science Foundation under grant R6110115+1 种基金the Chinese Universities Scientific Fund under grant 2009QNA4035the program of Key Team of Technological Innovation of Zhejiang Province under grant2011R09025-07
文摘Domain switching around electrically permeable and impermeable cracks in ferro-electric single crystals subjected to a mechanical load is investigated by using a phase field model.It is found that the electrical boundary conditions have little effect on the polarization distribution without any external load when the initial polarization is parallel to the crack,which is totally different from previous studies where the initial polarization is perpendicular to the crack.How-ever,the simulation results show that the electrical boundary conditions have great influence on the polarization distribution as well as the domain switching behavior when a mechanical load is applied.The critical mechanical load of domain switching with a permeable crack is much smaller than that in the case of an impermeable crack.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 51161003), the Natural Science Foundation of Guangxi Province (Grant No. 2012GXNSFDA053001) and Ministry-Province Jointly-Constructed Cultivation Base for State Key Laboratory of Processing for Non-Ferrous Metal and Featured Materials, Guangxi Zhuang Autonomous Region (Grant No. GXKFJ12-01).
文摘The phase field crystal (PFC) model is used to simulate the premelting dislocation movement of the symmetric tilt grain boundary (STGB) under strain action when the system temperature is at far from the melting point and close to the melting point, respectively. The results show a local premelting occurs surrounding the dislocations as the premelting temperature is approached to from below temperature. The premelting dislocations of the STGB can glide under strain action, and the premelting region is a companion for dislocation gliding. The process of STGB decay is very similar at the two high temperature conditions. As premelting presents, it diminishes the gliding resistance for the dislocations and leads to a faster movement of dislocations, and also brings about more energy reduction of the system during the decay process of STGB. In spite of applying strain to these premelting samples in whole decay processes of STGB, the premelting dislocation region does not obviously develop and extend. This indicates that the external strain action does not promote the premelting at the high temperature, and cannot induce more premelting dislocation, which can be owed to the premelting phase around the dislocation exhibit fluid-like properties and to the premelting dislocation easily gliding and relaxing the strain energy; this is in agreement with the results of experiments and molecular dynamics.
基金support from the National Natural Science Foundation of China (Nos. 51601078 and 51201147)the National Key R&D Program of China (Grant No. 2016YFB0701302)+1 种基金the Informalization Construction Program of Chinese Academy of Science (INFO-115-B01)Shenyang Supercomputer Centers for the computational resource of Chinese Academy of Science
文摘A quantitative phase field method of multi-component diffusion-controlled phase transformations coupled with the Kim-Kim-Suzuki model was applied to study the effect of initial particle size distribution (PSD) in 3D and space distribution in 2D on dissolution of α particles in Ti-6Al-4V alloy below β transus temperature in real time and length scale. The thermodynamic and mobility data were obtained from Thermo-Calc and DICTRA softwares, respectively. The results show that the volume fractions of α particles decay with time as: f =feq + (f0 -feq) exp(-Ktn) for four cases of PSD. The sequence of dissolution kinetics from fast to slow is: uniform PSD, normal PSD, lognormal PSD and bimodal PSD. The space distribution is found to be a major factor affecting the dissolution kinetics and the microstructures. When the distance of the particles is less than critical value, the dissolution rates reduce with the decrease in distance. The Al and V concentration fields around the particles appear more obvious soft impingement.
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The work is supported by the National Natural Science Foundation of China(No.11401467)China Postdoctoral Science Foundation(No.2013M542334.and No.2015T81012)Natural Science Foundation of Shaanxi Province(No.2015JQ1012).The work is also supported in part by funding from King Abdullah University of Science and Technology(KAUST)through the grant BAS/1/1351-01-01.
文摘In this paper,we study linearly first and second order in time,uniquely solvable and unconditionally energy stable numerical schemes to approximate the phase field model of solid-state dewetting problems based on the novel"scalar auxiliary variable"(SAV)approach,a new developed efficient and accurate method for a large class of gradient flows.The schemes are based on the first order Euler method and the second order backward differential formulas(BDF2)for time discretization,and finite element methods for space discretization.The proposed schemes are proved to be unconditionally stable and the discrete equations are uniquely solvable for all time steps.Various numerical experiments are presented to validate the stability and accuracy of the proposed schemes.