Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilt...Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle.Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations.A staggered algorithm is used to simulate the crack propagation.The polynomial splines over hierarchical T-meshes(PHT-splines)are adopted as the basis function,which owns the C1continuity.Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials.The electric boundary conditions may influence crack paths and fracture loads significantly.The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.展开更多
A novel phase-field model for the propagation of mixed-mode hydraulic fractures,characterized by the formation of mixed-mode fractures due to the interactions between fluids and solids,is proposed.In this model,the dr...A novel phase-field model for the propagation of mixed-mode hydraulic fractures,characterized by the formation of mixed-mode fractures due to the interactions between fluids and solids,is proposed.In this model,the driving force for the phase field consists of both tensile and shear components,with the fluid contribution primarily manifesting in the tension driving force.The displacement and pressure are solved simultaneously by an implicit method.The numerical solution's iterative format is established by the finite element discretization and Newton-Raphson(NR)iterative methods.The correctness of the model is verified through the uniaxial compression physical experiments on fluid-pressurized rocks,and the limitations of the hydraulic fracture expansion phase-field model,which only considers mode I fractures,are revealed.In addition,the influence of matrix mode II fracture toughness value,natural fracture mode II toughness value,and fracturing fluid injection rate on the hydraulic fracture propagation in porous media with natural fractures is studied.展开更多
Solidification structure is a key aspect for understanding the mechanical performance of metal alloys,wherein composition and casting parameters considerably influence solidification and determine the unique microstru...Solidification structure is a key aspect for understanding the mechanical performance of metal alloys,wherein composition and casting parameters considerably influence solidification and determine the unique microstructure of the alloys.By following the principle of free energy minimization,the phase-field method eliminates the need for tracking the solid/liquid phase interface and has greatly accelerated the research and development efforts geared toward optimizing metal solidification microstructures.The recent progress in the application of phasefield simulation to investigate the effect of alloy composition and casting process parameters on the solidification structure of metals is summarized in this review.The effects of several typical elements and process parameters,including carbon,boron,silicon,cooling rate,pulling speed,scanning speed,anisotropy,and gravity,on the solidification structure are discussed.The present work also addresses the future prospects of phase-field simulation and aims to facilitate the widespread applications of phase-field approaches in the simulation of microstructures during solidification.展开更多
Study on crack propagation process of brittle rock is of most significance for cracking-arrest design and cracking-network optimization in rock engineering.Phase-field model(PFM)has advantages of simplicity and high c...Study on crack propagation process of brittle rock is of most significance for cracking-arrest design and cracking-network optimization in rock engineering.Phase-field model(PFM)has advantages of simplicity and high convergence over the common numerical methods(e.g.finite element method,discrete element method,and particle manifold method)in dealing with three-dimensional and multicrack problems.However,current PFMs are mainly used to simulate mode-I(tensile)crack propagation but difficult to effectively simulate mode-II(shear)crack propagation.In this paper,a new mixed-mode PFM is established to simulate both mode-I and mode-II crack propagation of brittle rock by distinguishing the volumetric elastic strain energy and deviatoric elastic strain energy in the total elastic strain energy and considering the effect of compressive stress on mode-II crack propagation.Numerical solution method of the new mixed-mode PFM is proposed based on the staggered solution method with self-programmed subroutines UMAT and HETVAL of ABAQUS software.Three examples calculated using different PFMs as well as test results are presented for comparison.The results show that compared with the conventional PFM(which only simulates the tensile wing crack but not mode-II crack propagation)and the modified mixed-mode PFM(which has difficulty in simulating the shear anti-wing crack),the new mixed-mode PFM can successfully simulate the whole trajectories of mixed-mode crack propagation(including the tensile wing crack,shear secondary crack,and shear anti-wing crack)and mode-II crack propagation,which are close to the test results.It can be further extended to simulate multicrack propagation of anisotropic rock under multi-field coupling loads.展开更多
A two-dimensional phase field(PF)model was developed to simulate the dendritic solidification in magnesium alloy with hcp crystal structure.By applying a parallel-adaptive mesh refinement(Para-AMR)algorithm,the comput...A two-dimensional phase field(PF)model was developed to simulate the dendritic solidification in magnesium alloy with hcp crystal structure.By applying a parallel-adaptive mesh refinement(Para-AMR)algorithm,the computational efficiency of the numerical model was greatly improved.Based on the PF model,a series of simulation cases were conducted and the results showed that the anisotropy coefficient and coupling coefficient had a great influence on the dendritic morphology of magnesium alloy.The dendritic growth kinetics was determined by the undercooling and equilibrium solute partition coefficient.A significant finding is acquired that with a large undercooling,the maximum solute concentration is located on both sides of the dendrite tip in the liquid,whereas the maximum solute concentration gradient is located right ahead of the dendrite tip in the liquid.The dendrite tip growth velocity decreases with the increase of the equilibrium solute partition coefficient,while the variation trend of the dendrite tip radius is the opposite.Quantitative analysis was carried out relating to the dendritic morphology and growth kinetics,and the simulated results are consistent with the theoretical models proposed in the previously published works.展开更多
A three-dimensional(3D)multiple phase field model,which takes into account the grain boundary(GB)energy anisotropy caused by texture,is established based on real grain orientations and Read-Shockley model.The model is...A three-dimensional(3D)multiple phase field model,which takes into account the grain boundary(GB)energy anisotropy caused by texture,is established based on real grain orientations and Read-Shockley model.The model is applied to the grain growth process of polycrystalline Mg(ZK60)alloy to investigate the evolution characteristics in different systems with varying proportions of low-angle grain boundary(LAGB)caused by different texture levels.It is found that the GB energy anisotropy can cause the grain growth kinetics to change,namely,higher texture levels(also means higher LAGB proportion)result in lower kinetics,and vice versa.The simulation results also show that the topological characteristics,such as LAGB proportion and distribution of grain size,undergo different evolution characteristics in different systems,and a more serious grain size fluctuation can be caused by a higher texture level.The mechanism is mainly the slower evolution of textured grains in their accumulation area and the faster coarsening rate of non-textured grains.Therefore,weakening the texture level is an effective way for implementing a desired homogenized microstructure in ZK60 Mg alloy.The rules revealed by the simulation results should be of great significance for revealing how the GB anisotropy affects the evolution of polycrystalline during the grain growth after recrystallization and offer the ideas for processing the alloy and optimizing the microstructure.展开更多
We employ the Galerkin method to prove the global existence of weak solutions to a phase-field model which is suitable to describe a sort of interface motion driven by configurational forces.The higher-order derivativ...We employ the Galerkin method to prove the global existence of weak solutions to a phase-field model which is suitable to describe a sort of interface motion driven by configurational forces.The higher-order derivative of unknown S exists in the sense of local weak derivatives since it may be not summable over the original open domain.The existence proof is valid in the one-dimensional case.展开更多
A regularization of the surface tension anisotropic function used in vapor-liquid-solid nanowire growth was introduced into the quantitative phase-field model to simulate the faceted growth in solidification of alloys...A regularization of the surface tension anisotropic function used in vapor-liquid-solid nanowire growth was introduced into the quantitative phase-field model to simulate the faceted growth in solidification of alloys.Predicted results show that the value of δ can only affect the region near the tip,and the convergence with respect to δ can be achieved with the decrease of δ near the tip.It can be found that the steady growth velocity is not a mo no tonic function of the cusp amplitude,and the maximum value is approximately at ε=0.8 when the supersaturation is fixed.Moreover,the growth velocity is an increasing function of supersaturation with the morphological transition from facet to dendrite.展开更多
A quantitative multi-phase-field model for non-isothermal and polycrystalline solidification was developed and applied to dilute multicomponent alloys with hexagonal close-packed structures.The effects of Lewis coeffi...A quantitative multi-phase-field model for non-isothermal and polycrystalline solidification was developed and applied to dilute multicomponent alloys with hexagonal close-packed structures.The effects of Lewis coefficient and undercooling on dendrite growth were investigated systematically.Results show that large Lewis coefficients facilitate the release of the latent heat,which can accelerate the dendrite growth while suppress the dendrite tip radius.The greater the initial undercooling,the stronger the driving force for dendrite growth,the faster the growth rate of dendrites,the higher the solid fraction,and the more serious the solute microsegregation.The simulated dendrite growth dynamics are consistent with predictions from the phenomenological theory but significantly deviate from the classical JMAK theory which neglects the soft collision effect and mutual blocking among dendrites.Finally,taking the Mg-6Gd-2Zn(wt.%)alloy as an example,the simulated dendrite morphology shows good agreement with experimental results.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
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
In this article, we study the phase-field model of solidification for numerical simulation of dendritic crystal growth that occurs during the casting of metals and alloys. Phase-field model of solidification describes...In this article, we study the phase-field model of solidification for numerical simulation of dendritic crystal growth that occurs during the casting of metals and alloys. Phase-field model of solidification describes the physics of dendritic growth in any material during the process of under cooling. The numerical procedure in this work is based on finite difference scheme for space and the 4th-order Runge-Kutta method for time discretization. The effect of each physical parameter on the shape and growth of dendritic crystal is studied and visualized in detail.展开更多
A modified phase-field model is proposed for simulating the isothermal crystallization of polymer melts. The model consists of a second-order phase-field equation and a heat conduction equation. It obtains its model p...A modified phase-field model is proposed for simulating the isothermal crystallization of polymer melts. The model consists of a second-order phase-field equation and a heat conduction equation. It obtains its model parameters from the real material parameters and is easy to use with tolerable computational cost. Due to the use of a new free energy functional form, the model can reproduce various single crystal morphologies of polymer melts under quiescent conditions, including dendritic, lamellar branching, ring-banded, breakup of ring-banded, faceted hexagonal, and spherulitic structures. Simulation results of isotactic polystyrene crystals demonstrate that the present phase-field model has the ability to give qualitative predictions of polymer crystallization under isothermal and quiescent conditions.展开更多
This paper develops a new phase-field model for equiaxed dendrite growth of multiple grains in multicomponent alloys based on the Ginzberg-Landau theory and phase-field model of a single grain. Taking Al-Cu and Al-Cu-...This paper develops a new phase-field model for equiaxed dendrite growth of multiple grains in multicomponent alloys based on the Ginzberg-Landau theory and phase-field model of a single grain. Taking Al-Cu and Al-Cu-Mg alloys for example, it couples the concentration field and simulates the dendrite growth process of multiple grains during isothermal solidification. The result of the simulation shows dendrite competitive growth of multiple grains, and is reapplied to the process of dendrite growth in practical solidification.展开更多
Phase-field modeling for three-dimensional foam structures is presented. The foam structure, which is generally applicable for porous material design, is geometrically approximated with a space-filling structure, and ...Phase-field modeling for three-dimensional foam structures is presented. The foam structure, which is generally applicable for porous material design, is geometrically approximated with a space-filling structure, and hence, the analysis of the space-filling structure was performed using the phase field model. An additional term was introduced to the conventional multi-phase field model to satisfy the volume constraint condition. Then, the equations were numerically solved using the finite difference method, and simulations were carried out for several nuclei settings. First, the nuclei were set on complete lattice points for a bcc or fcc arrangement, with a truncated hexagonal structure, which is known as a Kelvin cell, or a rhombic dodecahedron being obtained, respectively. Then, an irregularity was introduced in the initial nuclei arrangement. The results revealed that the truncated hexagonal structure was stable against a slight irregularity, whereas the rhombic polyhedral was destroyed by the instability. Finally, the nuclei were placed randomly, and the relaxation process of a certain cell was traced with the result that every cell leads to a convex polyhedron shape.展开更多
A phase-field method was employed to study the influence of elastic field on the nucleation and microstructure evolution. Two kinds of nucleation process were considered: one using fixed nucleation probability and th...A phase-field method was employed to study the influence of elastic field on the nucleation and microstructure evolution. Two kinds of nucleation process were considered: one using fixed nucleation probability and the other calculated from the classical nucleation theory. In the latter case, the simulated results show that the anisotropic elastic strain field yields significant effects on the behavior of nucleation. With a large lattice misfit between the matrixes and the precipitates, the nucleation process does not appear fully random but displays some spatial correlation and has a preference for the elastic soft direction. However, with a small lattice misfit, this bias does not look quite clear. On the contrary, in the case of fixed nucleation probability, the elastic field has no influence on the nucleation process. The lattice mismatch also exerts influences on the microstructure morphology: with lattice mismatch becoming larger, the microstructure proves to align along the elastic soft direction.展开更多
The Cahn–Hilliard equations are a versatile model for describing the evolution of complex morphologies.In this paper we present a computational pipeline for the numerical solution of a ternary phase-field model for d...The Cahn–Hilliard equations are a versatile model for describing the evolution of complex morphologies.In this paper we present a computational pipeline for the numerical solution of a ternary phase-field model for describing the nanomorphology of donor–acceptor semiconductor blends used in organic photovoltaic devices.The model consists of two coupled fourth-order partial differential equations that are discretized using a finite element approach.In order to solve the resulting large-scale linear systems efficiently,we propose a preconditioning strategy that is based on efficient approximations of the Schur-complement of a saddle point system.We show that this approach performs robustly with respect to variations in the discretization parameters.Finally,we outline that the computed morphologies can be used for the computation of charge generation,recombination,and transport in organic solar cells.展开更多
Zinc(Zn)-air batteries are widely used in secondary battery research owing to their high theoretical energy density,good electrochemical reversibility,stable discharge performance,and low cost of the anode active mate...Zinc(Zn)-air batteries are widely used in secondary battery research owing to their high theoretical energy density,good electrochemical reversibility,stable discharge performance,and low cost of the anode active material Zn.However,the Zn anode also leads to many challenges,including dendrite growth,deformation,and hydrogen precipitation self-corrosion.In this context,Zn dendrite growth has a greater impact on the cycle lives.In this dissertation,a dendrite growth model for a Zn-air battery was established based on electrochemical phase field theory,and the effects of the charging time,anisotropy strength,and electrolyte temperature on the morphology and growth height of Zn dendrites were studied.A series of experiments was designed with different gradient influencing factors in subsequent experiments to verify the theoretical simulations,including elevated electrolyte temperatures,flowing electrolytes,and pulsed charging.The simulation results show that the growth of Zn dendrites is controlled mainly by diffusion and mass transfer processes,whereas the electrolyte temperature,flow rate,and interfacial energy anisotropy intensity are the main factors.The experimental results show that an optimal electrolyte temperature of 343.15 K,an optimal electrolyte flow rate of 40 ml·min^(-1),and an effective pulse charging mode.展开更多
Sintering,a well-established technique in powder metallurgy,plays a critical role in the processing of high melting point materials.A comprehensive understanding of structural changes during the sintering process is e...Sintering,a well-established technique in powder metallurgy,plays a critical role in the processing of high melting point materials.A comprehensive understanding of structural changes during the sintering process is essential for effective product assessment.The phase-field method stands out for its unique ability to simulate these structural transformations.Despite its widespread application,there is a notable absence of literature reviews focused on its usage in sintering simulations.Therefore,this paper addresses this gap by reviewing the latest advancements in phase-field sintering models,covering approaches based on energy,grand potential,and entropy increase.The characteristics of various models are extensively discussed,with a specific emphasis on energy-based models incorporating considerations such as interface energy anisotropy,tensor-form diffusion mechanisms,and various forms of rigid particle motion during sintering.Furthermore,the paper offers a concise summary of phase-field sintering models that integrate with other physical fields,including stress/strain fields,viscous flow,temperature field,and external electric fields.In conclusion,the paper provides a succinct overview of the entire content and delineates potential avenues for future research.展开更多
Phase-field method,as a powerful and popular approach to predict the mesoscale microstructure evolution in various materials science,provides a bridge from atomic-scale methods to the macroscale and has been widely us...Phase-field method,as a powerful and popular approach to predict the mesoscale microstructure evolution in various materials science,provides a bridge from atomic-scale methods to the macroscale and has been widely used at an ever-increasing rate.This paper aims to briefly review the origin,basic idea,and development of phase-field models in a historical manner.The focus is placed on the classical and state-of-the-art applications in China,including liquid–solid,solid–solid,gas–solid,ferroelectrics/ferromagnetics phase transformation,and crack propagation-fracture.After introducing the academic activities in the phase-field community in China,some suggestions for the future development directions of phase-field method are finally mentioned.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.12072297 and12202370)the Natural Science Foundation of Sichuan Province of China(No.24NSFSC4777)。
文摘Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle.Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations.A staggered algorithm is used to simulate the crack propagation.The polynomial splines over hierarchical T-meshes(PHT-splines)are adopted as the basis function,which owns the C1continuity.Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials.The electric boundary conditions may influence crack paths and fracture loads significantly.The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.
基金Project supported by the National Natural Science Foundation of China(No.42202314)。
文摘A novel phase-field model for the propagation of mixed-mode hydraulic fractures,characterized by the formation of mixed-mode fractures due to the interactions between fluids and solids,is proposed.In this model,the driving force for the phase field consists of both tensile and shear components,with the fluid contribution primarily manifesting in the tension driving force.The displacement and pressure are solved simultaneously by an implicit method.The numerical solution's iterative format is established by the finite element discretization and Newton-Raphson(NR)iterative methods.The correctness of the model is verified through the uniaxial compression physical experiments on fluid-pressurized rocks,and the limitations of the hydraulic fracture expansion phase-field model,which only considers mode I fractures,are revealed.In addition,the influence of matrix mode II fracture toughness value,natural fracture mode II toughness value,and fracturing fluid injection rate on the hydraulic fracture propagation in porous media with natural fractures is studied.
基金financially supported by the National Key Research and Development Program of China(No.2021YFB3702401)the National Natural Science Foundation of China(Nos.51901013,52122408,52071023)+3 种基金financial support from the Fundamental Research Funds for the Central Universities,China(University of Science and Technology Beijing(USTB),Nos.FRF-TP-2021-04C1,06500135)financial support from the Qilu Young Talent Program of Shandong University,Zhejiang Lab Open Research Project,China(No.K2022PE0AB05)the Shandong Provincial Natural Science Foundation,China(No.ZR2023MA058)the Guangdong Basic and Applied Basic Research Foundation,China(No.2023A1515011819)。
文摘Solidification structure is a key aspect for understanding the mechanical performance of metal alloys,wherein composition and casting parameters considerably influence solidification and determine the unique microstructure of the alloys.By following the principle of free energy minimization,the phase-field method eliminates the need for tracking the solid/liquid phase interface and has greatly accelerated the research and development efforts geared toward optimizing metal solidification microstructures.The recent progress in the application of phasefield simulation to investigate the effect of alloy composition and casting process parameters on the solidification structure of metals is summarized in this review.The effects of several typical elements and process parameters,including carbon,boron,silicon,cooling rate,pulling speed,scanning speed,anisotropy,and gravity,on the solidification structure are discussed.The present work also addresses the future prospects of phase-field simulation and aims to facilitate the widespread applications of phase-field approaches in the simulation of microstructures during solidification.
基金supports by National Natural Science Foundation of China(Grant Nos.51874351 and 52078495)Excellent Postdoctoral Innovative Talents Project of Hunan Province,China(Grant No.2020RC2001).
文摘Study on crack propagation process of brittle rock is of most significance for cracking-arrest design and cracking-network optimization in rock engineering.Phase-field model(PFM)has advantages of simplicity and high convergence over the common numerical methods(e.g.finite element method,discrete element method,and particle manifold method)in dealing with three-dimensional and multicrack problems.However,current PFMs are mainly used to simulate mode-I(tensile)crack propagation but difficult to effectively simulate mode-II(shear)crack propagation.In this paper,a new mixed-mode PFM is established to simulate both mode-I and mode-II crack propagation of brittle rock by distinguishing the volumetric elastic strain energy and deviatoric elastic strain energy in the total elastic strain energy and considering the effect of compressive stress on mode-II crack propagation.Numerical solution method of the new mixed-mode PFM is proposed based on the staggered solution method with self-programmed subroutines UMAT and HETVAL of ABAQUS software.Three examples calculated using different PFMs as well as test results are presented for comparison.The results show that compared with the conventional PFM(which only simulates the tensile wing crack but not mode-II crack propagation)and the modified mixed-mode PFM(which has difficulty in simulating the shear anti-wing crack),the new mixed-mode PFM can successfully simulate the whole trajectories of mixed-mode crack propagation(including the tensile wing crack,shear secondary crack,and shear anti-wing crack)and mode-II crack propagation,which are close to the test results.It can be further extended to simulate multicrack propagation of anisotropic rock under multi-field coupling loads.
基金financially supported by the National Natural Science Foundation of China(No.51805389)the Natural Science Foundation of Hubei Province,China(No.2018CFB210)the 111 Project(No.B17034)。
文摘A two-dimensional phase field(PF)model was developed to simulate the dendritic solidification in magnesium alloy with hcp crystal structure.By applying a parallel-adaptive mesh refinement(Para-AMR)algorithm,the computational efficiency of the numerical model was greatly improved.Based on the PF model,a series of simulation cases were conducted and the results showed that the anisotropy coefficient and coupling coefficient had a great influence on the dendritic morphology of magnesium alloy.The dendritic growth kinetics was determined by the undercooling and equilibrium solute partition coefficient.A significant finding is acquired that with a large undercooling,the maximum solute concentration is located on both sides of the dendrite tip in the liquid,whereas the maximum solute concentration gradient is located right ahead of the dendrite tip in the liquid.The dendrite tip growth velocity decreases with the increase of the equilibrium solute partition coefficient,while the variation trend of the dendrite tip radius is the opposite.Quantitative analysis was carried out relating to the dendritic morphology and growth kinetics,and the simulated results are consistent with the theoretical models proposed in the previously published works.
基金Project supported by the National Key Research and Development Program of China(Grant No.2016YFB0701204)the 111 Project,China(Grant No.B20029)+2 种基金the Fundamental Research Funds for the Central Universities,China(Grant Nos.N2002017 and N2007011)the National Natural Science Foundation of China(Grant No.51571055)the Science Fund from the Science and Technology Bureau of Jiangyin High-Tech Industrial Development Zone,China(Grant No.ZX20200062)。
文摘A three-dimensional(3D)multiple phase field model,which takes into account the grain boundary(GB)energy anisotropy caused by texture,is established based on real grain orientations and Read-Shockley model.The model is applied to the grain growth process of polycrystalline Mg(ZK60)alloy to investigate the evolution characteristics in different systems with varying proportions of low-angle grain boundary(LAGB)caused by different texture levels.It is found that the GB energy anisotropy can cause the grain growth kinetics to change,namely,higher texture levels(also means higher LAGB proportion)result in lower kinetics,and vice versa.The simulation results also show that the topological characteristics,such as LAGB proportion and distribution of grain size,undergo different evolution characteristics in different systems,and a more serious grain size fluctuation can be caused by a higher texture level.The mechanism is mainly the slower evolution of textured grains in their accumulation area and the faster coarsening rate of non-textured grains.Therefore,weakening the texture level is an effective way for implementing a desired homogenized microstructure in ZK60 Mg alloy.The rules revealed by the simulation results should be of great significance for revealing how the GB anisotropy affects the evolution of polycrystalline during the grain growth after recrystallization and offer the ideas for processing the alloy and optimizing the microstructure.
基金supported by the Science and Technology Commission of Shanghai Municipality of China(No.20JC1413600)。
文摘We employ the Galerkin method to prove the global existence of weak solutions to a phase-field model which is suitable to describe a sort of interface motion driven by configurational forces.The higher-order derivative of unknown S exists in the sense of local weak derivatives since it may be not summable over the original open domain.The existence proof is valid in the one-dimensional case.
基金Project supported by the National Key Research and Development Program of China(Grant No.2018YFB2001800)the National Natural Science Foundation of China(Grant No.21978298)+2 种基金the Natural Science Foundation of Shaanxi Province in China(Grant No.2020JM-111)Applied Basic Research Key Project of Yunnan,China(Grant No.202002AB080001-1)Henan Youth Talent Promotion Project.China(Grant No.2020HYTP019)。
文摘A regularization of the surface tension anisotropic function used in vapor-liquid-solid nanowire growth was introduced into the quantitative phase-field model to simulate the faceted growth in solidification of alloys.Predicted results show that the value of δ can only affect the region near the tip,and the convergence with respect to δ can be achieved with the decrease of δ near the tip.It can be found that the steady growth velocity is not a mo no tonic function of the cusp amplitude,and the maximum value is approximately at ε=0.8 when the supersaturation is fixed.Moreover,the growth velocity is an increasing function of supersaturation with the morphological transition from facet to dendrite.
基金the National Natural Science Foundation-Youth Science Foundation Project(No.51901208)the Henan University Key Scientific Research Project(No.20B430020)+1 种基金the Key Scientific and Technological Projects in Henan Province(Nos.202102210016,202102210272)the Major Innovation Project of Zhengzhou City(No.23101000010).
文摘A quantitative multi-phase-field model for non-isothermal and polycrystalline solidification was developed and applied to dilute multicomponent alloys with hexagonal close-packed structures.The effects of Lewis coefficient and undercooling on dendrite growth were investigated systematically.Results show that large Lewis coefficients facilitate the release of the latent heat,which can accelerate the dendrite growth while suppress the dendrite tip radius.The greater the initial undercooling,the stronger the driving force for dendrite growth,the faster the growth rate of dendrites,the higher the solid fraction,and the more serious the solute microsegregation.The simulated dendrite growth dynamics are consistent with predictions from the phenomenological theory but significantly deviate from the classical JMAK theory which neglects the soft collision effect and mutual blocking among dendrites.Finally,taking the Mg-6Gd-2Zn(wt.%)alloy as an example,the simulated dendrite morphology shows good agreement with experimental results.
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.
文摘In this article, we study the phase-field model of solidification for numerical simulation of dendritic crystal growth that occurs during the casting of metals and alloys. Phase-field model of solidification describes the physics of dendritic growth in any material during the process of under cooling. The numerical procedure in this work is based on finite difference scheme for space and the 4th-order Runge-Kutta method for time discretization. The effect of each physical parameter on the shape and growth of dendritic crystal is studied and visualized in detail.
基金Project supported by the National Key Basic Research Program of China (973 Program) (Grant No.2012CB025903)the Foundation for Fundamental Research of Northwestern Polytechnical University,China (Grant No.JCY20130141)+1 种基金the Doctorate Foundation of Northwestern Polytechnical University,China (Grant No.cx201019)the Fund for Doctoral Students Newcomer Awards from the Ministry of Education of China
文摘A modified phase-field model is proposed for simulating the isothermal crystallization of polymer melts. The model consists of a second-order phase-field equation and a heat conduction equation. It obtains its model parameters from the real material parameters and is easy to use with tolerable computational cost. Due to the use of a new free energy functional form, the model can reproduce various single crystal morphologies of polymer melts under quiescent conditions, including dendritic, lamellar branching, ring-banded, breakup of ring-banded, faceted hexagonal, and spherulitic structures. Simulation results of isotactic polystyrene crystals demonstrate that the present phase-field model has the ability to give qualitative predictions of polymer crystallization under isothermal and quiescent conditions.
基金supported by the National Natural Science Foundation of China(Grant No 50804019)Foundation for Doctoral Program of the Ministry of Education of China(Grant No 20070731001)
文摘This paper develops a new phase-field model for equiaxed dendrite growth of multiple grains in multicomponent alloys based on the Ginzberg-Landau theory and phase-field model of a single grain. Taking Al-Cu and Al-Cu-Mg alloys for example, it couples the concentration field and simulates the dendrite growth process of multiple grains during isothermal solidification. The result of the simulation shows dendrite competitive growth of multiple grains, and is reapplied to the process of dendrite growth in practical solidification.
文摘Phase-field modeling for three-dimensional foam structures is presented. The foam structure, which is generally applicable for porous material design, is geometrically approximated with a space-filling structure, and hence, the analysis of the space-filling structure was performed using the phase field model. An additional term was introduced to the conventional multi-phase field model to satisfy the volume constraint condition. Then, the equations were numerically solved using the finite difference method, and simulations were carried out for several nuclei settings. First, the nuclei were set on complete lattice points for a bcc or fcc arrangement, with a truncated hexagonal structure, which is known as a Kelvin cell, or a rhombic dodecahedron being obtained, respectively. Then, an irregularity was introduced in the initial nuclei arrangement. The results revealed that the truncated hexagonal structure was stable against a slight irregularity, whereas the rhombic polyhedral was destroyed by the instability. Finally, the nuclei were placed randomly, and the relaxation process of a certain cell was traced with the result that every cell leads to a convex polyhedron shape.
基金National Natural Science Foundation of China (50401013)
文摘A phase-field method was employed to study the influence of elastic field on the nucleation and microstructure evolution. Two kinds of nucleation process were considered: one using fixed nucleation probability and the other calculated from the classical nucleation theory. In the latter case, the simulated results show that the anisotropic elastic strain field yields significant effects on the behavior of nucleation. With a large lattice misfit between the matrixes and the precipitates, the nucleation process does not appear fully random but displays some spatial correlation and has a preference for the elastic soft direction. However, with a small lattice misfit, this bias does not look quite clear. On the contrary, in the case of fixed nucleation probability, the elastic field has no influence on the nucleation process. The lattice mismatch also exerts influences on the microstructure morphology: with lattice mismatch becoming larger, the microstructure proves to align along the elastic soft direction.
基金the Deutsche Forschungsgemeinschaft(DFG)for funding this work(Research Unit FOR 5387 POPULAR,Project No.461909888).
文摘The Cahn–Hilliard equations are a versatile model for describing the evolution of complex morphologies.In this paper we present a computational pipeline for the numerical solution of a ternary phase-field model for describing the nanomorphology of donor–acceptor semiconductor blends used in organic photovoltaic devices.The model consists of two coupled fourth-order partial differential equations that are discretized using a finite element approach.In order to solve the resulting large-scale linear systems efficiently,we propose a preconditioning strategy that is based on efficient approximations of the Schur-complement of a saddle point system.We show that this approach performs robustly with respect to variations in the discretization parameters.Finally,we outline that the computed morphologies can be used for the computation of charge generation,recombination,and transport in organic solar cells.
基金financially supported by the National Natural Science Foundation of China(22168019 and 52074141)the Major Science and Technology Projects in Yunnan Province(202202AB080014)+1 种基金The authors are grateful to the National Natural Science Foundation of Chinathe Major Science and Technology Projects in Yunnan Province for their support.
文摘Zinc(Zn)-air batteries are widely used in secondary battery research owing to their high theoretical energy density,good electrochemical reversibility,stable discharge performance,and low cost of the anode active material Zn.However,the Zn anode also leads to many challenges,including dendrite growth,deformation,and hydrogen precipitation self-corrosion.In this context,Zn dendrite growth has a greater impact on the cycle lives.In this dissertation,a dendrite growth model for a Zn-air battery was established based on electrochemical phase field theory,and the effects of the charging time,anisotropy strength,and electrolyte temperature on the morphology and growth height of Zn dendrites were studied.A series of experiments was designed with different gradient influencing factors in subsequent experiments to verify the theoretical simulations,including elevated electrolyte temperatures,flowing electrolytes,and pulsed charging.The simulation results show that the growth of Zn dendrites is controlled mainly by diffusion and mass transfer processes,whereas the electrolyte temperature,flow rate,and interfacial energy anisotropy intensity are the main factors.The experimental results show that an optimal electrolyte temperature of 343.15 K,an optimal electrolyte flow rate of 40 ml·min^(-1),and an effective pulse charging mode.
基金supported by the National Science and TechnologyMajor Project,China(No.J2019-IV-0014-0082)the National Key Research and Development Program of China(No.2022YFB4600700)+1 种基金the National Overseas Youth Talents Program,China,the Research Fund of State Key Laboratory of Mechanics and Control for Aerospace Structures,China(No.MCMS-I-0422K01)a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions,China.
文摘Sintering,a well-established technique in powder metallurgy,plays a critical role in the processing of high melting point materials.A comprehensive understanding of structural changes during the sintering process is essential for effective product assessment.The phase-field method stands out for its unique ability to simulate these structural transformations.Despite its widespread application,there is a notable absence of literature reviews focused on its usage in sintering simulations.Therefore,this paper addresses this gap by reviewing the latest advancements in phase-field sintering models,covering approaches based on energy,grand potential,and entropy increase.The characteristics of various models are extensively discussed,with a specific emphasis on energy-based models incorporating considerations such as interface energy anisotropy,tensor-form diffusion mechanisms,and various forms of rigid particle motion during sintering.Furthermore,the paper offers a concise summary of phase-field sintering models that integrate with other physical fields,including stress/strain fields,viscous flow,temperature field,and external electric fields.In conclusion,the paper provides a succinct overview of the entire content and delineates potential avenues for future research.
基金the National Natural Science Foundation of China(Nos.52074246,52201146,52205429,52275390,U1904214)the National Defense Basic Scientific Research Program of China(No.JCKY2020408B002)+1 种基金the Key Research and Development Program of Shanxi Province(No.202102050201011)L.Z.acknowledges the Natural Science Foundation of Hunan Province for Distinguished Young Scholars(No.2021JJ10062).
文摘Phase-field method,as a powerful and popular approach to predict the mesoscale microstructure evolution in various materials science,provides a bridge from atomic-scale methods to the macroscale and has been widely used at an ever-increasing rate.This paper aims to briefly review the origin,basic idea,and development of phase-field models in a historical manner.The focus is placed on the classical and state-of-the-art applications in China,including liquid–solid,solid–solid,gas–solid,ferroelectrics/ferromagnetics phase transformation,and crack propagation-fracture.After introducing the academic activities in the phase-field community in China,some suggestions for the future development directions of phase-field method are finally mentioned.