Anode-free lithium metal batteries are prone to capacity degradation and safety hazards due to the formation and growth of lithium dendrites.The interface between the current collector and deposited lithium plays a cr...Anode-free lithium metal batteries are prone to capacity degradation and safety hazards due to the formation and growth of lithium dendrites.The interface between the current collector and deposited lithium plays a critical role in preventing dendrite formation by regulating the thermodynamics and kinetics of lithium deposition.In this study,we develop a phase field model to investigate the influence of the current collector’s surface energy on lithium deposition morphology and its effect on the quality of the lithium metal film.It is demonstrated that a higher surface energy of the current collector promotes the growth of lithium metal along the surface of the current collector.Further,our simulation results show that a higher surface energy accelerates the formation of the lithium metal film while simultaneously reducing its surface roughness.By examining different contact angles and applied potentials,we construct a phase diagram of deposition morphology,illustrating that increased surface energy facilitates the dense and uniform deposition of lithium metal by preventing the formation of lithium filaments and voids.These findings provide new insights into the development and application of anode-free lithium metal batteries.展开更多
Flexoelectricity is a two-way coupling effect between the strain gradient and electric field that exists in all dielectrics,regardless of point group symmetry.However,the high-order derivatives of displacements involv...Flexoelectricity is a two-way coupling effect between the strain gradient and electric field that exists in all dielectrics,regardless of point group symmetry.However,the high-order derivatives of displacements involved in the strain gradient pose challenges in solving electromechanical coupling problems incorporating the flexoelectric effect.In this study,we formulate a phase-field model for ferroelectric materials considering the flexoelectric effect.A four-node quadrilateral element with 20 degrees of freedom is constructed without introducing high-order shape functions.The microstructure evolution of domains is described by an independent order parameter,namely the spontaneous polarization governed by the time-dependent Ginzburg–Landau theory.The model is developed based on a thermodynamic framework,in which a set of microforces is introduced to construct the constitutive relation and evolution equation.For the flexoelectric part of electric enthalpy,the strain gradient is determined by interpolating the mechanical strain at the node via the values of Gaussian integration points in the isoparametric space.The model is shown to be capable of reproducing the classic analytical solution of dielectric materials incorporating the flexoelectric contribution.The model is verified by duplicating some typical phenomena in flexoelectricity in cylindrical tubes and truncated pyramids.A comparison is made between the polarization distribution in dielectrics and ferroelectrics.The model can reproduce the solution to the boundary value problem of the cylindrical flexoelectric tube,and demonstrate domain twisting at domain walls in ferroelectrics considering the flexoelectric effect.展开更多
A phase-field model for growth of iron whiskers that includes convection around a particle was investigated during the process of fluidized pre-reduction. In the simulations, the phase-field method was coupled with fl...A phase-field model for growth of iron whiskers that includes convection around a particle was investigated during the process of fluidized pre-reduction. In the simulations, the phase-field method was coupled with flow field and reduction of iron oxide particles. The results showed that the reduction rate at local place had significant effects on the iron ions diffusion and the iron whiskers were more easily grown on the area containing low mole fraction of oxygen. The growth of iron whiskers in the model was investigated in two important simple situations: a velocity change flow and a CO concentration change flow. Because of high reduction rate and low surface energy, iron whiskers were more easily grown on the windward surface and the length of iron whiskers increased with gas velocity increasing. However, both the length and numbers of iron whiskers increased with CO concentration increasing due to the more nucleation site of iron whiskers created by CO adsorbed. When the gas velocity is higher than 0.3 m/s or CO mole fraction is high than 0.6, the nucleation incubation time would be rapidly decreased, which could give suggestions to control the operational parameters in the fluidized pre-reduction process.展开更多
Phase-field model was employed to quantitatively study the effect of convection on pattern selection and growth rate of 2D and 3D dendrite tip,as well as the effect of the different convection velocity on the dendriti...Phase-field model was employed to quantitatively study the effect of convection on pattern selection and growth rate of 2D and 3D dendrite tip,as well as the effect of the different convection velocity on the dendritic growth.The calculated results show that crystal is asymmetric in the priority direction of growth under flow.The dentritic growth is promoted in the upstream region and suppressed in the downstream region.Convection can cause deviation in the dendrite growth direction and the preferred direction of the columnar crystals.It has been found that both primary dendrite stem and secondary dendrite arm deflect significantly towards upstream direction,secondary dendrite arm in upstream direction is more developed than the primary dendrite in downstream direction.展开更多
The evolution of ordered interphase boundary (IPB) of Ni75AlxV25-x alloys was simulated using the microscopic phase-field method. Based on the atomic occupation probability figure on 2D and order parameters, it was fo...The evolution of ordered interphase boundary (IPB) of Ni75AlxV25-x alloys was simulated using the microscopic phase-field method. Based on the atomic occupation probability figure on 2D and order parameters, it was found that the IPB formed by different directions ofθ phase has great effect on the precipitation of γ ′ phase. The γ ′ phase precipitated at the IPB that is formed by [1 00]θ direction where the ( 001)θ plane is opposite, and then grows up and the shape is strap at final. The IPB structure between γ ′phase andθ phase is the same. There is no γ ′ phase precipitate at the IPB where the ( 002)θ and ( 001)θ planes are opposite, the ordered IPB is dissolved into disordered area. There is γ ′ phase precipitation at the IPB formed by the [ 001]θ and [1 00]θ directions, and the IPB structure is different between γ ′ phase and the different directions ofθ phase. The IPB where ( 001)γ′ and (1 00)θ plane opposite does not migrate during the γ ′ phase growth, and γ ′ phase grows along [1 00]θdirection.展开更多
Since the discovery of ferromagnetic morphotropic phase boundary(MPB)in 2010,the connotation and extension of MPB have been becoming more and more abundant.Over the last dozen years,much experimental work has been don...Since the discovery of ferromagnetic morphotropic phase boundary(MPB)in 2010,the connotation and extension of MPB have been becoming more and more abundant.Over the last dozen years,much experimental work has been done to design magnetostrictive materials based on the MPB principle.However,due to the difficulty in direct experimental observations and the complexity of theoretical treatments,the insight into the microstructure property relationships and underlying mechanisms near the ferromagnetic MPB has not been fully revealed.Here,we have reviewed our recent computer simulation work about the super-magnetoelastic behavior near the critical region of several typical materials.Phase-field modeling and simulation are employed to explore the domain configuration and engineering in single crystals as well as the grain size effect in polycrystals.Besides,a general nano-embryonic mechanism for superelasticity is also introduced.Finally,some future perspectives and challenges are presented to stimulate a deeper consideration of the research paradigm between multiscale modeling and material development.展开更多
Epoxy resin is widely used in electrical insulation because of its excellent mechanical and insulating properties;however,its performance can degrade over time owing to thermal aging.This study focuses on developing a...Epoxy resin is widely used in electrical insulation because of its excellent mechanical and insulating properties;however,its performance can degrade over time owing to thermal aging.This study focuses on developing a thermal aging region growth model for epoxy resin using the phase-field method.The reliability of the model is validated by applying a 20 MV/m electric field and observing the evolution of aging regions and the distribution of the internal energy density.A Gaussian-distributed aging region near the electrodes confirmed that the model accurately captured the uniform growth of aging regions under a constant electric field,with thermal energy playing a dominant role in the aging process.To examine the impact of internal defects,a fully aged region is introduced at the center of the simulation domain to simulate the effects of cavity discharge.The results indicated that while aging regions within defects grew rapidly,the overall growth remained slow and stable and is primarily influenced by charge diffusion.Further analysis explored the effects of the internal cavity defects near the electrodes.The presence of defects attracted the aging regions,causing them to grow uniformly without significant morphological changes,highlighting the interplay between thermal and charge-induced aging.The phase-field model effectively captures the dynamics of the aging regions influenced by internal defects,gradient energy,and charge diffusion.This comprehensive understanding enhances our ability to predict material degradation and informs the design of more reliable insulating materials for electrical applications.展开更多
In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
Convex feasibility problems are widely used in image reconstruction,sparse signal recovery,and other areas.This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery...Convex feasibility problems are widely used in image reconstruction,sparse signal recovery,and other areas.This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery.We rst derive the projection formulas for a vector onto the feasible sets.The centralized circumcentered-reection method is designed to solve the convex feasibility problem.Some numerical experiments demonstrate the feasibility and e ectiveness of the proposed algorithm,showing superior performance compared to conventional alternating projection methods.展开更多
Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The t...Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The traditional thermal elastic-plastic finite element method(TEP-FEM)can accurately predict welding deformation.However,its efficiency is low because of the complex nonlinear transient computation,making it difficult to meet the needs of rapid engineering evaluation.To address this challenge,this study proposes an efficient prediction method for welding deformation in marine thin plate butt welds.This method is based on the coupled temperature gradient-thermal strain method(TG-TSM)that integrates inherent strain theory with a shell element finite element model.The proposed method first extracts the distribution pattern and characteristic value of welding-induced inherent strain through TEP-FEM analysis.This strain is then converted into the equivalent thermal load applied to the shell element model for rapid computation.The proposed method-particularly,the gradual temperature gradient-thermal strain method(GTG-TSM)-achieved improved computational efficiency and consistent precision.Furthermore,the proposed method required much less computation time than the traditional TEP-FEM.Thus,this study lays the foundation for future prediction of welding deformation in more complex marine thin plates.展开更多
The ferroelectric domain formation(FDF) and polarization switching(FDPS) subjected to an external electric field are simulated using the phase-field(PF) method,and the FDPS mechanism under different external electric ...The ferroelectric domain formation(FDF) and polarization switching(FDPS) subjected to an external electric field are simulated using the phase-field(PF) method,and the FDPS mechanism under different external electric fields is discussed.The results show that the FDF is a process of nucleation and growth in ferroelectric without applying any external stress.Four kinds of parallelogram shaped ferroelectric domains are formed at the steady state,in which the 180° anti-phase domains regularly align along the 45° direction and the 90° anti-phase domains regularly distribute like a stepladder.Steady electric fields can rotate domain polarization by 90° and 180°,and force the orientation-favorite domains and the average polarization to grow into larger ones.The greater the steady electric field,the larger the average polarization at the steady state.In ferroelectrics subject to an alternating electric field,domain polarization switches to cause a hysteresis loop and an associated butterfly loop with the alternating electric field.The coercive field and remnant field are enhanced with the increase of the electric field frequency or strength,or with the decrease of temperature.展开更多
A mathematical model combined projection algorithm with phase-field method was applied. The adaptive finite element method was adopted to solve the model based on the non-uniform grid, and the behavior of dendritic gr...A mathematical model combined projection algorithm with phase-field method was applied. The adaptive finite element method was adopted to solve the model based on the non-uniform grid, and the behavior of dendritic growth was simulated from undercooled nickel melt under the forced flow. The simulation results show that the asymmetry behavior of the dendritic growth is caused by the forced flow. When the flow velocity is less than the critical value, the asymmetry of dendrite is little influenced by the forced flow. Once the flow velocity reaches or exceeds the critical value, the controlling factor of dendrite growth gradually changes from thermal diffusion to convection. With the increase of the flow velocity, the deflection angle towards upstream direction of the primary dendrite stem becomes larger. The effect of the dendrite growth on the flow field of the melt is apparent. With the increase of the dendrite size, the vortex is present in the downstream regions, and the vortex region is gradually enlarged. Dendrite tips appear to remelt. In addition, the adaptive finite element method can reduce CPU running time by one order of magnitude compared with uniform grid method, and the speed-up ratio is proportional to the size of computational domain.展开更多
In this paper,we present a new model developed in order to analyze phenomena which arise in the solidification of binary mixtures using phase-field method,which incorporates the convection effects and the action of ma...In this paper,we present a new model developed in order to analyze phenomena which arise in the solidification of binary mixtures using phase-field method,which incorporates the convection effects and the action of magnetic field.The model consists of flow,concentration,phase field and energy systems which are nonlinear evolutive and coupled systems.It represents the non-isothermal anisotropic solidification process of a binary mixture together with the motion in a melt with the applied magnetic field.To illustrate our model,numerical simulations of the influence of magnetic-field on the evolution of dendrites during the solidification of the binary mixture of Nickel-Copper(Ni-Cu)are developed.The results demonstrate that the dendritic growth under the action of magnetic-field can be simulated by using our model.展开更多
In the process of preparation of semi-solid metal materials, a variety of factors would influence the preparing time and the morphology of non-dendritic microstructure. The aim of this work is using phase-field method...In the process of preparation of semi-solid metal materials, a variety of factors would influence the preparing time and the morphology of non-dendritic microstructure. The aim of this work is using phase-field method to simulate non-dendritic growth during preparation of AI-4Cu-Mg semi-solid alloy by electromagnetic stirring method （EMS method）. Several factors such as the disturbance intensity, anisotropy, the thickness of the interface and the ratio of diffusivity in solid and liquid were considered. It is shown that decreasing the thickness of the interface results in more circular outline of particles, and increasing the diffusivity in solid can reduce degree of microsegregation. The disturbance intensity in the model can be connected with current intensity of stator or magnetic induction density impressed. Simulation results show that the larger the disturbance intensity or magnetic induction density, the more globular morphology the original phase in the matrix.展开更多
A coupled thermal-hydro-mechanical cohesive phase-field model for hydraulic fracturing in deep coal seams is presented.Heat exchange between the cold fluid and the hot rock is considered,and the thermal contribution t...A coupled thermal-hydro-mechanical cohesive phase-field model for hydraulic fracturing in deep coal seams is presented.Heat exchange between the cold fluid and the hot rock is considered,and the thermal contribution terms between the cold fluid and the hot rock are derived.Heat transfer obeys Fourier's law,and porosity is used to relate the thermodynamic parameters of the fracture and matrix domains.The net pressure difference between the fracture and the matrix is neglected,and thus the fluid flow is modeled by the unified fluid-governing equations.The evolution equations of porosity and Biot's coefficient during hydraulic fracturing are derived from their definitions.The effect of coal cleats is considered and modeled by Voronoi polygons,and this approach is shown to have high accuracy.The accuracy of the proposed model is verified by two sets of fracturing experiments in multilayer coal seams.Subsequently,the differences in fracture morphology,fluid pressure response,and fluid pressure distribution between direct fracturing of coal seams and indirect fracturing of shale interlayers are explored,and the effects of the cluster number and cluster spacing on fracture morphology for multi-cluster fracturing are also examined.The numerical results show that the proposed model is expected to be a powerful tool for the fracturing design and optimization of deep coalbed methane.展开更多
Magnesium is distinguished by its highly anisotropic inelastic deformation involving a profuse activity of deformation twinning.Instrumented micro/nano-indentation technique has been widely applied to characterize the...Magnesium is distinguished by its highly anisotropic inelastic deformation involving a profuse activity of deformation twinning.Instrumented micro/nano-indentation technique has been widely applied to characterize the mechanical properties of magnesium,typically through the analysis of the indentation load-depth response,surface topography,and less commonly,the post-mortem microstructure within the bulk material.However,experimental limitations prevent the real-time observation of the evolving microstructure.To bridge this gap,we employ a recently-developed finite-strain model that couples the phase-field method and conventional crystal plasticity to simulate the evolution of the indentation-induced twin microstructure and its interaction with plastic slip in a magnesium single-crystal.Particular emphasis is placed on two aspects:orientation-dependent inelastic deformation and indentation size effects.Several outcomes of our 2D computational study are consistent with prior experimental observations.Chief among them is the intricate morphology of twin microstructure obtained at large spatial scales,which,to our knowledge,represents a level of detail that has not been captured in previous modeling studies.To further elucidate on size effects,we extend the model by incorporating gradient-enhanced crystal plasticity,and re-examine the notion of‘smaller is stronger’.The corresponding results underscore the dominant influence of gradient plasticity over the interfacial energy of twin boundaries in governing the size-dependent mechanical response.展开更多
Viscoelastic solids,such as composite propellants,exhibit significant time and rate dependencies,and their fracture processes display high levels of nonlinearity.However,the correlation between crack propagation and v...Viscoelastic solids,such as composite propellants,exhibit significant time and rate dependencies,and their fracture processes display high levels of nonlinearity.However,the correlation between crack propagation and viscoelastic energy dissipation in these materials remains unclear.Therefore,accurately modeling and understanding of their fracture behavior is crucial for relevant engineering applications.This study proposes a novel viscoelastic phase-field model.In the numerical implementation,the adopted adaptive time-stepping iterative strategy effectively accelerates the coupling iteration efficiency between the phase-field and the displacement field.Moreover,all unknown parameters in the model,including the form of the phase-field degradation function,are identified through fitting against experimental data.Based on an introduced scaling factor,themechanical response behaviors of solid propellant dogbone specimens under cyclic loading,relaxation,and tension are analyzed,and the predictive capacity of the model is demonstrated by comparing the experimental data with the simulation results.Finally,modeling results for Mode-I and Mode-II crack propagation in single-edge-notched specimens indicate that the reduction of viscous energy dissipation will significantly increase the fracture growth rate,but under the same boundary conditions,the crack path remains unchanged.展开更多
A phase-field model integrated with the thermodynamic databases was constructed to investigate the impact of Ni content on the precipitation kinetics and phase transformation of the Cu-rich phase in Fe-Cu-Ni alloy at ...A phase-field model integrated with the thermodynamic databases was constructed to investigate the impact of Ni content on the precipitation kinetics and phase transformation of the Cu-rich phase in Fe-Cu-Ni alloy at 773 K.The results demonstrated that the Cu core-Ni shell structures form via the decomposition of Cu-Ni co-clusters,which is consistent with previous experimental results.As the Ni content increases,both the volume fraction and number density of Cu-rich precipitates increase,while their size decreases.With the increase in Ni content,the transformation from a Cu to 9R Cu is accelerated,which is the opposite to the result of increasing Mn content.Magnetic energy can increase the nucleation rate of the Cu-rich phase,but it does not affect the phase transformation driving force required for its crystal structure transformation.展开更多
Rechargeable batteries have a profound impact on our daily life so that it is urgent to capture the physical and chemical fundamentals affecting the operation and lifetime.The phase-field method is a powerful computat...Rechargeable batteries have a profound impact on our daily life so that it is urgent to capture the physical and chemical fundamentals affecting the operation and lifetime.The phase-field method is a powerful computational approach to describe and predict the evolution of mesoscale microstructures,which can help to understand the dynamic behavior of the material systems.In this review,we briefly introduce the theoretical framework of the phase-field model and its application in electrochemical systems,summarize the existing phase-field simulations in rechargeable batteries,and provide improvement,development,and problems to be considered of the future phase-field simulation in rechargeable batteries.展开更多
The local arc-length method is employed to control the incremental loading procedure for phase-field brittle fracture modeling.An improved staggered algorithm with energy and damage iterative tolerance convergence cri...The local arc-length method is employed to control the incremental loading procedure for phase-field brittle fracture modeling.An improved staggered algorithm with energy and damage iterative tolerance convergence criteria is developed based on the residuals of displacement and phase-field.The improved staggered solution scheme is implemented in the commercial software ABAQUS with user-defined element subroutines.The layered system of finite elements is utilized to solve the coupled elastic displacement and phase-field fracture problem.A one-element benchmark test compared with the analytical solution was conducted to validate the feasibility and accuracy of the developed method.Our study shows that the result calculated with the developed method does not depend on the selected size of loading increments.The results of several numerical experiments show that the improved staggered algorithm is efficient for solving the more complex brittle fracture problems.展开更多
基金supported by the National Key Research and Development Program of China(2022YFA1203602)the National Natural Science Foundation of China(Grant No.12025206)+1 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB0620101)the National Natural Science Foundations of China(Grant No.12202366).
文摘Anode-free lithium metal batteries are prone to capacity degradation and safety hazards due to the formation and growth of lithium dendrites.The interface between the current collector and deposited lithium plays a critical role in preventing dendrite formation by regulating the thermodynamics and kinetics of lithium deposition.In this study,we develop a phase field model to investigate the influence of the current collector’s surface energy on lithium deposition morphology and its effect on the quality of the lithium metal film.It is demonstrated that a higher surface energy of the current collector promotes the growth of lithium metal along the surface of the current collector.Further,our simulation results show that a higher surface energy accelerates the formation of the lithium metal film while simultaneously reducing its surface roughness.By examining different contact angles and applied potentials,we construct a phase diagram of deposition morphology,illustrating that increased surface energy facilitates the dense and uniform deposition of lithium metal by preventing the formation of lithium filaments and voids.These findings provide new insights into the development and application of anode-free lithium metal batteries.
基金funded by the National Natural Science Foundation of China(Grant No.12272020)Beijing Natural Science Foundation(Grant No.JQ21001)+1 种基金S.W.acknowledges support from the Fundamental Research Funds for the Central Universities(Grant No.YWF-23-SDHK-L-019)M.Y.acknowledges support from the National Natural Science Foundation of China(Grant Nos.12302134,12272173,and 11902150).
文摘Flexoelectricity is a two-way coupling effect between the strain gradient and electric field that exists in all dielectrics,regardless of point group symmetry.However,the high-order derivatives of displacements involved in the strain gradient pose challenges in solving electromechanical coupling problems incorporating the flexoelectric effect.In this study,we formulate a phase-field model for ferroelectric materials considering the flexoelectric effect.A four-node quadrilateral element with 20 degrees of freedom is constructed without introducing high-order shape functions.The microstructure evolution of domains is described by an independent order parameter,namely the spontaneous polarization governed by the time-dependent Ginzburg–Landau theory.The model is developed based on a thermodynamic framework,in which a set of microforces is introduced to construct the constitutive relation and evolution equation.For the flexoelectric part of electric enthalpy,the strain gradient is determined by interpolating the mechanical strain at the node via the values of Gaussian integration points in the isoparametric space.The model is shown to be capable of reproducing the classic analytical solution of dielectric materials incorporating the flexoelectric contribution.The model is verified by duplicating some typical phenomena in flexoelectricity in cylindrical tubes and truncated pyramids.A comparison is made between the polarization distribution in dielectrics and ferroelectrics.The model can reproduce the solution to the boundary value problem of the cylindrical flexoelectric tube,and demonstrate domain twisting at domain walls in ferroelectrics considering the flexoelectric effect.
基金This work is supported by the National Natural Science Foundation of China (51374263, 51674052)The authors are grateful for the Chongqing Research Program of Basic Research and Frontier Technology (cstc2018jcyjAX0003)National Natural Science Foundation of China (91634106, 51704048) is also acknowledged.
文摘A phase-field model for growth of iron whiskers that includes convection around a particle was investigated during the process of fluidized pre-reduction. In the simulations, the phase-field method was coupled with flow field and reduction of iron oxide particles. The results showed that the reduction rate at local place had significant effects on the iron ions diffusion and the iron whiskers were more easily grown on the area containing low mole fraction of oxygen. The growth of iron whiskers in the model was investigated in two important simple situations: a velocity change flow and a CO concentration change flow. Because of high reduction rate and low surface energy, iron whiskers were more easily grown on the windward surface and the length of iron whiskers increased with gas velocity increasing. However, both the length and numbers of iron whiskers increased with CO concentration increasing due to the more nucleation site of iron whiskers created by CO adsorbed. When the gas velocity is higher than 0.3 m/s or CO mole fraction is high than 0.6, the nucleation incubation time would be rapidly decreased, which could give suggestions to control the operational parameters in the fluidized pre-reduction process.
基金supported by National Natural Science Foundation of China under contract No.10964004Research Fund for the Doctoral Program of Higher Education of China under contract No.20070231001+1 种基金Natural Science Foundation of Gansu province under contract No. 096RJZA104Doctoral Fund of Lanzhou University of Technology under contract No.SB14200801
文摘Phase-field model was employed to quantitatively study the effect of convection on pattern selection and growth rate of 2D and 3D dendrite tip,as well as the effect of the different convection velocity on the dendritic growth.The calculated results show that crystal is asymmetric in the priority direction of growth under flow.The dentritic growth is promoted in the upstream region and suppressed in the downstream region.Convection can cause deviation in the dendrite growth direction and the preferred direction of the columnar crystals.It has been found that both primary dendrite stem and secondary dendrite arm deflect significantly towards upstream direction,secondary dendrite arm in upstream direction is more developed than the primary dendrite in downstream direction.
基金Project (50071046) supported by the National Natural Science Foundation of China Project (2002AA331051)supported by the National Hi-Tech Research and Development Program of China
文摘The evolution of ordered interphase boundary (IPB) of Ni75AlxV25-x alloys was simulated using the microscopic phase-field method. Based on the atomic occupation probability figure on 2D and order parameters, it was found that the IPB formed by different directions ofθ phase has great effect on the precipitation of γ ′ phase. The γ ′ phase precipitated at the IPB that is formed by [1 00]θ direction where the ( 001)θ plane is opposite, and then grows up and the shape is strap at final. The IPB structure between γ ′phase andθ phase is the same. There is no γ ′ phase precipitate at the IPB where the ( 002)θ and ( 001)θ planes are opposite, the ordered IPB is dissolved into disordered area. There is γ ′ phase precipitation at the IPB formed by the [ 001]θ and [1 00]θ directions, and the IPB structure is different between γ ′ phase and the different directions ofθ phase. The IPB where ( 001)γ′ and (1 00)θ plane opposite does not migrate during the γ ′ phase growth, and γ ′ phase grows along [1 00]θdirection.
基金supported by the Natural Science Foundation of China(Nos.51701091,12174210 and 52174346)Shandong Provincial Natural Science Foundation,China(Nos.ZR2020QE028 and ZR2022ME030)+2 种基金the Innovation Team of Higher Educational Science and Technology Program in Shandong Province(No.2019KJA025)the Research Foundation of Liaocheng University(No.318012119)the Science and Technology Innovation Foundation of Liaocheng University(No.CXCY2021139)。
文摘Since the discovery of ferromagnetic morphotropic phase boundary(MPB)in 2010,the connotation and extension of MPB have been becoming more and more abundant.Over the last dozen years,much experimental work has been done to design magnetostrictive materials based on the MPB principle.However,due to the difficulty in direct experimental observations and the complexity of theoretical treatments,the insight into the microstructure property relationships and underlying mechanisms near the ferromagnetic MPB has not been fully revealed.Here,we have reviewed our recent computer simulation work about the super-magnetoelastic behavior near the critical region of several typical materials.Phase-field modeling and simulation are employed to explore the domain configuration and engineering in single crystals as well as the grain size effect in polycrystals.Besides,a general nano-embryonic mechanism for superelasticity is also introduced.Finally,some future perspectives and challenges are presented to stimulate a deeper consideration of the research paradigm between multiscale modeling and material development.
文摘Epoxy resin is widely used in electrical insulation because of its excellent mechanical and insulating properties;however,its performance can degrade over time owing to thermal aging.This study focuses on developing a thermal aging region growth model for epoxy resin using the phase-field method.The reliability of the model is validated by applying a 20 MV/m electric field and observing the evolution of aging regions and the distribution of the internal energy density.A Gaussian-distributed aging region near the electrodes confirmed that the model accurately captured the uniform growth of aging regions under a constant electric field,with thermal energy playing a dominant role in the aging process.To examine the impact of internal defects,a fully aged region is introduced at the center of the simulation domain to simulate the effects of cavity discharge.The results indicated that while aging regions within defects grew rapidly,the overall growth remained slow and stable and is primarily influenced by charge diffusion.Further analysis explored the effects of the internal cavity defects near the electrodes.The presence of defects attracted the aging regions,causing them to grow uniformly without significant morphological changes,highlighting the interplay between thermal and charge-induced aging.The phase-field model effectively captures the dynamics of the aging regions influenced by internal defects,gradient energy,and charge diffusion.This comprehensive understanding enhances our ability to predict material degradation and informs the design of more reliable insulating materials for electrical applications.
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
基金Supported by the Natural Science Foundation of Guangxi Province(Grant Nos.2023GXNSFAA026067,2024GXN SFAA010521)the National Natural Science Foundation of China(Nos.12361079,12201149,12261026).
文摘Convex feasibility problems are widely used in image reconstruction,sparse signal recovery,and other areas.This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery.We rst derive the projection formulas for a vector onto the feasible sets.The centralized circumcentered-reection method is designed to solve the convex feasibility problem.Some numerical experiments demonstrate the feasibility and e ectiveness of the proposed algorithm,showing superior performance compared to conventional alternating projection methods.
基金Supported by the National Natural Science Foundation of China under Grant No.51975138the High-Tech Ship Scientific Research Project from the Ministry of Industry and Information Technology under Grant No.CJ05N20the National Defense Basic Research Project under Grant No.JCKY2023604C006.
文摘Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The traditional thermal elastic-plastic finite element method(TEP-FEM)can accurately predict welding deformation.However,its efficiency is low because of the complex nonlinear transient computation,making it difficult to meet the needs of rapid engineering evaluation.To address this challenge,this study proposes an efficient prediction method for welding deformation in marine thin plate butt welds.This method is based on the coupled temperature gradient-thermal strain method(TG-TSM)that integrates inherent strain theory with a shell element finite element model.The proposed method first extracts the distribution pattern and characteristic value of welding-induced inherent strain through TEP-FEM analysis.This strain is then converted into the equivalent thermal load applied to the shell element model for rapid computation.The proposed method-particularly,the gradual temperature gradient-thermal strain method(GTG-TSM)-achieved improved computational efficiency and consistent precision.Furthermore,the proposed method required much less computation time than the traditional TEP-FEM.Thus,this study lays the foundation for future prediction of welding deformation in more complex marine thin plates.
基金supported by the National Natural Science Foundation of China(Grant Nos.51075335,51174168,10902086,and 50875217)the NPU Foundation for Fundamental Research(Grant No.JC201005)
文摘The ferroelectric domain formation(FDF) and polarization switching(FDPS) subjected to an external electric field are simulated using the phase-field(PF) method,and the FDPS mechanism under different external electric fields is discussed.The results show that the FDF is a process of nucleation and growth in ferroelectric without applying any external stress.Four kinds of parallelogram shaped ferroelectric domains are formed at the steady state,in which the 180° anti-phase domains regularly align along the 45° direction and the 90° anti-phase domains regularly distribute like a stepladder.Steady electric fields can rotate domain polarization by 90° and 180°,and force the orientation-favorite domains and the average polarization to grow into larger ones.The greater the steady electric field,the larger the average polarization at the steady state.In ferroelectrics subject to an alternating electric field,domain polarization switches to cause a hysteresis loop and an associated butterfly loop with the alternating electric field.The coercive field and remnant field are enhanced with the increase of the electric field frequency or strength,or with the decrease of temperature.
基金Projects(51161011,11364024)supported by the National Natural Science Foundation of ChinaProject(1204GKCA065)supported by the Key Technology R&D Program of Gansu Province,China+1 种基金Project(201210)supported by the Fundamental Research Funds for the Universities of Gansu Province,ChinaProject(J201304)supported by the Funds for Distinguished Young Scientists of Lanzhou University of Technology,China
文摘A mathematical model combined projection algorithm with phase-field method was applied. The adaptive finite element method was adopted to solve the model based on the non-uniform grid, and the behavior of dendritic growth was simulated from undercooled nickel melt under the forced flow. The simulation results show that the asymmetry behavior of the dendritic growth is caused by the forced flow. When the flow velocity is less than the critical value, the asymmetry of dendrite is little influenced by the forced flow. Once the flow velocity reaches or exceeds the critical value, the controlling factor of dendrite growth gradually changes from thermal diffusion to convection. With the increase of the flow velocity, the deflection angle towards upstream direction of the primary dendrite stem becomes larger. The effect of the dendrite growth on the flow field of the melt is apparent. With the increase of the dendrite size, the vortex is present in the downstream regions, and the vortex region is gradually enlarged. Dendrite tips appear to remelt. In addition, the adaptive finite element method can reduce CPU running time by one order of magnitude compared with uniform grid method, and the speed-up ratio is proportional to the size of computational domain.
文摘In this paper,we present a new model developed in order to analyze phenomena which arise in the solidification of binary mixtures using phase-field method,which incorporates the convection effects and the action of magnetic field.The model consists of flow,concentration,phase field and energy systems which are nonlinear evolutive and coupled systems.It represents the non-isothermal anisotropic solidification process of a binary mixture together with the motion in a melt with the applied magnetic field.To illustrate our model,numerical simulations of the influence of magnetic-field on the evolution of dendrites during the solidification of the binary mixture of Nickel-Copper(Ni-Cu)are developed.The results demonstrate that the dendritic growth under the action of magnetic-field can be simulated by using our model.
文摘In the process of preparation of semi-solid metal materials, a variety of factors would influence the preparing time and the morphology of non-dendritic microstructure. The aim of this work is using phase-field method to simulate non-dendritic growth during preparation of AI-4Cu-Mg semi-solid alloy by electromagnetic stirring method （EMS method）. Several factors such as the disturbance intensity, anisotropy, the thickness of the interface and the ratio of diffusivity in solid and liquid were considered. It is shown that decreasing the thickness of the interface results in more circular outline of particles, and increasing the diffusivity in solid can reduce degree of microsegregation. The disturbance intensity in the model can be connected with current intensity of stator or magnetic induction density impressed. Simulation results show that the larger the disturbance intensity or magnetic induction density, the more globular morphology the original phase in the matrix.
基金Project supported by the National Natural Science Foundation of China(No.42202314)。
文摘A coupled thermal-hydro-mechanical cohesive phase-field model for hydraulic fracturing in deep coal seams is presented.Heat exchange between the cold fluid and the hot rock is considered,and the thermal contribution terms between the cold fluid and the hot rock are derived.Heat transfer obeys Fourier's law,and porosity is used to relate the thermodynamic parameters of the fracture and matrix domains.The net pressure difference between the fracture and the matrix is neglected,and thus the fluid flow is modeled by the unified fluid-governing equations.The evolution equations of porosity and Biot's coefficient during hydraulic fracturing are derived from their definitions.The effect of coal cleats is considered and modeled by Voronoi polygons,and this approach is shown to have high accuracy.The accuracy of the proposed model is verified by two sets of fracturing experiments in multilayer coal seams.Subsequently,the differences in fracture morphology,fluid pressure response,and fluid pressure distribution between direct fracturing of coal seams and indirect fracturing of shale interlayers are explored,and the effects of the cluster number and cluster spacing on fracture morphology for multi-cluster fracturing are also examined.The numerical results show that the proposed model is expected to be a powerful tool for the fracturing design and optimization of deep coalbed methane.
文摘Magnesium is distinguished by its highly anisotropic inelastic deformation involving a profuse activity of deformation twinning.Instrumented micro/nano-indentation technique has been widely applied to characterize the mechanical properties of magnesium,typically through the analysis of the indentation load-depth response,surface topography,and less commonly,the post-mortem microstructure within the bulk material.However,experimental limitations prevent the real-time observation of the evolving microstructure.To bridge this gap,we employ a recently-developed finite-strain model that couples the phase-field method and conventional crystal plasticity to simulate the evolution of the indentation-induced twin microstructure and its interaction with plastic slip in a magnesium single-crystal.Particular emphasis is placed on two aspects:orientation-dependent inelastic deformation and indentation size effects.Several outcomes of our 2D computational study are consistent with prior experimental observations.Chief among them is the intricate morphology of twin microstructure obtained at large spatial scales,which,to our knowledge,represents a level of detail that has not been captured in previous modeling studies.To further elucidate on size effects,we extend the model by incorporating gradient-enhanced crystal plasticity,and re-examine the notion of‘smaller is stronger’.The corresponding results underscore the dominant influence of gradient plasticity over the interfacial energy of twin boundaries in governing the size-dependent mechanical response.
基金funded by National Natural Science Foundation of China(Grant No.11872372)Graduate Innovation Foundation of Hunan Province of China(Grant No.CX20230018).
文摘Viscoelastic solids,such as composite propellants,exhibit significant time and rate dependencies,and their fracture processes display high levels of nonlinearity.However,the correlation between crack propagation and viscoelastic energy dissipation in these materials remains unclear.Therefore,accurately modeling and understanding of their fracture behavior is crucial for relevant engineering applications.This study proposes a novel viscoelastic phase-field model.In the numerical implementation,the adopted adaptive time-stepping iterative strategy effectively accelerates the coupling iteration efficiency between the phase-field and the displacement field.Moreover,all unknown parameters in the model,including the form of the phase-field degradation function,are identified through fitting against experimental data.Based on an introduced scaling factor,themechanical response behaviors of solid propellant dogbone specimens under cyclic loading,relaxation,and tension are analyzed,and the predictive capacity of the model is demonstrated by comparing the experimental data with the simulation results.Finally,modeling results for Mode-I and Mode-II crack propagation in single-edge-notched specimens indicate that the reduction of viscous energy dissipation will significantly increase the fracture growth rate,but under the same boundary conditions,the crack path remains unchanged.
基金supported by the National Natural Science Foundation of China(Grant No.51871086).
文摘A phase-field model integrated with the thermodynamic databases was constructed to investigate the impact of Ni content on the precipitation kinetics and phase transformation of the Cu-rich phase in Fe-Cu-Ni alloy at 773 K.The results demonstrated that the Cu core-Ni shell structures form via the decomposition of Cu-Ni co-clusters,which is consistent with previous experimental results.As the Ni content increases,both the volume fraction and number density of Cu-rich precipitates increase,while their size decreases.With the increase in Ni content,the transformation from a Cu to 9R Cu is accelerated,which is the opposite to the result of increasing Mn content.Magnetic energy can increase the nucleation rate of the Cu-rich phase,but it does not affect the phase transformation driving force required for its crystal structure transformation.
基金This work was supported by the National Natural Science Foundation of China(numbers U2030206,51802187,and 11874254)Shanghai Pujiang Program(number 2019PJD016)Shanghai Sailing Program(number 18YF1408700).
文摘Rechargeable batteries have a profound impact on our daily life so that it is urgent to capture the physical and chemical fundamentals affecting the operation and lifetime.The phase-field method is a powerful computational approach to describe and predict the evolution of mesoscale microstructures,which can help to understand the dynamic behavior of the material systems.In this review,we briefly introduce the theoretical framework of the phase-field model and its application in electrochemical systems,summarize the existing phase-field simulations in rechargeable batteries,and provide improvement,development,and problems to be considered of the future phase-field simulation in rechargeable batteries.
基金supports by the National Key R&D Program of China(No.2018YFD1100401)the National Natural Science Foundation of China(No.51578142)+1 种基金the Fundamental Research Funds for the Central Universities(No.LEM21A03)Jiangsu Key Laboratory of Engineering Mechanics(Southeast University)are gratefully acknowledged.
文摘The local arc-length method is employed to control the incremental loading procedure for phase-field brittle fracture modeling.An improved staggered algorithm with energy and damage iterative tolerance convergence criteria is developed based on the residuals of displacement and phase-field.The improved staggered solution scheme is implemented in the commercial software ABAQUS with user-defined element subroutines.The layered system of finite elements is utilized to solve the coupled elastic displacement and phase-field fracture problem.A one-element benchmark test compared with the analytical solution was conducted to validate the feasibility and accuracy of the developed method.Our study shows that the result calculated with the developed method does not depend on the selected size of loading increments.The results of several numerical experiments show that the improved staggered algorithm is efficient for solving the more complex brittle fracture problems.
