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
[Objective]This study aims to develop a thermodynamically consistent phase-field framework for modeling the initiation and evolution of discontinuous structures in geomaterials.[Methods]Our model introduces crack driv...[Objective]This study aims to develop a thermodynamically consistent phase-field framework for modeling the initiation and evolution of discontinuous structures in geomaterials.[Methods]Our model introduces crack driving forces derived from the volumetric-deviatoric strain decomposition strategy,incorporating distinct tension,compression,and shear degradation mechanisms.Inertia effects capture compaction-band formation driven by wave-like disturbances,grain crushing,and frictional rearrangement.A monolithic algorithm ensures numerical stability and rapid convergence.[Results]The framework reproduces tensile,shear,mixed tensile-shear,and compressive-shear failures using the Benzeggagh-Kenane criterion.Validation against benchmark simulations-including uniaxial compression of rock-like and triaxial compression of V-notched sandstone specimens-demonstrates accurate predictions of crack initiation stress,localization orientation,and energy dissipation.[Conclusions]The framework provides a unified and robust numerical tool for analyzing the spatiotemporal evolution of strain localization and fracture in geomaterials.[Significance]By linking microscale fracture dynamics with macroscale failure within a thermodynamically consistent scheme,this study advances predictive modeling of rock stability,slope failure,and subsurface energy systems,contributing to safer and more sustainable geotechnical practice.展开更多
The presence of clay coatings on the surfaces of quartz grains can play a pivotal role in determining the porosity and permeability of sandstone reservoirs,thus directly impacting their reservoir quality.This study em...The presence of clay coatings on the surfaces of quartz grains can play a pivotal role in determining the porosity and permeability of sandstone reservoirs,thus directly impacting their reservoir quality.This study employs a multiphase-field model of syntaxial quartz cementation to explore the effects of clay coatings on quartz cement volumes,porosity,permeability,and their interrelations in sandstone formations.To generate various patterns of clay coatings on quartz grains within three-dimensional(3D)digital sandstone grain packs,a pre-processing toolchain is developed.Through numerical simulation experiments involving syntaxial overgrowth cementation on both single crystals and multigrain packs,the main coating parameters controlling quartz cement volume are elucidated.Such parameters include the growth of exposed pyramidal faces,lateral encasement,coating coverage,and coating pattern,etc.The coating pattern has a remarkable impact on cementation,with the layered coatings corresponding to fast cement growth rates.The coating coverage is positively correlated with the porosity and permeability of sandstone.The cement growth rate of quartz crystals is the lowest in the vertical orientation,and in the middle to late stages of evolution,it is faster in the diagonal orientation than in the horizontal orientation.Through comparing the simulated results of dynamic evolution process with the actual features,it is found that the simulated coating patterns after 20 d and 40 d show clear similarities with natural samples,proving the validity of the proposed three-dimensional numerical modeling of coatings.The methodology and findings presented contribute to improved reservoir characterization and predictive modeling of sandstone formations.展开更多
Based on the principles of thermodynamics, we elucidate the fundamental reasons behind the hysteresis of spontaneous polarization in ferroelectric materials during heating and cooling processes. By utilizing the effec...Based on the principles of thermodynamics, we elucidate the fundamental reasons behind the hysteresis of spontaneous polarization in ferroelectric materials during heating and cooling processes. By utilizing the effective Hamiltonian method in conjuction with the phase-field model, we have successfully reproduced the thermal hysteresis observed in ferroelectric materials during phase transitions. The computational results regarding the electrocaloric effect from these two different computational scales closely align with experimental measurements. Furthermore, we analyze how the first-order ferroelectric phase transition gradually diminishes with an increasing applied electric field, exhibiting characteristics of second-order-like phase transition. By employing the characteristic parameters of thermal hysteresis, we have established a pathway for calculations across different computational scales, thereby providing theoretical support for further investigations into the properties of ferroelectric materials through concurrent multiscale simulations.展开更多
γʹvolume fraction(fv)plays a critical role in the mechanical properties of Ni-based single-crystal superalloys.A creep phase-field model is utilized to simulate the microstructure evolution and creep performance duri...γʹvolume fraction(fv)plays a critical role in the mechanical properties of Ni-based single-crystal superalloys.A creep phase-field model is utilized to simulate the microstructure evolution and creep performance during creep under different fv conditions.The influence mechanism of fv on creep properties is investigated based on the analysis of evolutions of internal stress and strain fields.As fv increases,the morphology ofγʹrafts changes from discontinuous to continuous,while the morphological change ofγchannels is opposite,the inclination ofγchannels from the[010]direction to(011)directions during tertiary creep first decreases and then increases,the creep life first increases and then decreases,and the main distribution of creep damage shifts fromγʹtoγʹ/γinterfaces andγchannels.The longest creep life under fv of 0.65 can be attributed to the stableγʹraft structure,the lowest stress and strain inγchannels,and the slowest damage accumulation.展开更多
All-solid-state lithium metal batteries represent leading candidates for the next generation of highenergy-density rechargeable batteries.However,the coupled mechanisms governing dendrite growth and crack propagation ...All-solid-state lithium metal batteries represent leading candidates for the next generation of highenergy-density rechargeable batteries.However,the coupled mechanisms governing dendrite growth and crack propagation within solid-state electrolytes(SSEs)remain inadequately understood.To address this knowledge gap,we propose an electrochemical-mechanical coupled phase-field model designed to simulate the complex processes of lithium deposition and crack propagation in SSEs.This framework systematically examines the influence of initial defect characteristics—including morphology,dimensions,and fracture toughness—on dendrite penetration dynamics.Furthermore,it identifies potential initiation pathways for detrimental lithium deposition within the electrolyte bulk.The model also quantifies the critical role of electrolyte elastic modulus and grain boundary orientation in modulating deposition behavior.Notably,simulation results demonstrate concordance with existing experimental observations,thereby establishing a fundamental theoretical framework for understanding failure mechanisms.This work provides crucial mechanistic insights and predictive capabilities to guide the rational design of failure-resistant SSEs for all-solid-state lithium metal batteries.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
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
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
In Ti-Al laminated composites,cracks nucleate preferentially at the Al_(3)Ti layer,but the inhibitory effect of Al_(3)Ti on crack extension is ignored.Interestingly,by combining experiment and phase-field crystal simu...In Ti-Al laminated composites,cracks nucleate preferentially at the Al_(3)Ti layer,but the inhibitory effect of Al_(3)Ti on crack extension is ignored.Interestingly,by combining experiment and phase-field crystal simulation,we found that the micrometer Al_(3)Ti particles in the diffusion layer play the role of crack deflection and passivation,which is attributed to the lattice distortion induced by Al_(3)Ti consumes the energy of the crack in extension.In addition,it is found that the growth process of Al_(3)Ti is divided into two stages:nucleation stage and growth stage.Compared with the growth stage,the Al_(3)Ti grains in the nucleation stage are finer in the growth layer.Finer grains show better crack deflection and avoid stress concentration.展开更多
The phase-field method is used to study the free dendritic crystal growth under forced convection with hypergravity,the hypergravity term is introduced into the liquid-phase momentum equation to examine the dendritic ...The phase-field method is used to study the free dendritic crystal growth under forced convection with hypergravity,the hypergravity term is introduced into the liquid-phase momentum equation to examine the dendritic growth.The paper focuses on the morphology of dendrite growth as well as the tip radius of the upstream dendritic arm and the average growth velocity of dendrite tips under different hypergravity levels.The results show that the morphology of dendrite changes significantly under represent simulation conditions when the hypergravity reaches 35_(g0),the upstream dendritic arm will bifurcate and the horizontal dendrite arms gradually tilt upwards.This change is mainly caused by the hypergravity and flow changing the temperature field near the dendrite interface.In addition,before the morphology of the dendrite is significantly altered,the radius of the tip of the dendrite upstream arm becomes larger with the increase in hypergravity,and the average growth velocity will increase linearly with it.The morphology of dendritic growth under different hypergravity and the changes in the tip radius along with the average growth velocity of the upstream dendritic tip with hypergravity are given in this paper.Finally,the reasons for these phenomena are analyzed.展开更多
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
Concrete materials are employed extensively in a variety of large-scale structures due to their economic viability and superior mechanical properties.During the service life of concrete structures,they are inevitably ...Concrete materials are employed extensively in a variety of large-scale structures due to their economic viability and superior mechanical properties.During the service life of concrete structures,they are inevitably subjected to damage from impact loading from natural disasters,such as earthquakes and storms.In recent years,the phasefield model has demonstrated exceptional capability in predicting the stochastic initiation,propagation,and bifurcation of cracks in materials.This study employs a phase-field model to focus on the rate dependency and failure response of concrete under impact deformation.A viscosity coefficient is introduced within the phase-field model to characterize the viscous behavior of dynamic crack propagation in concrete.The rate-dependent cohesive strength is defined within the yield function of concrete,where the rate sensitivity of cohesive strength facilitates the accumulation of the plastic driving force in the phase-field model.This process effectively captures the impact failure response of concrete.The applicability of the model was validated through unit cell experiments and numerical simulations of concrete under impact compression.Furthermore,the mechanical response and damage evolution mechanisms of concrete under impact loading were analyzed.It was observed that crack propagation in concrete initiates at material defects and,with increasing load,eventually develops in a direction perpendicular to the loading axis.展开更多
The effect of supercooled melt forced laminar flow at low Reynolds Number on dendritic growth perpendicular to melt flow direction was investigated with the phase-field method by incorporating melt convection and ther...The effect of supercooled melt forced laminar flow at low Reynolds Number on dendritic growth perpendicular to melt flow direction was investigated with the phase-field method by incorporating melt convection and thermal noise under non-isothermal condition. By taking the dendritic growth of high pure succinonitrile （SCN） supercooled melt as an example, side-branching shape difference of melts with flow and without flow was analyzed. Relationships among supercooled melt inflow velocity, deflexion angle of dendritic arm and dendritic tip growth velocity were studied. Results show that the melt inflow velocity has few effects on the dendritic tip growth velocity. A formula of relationship between the velocity of the melt in front of primary dendritic tip and the dendritic growth time was deduced, and the calculated result was in quantitative agreement with the simulation result.展开更多
A microscopic phase-field model was used to investigate a directional coarsening mechanism caused by the anisotropic growth of long period stacking and different effects of phases on precipitation in Ni-Al-V alloy.The...A microscopic phase-field model was used to investigate a directional coarsening mechanism caused by the anisotropic growth of long period stacking and different effects of phases on precipitation in Ni-Al-V alloy.The results show that DO22 mainly coarsens along its short axis,which may press the neighboring L12,leading to the interaction among atoms.Diffusion channels of Al are formed in the direction where the mismatch between γ＇ and γ reduces;the occupation probabilities are anisotropic in space;and direction coarsening of L12 occurs finally.With a rise of ageing temperature,phases appear later and DO22 is much later at a higher temperature,the average occupation probabilities of Al and V reduce,and Al changes more than V.展开更多
With microscopic phase-field kinetic model, atomic-scale computer simulation program for the precipitation sequence and microstructure evolution of the ordered intermetallic compound γ＇ and θ in ternary Ni75AlxV25-...With microscopic phase-field kinetic model, atomic-scale computer simulation program for the precipitation sequence and microstructure evolution of the ordered intermetallic compound γ＇ and θ in ternary Ni75AlxV25-x alloy were studied. The simulation results show that Al concentration has important effects on the precipitation sequence. When Al concentration in Ni75AlxV25-x alloy is low, 0（Ni3V） ordered phase will be firstly precipitated, followed by γ＇（Ni3Al） ordered phase. With Al concentration increasing, θ and γ＇ ordered phases are simultaneously precipitated. With A1 concentration further increasing, γ＇ ordered phase is firstly precipitated, followed by θ ordered phase. There is a competition relationship between θ and γ＇ ordered phases during growth and coarsening process. No matter which first precipitates, θ ordered phase always occupies advantage in the competition process of coarsening, thus, the microstructure with preferred orientation is formed.展开更多
Based on the entropy function, a two-dimensional phase field model of binary alloys was established. Meanwhile, an explicit difference method with uniform grid was adopted to solve the phase field and solute field con...Based on the entropy function, a two-dimensional phase field model of binary alloys was established. Meanwhile, an explicit difference method with uniform grid was adopted to solve the phase field and solute field controlled equations. And the alternating direction implicit(ADI) algorithm for solving temperature field controlled equation was also employed to avoid the restriction of time step. Some characteristics of the Ni-Cu alloy were captured in the process of non-isothermal solidification, and the comparative analysis of the isothermal and the non-isothermal solidification was investigated. The simulation results indicate that the non-isothermal model is favorable to simulate the real solidification process of binary alloys, and when the thermal diffusivity decreases, the non-isothermal phase-field model is gradually consistent with the isothermal phase-field model.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
The random distribution problem of dendrite preferred growth direction was settled by random grid method.This method was used to study the influence of forced laminar flow effect on multiple grains during solidificati...The random distribution problem of dendrite preferred growth direction was settled by random grid method.This method was used to study the influence of forced laminar flow effect on multiple grains during solidification.Taking high pure succinonitrile （SCN） undercooled melt as an example,the forced laminar flow effect on multiple grains was studied by phase-field model of single grain which coupled with flow equations at non-isothermal condition.The simulation results show that the random grid method can reasonably settle the problem of random distribution and is more effective.When the solid fraction is relatively low,melt particles flow around the downstream side of dendrite,and the flow velocity between two dendrite arms becomes high.At the stage of solidification time less than 1800Δt,every dendrite grows freely;the upstream dendrites are stronger than the downstream ones.The higher the melt flow rate,the higher the solid fraction.However,when the solid fraction is relatively high,the dendrite arm intertwins and only a little residual melt which is not encapsulated can flow;the solid fraction will gradually tend to equal to solid fraction of melt without flow.展开更多
The early precipitation process of Ni（75）Al（14）Mo（11） alloy was simulated by microscopic phase-field model at different temperatures.The microstructure of the alloy,the precipitation time of Llo structure and oc...The early precipitation process of Ni（75）Al（14）Mo（11） alloy was simulated by microscopic phase-field model at different temperatures.The microstructure of the alloy,the precipitation time of Llo structure and occupation probability of the three kinds of atoms were investigated.It is indicated that the non-stoichiometric Ll0（Ⅰ/Ⅱ） phases are found in the precipitation process.With the temperature increasing,the appearance time of Ll0 is brought forward.The Ll0（Ⅱ） structure always precipitates earlier than the Ll0（Ⅰ） structure.Compared with lower temperature,higher temperature brings the formation time of Ll0 phase forward and makes Ll0 phase have a higher order degree.But lower temperature shortens the process time of the Ll0 phase to the Ll2 phase.Al and Mo atoms tend to occupy γ site,Ni atom tends to occupy a and β sites.At the same temperature,Al atom has stronger occupation ability than Mo atom in the same site.Ni,Al and Mo collectively form the composited Ll2 structure.展开更多
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[Objective]This study aims to develop a thermodynamically consistent phase-field framework for modeling the initiation and evolution of discontinuous structures in geomaterials.[Methods]Our model introduces crack driving forces derived from the volumetric-deviatoric strain decomposition strategy,incorporating distinct tension,compression,and shear degradation mechanisms.Inertia effects capture compaction-band formation driven by wave-like disturbances,grain crushing,and frictional rearrangement.A monolithic algorithm ensures numerical stability and rapid convergence.[Results]The framework reproduces tensile,shear,mixed tensile-shear,and compressive-shear failures using the Benzeggagh-Kenane criterion.Validation against benchmark simulations-including uniaxial compression of rock-like and triaxial compression of V-notched sandstone specimens-demonstrates accurate predictions of crack initiation stress,localization orientation,and energy dissipation.[Conclusions]The framework provides a unified and robust numerical tool for analyzing the spatiotemporal evolution of strain localization and fracture in geomaterials.[Significance]By linking microscale fracture dynamics with macroscale failure within a thermodynamically consistent scheme,this study advances predictive modeling of rock stability,slope failure,and subsurface energy systems,contributing to safer and more sustainable geotechnical practice.
基金the Helmholtz association for funding the main parts of the modeling and simulation research work under the program“MTET:38.04.04”。
文摘The presence of clay coatings on the surfaces of quartz grains can play a pivotal role in determining the porosity and permeability of sandstone reservoirs,thus directly impacting their reservoir quality.This study employs a multiphase-field model of syntaxial quartz cementation to explore the effects of clay coatings on quartz cement volumes,porosity,permeability,and their interrelations in sandstone formations.To generate various patterns of clay coatings on quartz grains within three-dimensional(3D)digital sandstone grain packs,a pre-processing toolchain is developed.Through numerical simulation experiments involving syntaxial overgrowth cementation on both single crystals and multigrain packs,the main coating parameters controlling quartz cement volume are elucidated.Such parameters include the growth of exposed pyramidal faces,lateral encasement,coating coverage,and coating pattern,etc.The coating pattern has a remarkable impact on cementation,with the layered coatings corresponding to fast cement growth rates.The coating coverage is positively correlated with the porosity and permeability of sandstone.The cement growth rate of quartz crystals is the lowest in the vertical orientation,and in the middle to late stages of evolution,it is faster in the diagonal orientation than in the horizontal orientation.Through comparing the simulated results of dynamic evolution process with the actual features,it is found that the simulated coating patterns after 20 d and 40 d show clear similarities with natural samples,proving the validity of the proposed three-dimensional numerical modeling of coatings.The methodology and findings presented contribute to improved reservoir characterization and predictive modeling of sandstone formations.
基金Project supported financially by the National Natural Science Foundation of China (Grant No. 52372100)the National Key Research and Development Program of China (Grant No. 2019YFA0307900)。
文摘Based on the principles of thermodynamics, we elucidate the fundamental reasons behind the hysteresis of spontaneous polarization in ferroelectric materials during heating and cooling processes. By utilizing the effective Hamiltonian method in conjuction with the phase-field model, we have successfully reproduced the thermal hysteresis observed in ferroelectric materials during phase transitions. The computational results regarding the electrocaloric effect from these two different computational scales closely align with experimental measurements. Furthermore, we analyze how the first-order ferroelectric phase transition gradually diminishes with an increasing applied electric field, exhibiting characteristics of second-order-like phase transition. By employing the characteristic parameters of thermal hysteresis, we have established a pathway for calculations across different computational scales, thereby providing theoretical support for further investigations into the properties of ferroelectric materials through concurrent multiscale simulations.
基金the supports provided by the National Natural Science Foundation of China(Nos.52301171,52031012,51971174)the National Science and Technology Major Project,China(Nos.2019-VI-0020-0135)+1 种基金the Key Research and Development Program of Shaanxi Province,China(No.2020ZDLGY13-02)the Research Fund of the State Key Laboratory of Solidification Processing(NPU),China(No.2022-TZ-01)。
文摘γʹvolume fraction(fv)plays a critical role in the mechanical properties of Ni-based single-crystal superalloys.A creep phase-field model is utilized to simulate the microstructure evolution and creep performance during creep under different fv conditions.The influence mechanism of fv on creep properties is investigated based on the analysis of evolutions of internal stress and strain fields.As fv increases,the morphology ofγʹrafts changes from discontinuous to continuous,while the morphological change ofγchannels is opposite,the inclination ofγchannels from the[010]direction to(011)directions during tertiary creep first decreases and then increases,the creep life first increases and then decreases,and the main distribution of creep damage shifts fromγʹtoγʹ/γinterfaces andγchannels.The longest creep life under fv of 0.65 can be attributed to the stableγʹraft structure,the lowest stress and strain inγchannels,and the slowest damage accumulation.
基金supported by the National Natural Science Foundation of China(No.52476053,No.22409209)Beijing Natural Science Foundation(No.3242017)。
文摘All-solid-state lithium metal batteries represent leading candidates for the next generation of highenergy-density rechargeable batteries.However,the coupled mechanisms governing dendrite growth and crack propagation within solid-state electrolytes(SSEs)remain inadequately understood.To address this knowledge gap,we propose an electrochemical-mechanical coupled phase-field model designed to simulate the complex processes of lithium deposition and crack propagation in SSEs.This framework systematically examines the influence of initial defect characteristics—including morphology,dimensions,and fracture toughness—on dendrite penetration dynamics.Furthermore,it identifies potential initiation pathways for detrimental lithium deposition within the electrolyte bulk.The model also quantifies the critical role of electrolyte elastic modulus and grain boundary orientation in modulating deposition behavior.Notably,simulation results demonstrate concordance with existing experimental observations,thereby establishing a fundamental theoretical framework for understanding failure mechanisms.This work provides crucial mechanistic insights and predictive capabilities to guide the rational design of failure-resistant SSEs for all-solid-state lithium metal batteries.
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(Nos.52375394,52074246,52275390,52205429,52201146)the National Defense Basic Scientific Research Program of China(JCKY2020408B002)the Key Research and Development Program of Shanxi Province(202102050201011,202202050201014).
文摘In Ti-Al laminated composites,cracks nucleate preferentially at the Al_(3)Ti layer,but the inhibitory effect of Al_(3)Ti on crack extension is ignored.Interestingly,by combining experiment and phase-field crystal simulation,we found that the micrometer Al_(3)Ti particles in the diffusion layer play the role of crack deflection and passivation,which is attributed to the lattice distortion induced by Al_(3)Ti consumes the energy of the crack in extension.In addition,it is found that the growth process of Al_(3)Ti is divided into two stages:nucleation stage and growth stage.Compared with the growth stage,the Al_(3)Ti grains in the nucleation stage are finer in the growth layer.Finer grains show better crack deflection and avoid stress concentration.
基金supported by the National Natural Science Foundation of China(Grant No.52588202)。
文摘The phase-field method is used to study the free dendritic crystal growth under forced convection with hypergravity,the hypergravity term is introduced into the liquid-phase momentum equation to examine the dendritic growth.The paper focuses on the morphology of dendrite growth as well as the tip radius of the upstream dendritic arm and the average growth velocity of dendrite tips under different hypergravity levels.The results show that the morphology of dendrite changes significantly under represent simulation conditions when the hypergravity reaches 35_(g0),the upstream dendritic arm will bifurcate and the horizontal dendrite arms gradually tilt upwards.This change is mainly caused by the hypergravity and flow changing the temperature field near the dendrite interface.In addition,before the morphology of the dendrite is significantly altered,the radius of the tip of the dendrite upstream arm becomes larger with the increase in hypergravity,and the average growth velocity will increase linearly with it.The morphology of dendritic growth under different hypergravity and the changes in the tip radius along with the average growth velocity of the upstream dendritic tip with hypergravity are given in this paper.Finally,the reasons for these phenomena are analyzed.
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.
文摘Concrete materials are employed extensively in a variety of large-scale structures due to their economic viability and superior mechanical properties.During the service life of concrete structures,they are inevitably subjected to damage from impact loading from natural disasters,such as earthquakes and storms.In recent years,the phasefield model has demonstrated exceptional capability in predicting the stochastic initiation,propagation,and bifurcation of cracks in materials.This study employs a phase-field model to focus on the rate dependency and failure response of concrete under impact deformation.A viscosity coefficient is introduced within the phase-field model to characterize the viscous behavior of dynamic crack propagation in concrete.The rate-dependent cohesive strength is defined within the yield function of concrete,where the rate sensitivity of cohesive strength facilitates the accumulation of the plastic driving force in the phase-field model.This process effectively captures the impact failure response of concrete.The applicability of the model was validated through unit cell experiments and numerical simulations of concrete under impact compression.Furthermore,the mechanical response and damage evolution mechanisms of concrete under impact loading were analyzed.It was observed that crack propagation in concrete initiates at material defects and,with increasing load,eventually develops in a direction perpendicular to the loading axis.
基金Project (10964004) supported by the National Natural Science Foundation of ChinaProject (096RJZA104) supported by the Natural Science Foundation of Gansu Province, China
文摘The effect of supercooled melt forced laminar flow at low Reynolds Number on dendritic growth perpendicular to melt flow direction was investigated with the phase-field method by incorporating melt convection and thermal noise under non-isothermal condition. By taking the dendritic growth of high pure succinonitrile （SCN） supercooled melt as an example, side-branching shape difference of melts with flow and without flow was analyzed. Relationships among supercooled melt inflow velocity, deflexion angle of dendritic arm and dendritic tip growth velocity were studied. Results show that the melt inflow velocity has few effects on the dendritic tip growth velocity. A formula of relationship between the velocity of the melt in front of primary dendritic tip and the dendritic growth time was deduced, and the calculated result was in quantitative agreement with the simulation result.
基金Projects(51075335,10902086,50875217) supported by the National Natural Science Foundation of ChinaProject(JC201005) supported by the Northwestern Polytechnical University Foundation for Fundamental Research,ChinaProject(CX201007) supported by the Doctorate Foundation of Northwestern Polytechnical University,China
文摘A microscopic phase-field model was used to investigate a directional coarsening mechanism caused by the anisotropic growth of long period stacking and different effects of phases on precipitation in Ni-Al-V alloy.The results show that DO22 mainly coarsens along its short axis,which may press the neighboring L12,leading to the interaction among atoms.Diffusion channels of Al are formed in the direction where the mismatch between γ＇ and γ reduces;the occupation probabilities are anisotropic in space;and direction coarsening of L12 occurs finally.With a rise of ageing temperature,phases appear later and DO22 is much later at a higher temperature,the average occupation probabilities of Al and V reduce,and Al changes more than V.
基金Projects(51174168,51274167)supported by the National Natural Science Foundation of ChinaProject(2014JM7261)supported by the Natural Science Basic Research Plan in Shaanxi Province of ChinaProject(B08040)supported by "111" Project,China
文摘With microscopic phase-field kinetic model, atomic-scale computer simulation program for the precipitation sequence and microstructure evolution of the ordered intermetallic compound γ＇ and θ in ternary Ni75AlxV25-x alloy were studied. The simulation results show that Al concentration has important effects on the precipitation sequence. When Al concentration in Ni75AlxV25-x alloy is low, 0（Ni3V） ordered phase will be firstly precipitated, followed by γ＇（Ni3Al） ordered phase. With Al concentration increasing, θ and γ＇ ordered phases are simultaneously precipitated. With A1 concentration further increasing, γ＇ ordered phase is firstly precipitated, followed by θ ordered phase. There is a competition relationship between θ and γ＇ ordered phases during growth and coarsening process. No matter which first precipitates, θ ordered phase always occupies advantage in the competition process of coarsening, thus, the microstructure with preferred orientation is formed.
基金Projects(51161011,11364024)supported by the National Natural Science Foundation of China
文摘Based on the entropy function, a two-dimensional phase field model of binary alloys was established. Meanwhile, an explicit difference method with uniform grid was adopted to solve the phase field and solute field controlled equations. And the alternating direction implicit(ADI) algorithm for solving temperature field controlled equation was also employed to avoid the restriction of time step. Some characteristics of the Ni-Cu alloy were captured in the process of non-isothermal solidification, and the comparative analysis of the isothermal and the non-isothermal solidification was investigated. The simulation results indicate that the non-isothermal model is favorable to simulate the real solidification process of binary alloys, and when the thermal diffusivity decreases, the non-isothermal phase-field model is gradually consistent with the isothermal phase-field model.
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.
基金Project(10964004) supported by the National Natural Science Foundation of ChinaProject(20070731001) supported by Research Fund for the Doctoral Program of China+1 种基金 Project(096RJZA104) supported by the Natural Science Foundation of Gansu Province,ChinaProject(SB14200801) supported by the Doctoral Fund of Lanzhou University of Technology,China
文摘The random distribution problem of dendrite preferred growth direction was settled by random grid method.This method was used to study the influence of forced laminar flow effect on multiple grains during solidification.Taking high pure succinonitrile （SCN） undercooled melt as an example,the forced laminar flow effect on multiple grains was studied by phase-field model of single grain which coupled with flow equations at non-isothermal condition.The simulation results show that the random grid method can reasonably settle the problem of random distribution and is more effective.When the solid fraction is relatively low,melt particles flow around the downstream side of dendrite,and the flow velocity between two dendrite arms becomes high.At the stage of solidification time less than 1800Δt,every dendrite grows freely;the upstream dendrites are stronger than the downstream ones.The higher the melt flow rate,the higher the solid fraction.However,when the solid fraction is relatively high,the dendrite arm intertwins and only a little residual melt which is not encapsulated can flow;the solid fraction will gradually tend to equal to solid fraction of melt without flow.
基金Project(51275486)supported by the National Natural Science Foundation of China
文摘The early precipitation process of Ni（75）Al（14）Mo（11） alloy was simulated by microscopic phase-field model at different temperatures.The microstructure of the alloy,the precipitation time of Llo structure and occupation probability of the three kinds of atoms were investigated.It is indicated that the non-stoichiometric Ll0（Ⅰ/Ⅱ） phases are found in the precipitation process.With the temperature increasing,the appearance time of Ll0 is brought forward.The Ll0（Ⅱ） structure always precipitates earlier than the Ll0（Ⅰ） structure.Compared with lower temperature,higher temperature brings the formation time of Ll0 phase forward and makes Ll0 phase have a higher order degree.But lower temperature shortens the process time of the Ll0 phase to the Ll2 phase.Al and Mo atoms tend to occupy γ site,Ni atom tends to occupy a and β sites.At the same temperature,Al atom has stronger occupation ability than Mo atom in the same site.Ni,Al and Mo collectively form the composited Ll2 structure.
