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
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
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
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
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
Sintering,a well-established technique in powder metallurgy,plays a critical role in the processing of high melting point materials.A comprehensive understanding of structural changes during the sintering process is e...Sintering,a well-established technique in powder metallurgy,plays a critical role in the processing of high melting point materials.A comprehensive understanding of structural changes during the sintering process is essential for effective product assessment.The phase-field method stands out for its unique ability to simulate these structural transformations.Despite its widespread application,there is a notable absence of literature reviews focused on its usage in sintering simulations.Therefore,this paper addresses this gap by reviewing the latest advancements in phase-field sintering models,covering approaches based on energy,grand potential,and entropy increase.The characteristics of various models are extensively discussed,with a specific emphasis on energy-based models incorporating considerations such as interface energy anisotropy,tensor-form diffusion mechanisms,and various forms of rigid particle motion during sintering.Furthermore,the paper offers a concise summary of phase-field sintering models that integrate with other physical fields,including stress/strain fields,viscous flow,temperature field,and external electric fields.In conclusion,the paper provides a succinct overview of the entire content and delineates potential avenues for future research.展开更多
The continued existence of high-energy radiation in nuclear reactors at high temperatures results in the formation of radiation-induced voids,which will further lead to inevitable swellings of polycrystalline structur...The continued existence of high-energy radiation in nuclear reactors at high temperatures results in the formation of radiation-induced voids,which will further lead to inevitable swellings of polycrystalline structural components and thus premature failures.A deep understanding of the effect of temperature and grain boundary on void evolution in irradiated copper is significant for preventing this kind of failures.Here,the phase-field method was employed to study void evolution in irradiated copper under different temperatures and grain sizes.The results show that,due to the different sensitivities of point defect production rate and vacancy diffusion rate to temperature changes,both the nucleation-growth rate and the coarsening rate during void evolution increase first and then decrease with increasing temperature;moreover,the nucleation mechanism exhibits site-saturated nucleation at low temperatures while continuous nucleation at high temperatures.The presence of grain boundary can accelerate the emergence of void because grain boundaries can absorb more interstitials than vacancies.The finer the grain size,the stronger inhibitory effect of grain boundaries on the growth rate of void,due to the formation of void denuded zone near grain boundaries.At high temperatures,the growth rate of void in fine grains is significantly reduced due to the increase of vacancy diffusion rate and the enhancement of sink effect of grain boundary on vacancy.展开更多
By incorporating two different fracture mechanisms and salient unilateral effects in rock materials,we propose a thermomechanical phase-field model to capture thermally induced fracture and shear heating in the proces...By incorporating two different fracture mechanisms and salient unilateral effects in rock materials,we propose a thermomechanical phase-field model to capture thermally induced fracture and shear heating in the process of rock failure.The heat conduction equation is derived,from which the plastic dissipation is treated as a heat source.We then ascertain the effect of the non-associated plastic flow on frictional dissipation and show how it improves the predictive capability of the proposed model.Taking advantage of the multiscale analysis,we propose a phase-field-dependent thermal conductivity with considering the unilateral effect of fracture.After proposing a robust algorithm for solving involved three-field coupling and damage-plasticity coupling problems,we present three numerical examples to illustrate the abilities of our proposed model in capturing various thermo-mechanically coupled behaviors.展开更多
Hydride precipitation in zirconium cladding materials can damage their integrity and durability.Service temperature and material defects have a significant effect on the dynamic growth of hydrides.In this study,we hav...Hydride precipitation in zirconium cladding materials can damage their integrity and durability.Service temperature and material defects have a significant effect on the dynamic growth of hydrides.In this study,we have developed a phasefield model based on the assumption of elastic behaviour within a specific temperature range(613 K-653 K).This model allows us to study the influence of temperature and interfacial effects on the morphology,stress,and average growth rate of zirconium hydride.The results suggest that changes in temperature and interfacial energy influence the length-to-thickness ratio and average growth rate of the hydride morphology.The ultimate determinant of hydride orientation is the loss of interfacial coherency,primarily induced by interfacial dislocation defects and quantifiable by the mismatch degree q.An escalation in interfacial coherency loss leads to a transition of hydride growth from horizontal to vertical,accompanied by the onset of redirection behaviour.Interestingly,redirection occurs at a critical mismatch level,denoted as qc,and remains unaffected by variations in temperature and interfacial energy.However,this redirection leads to an increase in the maximum stress,which may influence the direction of hydride crack propagation.This research highlights the importance of interfacial coherency and provides valuable insights into the morphology and growth kinetics of hydrides in zirconium alloys.展开更多
Understanding the probabilistic nature of brittle materials due to inherent dispersions in their mechanical properties is important to assess their reliability and safety for sensitive engineering applications.This is...Understanding the probabilistic nature of brittle materials due to inherent dispersions in their mechanical properties is important to assess their reliability and safety for sensitive engineering applications.This is all the more important when elements composed of brittle materials are exposed to dynamic environments,resulting in catastrophic fatigue failures.The authors propose the application of a non-intrusive polynomial chaos expansion method for probabilistic studies on brittle materials undergoing fatigue fracture when geometrical parameters and material properties are random independent variables.Understanding the probabilistic nature of fatigue fracture in brittle materials is crucial for ensuring the reliability and safety of engineering structures subjected to cyclic loading.Crack growth is modelled using a phase-field approach within a finite element framework.For modelling fatigue,fracture resistance is progressively degraded by modifying the regularised free energy functional using a fatigue degradation function.Number of cycles to failure is treated as the dependent variable of interest and is estimated within acceptable limits due to the randomness in independent properties.Multiple 2D benchmark problems are solved to demonstrate the ability of this approach to predict the dependent variable responses with significantly fewer simulations than the Monte Carlo method.This proposed approach can accurately predict results typically obtained through 105 or more runs in Monte Carlo simulations with a reduction of up to three orders of magnitude in required runs.The independent random variables’sensitivity to the system response is determined using Sobol’indices.The proposed approach has low computational overhead and can be useful for computationally intensive problems requiring rapid decision-making in sensitive applications like aerospace,nuclear and biomedical engineering.The technique does not require reformulating existing finite element code and can perform the stochastic study by direct pre/post-processing.展开更多
The effect of undercooling DT and the interface energy anisotropy parameter e4 on the shape of the equiaxed dendritic tip has been investigated by using a quantitative phase-field model for solidification of binary al...The effect of undercooling DT and the interface energy anisotropy parameter e4 on the shape of the equiaxed dendritic tip has been investigated by using a quantitative phase-field model for solidification of binary alloys.It was found that the tip radius r increases and the tip shape amplitude coefficient A4 decreases with the increase of the fitting range for all cases.The dendrite tip shape selection parameter sdecreases and then stabilizes with the increase of the fitting range,and sincreases with the increase of e4.The relationship between sand e4 follows a power-law function sµea 4,and a is independent of DT but dependent on the fitting range.Numerical results demonstrate that the predicted sis consistent with the curve of microscopic solvability theory(MST)for e4<0.02,and sobtained from our phase-field simulations is sensitive to the undercooling when e4 is fixed.展开更多
A novel phase-field model for the propagation of mixed-mode hydraulic fractures,characterized by the formation of mixed-mode fractures due to the interactions between fluids and solids,is proposed.In this model,the dr...A novel phase-field model for the propagation of mixed-mode hydraulic fractures,characterized by the formation of mixed-mode fractures due to the interactions between fluids and solids,is proposed.In this model,the driving force for the phase field consists of both tensile and shear components,with the fluid contribution primarily manifesting in the tension driving force.The displacement and pressure are solved simultaneously by an implicit method.The numerical solution's iterative format is established by the finite element discretization and Newton-Raphson(NR)iterative methods.The correctness of the model is verified through the uniaxial compression physical experiments on fluid-pressurized rocks,and the limitations of the hydraulic fracture expansion phase-field model,which only considers mode I fractures,are revealed.In addition,the influence of matrix mode II fracture toughness value,natural fracture mode II toughness value,and fracturing fluid injection rate on the hydraulic fracture propagation in porous media with natural fractures is studied.展开更多
Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilt...Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle.Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations.A staggered algorithm is used to simulate the crack propagation.The polynomial splines over hierarchical T-meshes(PHT-splines)are adopted as the basis function,which owns the C1continuity.Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials.The electric boundary conditions may influence crack paths and fracture loads significantly.The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.展开更多
This study provides a potentially viable approach to manipulate the precipitation of primary carbides in molten steel by modifying the diffusion coefficient of carbon.The solidification process of a Fe-C alloy is simu...This study provides a potentially viable approach to manipulate the precipitation of primary carbides in molten steel by modifying the diffusion coefficient of carbon.The solidification process of a Fe-C alloy is simulated using the multi-phase-field method,and we focus on the impact of diffusion coefficient of carbon on the solute segregation and cementite precipitation.Two benefits have been revealed as the ratio of the diffusivities of carbon in solid to that in liquid is increased.A potential advantage is the re-duction in the volume fraction of the residual liquid enriched with carbon during the late solidification.Furthermore,the magnitude of the chemical driving force for the phase transition of cementite precip-itation will be lower.The combined influence of both factors results in an exponential decrease in the volume fraction of cementite formed at the end of solidification.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.
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 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supported by the National Science and TechnologyMajor Project,China(No.J2019-IV-0014-0082)the National Key Research and Development Program of China(No.2022YFB4600700)+1 种基金the National Overseas Youth Talents Program,China,the Research Fund of State Key Laboratory of Mechanics and Control for Aerospace Structures,China(No.MCMS-I-0422K01)a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions,China.
文摘Sintering,a well-established technique in powder metallurgy,plays a critical role in the processing of high melting point materials.A comprehensive understanding of structural changes during the sintering process is essential for effective product assessment.The phase-field method stands out for its unique ability to simulate these structural transformations.Despite its widespread application,there is a notable absence of literature reviews focused on its usage in sintering simulations.Therefore,this paper addresses this gap by reviewing the latest advancements in phase-field sintering models,covering approaches based on energy,grand potential,and entropy increase.The characteristics of various models are extensively discussed,with a specific emphasis on energy-based models incorporating considerations such as interface energy anisotropy,tensor-form diffusion mechanisms,and various forms of rigid particle motion during sintering.Furthermore,the paper offers a concise summary of phase-field sintering models that integrate with other physical fields,including stress/strain fields,viscous flow,temperature field,and external electric fields.In conclusion,the paper provides a succinct overview of the entire content and delineates potential avenues for future research.
基金supported by the National Natural Science Foundation of China(Grants No.51871183)supported by the Research Fund of the State Key Laboratory of Solidification Processing(NPU),China(Grant No.2020-TS-06).
文摘The continued existence of high-energy radiation in nuclear reactors at high temperatures results in the formation of radiation-induced voids,which will further lead to inevitable swellings of polycrystalline structural components and thus premature failures.A deep understanding of the effect of temperature and grain boundary on void evolution in irradiated copper is significant for preventing this kind of failures.Here,the phase-field method was employed to study void evolution in irradiated copper under different temperatures and grain sizes.The results show that,due to the different sensitivities of point defect production rate and vacancy diffusion rate to temperature changes,both the nucleation-growth rate and the coarsening rate during void evolution increase first and then decrease with increasing temperature;moreover,the nucleation mechanism exhibits site-saturated nucleation at low temperatures while continuous nucleation at high temperatures.The presence of grain boundary can accelerate the emergence of void because grain boundaries can absorb more interstitials than vacancies.The finer the grain size,the stronger inhibitory effect of grain boundaries on the growth rate of void,due to the formation of void denuded zone near grain boundaries.At high temperatures,the growth rate of void in fine grains is significantly reduced due to the increase of vacancy diffusion rate and the enhancement of sink effect of grain boundary on vacancy.
基金funding provided by the National Natural Science Foundation of China(No.12202137)TY's contribution is funded by the China and Germany Postdoctoral Exchange Program(Grant No.ZD202137).The first author(TY)would like to express his gratitude to Prof.Keita Yoshioka for reviewing this manuscript and for his invaluable feedback.
文摘By incorporating two different fracture mechanisms and salient unilateral effects in rock materials,we propose a thermomechanical phase-field model to capture thermally induced fracture and shear heating in the process of rock failure.The heat conduction equation is derived,from which the plastic dissipation is treated as a heat source.We then ascertain the effect of the non-associated plastic flow on frictional dissipation and show how it improves the predictive capability of the proposed model.Taking advantage of the multiscale analysis,we propose a phase-field-dependent thermal conductivity with considering the unilateral effect of fracture.After proposing a robust algorithm for solving involved three-field coupling and damage-plasticity coupling problems,we present three numerical examples to illustrate the abilities of our proposed model in capturing various thermo-mechanically coupled behaviors.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.U2230401,U1930401,and 12004048)the National Key Research and Development Program of China (Grant No.2021YFB3501503)+1 种基金the Science Challenge Project (Grant No.TZ2018002)the Foundation of LCP。
文摘Hydride precipitation in zirconium cladding materials can damage their integrity and durability.Service temperature and material defects have a significant effect on the dynamic growth of hydrides.In this study,we have developed a phasefield model based on the assumption of elastic behaviour within a specific temperature range(613 K-653 K).This model allows us to study the influence of temperature and interfacial effects on the morphology,stress,and average growth rate of zirconium hydride.The results suggest that changes in temperature and interfacial energy influence the length-to-thickness ratio and average growth rate of the hydride morphology.The ultimate determinant of hydride orientation is the loss of interfacial coherency,primarily induced by interfacial dislocation defects and quantifiable by the mismatch degree q.An escalation in interfacial coherency loss leads to a transition of hydride growth from horizontal to vertical,accompanied by the onset of redirection behaviour.Interestingly,redirection occurs at a critical mismatch level,denoted as qc,and remains unaffected by variations in temperature and interfacial energy.However,this redirection leads to an increase in the maximum stress,which may influence the direction of hydride crack propagation.This research highlights the importance of interfacial coherency and provides valuable insights into the morphology and growth kinetics of hydrides in zirconium alloys.
文摘Understanding the probabilistic nature of brittle materials due to inherent dispersions in their mechanical properties is important to assess their reliability and safety for sensitive engineering applications.This is all the more important when elements composed of brittle materials are exposed to dynamic environments,resulting in catastrophic fatigue failures.The authors propose the application of a non-intrusive polynomial chaos expansion method for probabilistic studies on brittle materials undergoing fatigue fracture when geometrical parameters and material properties are random independent variables.Understanding the probabilistic nature of fatigue fracture in brittle materials is crucial for ensuring the reliability and safety of engineering structures subjected to cyclic loading.Crack growth is modelled using a phase-field approach within a finite element framework.For modelling fatigue,fracture resistance is progressively degraded by modifying the regularised free energy functional using a fatigue degradation function.Number of cycles to failure is treated as the dependent variable of interest and is estimated within acceptable limits due to the randomness in independent properties.Multiple 2D benchmark problems are solved to demonstrate the ability of this approach to predict the dependent variable responses with significantly fewer simulations than the Monte Carlo method.This proposed approach can accurately predict results typically obtained through 105 or more runs in Monte Carlo simulations with a reduction of up to three orders of magnitude in required runs.The independent random variables’sensitivity to the system response is determined using Sobol’indices.The proposed approach has low computational overhead and can be useful for computationally intensive problems requiring rapid decision-making in sensitive applications like aerospace,nuclear and biomedical engineering.The technique does not require reformulating existing finite element code and can perform the stochastic study by direct pre/post-processing.
基金the National Key Research and De-velopment Program of China(Grant No.2021YFB3502600)Shenzhen Science and Technology Program(Grant No.JCYJ20220530161813029).
文摘The effect of undercooling DT and the interface energy anisotropy parameter e4 on the shape of the equiaxed dendritic tip has been investigated by using a quantitative phase-field model for solidification of binary alloys.It was found that the tip radius r increases and the tip shape amplitude coefficient A4 decreases with the increase of the fitting range for all cases.The dendrite tip shape selection parameter sdecreases and then stabilizes with the increase of the fitting range,and sincreases with the increase of e4.The relationship between sand e4 follows a power-law function sµea 4,and a is independent of DT but dependent on the fitting range.Numerical results demonstrate that the predicted sis consistent with the curve of microscopic solvability theory(MST)for e4<0.02,and sobtained from our phase-field simulations is sensitive to the undercooling when e4 is fixed.
基金Project supported by the National Natural Science Foundation of China(No.42202314)。
文摘A novel phase-field model for the propagation of mixed-mode hydraulic fractures,characterized by the formation of mixed-mode fractures due to the interactions between fluids and solids,is proposed.In this model,the driving force for the phase field consists of both tensile and shear components,with the fluid contribution primarily manifesting in the tension driving force.The displacement and pressure are solved simultaneously by an implicit method.The numerical solution's iterative format is established by the finite element discretization and Newton-Raphson(NR)iterative methods.The correctness of the model is verified through the uniaxial compression physical experiments on fluid-pressurized rocks,and the limitations of the hydraulic fracture expansion phase-field model,which only considers mode I fractures,are revealed.In addition,the influence of matrix mode II fracture toughness value,natural fracture mode II toughness value,and fracturing fluid injection rate on the hydraulic fracture propagation in porous media with natural fractures is studied.
基金Project supported by the National Natural Science Foundation of China(Nos.12072297 and12202370)the Natural Science Foundation of Sichuan Province of China(No.24NSFSC4777)。
文摘Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle.Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations.A staggered algorithm is used to simulate the crack propagation.The polynomial splines over hierarchical T-meshes(PHT-splines)are adopted as the basis function,which owns the C1continuity.Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials.The electric boundary conditions may influence crack paths and fracture loads significantly.The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.
基金supported by the National Sci-ence and Technology Major Project(No.J2019-VI-0019-0134)the National Natural Science Foundation of China(No.52203301)+1 种基金the China Postdoctoral Science Foundation(No.2021TQ0335)the Strategic Priority Research Program of the Chinese Academy of Sci-ences(No.XDC04040202).
文摘This study provides a potentially viable approach to manipulate the precipitation of primary carbides in molten steel by modifying the diffusion coefficient of carbon.The solidification process of a Fe-C alloy is simulated using the multi-phase-field method,and we focus on the impact of diffusion coefficient of carbon on the solute segregation and cementite precipitation.Two benefits have been revealed as the ratio of the diffusivities of carbon in solid to that in liquid is increased.A potential advantage is the re-duction in the volume fraction of the residual liquid enriched with carbon during the late solidification.Furthermore,the magnitude of the chemical driving force for the phase transition of cementite precip-itation will be lower.The combined influence of both factors results in an exponential decrease in the volume fraction of cementite formed at the end of solidification.
