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
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
The effects of temperature on atomic anti-site behaviors in L12-Ni3(AlFe) phases were studied using microscopic phase-field dynamic model in precipitation progress of Ni75Al20Fe5 alloy.The results show that with the i...The effects of temperature on atomic anti-site behaviors in L12-Ni3(AlFe) phases were studied using microscopic phase-field dynamic model in precipitation progress of Ni75Al20Fe5 alloy.The results show that with the increase of temperature,the formation of NiAl and AlNi anti-sites is much easier in Ni3(AlFe),and Ni and Al anti-site atoms show clearly stronger temperature-dependent than Fe anti-site atoms.The evolution progress of anti-site atoms is completed at the initial growth stage of L12-Ni3(AlFe) phases.The site occupation probabilities of Ni atoms on the sublattice A(NiNi,face centers sites of FCC),and Al and Fe atoms on the sublattice B(AlAl and FeAl,corners sites of FCC) all present the degressive tendency with the temperature increasing.Fe atoms mainly prefer to occupy the Al sublattice at the whole temperature range.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
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
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
Embedding optical fiber sensors into composite materials offers the advantage of real-time structural monitoring.However,there is an order-of-magnitude difference in diameter between optical fibers and reinforcing fib...Embedding optical fiber sensors into composite materials offers the advantage of real-time structural monitoring.However,there is an order-of-magnitude difference in diameter between optical fibers and reinforcing fibers,and the detailed mechanism of how embedded optical fibers affect the micromechanical behavior and damage failure processes within composite materials remains unclear.This paper presents a micromechanical simulation analysis of composite materials embedded with optical fibers.By constructing representative volume elements(RVEs)with randomly distributed reinforcing fibers,the optical fiber,the matrix,and the interface phase,the micromechanical behavior and damage evolution under transverse tensile and compressive loads are explored.The study finds that the presence of embedded optical fibers significantly influences the initiation and propagation of microscopic damage within the composites.Under transverse tension,the fiber-matrix interface cracks first,followed by plastic cracking in the matrix surrounding the fibers,forming micro-cracks.Eventually,these cracks connect with the debonded areas at the fiber-matrix interface to form a dominant crack that spans the entire model.Under transverse compression,plastic cracking first occurs in the resin surrounding the optical fibers,connecting with the interface debonding areas between the optical fibers and the matrix to form two parallel shear bands.Additionally,it is observed that the strength of the interface between the optical fiber and the matrix critically affects the simulation results.The simulated damage morphologies align closely with those observed using scanning electron microscopy(SEM).These findings offer theoretical insights that can inform the design and fabrication of smart composite materials with embedded optical fiber sensors for advanced structural health monitoring.展开更多
Accurate prediction of coal reservoir permeability is crucial for engineering applications,including coal mining,coalbed methane(CBM)extraction,and carbon storage in deep unmineable coal seams.Owing to the inherent he...Accurate prediction of coal reservoir permeability is crucial for engineering applications,including coal mining,coalbed methane(CBM)extraction,and carbon storage in deep unmineable coal seams.Owing to the inherent heterogeneity and complex internal structure of coal,a well-established method for predicting permeability based on microscopic fracture structures remains elusive.This paper presents a novel integrated approach that leverages the intrinsic relationship between microscopic fracture structure and permeability to construct a predictive model for coal permeability.The proposed framework encompasses data generation through the integration of three-dimensional(3D)digital core analysis and numerical simulations,followed by data-driven modeling via machine learning(ML)techniques.Key data-driven strategies,including feature selection and hyperparameter tuning,are employed to improve model performance.We propose and evaluate twelve data-driven models,including multilayer perceptron(MLP),random forest(RF),and hybrid methods.The results demonstrate that the ML model based on the RF algorithm achieves the highest accuracy and best generalization capability in predicting permeability.This method enables rapid estimation of coal permeability by inputting two-dimensional(2D)computed tomography images or parameters of the microscopic fracture structure,thereby providing an accurate and efficient means of permeability prediction.展开更多
To investigate the nucleation behavior during the single-phased metallic solidification process,the commercial ultrapure ferritic stainless steels with no(Initial steel)and various melt treatments(R1,MR1,Y2,MY1,and M1...To investigate the nucleation behavior during the single-phased metallic solidification process,the commercial ultrapure ferritic stainless steels with no(Initial steel)and various melt treatments(R1,MR1,Y2,MY1,and M1 steels)were used to carry out the differential scanning colorimetry(DSC)and high-temperature confocal laser scanning microscope(HT-CLSM)experiments.Based on the results of DSC experiments,the equilibrium solidification process as well as the relationship among the critical undercooling degree(△T_(c)^(DSC)),latent heat of fusion/crystallization(△H_(f)/△H_(c)),equiaxed grain ratio(ER),and average grain size(△_(ave)^(ingot))was revealed.ER is increased with the decreasing△T_(c)^(DSC)and increasing△H_(f)/△H_(c);however,△_(ave)^(ingot)is decreased with them.Referring to the results of HT-CLSM experiments,the average sizes of micro-/macrostructures(d_(ave)/D_(ave)/)are decreased with the increasing cooling rate,as well as the difference between and apparent critical undercooling degree(△T_(c)^(CLSM))was revealed.The heterogeneous nucleation of the crystal nuclei occurs only if△T_(c)^(CLSM)>△T_(c)^(DSC).Combining with the interfacial wetting-lattice mismatch heterogeneous nucleation model,the dynamic mechanism of the metallic solidification was revealed.The as-cast grains of the melt-treated samples were obviously refined,owing to the much higher actual heterogeneous nucleation rates(I_(heter.,i))obtained through melt treatments,and the heterogeneous nucleation rates(I_(heter.,ij))for all samples are increased with the cooling rates,firmly confirming that the as-cast grains of each sample could be refined by the increasing cooling rates.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
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 influence of temperature on the precipitation mechanism and sequence of L 12 and D022 phases during the early precipitation process of a Ni-15.Sat%Cr-14at%Al alloy was simulated based on the microscopic phase-fiel...The influence of temperature on the precipitation mechanism and sequence of L 12 and D022 phases during the early precipitation process of a Ni-15.Sat%Cr-14at%Al alloy was simulated based on the microscopic phase-field model. In the range from 873 to 1373 K, the precipitation mechanism transformed from spinodal decomposition to non-classic nucleation and growth; the incubation period prolonged gradually with increasing temperature. The volume fraction of L12 phases increased and that of D022 phases decreased. D022 phases disappeared at 1373 K, and finally single-phase L12 phases were formed.展开更多
Microscopic phase-field method was used to simulate the site occupation of a series of alloys with a stoichiometric composition of Ni75Al25?xFex (x=0, 5?10) aged at 1273 K. With the change of Fe content, quantitative ...Microscopic phase-field method was used to simulate the site occupation of a series of alloys with a stoichiometric composition of Ni75Al25?xFex (x=0, 5?10) aged at 1273 K. With the change of Fe content, quantitative calculations were made on each atomic site occupation probability (SOP) in L12-Ni3 (Al1?xFex), so as to find out the dynamic response law. The result of the study shows that, with the increase of Fe content, the Fe atom preferentially occupies the B sites (corner sites of FCC) with its SOP value being increased gradually, and the SOP of the Al atom on the B sites is greatly decreased. Meanwhile, AlNi and FeNi anti-sites form in the precipitation of L12 phase. Moreover, with the increase of Fe content, the formation of AlNi and FeNi anti-sites becomes much easier. In addition, it has been found that the instantaneous dynamic evolution of the atomic SOP is completed at the early stage of the growth of L12 phases.展开更多
Solidification structure is a key aspect for understanding the mechanical performance of metal alloys,wherein composition and casting parameters considerably influence solidification and determine the unique microstru...Solidification structure is a key aspect for understanding the mechanical performance of metal alloys,wherein composition and casting parameters considerably influence solidification and determine the unique microstructure of the alloys.By following the principle of free energy minimization,the phase-field method eliminates the need for tracking the solid/liquid phase interface and has greatly accelerated the research and development efforts geared toward optimizing metal solidification microstructures.The recent progress in the application of phasefield simulation to investigate the effect of alloy composition and casting process parameters on the solidification structure of metals is summarized in this review.The effects of several typical elements and process parameters,including carbon,boron,silicon,cooling rate,pulling speed,scanning speed,anisotropy,and gravity,on the solidification structure are discussed.The present work also addresses the future prospects of phase-field simulation and aims to facilitate the widespread applications of phase-field approaches in the simulation of microstructures during solidification.展开更多
Solid-state phase transformation is usually associated with excellent mechanical properties in steel materials.A deep understanding of the formation and evolution of phase structure is essential to tailor their servic...Solid-state phase transformation is usually associated with excellent mechanical properties in steel materials.A deep understanding of the formation and evolution of phase structure is essential to tailor their service performance.As a powerful tool for capturing the evolution of complex microstructures,phase-field simulation quantitatively calculates the phase structures evolution without explicit assumptions about transient microstructures.With the development of advanced numerical technology and computing ability,phase-field methods have been successfully applied to solid-state phase transformation in steels and greatly support the research and development of advanced steel materials.The phase-field simulations of solid-phase transformation in steels were summarized,and the future development was proposed.展开更多
Abstract The process of γ＇ phase precipitating from Ni75Al14MO11 is studied by a computational simulation technique based on microscopic phase-field kinetics model. We studied the phase transformation with the purpo...Abstract The process of γ＇ phase precipitating from Ni75Al14MO11 is studied by a computational simulation technique based on microscopic phase-field kinetics model. We studied the phase transformation with the purpose of clarifying the influence of the nearest interatomic potential V Ni-Al （the nearest interatomic potential） on the precipitation process of γ＇ phase. The result demonstrates that there are two kinds of ordered phases, respective Llo and L12 in the early stage, and Llo phase transforms into L12 phase subsequently. For L12 phase, Ni atoms mainly occupy α site （face center positions）, while Al and Mo atoms occupy fl sites （the vertex positions）. When VNi-Al is increased by 10 MeV, the occupation probability of Ni atoms on α sites and Al atoms on β sites are enhanced. Enhanced VNi-Al facilitates clustering and ordering of Al atom, which promotes the formation of the γ＇ phase. At last, the simulation result was discussed by employing the thermodynamic stability.展开更多
A two-dimensional phase field(PF)model was developed to simulate the dendritic solidification in magnesium alloy with hcp crystal structure.By applying a parallel-adaptive mesh refinement(Para-AMR)algorithm,the comput...A two-dimensional phase field(PF)model was developed to simulate the dendritic solidification in magnesium alloy with hcp crystal structure.By applying a parallel-adaptive mesh refinement(Para-AMR)algorithm,the computational efficiency of the numerical model was greatly improved.Based on the PF model,a series of simulation cases were conducted and the results showed that the anisotropy coefficient and coupling coefficient had a great influence on the dendritic morphology of magnesium alloy.The dendritic growth kinetics was determined by the undercooling and equilibrium solute partition coefficient.A significant finding is acquired that with a large undercooling,the maximum solute concentration is located on both sides of the dendrite tip in the liquid,whereas the maximum solute concentration gradient is located right ahead of the dendrite tip in the liquid.The dendrite tip growth velocity decreases with the increase of the equilibrium solute partition coefficient,while the variation trend of the dendrite tip radius is the opposite.Quantitative analysis was carried out relating to the dendritic morphology and growth kinetics,and the simulated results are consistent with the theoretical models proposed in the previously published works.展开更多
On the basis of the microscopic phase-field dynamic model and the microelasticity theory, the characteristics of the coarsening behavior of γ＇ phase in Ni-Al alloys have been systematically studied in a certain volu...On the basis of the microscopic phase-field dynamic model and the microelasticity theory, the characteristics of the coarsening behavior of γ＇ phase in Ni-Al alloys have been systematically studied in a certain volume fraction of the precipitates. It was found that the initial irregular shape, randomly distributed γ＇ phase, gradually transformed into cuboidal shape, regularly aligned along the [100] and [010] directions, and a highly preferential selected microstructure was formed during the later stage of precipitation. The volume fraction of the precipitates produced some effects on the precipitate morphology but did not produce an obvious effect on the regularities of precipitate distribution. The coarsening rate constant from the cubic growth law decreased as a function of volume fraction for small volume fractions, remained constant for intermediate volume fractions, and increased as a function of volume fraction for large volume fractions. During the coherent coarsening process, four ＂splitting＂ patterns between γ＇ phases, which belonged to different antiphase domains, were produced via particle aggregation, such as an L-shaped pattern, a doublet, a triplet, and a quartet.展开更多
With the microscopic phase-field dynamic model, the effects of temperature and concentration on the nucleation incubation time of Ni75AlxV25-x alloy were studied and the relation between the incubation time and precip...With the microscopic phase-field dynamic model, the effects of temperature and concentration on the nucleation incubation time of Ni75AlxV25-x alloy were studied and the relation between the incubation time and precipitation mechanism was investigated by using the atomic occupation probability picture and average order parameter curve. The simulation results demonstrate that there exists the incubation time for different precipitation mechanisms~ such as non-classical nucleation, the mixed style of non-classical nucleation and spinodal decomposition, and spinodal ordering; and the incubation time shortens in turn for the three kinds of mechanisms. With the increase of Al content of Ni75AlxV25-x alloy, the incubation time of Llz phases shortens continuously and that of DOzz phases is prolonged. The effects of temperature on the incubation time of Llz and DOzz phases are accordant, i.e. the incuba- tion time is greatly prolonged with the temperature rising.展开更多
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.
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.
基金Project(50671084) supported by the National Natural Science Foundation of ChinaProject(2009021028) supported by Science and Technique Foundation for Young Scholars of Shanxi Province, ChinaProject(20100470125) supported by National Science Foundation for Post-doctoral Scientists of China
文摘The effects of temperature on atomic anti-site behaviors in L12-Ni3(AlFe) phases were studied using microscopic phase-field dynamic model in precipitation progress of Ni75Al20Fe5 alloy.The results show that with the increase of temperature,the formation of NiAl and AlNi anti-sites is much easier in Ni3(AlFe),and Ni and Al anti-site atoms show clearly stronger temperature-dependent than Fe anti-site atoms.The evolution progress of anti-site atoms is completed at the initial growth stage of L12-Ni3(AlFe) phases.The site occupation probabilities of Ni atoms on the sublattice A(NiNi,face centers sites of FCC),and Al and Fe atoms on the sublattice B(AlAl and FeAl,corners sites of FCC) all present the degressive tendency with the temperature increasing.Fe atoms mainly prefer to occupy the Al sublattice at the whole temperature range.
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.
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 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funded by the National Key Research and Development Program of China(Grant No.2022YFB3402500)the National Natural Science Foundation of China(Grant No.12372129).
文摘Embedding optical fiber sensors into composite materials offers the advantage of real-time structural monitoring.However,there is an order-of-magnitude difference in diameter between optical fibers and reinforcing fibers,and the detailed mechanism of how embedded optical fibers affect the micromechanical behavior and damage failure processes within composite materials remains unclear.This paper presents a micromechanical simulation analysis of composite materials embedded with optical fibers.By constructing representative volume elements(RVEs)with randomly distributed reinforcing fibers,the optical fiber,the matrix,and the interface phase,the micromechanical behavior and damage evolution under transverse tensile and compressive loads are explored.The study finds that the presence of embedded optical fibers significantly influences the initiation and propagation of microscopic damage within the composites.Under transverse tension,the fiber-matrix interface cracks first,followed by plastic cracking in the matrix surrounding the fibers,forming micro-cracks.Eventually,these cracks connect with the debonded areas at the fiber-matrix interface to form a dominant crack that spans the entire model.Under transverse compression,plastic cracking first occurs in the resin surrounding the optical fibers,connecting with the interface debonding areas between the optical fibers and the matrix to form two parallel shear bands.Additionally,it is observed that the strength of the interface between the optical fiber and the matrix critically affects the simulation results.The simulated damage morphologies align closely with those observed using scanning electron microscopy(SEM).These findings offer theoretical insights that can inform the design and fabrication of smart composite materials with embedded optical fiber sensors for advanced structural health monitoring.
基金supported by the Zhejiang Provincial Natural Science Foundation of China(Grant No.LY23E040001)Fundamental Research Funding Project of Zhejiang Province,China(Project Category A,Grant No.2022YW06)National Key R&D Program of China(Grant No.2023YFF0614902).
文摘Accurate prediction of coal reservoir permeability is crucial for engineering applications,including coal mining,coalbed methane(CBM)extraction,and carbon storage in deep unmineable coal seams.Owing to the inherent heterogeneity and complex internal structure of coal,a well-established method for predicting permeability based on microscopic fracture structures remains elusive.This paper presents a novel integrated approach that leverages the intrinsic relationship between microscopic fracture structure and permeability to construct a predictive model for coal permeability.The proposed framework encompasses data generation through the integration of three-dimensional(3D)digital core analysis and numerical simulations,followed by data-driven modeling via machine learning(ML)techniques.Key data-driven strategies,including feature selection and hyperparameter tuning,are employed to improve model performance.We propose and evaluate twelve data-driven models,including multilayer perceptron(MLP),random forest(RF),and hybrid methods.The results demonstrate that the ML model based on the RF algorithm achieves the highest accuracy and best generalization capability in predicting permeability.This method enables rapid estimation of coal permeability by inputting two-dimensional(2D)computed tomography images or parameters of the microscopic fracture structure,thereby providing an accurate and efficient means of permeability prediction.
基金supported by the National Natural Science Foundation of China(Grant Nos.52274339,52174321,52074186,and 52104337)Natural Science Foundation of Jiangsu Province(Grant No.BK20231317)China Baowu Low-Carbon Metallurgy Innovation Fund(Grant No.BWLCF202108).
文摘To investigate the nucleation behavior during the single-phased metallic solidification process,the commercial ultrapure ferritic stainless steels with no(Initial steel)and various melt treatments(R1,MR1,Y2,MY1,and M1 steels)were used to carry out the differential scanning colorimetry(DSC)and high-temperature confocal laser scanning microscope(HT-CLSM)experiments.Based on the results of DSC experiments,the equilibrium solidification process as well as the relationship among the critical undercooling degree(△T_(c)^(DSC)),latent heat of fusion/crystallization(△H_(f)/△H_(c)),equiaxed grain ratio(ER),and average grain size(△_(ave)^(ingot))was revealed.ER is increased with the decreasing△T_(c)^(DSC)and increasing△H_(f)/△H_(c);however,△_(ave)^(ingot)is decreased with them.Referring to the results of HT-CLSM experiments,the average sizes of micro-/macrostructures(d_(ave)/D_(ave)/)are decreased with the increasing cooling rate,as well as the difference between and apparent critical undercooling degree(△T_(c)^(CLSM))was revealed.The heterogeneous nucleation of the crystal nuclei occurs only if△T_(c)^(CLSM)>△T_(c)^(DSC).Combining with the interfacial wetting-lattice mismatch heterogeneous nucleation model,the dynamic mechanism of the metallic solidification was revealed.The as-cast grains of the melt-treated samples were obviously refined,owing to the much higher actual heterogeneous nucleation rates(I_(heter.,i))obtained through melt treatments,and the heterogeneous nucleation rates(I_(heter.,ij))for all samples are increased with the cooling rates,firmly confirming that the as-cast grains of each sample could be refined by the increasing cooling rates.
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(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This work was financially supported by the National Natural Science Foundation of China (No.50071046) and the National High-Tech Research and Development Program of China (No.2002AA331051).
文摘The influence of temperature on the precipitation mechanism and sequence of L 12 and D022 phases during the early precipitation process of a Ni-15.Sat%Cr-14at%Al alloy was simulated based on the microscopic phase-field model. In the range from 873 to 1373 K, the precipitation mechanism transformed from spinodal decomposition to non-classic nucleation and growth; the incubation period prolonged gradually with increasing temperature. The volume fraction of L12 phases increased and that of D022 phases decreased. D022 phases disappeared at 1373 K, and finally single-phase L12 phases were formed.
基金Project(2013011014-1)supported by the Natural Science Funds of Shanxi Province,ChinaProject(2009021028)supported by Science and Technique Foundation for Young Scholars of Shanxi Province,China
文摘Microscopic phase-field method was used to simulate the site occupation of a series of alloys with a stoichiometric composition of Ni75Al25?xFex (x=0, 5?10) aged at 1273 K. With the change of Fe content, quantitative calculations were made on each atomic site occupation probability (SOP) in L12-Ni3 (Al1?xFex), so as to find out the dynamic response law. The result of the study shows that, with the increase of Fe content, the Fe atom preferentially occupies the B sites (corner sites of FCC) with its SOP value being increased gradually, and the SOP of the Al atom on the B sites is greatly decreased. Meanwhile, AlNi and FeNi anti-sites form in the precipitation of L12 phase. Moreover, with the increase of Fe content, the formation of AlNi and FeNi anti-sites becomes much easier. In addition, it has been found that the instantaneous dynamic evolution of the atomic SOP is completed at the early stage of the growth of L12 phases.
基金financially supported by the National Key Research and Development Program of China(No.2021YFB3702401)the National Natural Science Foundation of China(Nos.51901013,52122408,52071023)+3 种基金financial support from the Fundamental Research Funds for the Central Universities,China(University of Science and Technology Beijing(USTB),Nos.FRF-TP-2021-04C1,06500135)financial support from the Qilu Young Talent Program of Shandong University,Zhejiang Lab Open Research Project,China(No.K2022PE0AB05)the Shandong Provincial Natural Science Foundation,China(No.ZR2023MA058)the Guangdong Basic and Applied Basic Research Foundation,China(No.2023A1515011819)。
文摘Solidification structure is a key aspect for understanding the mechanical performance of metal alloys,wherein composition and casting parameters considerably influence solidification and determine the unique microstructure of the alloys.By following the principle of free energy minimization,the phase-field method eliminates the need for tracking the solid/liquid phase interface and has greatly accelerated the research and development efforts geared toward optimizing metal solidification microstructures.The recent progress in the application of phasefield simulation to investigate the effect of alloy composition and casting process parameters on the solidification structure of metals is summarized in this review.The effects of several typical elements and process parameters,including carbon,boron,silicon,cooling rate,pulling speed,scanning speed,anisotropy,and gravity,on the solidification structure are discussed.The present work also addresses the future prospects of phase-field simulation and aims to facilitate the widespread applications of phase-field approaches in the simulation of microstructures during solidification.
基金This work was financially supported by the National Natural Science Foundation of China(Nos.52071023,51901013,and 52122408)H.H.Wu also thanks to the financial support from the Fundamental Research Funds for the Central Universities(University of Science and Technology Beijing,Nos.FRF-TP-2021-04C1 and 06500135).
文摘Solid-state phase transformation is usually associated with excellent mechanical properties in steel materials.A deep understanding of the formation and evolution of phase structure is essential to tailor their service performance.As a powerful tool for capturing the evolution of complex microstructures,phase-field simulation quantitatively calculates the phase structures evolution without explicit assumptions about transient microstructures.With the development of advanced numerical technology and computing ability,phase-field methods have been successfully applied to solid-state phase transformation in steels and greatly support the research and development of advanced steel materials.The phase-field simulations of solid-phase transformation in steels were summarized,and the future development was proposed.
基金financially supported by the National Natural Science Foundation of China (Nos. 51,204,147 and 51274175)International Cooperation Project Supported by Ministry of Science and Technology of China (No. 2014DFA50320)International Science and Technology Cooperation Project of Shanxi Province (Nos. 2013081017 and 2012081013)
文摘Abstract The process of γ＇ phase precipitating from Ni75Al14MO11 is studied by a computational simulation technique based on microscopic phase-field kinetics model. We studied the phase transformation with the purpose of clarifying the influence of the nearest interatomic potential V Ni-Al （the nearest interatomic potential） on the precipitation process of γ＇ phase. The result demonstrates that there are two kinds of ordered phases, respective Llo and L12 in the early stage, and Llo phase transforms into L12 phase subsequently. For L12 phase, Ni atoms mainly occupy α site （face center positions）, while Al and Mo atoms occupy fl sites （the vertex positions）. When VNi-Al is increased by 10 MeV, the occupation probability of Ni atoms on α sites and Al atoms on β sites are enhanced. Enhanced VNi-Al facilitates clustering and ordering of Al atom, which promotes the formation of the γ＇ phase. At last, the simulation result was discussed by employing the thermodynamic stability.
基金financially supported by the National Natural Science Foundation of China(No.51805389)the Natural Science Foundation of Hubei Province,China(No.2018CFB210)the 111 Project(No.B17034)。
文摘A two-dimensional phase field(PF)model was developed to simulate the dendritic solidification in magnesium alloy with hcp crystal structure.By applying a parallel-adaptive mesh refinement(Para-AMR)algorithm,the computational efficiency of the numerical model was greatly improved.Based on the PF model,a series of simulation cases were conducted and the results showed that the anisotropy coefficient and coupling coefficient had a great influence on the dendritic morphology of magnesium alloy.The dendritic growth kinetics was determined by the undercooling and equilibrium solute partition coefficient.A significant finding is acquired that with a large undercooling,the maximum solute concentration is located on both sides of the dendrite tip in the liquid,whereas the maximum solute concentration gradient is located right ahead of the dendrite tip in the liquid.The dendrite tip growth velocity decreases with the increase of the equilibrium solute partition coefficient,while the variation trend of the dendrite tip radius is the opposite.Quantitative analysis was carried out relating to the dendritic morphology and growth kinetics,and the simulated results are consistent with the theoretical models proposed in the previously published works.
基金This work was financially supported by the National Natural Science Foundation of China (No.50671084)China Postdoctoral Science Foundation (No.20070420218).
文摘On the basis of the microscopic phase-field dynamic model and the microelasticity theory, the characteristics of the coarsening behavior of γ＇ phase in Ni-Al alloys have been systematically studied in a certain volume fraction of the precipitates. It was found that the initial irregular shape, randomly distributed γ＇ phase, gradually transformed into cuboidal shape, regularly aligned along the [100] and [010] directions, and a highly preferential selected microstructure was formed during the later stage of precipitation. The volume fraction of the precipitates produced some effects on the precipitate morphology but did not produce an obvious effect on the regularities of precipitate distribution. The coarsening rate constant from the cubic growth law decreased as a function of volume fraction for small volume fractions, remained constant for intermediate volume fractions, and increased as a function of volume fraction for large volume fractions. During the coherent coarsening process, four ＂splitting＂ patterns between γ＇ phases, which belonged to different antiphase domains, were produced via particle aggregation, such as an L-shaped pattern, a doublet, a triplet, and a quartet.
文摘With the microscopic phase-field dynamic model, the effects of temperature and concentration on the nucleation incubation time of Ni75AlxV25-x alloy were studied and the relation between the incubation time and precipitation mechanism was investigated by using the atomic occupation probability picture and average order parameter curve. The simulation results demonstrate that there exists the incubation time for different precipitation mechanisms~ such as non-classical nucleation, the mixed style of non-classical nucleation and spinodal decomposition, and spinodal ordering; and the incubation time shortens in turn for the three kinds of mechanisms. With the increase of Al content of Ni75AlxV25-x alloy, the incubation time of Llz phases shortens continuously and that of DOzz phases is prolonged. The effects of temperature on the incubation time of Llz and DOzz phases are accordant, i.e. the incuba- tion time is greatly prolonged with the temperature rising.
