It is well known that coarse-grained super-elastic NiTi shape memory alloys(SMAs)exhibit localized rather than homogeneous martensite transformation(MT),which,however,can be strongly influenced by either internal size...It is well known that coarse-grained super-elastic NiTi shape memory alloys(SMAs)exhibit localized rather than homogeneous martensite transformation(MT),which,however,can be strongly influenced by either internal size(grain size,GS)or the external size(geometric size).The coupled effect of GS and geometric size on the functional properties has not been clearly understood yet.In this work,the super-elasticity,one-way,and stress-assisted two-way shape memory effects of the polycrystalline NiTi SMAs with different aspect ratios(length/width for the gauge section)and different GSs are investigated based on the phase field method.The coupled effect of the aspect ratio and GS on the functional properties is adequately revealed.The simulated results indicate that when the aspect ratio is lower than about 4:1,the stress biaxiality and stress heterogeneity in the gauge section of the sample become more and more obvious with decreasing the aspect ratio,which can significantly influence the microstructure evolution in the process involving external stress.Therefore,the corresponding functional property is strongly dependent on the aspect ratio.With decreasing the GS and the aspect ratio(to be lower than 4:1),both the aspect ratio and GS can affect the MT or martensite reorientation in each grain and the interaction among grains.Thus,due to the strong internal constraint(i.e.,the constraint of grain boundary)and the external constraint(i.e.,the constraint of geometric boundary),the capabilities of the functional properties of NiTi SMAs are gradually weakened and highly dependent on these two factors.展开更多
As the demand for advanced material design and performance prediction continues to grow,traditional phase-field models are increasingly challenged by limitations in computational efficiency and predictive accuracy,par...As the demand for advanced material design and performance prediction continues to grow,traditional phase-field models are increasingly challenged by limitations in computational efficiency and predictive accuracy,particularly when addressing high-dimensional and complex data in multicomponent systems.To overcome these challenges,this study proposes an innovative model,LSGWO-BP,which integrates an improved Grey Wolf Optimizer(GWO)with a backpropagation neural network(BP)to enhance the accuracy and efficiency of quasi-phase equilibrium predictions within the KKS phase-field framework.Three mapping enhancement strategies were investigated–Circle-Root,Tent-Cosine,and Logistic-Sine mappings-with the Logistic mapping further improved via Sine perturbation to boost global search capability and convergence speed in large-scale,complex data scenarios.Evaluation results demonstrate that the LSGWO-BP model significantly outperforms conventional machine learning approaches in predicting quasi-phase equilibrium,achieving a 14%–28%reduction in mean absolute error(MAE).Substantial improvements were also observed in mean squared error,root mean squared error,and mean absolute percentage error,alongside a 7%–33%increase in the coefficient of determination(R2).Furthermore,the model exhibits strong potential for microstructural simulation applications.Overall,the study confirms the effectiveness of the LSGWO-BP model in materials science,especially in enhancing phase-field modeling efficiency and enabling accurate,intelligent prediction for multicomponent alloy systems,thereby offering robust support for microstructure prediction and control.展开更多
Shape memory alloys(SMAs)and shape memory ceramics(SMCs)exhibit high recovery ability due to the martensitic transformation,which complicates the fracture mechanism of SMAs and SMCs.The phase field method,as a powerfu...Shape memory alloys(SMAs)and shape memory ceramics(SMCs)exhibit high recovery ability due to the martensitic transformation,which complicates the fracture mechanism of SMAs and SMCs.The phase field method,as a powerful numerical simulation tool,can efficiently resolve the microstructural evolution,multi-field coupling effects,and fracture behavior of SMAs and SMCs.This review begins by presenting the fundamental theoretical framework of the fracture phase field method as applied to SMAs and SMCs,covering key aspects such as the phase field modeling of martensitic transformation and brittle fracture.Subsequently,it systematically examines the phase field simulations of fracture behaviors in SMAs and SMCs,with particular emphasis on how crystallographic orientation,grain size,and grain boundary properties influence the crack propagation.Additionally,the interplay between martensite transformation and fracture mechanisms is analyzed to provide deeper insights into the material responses under mechanical loading.Finally,the review explores future prospects and emerging trends in phase field simulations of SMA and SMC fracture behavior,along with potential advancements in the fracture phase field method itself,including multi-physics coupling and enhanced computational efficiency for large-scale simulations.展开更多
With the evolution of nickel-based single crystal superalloys,there is an increase in heavy elements such as Re and Ru.This has made solutal convection more pronounced during the directional solidification process,lea...With the evolution of nickel-based single crystal superalloys,there is an increase in heavy elements such as Re and Ru.This has made solutal convection more pronounced during the directional solidification process,leading to solute redistribution and increasing the risk of casting defects such as low-angle grain boundaries.To avoid casting defects,downward directional solidification(DWS)method is adopted to eliminate solutal convection and change solute redistribution.However,there is currently no in-situ characterization or quantitative simulation studying the solute redistribution during DWS and upward directional solidification(UWS)processes.A multicomponent phase field simulation coupled with lattice Boltzmann method was employed to quantitatively investigate changes in dendrite morphology,solutal convection and deviation of dendrite tips from the perspective of solute redistribution during UWS and DWS processes.The simulation of microstructure agrees well with the experimental results.The mechanism that explains how solutal convection affects side branching behavior is depicted.A novel approach is introduced to characterize dendrite deviation,elucidating the reasons why defects are prone to occur under the influence of natural convection and solute redistribution.展开更多
The two-phase flow in porous media is affected by multiple factors.In the present study,a two-dimensional numerical model of porous media was developed using the actual pore structure of the core sample.The phase fiel...The two-phase flow in porous media is affected by multiple factors.In the present study,a two-dimensional numerical model of porous media was developed using the actual pore structure of the core sample.The phase field method was utilized to simulate the impact of displacement velocity,the water-gas viscosity ratio,and the density ratio on the flow behavior of two-phase fluids in porous media.The effectiveness of displacement was evaluated by analyzing CO_(2)saturation levels.The results indicate that the saturation of CO_(2)in porous media increased as the displacement velocity increased.When the displacement velocity exceeded 0.01 m/s,there was a corresponding increase in CO_(2)saturation.Conversely,when the displacement velocity was below this threshold,the impact on CO_(2)saturation was minimal.An“inflection point,”M3,was present in the viscosity ratio.When the viscosity of CO_(2)is less than 8.937×10^(-5)Pa·s(viscosity ratio below M3),variations in the viscosity of CO_(2)had little impact on its saturation.Conversely,when the viscosity of CO_(2)exceeded 8.937×10^(-5)Pa·s(viscosity ratio greater than M3),saturation increased with an increase in the viscosity ratio.In terms of the density ratio,the saturation of CO_(2)increased monotonically with an increase in the density ratio.Similarly,increasing density ratios resulted in a monotonic increase in CO_(2)saturation,though this trend was less pronounced in numerical simulations.Analysis results of displacement within dead-end pores using pressure and velocity diagrams reveal eddy currents as contributing factors.Finally,the impact of pore throat structure on the formation of dominant channels was examined.展开更多
Accurate simulation of the cracking process caused by rust expansion of reinforced concrete(RC)structures plays an intuitive role in revealing the corrosion-induced failure mechanism.Considering the quasi-brittle frac...Accurate simulation of the cracking process caused by rust expansion of reinforced concrete(RC)structures plays an intuitive role in revealing the corrosion-induced failure mechanism.Considering the quasi-brittle fracture of concrete,the fracture phase field driven by the compressive-shear term is constructed and added to the traditional brittle fracture phase field model.The rationality of the proposed model is verified by a mixed fracture example under a shear displacement load.Then,the extended fracture phase model is applied to simulate the corrosion-induced cracking process of RC.The cracking patterns caused by non-uniform corrosion expansion are discussed for RC specimens with homogeneous macroscopically or heterogeneous with different polygonal aggregate distributions at the mesoscopic scale.Then,the effects of the protective layer on the crack propagation trajectory and cracking resistance are investigated,illustrating that the cracking angle and cracking resistance increase with the increase of the protective layer thickness,consistent with the experimental observation.Finally,the corrosion-induced cracking process of concrete specimens with large and small spacing rebars is simulated,and the interaction of multiple corrosion cracking is easily influenced by the reinforcement spacing,which increases with the decrease of the steel bar interval.These conclusions play an important role in the design of engineering anti-corrosion measures.The fracture phase field model can provide strong support for the life assessment of RC structures.展开更多
The flexoelectric effect describes the interplay between material polarization and strain gradient.While much research has focused on control strategies for flexoelectricity,the impact of ferroelectric domain structur...The flexoelectric effect describes the interplay between material polarization and strain gradient.While much research has focused on control strategies for flexoelectricity,the impact of ferroelectric domain structure on the flexoelectric effect remains elusive.Through phase field simulations,we conduct a comparative study on the flexoelectric response of two types of BaTiO_(3)–SrTiO_(3) binary films:BaTiO_(3)–SrTiO_(3) multilayers and(Ba,Sr)TiO_(3) solid solutions.Our findings reveal that the flexoelectric response of these two systems,at the same Ba/Sr ratio,differs not only in magnitude but also in other aspects like temperature dependence,linearity,and hysteresis,due to their different ferroelectric domain structures and evolution dynamics.Our study deepens our current understanding of flexoelectricity in ferroelectrics and suggests“domain engineering”as a potential way to tailor this effect.展开更多
Ab st ra ct Nanocrystalline materials exhibit unique properties due to their extremely high grain boundary(GB) density.However,this high-density characteristic induces grain coarsening at elevated temperatures,thereby...Ab st ra ct Nanocrystalline materials exhibit unique properties due to their extremely high grain boundary(GB) density.However,this high-density characteristic induces grain coarsening at elevated temperatures,thereby limiting the widespread application of nanocrystalline materials.Recent experimental observations revealed that GB segregation and second-phase pinning effectively hinder GB migration,thereby improving the stability of nanocry stalline materials.In this study,a mouified phase-field model that integrates mismatch strain,solute segregation and precipitation was developed to evaluate the influence of lattice misfit on the thermal stability of nanocrystalline alloys.The simulation results indicated that introducing a suitable mismatch strain can effectively enhance the microstructural stability of nanocrystalline alloys.By synergizing precipitation with an appropriate lattice misfit,the formation of second-phase particles in the bulk grains can be suppressed,thereby facilitating solute segregation/precipitation at the GBs.This concentrated solute segregation and precipitation at the GBs effectively hinders grain migration,thereby preventing grain coarsening.These findings provide a new perspective on the design and regulation of nanocrystalline alloys with enhanced thermal stability.展开更多
Texture is inevitably introduced during the manufacturing of most NiTi shape memory alloys(SMAs),and the textured nanocrystalline NiTi has been extensively employed in engineering.However,the effect of texture,and the...Texture is inevitably introduced during the manufacturing of most NiTi shape memory alloys(SMAs),and the textured nanocrystalline NiTi has been extensively employed in engineering.However,the effect of texture,and the joint effect of grain size(GS)and texture on the functional properties of NiTi SMAs and the corresponding microscopic mechanisms have not been clearly understood yet.In this work,based on the phase field method,the effect of texture on the GS-dependent functional properties of NiTi SMAs,including super-elasticity(SE),one-way shape memory effect(OWSME),and stress-assisted two-way shape memory effect(SATWSME),is investigated,and the corresponding microscopic mechanisms are revealed.Moreover,the samples with discrete geometrical gradients and/or texture gradients are designed to achieve graded functional properties.The simulation results indicate that the dependence of functional properties on texture is due to the effect of crystallographic orientation on martensite transformation and reorientation,which can lead to different inelastic strains.In the designed samples with texture gradients,the stress–strain responses of sheets with various textures are different,allowing for the coordination of overall deformation of the sample by combining such sheets,with varying inelastic deformation degrees.Thus,the overall response of the sample differs from that without texture gradient,leading to the achievement of graded functional properties.The simulation results and new findings in this work contribute to a deeper understanding of the effects of texture,GS,and their interaction on the functional properties of SMAs,and provide valuable reference for the design and development of SMA-based devices with desired functional properties.展开更多
The morphology of Ni_(4)Ti_(3) precipitates is important in tuning the martensitic transformation(MT)behavior and mechanical properties of nitinol.Constrained ageing is effective in engineering the morphology of Ni_(4...The morphology of Ni_(4)Ti_(3) precipitates is important in tuning the martensitic transformation(MT)behavior and mechanical properties of nitinol.Constrained ageing is effective in engineering the morphology of Ni_(4)Ti_(3) precipitates due to the variant selection effect of external load which is still lacking.In this work,maps of variant selection effect of external load applied along all crystallographic directions are obtained by using a combination of theoretical analyses and phase field simulations.It is found that maps produced by uniaxial tension and uniaxial compression are quite different.The number and types of Ni_(4)Ti_(3) variants preferred by external load vary as the loading direction changes.Moreover,factors influencing the strength of variant selection effect are discovered.This work provides insights on understanding the Ni_(4)Ti_(3) precipitation process and sheds light on the engineering of morphology of Ni_(4)Ti_(3) precipitates for desired mechanical and functional properties.展开更多
Natural fractures(NFs)are common in shale and tight reservoirs,where staged multi-cluster fracturing of horizontal wells is a prevalent technique for reservoir stimulation.While NFs and stress interference are recogni...Natural fractures(NFs)are common in shale and tight reservoirs,where staged multi-cluster fracturing of horizontal wells is a prevalent technique for reservoir stimulation.While NFs and stress interference are recognized as significant factors affecting hydraulic fracture(HF)propagation,the combined influence of these factors remains poorly understood.To address this knowledge gap,a novel coupled hydromechanical-damage(HMD)model based on the phase field method is developed to investigate the propagation of multi-cluster HFs in fractured reservoirs.The comprehensive energy functional and control functions are established,while incorporating dynamic fluid distribution between multiple perforation clusters and refined changes in rock mechanical parameters during hydraulic fracturing.The HMD coupled multi-cluster HF propagation model investigates various scenarios,including single HF and single NF,reservoir heterogeneity,single HF and NF clusters,and multi-cluster HFs with NF clusters.The results show that the HMD coupling model can accurately capture the impact of approach angle(θ),stress difference and cementation strength on the interaction of HF and NF.The criterion of the open and cross zones is not fixed.The NF angle(a)is not a decisive parameter to discriminate the interaction.According to the relationship between approach angle(θ)and NF angle(a),the contact relationship of HF can be divided into three categories(θ=a,θ<a,andθ>a).The connected NF can increase the complexity of HF by inducing it to form branch fracture,resulting in a fractal dimension of HF as high as2.1280 at angles of±45°.Inter-fracture interference from the heel to the toe of HF shows the phenomenon of no,strong and weak interference.Interestingly,under the influence of NFs,distant HFs from the injection can become dominant fractures.However,as a gradually increases,inter-fracture stress interference becomes the primary factor influencing HF propagation,gradually superseding the dominance of NF induced fractures.展开更多
The inelastic deformations of shape memory alloys(SMAs)always show poor controllability due to the avalanche-like martensite transformation,and the effective control for the deformation of precision de-vices has been ...The inelastic deformations of shape memory alloys(SMAs)always show poor controllability due to the avalanche-like martensite transformation,and the effective control for the deformation of precision de-vices has been not yet mature.In this work,the phase field method was used to investigate the shape memory effects(SMEs)of NiTi SMAs undergoing grain size(GS)engineering,to obtain tunable one-way and stress-assisted two-way SMEs(OWSME and SATWSME).The OWSME and SATWSME of the systems with various gradient-nanograin structures and bimodal grain structure,as well as that with geometric gradients were simulated.The simulated results indicate that due to the GS dependences of martensite transformation and reorientation,the occurrence and expansion of martensite reorientation,martensite transformation and its reverse can be efficaciously controlled via the GS engineering.When combining the GS engineering and geometric gradient design,since the effects of GS and stress gradient can be su-perimposed or competing,and the responses of martensite reorientation,martensite transformation and its reverse to this are different,the OWSME and SATWSME of the geometrically graded systems with various nanograin structures can exhibit different improvements in controllability.In short,the reorienta-tion hardening modulus during OWSME is increased and the transformation temperature window during SATWSME is widened by GS engineering,indicating the improved controllability of SMEs.The optimal GS engineering schemes revealed in this work provide the basic reference and guidance for designing tun-able SMEs and producing NiTi-based driving devices catering to desired functional performance in various engineering fields.展开更多
In contrast to conventional transformers, power electronic transformers, as an integral component of new energy power system, are often subjected to high-frequency and transient electrical stresses, leading to heighte...In contrast to conventional transformers, power electronic transformers, as an integral component of new energy power system, are often subjected to high-frequency and transient electrical stresses, leading to heightened concerns regarding insulation failures. Meanwhile, the underlying mechanism behind discharge breakdown failure and nanofiller enhancement under high-frequency electrical stress remains unclear. An electric-thermal coupled discharge breakdown phase field model was constructed to study the evolution of the breakdown path in polyimide nanocomposite insulation subjected to high-frequency stress. The investigation focused on analyzing the effect of various factors, including frequency, temperature, and nanofiller shape, on the breakdown path of Polyimide(PI) composites. Additionally, it elucidated the enhancement mechanism of nano-modified composite insulation at the mesoscopic scale. The results indicated that with increasing frequency and temperature, the discharge breakdown path demonstrates accelerated development, accompanied by a gradual dominance of Joule heat energy. This enhancement is attributed to the dispersed electric field distribution and the hindering effect of the nanosheets. The research findings offer a theoretical foundation and methodological framework to inform the optimal design and performance management of new insulating materials utilized in high-frequency power equipment.展开更多
In comparison to discrete descriptions of fracture process,the recently proposed phase field methodology averts the numerical tracking strategy of discontinuities in solids,which enables the numerical implement simpli...In comparison to discrete descriptions of fracture process,the recently proposed phase field methodology averts the numerical tracking strategy of discontinuities in solids,which enables the numerical implement simplification.An implicit finite element formulation based on the diffuse phase field is extended for stable and efficient analysis of complex dynamic fracture process in ductile solids.This exhibited formulation is shown to capture entire range of the characteristics of ductile material presenting J2-plasticity,embracing plasticization,cracks initiation,propagation,branching and merging while fulfilling the basic principle of thermodynamics.Herein,we implement a staggered time integration scheme of the dynamic elasto-plastic phase field method into the commercial finite element code.The numerical performance of the present advanced phase field model has been examined through several classic dynamic fracture benchmarks,and in all cases simulation results are in good agreement with the associated experimental data and other numerical results in previous literature.展开更多
The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifur...The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifurcation analysis to explore the mathematical solution structure of phase field models.Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions.To elucidate the idea,we apply this analytical approach to three representative phase field equations:the Allen-Cahn equation,the Cahn-Hilliard equation,and the Allen-Cahn-Ohta-Kawasaki system.The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.展开更多
Based on the Karma model and the Eggleston regularization technique of the strong interfacial energy anisotropy, a phase-field model was established for HCP materials. An explicit finite difference numerical method wa...Based on the Karma model and the Eggleston regularization technique of the strong interfacial energy anisotropy, a phase-field model was established for HCP materials. An explicit finite difference numerical method was used to solve phase field model and simulate the dendrite growth behaviors of HCP materials. Results indicate that the dendrite morphology presents obvious six-fold symmetry, and discontinuity in the variation of interface orientation occurs, resulting in a fact that the corners were formed at the tips of the main stem and side branches. When the interfacial energy anisotropy strength is lower than the critical value（1/35）, the steady-state tip velocity of dendrite increases with anisotropy as expected. As the anisotropy strength crosses the critical value, the steady-state tip velocity drops down by about 0.89%. With further increase in anisotropy strength, the steady-state tip velocity increases and reaches the maximum value at anisotropy strength of 0.04, then decreases.展开更多
The influence of supercooled melt forced lamina flow on microsegregation was investigated. The concentration distribution at solid-liquid boundary of binary alloy Ni-Cu was simulated using phase field model coupled wi...The influence of supercooled melt forced lamina flow on microsegregation was investigated. The concentration distribution at solid-liquid boundary of binary alloy Ni-Cu was simulated using phase field model coupled with flow field. The microsegregation, concentration maximum value, boundary thickness of concentration near upstream dendrite and normal to flow dendrite, and downstream dendrite were studied quantitatively in the case of forced lamia flow. The simulation results show that solute field and flow field interact complexly. Compared with melt without flow, in front of upstream dendrite tip, the concentration boundary thickness is the lowest and the concentration maximum value is the smallest for melt with flow. However, in front of downstream dendrite tip, the results are just the opposite. The zone of poor Cu in upstream dendrite where is the most severely microsegregation and shrinkage cavity is wider and the concentration is lower for melt with flow than that without flow.展开更多
By utilizing phase field method combined with analysis on free energy and interatomic potentials, pre-precipitation phase formation and transformation process of Ni0.75Al0.05Fe0.2 alloy in early precipitation stage du...By utilizing phase field method combined with analysis on free energy and interatomic potentials, pre-precipitation phase formation and transformation process of Ni0.75Al0.05Fe0.2 alloy in early precipitation stage during the ageing process under 1 000 K were studied. And free energy, microstructures, compositions and volume fractions of pre-precipitation phase and equilibrium phase were analyzed. The simulation results indicate that nonstoichiometric Llo pre-precipitation phase formed first, and then would gradually transform into L12 equilibrium phase. It is discovered that the phase transformation process was closely related to free energy and interatomic potentials. Additionally, it is revealed that free energy of Llo pre-precipitation phase was higher and interatomic potential was smaller than that of L12 equilibrium phase. Therefore, it is concluded that Llo phase was unstable, and phase transformation would occur to L12 which was more stable.展开更多
A thermodynamic consistent phase field model is developed to describe the sintering process with multiphase powders. In this model, the interface region is assumed to be a mixture of different phases with the same che...A thermodynamic consistent phase field model is developed to describe the sintering process with multiphase powders. In this model, the interface region is assumed to be a mixture of different phases with the same chemical potential, but with different compositions. The interface diffusion and boundary diffusion are also considered in the model. As an example, the model is applied to the sintering process with Fe-Cu powders. The free energy of each phase is described by the well-developed thermodynamic models, together with the published optimized parameters. The microstructure and solute distribution during the sintering process can both be obtained quantitively.展开更多
A novel approach based on the quantitative phase field model was proposed to calculate the interface mobility and applied to the α/β interface of a ternary Ti-6Al-4V alloy.Phase field simulations indicate that the h...A novel approach based on the quantitative phase field model was proposed to calculate the interface mobility and applied to the α/β interface of a ternary Ti-6Al-4V alloy.Phase field simulations indicate that the higher interface mobility leads to the faster transformation rate,but only a unique value of interface mobility matches the diffusion equation under the diffusion-controlled condition.By comparing the transformation kinetics from phase field simulations with that from classical diffusion equation,the interface mobility at different temperatures can be obtained.The results show that the calculated interface mobility increases with increasing temperature and accords with Arrhenius equation very well.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos.12202294 and 12022208)the Project funded by China Postdoctoral Science Foundation (Grant No.2022M712243)the Fundamental Research Funds for the Central Universities (Grant No.2023SCU12098).
文摘It is well known that coarse-grained super-elastic NiTi shape memory alloys(SMAs)exhibit localized rather than homogeneous martensite transformation(MT),which,however,can be strongly influenced by either internal size(grain size,GS)or the external size(geometric size).The coupled effect of GS and geometric size on the functional properties has not been clearly understood yet.In this work,the super-elasticity,one-way,and stress-assisted two-way shape memory effects of the polycrystalline NiTi SMAs with different aspect ratios(length/width for the gauge section)and different GSs are investigated based on the phase field method.The coupled effect of the aspect ratio and GS on the functional properties is adequately revealed.The simulated results indicate that when the aspect ratio is lower than about 4:1,the stress biaxiality and stress heterogeneity in the gauge section of the sample become more and more obvious with decreasing the aspect ratio,which can significantly influence the microstructure evolution in the process involving external stress.Therefore,the corresponding functional property is strongly dependent on the aspect ratio.With decreasing the GS and the aspect ratio(to be lower than 4:1),both the aspect ratio and GS can affect the MT or martensite reorientation in each grain and the interaction among grains.Thus,due to the strong internal constraint(i.e.,the constraint of grain boundary)and the external constraint(i.e.,the constraint of geometric boundary),the capabilities of the functional properties of NiTi SMAs are gradually weakened and highly dependent on these two factors.
基金supported by the National Natural Science Foundation of China(Grant Nos.52161002,51661020 and 11364024)。
文摘As the demand for advanced material design and performance prediction continues to grow,traditional phase-field models are increasingly challenged by limitations in computational efficiency and predictive accuracy,particularly when addressing high-dimensional and complex data in multicomponent systems.To overcome these challenges,this study proposes an innovative model,LSGWO-BP,which integrates an improved Grey Wolf Optimizer(GWO)with a backpropagation neural network(BP)to enhance the accuracy and efficiency of quasi-phase equilibrium predictions within the KKS phase-field framework.Three mapping enhancement strategies were investigated–Circle-Root,Tent-Cosine,and Logistic-Sine mappings-with the Logistic mapping further improved via Sine perturbation to boost global search capability and convergence speed in large-scale,complex data scenarios.Evaluation results demonstrate that the LSGWO-BP model significantly outperforms conventional machine learning approaches in predicting quasi-phase equilibrium,achieving a 14%–28%reduction in mean absolute error(MAE).Substantial improvements were also observed in mean squared error,root mean squared error,and mean absolute percentage error,alongside a 7%–33%increase in the coefficient of determination(R2).Furthermore,the model exhibits strong potential for microstructural simulation applications.Overall,the study confirms the effectiveness of the LSGWO-BP model in materials science,especially in enhancing phase-field modeling efficiency and enabling accurate,intelligent prediction for multicomponent alloy systems,thereby offering robust support for microstructure prediction and control.
基金supported by the National Natural Science Foundation of China(12202294)the Sichuan Science and Technology Program(2024NSFSC1346).
文摘Shape memory alloys(SMAs)and shape memory ceramics(SMCs)exhibit high recovery ability due to the martensitic transformation,which complicates the fracture mechanism of SMAs and SMCs.The phase field method,as a powerful numerical simulation tool,can efficiently resolve the microstructural evolution,multi-field coupling effects,and fracture behavior of SMAs and SMCs.This review begins by presenting the fundamental theoretical framework of the fracture phase field method as applied to SMAs and SMCs,covering key aspects such as the phase field modeling of martensitic transformation and brittle fracture.Subsequently,it systematically examines the phase field simulations of fracture behaviors in SMAs and SMCs,with particular emphasis on how crystallographic orientation,grain size,and grain boundary properties influence the crack propagation.Additionally,the interplay between martensite transformation and fracture mechanisms is analyzed to provide deeper insights into the material responses under mechanical loading.Finally,the review explores future prospects and emerging trends in phase field simulations of SMA and SMC fracture behavior,along with potential advancements in the fracture phase field method itself,including multi-physics coupling and enhanced computational efficiency for large-scale simulations.
基金supported by the stable support project and the Major National Science and Technology Project(2017-VII-0008-0101).
文摘With the evolution of nickel-based single crystal superalloys,there is an increase in heavy elements such as Re and Ru.This has made solutal convection more pronounced during the directional solidification process,leading to solute redistribution and increasing the risk of casting defects such as low-angle grain boundaries.To avoid casting defects,downward directional solidification(DWS)method is adopted to eliminate solutal convection and change solute redistribution.However,there is currently no in-situ characterization or quantitative simulation studying the solute redistribution during DWS and upward directional solidification(UWS)processes.A multicomponent phase field simulation coupled with lattice Boltzmann method was employed to quantitatively investigate changes in dendrite morphology,solutal convection and deviation of dendrite tips from the perspective of solute redistribution during UWS and DWS processes.The simulation of microstructure agrees well with the experimental results.The mechanism that explains how solutal convection affects side branching behavior is depicted.A novel approach is introduced to characterize dendrite deviation,elucidating the reasons why defects are prone to occur under the influence of natural convection and solute redistribution.
基金National Science Foundation of China,Grant/Award Number:5227090113Shenzhen Science and Technology Program,Grant/Award Numbers:KCXFZ20230731093901003,KCXFZ20211020163816023The Project of Hetao Shenzhen-Hong Kong Science and Technology Innovation Cooperation Zone,Grant/Award Number:HZQB-KCZYB-2020083。
文摘The two-phase flow in porous media is affected by multiple factors.In the present study,a two-dimensional numerical model of porous media was developed using the actual pore structure of the core sample.The phase field method was utilized to simulate the impact of displacement velocity,the water-gas viscosity ratio,and the density ratio on the flow behavior of two-phase fluids in porous media.The effectiveness of displacement was evaluated by analyzing CO_(2)saturation levels.The results indicate that the saturation of CO_(2)in porous media increased as the displacement velocity increased.When the displacement velocity exceeded 0.01 m/s,there was a corresponding increase in CO_(2)saturation.Conversely,when the displacement velocity was below this threshold,the impact on CO_(2)saturation was minimal.An“inflection point,”M3,was present in the viscosity ratio.When the viscosity of CO_(2)is less than 8.937×10^(-5)Pa·s(viscosity ratio below M3),variations in the viscosity of CO_(2)had little impact on its saturation.Conversely,when the viscosity of CO_(2)exceeded 8.937×10^(-5)Pa·s(viscosity ratio greater than M3),saturation increased with an increase in the viscosity ratio.In terms of the density ratio,the saturation of CO_(2)increased monotonically with an increase in the density ratio.Similarly,increasing density ratios resulted in a monotonic increase in CO_(2)saturation,though this trend was less pronounced in numerical simulations.Analysis results of displacement within dead-end pores using pressure and velocity diagrams reveal eddy currents as contributing factors.Finally,the impact of pore throat structure on the formation of dominant channels was examined.
基金the National Natural Science Foundation of China(Qing Zhang,Nos.11932006,U1934206,12172121)the Fundamental Research Funds for the Central Universities(Xin Gu,No.B210201031).
文摘Accurate simulation of the cracking process caused by rust expansion of reinforced concrete(RC)structures plays an intuitive role in revealing the corrosion-induced failure mechanism.Considering the quasi-brittle fracture of concrete,the fracture phase field driven by the compressive-shear term is constructed and added to the traditional brittle fracture phase field model.The rationality of the proposed model is verified by a mixed fracture example under a shear displacement load.Then,the extended fracture phase model is applied to simulate the corrosion-induced cracking process of RC.The cracking patterns caused by non-uniform corrosion expansion are discussed for RC specimens with homogeneous macroscopically or heterogeneous with different polygonal aggregate distributions at the mesoscopic scale.Then,the effects of the protective layer on the crack propagation trajectory and cracking resistance are investigated,illustrating that the cracking angle and cracking resistance increase with the increase of the protective layer thickness,consistent with the experimental observation.Finally,the corrosion-induced cracking process of concrete specimens with large and small spacing rebars is simulated,and the interaction of multiple corrosion cracking is easily influenced by the reinforcement spacing,which increases with the decrease of the steel bar interval.These conclusions play an important role in the design of engineering anti-corrosion measures.The fracture phase field model can provide strong support for the life assessment of RC structures.
基金support from the National Natural Science Foundation of China(Grant Nos.12222214,and 12132020)the Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices(No.2022B1212010008)+1 种基金the Shenzhen Science and Techonlogy Program(Grant Nos.202206193000001 and 20220818181805001)Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai)(SML2021SP405).
文摘The flexoelectric effect describes the interplay between material polarization and strain gradient.While much research has focused on control strategies for flexoelectricity,the impact of ferroelectric domain structure on the flexoelectric effect remains elusive.Through phase field simulations,we conduct a comparative study on the flexoelectric response of two types of BaTiO_(3)–SrTiO_(3) binary films:BaTiO_(3)–SrTiO_(3) multilayers and(Ba,Sr)TiO_(3) solid solutions.Our findings reveal that the flexoelectric response of these two systems,at the same Ba/Sr ratio,differs not only in magnitude but also in other aspects like temperature dependence,linearity,and hysteresis,due to their different ferroelectric domain structures and evolution dynamics.Our study deepens our current understanding of flexoelectricity in ferroelectrics and suggests“domain engineering”as a potential way to tailor this effect.
基金financially supported by the National Natural Science Foundation of China (Nos.52122408, 51901013,51971018,52101188,52225103,52071023 and U20B2025)the Funds for Creative Research Groups of NSFC (No.51921001)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Ab st ra ct Nanocrystalline materials exhibit unique properties due to their extremely high grain boundary(GB) density.However,this high-density characteristic induces grain coarsening at elevated temperatures,thereby limiting the widespread application of nanocrystalline materials.Recent experimental observations revealed that GB segregation and second-phase pinning effectively hinder GB migration,thereby improving the stability of nanocry stalline materials.In this study,a mouified phase-field model that integrates mismatch strain,solute segregation and precipitation was developed to evaluate the influence of lattice misfit on the thermal stability of nanocrystalline alloys.The simulation results indicated that introducing a suitable mismatch strain can effectively enhance the microstructural stability of nanocrystalline alloys.By synergizing precipitation with an appropriate lattice misfit,the formation of second-phase particles in the bulk grains can be suppressed,thereby facilitating solute segregation/precipitation at the GBs.This concentrated solute segregation and precipitation at the GBs effectively hinders grain migration,thereby preventing grain coarsening.These findings provide a new perspective on the design and regulation of nanocrystalline alloys with enhanced thermal stability.
基金The National Natural Science Foundation of China(12202294 and 12022208)the Project funded by China Postdoctoral Science Foundation(2022M712243)the Fundamental Research Funds for the Central Universities(2023SCU12098)are acknowledged.
文摘Texture is inevitably introduced during the manufacturing of most NiTi shape memory alloys(SMAs),and the textured nanocrystalline NiTi has been extensively employed in engineering.However,the effect of texture,and the joint effect of grain size(GS)and texture on the functional properties of NiTi SMAs and the corresponding microscopic mechanisms have not been clearly understood yet.In this work,based on the phase field method,the effect of texture on the GS-dependent functional properties of NiTi SMAs,including super-elasticity(SE),one-way shape memory effect(OWSME),and stress-assisted two-way shape memory effect(SATWSME),is investigated,and the corresponding microscopic mechanisms are revealed.Moreover,the samples with discrete geometrical gradients and/or texture gradients are designed to achieve graded functional properties.The simulation results indicate that the dependence of functional properties on texture is due to the effect of crystallographic orientation on martensite transformation and reorientation,which can lead to different inelastic strains.In the designed samples with texture gradients,the stress–strain responses of sheets with various textures are different,allowing for the coordination of overall deformation of the sample by combining such sheets,with varying inelastic deformation degrees.Thus,the overall response of the sample differs from that without texture gradient,leading to the achievement of graded functional properties.The simulation results and new findings in this work contribute to a deeper understanding of the effects of texture,GS,and their interaction on the functional properties of SMAs,and provide valuable reference for the design and development of SMA-based devices with desired functional properties.
基金supported by the National Natural Science Foundation of China(Grant No.12372152)the Qilu Young Talent Program of Shandong University,Zhejiang Lab Open Research Project(Grant No.K2022PE0AB05)+1 种基金Shandong Provincial Natural Science Foundation(Grant No.ZR2023MA058)Guangdong Basic and Applied Basic Research Foundation(Grant No.2023A1515011819).
文摘The morphology of Ni_(4)Ti_(3) precipitates is important in tuning the martensitic transformation(MT)behavior and mechanical properties of nitinol.Constrained ageing is effective in engineering the morphology of Ni_(4)Ti_(3) precipitates due to the variant selection effect of external load which is still lacking.In this work,maps of variant selection effect of external load applied along all crystallographic directions are obtained by using a combination of theoretical analyses and phase field simulations.It is found that maps produced by uniaxial tension and uniaxial compression are quite different.The number and types of Ni_(4)Ti_(3) variants preferred by external load vary as the loading direction changes.Moreover,factors influencing the strength of variant selection effect are discovered.This work provides insights on understanding the Ni_(4)Ti_(3) precipitation process and sheds light on the engineering of morphology of Ni_(4)Ti_(3) precipitates for desired mechanical and functional properties.
基金supported by the National Natural Science Foundation of China(No.52174045)。
文摘Natural fractures(NFs)are common in shale and tight reservoirs,where staged multi-cluster fracturing of horizontal wells is a prevalent technique for reservoir stimulation.While NFs and stress interference are recognized as significant factors affecting hydraulic fracture(HF)propagation,the combined influence of these factors remains poorly understood.To address this knowledge gap,a novel coupled hydromechanical-damage(HMD)model based on the phase field method is developed to investigate the propagation of multi-cluster HFs in fractured reservoirs.The comprehensive energy functional and control functions are established,while incorporating dynamic fluid distribution between multiple perforation clusters and refined changes in rock mechanical parameters during hydraulic fracturing.The HMD coupled multi-cluster HF propagation model investigates various scenarios,including single HF and single NF,reservoir heterogeneity,single HF and NF clusters,and multi-cluster HFs with NF clusters.The results show that the HMD coupling model can accurately capture the impact of approach angle(θ),stress difference and cementation strength on the interaction of HF and NF.The criterion of the open and cross zones is not fixed.The NF angle(a)is not a decisive parameter to discriminate the interaction.According to the relationship between approach angle(θ)and NF angle(a),the contact relationship of HF can be divided into three categories(θ=a,θ<a,andθ>a).The connected NF can increase the complexity of HF by inducing it to form branch fracture,resulting in a fractal dimension of HF as high as2.1280 at angles of±45°.Inter-fracture interference from the heel to the toe of HF shows the phenomenon of no,strong and weak interference.Interestingly,under the influence of NFs,distant HFs from the injection can become dominant fractures.However,as a gradually increases,inter-fracture stress interference becomes the primary factor influencing HF propagation,gradually superseding the dominance of NF induced fractures.
基金The National Natural Science Foundation of China(12022208)the Project funded by China Postdoctoral Science Foundation(2022M712243)the Fundamental Research Funds for the Cen-tral Universities are acknowledged.
文摘The inelastic deformations of shape memory alloys(SMAs)always show poor controllability due to the avalanche-like martensite transformation,and the effective control for the deformation of precision de-vices has been not yet mature.In this work,the phase field method was used to investigate the shape memory effects(SMEs)of NiTi SMAs undergoing grain size(GS)engineering,to obtain tunable one-way and stress-assisted two-way SMEs(OWSME and SATWSME).The OWSME and SATWSME of the systems with various gradient-nanograin structures and bimodal grain structure,as well as that with geometric gradients were simulated.The simulated results indicate that due to the GS dependences of martensite transformation and reorientation,the occurrence and expansion of martensite reorientation,martensite transformation and its reverse can be efficaciously controlled via the GS engineering.When combining the GS engineering and geometric gradient design,since the effects of GS and stress gradient can be su-perimposed or competing,and the responses of martensite reorientation,martensite transformation and its reverse to this are different,the OWSME and SATWSME of the geometrically graded systems with various nanograin structures can exhibit different improvements in controllability.In short,the reorienta-tion hardening modulus during OWSME is increased and the transformation temperature window during SATWSME is widened by GS engineering,indicating the improved controllability of SMEs.The optimal GS engineering schemes revealed in this work provide the basic reference and guidance for designing tun-able SMEs and producing NiTi-based driving devices catering to desired functional performance in various engineering fields.
基金supported in part by the National Key R&D Program of China (No.2021YFB2601404)Beijing Natural Science Foundation (No.3232053)National Natural Science Foundation of China (Nos.51929701 and 52127812)。
文摘In contrast to conventional transformers, power electronic transformers, as an integral component of new energy power system, are often subjected to high-frequency and transient electrical stresses, leading to heightened concerns regarding insulation failures. Meanwhile, the underlying mechanism behind discharge breakdown failure and nanofiller enhancement under high-frequency electrical stress remains unclear. An electric-thermal coupled discharge breakdown phase field model was constructed to study the evolution of the breakdown path in polyimide nanocomposite insulation subjected to high-frequency stress. The investigation focused on analyzing the effect of various factors, including frequency, temperature, and nanofiller shape, on the breakdown path of Polyimide(PI) composites. Additionally, it elucidated the enhancement mechanism of nano-modified composite insulation at the mesoscopic scale. The results indicated that with increasing frequency and temperature, the discharge breakdown path demonstrates accelerated development, accompanied by a gradual dominance of Joule heat energy. This enhancement is attributed to the dispersed electric field distribution and the hindering effect of the nanosheets. The research findings offer a theoretical foundation and methodological framework to inform the optimal design and performance management of new insulating materials utilized in high-frequency power equipment.
基金supported by the Na⁃tional Natural Science Foundation of China(No.12302176).
文摘In comparison to discrete descriptions of fracture process,the recently proposed phase field methodology averts the numerical tracking strategy of discontinuities in solids,which enables the numerical implement simplification.An implicit finite element formulation based on the diffuse phase field is extended for stable and efficient analysis of complex dynamic fracture process in ductile solids.This exhibited formulation is shown to capture entire range of the characteristics of ductile material presenting J2-plasticity,embracing plasticization,cracks initiation,propagation,branching and merging while fulfilling the basic principle of thermodynamics.Herein,we implement a staggered time integration scheme of the dynamic elasto-plastic phase field method into the commercial finite element code.The numerical performance of the present advanced phase field model has been examined through several classic dynamic fracture benchmarks,and in all cases simulation results are in good agreement with the associated experimental data and other numerical results in previous literature.
基金supported as part of the Computational Materials Sciences Program funded by the U.S.Department of Energy,Office of Science,Basic Energy Sciences,under Award No.DE-SC0020145Y.Z.would like to acknowledge support for his effort by the Simons Foundation through Grant No.357963 and NSF grant DMS-2142500.
文摘The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifurcation analysis to explore the mathematical solution structure of phase field models.Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions.To elucidate the idea,we apply this analytical approach to three representative phase field equations:the Allen-Cahn equation,the Cahn-Hilliard equation,and the Allen-Cahn-Ohta-Kawasaki system.The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.
基金Project(10834015)supported by the National Natural Science Foundation of ChinaProject(12SKY01-1)supported by the Doctoral Fund of Shangluo University,China
文摘Based on the Karma model and the Eggleston regularization technique of the strong interfacial energy anisotropy, a phase-field model was established for HCP materials. An explicit finite difference numerical method was used to solve phase field model and simulate the dendrite growth behaviors of HCP materials. Results indicate that the dendrite morphology presents obvious six-fold symmetry, and discontinuity in the variation of interface orientation occurs, resulting in a fact that the corners were formed at the tips of the main stem and side branches. When the interfacial energy anisotropy strength is lower than the critical value（1/35）, the steady-state tip velocity of dendrite increases with anisotropy as expected. As the anisotropy strength crosses the critical value, the steady-state tip velocity drops down by about 0.89%. With further increase in anisotropy strength, the steady-state tip velocity increases and reaches the maximum value at anisotropy strength of 0.04, then decreases.
基金Project (10964004) supported by the National Natural Science Foundation of ChinaProject (20070731001) supported by Research Fund for the Doctoral Program of ChinaProject (096RJZA104) supported by the Natural Science Foundation of Gansu Province,China
文摘The influence of supercooled melt forced lamina flow on microsegregation was investigated. The concentration distribution at solid-liquid boundary of binary alloy Ni-Cu was simulated using phase field model coupled with flow field. The microsegregation, concentration maximum value, boundary thickness of concentration near upstream dendrite and normal to flow dendrite, and downstream dendrite were studied quantitatively in the case of forced lamia flow. The simulation results show that solute field and flow field interact complexly. Compared with melt without flow, in front of upstream dendrite tip, the concentration boundary thickness is the lowest and the concentration maximum value is the smallest for melt with flow. However, in front of downstream dendrite tip, the results are just the opposite. The zone of poor Cu in upstream dendrite where is the most severely microsegregation and shrinkage cavity is wider and the concentration is lower for melt with flow than that without flow.
基金Projects(10902086, 50941020, 50875217) supported by the National Natural Science Foundation of China Projects(JC201005) supported by Basic Research Fund of Northwestern Polytechnical University, China Project supported by Graduate Starting Seed Fund and Doctoral Foundation of Northwestern Polytechnical University, China
文摘By utilizing phase field method combined with analysis on free energy and interatomic potentials, pre-precipitation phase formation and transformation process of Ni0.75Al0.05Fe0.2 alloy in early precipitation stage during the ageing process under 1 000 K were studied. And free energy, microstructures, compositions and volume fractions of pre-precipitation phase and equilibrium phase were analyzed. The simulation results indicate that nonstoichiometric Llo pre-precipitation phase formed first, and then would gradually transform into L12 equilibrium phase. It is discovered that the phase transformation process was closely related to free energy and interatomic potentials. Additionally, it is revealed that free energy of Llo pre-precipitation phase was higher and interatomic potential was smaller than that of L12 equilibrium phase. Therefore, it is concluded that Llo phase was unstable, and phase transformation would occur to L12 which was more stable.
基金Project(2011CB606306)supported by the National Basic Research Program of ChinaProject(51101014)supported by the National Natural Science Foundation of ChinaProject(SKLSP201214)supported by the State Key Laboratory of Solidification Processing in Northwestern Polytechnical University,China
文摘A thermodynamic consistent phase field model is developed to describe the sintering process with multiphase powders. In this model, the interface region is assumed to be a mixture of different phases with the same chemical potential, but with different compositions. The interface diffusion and boundary diffusion are also considered in the model. As an example, the model is applied to the sintering process with Fe-Cu powders. The free energy of each phase is described by the well-developed thermodynamic models, together with the published optimized parameters. The microstructure and solute distribution during the sintering process can both be obtained quantitively.
基金Project (51101059) supported by the National Natural Science Foundation of ChinaProject (20110490874) supported by the China Postdoctoral Science Foundation
文摘A novel approach based on the quantitative phase field model was proposed to calculate the interface mobility and applied to the α/β interface of a ternary Ti-6Al-4V alloy.Phase field simulations indicate that the higher interface mobility leads to the faster transformation rate,but only a unique value of interface mobility matches the diffusion equation under the diffusion-controlled condition.By comparing the transformation kinetics from phase field simulations with that from classical diffusion equation,the interface mobility at different temperatures can be obtained.The results show that the calculated interface mobility increases with increasing temperature and accords with Arrhenius equation very well.
