Fracture is a very common failure mode of the composite materials,which seriously affects the reliability and service-life of composite materials.Therefore,the study of the fracture behavior of the composite materials...Fracture is a very common failure mode of the composite materials,which seriously affects the reliability and service-life of composite materials.Therefore,the study of the fracture behavior of the composite materials is of great significance and necessity,which demands an accurate and efficient numerical tool in general cases because of the complexity of the arising boundary-value or initial-boundary value problems.In this paper,a phase field model is adopted and applied for the numerical simulation of the crack nucleation and propagation in brittle linear elastic two-phase perforated/particulate composites under a quasi-static tensile loading.The phase field model can well describe the initiation,propagation and coalescence of the cracks without assuming the existence and the geometry of the initial cracks in advance.Its numerical implementation is realized within the framework of the finite element method(FEM).The accuracy and the efficiency of the present phase field model are verified by the available reference results in literature.In the numerical examples,we first study and discuss the influences of the hole/particle size on the crack propagation trajectory and the force-displacement curve.Then,the effects of the hole/particle shape on the crack initiation and propagation are investigated.Furthermore,numerical examples are presented and discussed to show the influences of the hole/particle location on the crack initiation and propagation characteristics.It will be demonstrated that the present phase field model is an efficient tool for the numerical simulation of the crack initiation and propagation problems in brittle two-phase composite materials,and the corresponding results may play an important role in predicting and preventing possible hazardous crack initiation and propagation in engineering applications.展开更多
The population balance modeling is regarded as a universally accepted mathematical framework for dynamic simulation of various particulate processes, such as crystallization, granulation and polymerization. This artic...The population balance modeling is regarded as a universally accepted mathematical framework for dynamic simulation of various particulate processes, such as crystallization, granulation and polymerization. This article is concerned with the application of the method of characteristics (MOC) for solving population balance models describing batch crystallization process. The growth and nucleation are considered as dominant phenomena, while the breakage and aggregation are neglected. The numerical solutions of such PBEs require high order accuracy due to the occurrence of steep moving fronts and narrow peaks in the solutions. The MOC has been found to be a very effective technique for resolving sharp discontinuities. Different case studies are carried out to analyze the accuracy of proposed algorithm. For validation, the results of MOC are compared with the available analytical solutions and the results of finite volume schemes. The results of MOC were found to be in good agreement with analytical solutions and superior than those obtained by finite volume schemes.展开更多
We investigate the critical nucleus and equilibrium morphologies duringprecipitation of a second-phase particle in a solid. We show that a combination ofdiffuse-interface description and a constrained string method is...We investigate the critical nucleus and equilibrium morphologies duringprecipitation of a second-phase particle in a solid. We show that a combination ofdiffuse-interface description and a constrained string method is able to predict boththe critical nucleus and equilibrium precipitate morphologies simultaneously without a priori assumptions. Using the cubic to cubic transformation as an example, it isdemonstrated that the maximum composition within a critical nucleus can be eitherhigher or lower than that of equilibrium precipitate while the morphology of an equilibrium precipitate may exhibit lower symmetry than the critical nucleus resulted fromelastic interactions.展开更多
We study the critical nuclei morphologies of a binary alloy by the string method. The dynamic equation of the string, connecting the metastable phase (liquid) and stable phase (solid), is governed by Helmholtz free en...We study the critical nuclei morphologies of a binary alloy by the string method. The dynamic equation of the string, connecting the metastable phase (liquid) and stable phase (solid), is governed by Helmholtz free energy for the binary alloy system at a given temperature. The stationary string through the critical nucleus (saddle point) is obtained if the relaxation time of the string is su?ciently large. The critical nucleus radius and energy barrier to nucleation of a pure alloy with isotropic interface energy in two and three dimensions are calculated, which are consistent with the classical nucleation theory. The critical nuclei morphologies are sensitive to the anisotropy strength of interface energy and interface thickness of alloy in two and three dimensions. The critical nucleus and energy barrier to nucleation become smaller if the anisotropy strength of the interface energy is increased, which means that it is much easier to form a stable nucleus if the anisotropy of the interface energy is considered.展开更多
The frequency of heterogeneous nucleation during the solidification of Al-Sibinary alloy was estimated by comparing experimentally obtained macrostructures of castings withnumerically simulated ones. A molten alloy wa...The frequency of heterogeneous nucleation during the solidification of Al-Sibinary alloy was estimated by comparing experimentally obtained macrostructures of castings withnumerically simulated ones. A molten alloy was unidirectionally solidified from a water-cooledcopper chill in an adiabatic mold. The location of columnar to equiaxed transition (CET) in thesolidified alloy ingot was measured. A numerical simulation for grain structure formation based onthe Monte Carlo method was carried out, and the frequency of heterogeneous nucleation in the alloywas evaluated by producing similar structure with the experimental one. The frequency ofheterogeneous nucleation was expressed as a probabilistic function with an exponential form ofundercooling that deter-mines the probability of nucleation event in the simulation. The value ofthe exponent is regarded as the nucleation parameter. The nucleation parameter of Al-Si binary alloyvaried with initial Si content.展开更多
A large-scale atom simulation of nanoindentation into a thin nickel film using the quasicontinuum method was performed. The initial stages of the plasticity deformation of nickel were studied. Several useful results w...A large-scale atom simulation of nanoindentation into a thin nickel film using the quasicontinuum method was performed. The initial stages of the plasticity deformation of nickel were studied. Several useful results were obtained as follows： （1） The response of the load versus indentation depth on the load versus indentation depth curve, besides the straight parts corresponding to the elastic property of nickel, the sudden drop of the load occurred several times; （2） The phenomena of dislocation nucleation -- the dislocation nucleation took place when the load descended, which makes it clear that dislocation nucleation causes the drop of the load; （3） The mechanism of the dislocation emission - the Peierls-Nabarro dislocation model and a pow- erful criterion were used to analyze the dislocation emission. And the computational value was in good agreement with the predict value; （4） The density of geometrically necessary dislocations. A simple model was used to obtain the density of geometrically necessary dislocations beneath the indenter. Furthermore, the influence of the boundary conditions on the simulation results was discussed.展开更多
Spalling is a typical tensile failure that results from the coupling evolution of microstructure and microdamage under high strain-rate loading.To understand the spalling damage behavior of polycrystalline materials a...Spalling is a typical tensile failure that results from the coupling evolution of microstructure and microdamage under high strain-rate loading.To understand the spalling damage behavior of polycrystalline materials at mesoscale,this paper develops a spalling model by integrating the crystal plasticity theory and the microvoid growth theory.The model is implemented in ABAQUS simulation via the VUMAT subroutine to simulate a planar impact process of copper,and the results are compared with experimental data.Due to the inhomogeneity of crystal plastic slip,the local stress fluctuates severely near the grain boundary.Therefore,without introducing the fluctuation in the threshold stress for microdamage evolution,this model can simulate the heterogeneous feature of microvoid nucleation,growth,and coalescence in materials.The results show that microvoids tend to nucleate at 25°–50°misorientation angle grain boundaries,which undergo a high probability of stress fluctuation.展开更多
A computational study of superconducting states near the superconductingnormal phase boundary in mesoscopic finite cylinders is presented.The computational approach uses a finite element method to find numerical solut...A computational study of superconducting states near the superconductingnormal phase boundary in mesoscopic finite cylinders is presented.The computational approach uses a finite element method to find numerical solutions of the linearized Ginzburg-Landau equation for samples with various sizes,aspect ratios,and crosssectional shapes,i.e.,squares,triangles,circles,pentagons,and four star shapes.The vector potential is determined using a finite element method with two penalty terms to enforce the gauge conditions that the vector potential is solenoidal and its normal component vanishes at the surface(s)of the sample.The eigenvalue problem for the linearized Ginzburg-Landau equations with homogeneous Neumann boundary conditions is solved and used to construct the superconducting-normal phase boundary for each sample.Vortex-antivortex(V-AV)configurations for each sample that accurately reflect the discrete symmetry of each sample boundary were found through the computational approach.These V-AV configurations are realized just within the phase boundary in the magnetic field-temperature phase diagram.Comparisons are made between the results obtained for the different sample shapes.展开更多
石盐是表生环境下形成蒸发岩系的主要矿物,在形成过程中捕获大量的原生包裹体。通过低温冷冻测温技术,可以得到石盐中原生包裹体的一系列均一温度,如何正确理解这些数据是应用石盐原生包裹体恢复古气候的关键。石盐沉积可以发生在气水...石盐是表生环境下形成蒸发岩系的主要矿物,在形成过程中捕获大量的原生包裹体。通过低温冷冻测温技术,可以得到石盐中原生包裹体的一系列均一温度,如何正确理解这些数据是应用石盐原生包裹体恢复古气候的关键。石盐沉积可以发生在气水界面以及水体底部,其均一温度记录了卤水结晶的温度。Lowenstein et al.(1998)曾经用水浴法在恒定水温下合成了人工合成石盐,进行原生包裹体的均一温度研究,然而如何用水温来恢复古气温是古环境解释的关键。本次实验通过40℃下(气温,烘箱中蒸发)人工合成石盐,在岩相学观察基础上,对形成于气水界面漏斗晶中的包裹体和在底水沉积人字晶中的包裹体的均一温度进行低温冷冻测温法测定。测温过程中石盐包裹体可以得到一系列均一温度(10.6～39.9℃),而只有最大均一温度才能反映卤水结晶时的温度,两种类型的包裹体也显示了相似的最大均一温度。因此在浅水环境下,两种包裹体都可以用来反映古气温。展开更多
基金the National Natural Science Foundation of China(Grants U1333201 and U1833116)。
文摘Fracture is a very common failure mode of the composite materials,which seriously affects the reliability and service-life of composite materials.Therefore,the study of the fracture behavior of the composite materials is of great significance and necessity,which demands an accurate and efficient numerical tool in general cases because of the complexity of the arising boundary-value or initial-boundary value problems.In this paper,a phase field model is adopted and applied for the numerical simulation of the crack nucleation and propagation in brittle linear elastic two-phase perforated/particulate composites under a quasi-static tensile loading.The phase field model can well describe the initiation,propagation and coalescence of the cracks without assuming the existence and the geometry of the initial cracks in advance.Its numerical implementation is realized within the framework of the finite element method(FEM).The accuracy and the efficiency of the present phase field model are verified by the available reference results in literature.In the numerical examples,we first study and discuss the influences of the hole/particle size on the crack propagation trajectory and the force-displacement curve.Then,the effects of the hole/particle shape on the crack initiation and propagation are investigated.Furthermore,numerical examples are presented and discussed to show the influences of the hole/particle location on the crack initiation and propagation characteristics.It will be demonstrated that the present phase field model is an efficient tool for the numerical simulation of the crack initiation and propagation problems in brittle two-phase composite materials,and the corresponding results may play an important role in predicting and preventing possible hazardous crack initiation and propagation in engineering applications.
文摘The population balance modeling is regarded as a universally accepted mathematical framework for dynamic simulation of various particulate processes, such as crystallization, granulation and polymerization. This article is concerned with the application of the method of characteristics (MOC) for solving population balance models describing batch crystallization process. The growth and nucleation are considered as dominant phenomena, while the breakage and aggregation are neglected. The numerical solutions of such PBEs require high order accuracy due to the occurrence of steep moving fronts and narrow peaks in the solutions. The MOC has been found to be a very effective technique for resolving sharp discontinuities. Different case studies are carried out to analyze the accuracy of proposed algorithm. For validation, the results of MOC are compared with the available analytical solutions and the results of finite volume schemes. The results of MOC were found to be in good agreement with analytical solutions and superior than those obtained by finite volume schemes.
基金This research is supported in part by NSF-DMS 0712744,NSF DMR-0710483 and NSF-IIP 541674 Center for Computational Materials Design(CCMD).
文摘We investigate the critical nucleus and equilibrium morphologies duringprecipitation of a second-phase particle in a solid. We show that a combination ofdiffuse-interface description and a constrained string method is able to predict boththe critical nucleus and equilibrium precipitate morphologies simultaneously without a priori assumptions. Using the cubic to cubic transformation as an example, it isdemonstrated that the maximum composition within a critical nucleus can be eitherhigher or lower than that of equilibrium precipitate while the morphology of an equilibrium precipitate may exhibit lower symmetry than the critical nucleus resulted fromelastic interactions.
基金supported by National Natural Science Foundation of China (Young Scholars) (Grant No. 10701056)Science and Technology Commission of Shanghai Municipality (Grant No.08QA14036)+2 种基金National Natural Science Foundation of China (Grant No. 10871127)supported by the State Key Basic Research Project of China (Grant No. 2005CB321704)National Natural Science Foundation of China for Distinguished Young Scholars (Grant No. 10225103)
文摘We study the critical nuclei morphologies of a binary alloy by the string method. The dynamic equation of the string, connecting the metastable phase (liquid) and stable phase (solid), is governed by Helmholtz free energy for the binary alloy system at a given temperature. The stationary string through the critical nucleus (saddle point) is obtained if the relaxation time of the string is su?ciently large. The critical nucleus radius and energy barrier to nucleation of a pure alloy with isotropic interface energy in two and three dimensions are calculated, which are consistent with the classical nucleation theory. The critical nuclei morphologies are sensitive to the anisotropy strength of interface energy and interface thickness of alloy in two and three dimensions. The critical nucleus and energy barrier to nucleation become smaller if the anisotropy strength of the interface energy is increased, which means that it is much easier to form a stable nucleus if the anisotropy of the interface energy is considered.
文摘The frequency of heterogeneous nucleation during the solidification of Al-Sibinary alloy was estimated by comparing experimentally obtained macrostructures of castings withnumerically simulated ones. A molten alloy was unidirectionally solidified from a water-cooledcopper chill in an adiabatic mold. The location of columnar to equiaxed transition (CET) in thesolidified alloy ingot was measured. A numerical simulation for grain structure formation based onthe Monte Carlo method was carried out, and the frequency of heterogeneous nucleation in the alloywas evaluated by producing similar structure with the experimental one. The frequency ofheterogeneous nucleation was expressed as a probabilistic function with an exponential form ofundercooling that deter-mines the probability of nucleation event in the simulation. The value ofthe exponent is regarded as the nucleation parameter. The nucleation parameter of Al-Si binary alloyvaried with initial Si content.
文摘A large-scale atom simulation of nanoindentation into a thin nickel film using the quasicontinuum method was performed. The initial stages of the plasticity deformation of nickel were studied. Several useful results were obtained as follows： （1） The response of the load versus indentation depth on the load versus indentation depth curve, besides the straight parts corresponding to the elastic property of nickel, the sudden drop of the load occurred several times; （2） The phenomena of dislocation nucleation -- the dislocation nucleation took place when the load descended, which makes it clear that dislocation nucleation causes the drop of the load; （3） The mechanism of the dislocation emission - the Peierls-Nabarro dislocation model and a pow- erful criterion were used to analyze the dislocation emission. And the computational value was in good agreement with the predict value; （4） The density of geometrically necessary dislocations. A simple model was used to obtain the density of geometrically necessary dislocations beneath the indenter. Furthermore, the influence of the boundary conditions on the simulation results was discussed.
基金supported by the NSFC(Nos.12172367,11790292,11988102,and U2141204)the Strategic Priority Research Program(Nos.XDB22040302 and XDB22040303).
文摘Spalling is a typical tensile failure that results from the coupling evolution of microstructure and microdamage under high strain-rate loading.To understand the spalling damage behavior of polycrystalline materials at mesoscale,this paper develops a spalling model by integrating the crystal plasticity theory and the microvoid growth theory.The model is implemented in ABAQUS simulation via the VUMAT subroutine to simulate a planar impact process of copper,and the results are compared with experimental data.Due to the inhomogeneity of crystal plastic slip,the local stress fluctuates severely near the grain boundary.Therefore,without introducing the fluctuation in the threshold stress for microdamage evolution,this model can simulate the heterogeneous feature of microvoid nucleation,growth,and coalescence in materials.The results show that microvoids tend to nucleate at 25°–50°misorientation angle grain boundaries,which undergo a high probability of stress fluctuation.
文摘A computational study of superconducting states near the superconductingnormal phase boundary in mesoscopic finite cylinders is presented.The computational approach uses a finite element method to find numerical solutions of the linearized Ginzburg-Landau equation for samples with various sizes,aspect ratios,and crosssectional shapes,i.e.,squares,triangles,circles,pentagons,and four star shapes.The vector potential is determined using a finite element method with two penalty terms to enforce the gauge conditions that the vector potential is solenoidal and its normal component vanishes at the surface(s)of the sample.The eigenvalue problem for the linearized Ginzburg-Landau equations with homogeneous Neumann boundary conditions is solved and used to construct the superconducting-normal phase boundary for each sample.Vortex-antivortex(V-AV)configurations for each sample that accurately reflect the discrete symmetry of each sample boundary were found through the computational approach.These V-AV configurations are realized just within the phase boundary in the magnetic field-temperature phase diagram.Comparisons are made between the results obtained for the different sample shapes.
文摘石盐是表生环境下形成蒸发岩系的主要矿物,在形成过程中捕获大量的原生包裹体。通过低温冷冻测温技术,可以得到石盐中原生包裹体的一系列均一温度,如何正确理解这些数据是应用石盐原生包裹体恢复古气候的关键。石盐沉积可以发生在气水界面以及水体底部,其均一温度记录了卤水结晶的温度。Lowenstein et al.(1998)曾经用水浴法在恒定水温下合成了人工合成石盐,进行原生包裹体的均一温度研究,然而如何用水温来恢复古气温是古环境解释的关键。本次实验通过40℃下(气温,烘箱中蒸发)人工合成石盐,在岩相学观察基础上,对形成于气水界面漏斗晶中的包裹体和在底水沉积人字晶中的包裹体的均一温度进行低温冷冻测温法测定。测温过程中石盐包裹体可以得到一系列均一温度(10.6～39.9℃),而只有最大均一温度才能反映卤水结晶时的温度,两种类型的包裹体也显示了相似的最大均一温度。因此在浅水环境下,两种包裹体都可以用来反映古气温。
