This article proposes a modeling method for C/C-ZrC composite materials.According to the superposition of Gaussian random field,the original gray model is obtained,and the threshold segmentation method is used to gene...This article proposes a modeling method for C/C-ZrC composite materials.According to the superposition of Gaussian random field,the original gray model is obtained,and the threshold segmentation method is used to generate the C-ZrC inclusion model.Finally,the fiber structure is added to construct the microstructure of the three-phase plain weave composite.The reconstructed inclusions can meet the randomness of the shape and have a uniform distribution.Using an algorithm based on asymptotic homogenization and finite element method,the equivalent thermal conductivity prediction of the microstructure finite element model was carried out,and the influence of component volume fraction on material thermal properties was explored.The sensitivity of model parameters was studied,including the size,mesh sensitivity,Gaussian complexity,and correlation length of the RVE model,and the optimal calculation model was selected.The results indicate that the volume fraction of the inclusion phase has a significant impact on the equivalent thermal conductivity of the material.As the volume fraction of carbon fiber and ZrC increases,the equivalent thermal conductivity tensor gradually decreases.This model can be used to explore the impact of materialmicrostructure on the results,and numerical simulations have studied the relationship between structure and performance,providing the possibility of designing microstructure based on performance.展开更多
Nowadays,studies on the mechanism of macro-scopic nonlinear behavior of materials by accumulation of micro-scopic degradation are attracting more attention from researchers.Among numerous approaches,multiscale methods...Nowadays,studies on the mechanism of macro-scopic nonlinear behavior of materials by accumulation of micro-scopic degradation are attracting more attention from researchers.Among numerous approaches,multiscale methods have been proved as powerful and practical approaches in predicting macro-scopic material status by averaging and homogenizing physical information from associated micro-scopic mate-rial behavior.Usually in mechanical problem,the stress,consistent material modulus,and possible mate-rial state variables are quantities in interest through the upscaling process.However,the energy-related quantities are not studied much.Some initiative work has been done in the early year including but not limited to the Hill-Mandel condition in multiscale framework,which gives that the macro-scopic elastic strain energy density can be computed by volumetric averaging of that in the micro-scale.However,in the nonlinear analysis,the energy dissipation is an important quantity to measure the degradation status.In this manuscript,two typical multiscale methods,the first-order computational homogenization(FOCH)and reduced-order homogenization(ROH),are adopted to numerically analyze a fiber-reinforced compos-ite material with capability in material nonlinearity.With numerical experiments,it can be shown that energy dissipation is the same for both approaches.展开更多
Asymptotic homogenization(AH) is a general method for predicting the effective coefficient of thermal expansion(CTE) of periodic composites. It has a rigorous mathematical foundation and can give an accurate solution ...Asymptotic homogenization(AH) is a general method for predicting the effective coefficient of thermal expansion(CTE) of periodic composites. It has a rigorous mathematical foundation and can give an accurate solution if the macrostructure is large enough to comprise an infinite number of unit cells. In this paper, a novel implementation algorithm of asymptotic homogenization(NIAH) is developed to calculate the effective CTE of periodic composite materials. Compared with the previous implementation of AH, there are two obvious advantages. One is its implementation as simple as representative volume element(RVE).The new algorithm can be executed easily using commercial finite element analysis(FEA) software as a black box. The detailed process of the new implementation of AH has been provided. The other is that NIAH can simultaneously use more than one element type to discretize a unit cell, which can save much computational cost in predicting the CTE of a complex structure. Several examples are carried out to demonstrate the effectiveness of the new implementation.This work is expected to greatly promote the widespread use of AH in predicting the CTE of periodic composite materials.展开更多
Mge3Lie0.4Zr alloys containing RE elements(Gd,La,Nd)(Mge3LieREe0.4Zr alloys)are investigated to reveal the influence of homogenization treatment on microstructures and distributions of RE,Zr elements.It is found that...Mge3Lie0.4Zr alloys containing RE elements(Gd,La,Nd)(Mge3LieREe0.4Zr alloys)are investigated to reveal the influence of homogenization treatment on microstructures and distributions of RE,Zr elements.It is found that 300C24 h homogenization treatment shows better improvement on the microstructure including the refinement of grain size,the dispersion of cellular dendrite and low melting point particles.Before treatment,La and Nd segregate effectively at grain boundary and Zr segregates in the form of precipitates.Homogenization treatment induces the reduction of RE segregation.However,the segregation of Zr in precipitates cannot be abated due to the relatively low diffusion rate compared with RE elements.展开更多
This paper considers the initial and boundary value problem of some linear and semilinear Schrodinger equation with real potential and H01 initial data. The author obtains the homogenization of linear and semilinear S...This paper considers the initial and boundary value problem of some linear and semilinear Schrodinger equation with real potential and H01 initial data. The author obtains the homogenization of linear and semilinear Schrodinger equations and gives correctors for the homogenization of linear and semilinear Schrodinger equations.展开更多
The aim of this study was to investigate the effect of high-pressure homogenization on the droplet size and physical stability of different formulations of pectin–zein stabilized rice bran oil emulsions. The obtained...The aim of this study was to investigate the effect of high-pressure homogenization on the droplet size and physical stability of different formulations of pectin–zein stabilized rice bran oil emulsions. The obtained emulsions, both before and after passing through highpressure homogenizer, were subjected to stability test under environmental stress conditions,that is, temperature cycling at 4 °C/40 °C for 6 cycles and centrifugal test at 3000 rpm for 10 min. Applying high-pressure homogenization after mechanical homogenization caused only a small additional decrease in emulsion droplet size. The droplet size of emulsions was influenced by the type of pectin used;emulsions using high methoxy pectin(HMP) were smaller than that using low methoxy pectin(LMP). This is due to a greater emulsifying property of HMP than LMP. The emulsions stabilized by HMP–zein showed good physical stability with lower percent creaming index than those using LMP, both before and after passing through high-pressure homogenizer. The stability of emulsions after passing through high-pressure homogenizer was slightly higher when using higher zein concentration, resulting from stronger pectin–zein complexes that could rearrange and adsorb onto the emulsion droplets.展开更多
To investigate the microstructure, segregation, and suitable homogenization process of as-cast GH4169D alloy, the microstructure, elements segregation, and precipitates of cast GH4169D ingots prepared by vacuum induct...To investigate the microstructure, segregation, and suitable homogenization process of as-cast GH4169D alloy, the microstructure, elements segregation, and precipitates of cast GH4169D ingots prepared by vacuum induction melting (VIM) and vacuum arc remelting (VAR) were observed by optical microscopy (OM), scanning electron microscopy, and energy-dispersive X-ray spectroscopy (EDS). According to the residual segregation model and simulation results of DICTRA thermodynamic software, the homogenization temperature and time range were set as 1120–1170°C and 5–20 h, respectively. The experimental results showed that microscopic dendrite and element segregation occurred in the interior of ingots and the main segregation elements were Nb and Ti. In addition, the precipitates were mainly distributed in interdendritic regions and were composed of NbC, Laves,γ′, and δ phases. The homogenization process suggested that the interdendritic detrimental precipitated Laves phase can be eliminated or redissolved after homogenization at 1150°C for 20 h, suggesting it was the most suitable homogenization treatment. Thermal compression test results showed that the GH4169D alloys after homogenization treatment had no cracks and dynamic recrystallization occurred, with recrystallization volume fraction increasing with temperature, indicating a good working plasticity at temperatures from 1050 to 1200°C.展开更多
The aim of the present study was to investigate the effect of element segregation on the microstructure and γ′ phase in a γ/γ′ cobalt-based superalloy. Several samples were prepared from a cast alloy and homogeni...The aim of the present study was to investigate the effect of element segregation on the microstructure and γ′ phase in a γ/γ′ cobalt-based superalloy. Several samples were prepared from a cast alloy and homogenized at 1300°C for different times, with a maximum of 24 h. A microstructural study of the cast alloy using wavelength-dispersive spectroscopic analysis revealed that elements such as Al, Ti, and Ni segregated mostly within interdendritic regions, whereas W atoms were segregated within dendrite cores. With an increase in homogenization time, segregation decreased and the initial dendritic structure was eliminated. Field-emission scanning electron microscopy micrographs showed that the γ′ phases in the cores and interdendritic regions of the as-cast alloy were 392 and 124 nm, respectively. The size difference of γ′ was found to be due to the different segregation behaviors of constituent elements during solidification. After homogenization, particularly after 16 h, segregation decreased; thus, the size, chemical composition, and hardness of the precipitated γ′ phase was mostly uniform throughout the samples.展开更多
In this paper,a large-sized ingot of Mg–9Gd–3Y–1.5Zn–0.5Zr(wt%) alloy with a diameter of 600 mm was successfully prepared by the semi-continuous casting method.The alloy was subsequently annealed at a relatively l...In this paper,a large-sized ingot of Mg–9Gd–3Y–1.5Zn–0.5Zr(wt%) alloy with a diameter of 600 mm was successfully prepared by the semi-continuous casting method.The alloy was subsequently annealed at a relatively low temperature of 430°C for 12 h as a homogenization treatment.The microstructure and room-temperature mechanical properties of the alloy were investigated systematically.The results show that the as-cast alloy contained a mass of discontinuous lamellar-shaped 18 R long-period stacking ordered(LPSO) phases with a composition of Mg10 Zn Y and an α-Mg matrix,along with net-shaped Mg5(Y,Gd) eutectic compounds at the grain boundaries.Most of the eutectic compounds dissolved after the homogenization treatment.Moreover,the amount and dimensions of the lamellar-shaped LPSO phase obviously increased after the homogenization treatment.The structure of the phase transformed into 14H-type LPSO with composition Mg12Zn(Y,Gd).The mechanical properties of the heat-treated large-sized alloy ingot are uniform.The ultimate tensile strength(UTS) and tensile yield strength(TYS) of the alloy reached 207.2 MPa and 134.8 MPa,respectively,and the elongation was 3.4%.The high performances of the large-sized alloy ingot after the homogenization treatment is attributed to the strengthening of the α-Mg solid solution and to the plentiful LPSO phase distributed over the α-Mg matrix.展开更多
Fully grouted bolts are a key component of the support system for underground openings.Although considerable effort has been made in the simulation of the reinforcement effect of the fully grouted bolts on the rock ma...Fully grouted bolts are a key component of the support system for underground openings.Although considerable effort has been made in the simulation of the reinforcement effect of the fully grouted bolts on the rock masses surrounding underground openings,most of the work has limited significance since the structural element approach is used.This study proposes a local homogenization approach(L-H approach)that integrates elastoplastic mechanics,composite mechanics,and analytical approaches with numerical simulation to effectively simulate the reinforcement effect of the fully grouted bolt on deep surrounding rock masses.In the L-H approach,the representative volume of bolted rock mass(RVBRM)with a fully grouted bolt is established based on the original mesh model utilized in the rockbolt element approach.The RVBRM is a regular quadrangular prism with a cross-sectional size equal to the bolt spacing and a length equal to the bolt length.The RVBRM is homogenized by the L-H approach from a unidirectional bolt-reinforced composite into a homogeneous transversely isotropic medium whose mechanical properties are described by a new transversely isotropic elastoplastic model.The L-H parameters for the RVBRM are obtained using analytical approaches,composite mechanics,and known parameters of the rock mass and bolt.Using the L-H approach,the reinforcement effect of the fully grouted bolt on the bolted rock specimen and the surrounding rock mass in Jinping II Diversion Tunnel#2 with a depth greater than 2000 m is simulated.The results show that the predictions of the L-H approach are more in agreement with the physical model results of bolted rock specimen and provide a more realistic response of the bolted surrounding rock mass.The L-H approach demonstrates that fully grouted bolts with common bolt spacings and diameters substantially enhance the elastic modulus,shear strength,and tensile strength of the rock mass in the direction of the bolt axis.展开更多
The microstructures of five Al Mn Mg alloys with different Mn, Si and Fe contents were investigated in as cast and homogenized states. The influences of chemical composition and homogenizing process on the microstruct...The microstructures of five Al Mn Mg alloys with different Mn, Si and Fe contents were investigated in as cast and homogenized states. The influences of chemical composition and homogenizing process on the microstructure were studied. The results show that the morphology of the primary second particles are not influenced by the variation of Mn, Si and Fe level, and the amount of the primary α phase, the α precipitates and Mg 2Si phase are enhanced by the addition of Si; The average size of primary intermetallic particles reduces and the volume fraction of them decreases slightly with the increase in homogenization temperature and time; However, the volume fraction of primary secondary particles is increased by adding more Mn, Si and Fe elements in alloys. Moreover, a new MgSiCu rich eutectic in the as cast ingot has been found.展开更多
A crystallographic homogenization method is proposed and implemented to predict the evolution of plastic deformation induced texture and plastic anisotropy(earring) in the stamping of polycrystalline sheet metals.The ...A crystallographic homogenization method is proposed and implemented to predict the evolution of plastic deformation induced texture and plastic anisotropy(earring) in the stamping of polycrystalline sheet metals.The microscopic inhomogeneity of crystal aggregate has been taken into account with the microstructure made up of a representative aggregate of single crystal grains.Multi-scale analysis is performed by coupling the microscopic crystal plasticity with the macroscopic continuum response through the present homogenization procedure.The macroscopic stress is defined as the volume average of the corresponding microscopic crystal aggregations,which simultaneously satisfies the equation of motion in both micro-and macro-states.The proposed numerical implementation is based on a finite element discretization of the macrocontinuum,which is locally coupled at each Gaussian point with a finite element discretization of the attached micro-structure.The solution strategy for the macro-continuum and the pointwiseattached micro-structure is implemented by the simultaneous employment of dynamic explicit FE formulation.The rate-dependent crystal plasticity model is used for the constitutive description of the constituent single crystal grains.It has been confirmed that Taylor's constant strain homogenization assumption yields an undue concentration of the preferred crystal orientation compared with the present homogenization in the prediction of texture evolution,with the latter having relaxed the constraints on the crystal grains.Two kinds of numerical examples are presented to demonstrate the capability of the developed code:1) The texture evolution of three representative deformation modes,and 2) Plastic anisotropy(earring) prediction in the hemispherical cup deep drawing process of aluminum alloy A5052 with initial texture.By comparison of simulation results with those obtained employing direct crystal plasticity calculation adopting Taylor assumption,conclusions are drawn that the proposed dynamic explicit crystallographic homogenization FEM is able to more accurately predict the plastic deformation induced texture evolution and plastic anisotropy in the deep drawing process.展开更多
Hydrogen flakes and elemental segregation are the main causes of steel rejection. To eliminate hydrogen flaking, the present study focuses on the manufacture of AMS-4340 ultra-high-strength steel through an alternate ...Hydrogen flakes and elemental segregation are the main causes of steel rejection. To eliminate hydrogen flaking, the present study focuses on the manufacture of AMS-4340 ultra-high-strength steel through an alternate route. AMS-4340 was prepared using three different processing routes. The primary processing route consisted of melting in an electric arc furnace, refining in a ladle refining furnace, and vacuum degassing. After primary processing, the heat processes(D1, D2, and D3) were cast into cylindrical electrodes. For secondary processing, electroslag remelting(ESR) was carried out on the primary heats to obtain four secondary heats: E1, E2, E3, and E4. Homogenization of ingots E1, E2, E3, and E4 was carried out at 1220°C for 14, 12, 12, and 30 h, respectively, followed by an antiflaking treatment at 680°C and air cooling. In addition, the semi-finished ESR ingot E4 was again homogenized at 1220°C for 6–8 h and a second antiflaking treatment was performed at 680°C for 130 h followed by air cooling. The chemical segregation of each heat was monitored through a spectroscopy technique. The least segregation was observed for heat E4. Macrostructure examination revealed the presence of hydrogen flakes in heats E1, E2, and E3, whereas no hydrogen flakes were observed in heat E4. Ultrasonic testing revealed no internal defects in heat E4, whereas internal defects were observed in the other heats. A grain size investigation revealed a finer grain size for E4 compared with those for the other heats. Steel produced in heat E4 also exhibited superior mechanical properties. Therefore, the processing route used for heat E4 can be used to manufacture an AMS-4340 ultra-high-strength steel with superior properties compared with those of AMS-4340 prepared by the other investigated routes.展开更多
Microstructural improvement of Al-Cu-Li alloys with high Li content plays a critical role for the acquisition of excellent mechanical properties and ultra-low density.In this regard,the Al-Cu-Li alloy castings with hi...Microstructural improvement of Al-Cu-Li alloys with high Li content plays a critical role for the acquisition of excellent mechanical properties and ultra-low density.In this regard,the Al-Cu-Li alloy castings with high Li content from 1.5 wt.%to 4.5 wt.%were prepared by near-rapid solidification,followed by two-stage homogenization treatment(490℃/16 h and 530℃/16 h).The microstructural evolution and solidification behavior of the as-cast and homogenized alloys with different Li contents were systematically studied by combining experiments with calculations by Pandat software.The results indicate that with the increase of Li content,the grain sizes decrease,the solution ability of Cu in the matrixα-Al phase increases,while the content of secondary dendrites increases and the precipitated phases change from low melting point phases to high melting point phases under the near-rapid solidification.Additionally,by the coupling of near-rapid solidification and two-stage homogenization,the metastable precipitated phases(Al7Cu4Li and AlCu3)can be dissolved effectively in the alloys with Li content of 1.5 wt.%-2.5 wt.%;moreover,the stable precipitated phases(Al6CuLi3 and Al2CuLi)uniformly distribute at the grain boundaries in the alloys with Li content of 3.5 wt.%-4.5 wt.%.As a result,the refined and homogenized microstructure can be obtained.展开更多
The distribution of residual stresses through thickness of 5 mm-thick ME21 magnesium alloy extruded plates was analyzed non-destructively using short-wavelength X-ray diffraction(SWXRD),and the effect of homogenizatio...The distribution of residual stresses through thickness of 5 mm-thick ME21 magnesium alloy extruded plates was analyzed non-destructively using short-wavelength X-ray diffraction(SWXRD),and the effect of homogenization annealing before extrusion on the residual stress was discussed.The classic d 0 method with an annealed stress-free reference specimen was employed to determine the residual stress of the extruded plates.The residual stress results showed that the gradient of residual stress in the transverse direction was larger than that of the extrusion direction.The homogenization process prior to extrusion weaken the formed sample’s texture.The maximum residual stress of the as-extruded plate was reduced,and the residual stress distribution was homogenized.展开更多
The Mg-Al-Zn series AZ31 and AZ314+MM alloys are homogenized at 673, 723 and753K respectively. The hardness of alloy ingots at different heat-treated states ismeasured and the microstructures are observed. The optimum...The Mg-Al-Zn series AZ31 and AZ314+MM alloys are homogenized at 673, 723 and753K respectively. The hardness of alloy ingots at different heat-treated states ismeasured and the microstructures are observed. The optimum annealing temperatureis 723K and the time is 12h.展开更多
This study demonstrated that homogenization did not increase the activity of lipoprotein lipase (LPL) in spite of a fast accumulation of free fatty acids (FFA). Two homogenization pressures (100 and 170 bar) and two t...This study demonstrated that homogenization did not increase the activity of lipoprotein lipase (LPL) in spite of a fast accumulation of free fatty acids (FFA). Two homogenization pressures (100 and 170 bar) and two temperatures (40℃and 50℃) were examined. The activity of LPL was analyzed and the formation of FFA was measured with two different methods, the B.D.I.-method and a nonesterified fatty acids (NEFA) method. A homogenization temperature of 50℃ resulted in a decreased LPL activity compared to 40℃. No effect of homogenization pressure was found. Analyzing FFA concentration with the B.D.I.-method resulted in significant effect of homogenization temperature and no effect of pressure. The largest formation of FFA was found in milk homogenized at 40℃. Using the NEFA method, another result was obtained, indicating no effect of homogenization temperature and a larger FFA accumulation at 100 bar than at 170 bar. Both analytic methods demonstrated significant production of FFA during 60 min incubation at homogenization temperature after treatment. The level of FFA in the milk samples immediately after homogenization was very high, demonstrating that LPL cleaves the triglycerides very rapidly when the native membrane was damaged. The regression between the B.D.I.-method and the NEFA was fair in the interval between 4 and 14 mmol/100 g fat, whereas at higher concentrations, the correlation was poor.展开更多
1 Introduction The homogenization temperature of fluid inclusions reflects the temperatures of the brines from which halite crystals grew.Therefore,it is a powerful mean to reveal the paleoclimate.Northern Shaanxi Sal...1 Introduction The homogenization temperature of fluid inclusions reflects the temperatures of the brines from which halite crystals grew.Therefore,it is a powerful mean to reveal the paleoclimate.Northern Shaanxi Salt Basin is located in the central and eastern of Ordos Basin.We have detail petrographical research and the展开更多
In this paper, the power consumption, the vertical local void fraction and the local gas–liquid interfacial area are investigated in the aerated stirred tank reactors(STRs) equipped with a rigid-flexible impeller. Me...In this paper, the power consumption, the vertical local void fraction and the local gas–liquid interfacial area are investigated in the aerated stirred tank reactors(STRs) equipped with a rigid-flexible impeller. Meanwhile, the regressive correlation based on power consumption and interfacial area is proposed. Then a novel homogenization energy(HE = RSDPtm) expression based on power consumption and local interfacial area is redefined and used to indicate the mixing efficiency. The optimal operating mode is selected based on the change of the HE value. This paper can provide research ideas for structural optimization of stirred reactors.展开更多
The microstructure and tensile properties of the extruded Mg-Zn-Zr-RE alloy bars are studied.Theextruded bar without previous homogenization has the highest tensile strength,whereas the tensile strength of theextruded...The microstructure and tensile properties of the extruded Mg-Zn-Zr-RE alloy bars are studied.Theextruded bar without previous homogenization has the highest tensile strength,whereas the tensile strength of theextruded bar previously homogenized at 400℃ or 380℃ is lower.During long time homogenization,the trans-formation of rare earth compounds Mg<sub>3</sub>REZn<sub>6</sub>（Z phase）and Mg<sub>3</sub>RE<sub>2</sub>Zn<sub>3</sub>（W phase）into Mg<sub>41</sub>RE<sub>5</sub> andMg Zn phases occurr and the MgZn phase grow up.In addition,the dynamic recrystallization takes place in sub-sequent extrusion that caused decrease of the tensile strength.展开更多
基金Lisheng Liu acknowledges the support from the National Natural Science Foundation of China(No.11972267).
文摘This article proposes a modeling method for C/C-ZrC composite materials.According to the superposition of Gaussian random field,the original gray model is obtained,and the threshold segmentation method is used to generate the C-ZrC inclusion model.Finally,the fiber structure is added to construct the microstructure of the three-phase plain weave composite.The reconstructed inclusions can meet the randomness of the shape and have a uniform distribution.Using an algorithm based on asymptotic homogenization and finite element method,the equivalent thermal conductivity prediction of the microstructure finite element model was carried out,and the influence of component volume fraction on material thermal properties was explored.The sensitivity of model parameters was studied,including the size,mesh sensitivity,Gaussian complexity,and correlation length of the RVE model,and the optimal calculation model was selected.The results indicate that the volume fraction of the inclusion phase has a significant impact on the equivalent thermal conductivity of the material.As the volume fraction of carbon fiber and ZrC increases,the equivalent thermal conductivity tensor gradually decreases.This model can be used to explore the impact of materialmicrostructure on the results,and numerical simulations have studied the relationship between structure and performance,providing the possibility of designing microstructure based on performance.
基金the National Natural Science Foundation of China(Grant No.11988102)is gratefully acknowledged.
文摘Nowadays,studies on the mechanism of macro-scopic nonlinear behavior of materials by accumulation of micro-scopic degradation are attracting more attention from researchers.Among numerous approaches,multiscale methods have been proved as powerful and practical approaches in predicting macro-scopic material status by averaging and homogenizing physical information from associated micro-scopic mate-rial behavior.Usually in mechanical problem,the stress,consistent material modulus,and possible mate-rial state variables are quantities in interest through the upscaling process.However,the energy-related quantities are not studied much.Some initiative work has been done in the early year including but not limited to the Hill-Mandel condition in multiscale framework,which gives that the macro-scopic elastic strain energy density can be computed by volumetric averaging of that in the micro-scale.However,in the nonlinear analysis,the energy dissipation is an important quantity to measure the degradation status.In this manuscript,two typical multiscale methods,the first-order computational homogenization(FOCH)and reduced-order homogenization(ROH),are adopted to numerically analyze a fiber-reinforced compos-ite material with capability in material nonlinearity.With numerical experiments,it can be shown that energy dissipation is the same for both approaches.
基金supported by the National Natural Science Foundation of China (Grants 11332004, 11572071)the Program for Changjiang Scholars and Innovative Research Team in Dalian University of Technology (PCSIRT)+2 种基金111 Project (Grant B14013)the CATIC Industrial Production Projects (Grant CXY2013DLLG32)the Fundamental Research Funds for the Central Universities (Grant DUT15ZD101)
文摘Asymptotic homogenization(AH) is a general method for predicting the effective coefficient of thermal expansion(CTE) of periodic composites. It has a rigorous mathematical foundation and can give an accurate solution if the macrostructure is large enough to comprise an infinite number of unit cells. In this paper, a novel implementation algorithm of asymptotic homogenization(NIAH) is developed to calculate the effective CTE of periodic composite materials. Compared with the previous implementation of AH, there are two obvious advantages. One is its implementation as simple as representative volume element(RVE).The new algorithm can be executed easily using commercial finite element analysis(FEA) software as a black box. The detailed process of the new implementation of AH has been provided. The other is that NIAH can simultaneously use more than one element type to discretize a unit cell, which can save much computational cost in predicting the CTE of a complex structure. Several examples are carried out to demonstrate the effectiveness of the new implementation.This work is expected to greatly promote the widespread use of AH in predicting the CTE of periodic composite materials.
基金This work was supported by the Major State Basic Research Development Program of China(No.2013CB632203)National Key Technology R&D Program of China(2011BAE22B03)+3 种基金(2012BAF09B01)National Natural Science Foundation of China(51074207)Chinese Postdoctoral Science Foundation(2012M520634)the Fundamental Research Foundation of Central Universities(Grant Nos.N120509002 and N120309003).
文摘Mge3Lie0.4Zr alloys containing RE elements(Gd,La,Nd)(Mge3LieREe0.4Zr alloys)are investigated to reveal the influence of homogenization treatment on microstructures and distributions of RE,Zr elements.It is found that 300C24 h homogenization treatment shows better improvement on the microstructure including the refinement of grain size,the dispersion of cellular dendrite and low melting point particles.Before treatment,La and Nd segregate effectively at grain boundary and Zr segregates in the form of precipitates.Homogenization treatment induces the reduction of RE segregation.However,the segregation of Zr in precipitates cannot be abated due to the relatively low diffusion rate compared with RE elements.
基金The research was supported in part by the grant of ZARCF and NSFC
文摘This paper considers the initial and boundary value problem of some linear and semilinear Schrodinger equation with real potential and H01 initial data. The author obtains the homogenization of linear and semilinear Schrodinger equations and gives correctors for the homogenization of linear and semilinear Schrodinger equations.
基金financially supported by the Research and Development Institute, Silpakorn University
文摘The aim of this study was to investigate the effect of high-pressure homogenization on the droplet size and physical stability of different formulations of pectin–zein stabilized rice bran oil emulsions. The obtained emulsions, both before and after passing through highpressure homogenizer, were subjected to stability test under environmental stress conditions,that is, temperature cycling at 4 °C/40 °C for 6 cycles and centrifugal test at 3000 rpm for 10 min. Applying high-pressure homogenization after mechanical homogenization caused only a small additional decrease in emulsion droplet size. The droplet size of emulsions was influenced by the type of pectin used;emulsions using high methoxy pectin(HMP) were smaller than that using low methoxy pectin(LMP). This is due to a greater emulsifying property of HMP than LMP. The emulsions stabilized by HMP–zein showed good physical stability with lower percent creaming index than those using LMP, both before and after passing through high-pressure homogenizer. The stability of emulsions after passing through high-pressure homogenizer was slightly higher when using higher zein concentration, resulting from stronger pectin–zein complexes that could rearrange and adsorb onto the emulsion droplets.
基金the support of this research from the National Natural Science Foundation of China (Nos. 51571012 and 51771017)
文摘To investigate the microstructure, segregation, and suitable homogenization process of as-cast GH4169D alloy, the microstructure, elements segregation, and precipitates of cast GH4169D ingots prepared by vacuum induction melting (VIM) and vacuum arc remelting (VAR) were observed by optical microscopy (OM), scanning electron microscopy, and energy-dispersive X-ray spectroscopy (EDS). According to the residual segregation model and simulation results of DICTRA thermodynamic software, the homogenization temperature and time range were set as 1120–1170°C and 5–20 h, respectively. The experimental results showed that microscopic dendrite and element segregation occurred in the interior of ingots and the main segregation elements were Nb and Ti. In addition, the precipitates were mainly distributed in interdendritic regions and were composed of NbC, Laves,γ′, and δ phases. The homogenization process suggested that the interdendritic detrimental precipitated Laves phase can be eliminated or redissolved after homogenization at 1150°C for 20 h, suggesting it was the most suitable homogenization treatment. Thermal compression test results showed that the GH4169D alloys after homogenization treatment had no cracks and dynamic recrystallization occurred, with recrystallization volume fraction increasing with temperature, indicating a good working plasticity at temperatures from 1050 to 1200°C.
文摘The aim of the present study was to investigate the effect of element segregation on the microstructure and γ′ phase in a γ/γ′ cobalt-based superalloy. Several samples were prepared from a cast alloy and homogenized at 1300°C for different times, with a maximum of 24 h. A microstructural study of the cast alloy using wavelength-dispersive spectroscopic analysis revealed that elements such as Al, Ti, and Ni segregated mostly within interdendritic regions, whereas W atoms were segregated within dendrite cores. With an increase in homogenization time, segregation decreased and the initial dendritic structure was eliminated. Field-emission scanning electron microscopy micrographs showed that the γ′ phases in the cores and interdendritic regions of the as-cast alloy were 392 and 124 nm, respectively. The size difference of γ′ was found to be due to the different segregation behaviors of constituent elements during solidification. After homogenization, particularly after 16 h, segregation decreased; thus, the size, chemical composition, and hardness of the precipitated γ′ phase was mostly uniform throughout the samples.
基金supported by the Youth Science Fund Project of the National Natural Science Fund of China(No.51401070)the Program for New Century Excellent Talents in Universities(No.NCET-12-0849)the Fundamental Research Funds for the Central Universities(No.2014ZZD03)
文摘In this paper,a large-sized ingot of Mg–9Gd–3Y–1.5Zn–0.5Zr(wt%) alloy with a diameter of 600 mm was successfully prepared by the semi-continuous casting method.The alloy was subsequently annealed at a relatively low temperature of 430°C for 12 h as a homogenization treatment.The microstructure and room-temperature mechanical properties of the alloy were investigated systematically.The results show that the as-cast alloy contained a mass of discontinuous lamellar-shaped 18 R long-period stacking ordered(LPSO) phases with a composition of Mg10 Zn Y and an α-Mg matrix,along with net-shaped Mg5(Y,Gd) eutectic compounds at the grain boundaries.Most of the eutectic compounds dissolved after the homogenization treatment.Moreover,the amount and dimensions of the lamellar-shaped LPSO phase obviously increased after the homogenization treatment.The structure of the phase transformed into 14H-type LPSO with composition Mg12Zn(Y,Gd).The mechanical properties of the heat-treated large-sized alloy ingot are uniform.The ultimate tensile strength(UTS) and tensile yield strength(TYS) of the alloy reached 207.2 MPa and 134.8 MPa,respectively,and the elongation was 3.4%.The high performances of the large-sized alloy ingot after the homogenization treatment is attributed to the strengthening of the α-Mg solid solution and to the plentiful LPSO phase distributed over the α-Mg matrix.
基金funded by the National Natural Science Foundation of China(Nos.51979268,U1765206,and 52079027)。
文摘Fully grouted bolts are a key component of the support system for underground openings.Although considerable effort has been made in the simulation of the reinforcement effect of the fully grouted bolts on the rock masses surrounding underground openings,most of the work has limited significance since the structural element approach is used.This study proposes a local homogenization approach(L-H approach)that integrates elastoplastic mechanics,composite mechanics,and analytical approaches with numerical simulation to effectively simulate the reinforcement effect of the fully grouted bolt on deep surrounding rock masses.In the L-H approach,the representative volume of bolted rock mass(RVBRM)with a fully grouted bolt is established based on the original mesh model utilized in the rockbolt element approach.The RVBRM is a regular quadrangular prism with a cross-sectional size equal to the bolt spacing and a length equal to the bolt length.The RVBRM is homogenized by the L-H approach from a unidirectional bolt-reinforced composite into a homogeneous transversely isotropic medium whose mechanical properties are described by a new transversely isotropic elastoplastic model.The L-H parameters for the RVBRM are obtained using analytical approaches,composite mechanics,and known parameters of the rock mass and bolt.Using the L-H approach,the reinforcement effect of the fully grouted bolt on the bolted rock specimen and the surrounding rock mass in Jinping II Diversion Tunnel#2 with a depth greater than 2000 m is simulated.The results show that the predictions of the L-H approach are more in agreement with the physical model results of bolted rock specimen and provide a more realistic response of the bolted surrounding rock mass.The L-H approach demonstrates that fully grouted bolts with common bolt spacings and diameters substantially enhance the elastic modulus,shear strength,and tensile strength of the rock mass in the direction of the bolt axis.
文摘The microstructures of five Al Mn Mg alloys with different Mn, Si and Fe contents were investigated in as cast and homogenized states. The influences of chemical composition and homogenizing process on the microstructure were studied. The results show that the morphology of the primary second particles are not influenced by the variation of Mn, Si and Fe level, and the amount of the primary α phase, the α precipitates and Mg 2Si phase are enhanced by the addition of Si; The average size of primary intermetallic particles reduces and the volume fraction of them decreases slightly with the increase in homogenization temperature and time; However, the volume fraction of primary secondary particles is increased by adding more Mn, Si and Fe elements in alloys. Moreover, a new MgSiCu rich eutectic in the as cast ingot has been found.
基金support of the research work under the project PolyU520707,PolyU5213/06Esponsorship of Foundation of the State Key Laboratory of Plastic Forming Simulation and Die and Mould Technology,HUST
文摘A crystallographic homogenization method is proposed and implemented to predict the evolution of plastic deformation induced texture and plastic anisotropy(earring) in the stamping of polycrystalline sheet metals.The microscopic inhomogeneity of crystal aggregate has been taken into account with the microstructure made up of a representative aggregate of single crystal grains.Multi-scale analysis is performed by coupling the microscopic crystal plasticity with the macroscopic continuum response through the present homogenization procedure.The macroscopic stress is defined as the volume average of the corresponding microscopic crystal aggregations,which simultaneously satisfies the equation of motion in both micro-and macro-states.The proposed numerical implementation is based on a finite element discretization of the macrocontinuum,which is locally coupled at each Gaussian point with a finite element discretization of the attached micro-structure.The solution strategy for the macro-continuum and the pointwiseattached micro-structure is implemented by the simultaneous employment of dynamic explicit FE formulation.The rate-dependent crystal plasticity model is used for the constitutive description of the constituent single crystal grains.It has been confirmed that Taylor's constant strain homogenization assumption yields an undue concentration of the preferred crystal orientation compared with the present homogenization in the prediction of texture evolution,with the latter having relaxed the constraints on the crystal grains.Two kinds of numerical examples are presented to demonstrate the capability of the developed code:1) The texture evolution of three representative deformation modes,and 2) Plastic anisotropy(earring) prediction in the hemispherical cup deep drawing process of aluminum alloy A5052 with initial texture.By comparison of simulation results with those obtained employing direct crystal plasticity calculation adopting Taylor assumption,conclusions are drawn that the proposed dynamic explicit crystallographic homogenization FEM is able to more accurately predict the plastic deformation induced texture evolution and plastic anisotropy in the deep drawing process.
文摘Hydrogen flakes and elemental segregation are the main causes of steel rejection. To eliminate hydrogen flaking, the present study focuses on the manufacture of AMS-4340 ultra-high-strength steel through an alternate route. AMS-4340 was prepared using three different processing routes. The primary processing route consisted of melting in an electric arc furnace, refining in a ladle refining furnace, and vacuum degassing. After primary processing, the heat processes(D1, D2, and D3) were cast into cylindrical electrodes. For secondary processing, electroslag remelting(ESR) was carried out on the primary heats to obtain four secondary heats: E1, E2, E3, and E4. Homogenization of ingots E1, E2, E3, and E4 was carried out at 1220°C for 14, 12, 12, and 30 h, respectively, followed by an antiflaking treatment at 680°C and air cooling. In addition, the semi-finished ESR ingot E4 was again homogenized at 1220°C for 6–8 h and a second antiflaking treatment was performed at 680°C for 130 h followed by air cooling. The chemical segregation of each heat was monitored through a spectroscopy technique. The least segregation was observed for heat E4. Macrostructure examination revealed the presence of hydrogen flakes in heats E1, E2, and E3, whereas no hydrogen flakes were observed in heat E4. Ultrasonic testing revealed no internal defects in heat E4, whereas internal defects were observed in the other heats. A grain size investigation revealed a finer grain size for E4 compared with those for the other heats. Steel produced in heat E4 also exhibited superior mechanical properties. Therefore, the processing route used for heat E4 can be used to manufacture an AMS-4340 ultra-high-strength steel with superior properties compared with those of AMS-4340 prepared by the other investigated routes.
基金the National Key Research and Development Program of China(Grant No.2017YFA0403804)the National Natural Science Foundation of China(Grant No.51425402)。
文摘Microstructural improvement of Al-Cu-Li alloys with high Li content plays a critical role for the acquisition of excellent mechanical properties and ultra-low density.In this regard,the Al-Cu-Li alloy castings with high Li content from 1.5 wt.%to 4.5 wt.%were prepared by near-rapid solidification,followed by two-stage homogenization treatment(490℃/16 h and 530℃/16 h).The microstructural evolution and solidification behavior of the as-cast and homogenized alloys with different Li contents were systematically studied by combining experiments with calculations by Pandat software.The results indicate that with the increase of Li content,the grain sizes decrease,the solution ability of Cu in the matrixα-Al phase increases,while the content of secondary dendrites increases and the precipitated phases change from low melting point phases to high melting point phases under the near-rapid solidification.Additionally,by the coupling of near-rapid solidification and two-stage homogenization,the metastable precipitated phases(Al7Cu4Li and AlCu3)can be dissolved effectively in the alloys with Li content of 1.5 wt.%-2.5 wt.%;moreover,the stable precipitated phases(Al6CuLi3 and Al2CuLi)uniformly distribute at the grain boundaries in the alloys with Li content of 3.5 wt.%-4.5 wt.%.As a result,the refined and homogenized microstructure can be obtained.
基金This work is supported by the National Key R&D Plan(grant No.2016YFB0301105)the Fundamental Research Funds for the Central Universities(grant No.FRF-TP-16-016A1).
文摘The distribution of residual stresses through thickness of 5 mm-thick ME21 magnesium alloy extruded plates was analyzed non-destructively using short-wavelength X-ray diffraction(SWXRD),and the effect of homogenization annealing before extrusion on the residual stress was discussed.The classic d 0 method with an annealed stress-free reference specimen was employed to determine the residual stress of the extruded plates.The residual stress results showed that the gradient of residual stress in the transverse direction was larger than that of the extrusion direction.The homogenization process prior to extrusion weaken the formed sample’s texture.The maximum residual stress of the as-extruded plate was reduced,and the residual stress distribution was homogenized.
文摘The Mg-Al-Zn series AZ31 and AZ314+MM alloys are homogenized at 673, 723 and753K respectively. The hardness of alloy ingots at different heat-treated states ismeasured and the microstructures are observed. The optimum annealing temperatureis 723K and the time is 12h.
文摘This study demonstrated that homogenization did not increase the activity of lipoprotein lipase (LPL) in spite of a fast accumulation of free fatty acids (FFA). Two homogenization pressures (100 and 170 bar) and two temperatures (40℃and 50℃) were examined. The activity of LPL was analyzed and the formation of FFA was measured with two different methods, the B.D.I.-method and a nonesterified fatty acids (NEFA) method. A homogenization temperature of 50℃ resulted in a decreased LPL activity compared to 40℃. No effect of homogenization pressure was found. Analyzing FFA concentration with the B.D.I.-method resulted in significant effect of homogenization temperature and no effect of pressure. The largest formation of FFA was found in milk homogenized at 40℃. Using the NEFA method, another result was obtained, indicating no effect of homogenization temperature and a larger FFA accumulation at 100 bar than at 170 bar. Both analytic methods demonstrated significant production of FFA during 60 min incubation at homogenization temperature after treatment. The level of FFA in the milk samples immediately after homogenization was very high, demonstrating that LPL cleaves the triglycerides very rapidly when the native membrane was damaged. The regression between the B.D.I.-method and the NEFA was fair in the interval between 4 and 14 mmol/100 g fat, whereas at higher concentrations, the correlation was poor.
文摘1 Introduction The homogenization temperature of fluid inclusions reflects the temperatures of the brines from which halite crystals grew.Therefore,it is a powerful mean to reveal the paleoclimate.Northern Shaanxi Salt Basin is located in the central and eastern of Ordos Basin.We have detail petrographical research and the
基金Supported by the National Natural Science Foundation of China(21576033,21636004)Central University of Basic Scientific Research Special Project(106112017CDJQJ228808)+2 种基金Chongqing Special Social Undertakings and People's Livelihood Security Science and Technology Innovation(cstc2017shmsA90016)National Key Research and Development Project(2017YFB0603105)National Sci-Tech Support Plan(2015BAB17B01)
文摘In this paper, the power consumption, the vertical local void fraction and the local gas–liquid interfacial area are investigated in the aerated stirred tank reactors(STRs) equipped with a rigid-flexible impeller. Meanwhile, the regressive correlation based on power consumption and interfacial area is proposed. Then a novel homogenization energy(HE = RSDPtm) expression based on power consumption and local interfacial area is redefined and used to indicate the mixing efficiency. The optimal operating mode is selected based on the change of the HE value. This paper can provide research ideas for structural optimization of stirred reactors.
文摘The microstructure and tensile properties of the extruded Mg-Zn-Zr-RE alloy bars are studied.Theextruded bar without previous homogenization has the highest tensile strength,whereas the tensile strength of theextruded bar previously homogenized at 400℃ or 380℃ is lower.During long time homogenization,the trans-formation of rare earth compounds Mg<sub>3</sub>REZn<sub>6</sub>（Z phase）and Mg<sub>3</sub>RE<sub>2</sub>Zn<sub>3</sub>（W phase）into Mg<sub>41</sub>RE<sub>5</sub> andMg Zn phases occurr and the MgZn phase grow up.In addition,the dynamic recrystallization takes place in sub-sequent extrusion that caused decrease of the tensile strength.
