Effect of growth rate on microstructure and solute distribution of Al-Zn-Mg alloy

An Al-5.3%Zn-5.3%Mg alloy was unidirectionally solidified to determine morphological transition and solute distribution by a modification of the Bridgman technique for crystal growth with growth rates ranging from 4-500 μm/s and a temperature gradient of 25 K/cm. It was determined that growth rates from 6.5-9.5 μm/s generated a cell morphology, where the lower limit corresponds to the plane front to cellular transition and the upper limit indicates the cellular to columnar dendrite transition. The microstructures of the alloys solidified from 30 μm/s to growth rates less than 500 μm/s were mainly composed of columnar dendrites, while the microstructures solidified at growth rates greater than 500 μm/s were equiaxed. Regarding experimental results on solute distribution, a prediction of the model developed by Rappaz and Boettinger for dendrite solidification of multicomponent alloys was applied with excellent agreement. Results of solute distribution were employed to derive the precipitation fraction of τ-phase needed to increase the electrochemical properties of the alloy to be used as an Al-sacrificial anode.

Solute distribution in KNbO 3 melt-solution and its effect on dendrite growth during rapid solidification

This paper reports that the rapid solidification of mixed Li2B4O7 and KNbO3 melted in a Pt loop heater has been performed experimentally by the method of quenching, and various morphologies of KNbO3 crystals have been observed in different regions of the quenched melt-solution. Dendrites were formed in the central region where mass transfer is performed by diffusion, whereas polygonal crystals with smooth surface grew in the marginal region where convection dominates mass transport. Based on measurement of KNbO3 concentration along crystal interface by electronic probe analysis, it finds the variety of crystal morphologies, which is the result of different solute distributions： in the central region the inhomogeneity of solute concentration is much sharper and morphological instability is easier to take place; nevertheless in the marginal region the concentration homogeneity has been greatly enhanced by convection which prevents the occurrence of morphological instability. Additional solute distribution in the melt along the primary dendrite trunk axis as well as that in mushy zones has also been determined. Results show that the solute concentration in the liquid increases linearly with distance from the trunk tip and more solutes were found to be concentrated in mushy zones. The closer the mushy zone is to trunk tip, the lower the solute concentration will be there.

Solute Distribution in Columnar Crystal Zone and Influences of Correlative Factors for Continuous Casting Slabs

The expression of the solute distribution in columnar crystal zone was deduced when the solid-liquid interface bended periodically, and the quantitative calculations of macrosegregation were also made in the process of the continuous casting. The solute distribution along the thickness direction of the slabs was obtained, which verified the theoretical calculation. The effect of the bulge size, solidification speed, and solidification shrinkage speed on macrosegregation of the slabs was calculated. It can be concluded that normal segregation and negative segregation alternatively appear as a result of the bulge. The normal segregation exponentially depends on the bulge size, and the negative segregation linearly depends on the bulge size. The extent of the normal segregation is greater than that of the negative segregation when the bulge size is the same. The macrosegregation of the same position along the thickness direction of the slabs changes in a sine wave with increasing the solidification rate, and the amplitude is larger at the casting blank center. The normal segregation linearly decreases with increasing the solidification shrinkage speed, and when the solidification shrinkage speed exceeds a critical value, the segregation appears negatively and increases linearly.

Ordered Sn distribution adjacent to the precipitate-matrix interface in a Mg-9.8wt.%Sn alloy

The major interface betweenβ-Mg_(3)Sn precipitate plate and theα-Mg matrix in a Mg-9.8wt.%alloy has been investigated using aberrationcorrected scanning transmission electron microscopy and first-principles calculations.It is found that Sn atoms orderly distribute in the single layer of theα-Mg matrix immediately adjacent to the broad surface ofβat the early stage of ageing.These Sn atoms substitute Mg atoms located at the centers of equilateral triangles constituted by three Mg columns in the outmost layer ofβ.First-principles calculations suggest that the ordered Sn distribution is energetically favored and it not only decreases the interfacial energy of theβ-matrix interface but also hinders the occurrence of 1/3<01■0>αshear that thickens theβplate.

Analytical Models for Velocity Distributions in Compound Channels with Emerged and Submerged Vegetated Floodplains

The lateral distributions of depth-averaged velocity in open compound channels with emerged and submerged vegetated floodplains were analyzed based on the analytical solution of the depth-integrated Reynolds-Averaged Navier-Stokes equation with a term to account for the effects of vegetation.The three cases considered for open channels were two-stage rectangular channel with emerged vegetated floodplain,rectangular channel with submerged vegetated corner,and two-stage rectangular channel with submerged vegetated floodplain,respectively.To predict the depth-averaged velocity with submerged vegetated floodplains,we proposed a new method based on a two-layer approach where flow above and through the vegetation layer was described separately.Moreover,further experiments in the two-stage rectangular channel with submerged vegetated floodplain were carried out to verify the results.The analytical solutions of the cases indicated that the corresponding analytical depth-averaged velocity distributions agree well with the simulated and experimental prediction.The analytical solutions of the cases with theoretical foundation and without programming calculation were reasonable and applicable,which were more convenient than numerical simulations.The analytical solutions provided a way for future researches to solve the problems of submerged vegetation and discontinuous phenomenon of depth-averaged velocity at the stage point for compound channels.Understanding the hydraulics of flow in compound channels with vegetated floodplains is very important for supporting the management of fluvial processes.

Liquid phase separation and subsequent dendritic solidification of ternary Fe_(35)Cu_(35)Si_(30) alloy

Liquid Fe35Cu35Si30alloy has achievedthemaximum undercooling of 328 K （0.24TL） with glass fluxing method, and it displayed triple solidification mechanisms. A critical undercooling of 24 K was determined for metastable liquid phase separation. At lower undercoolings,α-Fe phase was the primary phase and the solidification microstructure appeared as homogeneous well-defined dendrites. When the undercooling exceeded 24 K, the sample segregated into Fe-rich and Cu-rich zones. In the Fe-rich zone, FeSi intermetallic compound was the primary phase within the undercooling regime below 230 K, while Fe5Si3intermetallic compound replaced FeSi phase as the primary phase at larger undercoolings. The growth velocity of FeSi phase increased whereas that ofFe5Si3 phase decreased with increasing undercooling. For the Cu-rich zone, FeSi intermetallic compound was always the primary phase. Energy-dispersive spectrometry analyses showed that the average compositions of separated zones have deviated substantially from the original alloycomposition.

Molecular Dynamics Study on Microstructure of Potassium Dihydrogen Phosphates Solution

Molecular dynamics simulations were carried out to study the internal energy and microstructure of potassium dihydrogen phosphates （KDP） solution at different temperatures. The water molecule was treated as a simple-point-charge model, while a seven-site model for the dihydrogen phosphate ion was adopted. The internal energy functions and the radial distribution functions of the solution were studied in detail. An unusually large local particle number density fluctuation was observed in the system at saturation temperature. It has been found that the specific heat of oversaturated solution is higher than that of unsaturated solution, which indicates the solution experiences a crystallization process below saturation temperature. The radial distribution function between the oxygen atom of water and the hydrogen atom of the dihydrogen phosphate ion shows a very strong hydrogen bond structure. There are strong interactions between potassium cation and oxygen atom of dihydrogen phosphate ion in KDP solution, and much more ion pairs were formed in saturated solution.

Stresses induced by post-tensioned anchor in jointed rock mass

A new analytical study on stresses around a post-tensioned anchor in rocks with two perpendicular joint sets is presented. The assumptions of orthotropic elastic rock with plane strain conditions are made in derivation of the formulations. A tri-linear bond-slip constitutive law is used for modeling the tendon-grout interface behavior and debonding of this interface. The bearing plate width is also considered in the analysis. The obtained solutions are in the integral forms and numerical techniques that have been used for evaluation. In the illustrative example given, the major principal stress is compressive in the anchor free zone and compressive stress concentrations of 815 k Pa and 727 k Pa(for the anchor load of 300 k N) are observed under the bearing plate and the bond length proximal end, respectively. However, large values of tensile stresses with the maximum of-434 k Pa are formed at the bond length distal end. The results obtained using the proposed solution are compared very those of numerical method(FEM).

MATHEMATIC MODEL AND ANALYTIC SOLUTION FOR CYLINDER SUBJECT TO UNEVEN PRESSURES

According to the inverse solution of elasticity mechanics, a stress function is constructed which meets the space biharmonic equation, this stress functions is about cubic function pressure on the inner and outer surfaces of cylinder. When borderline condition that is predigested according to the Saint-Venant＇s theory is joined, an equation suit is constructed which meets both the biharmonic equations and the boundary conditions. Furthermore, its analytic solution is deduced with Matlab. When this theory is applied to hydraulic bulging rollers, the experimental results inosculate with the theoretic calculation. Simultaneously, the limit along the axis invariable direction is given and the famous Lame solution can be induced from this limit. The above work paves the way for mathematic model building of hollow cylinder and for the analytic solution of hollow cvlinder with randomly uneven pressure.

Drag Effects of Solute and Second Phase Distributions on the Grain Growth Kinetics of Pre-Extruded Mg-6Zn Alloy

In order to control the grain size during hot forming,grain growth behavior of a pre-extruded Mg-6Zn magnesium alloy and its correlation with solute and second phase distribution were investigated.Isothermal annealing was conducted on a Gleeble-1500 thermo-mechanical simulator.The mean grain size Dg of each annealed specimen was measured by the quantitative metallography technique.The grain growth kinetics of the Mg-6Zn alloy annealed at 473-623 K was obtained as Dg^4- Dg0^4=2.25 ×10^11 exp（-95450）by the least square linear regression method.The deviation of grain growth exponent n = 4 from the theoretical value of 2 may be attributed to the presence of solute zinc and second phases which will retard the boundary migration.Microscopic observations show that the non-uniform distribution of grain size for samples pre-extruded or annealed at low temperatures is closely related to the non-uniform distribution of fine and dispersed second phases but not to the non-uniform distribution of solute zinc.This indicates that second phase pinning effect plays an important role in microstructure refinement.

Multi-timescale Energy Sharing with Grid-BESS Capacity Rental Considering Uncertainties

The growing number of distributed energy resources(DERs)in distribution networks brings new opportunities for local energy sharing.This paper proposes a multi-timescale en-ergy sharing approach among DER aggregators and distribution system operators(DSOs)considering grid-battery energy storage system(BESS)capacity rental and network operations.An energy sharing coordinator is created to manage the energy sharing with price determination.In an hour-ahead stage,the buying/selling energy and required grid-BESS rental capacity are optimally determined by the aggregators while the network operation is robustly considered by the DSO.In addition to renewable generation and loads,the power exchanges of the aggregators are treated as uncertainties.Then during each hour,15-min-ahead energy transaction and controllable DERs are optimized to track uncertainty realization.The uncertainties in the aggregators and the DSO are addressed by stochastic and robust optimization methods,respectively.To efficiently solve the proposed energy sharing problem,a distributed solution algorithm with step length control and step reduction techniques is developed.The simulation results verify the high efficiency of the proposed energy sharing approach.Index Terms-Battery capacity rental,distributed solution algorithm,energy sharing,optimization,uncertainty.

Electric Vehicle Charging Scheduling Strategy for Supporting Load Flattening Under Uncertain Electric Vehicle Departures

The scheduled electric vehicle(EV)charging flexibility has great potential in supporting the operation of power systems,yet achieving such benefits is challenged by the uncertain and user-dependent nature of EV charging behavior.Existing research primarily focuses on modeling the uncertain EV arrival and battery status yet rarely discusses the uncertainty in EV departure.In this paper,we investigate the EV charging scheduling strategy to support load flattening at the distribution level of the utility grid under uncertain EV departures.A holistic methodology is proposed to formulate the unexpected trip uncertainty and mitigate its negative impacts.To ensure computational efficiency when large EV fleets are involved,a distributed solution framework is developed based on the alternating direction method of multipliers(ADMM)algorithm.The numerical results reveal that unexpected trips can severely damage user convenience in terms of EV energy content.It is further confirmed that by applying the proposed methodology,the resultant critical and sub-critical user convenience losses due to scheduled charging are reduced significantly by 83.5%and 70.5%,respectively,whereas the load flattening performance is merely sacrificed by 17%.

An operating state estimation model for integrated energy systems based on distributed solution

In view of the disadvantages of the traditional energy supply systems,such as separate planning,separate design,independent operating mode,and the increasingly prominent nonlinear coupling between various subsystems,the production,transmission,storage and corn sumption of multiple energy sources are coordinated and optimized by the integrated energy system,which improves energy and infrastructure utilization,promotes renewable energy consumption,and ensures reliability of energy supply.In this paper,the mathematical model of the electricity-gas interconnected integrated energy system and its state estimation method are studied.First,considering the nonlinearity between measurement equations and state variables,a performance simulation model is proposed.Then,the state consistency equations and constraints of the coupling nodes for multiple energy sub-systems are established,and constraints are relaxed into the objective function to decouple the integrated energy system.Finally,a distributed state estimation framework is formed by combining the synchronous alternating direction multiplier method to achieve an efficient estimation of the state of the integrated energy system.A simulation model of an electricity-gas interconnected integrated energy system verifies the efficiency and accuracy of the state estimation method proposed in this pape.The results show that the average relative errors of voltage amplitude and node pressure estimated by the proposed distributed state estimation method are only 0.0132%and 0.0864%,much lower than the estimation error by using the Lagrangian relaxation method.Besides,compared with the centralized estimation method,the proposed distributed method saves 5.42 s of computation time.The proposed method is more accurate and efficient in energy allocation and utilization.

Position optimization of particular solution sources for distributed source boundary point method by volume velocity-matching

Choosing particular solution source and its position have great influence on accu- racy of sound field prediction in distributed source boundary point method. An optimization method for determining the position of particular solution sources is proposed to get high accu- racy prediction result. In this method, tripole is chosen as the particular solution. The upper limit frequency of calculation is predicted by setting 1% volume velocity relative error limit using vibration velocity of structure surface. Then, the optimal position of particular solution sources, in which the relative error of volume velocity is minimum, is determined within the range of upper limit frequency by searching algorithm using volume velocity matching. The transfer matrix between pressure and surface volume velocity is constructed in the optimal position. After that, the sound radiation of structure is calculated by the matrix. The results of numerical simulation show that the calculation error is significantly reduced by the proposed method. When there are vibration velocity measurement errors, the calculation errors can be controlled within 5% by the method.

Determination of large diameter bored pile's effective length based on Mindlin's solution

The calculation equation of large diameter bored pile＇s effective length is connected with its distribution of pile shaft resistance. Thus, there is a great difference between the calculation results under the different distributions of pile shaft resistance. Primarily, this paper summarizes the conceptualized mode of pile shaft resistance under the circum- stance that the soil surrounding the piles presents different layer distributions. Secondly, based on Mindlin＇s displacement solution and in consideration of the effect of pile diam- eter, the calculation equation is optimized with the assumption that the pile shaft resis- tance has a parabolic distribution. The influencing factors are analyzed according to the calculation result of effective pile length. Finally, combined with an engineering example, the calculation equation deduced in this paper is analyzed and verified. The result shows that both the Poisson ratio of soil and pile diameter have impacted the effective pile length. Compared with the Poisson ratio of soil, the effect of pile diameter is more significant. If the pile diameter remains the same, the effect of the Poisson ratio of soil to the effective pile length decreases as the ratio of pile elastic modulus and soil share modulus increases. If the Poisson ratio of soil remains the same, the effect of the pile diameter to the effective pile length increases as the ratio of pile elastic modulus and soil share modulus increases. Thus the optimized calculation result of pile effective length under the consideration of pile diameter effect is more close to the actual situation of engineering and reasonably practicable.