Use of experiment and an inverse method to study interface heat transfer during solidification in the investment casting process

A technique to determine the thermal boundary conditions existing during the solidification of metallic alloys in the investment casting process is presented. Quantitative information about these conditions is needed so that numerical models of heat transfer in this process produce accurate results. In particular, the variation of the boundary conditions both spatially and temporally must be known. The method used involves the application of a new inverse heat conduction method to thermal data recorded during laboratory experiments of aluminium alloy solidification in investment casting shell moulds. The resultant heat transfer coefficient for the alloy/mould interface is calculated. An experimental programme to determine requisite mould thermal properties was also undertaken. It was observed that there is significant variation of the alloy/mould heat transfer coefficient during solidification. It is found to be highly dependent on the alloy type and on the vertical position below the initial free surface of the liquid metal. The aluminium casting alloys used in this study were 413, A356, 319 (Aluminum Association designations), and commercially pure aluminium. These alloys have significantly different freezing ranges. In particular, it was found that alloys with a high freezing range solidify with rates of heat transfer to the mould which are very sensitive to metallostatic head.     

An investigation of the microporosity formation in an Al–4.1% Cu alloy casting in microgravity and in standard gravity

 The microporosity formation in a vertical unidirectionally solidifying Al–4.1%Cu alloy casting is modeled in both microgravity and standard gravity as well as in the conditions of decreased (Moon, Mars) and increased (Jupiter) gravity. Due to the unique opportunities offered by a low-gravity environment (absence of metallostatic pressure and of natural convection in the solidifying alloy) future microgravity experiments will significantly contribute to attaining a better physical understanding of the mechanisms of microporosity formation. One of the aims of the present theoretical investigation is to predict what microporosity patterns will look like in microgravity in order to help plan a future microgravity experiment. To perform these simulations, the authors suggest a novel three-phase model of solidification that accounts for the solid, liquid, and gas phases in the mushy zone. This model accounts for heat transfer, fluid flow, macrosegregation, and microporosity formation in the solidifying alloy. Special attention is given to the investigation of the influence of microporosity formation on the inverse segregation. Parametric analyses for different initial hydrogen concentrations and different gravity conditions are carried out. Received on 14 April 2000     

快速凝固过共晶铝硅合金的微观组织特征及耐磨性研究

利用单辊旋淬快速凝固法制备Al-21Si和Al-30Si过共晶铝硅合金,采用扫描电镜、透射电镜及XRD技术对所制备合金的组织形貌和相结构进行表征.结果表明:快速凝固合金形成微纳米晶组织,晶粒明显细化.Al-21Si过共晶合金凝固组织由羽毛针状(α-Al+β-Si)共晶体和雪花状α-Al相组成;快速凝固有效抑制初生硅相的形核与生长,α-Al相领先共晶形核生长,形成微纳米级亚共晶组织.Al-30Si高硅过共晶合金初生硅相细小钝化,初晶Si相显微结构为孪晶形貌,呈典型的过共晶组织特征.快速凝固显著提高了合金的显微度和耐磨性,快速凝固Al-21Si合金的耐磨性是传统铸造合金的5倍.     

Numerical simulation of heat transfer in pressurized solidification of Magnesium alloy AM50

Based on finite difference and control-volume scheme, a model was developed to simulate fluid flow in forced convection and heat transfer in pressurized solidification of a cylindrical squeeze casting of magnesium alloy AM50. Pressure-dependent heat transfer coefficients (HTC) and non-equilibrium solidification temperatures were determined by experimental measurements. With the measured HTC and temperatures under the different pressures, the temperature distributions and the cooling behaviors of squeeze cast were simulated.     

Fluidization behavior of graphitized glassy particles in a fluidized carbon bed cooling process for investment casting

Fluidized Carbon Bed Cooling (FCBC) is an innovative investment casting process for directional solidification of superalloy components. It takes advantage of a fluidized bed with a base of small glassy carbon beads for cooling and other low-density particles that form an insulating layer by floating to the bed surface. This so-called “Dynamic Baffle” protects the fluidized bed from the direct heat input from the high-temperature heating zone and provides the basis for an improved bed microstructure. The prerequisites for a stable casting process are stable fluidization conditions where neither collapse of the bed nor particle blow out at excessive bubble formation occur.This work aimed to investigate the fluidization behavior of spherical carbon bed material in argon and air at temperatures between 20 to 350 °C. Systematic studies at reduced pressures using the FCBC prototype device were performed to understand the stable fluidization conditions at all stages of the investment casting process. The particle shape factor and size distribution characterization and the measurement of the powder’s minimum fluidization velocity and bed voidage show that this material can be fully utilized as a cooling and buoyancy medium during the FCBC process.     

铸件凝固温度场有限元分析中界面热阻的处理

提出一种处理铸件与铸型界面热阻问题的虚拟界面单元法，并给出了有限元计算公式。由于该公式不显含单元厚度(△l)，故该单元厚度△l可取任意值。当△l取为零时，使问题处理变得极为方便。针对某一具体金属型铝合金活塞的铸造凝固过程，按考虑和不考虑铸件与铸型间热阻影响两种方法作了有限元计算，通过与实测值相比较，本文提出的算法其计算精度远高于不考虑铸件与铸型间热阻影响的计算结果。另外．该方法使有限元建模方便、通用性强。     

Solidification of hypereutectic and hypoeutectic binary alloys with buoyancy and surface tension driven natural convection

Convection patterns and evolution of macrosegregation during solidification of hypereutectic and hypoeutectic NH₄CL-H₂O binary systems in rectangular side chilled ingots have been numerically investigated. Under the conditions of pure thermal/solutal convection, without a free surface, solidification of NH₄CL 70%-H₂O hypereutectic alloy is characterized by the formation of channels and A-segregates, while solidification of NH₄CL 10%-H₂O hypoeutectic alloy is characterized by the formation of circulation cells in the narrow melt and V-segregates. Surface tension effects during solidification of NH₄CL 70%-H₂O results in establishing a counterclockwise rotating cell at the cavity top, changing the number and orientation of developed channels, and creating an area of negative segregation at the cavity top. During solidification of NH₄CL 10%-H₂O, surface tension effects increase the intensity of flow and results in a higher degree of macrosegregation. Received on 9 June 1998     

Determination of heat transfer coefficients at metal/chill interface in the casting solidification process

The present work focuses on the determination of interfacial heat transfer coefficients (IHTCs) between the casting and metal chill during casting solidification. The proposed method is established based on the least-squares technique and sequential function specification method and can be applied to calculate heat fluxes and IHTCs for other alloys. The accuracy and stability of the method has been investigated by using a typical profile of heat fluxes simulating the practical conditions of casting solidification. In the test process, the effects of various calculation parameters in the inverse algorithm are also analyzed. Moreover, numerically calculated and experimental results are compared by applying the determined IHTCs into the forward heat conduction model with the same boundary conditions. The results show that the numerically calculated temperatures are in good agreement with those measured experimentally. This confirms that the proposed method is a feasible and effective tool for determination of the casting-mold IHTCs.     

Development of an inverse heat conduction model and its application to determination of heat transfer coefficient during casting solidification

The interfacial heat transfer coefficient (IHTC) is required for the accurate simulation of heat transfer in castings especially for near net-shape processes. The large number of factors influencing heat transfer renders quantification by theoretical means a challenge. Likewise experimental methods applied directly to temperature data collected from castings are also a challenge to interpret because of the transient nature of many casting processes. Inverse methods offer a solution and have been applied successfully to predict the IHTC in many cases. However, most inverse approaches thus far focus on use of in-mold temperature data, which may be a challenge to obtain in cases where the molds are water-cooled. Methods based on temperature data from the casting have the potential to be used however; the latent heat released during the solidification of the molten metal complicates the associated IHTC calculations. Furthermore, there are limits on the maximum distance the thermocouples can be placed from the interface under analysis. An inverse conduction based method have been developed, verified and applied successfully to temperature data collected from within an aluminum casting in proximity to the mold. A modified specific heat method was used to account for latent heat evolution in which the rate of change of fraction solid with temperature was held constant. An analysis conducted with the inverse model suggests that the thermocouples must be placed no more than 2 mm from the interface. The IHTC values calculated for an aluminum alloy casting were shown to vary from 1,200 to 6,200 Wm^?2 K^?1. Additionally, the characteristics of the time-varying IHTC have also been discussed.     

Influence of shear and orthogonal vibration on semisolid aluminum flow properties

Understanding flow properties and flow effects of liquid and semisolid aluminum became a key solution for know-how of the casting processes. It is essential to find and study a new solution of interactive and efficient structure control of processed aluminum suspension. This task was solved by an adaptation of an electromagnetic actuator and high-resolution tempering unit to a conventional rotational rheometer. Initially, the research reveals a precise detection of transition temperatures in steady and transient shear flow. It was found that superposition of mechanical vibration orthogonal to the shear flow radically decreases shear viscosity of semisolid slurry. However, liquid state rheological properties show structural behavior, but stayed insensitive to mechanical oscillations. Analysis of boundary conditions before fundamental experiment shows that no considerable side effects were present during the experiment under vibration. The study reveals transition of strongly shear-thinning concentrated aluminum suspension to almost Newtonian fluid under vibration in shear flow. It is recommended to relate such phenomenon to non-equilibrium between structure formation and structure break-up under vibration and hydrodynamic forces of shear flow. The results illustrate how sensitive the structure of slurry is to vibration in general and in particular during the solidification phase. The revealed results provide a solid basis for further fundamental investigations.     

Eutectic solidification patterns: Interest of microgravity environment

The solidification of binary eutectic alloys produces two-phase composite materials in which the microstructure, that is, the geometrical distribution of the two solid phases, results from complex pattern-formation processes at the moving solid–liquid interface. Since the volume fraction of the two solids depends on the local composition, solidification dynamics can be strongly influenced by thermosolutal convection in the liquid. In this contribution, we review our experimental and numerical work devoted to the understanding of eutectic solidification under purely diffusive conditions, which will soon be tested and extended during the microgravity experiment TRANSPARENT ALLOYS planned by the European Space Agency (ESA).     

An inverse finite element method with an application to extrusion with solidification

The flow and solidification of planar jets are analysed by means of an efficient inverse isotherm finite element method. The method is based on a tessellation that is constructed by isotherms as characteristic co-ordinate lines transverse to the flow direction. Thus opposite sides of finite elements lie on isotherms. The method allows the simultaneous determination of the location of the isotherms with the primary unknowns, namely, the velocity, the pressure, the temperature and the location of the free surface. Thus the determination of the location of the solidification front (which is known to pose significant computational difficulties) is automatic. This facilitates the control of the location of the solidification front by controlling macroscopic variables such as the flow rate, the cooling rate and the capillary design. The location of the solidification may then be suitably chosen to influence the frozen-in orientation and structure in extrusion of high-performance materials such as composites and polymers, in continuous casting of metals and in growth of crystals.     

Comparison between Lever and Scheil Rules for Modeling of Microporosity Formation during Solidification

Segregation and microporosity formation are two important physicalphenomena that occur during solidification of binary alloys. The aim ofthis study is to investigate the effect of the model of solute diffusionat the local scale (which means at the local scale of the microscopicrepresentative elemental average volume (REV)) on solute transport andthe microporosity formation during this process. The Scheil rule and thelever rule are used to describe the solute diffusion at the local scale.Results indicate that solute diffusion at the local scale is animportant factor in microporosity formation. Also, microporosityformation slightly reduces inverse segregation because it partiallycompensates for shrinkage. The increase of the external pressure at thefree surface or the decrease of the initial hydrogen concentration inthe molten alloy can be effectively utilized to control microporosityformation.     

An analytical solution for the solidus and liquidus position in the solidification of materials with a phase change range applied to the continuous casting of steel

In continuous casting processes it is important to know how the growth of the solidification layer thickness depends on the properties of the material to be casted. With help of a known approximate solution for the one dimensional solidifcation of a body with fixed wall temperature the solidified layer thickness can be calculated. In this paper it has been done for steel. Also a temperature transition range for the solidification process has been taken into account. The results are given in a few dimensionless numbers representing the relation between the solidification front position and time. The data obtained can be used as an estimation for the effects that occur in practice with steel casting processes.     

Modelling impingement of hollow metal droplets onto a flat surface

Despite many theoretical and experimental works dealing with the impact of dense melt droplets on the substrate during the process of thermal spray coating, the dynamics of the impingement of hollow melt droplet and the subsequent splat formation are not well addressed. In this paper a model study for the dynamic impingement of hollow droplet is presented. The hollow droplet is modelled such that it consists of a liquid shell enclosing a gas cavity. The impingement model considers the transient flow dynamics during impact, spreading and solidification of the droplet using the volume of fluid surface tracking method (VOF) coupled with a solidification model within a one-domain continuum formulation. The results for spreading, solidification and formation of splats clearly show that the impingement process of hollow droplet is distinctly different from the dense droplet. Study with different droplet void fractions and void distribution indicates that void fraction and void distribution have a significant influence on the flow dynamics during impact and on the final splat shape. The results are likely to provide insights for the less-explored behaviour of hollow melt droplets in thermal spray coating processes.     

SiC_p/Al-Si合金梯度材料的磨损特性

采用离心铸造技术制备了 Si Cp/ Al- 8.8% Si合金梯度材料 ,并用扫描电子显微镜、HV- 5型小负荷维氏硬度计和ML- 10 0型销 -盘磨粒磨损试验机等设备研究了该梯度材料组织、硬度及耐磨性的梯度分布规律 .结果表明 :因 Si C颗粒的密度比铝合金液的大 ,其在离心力场中偏聚于试样的外侧 ,含量由外向内逐渐降低直至消失 ,呈梯度变化 ;Si Cp/Al- 8.8% Si合金梯度材料的硬度由外向内逐渐降低 ,呈梯度变化 ,与 Si C颗粒的分布规律一致 ;Si Cp/ Al- 8.8% Si合金梯度材料的耐磨性能取决于 Si C颗粒的数量及其分布 ,耐磨性能由外向内逐渐变差 ,呈梯度变化 ,与硬度的分布规律一致     

Sensitivity of mesh spacing on simulating macrosegregation during directional solidification of a superalloy

The sensitivity of mesh spacing on simulations of macrosegregation, particularly ‘freckles’, during vertical directional solidification of a superalloy in a rectangular mold was systematically analyzed to achieve accurate predictions in finite element calculations. It was observed that a coarser mesh spacing in the x‐direction horizontal tends to minimize the simulated macrosegregation, whereas a coarser mesh spacing in the y‐direction vertical artificially tends to make the system appear to have more macrosegregation. When solidification conditions either lead to a well‐established freckling case or to a well‐established non‐freckling case, the simulated results are not sensitive to the mesh spacing provided the elements are no larger than about 2d₁ by 2 D/V and 3d₁ by 4 D/V respectively, where d₁ is the primary dendrite arm spacing, D is the diffusivity of the alloy solute with the smallest diffusivity in the liquid, and V is the growth rate. However, when solidification conditions are very close to the transition between freckling and no freckling, the simulated results are sensitive to the mesh spacing, especially in the y‐direction. Based on the mesh sensitivity analysis from the two‐dimensional simulations of rectangular castings of René N5, the mesh with element dimensions no larger than 2d₁ in the x‐direction and 1.5 D/V in the y‐direction are recommended as the most stringent element size. Copyright © 2001 John Wiley & Sons, Ltd.     

Boundary-conforming mapping applied to computations of highly deformed solidification interfaces

A new boundary-conforming mapping is developed for the calculation of highly deformed cellular solidification interfaces in a model of directional solidification of a binary alloy. The mapping is derived through a variational fomulation that is designed so that the grid penetrates the grooves between cells along the interface without causing a loss of ellipticity of the mapping equations. A finite element/Newton method is presented for simultaneous solution of the free boundary problem described by the solutal model of directional solidification and the mapping equations. Results are compared to previous calculations and demonstrate the importance of accurate representation of the interface shape for understanding the solution structure.     

定向凝固多晶铁磁形状记忆合金力-温度耦合的实验研究

铁磁形状记忆合金兼具大输出应变与高响应频率等综合特性,是新一代驱动与传感材料。采用定向凝固技术制成的多晶铁磁形状记忆合金具有较多优越的力学性能。本文对温度和应力耦合作用下的定向凝固多晶铁磁形状记忆合金的力学特性进行了实验测试,分别获得了定向凝固多晶Ni-Mn-Ga试样在不同恒定温度时的应力-应变循环曲线,以及试样在压缩时两个互相垂直方向的数字散斑图。结果表明:同一恒定温度时,随着应力循环次数的增加,其应变值逐渐减小;同一压缩应力时,不同温度作用过程中定向凝固方向的应力,随着温度的升高逐渐减小。本文结果可为铁磁形状记忆合金在工程中的应用提供一定的指导作用。     

An experimental investigation of nucleation probability of supercooled water inside cylindrical capsules

This article experimentally investigates the nucleation probability of supercooled water inside cylindrical capsules with or without nucleators during a cold storage process. The nucleation probability curves of initial appearance of dendritic ice as a function of coolant temperature, size of capsule, and mass of different heterogeneous nucleators are characterized, respectively, by performing a number of experiments. The results show that the lower the coolant temperature, the greater the nucleation probability. The larger the volume of water contained, the higher the nucleation temperature. The addition of nucleating agents, such as iron ore, iron chips and silver iodide, into the water container can effectively improve the nucleation probability, and thus increase the coefficient of performance (COP) of a thermal storage air-conditioning system. Since the crystal structure of silver iodide is very similar to that of ice, the comparison among three types of agents indicates that it has the best effect in facilitating nucleation.