MODEL OF THE EFFECT OF ALLOY CONTENT ON SHELL STRENGTH DURING SOLIDIFICATION OF BINARY ALLOYS

A thermomechanical model of unidirectional solidification of binary alloy systems is presented. The goal of the model is to begin to explore the effect of alloy content on the mechanical behavior of the solidifying shell by first examining the effect on lateral strength. The shell solidifies onto a semi-infinite mold proceeding behind a mushy zone that grows into an initially quiescent fluid. Deformation of the shell is modeled with a thermohypoelasioviscous constitutive law that allows for examination of the idealized case of elastic deformation of the casting as well as the case where strain rate relaxation due to viscous creep predominates. Any effects of alloy content on the coefficients in the constitutive model are ignored so that the calculated effects on strength arise entirely from the size of the mushy zone. Aluminum-magnesium alloys solidifying onto a copper mold are considered as specific examples using a linearized portion of the Al-Mg phase diagram. The material with the smallest alloy content exhibits the greatest shell strength for the same cooling histories. That material with the widest freezing range has the lowest strength. For the elastic model, the average strength always increases with time, whereas for the elastoviscous case it can decrease with time to the point where the alloy content has virtually no effect on strength.     

Modeling and simulation of heat transfer phenomena during investment casting

Determining the heat transfer phenomena during casting processes is an important parameter for measuring the overall performance of process. It gives information about the properties of the metal being casted and its possible behavior in the mold during casting process. Improper determination of heat transfer phenomena and use of improper molding materials and casting conditions leads to defects such as misruns, cold shuts, shrinkage, pin holes, air holes and porosity in final product. A mathematical model was developed using standard transport equations incorporating all heat transfer coefficients to calculate the time for solidification of metal in casting and computer simulation of the model was carried out in C++ to validate the model. The metal used was pure iron casted in investment molds of silica sand with zircon coating. It was shown that airflow near the mold surfaces was partially restricted due to geometry of the molds and arrangement of the pieces around a tree. So, the changes in heat transfer coefficient also contribute towards time of solidification. The time calculated was found to be in good agreement with experimental values.     

精铸工艺对重型燃机叶片质量的影响研究

采用数值模拟的方法,研究精铸工艺参数对某重型燃机叶片铸件质量的影响规律,优化工艺参数,指导生产实际。研究结果表明：在文章研究范围内,随着浇注温度的升高,叶根缺陷大幅度减少,叶身缺陷变化不大;随着模壳温度的升高,叶身的缺陷大幅度增多,叶根缺陷略有下降,叶顶缺陷变化不明显;随着模壳厚度的增加,叶根和叶身的缺陷急剧减少,叶顶的缺陷变化不明显。     

A Numerical Study of 3D Turbulent Melt Flow and Solidification in a Direct Chill Slab Caster with a Porous Combo Bag Melt Distributor

A 3D turbulent melt flow and solidification of an aluminum alloy (AA-1050) for an industrial-sized direct chill slab casting process is modeled. The melt is delivered through a rectangular submerged nozzle and a non-deformable combo bag fitted with a bottom porous filter. The non-Darcian model, incorporating the Brinkman and Forchheimer extensions, is used to characterize the turbulent melt flow behavior passing through the porous filter. The casting speed and the effective heat transfer coefficient at the metal–mold contact region within the mold are varied. The above two parameters are found to have significant influence on the solidification process.     

SOLIDIFICATION OF A PURE METAL WITH FINITE THERMAL CAPACITANCE ON A SINUSOIDAL MOLD SURFACE

Previous models of mold microgeometry-induced gap nucleation during pure metal solidification neglected the thermal capacitance of the solidifying shell: this is equivalent to the assumption that the shell has a small Stefan number. Although this assumption leads to steady heat conduction in the shell, and hence simplifies the solution for the thermal field, the corresponding assumption of a small Stefan number material is generally not appropriate for metals. In the present work, we remove the small Stefan number restriction used in a previous model for solidification of a pure metal on a rigid, perfectly conducting mold. The mold has a sinusoidal surface microgeometry for which the ratio of the amplitude to the wavelength is much less than one. This makes the aspect ratio a convenient perturbation parameter. Molten metal initially at its fusion temperature is assumed to wet the mold surface perfectly, which is held a constant temperature below the fusion temperature. The temperature field in the growing metal shell is numerically evaluated, and the instantaneous temperature field is incorporated into an analytical solution for the stress field in the shell. The evolving thermomechanical distortion of the shell is modeled assuming that the shell material follows a thermohypoelastic constitutive law that is a rate formulation of thermoelasticity. The contact pressure profile at the shell/asperity interface, which is indicative of shell distortion due to the asperity geometry, is obtained from the stress field. The effects of the mold wavelength and shell thermal capacitance on the contact pressure, temporal and spatial evolution of gap nucleation at the shell/mold interface, and mean shell thickness are examined for pure aluminum and iron shells.     

Role of the Mold Properties on Gap Nucleation in Solidification

The role of the mold properties on gap nucleation in pure metal solidification is investigated. The mold is assumed to be finite and deformable, and has a sinusoidal surface micro-geometry. Unlike previous models, the model developed herein assumes that the mold material has a non-negligible thermal capacitance. Of particular interest are the roles played by the mold thickness and mold thermal capacitance on the existence of critical mold surface wavelength that corresponds to the situation where both contact pressure and its time derivative simultaneously fall to zero. The present work also assumes that the thermal and mechanical problems in the mold-shell interface are uncoupled. It is shown that the inclusion of the thermal capacitance of the mold material, together with thermal capacitance of the shell and the mold distortion, may be sufficient to predict a critical wavelength beyond which no gap nucleation occurs at the troughs. The role of the mold properties is examined through qualitative comparisons of the present and previous models. Gap nucleation times, associated mean shell thicknesses, and critical wavelengths are calculated for pure copper and pure iron molds under identical process conditions. It is found that a copper mold leads to faster gap nucleation compared to an iron mold. The associated critical wavelengths of iron molds are shown to be larger than those of copper. An optimum mean mold thickness corresponding to the longest gap nucleation time for a given set of process parameters is determined. The effect of the mean pressure on the optimum mold thickness is also investigated.     

Spatial variation of heat flux at the metal–mold interface due to mold filling effects in gravity die-casting

Most of the research work pertaining to metal–mold heat transfer in casting solidification either assumes no spatial variation in the air gap formation or limits the study to only those experimental systems in which air gap formation is uniform. However, in gravity die-casting, filling effects induce variation in thermal field in the mold and casting regions. In this paper, we show that this thermal field variation greatly influences the time of air gap initiation along a vertical mold wall, which subsequently leads to the spatial variation of air gap and in turn, the heat flux at the metal–mold interface.In order to study the spatial variation of heat flux at the metal–mold interface, an experimental setup that involved mold filling was devised. A Serial-IHCP (inverse heat conduction problem) algorithm was used to estimate the multiple heat flux transients along the metal–mold interface. The analysis indicates that the fluxes at different mold segments (bottom, middle, and top) of the metal–mold interface reaches the peak value at different time steps, which shows that the initiation of air gap differs along the mold wall. The experimental and numerical results show that the heat transfer in the mold is two-dimensional during the entire period of phase change, which is initially caused by the filling effects and further enhanced by the spatial variation of the air gap at the metal–mold interface.     

STRAIN RATE RELAXATION EFFECT ON FREEZING FRONT GROWTH INSTABILITY DURING PLANAR SOLIDIFICATION OF PURE METALS,PART 1. UNCOUPLED THEORY

Previous models of thermomechanically induced freezing front growth instability have assumed that the casting accumulates elastic strains as it solidifies. While this assumption is useful in providing insight into solidification thermomechanics, it fails to account for inelastic strains that normally accompany elevated temperature deformations. In this paper, growth instability during solidification of a pure metal is reexamined, assuming that the strain rate within the solidifying shell is the sum of elastic, thermal, and viscous components. This requires that a theoretical framework for plane strain thermoviscoelasticity be developed for a solidifying metal. The viscous component leads to strain rate relaxation within the casting and subsequently influences the evolution of the contact pressure and macromorphology of the freezing front. We define a strain rate relaxation parameter that determines the extent to which the casting deforms due to viscous creep. Both short-time and long-time solutions for the contact pressure are developed and subsequently examined for selected values of the strain rate relaxation parameter. The thermal and mechanical fields are assumed to be uncoupled along the metal /mold interface in the present paper while they are coupled along this interface in the companion paper.     

Fluid flow and heat transfer behavior of liquid steel in slab mold with different corner structures. Part 2: Fluid flow,heat transfer,and solidification characteristics

In this article, the complex transmission behavior was discussed in the slab mold with different corner structures. Results show that the up backflow is stronger than the down backflow. The cooling water temperature rise and heat flux through the wide face in the right-angle mold are the largest, while those through the narrow face in the multichamfered mold are larger than those in the big-chamfered mold. The corner temperature at mold exit of the right-angle, big-chamfered, and multichamfered strand increases. The shell thickness at the narrow face center in the chamfered mold is thinner than that in the right-angle mold.     

GROWTH INSTABILITY DURING PLANAR SOLIDIFICATION WITH A MOLD OF FINITE THERMAL CAPACITY

The temperature and the stress fields in the solidified layer and in the mold of finite thickness for a unidirectional casting process are investigated. Earlier solutions are extended to include the effect of the thermal capacity of the mold on the freezing front growth instability. A numerical solution is obtained for both the heat conduction and the residual stress problem. The results show that the perturbation in contact pressure tends asymptotically to a maximum value at larger times for the lower values of the thermal capacities of the mold materials. The magnitude of the contact pressure perturbation is decreased by the inclusion of the thermal capacity of the mold material, and this effect is enhanced for less distortive and thicker molds. The present article assumes that the thermal and mechanical problems are uncoupled along the casting mold interface. Despite this limitation, the results presented in this article indicate that a mold with a higher thermal capacity (or lower thermal diffusivity) might be less susceptible to thermoelastic instabilities associated with the contact pressure and its dependence on the thermal contact resistance at the casting mold interface.     

Perturbation solution for solidification of pure metals on a sinusoidal mold surface

A linear perturbation method is used to solve two-dimensional heat conduction problem in which a liquid, becomes solidified by heat transfer to a sinusoidal mold of finite thickness. The finite difference method is used to discretize the governing equations. The molten metal perfectly wets the mold surface prior to the beginning of solidification, and this leads to a corresponding undulation of the metal shell thickness. The influence of physical parameters such as the thermal capacities of shell and mold materials, and mold surface wavelength on the growth of solidified shell thickness is investigated. Analytical results are obtained for the limiting case in which diffusivities of the solidified shell and the mold materials are infinitely large, and compared with the numerical predictions to establish the validity of the model and the numerical approach.     

Modeling of transport phenomena in continuous casting of non-dendritic billets

A macroscopic model for simulating the phase change process and transport of solid fraction is developed for the case of solidification during direct chill continuous casting of a non-dendritic Al-alloy billet, in presence of electromagnetic stirring. Maxwell’s equations are solved to obtain the electromagnetic force field, which is incorporated in the momentum conservation equations as body force source terms. Thereafter, the complete set of equivalent single-phase governing equations (mass, momentum, energy, species conservation and transport of solid fraction) are solved using a pressure-based finite volume method. A variable viscosity approach is employed to model fluid flow in presence of phase change. The model is first validated against some experimental and numerical results available in the literature, pertaining to the case of conventional continuous casting without any externally imposed stirring. The model predicts the temperature, velocity, species and most importantly, the solid fraction distribution in the mold. These predictions are then used for studying the influence of initial superheat, stirring intensity and cooling rate on the macroscopic behavior of the system.     

A THERMOMECHANICAL MODEL OF SOLIDIFICATION ON A MOLD MOVING WITH CONSTANT VELOCITY

A thermomechanical model of pure metal solidification on a moving mold plate is considered. The goal of the model is to obtain a formula for the contact pressure at the shell/mold interface as the mold moves into the molten liquid. From the contact pressure it is possible to infer the effects of the mold velocity and the mold microgeometry on the time and location of gap nucleation which results from irregular distortion of the shell as it grows from the melt. The mold, which moves at a constant velocity into the molten liquid, has a sinusoidal surface with a low aspect ratio: this means that its wavelength greatly exceeds its amplitude. The mold is of infinite area and is assumed to be perfectly conducting and thermomechanically rigid. We therefore neglect the complexities associated with the physics of edge constraints and/or free boundaries of the solidifying shell and the interacting distortions between deformable mold and shell materials along their interface. The ratio of the velocity of the solid/liquid interface to the mold velocity is identified as another dimensionless parameter in the analysis. In order to arrive at an analytical solution for the contact pressure along the shell/mold interface, we assume that this parameter is small. This makes the velocity ratio a convenient perturbation parameter for the analysis of thermomechanical distortion of the thin shell material as it grows from the melt. This necessarily limits the analysis to situations where the mold moves at faster rather than slower speeds. It is assumed that there is zero tangential shear stress between the fluid and the solidifying shell. As the molten liquid flows over the mold, it perfectly wets the surface. This precludes wetting effects due to surface tension. A hypoelastic constitutive law, which is a rate formulation of thermoelasticity, is assumed to govern deformation of the shell as it grows from the molten liquid. Latent heat liberated at the freezing front is extracted across a constant contact resistance at the shell/mold interface. Peculiar fluid motion at the tip is neglected. A solution for the contact pressure that is valid near the liquid surface (i.e., the meniscus) is derived from the main theoretical developments. Beyond the time of gap nucleation at the shell/mold interface, the model is no longer valid since it cannot account for gross distortion of the shell (i.e., distortions that greatly exceed the spatial perturbations considered in the model).     

应用三维有限元法分析烧瓦对曲轴的影响

针对连杆轴瓦烧损情况,研究烧瓦对曲轴的影响。采用三维有限元技术计算曲轴的温度场。研究结果表明,由烧瓦所引起的曲轴故障表现为轴颈表面的微裂纹或裂纹。轻微烧瓦使轴颈处于回火状态,轴颈材料由于具有回火脆性而使冲击韧性显著下降,冷却后较高的残余热应力导致裂纹的产生。剧烈烧瓦使轴颈部分处于淬火状态,恶劣的淬火条件使曲轴冷却后产生很大的热应力,淬火热应力超过材料的屈服极限和破断抗力,导致曲轴产生变形甚至开裂。     

不同拉速条件下FTSC结晶器内钢液流动行为的物理模拟研究

通过物理模拟研究FTSC结晶器内的钢液流动行为,考察了拉速对结晶器内液面波动、液面裸露、卷渣及夹杂物去除的影响作用。实验结果表明:在本实验条件下,使用4孔水口浇注会在FTSC结晶器内水口一侧形成4个明显的回流区。随着拉速的增加,结晶器内液面波动逐渐加剧,出现液面裸露及卷渣的几率逐渐增大,夹杂物的去除率逐渐减小。     

Numerical Method for Calculation of Complete Casting Processes—Part I: Theory

This article presents a method for calculation of the complete casting process, including the pouring of the liquid metal into the mold, its solidification, the deformation of the solidified cast, the formation of airgaps between the cast and the mold and their influence on the heat transfer, and the residual stresses. An original phase-change procedure is developed, valid for an arbitrary number of pure metals and/or alloys. A collocated version of a segregated finite-volume method is used to calculate both the liquid metal flow and the deformations and stresses in solids.     

Determination of the interfacial heat transfer coefficient h in unidirectional heat flow by Beck's non linear estimation procedure

In the numerical simulation of casting solidification, the thermal behavior of the casting/mold interface is characterized by the interfacial heat transfer coefficient, ‘h’. The determination of h is difficult as it involves the solution of the Inverse Heat Conduction Problem (IHCP). One of the satisfactory solution procedures for solving the IHCP is the Beck's non linear estimation procedure. In this work, this procedure has been used successfully by the authors for the determination of h in steady state unidirectional heat flow.     

Fluid flow and heat transfer behavior of liquid steel in slab mold with different corner structures. Part 1: Mathematical model and verification

A three-dimensional model considering the fluid and temperature field of the liquid steel and cooling water, along with the copper plate temperature was established to study the fluid flow and heat transfer behavior of liquid steel in slab mold with different corner structures. Then, a two-dimensional stress–strain model was established to calculate the strand shrinkage. The two-dimensional stress and three-dimensional temperature were connected through the thermal resistance. The model was validated by the measured solidification shell, copper plate temperature, and cooling water temperature rise. Results show that this model is suitable to study the complex transmission behavior in slab mold.     

Numerical simulation of the casting process of a wind turbine rotor hub

An integrated numerical model was applied to simulate the mold filling and solidification process as well as predict the occurrence of relative casting defects for a rotor hub casting. The goal was to conduct a numerical experimentation to obtain an optimal alloy design of ductile cast iron for the rotor hub casting. A computer‐aided engineering software based on the finite element method was employed in this study. Numerical simulations were conducted for the rotor hub casting with two different types of alloy composition for ductile cast iron. The mold filling and solidification process were examined to predict the occurrence and extent of casting defects and a better alloy design was then proposed based on the simulated results to alleviate casting defects of the rotor hub casting. Copyright © 2010 John Wiley & Sons, Ltd.