连铸坯微观及宏观偏析数学模型的研究进展

对连铸坯微观和宏观偏析模型及树枝晶间液相流动的研究进展进行了评述，采用近平衡凝固过程溶质再分配理论并结合连铸传热数学模型对连铸坯微观及宏观偏析的定量解析方法进行了分析。     

热边界条件对双辊薄带凝固过程的影响

双辊薄带连铸的宏观温度场和凝固微观组织会受到铸辊和涂层的换热影响。建立了双辊薄带凝固坯壳-涂层-铸辊的物理模型,探究凝固坯壳与涂层间的换热系数(h_1)和涂层与铸辊间的换热系数(h_2)对薄带凝固过程在宏观温度场与微观组织上的影响。研究结果表明:双辊薄带的钢液凝固符合平方根定律;h_1的增大可以有效改善涂层表面裂纹的产生,加快钢液凝固,让铸坯微观组织的平均晶粒面积增大;h_2的增大可以改善涂层剥离情况,但会增加涂层表面开裂的可能,同时能使铸坯微观组织的平均晶粒面积增大。     

用于铸坯凝固的简易微观偏析模型

针对目前微观偏析模型形式复杂、求解困难等问题,在比较了目前几个主要的微观偏析模型的计算结果后,基于Scheil模型的方程形式和CK模型在1℃/s冷却速率下的变化趋势,建立了适合连铸坯凝固的简易微观偏析模型.研究表明,该模型可快速并准确预测枝晶间液相浓度与钢的零强度温度(ZST),并可对连铸坯各元素间宏观偏析的关系进行定量判断,大幅度降低了使用难度.     

激光诱导击穿光谱原位分析仪和电子探针在CrMo耐磨铸钢元素偏析分析中的联合应用

CrMo耐磨铸钢是重要的耐磨钢铁材料,凝固过程中的溶质元素偏析是影响CrMo耐磨铸钢组织和性能的重要因素,了解凝固过程中的溶质元素偏析对于CrMo耐磨铸钢的工业化生产具有重要的借鉴意义。宏观偏析和微观偏析是衡量材料偏析程度的两个指标,准确的测量其偏析状况是研究溶质元素偏析的基础。实验以CrMo耐磨铸钢为研究对象,采用激光诱导击穿光谱原位分析仪(LIBSOPA)和电子探针(EPMA)分析钢锭不同部位的宏观偏析和凝固组织中的微观偏析,结果发现,Cr、V和Mn元素在CrMo耐磨铸钢铸锭中宏观偏析程度较小,偏析比接近1,而Mo元素宏观偏析程度较大,其最大宏观偏析比超过1.20;Cr、Mo、V和Mn元素在CrMo钢凝固组织中均存微观偏析,且随着冷却速度的增加,Cr、Mo、V和Mn微观偏析程度也随之增加,其最大微观偏析比分别为1.39、2.63、3.47和1.83。LIBSOPA与EPMA在CrMo耐磨铸钢元素偏析分析中的联合应用,对全面了解CrMo钢铸锭元素偏析,优化铸造以及后续的热加工工艺具有重要借鉴意义。     

连铸坯的半宏观偏析

1.序言现已查明,在连铸坯轴心部位存在的偏析中,历来认为不成问题的小型偏析(半宏观偏析),也是妨碍钢板质量均质性的重要因素。因此,人们开始重视半宏观偏析问题,并对连铸条件、凝固组织的影响和偏析程度等进行了调查研究。半宏观偏析主要是伴随凝固收缩而形成的高浓度液相的流动、积聚凝固而产生的。它的大小介于宏观偏析和微观偏析之间。     

薄板坯连铸及其凝固机理研究

摘自冶金部钢铁研究总院研究生干 勇的博士学位论文,导师:李文采。 本文针对铸态组织质量的关键问题之一——柱状晶和等轴晶的竟相生长机理,通过宏观和微观分析,建立了一个适合薄板坯凝固全过程中柱状晶一等轴晶转变(CET)的整体模型。以该模型的概念为基础开发的计算模型结果,通过30%氯化铵溶液和碳钢凝固试验加以比较,结果相当一致,所得结论     

影响连铸传输模型精度的热物理性质

对影响连铸过程动量、能量及溶质传输模型计算精度的几个最重要的热物理性质(即钢的密度、导热系数和溶质分配系数)在凝固过程中的变化情况进行了考虑.根据Fe-C二元平衡相图以及宏观传输-微观偏析计算获得了Q235钢连铸过程中局部热物理性质与相组成及温度之间的函数关系式,为连铸传输模型数值计算的精确度提供了保证.     

耦合枝晶凝固微观特性的连铸宏观传输模型

在建立的连铸三维宏观传输数学模型中,对枝晶凝固微观结构参数的影响效果进行了充分地耦合研究。采用微观偏析半解析模型对浇铸钢种的非平衡凝固路径进行近似确定;采用复合理论方法对两相糊状区的渗透特性加以描述;在确定多孔介质的渗透率时,考虑了枝晶凝固模式的影响效果。应用该三维耦合模型,并结合早前建立的连铸二维传热模型,针对某钢厂方坯连铸机进行了复合数值模拟研究,且研究成果已投入到铸机的实际生产中。现场生产状况表明,仿真结果具有较好的合理性和实用性,说明耦合模型具有良好的仿真精度,可广泛应用于实际连铸过程的数值仿真研究中。     

用蒙特卡罗法模拟连铸坯的凝固组织

为了创建一种直接以图形显示晶粒形貌的连铸坯凝固组织计算机模拟方法,结合宏观传热计算和凝固理论,用改进的蒙特卡罗法建立了连铸坯凝固组织的计算机仿真模型。用此模型模拟了硅钢连铸坯的凝固组织并与实际铸坯的宏观组织进行了对比,模拟结果与实际结果基本吻合。在此基础上还模拟了不同过热度下铸坯的凝固组织。     

连铸坯凝固晶粒组织的模拟

本文的目的在于创建一种直接以图形显示晶粒形貌的连铸坯凝固组织计算机模拟方法.结合宏观传热计算与凝固理论,用改进的蒙特卡罗法建立了连铸坯凝固组织的计算机仿真模型.用本文的模型模拟了硅钢连铸坯的凝固组织并与实际的铸坯宏观组织进行了对比,模拟结果与实际结果基本吻合.在此基础上模拟了不同过热度下铸坯的凝固组织.     

Modeling of equiaxed microstructure formation in casting

A general micro/macroscopic model of solidification for 2-D or 3-D castings, valid for both dendritic and eutectic equiaxed alloys, is presented. At the macroscopic level, the heat diffusion equation is solved with an enthalpy formulation using a standard FEM implicit scheme. However, instead of using a unique relationship between temperature and enthalpy (i.e., a unique solidification path), the specific heat and latent heat contributions, whose sum equals the variation of enthalpy at a given node, are calculated using a microscopic model of solidification. This model takes into account nucleation of new grains within the undercooled melt, the kinetics of the dendrite tips or of the eutectic front, and a solute balance at the scale of the grain in the case of dendritic alloys. The coupling between macroscopic and microscopic aspects is carried out using two time-steps, one at the macroscopic level for the implicit calculation of heat flow, and the other, much finer, for the microscopic calculations of nucleation and growth. This micro/macroscopic approach has been applied to one-dimensional and axisymmetric castings of Al-7 pct Si alloys. The calculated recalescences and grain sizes are compared with values measured for one-dimensional ingots cast under well-controlled conditions. Furthermore, the influence of casting conditions on temperature field, undercooling, grain size, and microstructural spacings is shown to be predicted correctly from axisymmetric calculations with regard to the expected experimental behavior.     

Heat transfer-solidification kinetics modeling of solidification of castings

A close examination of the recent developments in the field of computer simulation of solidification process reveals that a combination of both macroscopic and microscopic models is necessary in order to accurately describe the solidification of castings. Currently available macroscopic models include models that describe heat transfer from metal to mold, fluid flow of liquid metal during mold filling, and stress field in the casting. At the microscopic level, the models should include more intricate issues such as solidification kinetics and fluid flow in the mushy zone. Although significant progress has been accomplished over the years in each field, the task of including all of these models into a comprehensive package is far from being complete. This paper describes the state of the art on coupling the macroscopic heat transfer (HT) and microscopic solidification kinetics (SK) models and introduces thelatent heat method as a more accurate method for solving the heat source term in the heat conduction equation. A new method for calculation of fraction of solid evolved during solidification based on computer-aided cooling curve analysis (CA-CCA), as well as a method based on nucleation and growth kinetics laws, is discussed. A new nucleation model based on the concept of instantaneous nucleation, which is used to describe equiaxed eutectic solidification of commercial alloys, has been introduced. It is demonstrated that the instantaneous nucleation model agrees well with the experimental results in terms of cooling curves and of evolution of the fraction of solid during solidification. Validation results are also shown for SK models that are based on CA-CCA coupled with HT models for eutectic Al-Si and gray cast iron alloys.     

Modeling the discontinuous liquid flow in a blast furnace

This article presents a mathematical model to describe the discontinuous flow of an isothermal liquid in packed beds, simulating in part the flow condition in and below the blast furnace cohesive zone. The model is developed based on a force balance approach to describe the discrete liquid flow and a stochastic treatment to take into account the complex packing structure. The interaction between gas and liquid flows has also been included in the governing equations, so that the localized liquid flow in a packed bed can be modeled with or without gas flow. The difference between the microscopic and macroscopic approaches is discussed, and it is argued that at this stage of development, liquid flow modeling should be conducted at the macroscopic level. Techniques for numerical solution are provided. The validity of the proposed model is demonstrated by comparing model predictions with measurements obtained using a two-dimensional cold model apparatus under different gas and/or liquid flow conditions.     

The portevin-Le Chatelier effect in deformation with constant stress rate

A mathematical model is presented which provides a link between the microscopic and the macroscopic aspects of nonuniform plastic flow associated with the Portevin-Le Chatelier (PLC) effect. As in an earlier model due to Penning, the local relation between the stress and the strain rate is given by a function F(g3) which may be decreasing in a certain range of strain rates. The macroscopic behavior is obtained by summing up the contributions to the total strain rate from the individual cross-sections over the whole specimen length. It is shown that the nonlinear differential system describing the PLC effect for the case of loading with constant stress rate (both with and without recovery) can be solved exactly. The PLC effect in pure creep is then analyzed in a natural way, as a limiting case of zero stress rate. The conditions for the occurrence of propagating deformation bands are found and their characteristics are analytically expressed in terms of the experimental parameters and of the parameters associated with the dynamics of dislocations. The formulae obtained make it possible to calculate macroscopic deformation curves, incorporating the PLC effect, on the basis of microscopic models and thus provide a means of checking on their applicability via mechanical testing.     

A volume-averaged two-phase model for transport phenomena during solidification

A basic model of the transport phenomena occurring during solidification of multicomponent mixtures is presented. The model is based on a two-phase approach, in which each phase is treated separately and interactions between the phases are considered explicitly. The macroscopic transport equations for each phase are derived using the technique of volumetric averaging. The basic forms of the constitutive relations are developed. These relations link the macroscopic transport phenomena to microscopic processes such as microstructure development, interfacial stresses, and interfacial heat and mass transfer. Thermodynamic relations are presented, and it is shown that nonequilibrium effects can be addressed within the framework of the present model. Various simplifications of the model are examined, and future modeling needs are discussed.     

Soil-Water Characteristic Curves and Dual Porosity of Sand–Diatomaceous Earth Mixtures

The soil-water characteristic curves (SWCCs) for sand–pelletized diatomaceous earth mixtures are measured. The measured SWCCs are bimodal due to two distinct pore-size distributions associated with the microscopic (intrapellet) and macroscopic (interpellet) porosity regions of the pelletized diatomaceous earth. The measured data for the bimodal SWCCs are fit with modified forms of the Brooks-Corey, van Genuchten, and Fredlund-Xing SWCC functions, and the microscopic and macroscopic porosity portions of the mixtures are determined from the SWCC fits. Both the total and the microscopic porosity of the mixtures increase with increased percentage by dry weight of diatomaceous earth in the mixtures. However, the macroscopic porosity of the mixtures is essentially independent of the diatomaceous earth content due to the similarity in the particle-size distributions of the sand and the diatomaceous earth. The results suggest that sand–diatomaceous earth mixtures may be useful in applications where an increase in water-holding capacity (that is, relative to sand) is desired, such as in landfill covers. In such applications, a balance between the increase in cost and the increase in water-holding capacity due to the use of the diatomaceous earth must be achieved.     

Equiaxed dendritic solidification with convection: Part I. Multiscale/multiphase modeling

Equiaxed dendritic solidification in the presence of melt convection and solid-phase transport is investigated in a series of three articles. In part I, a multiphase model is developed to predict com-position and structure evolution in an alloy solidifying with an equiaxed morphology. The model accounts for the transport phenomena occurring on the macroscopic (system) scale, as well as the grain nucleation and growth mechanisms taking place over various microscopic length scales. The present model generalizes a previous multiscale/multiphase model by including liquid melt convec-tion and solid-phase transport. The macroscopic transport equations for the solid and the interdendritic and extradendritic liquid phases are derived using the volume averaging technique and closed by supplementary relations to describe the interfacial transfer terms. In part II, a numerical application of the model to equiaxed dendritic solidification of an Al-Cu alloy in a rectangular cavity is dem-onstrated. Limited experimental validation of the model using a NH₄C1-H₂O transparent model alloy is provided in part III.     

Quantifying the radiation dosage to individual skeletal lesions treated with samarium-153-EDTMP

Samarium-153ethylenediaminetetramethylenephosphonate (EDTMP) is used in the treatment of painful skeletal lesions. This study attempted to quantify the radiation dosage to individual lesions on both the macroscopic and microscopic level. METHODS: A gamma camera-based quantification technique was adapted and refined for 153Sm. The accuracy of the technique was determined by using a realistic phantom. The activity and volume of lesions as well as normal bone were determined and used to estimate the radiation dosages to these regions. Two patients died of unrelated causes shortly after receiving 153Sm-EDTMP. This made it possible to compare the gamma camera results with direct measurements. It also allowed for autoradiographic examination of the lesions. Finally, the microscopic radiation dosages were estimated. RESULTS: The phantom study indicated that the quantification technique was off, on average, by 4.1% (s.d. = 8.1%). The absolute activity concentration of trabecular bone was found to be approximately 0.22 MBq/g, and that of cortical bone was found to be approximately 0.1 MBq/g, regardless of the dosage administered. The corresponding concentrations for lesions were between 3 and 7 times higher than that of normal bone, with no apparent ceiling. From these results, the macroscopic radiation dosage could be estimated. The dosage to normal bone varied between 0.9 and 3.9 cGy x kg/MBq, and that of the lesions varied between 5.2 and 27.1 cGy x kg/MBq. The autopsy results confirmed that the gamma camera technique was accurate. The autoradiography showed clearly that the activity was associated with the surface of the bone. From these findings, the microscopic radiation dosage distribution was estimated for cortical and trabecular bone as well as osteoblastic lesions. The variation in the microscopic dosage compared to the macroscopic dosage was quite large. Microscopic dosages, when compared to the macroscopic dosages, were as high as 965% and as low as 14.9%. CONCLUSION: The techniques used have been proven to be accurate. The activity in normal bone may be at a ceiling value for all the administered doses, which could explain the small variation. This is not true for the lesions. The large variation in dosages on a microscopic scale, combined with the ceiling in normal bone, may explain the lower than expected toxicity and relatively quick relapse of the patients.