A Microscale Model for Ausferritic Transformation of Austempered Ductile Irons

This paper presents a new metallurgical model for the ausferritic transformation of ductile cast iron. The model allows predicting the evolution of phases in terms of the chemical composition, austenitization and austempering temperatures, graphite nodule count, and distribution of graphite nodule size. The ferrite evolution is predicted according to the displacive growth mechanism. A representative volume element is employed at the microscale to consider the phase distributions, the inhomogeneous austenite carbon content, and the nucleation of ferrite subunits at the graphite nodule surface and at the tips of existing ferrite subunits. The performance of the model is evaluated by comparison with experimental results. The results indicate that the increment of the ausferritic transformation rate, which is caused by increments of austempering temperature and graphite nodule count, is adequately represented by this model.

     

Modeling of ferrite growth in nodular cast iron

In nodular cast iron, ferrite forms around the graphite nodules and growth proceeds until pearlite nucleates and consumes the remaining austenite. In order to simulate the structure, it is therefore necessary to have accurate models for the ferrite growth. Some investigators have proposed that the growth is completely governed by carbon diffusion through the ferrite shell. In the present work, it is shown that the ferrite growth in nodular cast iron can be divided into three different stages where the growth initially is governed by carbon diffusion in the austenite until the graphite nodule is entirely enveloped by a ferrite shell. During the second stage, it is proposed that the growth is controlled by the incorporation rate of carbon atoms on the graphite nodule. During the later stages of the transformation, the diffusion distance has increased considerably, and therefore, the diffusion of carbon through the ferrite shell will determine the growth rate.     

A kinetic model of the γ → α + Gr eutectoid transformation in spheroidal graphite cast irons

The eutectoid transformation of austenite in spheroidal graphite cast iron can follow one of two paths: (a) transformation to a mixture of ferrite and graphite or (b) transformation to pearlite. The extents to which the two reactions occur determine the relative amounts of ferrite and pearlite in the microstructure and, hence, the properties of the iron. In this paper, the kinetics of the γ → α+ Gr reaction is studied, and a model is developed to predict the isothermal transformation rates. The transformation occurs at a rate determined by the rate of carbon diffusion. The diffusion of carbon through ferrite, as well as through austenite, has been considered. The model predicts that the volume fraction of austenite transformed isothermally increases with increasing number density of graphite spheroids. Predictions of the model are compared with data available in literature.     

Analysis of Local Conditions on Graphite Growth and Shape During Solidification of Ductile Cast Iron

3D X-ray tomography recordings have been used to study graphite growth during solidification of ductile cast iron. Using data from such recordings, it is shown how local growth conditions influence growth rate and morphology of nodules during solidification. Experiments show that it is common for nodules to gradually change shape during solidification so that sphericity decreases. It is also found that different shaped nodules can evolve in direct contact with liquid iron and also after they are encapsulated in austenite. It is observed that a significant proportion of originally complete spherical nodules become less spherical via formation of protrusions on the surface; these new surfaces are observed to grow relatively faster. It is shown that encapsulation of the graphite nodule by austenite may be incomplete and that at the end of solidification, partial encapsulation and the effect of the number of nearest graphite nodules play a crucial role in determining the final graphite morphology.     

Thermal Microstructural Multiscale Simulation of Solidification and Eutectoid Transformation of Hypereutectic Gray Cast Iron

Although the gray cast iron solidification process has been the subject of several modeling studies, almost all available models appear to deal with only the more widely used hypoeutectic compositions. Models related to hypereutectic gray iron compositions with lamellar (or flake) graphite, and in particular for the proeutectic and eutectoid zones, are hard to find in the open literature. Hence, in the present work, a thermal microstructural multiscale model is proposed to describe the solidification and eutectoid transformation of a slightly hypereutectic composition leading to lamellar graphite gray iron morphology. The main predictions were: (a) temperature evolutions; (b) fractions of graphite, ferrite, and pearlite; (c) density; and (d) size of ferrite, pearlite, and gray eutectic grains; (e) average interlamellar graphite spacing; and (f) its thickness. The predicted cooling curves and fractions for castings with two different compositions and two different pouring temperatures were validated using experimental data. The differences between this model and existing models for hypoeutectic compositions are discussed.     

Modelling of austenite decomposition of hot‐rolled plain carbon steels under complex cooling conditions

The purpose of the present work is to develop a mathematical model allowing the simultaneous prediction of both transformation product portions and mean ferrite grain size from the same common principles as a result of austenite decomposition during continuous cooling of plain carbon steels. The transformation products considered specifically are polygonal ferrite and pearlite. The model is based on the classical equations of nucleation‐growth theory and also contains some empirical parameters. The chemical driving forces for nucleation and composition of elements at the phase interfaces are derived from thermodynamic analysis. Three modes of ferrite nucleation are taken into account that correspond to the nucleation on the austenite grain corners, edges and faces. The model considers the reduction of the nucleation sites due to the occupation of austenite grain boundary surface by ferrite grains. Pearlite transformation starts at the γ/α interface and suppresses further ferrite grain growth. The parameters related to ferrite reaction were determined on the basis of a series of austenite transformation kinetic curves and grain size measurements for a steel with the composition 0.084%C‐0.58%Mn‐0.02%Si obtained by dilatometric technique for cooling rates from 0.032 to 2.5 K/s. The parameters related to pearlite reaction were determined on the basis of the data for a steel with 0.66%C. After determination of the model parameters the model was applied to complex cooling conditions of the run‐out table of the hot strip mill at Voest‐Alpine Stahl Linz GmbH. Predicted ferrite grain size appeared to be 1.2 ?1.3 times smaller than the observed one. With regard to experimental data on grain growth in iron, it was suggested that the underestimation of grain size is due to additional ferrite grain growth occurring after the coiling of the steel sheet. Taking that into account provided satisfactory agreement with observed values.     

Role of Sulfur on the Transition from Graphite to Cementite Eutectic in Cast Iron

In the current study, an analytic solution is considered to explain the influence of sulfur on the transition from graphite to cementite eutectic in cast iron. The outcome from the current study indicates that this transition can be related to (a) the graphite nucleation potential (directly characterized by the cell count and indirectly by the nucleation coefficients; (b) the eutectic graphite growth rate coefficient; (c) the temperature range between the equilibrium temperature for graphite eutectic and the formation temperature for cementite eutectic; and (d) the liquid volume fraction, after pre-eutectic austenite solidification. In addition, the absolute and the relative chilling tendencies, as well as critical cooling rates including the chill width of the cast iron can be predicted from the current study. The analytic model was experimentally verified for castings with various sulfur contents. It is found that the main role of sulfur on the transition from graphite to cementite eutectic is through its effect on lowering the growth coefficient, and hence, the graphite eutectic growth rate. In addition, it is found that with the increasing sulfur content, the critical cooling rate is significantly reduced, thus increasing the absolute and the relative chilling tendency values, including the chill width.     

Stable Eutectoid Transformation in Nodular Cast Iron: Modeling and Validation

This paper presents a new microstructural model of the stable eutectoid transformation in a spheroidal cast iron. The model takes into account the nucleation and growth of ferrite grains and the growth of graphite spheroids. Different laws are assumed for the growth of both phases during and below the intercritical stable eutectoid. At a microstructural level, the initial conditions for the phase transformations are obtained from the microstructural simulation of solidification of the material, which considers the divorced eutectic and the subsequent growth of graphite spheroids up to the initiation of the stable eutectoid transformation. The temperature field is obtained by solving the energy equation by means of finite elements. The microstructural (phase change) and macrostructural (energy balance) models are coupled by a sequential multiscale procedure. Experimental validation of the model is achieved by comparison with measured values of fractions and radius of 2D view of ferrite grains. Agreement with such experiments indicates that the present model is capable of predicting ferrite phase fraction and grain size with reasonable accuracy.     

Thermal dependence of austempering transformation kinetics of compacted graphite cast iron

The evolution of the relative fraction of high-carbon austenite with austempering time and temperature was analyzed in a compacted graphite (CG) cast iron (average composition, in wt pct: 3.40C, 2.8Si, 0.8Mn, 0.04Cu, 0.01P, and 0.02S) at five different austempering temperatures between 573 and 673 K. Samples were characterized by Mössbauer spectroscopy, hardness measurements, and optical microscopy. During the first stage of transformation, the kinetics parameters were determined using the Johnson-Mehl’s equation, and their dependence with temperature in the range from 573 to 673 K indicates that the transformation is governed by nucleation and growth processes. The balance between growth-rate kinetics and nucleation kinetics causes the kinetics parameter (k) to have a maximum at ≈623 K of 3.9×10^?3(s^?1). The evolution of the C content in the high-carbon austenite was found to be controlled by the volume diffusion of carbon atoms from the ferrite/austenite interface into austenite, with a dependence of t ^0.40±0.05 on the austempering time (t).     

Modeling of the liquid/solid and the eutectoid phase transformations in spheroidal graphite cast iron

A model of phase transformations in spheroidal graphite (SG) cast iron has been developed to quantitatively describe the microstructural evolution during solidification and the subsequent solid-state phase transformations (eutectoid reaction) during continuous cooling and to predict some of the microstructural characteristics of final phases formed in SG iron castings. Such characteristics include phase fractions, phase spacings, and grain dimensions. In the model, the nucleation and growth of primary dendrites and eutectics were described based on existing theories, whereas the mathematical formulation for the eutectoid reaction,i.e., the formation of pearlite and ferrite from the as-cast austenite, was developed based on theories as well as physical evidence obtained from the experimental work. The Johnson-Mehl equation and the Avrami equation were used to calculate the fraction of transformed phases under continuous cooling conditions. The role of the grain impingement factor used in these two equations and the significance of the additivity principle in treating nonisothermal transformations were briefly discussed. The latent heat method was used for the numerical treatment of the release of latent heat during phase transformations. A two-dimensional finite element code which can be used in either Cartesian or cylindrical coordinates (ALCAST-2D) was used to solve the time-dependent temperature distribution throughout the metal/mold system. Numerical predictions were validated against experimental results, and good agreement was obtained. DONGKAI SHANGGUAN, Previously Assistant Research Engineer, The University of Alabama,     

Analysis of the Grain Size Evolution for Ferrite Formation in Fe-C-Mn Steels Using a 3D Model Under a Mixed-Mode Interface Condition

A 3D model has been developed to predict the average ferrite grain size and grain size distribution for an austenite-to-ferrite phase transformation during continuous cooling of an Fe-C-Mn steel. Using a Voronoi construction to represent the austenite grains, the ferrite is assumed to nucleate at the grain corners and to grow as spheres. Classical nucleation theory is used to estimate the density of ferrite nuclei. By assuming a negligible partition of manganese, the moving ferrite–austenite interface is treated with a mixed-mode model in which the soft impingement of the carbon diffusion fields is considered. The ferrite volume fraction, the average ferrite grain size, and the ferrite grain size distribution are derived as a function of temperature. The results of the present model are compared with those of a published phase-field model simulating the ferritic microstructure evolution during linear cooling of an Fe-0.10C-0.49Mn (wt pct) steel. It turns out that the present model can adequately reproduce the phase-field modeling results as well as the experimental dilatometry data. The model presented here provides a versatile tool to analyze the evolution of the ferrite grain size distribution at low computational costs.     

A process model for the microstructure evolution in ductile cast iron: Part I. the model

In the present investigation, the multiple phase changes occurring during solidification and subsequent cooling of near-eutectic ductile cast iron have been modeled using the internal state variable approach. According to this formalism, the microstructure evolution is captured mathematically in terms of differential variation of the primary state variables with time for each of the relevant mechanisms. Separate response equations have then been developed to convert the current values of the state variables into equivalent volume fractions of constituent phases utilizing the constraints provided by the phase diagram. The results may conveniently be represented in the form of C curves and process diagrams to illuminate how changes in alloy composition, graphite nucleation potential, and thermal program affect the microstructure evolution at various stages of the process. The model can readily be implemented in a dedicated numerical code for the thermal field in real castings and used as a guiding tool in design of new treatment alloys for ductile cast irons. An illustration of this is given in an accompanying article (Part II).     

CSP 流程低碳铝镇静钢铸坯碳覆夹杂物析出行为

在使用 CSP 工艺生产低碳或超低碳钢时,在铸坯中,特别是铸坯宽面的中心经常观察到相当数量的微米级碳覆夹杂物.通过对 CSP 流程不同的钢种铸坯取样,研究了这类夹杂物的结构特点和析出机制.指出碳覆夹杂物呈双层结构,外面包裹一层富碳层、中心为钙铝酸盐或含 CaO 的复合夹杂物.热力学计算结果显示这层富碳物质并非 CaC2.通过对比球墨铸铁中球状石墨的形成条件,指出 CSP 铸坯中存在冷却速度快、S 元素含量低、加钙处理后促球化元素 Ca、Mg 含量相对较高,有大量夹杂物作为形核核心等促进碳覆夹杂物析出的有利条件.C 为易偏析元素,在低碳或超低碳钢铸坯凝固过程中液芯中 C 含量的升高,能够析出球状的碳覆夹杂物.并指出由于碳覆夹杂物的析出,中心钢基体 C 含量降低,碳覆夹杂物析出能够减轻铸坯凝固过程中 C元素的偏析程度.     

Nodule Evolution of Ductile Cast Iron During Solidification

Ductile cast irons are ferrous alloys in which precipitation of graphite in the form of spherical nodules is embedded in a metal matrix to obtain ductility on the material. Despite the importance of the shape of the nodules, the models proposed to predict the solidification of ductile irons assume a perfect spherical shape during the growing process up to the final solidification of the material, which is proved not to be the case in all castings depending on the processing conditions. The influence of the process parameters on the geometry of the nodules in ductile irons was experimentally evaluated and a model to predict the evolution of nodules during solidification was proposed. The proposed model for growth predicts changes in the nodule count as well as in the nodularity based on different laws for carbon diffusion according to the solid fraction, helping to understand the trends found experimentally.     

Phase-field model prediction of nucleation and coarsening during austenite/ferrite transformation in steels

A phase-field simulation is performed to study the kinetics of austenite to ferrite (γ → α) transformation in a low-carbon steel during continuous cooling. Emphasis is placed on the influence of nucleation, along with ferrite grain coarsening behind the transformation front, on microstructural evolution. Results show that grain coarsening is significant even before all nucleation has been completed and occurs via two different coarsening mechanisms, grain boundary migration and ferrite grain crystallographic rotation, both of which can be clearly observed occurring as the simulated microstructure evolves. For some grains, sudden growth jumps are predicted by the model—a phenomenon that has been observed before by synchrotron X-ray diffraction. This study quantitatively demonstrates the phenomenon that increasing cooling rate leads to nucleation off initial austenite grain boundaries, which is also verified by studying the morphology of ferrite grains as predicted using different nucleation mode assumptions. A relationship between nucleation site distribution and the nucleation rate is demonstrated by computer simulation.     

Thermomechanical processing of microalloyed powder forged steels and a cast vanadium steel

The effects of controlled rolling on transformation behavior of two powder forged (P/F) microalloyed vanadium steels and a cast microalloyed vanadium steel were investigated. Rolling was carried out in the austenitic range below the recrystallization temperature. Equiaxed grain structures were produced in specimens subjected to different reductions and different cooling rates. The ferrite grain size decreased with increasing deformation and cooling rate. Ferrite nucleated on second phase particles, deformation bands, and on elongated prior austenite grain boundaries; consequently a high fractional ferrite refinement was achieved. Deformation raised the ferrite transformation start temperature while the time to transformation from the roll finish temperature decreased. Cooling rates in the cast steel were higher than in P/F steels for all four cooling media used, and the transformation start temperatures of cast steels were lower than that of P/F steel. Intragranular ferrite nucleation, which played a vital role in grain refinement, increased with cooling rate. Fully bainitic microstructures were formed at higher cooling rates in the cast steel. In the P/F steels inclusions and incompletely closed pores served as sites for ferrite nucleation, often forming a ‘secondary’ ferrite. The rolling schedule reduced the size of large pores and particle surface inclusions and removed interconnected porosity in the P/F steels. Formerly Postgraduate Researcher in the Department of Metallurgy and Materials Science, UMIST/University of Manchester, United Kingdom     

热轧低碳钢不同冷却模式下的相变模拟与验证

利用计算机模拟技术，研究了控轧控冷中输出辊道上冷却模式对低碳钢相变的影响。以低碳钢SS400为例，针对鞍钢热轧带钢厂1780生产线，计算了输出辊道上3种不同冷却模式下低碳钢的相变行为，包括铁素体转变开始温度、组成相体积分数随时间的变化以及铁素体体积分数沿带钢长度方向的分布。研究表明，冷却模式对输出辊道上带钢的温度一时间曲线、铁素体转变开始温度及组成相的演化过程影响较大，但对最终组成相的体积分数影响较小。     

稀土变质铸铁中石墨—奥氏体共晶的生长方式

用Ｂｒｉｄｇｍ ａｎ 定向凝固技术制取了稀土变质共晶铸铁不同石墨形态时的液－固平界面试样。观察结果表明,稀土变质铸铁共晶凝固过程中,石墨相不论形态如何均为领先相;石墨与奥氏体共晶有共生生长和离异生长两种生长方式。在共生生长情况下,奥氏体紧贴石墨片两侧协同生长,形成锯齿状的液－固界面结构;在离异生长情况下,石墨相单独在液相中析出并充分长大,随后被奥氏体包围,液－固界面形态主要取决于奥氏体－液相界面的稳定性。分析表明,稀土在石墨－液相界面的富集是导致石墨－奥氏体共晶离异生长的主要原因。