Numeric simulation of the solidification of the pure iron varying the solidification process parameters 

A.C. Mossi ¹ and M.M. Pariona² 

¹Profesor del Departamento de Matemática e Estadística y del Postgrado de Ingeniería e Ciencia de Materiales. ²Aluno de Iniciación Científica, Universidad Estadual de Ponta Grossa. Universidad Estadual de Ponta Grossa, Campus Uvaranas, Bloco CIPP, Laboratório Limac, CEP 84030-900, Uvaranas. Ponta Grossa – PR, Brasil. Fone (042) 220-3056.  E-mail: mmpariona@uepg.br 

Abstract 

In the study reported in this work, two-dimensional numerical simulations were made of pure iron solidification in industrial AI 50/60 AFS greensand and mullite molds, using the finite element technique and the ANSYS software program. For this purpose, the thermophysical properties of iron were considered temperature-dependent, while for sand and mullite these properties were considered constant, and the convection phenomenon was also considered on the external surface of the mold. In order to study the influences of the parameters in the solidification process, such as, sand and mullite mold types, preheating temperature of the mold (ambient and heated), superheating temperature of the liquid metal and loss of heat on the mold by convection, the optimization through the factorial design was accomplished. Metallurgical characteristics, such as the attack zone in the feed head and hot top, were not taken into account in this study, since they are irrelevant to the behavior of metal to mold heat transfer. Owing to the temperature-dependent thermo-physical properties of iron, this type of problem is of nonlinear characteristic. The results of the heat transfer are shown throughout the 2D system, as thermal flow, thermal gradient, the cooling curves at various points of the solidified specimen were determined, as well as the analysis of the factorial design of the result and heating or/and cooling in the molds were also accomplished. Through the analysis of the factorial design result of the parameters it was found which mold type influences negatively the result and the interaction of the metal temperature with the convection phenomenon contributed significantly to the result. The cooling curves characterize the grain size and mechanical properties of metal; hence, owing to the smaller grain size of metal cast in mullite molds, this type of mold grants better mechanical properties to the cast part. 

Key words: Numerical simulation, finite elements, solidification of iron, sand and mullite molds. 

Simulación numérica de la solidificación del hierro puro variando los parámetros del proceso
de solidificación 

Resumen 

En este trabajo se realizó la simulación numérica en dos dimensiones de la solidificación del hierro en moldes de arena sintética al verde industrial, Al 50/60 y mulita por medio de la técnica de elementos finitos con el programa ANSYS. Las propiedades termofísicas del hierro fueron consideradas dependientes de la temperatura, mientras que estas propiedades para la arena y la mulita se consideraron constantes; adicionalmente, se tomó en cuenta el fenómeno de convección en la superficie externa del molde. Se estudió el efecto de los siguientes parámetros en el proceso de solidificación: tipo de arena y mulita, temperatura de precalentamiento del molde (ambiente y calentado), temperaturas de supercalentamiento del metal líquido y la pérdida de calor por convección en el molde. La optimización de estos parámetros se realizó por el método de diseño factorial. Las características metalúrgicas del cabezal de alimentación y del tope caliente no se consideraron en este estudio, ya que son irrelevantes en el comportamiento de la transferencia de calor entre el metal y el molde. Debido a que las propiedades termofísicas del hierro dependen con la temperatura, este es un tipo de problema de característica no lineal. Los resultados de la transferencia de calor se presentan en un sistema de dos dimensiones para el flujo térmico, el gradiente térmico, las curvas de enfriamiento en varios puntos de la pieza solidificada y las curvas de calentamiento y/o enfriamiento en los moldes; así como también, el análisis de los resultados por el método de planeamiento factorial fueron realizados, pues, mediante esta análisis fue encontrado que el tipo de molde influencia negativamente en el resultado, por otro lado, la interacción de la temperatura del metal con el fenómeno de confección contribuyo significativamente en el resultado. 

Palabras clave: Simulación numérica, elementos finitos, solidificación del hierro, moldes de arena y mulita. 

Recibido el 08 de Marzo de 2005 

Introduction 

The technological difficulties involved in casting processes vary considerably according to the melting temperature characteristics of the metal, which in turn are related to the physicochemical properties and structures of metals and alloys. These difficulties also involve a series of properties, which include differences in chemical activities between the elements that constitute the alloy, solubility of the gases, method of solidification among the chemical elements, type of molding, and coefficients of solidification shrinkage [1, 2]. On the other hand, the cooling process is influenced by the flow of molten metal, the mold filling and properties of the metal, all these factors can produce variations in the geometrical dimensions, the shape of the surface finishing and the quality of the cast part [3]. 

The present study investigated the solidification of pure iron in industrial greensand molds, AI 50/60 AFS, and mullite molds (the latter material is frequently used in the Shaw process). The thermo-physical properties were considered as a function of the temperature, i.e., thermal conductivity and enthalpy. The properties of the sand and mullite were considered constant because these temperature-dependent properties were not found in literature. The presence of the convection phenomenon on the external surface of the mold was also taken into account. In order to study with more details the influences of the parameters in the solidification process, such as, sand and mullite mold types, preheating temperature of the mold (ambient and heated), superheating temperature of liquid metal and heat loss on the mold for convection, a factorial design of these parameters to optimize the process was accomplished. This type of problem has a nonlinear characteristic and was solved by means of the finite element method and, to render the solution feasible, the convergence was controlled. 

The purpose of this work was to make a comparative study of the different types of molds, varying those parameters. As a result, heat transfer was observed in the cast metal, at the interface and in the mold, as well as cooling curves at different points in the cast metal, beyond that, heating and cooling curves at different points in the mold. Thus, the microstructural quality and mechanical properties of the cast part depend not only on the casting technique employed, but also on the characteristics and properties of the molding process and cast metal used. 

Numerical Simulation 

Solidification is accompanied by the release/absorption of latent heat at the solid-liquid and solid-solid interfaces. Consequently, solidification process involves phase changes, in this case, the enthalpy method is the more appropriated modeling to describe this process, because in this method the latent heat is inserted in enthalpy, which represents the phase transformation. Then, the differential equation of thermal flow for the transient nonlinear state that describes this phenomenon was presented as proceeds [4-6]: 

,    (1) 

where the enthalpy, subject to the convective boundary condition: 

     .        (2) 

where q is the heat, K is the thermal conductivity, c is the specific heat, and r is the density of the material. These properties may be temperature-dependent, in which case equation (1) is transformed into a nonlinear transient equation. h_f is the coefficient of convective heat transfer on the mold’s external surface, T is the temperature, and T_B is the temperature of the environment. 

Through equations (1) and (2) one can determine the distribution of temperature or transfer of heat during the process of solidification in the casting of pure iron in sand or mullite molds. In this case, the solution of those equations were considered in 2-D. 

Methodology of the Numerical Simulation 

The finite element method studied by several authors [6-10]. Software programs were used to simulate the solidification of pure iron in greensand and mullite molds, with the aid of a Pentium III 1GHz microcomputer. The following procedures were adopted for the simulations: 

a. The geometric project for sand or mullite mold is illustrated in Figure 1 (a), which represents the symmetry in three-dimensions, showing the entry of the cast metal in the upper part of the figure. The simulation did not consider the positioning of the feed head, hot top and conventional book mold model normally used. The symmetry was used in order to reduce the number of grid points, i.e., to facilitate the computation of the system of nonlinear equations and avoid overloading the computer’s capacity. However, in this work the solution of Equations (1) and (2) was made for half symmetry in 2-D, which is illustrated in Figure 1 (b). 

b. A selection of the types of materials was made then, in this case, pure iron and sand or mullite. 

The phase transformation in pure iron may be represented as follows [11], 

         
       .    (3) 

The properties, such as, specific heat (C_P) and latent heat (DH) are shown for 

pure iron in function of the temperature (T). They are shown as follow [11]: 

In addition, the thermal gradients were determined for both systems. The result is presented in Figure 4, in magnitude and in vectorial form. As it can be seen in the graph, the thermal gradient is larger in the sand mold than in the mullite mold, that is, due to that, the conductivity of the sand is much smaller in relation to the mullite mold. Also, the maximum and minimum thermal gradients are located exactly at the same points that the thermal flow happened. In this case, it is noticeable in graphs (c) and (d), that the direction of the thermal gradient is contrary to the thermal flow. The direction of the thermal gradient corresponds to the direction of the solidification, from the cold zone to the hot zone. 

According to Table 2, the most representative result for the solidification time of 1.5 h was that corresponding to lines 2 and 7 for the sand mold, line 2 corresponding to the smallest solidification temperature (118.4 K), in this case, the mold temperature was that of the environment, the liquid metal was considered without superheating and it was considered high loss of heat on the mold by convection (25 W/(m².K), and line 7 corresponds to the largest solidification temperature (1405.6 K), in this case, the temperature of the mold was preheated (423 K), liquid metal was superheated (80 K). 

Lines 10 and 15 were relevant for the mullite mold, line 10 corresponding to the smallest solidification temperature (743.36 K), where, it was established without preheating the mold, it was also established without superheating the liquid metal; a strong loss of heat on the mold by convection (25 W/(m².K) has happened, and line 15 corresponds to the largest solidification temperature (1004.41 K), because the preheating temperature of the mold was (423 K), high superheating temperature of the liquid metal (80 K) was fixed and loss of heat in the mold by convection (5 W/(m².K) was established. According to the result, a larger cooling in the mullite mold than in the sand mold was observed, because the physical properties of the materials are different, especially the thermal conductivity of the mullite influences. Obviously, for the conditions without preheating the mold and without superheating the liquid metal and for a strong loss of heat in the mold due to the convection phenomenon, consequently these conditions generated slower solidification temperatures as much in the sand mold as in the mullite mold (lines 2 and 10). 

Inside the cast metal some points were numbered, these points are shown in Figure 5. At these points the cooling curves were determined, that is shown in Figure 6. The data of the last column of Table 2 present the solidification temperature after 1.5 h of solidification. Observing in more detail Figure 6, in the sand mold the phase change of Fe-d to Fe-g happened, around the temperature of 1673 K, but, the other phase changes didn’t happen. In the mullite mold, the phase change was not very well defined, that is, it depends on the situation of the design and properties of this material. For instance, for line 10, the phase change of Fe-b to Fe-a happened around 1060 K, at the other points the phase transformation happened at the temperature of 947 K, for this temperature does not correspond to the transformation given by equation (3), this temperature could correspond to supercooling phenomenon. For line 15, phase transformation exists at some points, for instance, of Fe-g to Fe-b for the temperature of 1158 K and in the other points happened the transformation of Fe-b to Fe-a in 1033 K. On the other hand, the phase transformation for high temperatures did not happen. The result of phase change of iron during the cooling in different molds was not possible of to corroborate with the literature, for this study type was not found in the literature, because even this research type is relatively new.