Numerical Processing of Cooling Curves to Obtain Growth Parameters During Eutectic Solidification
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Numerical Processing of Cooling Curves to Obtain Growth Parameters During Eutectic Solidification M. Morua1, E. Peña1, R. Aparicio2, M.Ramirez-Argaez1 and C. Gonzalez-Rivera1 1 Departamento de Ingeniería Metalúrgica, Facultad de Química, UNAM, Edificio D Circuito de los Institutos s/n Cd. Universitaria Mexico D.F., Mexico. 2 Cinvestav Querétaro Libramiento Norponiente 2000, Real de Juriquilla, 76230 Querétaro Qro. Mexico. ABSTRACT In this work a methodology to measure kinetic parameters to describe grain growth during equiaxed eutectic solidification is proposed. This methodology includes the numerical processing of two cooling curves and requires input data concerning the number of grains per unit volume. In addition, free grain growth before impingement and an exponential dependence of the grain growth rate on undercooling are assumed. The evolution of solid fraction of the sample as a function of time is obtained by applying the Fourier thermal analysis (FTA) method. Information collected is processed numerically in order to find numerical values for the pre-exponential and exponential parameters that characterize the grain growth kinetics as a function of undercooling. To validate this methodology a mechanistic model that simulates the cooling and solidification of eutectic Al-Si alloy in a sand mold is used. The results suggest that this methodology can be used to measure the kinetic parameters of equiaxed growth from the numerical processing of cooling curves and grain density data. INTRODUCTION The control of solidification microstructures is vital for the development and improvement of the quality and properties of the final cast products. Prediction of the formation and evolution of the cast microstructure is an essential element in the control of these microstructures during solidification and therefore the modeling of these microstructures is of considerable interest. As a result, several kinds of models have been developed in the last couple of decades [1-4]. These models include calculations on nucleation and growth kinetics which in turn depend on the availability of nucleation and growth models capable to reproduce the experimental behavior of the alloy under study. This work is focused on the development of a methodology which allows obtaining growth models for equiaxed eutectic solidification from experimental data. It has been found that, during solidification, grain growth rate depends on undercooling, defined as the difference between equilibrium solidification temperature and the actual temperature present during the phase change. Previous efforts have been done to develop methodologies allowing grain growth characterization [5, 6]. The following exponential equation has been used to describe grain growth, where R is the mean grain radius, t is the time, dR/dt is the grain growth rate, 'T is the undercooling, and µ and n are the grain growth coefficients. § dR · n ¨ ¸ P'7 © dt ¹
(1)
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The purpose of this work is the development and validation of a method for determination of equiaxed eutec
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