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Mathematical modelling of phase transformation in a plain carbon eutectoid steel Iyer, Jayaraman Rajagopalan


With the ultimate objective of quantitatively predicting the mechanical properties of steels, a mathematical model has been developed to compute the transient temperature distribution and austenite-pearlite transformation in an eutectoid steel rod during controlled cooling. The model is based on one-dimensional, unsteady-state heat conduction and incorporates empirical TTT data in the form of the parameters n and b(T) from the Avrami equation and the CCT start time, t[sub AV-CCT]. This data was obtained using a diametral dilatometer for an eutectoid steel of composition 0.82% C -0.82% Mn - 0.26% Si and a grain size of 5-7 ASTM. CCT kinetics are predicted from the TTT data by the additivity principle originally proposed by Scheil. The adequacy of the model was cheeked by comparing model1 predictions of the centre-line temperature of 9 and 10 mm diameter rods to measurements made during air cooling from an initial temperature between 840 and 870°C. The agreement obtained was good. Also the conditions determined by Avrami and Cahn for the additivity principle to hold were checked. Even though model predictions of CCT from TTT data generally were good, the application restrictions were not satisfied. Thus a new sufficient condition has been proposed which holds for the steel under study and establishes a firm theoretical foundation for model calculations. The condition, termed "effective site saturation", indicates that for growth dominated reactions, wherein the rate of reaction is governed by the growth of nuclei nucleated very early in the reaction, the kinetics can be considered additive due to the relative unimportance of subsequent nucleation. This condition suggests that the additivity rule may have a much broader range of applicability than was originally supposed. The calculation of TTT from CCT has been studied and a new method, involving an interative procedure using the additivity rule, has been derived. Agreement between calculated and measured TTT data is good. Finally the model has been employed to study the effect of centre segregation of manganese on the transformation behaviour of eutectoid steel rods and also to predict the mechanical properties of the same steel. Calculations indicate that segregation can lead to the formation of martensite at the centre of the rods with faster cooling rates. The calculation of mechanical properties is based on published relationships between pearlite spacing, undercooling and mechanical properties.

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