The principle of additivity and the
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I.
INTRODUCTION
AN examination of the literature on transformation studies in steels reveals that considerable research has been conducted to characterize microstructural changes under predominantly isothermal conditions, for example, as indicated in time-temperature-transformation diagrams. Ill Since industrial thermomechanical processes are usually performed under nonisothermal conditions, continuous-cooling-transformation diagrams have also been developed, t2-s~ However, since each of these diagrams is valid for a single grain size and a specific thermal history, more general mathematical models are required which incorporate heat flow and physical metallurgy principles to characterize the continuous microstructural changes occurring during heating or cooling. The additivity principle, whereby continuous-cooling (or heating) transformation behavior has been described as the summation of a series of short durations of fractional isothermal transformation events, has been applied successfully to predict nonisothermal transformations. However, there has been very little work done to provide an explanation as to why the additivity principle is applicable and the conditions under which it is applicable from a fundamental point of view. In this article, the validity of applying the additivity principle to austeniteto-proeutectoid ferrite transformation in hypoeutectoid R.G. KAMAT, formerly Ph.D. Student, Metals and Materials Engineering Department, University of British Columbia, is OCMR Postdoctoral Fellow, Department of Materials and Metallurgical Engineering, Queen's University, Kingston, ON, K7L 3N6 Canada. E.B. HAWBOLT and L.C. BROWN, Professors, Department of Metals and Materials Engineering, and J.K. BRIMACOMBE, Stelco/NSERC Professor and Director of the Centre for Metallurgical Process Engineering, are with the University of British Columbia, Vancouver, BC V6T 1W5 Canada. Manuscript submitted August 12, 1991. METALLURGICAL TRANSACTIONS A
plain-carbon steels has been assessed experimentally and by developing appropriate mathematical models based on fundamental transformation behavior.
II. T H E P R I N C I P L E O F ADDITIVITY AND ITS A P P L I C A B I L I T Y The principle of additivity is based on the theory advanced by Scheil t6] who proposed that the start of a transformation under nonisothermal conditions could be predicted by calculating the consumption of fractional incubation time at each isothermal temperature, with the transformation starting when the sum is equal to unity. The Scheil theory has been extended to phase transformations to predict continuous-cooling transformation kinetics from isothermal data. Isothermal kinetic data can be related to continuous cooling transformation behavior if the rate of transformation depends only on the state of the assembly and not on the thermal path by which that state is reached, t7] Mathematically, Rx = f ( X , T)
[l]
where R x is the rate ot~ transformation, X is the amount of transformation product already present, and T is the instantaneous temperatu
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