The effect of the thermal path to reach isothermal temperature on transformation kinetics
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I.
INTRODUCTION
FOR a long time,
studies of transformations under isothermal conditions have been basic sources of information about their kinetics. This information is used as a base for evaluation of transformation kinetics during cooling, tml Isothermal studies are performed in such a way that specimens are cooled or heated to a required temperature at a certain average rate. The required temperature is usually reached following a different thermal path in different places of the specimen's section because of limited thermal conductivity of the material, e.g., different thermal paths at different distances from the surface. Therefore, it is important to know if and how the thermal path can influence the results of isothermal studies. II.
THEORY
A. Basic Suppositions Every transformation is time- and temperaturedependent to a greater or smaller extent. Suppose that for every isothermal transformation (IT), there exists only one particular function describing the dependence of the moment when the transformation starts at the transformation temperature. Another particular function describes the dependence of a certain fraction transformed (x) on time and transformation temperature under isothermal conditions. If such functions are dependent only on the material considered and characterize the transformation independently of the experiment's condition, they can be called the true transformation functions. The
time interval determined by the true transformation function can be called true transformation time [tx(T)] for a certain fraction transformed (x) at a specific temperature (T). The transformation starts when the first growing nucleus of the new phase appears in the parent phase. The time period necessary to produce the nucleus is called the nucleation or incubation time [ti(T)] at a specific temperature (T). During isothermal experiments, the transformation starts when the time (t) at which a specimen is isothermally held equals the incubation time of the transformation (tl), Then, t= ~
[1]
ti(T) = f ( T ) . The concept of fractional incubation time was the basis of Scheil's theory applied originally to actual incubation time. t3} From this theory (Figure 1), one can postulate that the heat treatment in which the sum of all the fractions t/ti is equal to unity will bring the material to the start of the transformation. As shown in Figure 1, the cooling curve to isothermal temperature is approximated by a large number of isothermal time steps, At,, connected by infinitely fast cooling sections. Thus, when the number of fractions n increase from n = 1 to n = m,
" At.
n=l ti.
METALLURGICAL TRANSACTIONS A
1
If a specimen is held at a particular temperature for the time tl and t~ < ti, it may be said to have undergone a "fractional incubation (nucleation)" of tl/ti. It is well known that the incubation time of the IT strongly depends on temperature; therefore, one can write that
~'.I.A. WIERSZYEEOWSKI, formerly with the Laboratory of Metallurgy, Delft University of Technology, 2628 AL Delft, The Nethe
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