Application of, and precautions for the use of, the Rule of additivity in phase transformation

Abstract

The rule of additivity was first proposed for predicting the incubation time for nucleation of solid phases during continuous-cooling phase transformations, and has since been widely used for both the nucleation incubation and the entire process of phase transformation. While having been successfully used to calculate the transformed volume fraction during continuous cooling in many steel alloy systems, there is experimental evidence which shows that the rule of additivity is not rigorously valid for describing the incubation time for nucleation. We have recently used the classical nucleation theory to demonstrate the limits of validity of the rule of additivity. The general condition for the rule of additivity to be valid for phase transformation is that the kinetics of phase transformation be a state function independent of temperature history. In practice, the relative error caused by using the rule of additivity may be negligibly small in many cases. For better accuracy, the incubation time for nucleation should be excluded when applying the rule of additivity to phase transformation. Applications and precautions, when using the rule of additivity in nucleation incubation, phase transformation, and determination of equilibrium phase-transformation temperature, will be discussed.

Modeling of the austenite decomposition kinetics in a low-alloyed steel enriched in carbon and nitrogen

“…( ) In our approach, the kinetic parameters are extracted from experimentally determined isothermal kinetics, as will be seen in the following. This implicitly assumes the additivity hypothesis, which was deeply discussed in the literature [17,[21][22][23][24]. Under anisothermal conditions, the calculation of the phase transformations progression is preceded by the calculation of the incubation time [25,26].…”

On the application of the additivity rule in pearlitic transformation in low alloy steels

“…Following Eq. [21,24] Both the growth rate and the nucleation rate contribute to the rate of a transformation, [25] i.e., [3] where d f n /dt and d f g /dt are the pearlitic transformation rates from nucleation and from growth, respectively. [1] can be mathematically derived.…”

“…The rate of pearlitic transformation from nucleation can be expressed as [25] d f n dt = αV n V 0 dn dt [5] where V 0 is the initial volume of the matrix phase, V n the volume of the new phase, and α a constant related to the volume change when the matrix phase decomposes to a new phase. During the pearlite transformation, the transformed matrix phase is not available for further nucleation.…”

Effects of Chemical Composition and Austenite Deformation on the Onset of Ferrite Formation for Arbitrary Cooling Paths

“…However, it has been shown that using such isothermal transformation data to calculate the transformation start for cooling conditions by applying the additivity rule can give incorrect estimates [16,17]. For cooling, the application of the so-called ideal (or true) incubation time [18,19] gives a better estimate for the transformation start for an arbitrary cooling path [20], as it gives exactly the correct continuous cooling transformation (CCT) diagram for constant cooling rates when Scheil's additivity principle is applied.…”