Assessment of the theoretical basis of the Rule of Additivity for the nucleation incubation time during continuous cooling

The rule of additivity was first proposed by Scheil and Steinberg 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 that shows rule of additivity to be invalid for describing the incubation time for nucleation. Attempts to prove the validity of the rule of additivity for the incubation time have not met with much success, and much confusion still exists about its applicability to the incubation time. This article investigates the additivity of the consumption of the incubation time for nucleation during continuous cooling through an analysis based upon classical nucleation theory. It is rigorously demonstrated that the rule of additivity is invalid for the incubation time for nucleation. However, in practice, the relative error caused by using the rule of additivity could be very small in many cases due to the resolution limit of current experimental techniques. The present theory provides an explanation for the failure of the rule of additivity in predicting the incubation time for nucleation during continuous cooling. copyright 1997 American Institute of Physics