A novel mathematical approach for the independent quantification of phase fractions in multiple simultaneous phase transformations is introduced. The proposed dilation curve analysis is very general, relying only on raw dilatation data and the density of some of the constituents involved in the transformations. Transformation start and end temperatures and instantaneous phase fractions are accurately measured using this method. As an example, the simultaneous transformation of austenite to bainite and martensite in seven cylindrical AISI 4140 steel samples cooled at rates between 1 and 4 K/s from 1223 K (950 °C) is used to show the feasibility of this new methodology. The martensite and bainite fractions calculated using the presented methodology for all seven samples are in good agreement with the ones measured with quantitative metallography. Hot stage microscopy was also performed on a sample of the same batch, yielding quantitative results consistent with the start temperatures from the analysis proposed.

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