Martensite transformation usually occurs on cooling, with the volume fraction of martensite depending upon the temperature as shown in the first two examples below. Martensite transformation is often thought only to depend upon the temperature, but has been shown to also depend upon the time. It should therefore be represented by it’s own C-curve on a time-temperature-transformation graph. The strong temperature dependence may be caused by the large driving force necessary before transformation can proceed.

**The Koistinen-Marburger equation**

This equation due to Koistinen[1] and Marburger can be used to estimate the fraction of martensite as a function of temperature.

Steels were quenched to various temperatures and the austenite volume fraction determined by X-ray diffraction. The results plotted logarithmically against Ms-Tq, where Ms is the martensite start temperature and Tq is the quench temperature.

V_gamma = exp [-b(Ms-Tq)] where b is 1.1×10^{-2}

Magee[2] later showed that an equation of this form can be justified based on martensite nucleation theory.

Rearranging the formula is simple to give the volume fraction of austenite transforming to martensite on cooling to room temperature as a function of the MS temperature of the steel.

Khan and Bhadeshia [3] have produced a modified equation which also considered autocatalytic nucleation of martensite to allow better matching to dilatometry results. This changed the goodness of the fit by regression from 0.9 to 0.94, when analysing the data of volume fraction against temperature obtained from their own experiments. This work used one alloy (300M) but changed the starting conditions by partial transformation to bainite.

[1] D. P. Koistinen and R. E. Marburger, Acta Metallurgica, 7, p59-60, 1959

[2] C. L. Magee, The nucleation of martensite, In “Phase transformations”, p115-156, Ed: H. I. Aaronson and V. F. Zackay, ASM, Metals Park, Ohio, 1970.

[3] S. A. Khan and H. K. D. H. Bhadeshia “Kinetics of Martensitic Transformation in Partially Bainitic 300M Steel” Materials Science and Engineering A, Vol. A129, 1990, pp. 257-272.

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