Quantification of phase transformations using calorimetry and dilatometry

Abstract

Dilatometry and calorimetry are well-established techniques, and have been used successfully for decades; however, they are seldom used to quantify the progress of a transformation. Most often, these techniques are used to detect start and finish of transformations. When used quantitatively, current analysis of dilation data does not account for the different changes in density for the multiple transformed phases. Similarly, quantitative calorimetric analysis does not account for different rates of enthalpy release for different transformed phases. The technique proposed for both dilatometry and calorimetry consists on posing a differential equation based on dilation or temperature data generated under controlled experimental conditions. When integrated, this equation extracts phase fraction evolution from the experimental data. Like all differential equations, the equation posed involves coefficients and integration constants. The work presented differs from other similar work in that the coefficients are obtained from calibration before, after, and at transition points for each transformation, with a minimum of need of previously tabulated data. These methods can go beyond any previous approach by quantifying partial transformations and making in-situ measurements of phase fractions in complex simultaneous phase transformations possible. This is possible because of a rigorous framework that reduces the number of unknown parameters to its minimum. The mathematical treatments will be introduced, and applications will be discussed involving precipitation during solidification in aluminum A356 alloy, martensitic transformation in creep-resistant steel, and simultaneous bainitic and martensitic transformations in AISI 4140 steel.