On the evaluation of dilatometer experiments

Abstract

The goal of this article is a mathematical investigation of dilatometer experiments. These are used to detect the kinetics of solid–solid phase transitions in steel upon cooling from the high-temperature phase. Usually, the data are only used for measuring the start and end temperatures of the phase transition. In the case of several coexisting product phases, expensive microscopic investigations have to be performed to obtain the resulting fractions of the different phases. In contrast, it is shown in this article that in the case of at most two product phases the complete phase transition kinetics including the final phase fractions are uniquely determined by the dilatometer data. Numerical results confirm the theoretical result.

Keywords:

• dilatometer
• phase transitions
• inverse problem

AMS Subject Classifications:

• 35R30
• 74F05
• 74N99

Acknowledgements

D. Hömberg was partially supported by the DFG Research Center MATHEON ‘Mathematics for key technologies’. N. Togobytska was supported by the DFG SPP 1204 ‘Algorithms for fast, material specific process-chain design and -analysis in metal forming’. M. Yamamoto was partly supported by Grant 15340027 from the Japan Society for the Promotion of Science and Grant 17654019 from the Ministry of Education, Cultures, Sports and Technology. D. Hömberg has also been partially supported by the DFG Research Center MATHEON ‘Mathematics for key technologies'.