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A unified tensorial driving force for phase transitions – calculation of the onset of the transformation
Author(s) -
ObersteBrandenburg C.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310085
Subject(s) - cauchy stress tensor , phase transition , stress (linguistics) , materials science , hydrostatic stress , hydrostatic equilibrium , scalar (mathematics) , dissipation , thermodynamics , mechanics , transformation (genetics) , statistical physics , finite element method , classical mechanics , physics , mathematics , geometry , chemistry , linguistics , philosophy , biochemistry , quantum mechanics , gene
The transformation kinetics during phase transitions in solids are often described by a pair of scalar variables for both the thermodynamic force and flux. Based on the use of the Eshelby‐Tensor as the thermodynamic driving force for the phase‐transition, a tensorial measure is introduced which is used as the associated thermodynamic flux. Based on the assumption that the process maximizes the dissipation, these measures are used to describe the transformation kinetics during the phase transition. The tensorial description reduces to a description with the Gibbs‐energy as the driving force and the mass change of the phases as the thermodynamic flux for a hydrostatic stress state. These considerations serve as the base for a phenomenological material‐law which describes the austenite‐martensite transformation in steels. In order to incorporate the different behavior of the phases, they are modeled independently. The model have been implemented into a finite‐element‐code which allows thermodynamically coupled calculations. A quenching‐test of a cylindrical specimen under biaxial mechanical load is simulated. The influence of the sequence of the change of the thermomechanical load in the stress‐temperature space (temperature→stress vs. temperature→stress) is studied. Furthermore, the influence of the direction of the applied stress is presented.