Calculation of the onset and progress of the martensitic transformation using tensorial measures for the transformation kinetics

摘要

The description of the transformation kinetics during a martensitic phase transition in solids is usually performed by scalar variables for both the thermodynamic force and flux. In a local description at the phase boundary, the movement of the boundary during the martensitic transformation can be described in terms of the second order Eshelby Tensor (or asymmetric chemical potential tensor) and the local orientation of the phase boundary. Transferring this local consideration to a macroscopic description by applying appropriate ho-mogenization techniques, the Eshelby Tensor is introduced as the macroscopic thermodynamic driving force for the phase transformation. Consequently, a second order tensor is introduced as the associated thermodynamic flux. This tensorial description collapses to the classical case for a hydrostatic stress state. A constitutive relation between these tensorial variables is postulated based upon the assumption of the maximization of the dissipation and the existence of a threshold value for the thermodynamic force. Considering shape memory alloys, the onset and progress of the transformation for various thermomechanical loading path is calculated. The influence of the direction and magnitude of the stress and the temperature on the transformation is investigated. Furthermore, restrictions on the choice of the parameters of the model are derived.