A thermodynamical description of the martensitic transformation. A model with small volume of averaging

Abstract

In the paper a thermomechanical model of the martensitic transformation in a single crystal is introduced. The model is related to a small volume of averaging. It means that detailed phenomena such as motion of single interfaces, internal rotations towards habit planes, separate mechanisms of dissipation or nucleation of different martensite variants can be discussed in the framework of the model. Such a description is attained mainly by means of the introduced free energy. Therefore, the construction of this function is a central part of this paper. The free energy depends on the Lagrangean strain tensor which describes the dominant part of deformation, relative displacement vectors for modelling shuffles and variables which are introduced with the aid of material directors. With the help of the last variables, an internal rotation is discussed. Furthermore, higher gradients of deformation are also taken into account. A general thermodynamical formulation for this small scale model is considered.