THERMOMECHANICAL CONSTITUTIVE EQUATIONS FOR SHAPE MEMORY ALLOYS

Abstract
Shape Memory Alloys present a large variety of behaviour in function of the thermomechanical loading pathes and the microstructural states of the material. These responses are due to different physical mechanisms of deformation which are associated to the thermoelastic martensitic transformation : - oriented growth of the martensitic plates by the applied stress in Superelasticity ; - mobility of the interfaces between the variants of martensitic in the so-called Shape Memory Effect ; - capability of the internal stress field produced in the material by oriented defects left by some previous transformation sequences, to influence the growing of the martensite in the Two-Way Shape Memory Effect. The determination of the constitutive equations for the mechanical behaviour of these alloys must take into account these particular mechanisms of deformation. For each physical mechanism it is necessary, at first, to make a kinematical study of the strain associated to it. After this step, an energy balance between the driving and the resistive forces is established in each case from the analysis of the Gibb's free energy of the transformation or by using the Eshelby formalism of energy momentum. Phenomenological flow rules are then determined from the classical concept of normality rule. In this contribution, the micromechanical aspects of the phase transformation mechanisms are presented both from the statical and the kinematical point of view. Special attention is given to the internal stress state associated with variant and grain interactions.