A Thermodynamical Constitutive Model for Shape Memory Materials. Part I. the Monolithic Shape Memory Alloy

Pseudoelasticity and the shape memory e ect (SME) due to martensitic transformation and reorientation of polycrystalline shape memory alloy (SMA) materials are modelled using a free energy function and a dissipation potential. Three di erent cases are considered, based on the number of internal state variables in the free energy: (1) Austenite plus a variable number of martensite variants; (2) Austenite plus two types of martensite; and (3) Austenite and one type of martensite. Each model accounts for three dimensional simultaneous transformation and reorientation. The single-martensite model was chosen for detailed study because of its simplicity and its ease of experimental veri cation. Closed form equations are derived for the damping capacity and the actuator e ciency of converting heat into work. The rst law of thermodynamics is used to demonstrate that signi cantly more work is required to complete the adiabatic transformation than the isothermal transformation. Also, as the hardening due to the austenite/martensite mist stresses approaches zero, the transformation approaches the isothermal, in nite speci c heat conditions of a rst order transformation. In a second paper, the single-martensite model is used in a mesomechanical derivation of the constitutive equations of an active composite with a SMA phase.