A thermodynamical constitutive model for shape memory materials. I: The monolithic shape memory alloy. (English) Zbl 0898.73020
Pseudoelasticity and the shape memory effect due to martensitic transformation and reorientation of polycrystalline shape memory alloy materials are modeled using a free energy function and a dissipation potential. Three different 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. Closed form equations are derived for the damping capacity and the actuator efficiency of converting heat into work. The first law of thermodynamics is used to demonstrate that significantly more work is required to complete the adiabatic transformation than the isothermal transformation. Also, as the hardening due to the austenite/martensite misfit stresses approaches zero, the transformation approaches the isothermal, infinite specific heat conditions of a first-order transformation.
MSC:
74C99 | Plastic materials, materials of stress-rate and internal-variable type |
74A15 | Thermodynamics in solid mechanics |
74A60 | Micromechanical theories |
74M25 | Micromechanics of solids |