The Constitutive Models Of Shape Memory Alloys

As a new intelligent material, shape memory alloy has be used widely in many fields such as civil engineering, control engineering, medical treatment engineering, energy mechanism engineering due to its special shape memory effect and superelasticity. It is significant to develop the constitutive model that can describe thermomechanics behavior of shape memory alloy precisely.Based on the results of Differential Scanning Calorimetry(DSC), the relationship of heat flow and temperature was supposed to be linear in each subsection during the phase transformation. A polynomial phase transformation equation was derived from the differential relationship of phase transformation free energy, martensite volume fraction and temperature. Especially, it can predict the phase transformation behaviors of shape memory alloy precisely more than all previous phase transformation equations because the effect of phase peak temperature is considered in the polynomial phase transformation equation. A micromechanical 3-dimension with the polynomial phase transformation equation was developed according to the principles of thermodynamics and micromechanics.A new internal variable, shape memory factor, was defined, it can describe the shape memory effect and superelasticity of shape memory alloy and possesses clear physical meaning. A shape memory evolvement equation was derived from the phase dynamical equation for metals given by Magee, it possesses more simple mathematical expression than the previous phase transformation equation with the same functions. Based on the previous works of Tanaka, Liang and Brinson, a macro phenomenal constitutive model with the shape memory evolvement equation was derived according to the principles of thermodynamics.The vibrational behaviors of shape memory alloy composite beam were studied based on the macro phenomenal constitutive model, Tanaka's constitutive model, Liang's constitutive model and Brinson's constitutive model respectively. The recovery force equations and the relational equations of frequency and temperature were derived from above four constitutive models respectively. The relationships of bean frequency and temperature were visualized and analyzed through numerical calculations.The thermomechanical behaviors of shape memory alloy torsion actuator were studied based on the macro phenomenal constitutive model and Brinson's constitutive model respectively. The driving force formulas and torsion angle formulas were developed from above two constitutive models respectively. Both the relationship of torsion angle and temperature and the effects of geometrical...