A Thermo-mechanical Constitutive Model Of Shape Memory Alloy With Temperature Memory Effect

Temperature memory effect occurring in some shape memory alloys (SMAs) haspotential values in various fields such as smart materials and structures，and so on. It is oftheoretical and practical interests to develop a new constitutive model to overcome thelimitation that the previous constitutive models of SMA failed to express the temperaturememory effect of SMA.Austenite stopping temperature and austenite continuing temperature are defined torelate the temperature memory effect of SMA. A martensite volume fraction equation isdeveloped to express the relationship between martensite volume fraction and temperature.This equation can describe the temperature memory effect of SMA.Based on the martensite volume fraction equation and the relationship between phasetransformation critical stresses and temperature, a shape memory equation is established toexpress the relationship between shape memory factor, stress and temperature of SMA. Thisshape memory equation is able to overcome the limitation that the previous shape memoryequations or martensite phase transformation equations of SMA failed to express thetemperature memory effect of SMA.Using the shape memory factor as an internal variable and the differential relationshipbetween the free energy of Gibbs, stress and strain, a thermo-mechanical differential equationis established to express the differential relationship between stress, strain, shape memoryfactor and temperature of SMA. The thermo-mechanical boundary conditions to solve thethermo-mechanical differential equation are pointed out.The thermo-mechanical constitutive equation of SMA is established by solving thethermo-mechanical differential equation with the thermo-mechanical boundary conditions.This thermo-mechanical constitutive equation can overcome the limitation that the previousconstitutive models of SMA failed to express the temperature memory effect of SMA.The relationships of martensite volume fraction and temperature under various stresses,shape memory factor and stress under various temperatures, and stress and strain undervarious temperatures are numerically simulated. The results of numerical simulation showthat the shape memory equation and thermo-mechanical constitutive equation supposed in thispaper not only well predict the super-elasticity and shape memory effect of SMA but also can express the temperature memory effect of SMA, which overcome the limitation that theprevious constitutive models of SMA failed to express the temperature memory effect ofSMA.