Finite Strain Shape Memory Alloys Modeling - Scuola di Dottorato in ...

It is interesting to evaluate how many experimental tests are necessary to completelyidentify the constitutive model parameters with a sufficient degree of accuracy:Two loading and unloading tensile and compressive uniaxial tests should beperformed at two different high enough temperature values in order to assess theposition of the phase transformation straight lines which define the starting and thefinishing of the austenite to single variant martensite and of the reverse transitions.Considering the results of these tests in terms of stress-strain, the pointscorresponding to the starting and the finishing of the phase transition at the twodifferent temperatures can be defined in the diagram σ − T . In this way the straightlines defining the forward and the reverse phase transformation can be obtained.These lines have a slope which is linked, in tension, to the model parameter βt. Inparticular, if p represents the slope of these lines it can be pointed out that:2βt= p(7.29)3The same result can be obtained in compression.The material constant ε Lcan be easily derived from a uniaxial loading-unloadingtest estimating the maximum inelastic strain attained in the case of elastic unloadingwhen the material is fully martensite.Furthermore, the lines corresponding to the start and the end of the A→ S and of theS→ A transitions are far from each other of a quantity equal to 3 hε 2L, so thatalso the parameter h can be evaluated.The lines corresponding to the single variant martensite to austenite transition crossthe temperature axis in two points indicating the two characteristic temperaturesAsandAf. For temperature aboveAfthe pseudo-elasticity range occurs: at the end ofeach loading-unloading cycle the material recovers all the deformation, and the123