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

Accordingly, the tensor α plays a role similar to the back-stress of the classicalplasticity and X is the relative stress.Introducing a yield function that is assumed to depend on the deviatoric part of thedevthermodynamic force f ( X ), the equation describing the associative normalityrule for the internal variable εtis given by:devdev∂f( X ) dev ∂f( X )ε t= ζ = ζI (6.32)dev∂X∂Xwith ζ the so-called plastic multiplier and ( dev = − 1)( : )X X X 1 1. From the3analysis of the flow rule form (6.28) it can be pointed out that the transformationstrain tensor ε tis a deviatoric tensor. This fact appears in a perfect agreement withthe experimental evidences indicating no volume variations during the phasetransition.Furhermore, between tension and compression pseudoelastic experiments, anasymmetric behavior is observed. In particular, at a given test temperature it is foundthat: (i) the stress level required to nucleate the martensitic phase from the austeniticphase is considerably higher in compression than in tension; (ii) the transformationstrain measured in compression is smaller than that in tension; (iii) the hysteresisloop generated in compression is wider (along the stress axis) than the hysteresisloop generated in tension. These major differences between the tension andcompression response of a Ni-Ti alloy in pseudoelastic experiments are shown inFig. 6.1.To catch the asymmetric behavior of SMA during tension-compression tests, theactivation of the phase transition, i.e. the evolution of the inelastic strain ε t, is102