Parameter determination for thermodynamical models of the pseudoelastic behaviour of shape memory alloy by resistivity measurements and infrared thermography

Two thermodynamical models of pseudoelastic behaviour of shape memory alloys have been formulated. The first corresponds to the ideal reversible case. The second takes into account the hysteresis loop characteristic of this shape memory alloys.Two totally independent techniques are used during a loading-unloading tensile test to determine the whole set of model parameters, namely resistivity and infrared thermography measurements. In the ideal case, there is no difficulty in identifying parameters.Infrared thermography measurements are well adapted for observing the phase transformation thermal effects.Notations 1 austenite 2 martensite - ₍₎ Macroscopic infinitesimal strain tensor of phase - ₍₂₎^f Traceless strain tensor associated with the formation of martensite phase - Macroscopic infiniesimal strain tensor - Macroscopic infinitesimal strain tensor deviator - _f Trace - Equivalent strain - ^pe Macroscopic pseudoelastic strain tensor - x Distortion due to parent (austenite =1)product (martensite =2) phase transformation (traceless symmetric second order tensor) - M Total mass of a system - M() Total mass of phase - V Total volume of a system - V() Total volume of phase - z=M(2)/M Weight fraction of martensite - 1-z=M(1)/M Weight fraction of austenite - u₀^*() Specific internal energy of phase (=1,2) - s₀^*() Specific internal entropy of phase - Specific configurational energy - Specific configurational entropy - ₀^f(T) Driving force for temperature-induced martensitic transformation at stress free state (₀^fT) = T^*–Ts^*) - Kirchhoff stress tensor - Kirchhoff stress tensor deviator - Equivalent stress - Cauchy stress tensor - Mass density - K Bulk moduli (K₀=K) - L Elastic moduli tensor (order 4) - E Young modulus - Energetic shear (₀ = ) - Poisson coefficient - M_s^o(M_F^o) Martensite start (finish) temperature at stress free state - A_s^o(A_F^o) Austenite start (finish) temperature at stress free state - C_v Specific heat at constant volume - k Conductivity - Pseudoelastic strain obtained in tensile test after complete phase transformation (AM) (unidimensional test) - ₀ Thermal expansion tensor - r Resistivity - 1MPa 10⁶N/m² - ⁽⁾ Specific free energy of phase - _n Specific free energy at non equilibrium (R model) - _n^eq Specific free energy at equilibrium (R model) - _n^v Volumic part of ^eq - Specific free energy at non equilibrium (R_L model) - _conf Specific coherency energy (R_L model) - _c Specific free energy at constrained equilibria (R_L model) - _it (T) Coherency term (R_L model)