Stochastic multiscale modeling of the thermomechanical behavior of polycrystalline shape memory alloys
Résumé
A multi-scale model simulating hysteretic thermomechanical behavior of polycrystalline shape memory alloys (SMA) is presented. Using a kinetic Monte-Carlo approach, the energy-based model estimates the stochastic average in terms of volume fraction for a phase or phase variant deriving from the Gibbs free energy density as a selection inside a given population. Indeed pseudo-elastic behavior for example is well-known to be associated with the nucleation of martensite plates inside the austenite parent phase. Associated variants are similar to sub-domains inside a thermodynamic system following the statistical definition of [37]. The germination process of a variant is on the other hand dictated by a germination potential barrier identified from a differential scanning calorimetry (DSC) measurement. The stochas-tic average for each type of variants inside a grain leads then to the numerical simulation of hysteresis phenomena at the single crystal scale. Homogenization operations allow finally macroscopic quantities (phases fraction, deformation and temperature) to be calculated at the polycrystalline scale. This procedure is applied to model the whole thermomechanical behavior of an equiatomic Ni-Ti SMA polycrystalline alloy considering the phase transformation between austenite, R-phase and martensite.
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