Stochastic multiscale modeling of the thermomechanical behavior of polycrystalline shape memory alloys

Abstract

A multi-scale model simulating hysteretic thermomechanical behavior of polycrystalline shape memory alloys (SMA) is presented. Using a kinetic Monte-Carlo approach, the energybased 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 stochastic 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.

Three-phase material mapping with incomplete X-ray diffraction spectral information

“…5, a series of raw spectra D(2, y) are obtained, each of which is composed of the three phases of NiTinol: A, M and R. For the proper identification of these phases, it is possible to prepare the specimen to obtain pure A and M phases with either a load-free state at high temperature (austenite) or under load after a full transformation (martensite), with a representative anisotropy along the tensile axis due to the selection of variants. However, this is not the case for the R phase: in a previous study (Chang et al, 2020), by conducting differential scanning calorimetry (DSC) over the NiTinol specimen, it was shown that the R phase is present only in the intermediate stages and never uniformly.…”

“…5(a) at 2 = 49 and 92 correspond to A{110} and A{211}, respectively, which are consistent with the theoretical XRD diffractograms. The {200} peak is not visible in the experimental spectra because of the pronounced crystallographic texture of this laminated material (Chang et al, 2020). Therefore, at this stage, the collected experimental diffraction spectra are taken as the data profile for pure austenite.…”

Piezomagnetic behavior: experimental observations and multiscale modeling

“…This calculation is complemented by a minimization process of g α regarding the direction cosines of domain families α to take the so-called magnetization rotation mechanism into account. Following this strategy, a Boltzmann function gives the solution of the stochastic approach [13] (with V 0 a reference microscopic volume, k B the Boltzmann constant (1.38 × 10 −23 J.K −1 ) and T the temperature (293 K)).…”