Elastic investigation for the existence of B33 phase in TiNi shape memory alloys using atomistically informed Eshelby’s ellipsoidal inclusion

Ab initio prediction of temperature-dependent stability of heterogeneous B19′ phase in TiNi alloy using atomistically informed Eshelby’s ellipsoidal inclusion

“…The monoclinic angle of the B19' structure was 102.1 • , which is consistent with previous DFT studies [9,10,27] but is larger than the experimentally obtained value of 97.9 • [3]. The reason for this discrepancy, as explained from a micromechanical viewpoint in our previous work, is due to the heterogeneity of the experimentally observed B19' phase in the B2 matrix [23]. The free energy F per unit cell, which is a function of the temperature T and strain ε ij , can be described as follows:…”

“…where J T = H B19 ′ (H B2 ) −1 denotes the deformation tensor [22]. The calculated temperature-dependent eigenstrains are shown in Fig.…”

“…Due to tensor symmetry, C ijkl = C jikl = C ijlk = C klij and the rest of the elastic constants not mentioned here were assumed to be zero. It must be mentioned that we have included C B19 ′ 2223 of the B19' structure in our calculations because previous studies have reported that it has a non-negligibly large value [23,26,31,32].…”

“…, where a i is the half-axis of the ellipsoid along the three orthogonal directions. Considering that previous studies have suggested that the B19' phase in the B2 matrix of TiNi alloys are disk-shaped [23,[42][43][44], we simply used (a 1 ; a 2 ; a 3 ) = (10/ √ 2; 10/ √ 2; 1). Then, the stable orientation of the B19' phase with the minimum elastic energy increment ∆E in the B2 matrix was evaluated, and its total strains for this orientation were calculated.…”

“…By combining DFT atomistic and micromechanical [21] elastic analyses, we investigated the temperature-dependent stability of the B19' phase in B2 matrix while accounting for its heterogeneity. In particular, considering heterogeneous B19' phase in B2 matrix as Eshelby's ellipsoidal inclusion, which temperature-dependent eigenstrains and elastic constants were calculated using DFT and phonon analysis under quasi-harmomic approximation (QHA), we predicted temperature-dependent morphology of heterogeneous B19' phase and the total strains of heterogeneous B19' phase, which describe the elastically deformed shape of heterogeneous B19' phase in B2 matrix [22,23]. Using the total strains, we reproduced the elastically deformed B19' atomic structure and calculated its free energy using DFT and phonon analysis again.…”