Linking simulations and experiments for the multiscale tracking of thermally induced martensitic phase transformation in NiTi SMA

Abstract

Martensitic phase transformation in NiTi shape memory alloys (SMA) occurs over a hierarchy of spatial scales, as evidenced from observed multiscale patterns of the martensitic phase fraction, which depend on the material microstructure and on the size of the SMA specimen. This paper presents a methodology for the multiscale tracking of the thermally induced martensitic phase transformation process in NiTi SMA. Fine scale stochastic phase field simulations are coupled to macroscale experimental measurements through the compound wavelet matrix method (CWM). A novel process for obtaining CWM fine scale wavelet coefficients is used that enhances the effectiveness of the method in transferring uncertainties from fine to coarse scales, and also ensures the preservation of spatial correlations in the phase fraction pattern. Size effects, well-documented in the literature, play an important role in designing the multiscale tracking methodology. Molecular dynamics (MD) simulations are employed to verify the phase field simulations in terms of different statistical measures and to demonstrate size effects at the nanometer scale. The effects of thermally induced martensite phase fraction uncertainties on the constitutive response of NiTi SMA is demonstrated.

Length scale effects and multiscale modeling of thermally induced phase transformation kinetics in NiTi SMA

“…It can be expected that, at the atomic to meso scales, interaction of the different phases (B2 and B19) with the free surfaces causes significant variation in the phase fraction evolution process and transformation kinetics, as briefly addressed in recent computational studies by the authors [8,15]. However, in those previous studies by authors [8,15], as well as in some other relevant studies [11,13], the coupled effect of grain size and length scale, on the thermally induced martensitic phase transformation (MPT) was not addressed. Rather, all those previous studies [8,11,13,15] mainly explore the effects of the side length (thin samples of constant thickness i.e.…”

“…Along the same lines, it has been observed that due to the evolution of different variants of B19 and B2 phases, the phase transformation process becomes inherently stochastic in nature [1,3,8] and occurs hierarchically over a very wide range of spatiotemporal scales [1,3,8,15]. However, the ins and outs of such aspects remain poorly understood.…”

“…Therefore, herein, small size NiTi samples are studied via MD simulations, and larger size samples are studied via stochastic phase field (PhF) simulations. A concurrent multiresolution (wavelet) based multiscale methodology, namely the compound wavelet method (CWM) [8,[35][36][37][38][39][40] is used to link the MD and PhF simulations along spatial scales, yielding a length-wise compound representation of the thermally induced martensitic phase transformation process. Finally, the CWM method is used to feed the information on length scale effects (obtained from the MD and PhF simulation of NiTi single crystals), onto a phenomenological material model, which was originally developed by Zotov et al [42] based on their experimental study.…”

“…However, in those previous studies by authors [8,15], as well as in some other relevant studies [11,13], the coupled effect of grain size and length scale, on the thermally induced martensitic phase transformation (MPT) was not addressed. Rather, all those previous studies [8,11,13,15] mainly explore the effects of the side length (thin samples of constant thickness i.e. 2 nm) or the size effect (nano particles or spheres) on the thermally induced martensitic phase transformation process for NiTi single crystal.…”

“…2 nm) or the size effect (nano particles or spheres) on the thermally induced martensitic phase transformation process for NiTi single crystal. A general spatial multiscale coupling framework is proposed by the authors [8], to transfer information from fine to coarse scales in the solid to solid phase transformation process. In that study [8], considering a single size case (i.e.…”