A multiscale continuum model of the grain-size dependence of the stress hysteresis in shape memory alloy polycrystals

Abstract. This work presents a multiscale approach aimed at the modelling of evolution of martensitic microstructures with account for the interfacial energy effects. The total Helmholz free energy and the energy dissipated in the system are split into contributions from the bulk material, from phase interfaces and from other boundaries. Microstructure evolution is then determined by the incremental energy minimization. As an application, stress-induced transformation is considered which proceeds by formation and growth of internally twinned martensite plates within the austenite matrix. The interfacial energy is examined at three scales, namely at twin boundaries, austenite-martensite interfaces and at grain boundaries. Both atomic-scale and the elastic micro-strain interfacial energies are included and respective estimates are taken from the materials science literature or predicted using micromechanical finite element analysis. Examples are provided for the cubic-to-orthorhombic transformation in a CuAlNi shape memory alloy. They illustrate the effect of grain size on the macroscopic stress-strain response including the hysteresis width.

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“…[8]. Note that an inverse relationship is observed in nano-crystalline materials [16], however, this effect is not covered by the present study.…”

Section: Minimization Of Total Incremental Energy Supplycontrasting

confidence: 58%

On dissipation, interfacial energy and size eﬀects in shape memory alloys

Stupkiewicz

Petryk

2009

ESOMAT 2009 - 8th European Symposium on Martensitic Transformations

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“…3-6 It has been reported that the H of the nanostructured polycrystalline NiTi SMA is very sensitive to the GS 7,8 and that the thermally-induced martensitic PT can be completely suppressed when the GS falls below 60 nm. 9 In many applications, H and dr=dT are the most important properties 10,11 and design parameters of the SMA device and structures.…”

Section: 2mentioning

confidence: 99%

“…4). 22 For the stress-induced PT process in polycrystalline NiTi, it has been shown that 7,23 the hysteresis originates from the nucleation of martensite in individual grains as the result of numerous microscopic instability of the system. To illustrate the GS effect on hysteresis (dissipation) in the simplest way, we consider the specific Helmholtz free energy change DW of a single one-dimensional cylindrical grain before and after PT under external stretching as shown in Fig.…”

Section: 2mentioning

confidence: 99%

Stress hysteresis and temperature dependence of phase transition stress in nanostructured NiTi—Effects of grain size

Ahadi¹,

Sun²

2013

Appl. Phys. Lett.

221

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“…Simulation of martensitic phase transformation in SMAs such as NiTi is computationally challenging due to the intricate stochasticity associated with the formation of different martensite phases (different martensite variants) occurring over a hierarchy of spatiotemporal scales [11,12]. The developed mechanisms in terms of internal strain or energy associated with the phase transformation from the parent austenite phase to the various martensite variants varies with the variants, thus, quantification of all different phase transformation mechanisms requires a large number of computationally burdensome fine scale simulations.…”

Section: Introductionmentioning

confidence: 99%

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

Gur

Frantziskonis

2016

Modelling Simul. Mater. Sci. Eng.

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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.

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A multiscale continuum model of the grain-size dependence of the stress hysteresis in shape memory alloy polycrystals

Abstract: International audienc

Cited by 135 publications

References 60 publications

On dissipation, interfacial energy and size eﬀects in shape memory alloys

On dissipation, interfacial energy and size eﬀects in shape memory alloys

Stress hysteresis and temperature dependence of phase transition stress in nanostructured NiTi—Effects of grain size

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

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