A Multiscale Modeling of Magnetic Shape Memory Alloys: Application to NiMnGa Single Crystal

Fall, Mame Daro; Hubert, Olivier; Mazaleyrat, F.; Lavernhe-Taillard, Karine; Pasko, Alexandre

doi:10.1109/tmag.2016.2514705

Cited by 7 publications

(6 citation statements)

References 11 publications

(21 reference statements)

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“…Local magnetic and mechanical loadings ( H gr and σ gr ) are then different from the global loadings ( H and σ). Typically the calculation of the local loadings are carried out on each grain through a self-consistent polycrystalline scheme [22], where loadings at the grain scale are derived from the macroscopic loadings, using equations (43) and (44). The gap between local and global quantities defines the demagnetizing field and the residual stress.…”

Section: Constitutive Behavior Localization and Homogenizationmentioning

confidence: 99%

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Multiscale magneto-elastic modeling of magnetic materials including isotropic second order stress effect

Hubert

2019

Journal of Magnetism and Magnetic Materials

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Compact and high speed electromechanical systems lead to higher and higher levels of multiaxial mechanical stress, that may strongly change the magnetic behavior of materials, making the development of highly accurate magnetic models a very important task. Among all available magnetoelastic models, multiscale approaches seem to be the most promising.The coupling effect is introduced at the single crystal scale, mainly attributed to the evolution of magnetic domain structures under magneto-mechanical loading. All these models use however a formulation of free energy where the energetic term describing magneto-elastic coupling is linearly stress dependent, that hardly allow (using artificial mechanisms) providing non-monotonic stress effect on the magnetic behavior. The proposition detailed in this paper is to consider a second order stress term in the free energy expression, allowing a linear dependance of magnetostriction tensor with stress to be defined and providing the non-monotonous stress effect. This introduction leads to a more complex description of magnetoelastic effect that needs the identification of a large number of complementary material constants. In this paper, developments are made in the frame of cubic symmetry for first order magneto-elastic term (joining the classical description) and considering an isotropic second order stress effect for the sick of simplicity. This simplification leads to only two additive physical constants to be identified. An identification procedure is proposed and applied to model the magnetoelastic behavior a non-oriented (NO) 3wt%silicon-iron electrical steel.

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Section: Constitutive Behavior Localization and Homogenizationmentioning

confidence: 99%

“…the modeling applies to single or multiphased materials where one phase at minimum is ferro(ferri)magnetic but remains at constant volume fraction. Extension to phase change is possible and applies for magnetic shape memory alloys for example[44].…”

mentioning

confidence: 99%

Multiscale magneto-elastic modeling of magnetic materials including isotropic second order stress effect

Hubert

2019

Journal of Magnetism and Magnetic Materials

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“…A first attempt of multiscale modelling of these materials has been proposed in [15]. In this model, the variant scale φ (meaning martensite variant or the austenite phase) has been introduced between the grain g and domain α scales.…”

Section: Magnetic Shape Memory Alloysmentioning

confidence: 99%

Multiscale Modeling of Magnetostrictive Materials

Hubert¹,

Daniel²,

Bernard³

2022

Encyclopedia of Smart Materials

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“…The Gibbs free energy density mapping is first built. It has been shown in [12] that β s , seen as temperature independent in the framework of reversible modeling, is related to the maximal heat flux q m (W.m −3 ) of a DSC peak emission (using A to R phase or R to M emission peak), variation of enthalpy and entropy densities (∆h and ∆s) and temperature rateṪ used during the experiment (Equation 77).…”

Section: Calibration Of Germination Energy Based On Dscmentioning

confidence: 99%

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

Chang

Lavernhe-Taillard

Hubert

2020

Mechanics of Materials

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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.

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A Multiscale Modeling of Magnetic Shape Memory Alloys: Application to NiMnGa Single Crystal

Abstract: The paper presents a new multiscale modeling dedicated to magnetic shape memory alloys. It involves four scales from the domain scale to the macroscale. The model is presented and simulation results are compared to experiments carried out on a NiMnGa single crystal.

Cited by 7 publications

References 11 publications

Multiscale magneto-elastic modeling of magnetic materials including isotropic second order stress effect

Multiscale magneto-elastic modeling of magnetic materials including isotropic second order stress effect

Multiscale Modeling of Magnetostrictive Materials

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

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