Constitutive model for shape memory alloys including phase transformation, martensitic reorientation and twins accommodation

Chemisky, Yves; Duval, Arnaud; Patoor, Étienne; Zineb, Tarak Ben

doi:10.1016/j.mechmat.2011.04.003

Cited by 169 publications

(139 citation statements)

References 43 publications

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“…The current work does, and also differs by adopting a new formulation for transformation surfaces that follows from a formula introduced by Cazacu et al (2006) to describe anisotropic and asymmetric plastic yield surfaces; this change improves the ability to capture transformation asymmetry and processing-induced material anisotropy of SMAs. The present model has similarities to those of Panico and Brinson (2007) and Chemisky et al (2011). Those models make a distinction between selfaccommodated and oriented martensite, hence they capture some of the features describe above.…”

mentioning

confidence: 54%

A micromechanics-inspired constitutive model for shape-memory alloys that accounts for initiation and saturation of phase transformation

Kelly

Stebner

Bhattacharya

2016

Journal of the Mechanics and Physics of Solids

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a b s t r a c tA constitutive model to describe macroscopic elastic and transformation behaviors of polycrystalline shape-memory alloys is formulated using an internal variable thermodynamic framework. In a departure from prior phenomenological models, the proposed model treats initiation, growth kinetics, and saturation of transformation distinctly, consistent with physics revealed by recent multi-scale experiments and theoretical studies. Specifically, the proposed approach captures the macroscopic manifestations of three micromechanial facts, even though microstructures are not explicitly modeled: (1) Individual grains with favorable orientations and stresses for transformation are the first to nucleate martensite, and the local nucleation strain is relatively large. (2) Then, transformation interfaces propagate according to growth kinetics to traverse networks of grains, while previously formed martensite may reorient. (3) Ultimately, transformation saturates prior to 100% completion as some unfavorably-oriented grains do not transform; thus the total transformation strain of a polycrystal is modest relative to the initial, local nucleation strain. The proposed formulation also accounts for tension-compression asymmetry, processing anisotropy, and the distinction between stress-induced and temperature-induced transformations. Consequently, the model describes thermoelastic responses of shape-memory alloys subject to complex, multi-axial thermo-mechanical loadings. These abilities are demonstrated through detailed comparisons of simulations with experiments.

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mentioning

confidence: 54%

A micromechanics-inspired constitutive model for shape-memory alloys that accounts for initiation and saturation of phase transformation

Kelly

Stebner

Bhattacharya

2016

Journal of the Mechanics and Physics of Solids

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“…such temperature, at which G A = G As for the elastic inter-phase stress energy G mix , it grows with the martensite variants fractions ) n and it is decreased by oriented defects b n , produced by micro plastic deformations H n p . In the works [7,8] the authors considered martensite variants originated by an invariant plane deformation and characterized by the habit plane and the amount of shear. They suggested to calculate the energy of the variants interaction by a quadratic form.…”

Section: Transformation Conditionsmentioning

confidence: 99%

Model of the Evolution of Deformation Defects and Irreversible Strain at Thermal Cycling of Stressed TiNi Alloy Specimen

Volkov

Belyaev

Evard

et al. 2015

MATEC Web of Conferences

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Abstract. This microstructural model deals with simulation both of the reversible and irreversible deformation of a shape memory alloy (SMA). The martensitic transformation and the irreversible deformation due to the plastic accommodation of martensite are considered on the microscopic level. The irreversible deformation is described from the standpoint of the plastic flow theory. Isotropic hardening and kinematic hardening are taken into account and are related to the densities of scattered and oriented deformation defects. It is supposed that the phase transformation and the micro plastic deformation are caused by the generalized thermodynamic forces, which are the derivatives of the Gibbs' potential of the two-phase body. In terms of these forces conditions for the phase transformation and for the micro plastic deformation on the micro level are formulated. The macro deformation of the representative volume of the polycrystal is calculated by averaging of the micro strains related to the evolution of the martensite Bain's variants in each grain comprising this volume. The proposed model allowed simulating the evolution of the reversible and of the irreversible strains of a stressed SMA specimen under thermal cycles. The results show a good qualitative agreement with available experimental data. Specifically, it is shown that the model can describe a rather big irreversible strain in the first thermocycle and its fast decrease with the number of cycles.

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“…The formulation of the phenomenological constitutive model of Chemisky et al [7] is based on the description of a thermodynamic free energy potential employing a chosen set of complementary independent state variables (external and internal). Thermodynamic transformation forces are derivated from this free energy potential.…”

Section: Constitutive Model and Description Of Tension-compression Asmentioning

confidence: 99%

“…All of these models are based on the J 2 -J 3 invariants of the stress or the transformation strain tensor. In a recent work, Chemisky et al [7] have shown that such a formulation can be explicitely defined by the two maximum transformation strain in tension and compression, respectively. The identification of such parameters usually requires one tensile and one compression test on a SMA that is initially in the austenitic state.…”

Section: Introductionmentioning

confidence: 99%

“…It is shown that heterogeneous strain fields obtained with DIC (Digital Image Correlation), where each material point has a different loading path is sufficient to identify the asymmetric parameters using inverse methods. Utilizing the constitutive model proposed by Chemisky et al [7], finite element simulations are carried out to predict the strain fields on the area of interest of the specimen. An optimization algorithm is further required to minimize the error between the experimental and numerically-computed strain fields.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Determination of the Characteristic Parameters of Tension-Compression Asymmetry of Shape Memory Alloys Using Full-Field Measurements

Chemisky

Echchorfi

Meraghni

et al. 2013

MSF

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Abstract. In this work, a method for the identification of the transformation surface of Shape Memory Alloys based on full field measurements is presented. An inverse method coupled with a gradientbased algorithm has been developed to determine the characteristic parameters of the transformation surface. The constitutive equations of the chosen model that capture the macroscopic behavior of Shape Memory Alloys are first presented. The material parameters, to be identified, that are characteristic of the tension-compression asymmetry of the alloy are detailed. The identification algorithm, based on full field measurements obtained by Digital Image Correlation (DIC) and numerical simulation by Finite Element Analysis are introduced. The identification algorithm is validated using a numerically generated strain field on a Meuwissen-type specimen.

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Constitutive model for shape memory alloys including phase transformation, martensitic reorientation and twins accommodation

Cited by 169 publications

References 43 publications

A micromechanics-inspired constitutive model for shape-memory alloys that accounts for initiation and saturation of phase transformation

A micromechanics-inspired constitutive model for shape-memory alloys that accounts for initiation and saturation of phase transformation

Model of the Evolution of Deformation Defects and Irreversible Strain at Thermal Cycling of Stressed TiNi Alloy Specimen

Determination of the Characteristic Parameters of Tension-Compression Asymmetry of Shape Memory Alloys Using Full-Field Measurements

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