Micromechanical Modelling of Superelasticity in Shape Memory Alloys

Patoor, Étienne; Eberhardt, A.; Berveiller, M.

doi:10.1051/jp4:1996127

Cited by 132 publications

(124 citation statements)

References 3 publications

(4 reference statements)

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“…For example Patoor et. al [17] in efforts to develop microscopically motivated macroscopic SMA model as a basic ingredients distinguished habit plane variants of martensite (n = 24 for CuZnAl alloy) and introduced so-called interaction matrix H mn characterizing energy interactions between the martensitic variants. Some modeling results and discussion on advantages and drawbacks of this approach can be found in, e.g., Peultier et.…”

Section: Special Class Of Experiment-oriented Seim Estimation (A αβ )mentioning

confidence: 99%

On consistent micromechanical estimation of macroscopic elastic energy, coherence energy and phase transformation strains for SMA materials

Ziółkowski

2016

Continuum Mech. Thermodyn.

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An apparatus of micromechanics is used to isolate the key ingredients entering macroscopic Gibbs free energy function of a shape memory alloy (SMA) material. A new self-equilibrated eigenstrains influence moduli (SEIM) method is developed for consistent estimation of effective (macroscopic) thermostatic properties of solid materials, which in microscale can be regarded as amalgams of n-phase linear thermoelastic component materials with eigenstrains. The SEIM satisfy the self-consistency conditions, following from elastic reciprocity (Betti) theorem. The method allowed expressing macroscopic coherency energy and elastic complementary energy terms present in the general form of macroscopic Gibbs free energy of SMA materials in the form of semilinear and semiquadratic functions of the phase composition. Consistent SEIM estimates of elastic complementary energy, coherency energy and phase transformation strains corresponding to classical Reuss and Voigt conjectures are explicitly specified. The Voigt explicit relations served as inspiration for working out an original engineering practice-oriented semiexperimental SEIM estimates. They are especially conveniently applicable for an isotropic aggregate (composite) composed of a mixture of n isotropic phases. Using experimental data for NiTi alloy and adopting conjecture that it can be treated as an isotropic aggregate of two isotropic phases, it is shown that the NiTi coherency energy and macroscopic phase strain are practically not influenced by the difference in values of austenite and martensite elastic constants. It is shown that existence of nonzero fluctuating part of phase microeigenstrains field is responsible for building up of so-called stored energy of coherency, which is accumulated in pure martensitic phase after full completion of phase transition. Experimental data for NiTi alloy show that the stored coherency energy cannot be neglected as it considerably influences the characteristic phase transition temperatures of SMA material.Keywords SMA · NiTi alloys · Adaptive composite · Macroscopic free energy functions · Gibbs energy · Micromechanics · Coherence energy · Stored coherency energy · Ultimate phase transformation eigenstrains · Self-equilibrated eigenstrains influence moduli · SEIM · Effective property estimates · Martensitic phase transformationThe coming into existence of the present paper would not be possible without contributions and long discussions with Professor Bogdan Raniecki who passed away suddenly on August 2014. I dedicate this work to his memory. dx is an average of a local field over a region occupied by volume V α . When volume V α is occupied by phase α then A α denotes α phase average.It is accepted that internal energy and internal entropy of all kinds of martensitic phases at microscopic thermodynamic reference state (m.t.r.s.)-i.e., at zero local stresses ( σ (x) = 0) and reference temperature (T = T 0 ), are the same, e.g., (u 0 α, α =1 = u M α = u A − u 0 , u A ≡ u 0 1 ) and (s 0 α, α =1 = s M α = s A − s 0 , s A ≡...

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Section: Special Class Of Experiment-oriented Seim Estimation (A αβ )mentioning

confidence: 99%

On consistent micromechanical estimation of macroscopic elastic energy, coherence energy and phase transformation strains for SMA materials

Ziółkowski

2016

Continuum Mech. Thermodyn.

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“…The maximum transformation work done by the applied stress on the transformation strain is a comprehensive driving force which has been widely used in many constitutive models (Patoor et al 1993, 1994, Bekker and Brinson 1997, Goo and Lexcellent 1997, Lu and Wang 1997, Huang and Bunsen 1998. It was also used as a variant selection rule in some literature (Chu 1993, Shield 1995.…”

Section: The Maximum Transformation Work Criterionmentioning

confidence: 99%

“…The second category contains the micromechanics-based macroscopic models. These use thermodynamics laws to describe the transformation and micromechanics to estimate the interaction energy due to the transformation in the material, which is a key factor in the transformation mechanism (Patoor et al 1993, 1994, Sun and Hwang 1993a, b, Goo and Lexcellent 1997, Lu and Wang 1997, Huang and Brinson 1998, Gao and Brinson 2000.…”

Section: Introductionmentioning

confidence: 99%

The variant selection criteria in single-crystal CuAlNi shape memory alloys

Zhang

Brinson

Sun

2000

Smart Mater. Struct.

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Abstract. Two variant selection criteria are often used in shape memory alloys (SMAs). One is the maximum resolved shear stress (RSS) criterion and the other is the maximum transformation work criterion. In this paper these two measures are calculated using the crystallographic theory of martensite (CTM) for the shape memory effect (SME) case and the crystallographic theory of martensite + detwinning, distortion and slip (CTM + DDS) for the superelasticity (SE) case. The results are compared with the experimental measurements of a CuAlNi single-crystal SMA. The comparisons show that work is better as a variant selection criterion than RSS. In the SME case, type-II twin variants are more favorable under uniaxial tension; while type-I twin variants are more favorable under uniaxial compression. The calculation also shows that a great tension-compression asymmetry exists in CuAlNi single crystals.

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“…Among existing models one can single out the macroscopic [13 -16] and the microstructural microstructural [17][18][19] ones. Macroscopic models are distinguished by few constants and high computation speed.…”

Section: Introductionmentioning

confidence: 99%

Modeling of Functional Properties of Porous Shape Memory Alloy

Volkov

Evard

Iaparova

2015

MATEC Web of Conferences

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Abstract.A model accounting for the microstructure of porous TiNi shape memory alloy samples fabricated by selfpropagating high temperature synthesis has been proposed for simulation of their functional-mechanical properties. Structural elements of a porous sample have been approximated by curved beams. An analysis of shapes and sizes of pores and ligaments permitted to identify characteristic sizes of the beams. A mathematical object consisting of rigidly connected small curve beams has been considered. The stress-strain state of a beam was estimated by the classical methods of strength of materials. The microstructural model was used for calculation of the phase deformation of the shape memory material. Simulation of stress-strain curves and phase deformation of a porous TiNi sample on cooling and heating under a constant stress has shown a good correspondence between the experimental data and the results of modeling.

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Micromechanical Modelling of Superelasticity in Shape Memory Alloys

Cited by 132 publications

References 3 publications

On consistent micromechanical estimation of macroscopic elastic energy, coherence energy and phase transformation strains for SMA materials

On consistent micromechanical estimation of macroscopic elastic energy, coherence energy and phase transformation strains for SMA materials

The variant selection criteria in single-crystal CuAlNi shape memory alloys

Modeling of Functional Properties of Porous Shape Memory Alloy

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