A 3-D constitutive model for shape memory alloys incorporating pseudoelasticity and detwinning of self-accommodated martensite

Popov, Peter; Lagoudas, Dimitris C.

doi:10.1016/j.ijplas.2007.03.011

Cited by 201 publications

(92 citation statements)

References 51 publications

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“…Note also that Fig. 1 SMA stress-temperature phase diagram (schematic) [10] polycrystalline SMA materials often show significantly different transformation behaviour in compression as opposed to tension. This tension/compression asymmetry is not accounted for in this description, but a complete discussion has been provided in reference [11].…”

Section: Properties Of Sma Behaviourmentioning

confidence: 99%

Aerospace applications of shape memory alloys

Hartl

Lagoudas

2007

Proceedings of the Institution of Mechanical Engineers, Part G:

724

336

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With the increased emphasis on both reliability and multi-functionality in the aerospace industry, active materials are fast becoming an enabling technology capturing the attention of an increasing number of engineers and scientists worldwide. This article reviews the class of active materials known as shape memory alloys (SMAs), especially as used in aerospace applications. To begin, a general overview of SMAs is provided. Their useful properties and engineering effects are described and the methods in which these may be utilized are discussed. A review of past and present aerospace applications is presented. The discussion addresses applications for both atmospheric earth flight as well as space flight. To complete the discussion, SMA design challenges and methodologies are addressed and the future of the field is examined.

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Section: Properties Of Sma Behaviourmentioning

confidence: 99%

Aerospace applications of shape memory alloys

Hartl

Lagoudas

2007

Proceedings of the Institution of Mechanical Engineers, Part G:

724

336

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“…also Popov and Lagoudas [19] and chapter 3 in Ziolkowski [32]. The appearance of this effect itself delivers experimental premise for presence of nonzero, incompatible, phase fluctuation 2 in NiTi alloys, induced by phase transitions resulting from thermomechanical loadings.…”

Section: Stored Coherency Energy and Fluctuating Part Of Microeigenstmentioning

confidence: 96%

“…Surveys on behavior and thermodynamics of SMA materials including diverse modeling approaches can be found, e.g., in [3,9,10] or chapter 3 in [32]. A minute inspection of, e.g., [20] or [19], reveals that the determination of the macroscopic Gibbs free energy function g for the representative volume element (RVE) requires specification of three fundamental terms: (a) the elastic complementary energy g el (or the effective elastic compliance, M), (b) the coherence energy φ coh -a term coined by Müller and Seelecke [13] and (c) the macroscopic phase strain ε pt or the phase transformation work-bounded by the ultimate potential energy g ult of an external devise-g ult ≡ σ · ε pt .…”

Section: Introductionmentioning

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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“…Indeed, SMA behavior has been investigated at all scales (microscopic, mesoscopic with volume fractions, macroscopic) and by means of a full menagerie of modelling perspectives. Even restricting to the realm of macroscopic-phenomenological models (which is the focus of this paper), the different modelling options available are many and diversified and the corresponding cross-validation is still under assessment [6,18,19,21,22,27,28,[35][36][37][38][39]42,43]. On the contrary, the mathematical treatment of full thermo-mechanical problems for SMAs is less developed for the only comprehensive results in this sense refer to either the original formulations or modifications of the Frémond [19] and the Falk and Konopka [17,18] models.…”

Section: Introductionmentioning

confidence: 99%