Shape‐Memory Materials, Modeling

The present study is an extension of a recent paper of Freed et al. (J Mech Phys Solids 56:3003-3020, 2008). The final aim is to describe the transformation toughening behavior of a static crack along an interface between a shape memory alloy (SMA) and a linear elastic isotropic material. With an SMA as an equivalent Huber-Von Mises stress model (hypothesis of symmetric behavior between tension and compression), Freed et al. determine the initiation (ending) phase transformation yield surfaces in terms of the local phase angle introduced by Rice et al. (Metal ceramic interfaces, Pergamon Press, New York, pp 269-294, 1990). In this paper we give the general framework to determine this angle for a model integrating the asymmetry between tension and compression (experimentally measured: Vacher and Lexcellent in Proc ICM 6:231-236, 1991; Orgéas and Favier in Acta Mater 46(15): [5579][5580][5581][5582][5583][5584][5585][5586][5587][5588][5589][5590][5591] 2000), the Huber-Von Mises model being only a particular case. We demonstrate the local phase angle existence in an appropriate framing domain and give a sufficient hypothesis for its uniqueness and an algorithm to obtain it. Estimates are obtained in terms of physical quantities such as the Young modulus ratio, the bimaterial Poisson modulus values and also the choice of the yield loading functions. Finally, we illustrate this theoretical study by an application linking the asymmetry intensity on the width and the shape on predicted phase transformation surfaces and by a comparison with the symmetric case.

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“…Inequality (11) remains true because (10) remains true for (13). This is not the case for Equality (12), which is no longer true.…”

Section: Remark 1 Practicallymentioning

confidence: 96%

Rice Local Phase Angle Study for a Delamination Problem Between a Shape Memory Alloy and an Elastic Material

Laydi

Lexcellent

2012

Arch Rational Mech Anal

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“…Elucidating clue for such an operation is delivered by two equivalent forms of formulas (43) 1,2 and (43) 3,4 for tensors…”

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

confidence: 99%

“…In general, it may depend on phase composition and parameters describing the current geometry of microstructure. In that case all L V +A αβ defined in (48) 3 reduce to a single tensor…”

Section: Two Parameter Estimation For Isotropic Aggregate Of N Isotromentioning

confidence: 99%

“…They can be generally divided into the pseudoelasticity effects at higher temperatures T and the oneway memory (quasi-plasticity) effects at lower temperatures. 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%

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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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“…The resulting equations for the macroscopic behavior fit into the framework of internal variable models (Bernardini, 2001). Several models fitting into this basic framework have been proposed although sometimes employing quite different formalisms (Fischer et al, 1994;Birman, 1997;Bernardini and Pence, 2002). All of them involve a constitutive information prescribed via state equations and kinetic equations for the internal variables.…”

Section: Introductionmentioning

confidence: 99%

Stress-induced phase-transition front propagation in thermoelastic solids

Berezovski

Maugin

2005

European Journal of Mechanics - A/Solids

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A simplest possible mathematical model of martensitic phase transition front propagation is considered in the paper. Martensite and austenite phases are treated as isotropic linear thermoelastic materials. The phase transition front is viewed as an ideal mathematical discontinuity surface. Only one variant of martensite is involved. The problem remains nonlinear even in this simplified description that supposes a numerical solution. A non-equilibrium description of the process is provided by means of non-equilibrium jump relations at the moving phase boundary, which are formulated in terms of contact quantities. The same contact quantities are used in the construction of a finite-volume numerical scheme. The additional constitutive information is introduced by a certain assumption about the entropy production at the phase boundary. Results of numerical simulations show that the proposed approach allows us to capture experimental observations while corresponding to theoretical predictions in spite of the idealization of the process.

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Shape‐Memory Materials, Modeling

Cited by 16 publications

References 42 publications

Rice Local Phase Angle Study for a Delamination Problem Between a Shape Memory Alloy and an Elastic Material

Rice Local Phase Angle Study for a Delamination Problem Between a Shape Memory Alloy and an Elastic Material

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

Stress-induced phase-transition front propagation in thermoelastic solids

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