On the macroscopic free energy functions for shape memory alloys

Bernardini, Davide

doi:10.1016/s0022-5096(00)00050-8

Cited by 29 publications

(51 citation statements)

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“…In the present paper elaborations presented in Bernardini, Ziolkowski and Raniecki [2,31] are further advanced among the others to verify the aptness of expressing the macroscopic coherence energy in the form of a quadratic function of phase composition-an ad hoc postulate in many papers devoted to SMA materials modeling. Attention is focused on micromechanics-based phenomenological modeling of properties of nphase SMA material consisting of austenite A and n − 1 generic martensitic objects M i .…”

Section: Introductionmentioning

confidence: 89%

“…In the present work it is called stored coherency energy. In completely independent effort the issue of structure of macroscopic free energy of SMA material was addressed by Bernardini [2], who elaborated micromechanics-based method of the combined estimation of all three terms (a)-(c) for two-phase RVE. He took advantage of the fact that in the case of two-phase medium there are unique connections between fourth-order dimensionless mechanical concentration factor tensors, commonly denoted by the symbol B α -cf., e.g., [5,6,8]-and other properly selected tensor measures of stress concentration.…”

Section: Introductionmentioning

confidence: 99%

“…It can be shown that at fixed microstructure geometry and microscopic phase strain field, the tensors B α , ε pt -(c) and scalar φ coh -(b) become unique functions of M. Estimate of M entails definite estimations of the terms (b) and (c). Thus, Bernardini [2] showed that for two-phase RVE the Gibbs free energy can be evaluated with the same level of approximation involved in the estimate of the effective elastic moduli. However, for multiphase medium comprising more than two phases (n > 2), unique connections between B α and M do not exist.…”

Section: Introductionmentioning

confidence: 99%

“…The results of classical homogenization theory presented in Dvorak and Benveniste, Dvorak [5,6] cf. also [2] are used in a unique modified manner which employs symmetric and skew-symmetric ingredients of self-equilibrated eigenstrains influence moduli (SEIM) to propose a new estimation method. The method served for presenting the terms (a) and (b) in the form of semilinear and/or semiquadratic functions of phase composition.…”

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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Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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“…The second part represents the energy storage due to internal stress fields (internal variables). 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).…”

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

Bernardini

Pence

2002

Encyclopedia of Smart Materials

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An understanding of shape‐memory behavior requires knowledge of various physical processes that operate on different length scales. The crystallographic shifts that are responsible for shape‐memory behavior take place in unit cells of atomic dimension. Here, however, these microscopic length scales are not the focus, rather, this article considers the macroscopic scale modeling that is useful for the engineering assessment of thermomechanical response (stress–strain–temperature) and energy balances (including damping) for devices such as connectors, actuators, vibration absorbers, and biomedical stents. The macro scale is involves primary design evaluation such as predicting triggering forces and determining range of motion. Since the shape‐memory material is incorporated into a larger engineered device or structure, there is also required detailed computational simulation of the system as a whole.

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On the macroscopic free energy functions for shape memory alloys

Cited by 29 publications

References 30 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

Stress-induced phase-transition front propagation in thermoelastic solids

Shape‐Memory Materials, Modeling

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