Creep and yield in martensitic transformations

Achenbach, M.; Müller, Ingo

doi:10.1007/bf00532524

Cited by 29 publications

(6 citation statements)

References 2 publications

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“…The scheme was actually demonstrated in In-Pb alloys by Nittono [11]. Muller and Wilmanski [12,13] established their theory based on the statistical physics, and calculated the stress, strain and temperature changes during the martensitic transformation [14]. Tanaka [15,16], on the other hand, employed the continuum mechanics with an internal variable to describe the transformation pseudoelasticity and the shape memory effect due to the thermoelastic martensitic transformation.…”

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confidence: 99%

A Phenomenological Description on Thermomechanical Behavior of Shape Memory Alloys

Tanaka¹

1990

Journal of Pressure Vessel Technology

135

104

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A constitutive theory, which consists of the constitutive equation and the transformation kinetics, is proposed to describe the thermomechanical behaviors of the shape memory alloys. Simulation in Ti-Ni alloy proves a good applicability of the theory when the overall characteristics of the stress-strain-temperature relation and the recovery stress induced in the heating process are studied in the uniaxial state. IntroductionWhen a specimen in the shape memory alloys is stressed at a temperature, inelastic deformation is observed above a critical stress. The inelastic strain induced in the loading process, however, fully recovers during the subsequent unloading. The stress-strain curve, as a result, forms a hysteresis loop. The same material behaves very differently at lower temperature, since some amount of strain remains even after complete unloading. The residual strain, however, recovers if the specimen is heated. The former behavior is called the transformation pseudoelasticity or the superelasticity, and the latter the shape memory effect [1][2][3]. Intensive metallurgical studies have revealed that such behavior of shape memory alloys was closely connected with the thermoelastic martensitic transformation and its reverse transformation which progress under a certain thermal and/or mechanical circumstances [4-7].As any shape memory devices used under complicated thermomechanical conditions, phenomenological or macroscopic study is more helpful than metallurgical or microscopic study for predicting the behavior of shape memory alloys. Among studies so far carried out along this line, we could list the following pioneering attempts: Falk [8,9] first suggested that Landau's transformation theory [10] could be used to explain the temperature-dependence of stress-strain curves of the shape memory alloys; that is, the stress-strain curve can be derived as a consequence of the thermodynamic considerations if the form of Helmholtz free energy is chosen approximately. The scheme was actually demonstrated in In-Pb alloys by Nittono [11]. Muller and Wilmanski [12,13] established their theory based on the statistical physics, and calculated the stress, strain and temperature changes during the martensitic transformation [14]. Tanaka [15,16], on the other hand, employed the continuum mechanics with an internal variable to describe the transformation pseudoelasticity and the shape memory effect due to the thermoelastic martensitic transformation.In this study, the thermomechanical models of the material

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confidence: 99%

A Phenomenological Description on Thermomechanical Behavior of Shape Memory Alloys

Tanaka¹

1990

Journal of Pressure Vessel Technology

135

104

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“…Up to now, no result on local existence of solutions is known when all these terms are absent although numerical results seem to indicate that even in this case solutions do exist. (2) The case a > 0 has a questionable physical meaning since the second law of thermodynamics is not satisfied in this case. (3) No rigorous proof on local existence for the case a = 0 has been given before.…”

Section: A One-dimensional Mathematical Modelmentioning

confidence: 99%

“…Between 1968 and1986 several mathematical models were proposed and studied ( [1], [2], [3], [ ). However, most of these SMA models did not take into account the strong coupling between the thermal and the mechanical properties which characterize their behavior.…”

Section: Introductionmentioning

confidence: 99%

<title>Well-posedness and finite dimensional approximations of a mathematical model for the dynamics of shape-memory alloys</title>

Spies

1993

SPIE Proceedings

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Shape Memory Alloys (SMA's) are intermetallic materials (chemical compounds of two or more elements) that are able to sustain a residual deformation after the application of a large stress, but they "remember" the original shape to which they creep back, without the application of any external force, after they are heated above a certain critical temperature. We present here a general one-dimensional dynamic mathematical model which reflects the balance laws for linear momentum and energy. The system accounts for thermal coupling, time-dependent distributed and boundary inputs and internal variables. Well-posedness is obtained using an abstract formulation in an appropriate Hilbert space and explicit decay rates for the associated linear semigroup are derived. Numerical experiments using finite-dimensional approximations are performed for the case in which the thermodynamic potential is given in the Landau-Devonshire form. The sensitivity of the solutions with respect to the model parameters is studied.

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“…We do not include the force TT in (13) as it acts internally to V. In this sense n has a role analogous to that of the internal forces G 1 and g 1 in Ericksen's theory of liquid crystals [24], since TT enters a balance equation but does not contribute to the working. 6 If we use (5) t and (ll) x to eliminate the external forces 6 and 7 from the local form of (13), we arrive at the local dissipation inequalitŷ -S.F-<tp> + <*,£><0, …”

Section: Dissipation Inequalitymentioning

confidence: 99%