A Model for Shape Memory

Achenbach, M.; Müller, Ingo

doi:10.1051/jphyscol:1982418

Cited by 28 publications

(24 citation statements)

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“…It is easy to check that if the triangle is replaced by the curvilinear triangle (Fig-5) we obtain the experimental law (cf. [1,7,12,13]). This means that the only possible mixtures are those represented by the triangle !3~c and that the two martensites always coexist.…”

Section: J9fmentioning

confidence: 99%

“…As far as we know, all other macroscopic models using the same variables are in a single dimension of space and involve complicated free energy expressions [1,2,7,16]. However, there are several other approaches accounting for microscopic properties [3,14], Our model is based on simple and well-known expressions for the free energies of the phases, and the phase proportions are here regarded as thermodynamic quantities.…”

mentioning

confidence: 99%

“…Some metallic alloys exhibit the following unusual behaviour: they can be permanently deformed (up to 8% under traction), but they totally recover their initial shape just by thermal means. This phenomenon is called shape memory, and can be interpreted as the effect of an austenite-martensite phase transition [1,7,12,13].…”

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confidence: 99%

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Thermo-mechanical evolution of shape memory alloys

Colli¹,

Frémond²,

Visintin³

1990

Quart. Appl. Math.

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Abstract. In certain alloys, after deformation the original shape can be recovered just by thermal means. This shape memory behaviour can be interpreted as the effect of an austenite-martensite phase transition. We model this phenomenon by assuming the free energy to depend on the volumetric proportions of the different phases.The thermo-mechanical evolutions of a three dimensional body of such a material is here modelled in the framework of a second gradient theory. A variational formulation in Sobolev spaces is given; existence and uniqueness of the solution are proven by means of a fixed point argument.

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Section: J9fmentioning

confidence: 99%

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confidence: 99%

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Thermo-mechanical evolution of shape memory alloys

Colli¹,

Frémond²,

Visintin³

1990

Quart. Appl. Math.

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“…The comparative sample was a Ni-Ti wire with a diameter of 0.6 mm and a clamping length of 90 mm. The underlying model of the simulation is a modification of the thermomechanically coupled Müller-Achenbach-Seelecke (MAS) model 23,24,19 . The model was extended to allow for the simulation of localized phase transformation and inhomogeneous temperature distribution.…”

Section: Cooling Processmentioning

confidence: 99%

Experimental Methods for Investigation of Shape Memory Based Elastocaloric Cooling Processes and Model Validation

Schmidt

Ullrich

Wieczorek

et al. 2016

JoVE

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Shape Memory Alloys (SMA) using elastocaloric cooling processes have the potential to be an environmentally friendly alternative to the conventional vapor compression based cooling process. Nickel-Titanium (Ni-Ti) based alloy systems, especially, show large elastocaloric effects. Furthermore, exhibit large latent heats which is a necessary material property for the development of an efficient solid-state based cooling process. A scientific test rig has been designed to investigate these processes and the elastocaloric effects in SMAs. The realized test rig enables independent control of an SMA's mechanical loading and unloading cycles, as well as conductive heat transfer between SMA cooling elements and a heat source/sink. The test rig is equipped with a comprehensive monitoring system capable of synchronized measurements of mechanical and thermal parameters. In addition to determining the process-dependent mechanical work, the system also enables measurement of thermal caloric aspects of the elastocaloric cooling effect through use of a high-performance infrared camera. This combination is of particular interest, because it allows illustrations of localization and rate effects -both important for efficient heat transfer from the medium to be cooled.The work presented describes an experimental method to identify elastocaloric material properties in different materials and sample geometries. Furthermore, the test rig is used to investigate different cooling process variations. The introduced analysis methods enable a differentiated consideration of material, process and related boundary condition influences on the process efficiency. The comparison of the experimental data with the simulation results (of a thermomechanically coupled finite element model) allows for better understanding of the underlying physics of the elastocaloric effect. In addition, the experimental results, as well as the findings based on the simulation results, are used to improve the material properties.

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“…A lot of publications may be found which are concerned with the modeling and computational analysis of shape memory alloys. An early publication is made by Achenbach and Müller [1]. Classical tools of statistical mechanics are used to represent the stress-strain-behavior at different temperatures.…”

Section: Introductionmentioning

confidence: 99%

Constitutive Modeling of Prestressed Shape Memory Fiber–matrix Compounds

Kohlhaas¹,

Klinkel²

2014

Proceedings of 10th World Congress on Computational Mechanics

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Abstract. This contribution is concerned with a constitutive model for shape memory alloy (SMA) fibers. The model accounts for all material phenomena. It incorporates pseudoplasticity and the shape memory effect (SME). These phenomena occur in the low temperature range. For high temperature phase, the pseudoelastic behavior occurs. Additionally, the constrained SME (CSME) and the two-way SME are captured by the model. With respect to the assumption of small strains an additive split of the strain in an elastic and inelastic part is suggested. A free energy function is defined as a function of the elastic strain and an internal hardening variable. The constitutive equations for the stress and the conjugate hardening variable are derived from free energy. The elastic range is defined by two yield criteria, which are similar to kinematic hardening, known from classical plasticity theory. Here, the cases of loading and unloading are distinguished. These criteria are functions of the stress, the conjugate hardening variable and the energy difference between the austenitic and the martensitic phase, the so-called driving variable. The evolution equations for the inelastic state variables, namely the inelastic strain, the internal hardening variable and an inner variable, describing the martensitic volume evolution, are in accordance with the second law of thermodynamics. They are derived from the principle of maximum dissipation with the yield criteria as constraint. Following standard arguments, the martensite volume fraction is decomposed into twinned and oriented martensite. The first one is able to transform into austenite due to heating and vice versa. Just as well, it can change into the second one applying mechanical stress. The constitutive model is embedded in a one-dimensional truss formulation and implemented into a finite element analysis program. Numerical examples show the capability of the formulation. Simulations demonstrate the wide range of possible applications of SMA. A fiber-matrix composite is discussed, which allows for prestressing structures. This necessitates a precise description of the CSME. Likewise, this effect is used to prestress a representative volume element.

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A Model for Shape Memory

Cited by 28 publications

References 0 publications

Thermo-mechanical evolution of shape memory alloys

Thermo-mechanical evolution of shape memory alloys

Experimental Methods for Investigation of Shape Memory Based Elastocaloric Cooling Processes and Model Validation

Constitutive Modeling of Prestressed Shape Memory Fiber–matrix Compounds

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