Thermomechanics of Hysteresis Effects in Shape Memory Alloys

Favier, Damien; Guélin, P.; Pegon, P.

doi:10.4028/www.scientific.net/msf.56-58.559

Cited by 17 publications

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“…As proposed in [1,2], the permanence of the simultaneous existence of reversible processes and hysteresis in the thermomechanical behaviour of shape memory alloys suggests to express the total stress σ as the addition of two partial stresses, the first σ r being hyperelastic while the second one is related to hysteresis of elastoplastic type [3][4][5]. A 1-D illustration of the "elastohysteresis model" is shown in figure 1a.…”

Section: The Elastohysteresis Modelmentioning

confidence: 99%

Elastohysteresis model implemented in the ﬁnite element sofware HEREZH++

Rio

Favier

Liu

2009

ESOMAT 2009 - 8th European Symposium on Martensitic Transformations

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Abstract. This short paper describes the simulation results obtained with the elasto-hysteresis model implemented in the finite element software Herezh++ and compares them with the experimental data of the Roundrobin SMA Modelling benchmark. The elastohysteresis modelAs proposed in [1,2], the permanence of the simultaneous existence of reversible processes and hysteresis in the thermomechanical behaviour of shape memory alloys suggests to express the total stress σ as the addition of two partial stresses, the first σ r being hyperelastic while the second one is related to hysteresis of elastoplastic type [3][4][5]. A 1-D illustration of the "elastohysteresis model" is shown in figure 1a. In the present work, the partial hyperelastic stress tensor is calculated from the hyperelastic potential proposed by Orgéas [6,7], which leads in the 1-D case (shear test) to the stress-strain curve shown in figure 1b. In the case of shape memory alloys [2], the potential ω = ω(V, Q ε , ϕ ε ) is expressed as function of 3 invariants of the Almansi strain tensor: the relative variation of volume V, the intensity of the deviatoric deformation Q ε , and ϕ ε a measure of the angle giving the direction of the deformation tensor in the deviatoric plane. The hysteresis is described by an incremental model of hypoelastic type :σ = 2µD + βφ∆ t Rσ and an algorithm to manage discrete memory points σ R introduced by P.Guélin [3] and used in the model.D is the deviatoric strain rate tensor and ∆σ = σ(t) − σ R . More details can be found in [2,[4][5][6]9]. Figures 1b-e show the meaning of the parameters used in this work. Process to parameter identificationFirstly, eight parameters independent of the temperature are used in this model, including 6 parameters involved in the hyperelastic potential and 2 parameters of the hysteresis scheme. The 6 parameters independent of the temperature of the hyperelastic potential (cf. fig. 1 b ) are: the 3 slopes: µ 1 µ 2 µ 3 , the 2 curvatures for the transitions: α 1 α 2 and the bulk modulus K. The 2 hysteresis parameters indepedent of the temperature (cf. fig. 1 c )are: the initial slope µ and the Prager parameter np which controls the transition to the saturation of the hypoelastic scheme). The bulk modulus K is chosen from the literature. The 7 other parameters independent of the temperature are determined from one isothermal tensile test performed at a temperature above Af.a

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Section: The Elastohysteresis Modelmentioning

confidence: 99%

Elastohysteresis model implemented in the ﬁnite element sofware HEREZH++

Rio

Favier

Liu

2009

ESOMAT 2009 - 8th European Symposium on Martensitic Transformations

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“…Some mechanistic models aimed at describing the behaviour of shape memory alloys have been reported in the literature [5--9]. Some of the models have been the basis of three-dimensional constitutive equations [7]. Most of the models focus on the hysteretic behaviour of the transformations, with no distinction between thermally induced and mechanically induced processes.…”

Section: Introductionmentioning

confidence: 99%

Mechanistic simulation of thermomechanical behaviour of thermoelastic martensitic transformations in polycrystalline shape memory alloys

2004

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This paper proposes a mechanistic model to simulate the thermal and mechanical behaviour of shape memory alloys. The model is based on the thermodynamic concept of chemical, elastic and frictional energies for thermoelastic martensitic transformations and plasticity concept of grain interior and grain boundary phases. In a thermoelastic martensitic transformation system, a thermally induced transformation and a mechanically induced (stress-induced) transformation require different operating mechanisms from a mechanistic viewpoint. For a thermally induced transformation, the driving force arises from within the matrix and internal stresses are created as a result of frictional movement. For a mechanically induced transformation, the driving force is provided externally and the frictional movement occurs when the stress exceeds a critical value. This paper proposes a unified mechanistic model taking into account this difference. The model is able to describe, in a schematic and qualitative manner, the behaviour of a thermoelastic martensitic transformation system in both thermally induced and mechanically induced processes, including full and partial thermal transformation cycles, stress-induced martensitic transformation, pseudoelastic deformation and ferroelastic deformation via martensite variant reorientation. Such a model allows the discussion of several aspects concerning the thermal and mechanical behaviour of thermoelastic martensitic transformations, such as the non-linear pseudoelasticity, deformation-induced two-way memory effect, strain dependence of mechanical hysteresis and minor loop behaviour of deformation.

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“…A first hyperelastic part is completed with a viscous part, a damage part or both of them. Even though such a representation is usually used for elastomers, it was also used for other materials, for example to study metallic alloys and magnetization phenomena [26,27].…”

Section: Decomposition Of the Materials Behaviormentioning

confidence: 99%

Hyperelasticity with rate-independent microsphere hysteresis model for rubberlike materials

Rey

Chagnon

Favier

et al. 2014

Computational Materials Science

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with rateindependent microsphere hysteresis model for rubberlike materials. Computational Materials Science, Elsevier, 2014Elsevier, , 90, pp.89-98. 10.1016Elsevier, /j.commatsci.2014 Hyperelasticity with rate-independent microsphere hysteresis model The mechanical behavior of elastomers strongly differs from one to another. Among these differences, hysteresis upon cyclic load can take place, and can be either rate-dependent or rate-independent. In the present paper, a microsphere model taking into account rate-independent hysteresis is proposed and applied to model filled silicone rubbers behavior. The hysteresis model is based on a combination of monodimensional constitutive equations distributed in space. The behavior of each direction is described by a collection of parallel spring slider elements. The sliders are Coulomb dampers with non-zero break-free force in tension. This model is tested on a filled silicone rubber by the way of uniaxial tensile and pure shear tests. The mechanical response of the material is well predicted for such tests. Finally, the constitutive equations are implemented in the finite element software ABAQUS. Calculation results highlight good performances of the proposed model.

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Thermomechanics of Hysteresis Effects in Shape Memory Alloys

Cited by 17 publications

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Elastohysteresis model implemented in the ﬁnite element sofware HEREZH++

Elastohysteresis model implemented in the ﬁnite element sofware HEREZH++

Mechanistic simulation of thermomechanical behaviour of thermoelastic martensitic transformations in polycrystalline shape memory alloys

Hyperelasticity with rate-independent microsphere hysteresis model for rubberlike materials

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