On the modeling of shape memory alloys using tensorial internal variables

Luig, Patrick; Bruhns, Otto T.

doi:10.1016/j.msea.2007.03.123

Cited by 28 publications

(10 citation statements)

References 10 publications

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“…In particular, the forward martensitic transformation occurring under proportional axisymmetric loading and plane stress conditions is investigated systematically. The phenomenological SMA constitutive model adopted here assumes that the Martensite fractions evolve as linear functions of the Tresca effective stress, in agreement with the constitutive models proposed by Kasper (1997, 1999 ), Arghavani et al (2010), Marfia and Rizzoni (2013) for multi-variants Martensite and by Videnic et al (2008) and Luig and Bruhns (2008) for single variant Martensite. These models are derived from the theory of generalized plasticity developed by Lubliner and Auricchio (1996) and Auricchio and Lubliner (1997) .…”

Section: Introductionsupporting

confidence: 56%

Evolution of multiple Martensite variants in a SMA thick-walled cylinder loaded by internal pressure

Radi

2018

International Journal of Solids and Structures

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The stress and deformation fields in a SMA ring or a thick-walled cylinder loaded by internal pressure at constant temperature (over the start temperature of the martensitic transformation) are determined in closed form under plane stress loading conditions. The phenomenological SMA constitutive model incorporates the volume fractions of multi-variants Martensite, which are assumed to evolve linearly with the Tresca effective stress, according to the associative flow rule and the corner flow rule. Initially, the cylinder is everywhere in a state of Austenite. The application of an internal pressure then triggers the martensitic transformation starting from the inner radius of the cylinder wall and extending towards the outer radius. If the wall thickness is large enough, the tangential stress may vanish at the inner radius and correspondingly the stress state may reach a corner of the Tresca transformation condition, thus originating two different Martensite variants according to the corner transformation rule. The admissible phase partitions within the wall thickness originating during the loading process have been systematically investigated according to the ratio between the outer and inner radii. The results obtained here suggest that the loading process should be interrupted soon after the complete martensitic transformation is achieved at the inner radius of the cylinder to avoid permanent plastic deformations.

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Section: Introductionsupporting

confidence: 56%

Evolution of multiple Martensite variants in a SMA thick-walled cylinder loaded by internal pressure

Radi

2018

International Journal of Solids and Structures

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“…For example, a comparison between experimental characterisation and micromechanical modelling of superelastic response of a porous NiTi shape memory alloy [30], a comparison of several models for the determination of the phase transformation yield surface in SMA with experimental data [31], and another comparison of models with experimental results in a test in simple tension [32]. In this study, a thermomechanical modelling of recovery stresses in SMA will be proposed.…”

Section: Sma Modellingmentioning

confidence: 99%

Recovery stresses in SMA wires for civil engineering applications: experimental analysis and thermomechanical modelling

Tran

Balandraud²,

Destrebecq

2011

Materialwissenschaft Werkst

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The present study deals with the creation of so-called "recovery stresses" in SMA wires. Two approaches are developed. First, experiments are performed on nickel-titanium wires with suitable transformation temperatures. The wires are stretched in the martensite state at ambient temperature. A thermal cycle at constant strain is applied to transform the martensite to austenite, in order to activate the shape memory effect. During the thermal loading, both the phase transformation and the thermal expansion lead to stresses in the wires. Second, a thermomechanical model is used to analyze the experimental results. The model accounts for the phase transformations caused by combinations of stress and temperature loadings. The results are then discussed in the framework of application to concrete component reinforcement.

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“…Similar choices, but again in a small strain non-structured setting, have been successfully pursued in other works [6,[21][22][23].…”

Section: Configuration Fields and Choice Of The Microstructural Descrmentioning

confidence: 89%

A structured continuum modelling framework for martensitic transformation and reorientation in shape memory materials

Bernardini

Pence

2016

Phil. Trans. R. Soc. A.

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Models for shape memory material behaviour can be posed in the framework of a structured continuum theory. We study such a framework in which a scalar phase fraction field and a tensor field of martensite reorientation describe the material microstructure, in the context of finite strains. Gradients of the microstructural descriptors naturally enter the formulation and offer the possibility to describe and resolve phase transformation localizations. The constitutive theory is thoroughly described by a single free energy function in conjunction with a path-dependent dissipation function. Balance laws in the form of differential equations are obtained and contain both bulk and surface terms, the latter in terms of microstreses. A natural constraint on the tensor field for martensite reorientation gives rise to reactive fields in these balance laws. Conditions ensuring objectivity as well as the relation of this framework to that provided by currently used models for shape memory alloy behaviour are discussed.

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On the modeling of shape memory alloys using tensorial internal variables

Cited by 28 publications

References 10 publications

Evolution of multiple Martensite variants in a SMA thick-walled cylinder loaded by internal pressure

Evolution of multiple Martensite variants in a SMA thick-walled cylinder loaded by internal pressure

Recovery stresses in SMA wires for civil engineering applications: experimental analysis and thermomechanical modelling

A structured continuum modelling framework for martensitic transformation and reorientation in shape memory materials

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