Thermomechanical Behavior of Shape Memory Alloys

Patoor, Étienne; Eberhardt, A.; Berveiller, M.

doi:10.1051/esomat/198903002

Cited by 46 publications

(53 citation statements)

References 7 publications

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“…The empirical coefficients CS, CE (4) were calculated for each specimen from the data of the first two loops and used to determine the energetically equivalent values of shear stress, rinv, (equation 5) and shear strain,yinv, (equation 5), from the original T and y values defined by (3). The equivalent stresses and strains in simultaneous tension -torsion loadings were calculated by equations (6). Such technique to determine the energetically equivalent values of uniform stresses and strains can theoretically be used for elastic strains only.…”

Section: Methodsmentioning

confidence: 99%

On Transformation Pathways of General Stress Controlled Thermoelastic Martensitic Transformation in Shape Memory Alloys

et al. 1996

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Section: Methodsmentioning

confidence: 99%

On Transformation Pathways of General Stress Controlled Thermoelastic Martensitic Transformation in Shape Memory Alloys

et al. 1996

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“…Falk [29][30][31][32], Ball and James [9], Abeyarantne and co-workers [1][2][3][4], Krumhansl [51], Lindgrad [55], etc., to develop a microscopic model for PTs. Patoor, Eberhardt, and Berveiller [62] initiated to work at macro scale using the information from microscopic scale. Therein, habit planes, Cauchy-Born hypothesis of lattice-continuum link, martensitic phase variants, etc.…”

Section: State Of the Art Of Engineering Theories And Computational Mmentioning

confidence: 99%

Contributions on the theory and computation of mono‐ and poly‐crystalline cyclic martensitic phase transformations

Sagar

Stein

2010

Z Angew Math Mech

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In this article new contributions to the theory and computation of cyclic martensitic phase transformations (PT) in monoand poly-crystalline metallic shape memory alloys are presented. The PT models of the non-convex variational problem are based on the Cauchy-Born hypothesis and Bain's principle. A quasi-convexified C 1 -continuous thermo-mechanical micromacro constitutive model for metallic monocrystals is developed which is represented together with the phase transformation constraints by a unified Lagrangian variational functional including phase evolution equations with mass conservation. The unified setting presented here includes poly-crystalline shape memory alloys whose microstructure is modeled using lattice variants. A pre-averaging scheme for randomly distributed poly-crystalline variants of transformation strains is used to transform them into those of a fictitious monocrystal. Thus, the incremental integration in process time and the spatial integration algorithms of the discrete variational problems for both mono-and poly-crystalline phase transformations can be implemented into a unified algorithm with branching for mono-and poly-crystalline phase transformations. Furthermore, an error-controlled adaptive 3D finite element method in space is presented for phase transformation problems using explicit error indicator with gradient smoothing and mesh refinements via new mesh generation in each adaptive step. Computations of informative examples with convergence studies, and comparisons with published experimental results are presented using 3D finite elements. Shape memory alloys: phenomenology, physical effects, and applicationsShape memory alloys (SMAs) have immense technological potential because of various aspects of their special thermomechanical behavior, such as shape memory effect (SME) in form of reversible quasiplastic (QP) deformation, superelasticity (SE), and bio-compatibility. Nowadays, it is widely used for biomedical systems e.g. endovascular stents, orthodontic arc wires; for controlling and activating mechanical systems such as actuators and connectors and also for structural systems e.g. vibration control devices.SMAs exhibit a strong nonlinear thermomechanical behavior associated with abrupt changes in their lattice structure called martensitic phase transformation (PT). They have intrinsic ability to transform between austenite (parent phase) and a number of symmetry-related martensitic variants (product phases). Those SMAs considered here are copper based alloy CuAlNi and nickel based alloy NiTi, which both can behave as QP and SE depending on the operating temperature.Martensitic PT is considered as a diffusionless first-order transformation between 'high' temperature, θ > A s , austenite and 'low' temperature martensitic phases, θ < M s , Fig. 1. A s and M s are the so-called austenite and martensite start temperatures. Other critical temperatures are austenite and martensite finish temperatures which are denoted by A f and M f , respectively. SMAs exhibit a specific feature...

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“…Micro-macro modeling was originated by Patoor et al [26]. In this theory, habit planes, CauchyBorn hypothesis of lattice-continuum link, martensitic phase variants, etc.…”

Section: Overview On Constitutive and Computational Modelingmentioning

confidence: 99%

Theory and finite element computation of cyclic martensitic phase transformation at finite strain

Stein

Sagar

2007

Numerical Meth Engineering

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SUMMARYA generalized variational formulation, including quasi-convexification of energy wells for arbitrarily many martensitic variants in case of mono-crystals for linearized strains, was developed by Govindjee and Miehe (Comp. Meth. Appl. Mech. Eng. 2001; 191(3-5):215-238) and computationally extended by Stein and Zwickert (Comput. Mech. 2006; in press). This work is generalized here for finite strain kinematics with monotonous hyperelastic stress-strain functions in order to account for large transformation strains that can reach up to 15%.A major theoretical and numerical difficulty herein is the convexification of the finite deformation phase transformation (PT) problems for multiple phase variants, n 2. The zigzag-type experimental stressstrain curve within PT at loading, called 'yield tooth', is approximated within the finite element analysis by a smoothly decreasing and then increasing axial stress which could not be achieved with linearized kinematics yielding a constant axial stress during PT.

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Thermomechanical Behavior of Shape Memory Alloys

Abstract: The overall thermomechanical behavior of Shape Memory Alloys is described from a microphysical point of view. Results obtained in that way are in good agreement with uniaxial tension test experiments performed on a Cu -Zn -Al Shape Memory Alloy.

Cited by 46 publications

References 7 publications

On Transformation Pathways of General Stress Controlled Thermoelastic Martensitic Transformation in Shape Memory Alloys

On Transformation Pathways of General Stress Controlled Thermoelastic Martensitic Transformation in Shape Memory Alloys

Contributions on the theory and computation of mono‐ and poly‐crystalline cyclic martensitic phase transformations

Theory and finite element computation of cyclic martensitic phase transformation at finite strain

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