Micromechanics modelling for the constitutive behavior of polycrystalline shape memory alloys—I. Derivation of general relations

Sun, Qinglei; Hwang, Keh Chih

doi:10.1016/0022-5096(93)90060-s

Cited by 373 publications

(145 citation statements)

References 14 publications

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“…Therefore, the transformation volume strain is neglected in our analysis. mathematical models can be found in literatures [15][16][17][18]. To avoid the complexity of tracking the detailed evolution of the material microstructure during the phase transformations, a phenomenological model is adopted in the present investigation [19,20].…”

Section: Materials Modelmentioning

confidence: 99%

Spherical indentation hardness of shape memory alloys

Yan

Sun

Liu

2006

Materials Science and Engineering: A

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Using dimensional analysis and the finite element method, the spherical indentation hardness of SMAs is investigated. The scaling relationship between the hardness and the mechanical properties of a SMA, such as the forward transformation stress, the maximum transformation strain magnitude, has been derived. Numerical results demonstrated that the hardness increases with the indentation depth but there is no threefold relationship between the hardness and the forward transformation stress. Increasing the maximum transformation strain magnitude would reduce the hardness of the material. These research results enhance our understanding of the hardness from the spherical indentation of SMAs.

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Section: Materials Modelmentioning

confidence: 99%

Spherical indentation hardness of shape memory alloys

Yan

Sun

Liu

2006

Materials Science and Engineering: A

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“…Research work by Sun and Hwang [82][83][84] also belongs to this group since no variants were considered but grains are interacting.…”

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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“…Fischer and Tanaka [12] attacked the problem by introducing hvo material structural levels; microregion and mcsodomain. It should be noted the work of Sun et al [13,14] who tried to establish a unified theory of transformation and thcrmomechanics in order to explain the transformation toughening in ceramics.…”

Section: Introductionmentioning

confidence: 99%

Transformation Thermomechanics of Alloy Materials in the Process of Martensitic Transformation : A Unified Theory

et al. 1996

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Abstract:A unified theory on the transformation aid thermomechanical behavior of alloy materials is proposed in the processes of plastic deformation and martensitic transformation. A transformation condition is introduced to describe the start and progress of the transformation, together with the yield condition for plasticity. n i e constitutive equations, thermomechanical and calorimetric, are derived following the conventional col~tiriuum mechanics whereas the evolutional equations for the internal variables are obtained by solving a cor~ditional extremum problem. The heat conduction eq~lation is presented. The transformation kinetics is discussed to reach Magee's kinetics.

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Micromechanics modelling for the constitutive behavior of polycrystalline shape memory alloys—I. Derivation of general relations

Cited by 373 publications

References 14 publications

Spherical indentation hardness of shape memory alloys

Spherical indentation hardness of shape memory alloys

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

Transformation Thermomechanics of Alloy Materials in the Process of Martensitic Transformation : A Unified Theory

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