A 3D model of the cyclic thermomechanical behavior of shape memory alloys

Zaki, Wael; Moumni, Ziad

doi:10.1016/j.jmps.2007.03.011

Cited by 165 publications

(74 citation statements)

References 14 publications

(14 reference statements)

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“…These include papers that propose constitutive equations for martensitic materials from which hysteresis loops are computed ( [43], [24], [6], [44], [26], [48]), those that discuss hysteresis in martensites in the presence of disorder ( [39], [46]); papers that relate hysteresis to the attainment of a self-organized critical state [34], to metastability induced by incompatibility [2], and to pinning of interfaces by defects ( [22], [49]). Another line of work models hysteresis using the Preisach model and its generalizations [4].…”

Section: Introductionmentioning

confidence: 99%

Energy barriers and hysteresis in martensitic phase transformations

2009

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Abstract. We report results from a systematic program of changing composition of alloys in the system TiNiX, X= Cu, Pt, Pd, Au, to pursue certain special lattice parameters that have been identified previously with low hysteresis. We achieve λ 2 = 1, where λ 2 is the middle eigenvalue of the transformation strain matrix, for alloys with X = Pt, Pd, Au. In all cases there is a sharp drop of the graph of hysteresis vs. composition at the composition where λ 2 = 1. When the size of the hysteresis is replotted vs. λ 2 we obtain an universal graph for these alloys, which also agrees with trends in an earlier combinatorial study of alloys in the system TiNiCu. Motivated by these experimental results, we present a new theory for the size of the hysteresis based on the growth from a small scale of fully developed austenite martensite needles. In this theory the energy of the transition layer plays a critical role. New methods for calculation the optimal layer are developed that rely on Γ-convergence arguments, the small parameter being |λ 2 − 1|. The limiting energy of the transition layer is found to be governed by a nonstandard linear elasticity problem. Overall, the results point to a simple systematic method of achieving low hysteresis and a high degree of reversibility in transforming materials.

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Section: Introductionmentioning

confidence: 99%

Energy barriers and hysteresis in martensitic phase transformations

2009

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“…For full details regarding the model presented in this section, the reader is referred to [Zaki 2006;Zaki and Moumni 2007a;2007b;Moumni et al 2008].…”

Section: 2mentioning

confidence: 99%

“…In this regard, several models exist that are capable of handling cyclic, mainly superelastic, SMA behavior; see, for instance, [Liu et al 1999;Abeyaratne and Kim 1997;Lim and McDowell 2002;Tanaka et al 1995;Lexcellent and Bourbon 1996;Bo and Lagoudas 1999;Zaki and Moumni 2007a].…”

Section: Introductionmentioning

confidence: 99%

“…Section 2 is devoted to the presentation of the cyclic Zaki-Moumni model, where the behavior is described using three state variables representing residual strain induced by cyclic loading, internal stress induced by repeated phase change, and the cumulated martensite volume fraction. See [Zaki and Moumni 2007a;2007b] for a detailed discussion of the model. Section 3 discusses the low cycle fatigue law and numerical simulations of the dissipated energy at the stabilized cycle, along with a validation against experimental data in the case of cyclic superelasticity.…”

Section: Introductionmentioning

confidence: 99%

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Cyclic behavior and energy approach to the fatigue of shape memory alloys

Moumni

Zaki

Maïtournam

2009

J. Mech. Mater. Struct.

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We present an energy-based low-cycle fatigue criterion that can be used in analyzing and designing structures made from shape memory alloys subjected to cyclic loading. Experimentally, a response similar to plastic shakedown is observed. During the first cycles the stress-strain curve shows a hysteresis loop which evolves during the first few cycles before stabilizing. By adopting an analogy with plastic fatigue, it is shown that the dissipated energy of the stabilized cycle is a relevant parameter for estimating the number of cycles to failure of such materials. Following these observations, we provide an application of the cyclic model, previously developed by the authors within the framework of generalized standard materials with internal constraints in order to evaluate such parameter. Numerical simulations are presented along with a validation against experimental data in case of cyclic superelasticity.

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“…The present work focuses on proper numerical integration of the Zaki-Moumni model for SMAs [8,17,18] subjected to complex multiaxial loading in the superelastic range. The inelastic deformation of the material is accomplished in this case by means of two distinct physical processes: a solid-solid phase transformation from a single-variant parent phase called austenite to a multivariant product phase called martensite, and a reorientation of martensite by the formation of preferred variants at the expense of others as a result of changes in the magnitude and orientation of the stress experienced by the martensite.…”

Section: Introductionmentioning

confidence: 99%

Time Integration and Assessment of a Model for Shape Memory Alloys Considering Multiaxial Nonproportional Loading Cases

Zaki

Morin

et al. 2014

Volume 1: Development and Characterization of Multifunctional Materials; Modeling, Simulation and Control of Adaptive Systems;

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The paper presents a numerical implementation of the ZM model for shape memory alloys that fully accounts for non-proportional loading and its influence on martensite reorientation and phase transformation. Derivation of the time-discrete implicit integration algorithm is provided. The algorithm is used for finite element simulations using Abaqus, in which the model is implemented by means of a user material subroutine. The simulations are shown to agree with experimental and numerical simulation data taken from the literature.

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A 3D model of the cyclic thermomechanical behavior of shape memory alloys

Cited by 165 publications

References 14 publications

Energy barriers and hysteresis in martensitic phase transformations

Energy barriers and hysteresis in martensitic phase transformations

Cyclic behavior and energy approach to the fatigue of shape memory alloys

Time Integration and Assessment of a Model for Shape Memory Alloys Considering Multiaxial Nonproportional Loading Cases

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