Phenomenological analysis on subloops and cyclic behavior in shape memory alloys under mechanical and/or thermal loads

Tanaka, Kikuaki; Nishimura, Futoshi; Hayashi, Tateki; Tobushi, Hisaaki; Lexcellent, Christian

doi:10.1016/0167-6636(94)00038-i

Cited by 152 publications

(88 citation statements)

References 23 publications

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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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“…Again, the proposed model captures the general behavior of internal subloops related to pseudoelasticity. Tanaka et al [29] analyze subloops related to either the stress-strain or strain-temperature curves. The proposed model is based on the model with assumed phase-transformation kinetics previously presented by Tanaka and Nagaki [27].…”

Section: Introductionmentioning

confidence: 99%

Describing internal subloops due to incomplete phase transformations in shape memory alloys

Savi

Paiva

2005

Arch Appl Mech

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The hysteretic response of shape memory alloys (SMAs) is one of their essential characteristics and is related to the martensitic phase transformation. The hysteresis loop may be observed either in stressstrain or strain-temperature curves. In brief, it is possible to say that the major (or external) hysteresis loop can be defined as the envelope of all minor (or internal) hysteresis loops, usually denoted as subloops. The macroscopic description of the SMA hysteresis loops, together with their subloops due to incomplete phase transformations, is an important aspect in the phenomenological description of the thermomechanical behavior of SMAs, being of great interest in technological applications. This contribution exploits the description of these internal subloops and employs a constitutive model previously proposed by [1,20,25]. Numerical investigations of the phenomenon are carried out to show the capability of this model to describe these inner subloops. Comparisons between numerical and experimental results show that they are in close agreement. Moreover, numerical simulations are carried out to elucidate different aspects of this hysteretic behavior.

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“…Repeated forward and reverse phase changes create some defects within the material [Abeyaratne and Kim 1997], which result in localized internal stresses [Tanaka et al 1995], allowing SMAs to exhibit twoway shape memory. In this case the material is said to be trained (training phenomena).…”

Section: Introductionmentioning

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%

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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Phenomenological analysis on subloops and cyclic behavior in shape memory alloys under mechanical and/or thermal loads

Cited by 152 publications

References 23 publications

Energy barriers and hysteresis in martensitic phase transformations

Energy barriers and hysteresis in martensitic phase transformations

Describing internal subloops due to incomplete phase transformations in shape memory alloys

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

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