Variational Modeling and Finite-Element Simulation of Functional Fatigue in Polycrystalline Shape Memory Alloys

authored by: Johanna Waimann, Klaus Hackl, Philipp Junker
Abstract: Based on our previous works, we present the finite-element implementation of an energy-based material model that displays the effect of functional fatigue of shape memory alloys during cyclic loading. The functional degradation is included in our model by taking account of irreversible martensitic volume fractions. Three internal variables are used: reversible and irreversible volume fractions for the crystallographic phases and Euler angles for parametrization of the martensite strain orientation. The evolution of the volume fractions is modeled in a rate-independent manner, whereas a viscous approach is employed for the Euler angles, which account for the materials’ polycrystalline structure. For the case of a cyclically loaded wire, we calibrate our model using experimental data. The calibration serves as input for the simulation of two more complex boundary value problems to demonstrate the functionality of our material model for localized phase transformations.
External Organisation(s): RWTH Aachen University
Ruhr-Universität Bochum
Type: Article
Journal: Journal of Optimization Theory and Applications
Volume: 184
Pages: 98-124
No. of pages: 27
ISSN: 0022-3239
Publication date: 30.01.2019
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Control and Optimization, Management Science and Operations Research, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s10957-019-01476-0 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{9671f51b00bd4798b4884815887306e1,
title = "Variational Modeling and Finite-Element Simulation of Functional Fatigue in Polycrystalline Shape Memory Alloys",
abstract = "Based on our previous works, we present the finite-element implementation of an energy-based material model that displays the effect of functional fatigue of shape memory alloys during cyclic loading. The functional degradation is included in our model by taking account of irreversible martensitic volume fractions. Three internal variables are used: reversible and irreversible volume fractions for the crystallographic phases and Euler angles for parametrization of the martensite strain orientation. The evolution of the volume fractions is modeled in a rate-independent manner, whereas a viscous approach is employed for the Euler angles, which account for the materials{\textquoteright} polycrystalline structure. For the case of a cyclically loaded wire, we calibrate our model using experimental data. The calibration serves as input for the simulation of two more complex boundary value problems to demonstrate the functionality of our material model for localized phase transformations.",
keywords = "Finite-element method, Functional fatigue, Irreversible phase transformation, Shape memory alloys, Variational modeling",
author = "Johanna Waimann and Klaus Hackl and Philipp Junker",
note = "Publisher Copyright: {\textcopyright} 2019, Springer Science+Business Media, LLC, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2019",
month = jan,
day = "30",
doi = "10.1007/s10957-019-01476-0",
language = "English",
volume = "184",
pages = "98--124",
journal = "Journal of Optimization Theory and Applications",
issn = "0022-3239",
publisher = "Springer New York",
number = "1",
}