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

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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.

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Authors and Affiliations

  1. Institute of Applied Mechanics, RWTH Aachen University, Aachen, Germany

    Johanna Waimann

  2. Institute of Mechanics of Materials, Ruhr-Universität Bochum, Bochum, Germany

    Klaus Hackl & Philipp Junker

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  1. Johanna Waimann
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  2. Klaus Hackl
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  3. Philipp Junker
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Correspondence to Johanna Waimann.

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Waimann, J., Hackl, K. & Junker, P. Variational Modeling and Finite-Element Simulation of Functional Fatigue in Polycrystalline Shape Memory Alloys. J Optim Theory Appl 184, 98–124 (2020). https://doi.org/10.1007/s10957-019-01476-0

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