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One-Dimensional Shape Memory Alloys Material Phenomenological Constitutive Model Based on Stress Due to Mechanical and Chemical Energy Change

Received: 5 October 2023    Accepted: 26 October 2023    Published: 9 November 2023
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Abstract

Shape Memory Alloy (SMA) is a material that has the ability to memorize previous shapes after deforming. That is it regains its original shape when temperature increases, converting thermal energy to mechanical energy. This property of the plastic-like deformation which subsequently recovers its original shape is referred to as Shape Memory Effects (SMEs). The history of this material began in the year 1800s. Because of their unique behavior, SMA has great industrial applications. Many constituted models of SMA behavior are formed describing SMA behavior. Most of them are based on experimental phenomenological macroscopic constitutive models consisting of variables that reveal the degree of phase transition that describes the phenomenological macroscopic behavior of SMA. These types of models are very easy and the parameters are also very easy to determine. In this research, a constitutive model is formulated based on the obserbation of experimental data, the SMA behavior is simulated using Artificial Neural Networks (ANN). The phenomenological constitutive model comprises both mechanical and chemical change. In the parameter estimation, the Back-Progation (BP) algorithm and the nonlinear optimization algorithm are used. A numerical simulation is performed, and the phenomenological constitutive model captures well the uniaxial tension and compression experimental data, therefore the constitutive model is verified.

Published in American Journal of Mechanics and Applications (Volume 11, Issue 1)
DOI 10.11648/j.ajma.20231101.12
Page(s) 6-14
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

NiTi Shape Memory Alloy, Phenomenological Model, Artificial Neural Network

References
[1] P. Sittner, “Deformation twinning in martensite affecting functional behavior of NiTi shape memory alloys,” Materialia, vol. 9, no. March, p. 100506, 2019.
[2] L. G. Machado, M. A. Savi, R. De Janeiro, and R. De Janeiro, “Medical applications of shape memory alloys,” Brazilian J. Med. Biol. Res., vol. 36, no. 6, pp. 683–691, 2003.
[3] M. R. Nagendra, M. Tamilselvan, and C. Sadhasivam, “Computation and investigation of an SMA engine using low heat recovery,” Int. J. Pure Appl. Math., vol. 118, no. 20, pp. 57–62, 2018.
[4] A. M. Halahla et al., “The effect of shape memory alloys on the ductility of exterior reinforced concrete beam-column joints using the damage plasticity model,” Eng. Struct., vol. 200, no. September, p. 109676, 2019.
[5] S. Shiva, N. Yadaiah, I. A. Palani, C. P. Paul, and K. S. Bindra, “Thermo-mechanical analyses and characterizations of TiNiCu shape memory alloy structures developed by laser additive manufacturing,” J. Manuf. Process., vol. 48, no. February 2018, pp. 98–109, 2019.
[6] J. J. Zhu, N. G. Liang, W. M. Huang, and K. M. Liew, “Energy conversion in shape memory alloy heat engine part I: Simulation,” J. Intell. Mater. Syst. Struct., vol. 12, no. 2, pp. 133–140, 2001.
[7] V. N. Melnik Roderick, L. Wang, P. Matus, and I. Rybak, “Computational aspects of conservative difference schemes for shape memory alloys,” in International Conference on Computational Science and Its Applications, C. L. Gerhard Goos, Juris Hartmanis, Ed., Berlin, Heidelberg: Springer, 2003, pp. 791–800.
[8] L. Wang and R. V. N. Melnik, “Thermo-mechanical wave propagations in shape memory alloy rod with phase transformations,” Mech. Adv. Mater. Struct., vol. 14, no. 8, pp. 665–676, 2007.
[9] C. B. Churchill and J. Shaw, “Thermo-mechanical modeling of shape memory allow heat engine,” in Proceedings of the ASME 2011 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, Scottsdale, Arizona, USA: ASME, 2011, pp. 641–650.
[10] L. LECCE and C. Antonio, Shape Memory Alloy Engineering. Amsterdam: Elsevier, 2015.
[11] V. Alexandrakis, J. Manuel, and A. Pérez-checa, “Combinatorial synthesis of Ni–Mn–Ga-(Fe, Co, Cu) high temperature ferromagnetic shape memory alloys thin films,” Scr. Mater., vol. 178, no. March, pp. 104–107, 2020.
[12] E. Fritsch, M. Izadi, and E. Ghafoori, “Development of nail-anchor strengthening system with iron-based shape memory alloy (Fe-SMA) strips,” Constr. Build. Mater., vol. 229, p. 117042, 2019.
[13] H. Huang, P. Yao, and Y. Su, “Stress relaxation behavior of columnar-grained Cu-Al-Mn shape memory alloys,” Mater. Sci. Eng. A, vol. 768, no. September, p. 138432, 2019.
[14] X. Fei, Y. Haifeng, L. Kun, M. Jiaxiang, and C. Haoxue, “Forming and two-way shape memory effect of NiTi alloy induced by laser shock imprinting,” Opt. Laser Technol., vol. 120, no. April, p. 105762, 2019.
[15] P. Honarmandi, L. Johnson, and R. Arroyave, “Bayesian probabilistic prediction of precipitation behavior in Ni-Ti shape memory alloys,” Comput. Mater. Sci., vol. 172, no. September 2019, 2020.
[16] D. Patil and G. Song, “Shape memory alloy actuated accumulator for ultra-deepwater oil and gas exploration,” Smart Mater. Struct., vol. 25, no. 4, 2016, doi: 10.1088/0964-1726/25/4/045012.
[17] L. Pellone, S. Ameduri, N. Favaloro, and A. Concilio, “SMA-based system for environmental sensors released from an unmanned aerial vehicle,” Aerospace, vol. 4, no. 1, 2017, doi: 10.3390/aerospace4010004.
[18] G. Costanza, G. Leoncini, F. Quadrini, and M. E. Tata, “Design and Characterization of a Small-Scale Solar Sail Prototype by Integrating NiTi SMA and Carbon Fibre Composite,” in Advances in Materials Science and Engineering, D. C. Lagoudas, Ed., TX. USA: 8 Springer Science+Business Media, LLC, 2017, p. 1. doi: 10.1155/2017/8467971.
[19] U. Roshan, J. B. Basnayake, R. Amarasinghe, and N. Dayananda, “Design and Development of a Force Feedback System for a SMA Based Gripper as a Minimally Invasive Surgical Tool,” Proc. IEEE Sensors, vol. 2019-Octob, no. July 2021, pp. 1–4, 2019, doi: 10.1109/SENSORS43011.2019.8956849.
[20] S. H. Adarsh and V. Sampath, “Hot deformation behavior of Fe-28Ni-17Co-11.5Al-2.5Ta-0.05B (at.%) shape memory alloy by isothermal compression,” Intermetallics, vol. 115, no. December, p. 106632, 2019.
[21] H. Cho, Y. Takeda, and T. Sakuma, “Fabrication and output power characteristics of heat-engines using tape-shaped SMA element,” Adv. Struct. Mater., vol. 73, pp. 1–15, 2017.
[22] A. Paiva and M. A. Savi, “An overview of constitutive models for shape memory alloys,” Math. Probl. Eng., vol. 2006, no. September 2004, pp. 1–30, 2006, doi: 10.1155/MPE/2006/56876.
[23] F. Auricchio and E. Sacco, “A one-dimensional model for superelastic shape-memory alloys with different elastic properties between austenite and martensite,” Int. J. Non. Linear. Mech., vol. 32, no. 6, pp. 1101–1114, 1997, doi: 10.1016/s0020-7462(96)00130-8.
[24] R. Abeyaratne and J. K. Knowles, “A continuum model of a thermoelastic solid capable of undergoing phase transitions,” J. Mech. Phys. Solids, vol. 41, no. 3, pp. 541–571, 1993, doi: 10.1016/0022-5096(93)90048-K.
[25] T. Kikuak, K. Shigenori, and S. Yoshio, “Thermomechanics of transformation pseudoelasticity and shape memory effect in alloys,” Int. J. Plast., vol. 2, no. 1, pp. 59–72, 1986.
[26] C. A. Liang, C., & Rogers, “One-dimensional thermo-mechanical constitutive relations for shape memory materials,” J. Intell. Mater. Syst. Struct., vol. 1(2), pp. 207-234., 1990.
[27] L. C. Brinson, “One-dimensional constitutive behavior of shape memory alloys: Thermomechanical derivation with non-constant material functions and redefined martensite internal variable,” J. Intell. Mater. Syst. Struct., vol. 4, no. 2, pp. 229–242, 1993.
[28] F. Wang and L. Wang, “A phenomenological constitutive model for one-dimensional shape memory alloys based on artificial neural network,” vol. 32, no. 1983, pp. 2338–2348, 2021, doi: 10.1177/1045389X21995876.
[29] B. C. Chang, J. A. Shaw, and M. A. Iadicola, “Thermodynamics of shape memory alloy wire: Modeling, experiments, and application,” Contin. Mech. Thermodyn., vol. 18, no. 1–2, pp. 83–118, 2006, doi: 10.1007/s00161-006-0022-9.
[30] R. Natalia and B. Sergey, “Entropy change in the B2 → B19′ martensitic transformation in TiNi alloy,” Thermochim. Acta, vol. 602, pp. 30–35, 2015, doi: 10.1016/j.tca.2015.01.004.
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  • APA Style

    Ahmad Abubakar, R. (2023). One-Dimensional Shape Memory Alloys Material Phenomenological Constitutive Model Based on Stress Due to Mechanical and Chemical Energy Change. American Journal of Mechanics and Applications, 11(1), 6-14. https://doi.org/10.11648/j.ajma.20231101.12

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    ACS Style

    Ahmad Abubakar, R. One-Dimensional Shape Memory Alloys Material Phenomenological Constitutive Model Based on Stress Due to Mechanical and Chemical Energy Change. Am. J. Mech. Appl. 2023, 11(1), 6-14. doi: 10.11648/j.ajma.20231101.12

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    AMA Style

    Ahmad Abubakar R. One-Dimensional Shape Memory Alloys Material Phenomenological Constitutive Model Based on Stress Due to Mechanical and Chemical Energy Change. Am J Mech Appl. 2023;11(1):6-14. doi: 10.11648/j.ajma.20231101.12

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  • @article{10.11648/j.ajma.20231101.12,
      author = {Rabiu Ahmad Abubakar},
      title = {One-Dimensional Shape Memory Alloys Material Phenomenological Constitutive Model Based on Stress Due to Mechanical and Chemical Energy Change},
      journal = {American Journal of Mechanics and Applications},
      volume = {11},
      number = {1},
      pages = {6-14},
      doi = {10.11648/j.ajma.20231101.12},
      url = {https://doi.org/10.11648/j.ajma.20231101.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajma.20231101.12},
      abstract = {Shape Memory Alloy (SMA) is a material that has the ability to memorize previous shapes after deforming. That is it regains its original shape when temperature increases, converting thermal energy to mechanical energy. This property of the plastic-like deformation which subsequently recovers its original shape is referred to as Shape Memory Effects (SMEs). The history of this material began in the year 1800s. Because of their unique behavior, SMA has great industrial applications. Many constituted models of SMA behavior are formed describing SMA behavior. Most of them are based on experimental phenomenological macroscopic constitutive models consisting of variables that reveal the degree of phase transition that describes the phenomenological macroscopic behavior of SMA. These types of models are very easy and the parameters are also very easy to determine. In this research, a constitutive model is formulated based on the obserbation of experimental data, the SMA behavior is simulated using Artificial Neural Networks (ANN). The phenomenological constitutive model comprises both mechanical and chemical change. In the parameter estimation, the Back-Progation (BP) algorithm and the nonlinear optimization algorithm are used. A numerical simulation is performed, and the phenomenological constitutive model captures well the uniaxial tension and compression experimental data, therefore the constitutive model is verified.
    },
     year = {2023}
    }
    

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  • TY  - JOUR
    T1  - One-Dimensional Shape Memory Alloys Material Phenomenological Constitutive Model Based on Stress Due to Mechanical and Chemical Energy Change
    AU  - Rabiu Ahmad Abubakar
    Y1  - 2023/11/09
    PY  - 2023
    N1  - https://doi.org/10.11648/j.ajma.20231101.12
    DO  - 10.11648/j.ajma.20231101.12
    T2  - American Journal of Mechanics and Applications
    JF  - American Journal of Mechanics and Applications
    JO  - American Journal of Mechanics and Applications
    SP  - 6
    EP  - 14
    PB  - Science Publishing Group
    SN  - 2376-6131
    UR  - https://doi.org/10.11648/j.ajma.20231101.12
    AB  - Shape Memory Alloy (SMA) is a material that has the ability to memorize previous shapes after deforming. That is it regains its original shape when temperature increases, converting thermal energy to mechanical energy. This property of the plastic-like deformation which subsequently recovers its original shape is referred to as Shape Memory Effects (SMEs). The history of this material began in the year 1800s. Because of their unique behavior, SMA has great industrial applications. Many constituted models of SMA behavior are formed describing SMA behavior. Most of them are based on experimental phenomenological macroscopic constitutive models consisting of variables that reveal the degree of phase transition that describes the phenomenological macroscopic behavior of SMA. These types of models are very easy and the parameters are also very easy to determine. In this research, a constitutive model is formulated based on the obserbation of experimental data, the SMA behavior is simulated using Artificial Neural Networks (ANN). The phenomenological constitutive model comprises both mechanical and chemical change. In the parameter estimation, the Back-Progation (BP) algorithm and the nonlinear optimization algorithm are used. A numerical simulation is performed, and the phenomenological constitutive model captures well the uniaxial tension and compression experimental data, therefore the constitutive model is verified.
    
    VL  - 11
    IS  - 1
    ER  - 

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Author Information
  • Institute of Mechanical engineering Design, Mechanical Engineering Department, Zhejiang University, Hangzhou, China

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