Application of the Nelder-Mead method to optimize the selecting of the Likhachev-Volkov model constants
DOI:
https://doi.org/10.21638/spbu01.2022.411Abstract
A new method was proposed for selecting constants of the modified Likhachev - Volkov microstructural model to describe the reversible strain variation during isothermal martensitic transformation in Ti49Ni51 alloy. The experimental data were approximated by solving the optimization problem using the Nelder - Mead method. A set of model parameters was found that provided the best approximation. Using the selected constants set, model qualitatively and quantitatively describe the strain variation during cooling and heating of the model sample, as well as during isothermal holding under constant stress. The proposed method of selecting constants allowed performing the smallest number of numerical experiments without requiring additional real experiments.Keywords:
shape memory alloys, martensitic transformation, isothermal martensitic transformation, microstructural model, Nelder - Mead method
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Литература
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18. Demidova E.S., Belyaev F.S., Belyaev S.P., Resnina N.N., Volkov A.E. Simulation of isothermal reversible strain in the Ti40.7Hf9.5Ni44.8Cu5 alloy using a microstructural model. Letters on Materials 11 (3), 327-331 (2021). https://doi.org/10.22226/2410-3535-2021-3-327-331
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References
1. Mohd Jani J., Leary M., Subic A., Gibson M.A. A review of shape memory alloy research, applications and opportunities. Mater. Des. 56, 1078-1113 (2014). https://doi.org/10.1016/j.matdes.2013.11.084
2. Razov A., Cherniavsky A. Application of SMAs in modern spacecraft and devices. Journal of Physics IV France 112, 1173-1176 (2003). https://doi.org/10.1051/jp4:20031091
3. Otsuka K., Ren X. Physical metallurgy of Ti-Ni-based shape memory alloys. Progress in Materials Science 50, 511-678 (2005). https://doi.org/10.1016/j.pmatsci.2004.10.001
4. Kustov S., Salas D., Cesari E., Santamarta R., Van Humbeeck J. Isothermal and athermal martensitic transformations in Ni-Ti shape memory alloys. Acta Materialia 60, 2578-2592 (2012). https://doi.org/10.1016/j.actamat.2012.01.025
5. Fukuda T., Yoshida S., Kakeshita T. Isothermal nature of the B2-B19’ martensitic transformation in a Ti-51.2Ni (at. %) alloy. Scripta Materialia 68, 984-987 (2013). https://doi.org/10.1016/j.scriptamat.2013.02.057
6. Ji Y., Wang D., Ding X., Otsuka K., Ren X. Origin of an Isothermal R-Martensite Formation in Ni-rich Ti-Ni Solid Solution: Crystallization of Strain Glass. Physical Review Letters 114, 055701 (2015). https://doi.org/10.1103/PhysRevLett.114.055701
7. Resnina N., Belyaev S., Demidova E., Ivanov A., Andreev V. Kinetics of isothermal B2→B19 martensitic transformation in Ti49Ni51 shape memory alloy. Materials Letters 228, 348-350 (2018). https://doi.org/10.1016/j.matlet.2018.06.055
8. Resnina N., Belyaev S., Shelyakov A. Isothermal B2→B19 martensitic transformation in Ti40.7Hf9.5Ni44.8Cu5 shape memory alloy. Scripta Materialia 112, 106-108 (2016). https://doi.org/10.1016/j.scriptamat.2015.09.024
9. Demidova E., Belyaev S., Resnina N., Shelyakov A. Influence of the holding temperature on the kinetics of the isothermal B2→B19 transformation in TiNi-based shape memory alloy. Journal of Thermal Analysis and Calorimetry 139, 2965-2970 (2020). https://doi.org/10.1016/10.1007/s10973- 019-08717-4
10. Demidova E., Belyaev S., Resnina N., Shelyakov A. Strain variation during the isothermal martensitic transformation in Ti40.7Hf9.5Ni44.8Cu5 alloy. Materials Letters 254, 266-268 (2019). https://doi.org/10.1016/j.matlet.2019.07.077
11. Ivanov A., Belyaev S., Resnina N., Andreev V. Strain variation during the isothermal martensitic transformation in the Ni51Ti49 shape memory alloy. Sensors and Actuators A 297, 111543 (2019). https://doi.org/10.1016/j.sna.2019.111543
12. Tanaka K., Nagaki S.A. A thermomechanical description of materials with internal variables in the process of phase transitions Ingenieur-Archiv 51, 287-299 (1982). https://doi.org/10.1016/0029- 5493(83)90054-7
13. Lagoudas D.C., Bo Z., Qidwai M.A. A unified thermodynamic constitutive model for SMA and finite element analysis of active metal matrix composites. Mech. Composite Material Structure 3 (2), 153-179 (1996). https://doi.org/10.1080/10759419608945861
14. Patoor E., Eberhardt A., Berveiller M. Micromechanical Modelling of Superelasticity in Shape Memory Alloys. Journal de Physique IV France 6, 277-292 (1996). https://doi.org/10.1051/jp4:1996127
15. Movchan A.A., Klimov K.Yu. Simulation of rheonomic properties of shape memory alloys. Composites: Mechanics, Computations, Applications 2 (3), 171-185 (2011). https://doi.org/10.1615 /CompMechComputApplIntJ.v2.i3.10
16. Volkov A.E., Belyaev F.S., Evard M.E., Volkova N.A. Model of the evolution of deformation defects and irreversible strain at thermal cycling of stressed TiNi alloy specimen. MATEC Web of Conferences 33, 1-5 (2015). https://doi.org/10.1051/matecconf/20153303013
17. Beliaev F.S., Evard M.E., Ostropiko E.S., Razov A.I., Volkov A.E. Aging effect on the One-way and Two-way Shape Memory in TiNi Based Alloys. Shape Memory Superelasticity 5, 218-229 (2019). https://doi.org/10.1007/s40830-019-00226-5
18. Demidova E.S., Belyaev F.S., Belyaev S.P., Resnina N.N., Volkov A.E. Simulation of isothermal reversible strain in the Ti40.7Hf9.5Ni44.8Cu5 alloy using a microstructural model. Letters on Materials 11 (3), 327-331 (2021). https://doi.org/10.22226/2410-3535-2021-3-327-331
19. Belyaev F.S. Microstructural model of irreversible deformation and defects in shape memory alloys. Candidate dissertation (2016). (In Russian)
20. Nelder J.A., Mead R. A simplex method for function minimization. The Computer Journal 7, 308-313 (1965). https://doi.org/10.1093/comjnl/7.4.308
21. Chambers L.D. The practical handbook of genetic algorithms: applications. Boca Raton, Chapman and Hall/CRC (2001)
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Published
2022-12-26
How to Cite
Ivanov, A. M., Belyaev, F. S., Volkov, A. E., Belyaev, S. P., & Resnina, N. N. (2022). Application of the Nelder-Mead method to optimize the selecting of the Likhachev-Volkov model constants. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9(4), 693–704. https://doi.org/10.21638/spbu01.2022.411
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
