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http://dx.doi.org/10.12989/sss.2022.30.3.245

Microstructural modeling of two-way bent shape change of composite two-layer beam comprising a shape memory alloy and elastoplastic layers  

Belyaev, Fedor S. (Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences)
Evard, Margarita E. (Saint-Petersburg State University)
Volkov, Aleksandr E. (Saint-Petersburg State University)
Volkova, Natalia A. (St. Petersburg State Technological Institute (Technical University))
Vukolov, Egor A. (Saint-Petersburg State University)
Publication Information
Smart Structures and Systems / v.30, no.3, 2022 , pp. 245-253 More about this Journal
Abstract
A two-layer beam consisting of an elastoplastic layer and a functional layer made of shape memory alloy (SMA) TiNi is considered. Constitutive relations for SMA are set by a microstructural model capable to calculate strain increment produced by arbitrary increments of stress and temperature. This model exploits the approximation of small strains. The equations to calculate the variations of the strain and the internal variables are based on the experimentally registered temperature kinetics of the martensitic transformations with an account of the crystallographic features of the transformation and the laws of equilibrium thermodynamics. Stress and phase distributions over the beam height are calculated by steps, by solving on each step the boundary-value problem for given increments of the bending moment (or curvature) and the tensile force (or relative elongation). Simplifying Bernoulli's hypotheses are applied. The temperature is considered homogeneous. The first stage of the numerical experiment is modeling of preliminary deformation of the beam by bending or stretching at a temperature corresponding to the martensitic state of the SMA layer. The second stage simulates heating and subsequent cooling across the temperature interval of the martensitic transformation. The curvature variation depends both on the total thickness of the beam and on the ratio of the layer's thicknesses.
Keywords
bending; boundary-value problem; modelling; shape memory alloys;
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Times Cited By KSCI : 4  (Citation Analysis)
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1 Casciati, S. (2019), "SMA-based devices: insight across recent proposals toward civil engineering applications", Smart Struct. Syst., Int. J., 24(1), 111-125. https://doi.org/10.12989/sss.2019.24.1.111   DOI
2 Erglis, I.V., Ermolaev, V.A. and Volkov, A.E. (1995), "A model of martensitic unelasticity accounting for the crystal symmetry of the material", Le Journal de Physique IV, 5(C8), 239-244. https://doi.org/10.1051/jp4:1995833   DOI
3 Evard, M.E. and Volkov, A.E. (1999), "Modeling of the martensite accommodation effect on mechanical behavior of shape memory alloys", J. Eng. Mater. Technol., 121, 102-104.   DOI
4 Evard, M.E., Volkov, A.E. and Bobeleva, O.V. (2006), "An approach for modelling fracture of shape memory alloy parts", Smart Struct. Syst., Int. J., 2(4), 357-363. https://doi.org/10.12989/sss.2006.2.4.357   DOI
5 Evard, M.E., Volkov, A.E. and Belyaev, F.S. (2015), "A microstructural model of SMA with microplastic deformation and defects accumulation: Application to thermocyclic loading", Materials Today: Proceedings, 2(3), S583-S587. https://doi.org/10.1016/j.matpr.2015.07.352   DOI
6 Fall, M.D., Patoor, E., Hubert, O. and Lavernhe-Taillard, K. (2019), "Comparative study of two multiscale thermosmechanical models of polycrystalline shape memory alloys: Application to a representative volume element of titanium- niobium", Shape Memory Superelast., 5, 163-171. https://doi.org/10.1007/s40830-019-00216-7   DOI
7 Fischlschweiger, M., Oberaigner, E.R., Antretter, T. and Cailletaud, G. (2011), "A multi-block-spin approach for martensitic phase transformation based on statistical physics", Proceedings of Behavior and Mechanics of Multifunctional Materials and Composites, Vol. 7978, pp. 398-405, San Diego, CA, USA. https://doi.org/10.1117/12.881960   DOI
8 Chatziathanasiou, D., Chemisky, Y., Meraghni, F., Chatzigeorgiou, G. and Patoor, E. (2015), "Phase transformation of anisotropic shape memory alloys: theory and validation in superelasticity", Shape Memory Superelast., 1, 359-374. https://doi.org/10.1007/s40830-015-0027-y   DOI
9 Duerig, T.W., Melton, K.N. and Stockel, D. (eds.) (1990), Engineering Aspects of Shape Memory Alloys, Butterworth-Heinemann, New York, NY, USA.
10 AnsysⓇ Academic Research Mechanical APDL, Release 14.0, Help System, Material Reference/3.24, ANSYS, Inc.
11 Auricchio, F. and Petrini, L. (2002), "Improvements and algorithmical considerations on a recent three-dimensional model describing stress-induced solid phase transformations", Int. J. Numer. Methods, 55(11), 1255-1284. https://doi.org/10.1002/nme.619   DOI
12 Belyaev, F.S., Evard, M.E. and Volkov, A.E. (2022), "Effect of plastic deformation on the martensitic transformations in TiNi alloy", Smart Struct. Syst., Int. J., 29(2), 311-319. https://doi.org/10.12989/sss.2022.29.2.311   DOI
13 Belyaev, S., Rubanik, V., Resnina, N., Rubanik Jr, V., Rubanik, O. and Borisov, V.J.P.T. (2010a), "Martensitic transformation and physical properties of 'steel-TiNi' bimetal composite, produced by explosion welding", Phase Transitions, 83(4), 276-283. https://doi.org/10.1080/01411591003656757   DOI
14 Belyaev, S., Rubanik, V., Resnina, N., Rubanik Jr, V., Rubanik, O., Borisov, V. and Lomakin, I. (2010b), "Functional properties of bimetal composite of "stainless steel - TiNi alloy" produced by explosion welding", Physics Procedia, 10, 52-57. https://doi.org/10.1016/j.phpro.2010.11.074   DOI
15 Belyaev, S., Rubanik, V., Resnina, N. and Rubanik, O. (2011), "Effect of annealing on martensitic transformations in "steel - TiNi alloy" explosion welded bimetallic composite", Metal Sci. Heat Treat., 52(9), 432-436. https://doi.org/10.1007/s11041-010-9310-x   DOI
16 Huang, M. and Brinson, L.C. (1998), "A multivariant model for single crystal shape memory alloy behavior", J. Mech. Phys. Solids, 46(8), 1379-1409. https://doi.org/10.1016/S0022-5096(97)00080-X   DOI
17 Imamura, T., Nishiura, T., Kawano, H., Hosoda, H. and Nishida, M. (2012), "Self-accommodation of B19' martensite in Ti-Ni shape memory alloys - Part III. Analysis of habit plane variant clusters by the geometrically nonlinear theory", Philosophical Magazine, 92, 2247-2263.   DOI
18 Lagoudas, D.C. (2008), Shape Memory Alloys: Modeling and Engineering Applications, Springer, Berlin, Germany.
19 Jani, J.M., Leary, M., Subic, A. and Gibson, M.A. (2014), "A review of shape memory alloy research, applications and opportunities", Mater. Des., 56, 1078-1113. https://doi.org/10.1016/j.matdes.2013.11.084   DOI
20 Kukhareva, A., Kozminskaia, O. and Volkov, A. (2020), "Calculation of the transformation plasticity strain in the shape memory cylinder", In: E3S Web of Conferences, Vol. 157, p. 06016. https://doi.org/10.1051/e3sconf/202015706016   DOI
21 Li, Q., Seelecke, S., Kohl, M. and Krevet, B. (2006), "Thermomechanical finite element analysis of a shape memory alloy cantilever beam", Proceedings of SPIE 6166, Smart Structures and Materials 2006: Modeling, Signal Processing, and Control, Vol. 6166, pp. 562-569.San Diego, CA, USA, March, SPIE 06-6166-73. https://doi.org/10.1117/12.677238   DOI
22 Likhachev, V.A., Razov, A.I. and Volkov, A.E. (1997), "Finite difference simulation of a thermomechanical coupling", A.R. Pelton, D. Hodgson, S.M. Russel, T. Duerig (eds.), Proceedings of the Second International Conference on Shape Memory and Superelastic Technologies SMST-97, March, Pacific Grove, CA, USA, pp. 335-340.
23 Nae, F.A., Matsuzaki, Y. and Ikeda, T. (2003), "Micromechanical modeling of polycrystalline shape-memory alloys including thermo-mechanical coupling", Smart Mater. Struct., 12, 6-17. https://doi.org/10.1088/0964-1726/12/1/302   DOI
24 Petrini, L., Bertini, A., Berti, F., Pennati, G. and Migliavacca, F. (2017), "The role of inelastic deformations in the mechanical response of endovascular shape memory alloy devices", J. Eng. Med., 231(5), 391-404. https://doi.org/10.1177/0954411917696336   DOI
25 Niclaeys, C., Zineb, T.B. and Patoor, E. (2004), "Influence of microstructural parameters on shape memory alloys behavior", Ahzi, S., Cherkaoui, M., Khaleel, M.A., Zbib, H.M., Zikry, M.A. and Lamatina, B. (eds.), Proceedings of IUTAM Symposium on Multiscale Modeling and Characterization of Elastic-Inelastic Behavior of Engineering Materials. Solid Mechanics and Its Applications, Vol. 114, Springer, Dordrecht, The Netherlands. https://doi.org/10.1007/978-94-017-0483-0_33   DOI
26 Nishida, M., Nishiura, T., Kawano, H. and Imamura, T. (2012a), "Self-accommodation of B19' martensite in Ti-Ni shape memory alloys - Part I. Morphological and crystallographic studies of variant selection rule", Philosophical Magazine, 92, 2215-2233.   DOI
27 Nishida, M., Okunishi, E., Nishiura, T., Kawano, H., Imamura, T., Ii, S. and Hara, T. (2012b), "Self-accommodation of B19' martensite in Ti-Ni shape memory alloys - Part II. Characteristic interface structures between habit plane variants", Philosophical Magazine, 92, 2234-2246.   DOI
28 Oberaigner, E.R. and Leindl, M. (2012), "Statistical physics concepts for the explanation of effects observed in martensitic phase transformations", Smart Mater. Struct., 21(9), 094020. https://doi.org/10.1088/0964-1726/21/9/094020   DOI
29 Patoor, E, Eberhardt, A. and Berveiller, M. (1996), "Micromechanical modelling of superelasticity in shape memory alloys", J. de Physique IV, 6(C1), 277-292. https://doi.org/10.1051/jp4:1996127   DOI
30 Prummer, R. and Stockel, D. (2001), "NITINOL - stainless steel compound material, made by explosion welding", K.P. Staudhammer, L.E. Murr, and M.A. Meyers (eds.), In: Fundamental Issues and Applications of Shock-Wave and High-Strain-Rate Phenomena, Elsevier, pp. 581-584.
31 Rogovoy, A.A. and Stolbova, O.S. (2019), "Numerical simulation of the phase transition control in torsion of a hollow cylinder made of Heusler alloy", PNRPU Mech. Bull., (3), 75-87.
32 Volkov, A.E., Kukhareva, A.S., Volkova, N.A. and Malkova, Y.V. (2017), "Size effects in a shape memory alloy rod caused by inhomogeneity of temperature and stress fields studied through solving of a 1d connected thermal and mechanical problem", Proceedings of the 8th Conference on Smart Structures and Materials, SMART 2017 and 6th International Conference on Smart Materials and Nanotechnology in Engineering, January, pp. 1582-1589.
33 Torra, V., Carreras, G., Casciati, S. and Terriault, P. (2014), "On the NiTi wires in dampers for stayed cables", Smart Struct. Syst., Int. J., 13(3), 353-374. https://doi.org/10.12989/sss.2014.13.3.353   DOI
34 Volkov, A.E. and Casciati, F. (2001), "Simulation of dislocation and transformation plasticity in shape memory alloy polycrystals", Auricchio F, Faravelli L, Magonette G and Torra V (eds.), In: Shape Memory Alloys. Advances in Modelling and Applications, Barcelona, Spain, pp. 88-104.
35 Volkov, A.E., Emelyanova, E.V., Evard, M.E. and Volkova, N.A. (2013), "An explanation of phase deformation tension-compression asymmetry of TiNi by means of microstructural modeling", J. Alloys Compounds, 577(S1), S127-S130. https://doi.org/10.1016/j.jallcom.2012.05.131   DOI
36 Volkov A.E., Evard, M.E., Volkova, N.A. and Vukolov, E.A. (2019), "Application of a microstructural model to simulation of a TiNi beam bending performance and calculation of thickness stress distributions", Proceedings of the 9th ECCOMAS Thematic Conference on Smart Structures and Materials, SMART 2019, pp. 686-695.
37 Wanhill, R.J.H. and Ashok, B. (2017), "Shape Memory Alloys (SMAs) for Aerospace Applications", Prasad, N., Wanhill, R. (eds.), In: Aerospace Materials and Material Technologies, Indian Institute of Metals Series, Springer, Singapore.
38 Salzbrenner, R.J. and Cohen, M. (1979), "On the thermodynamics of thermoelastic martensitic transformations", Acta Metallurgica, 27(5), 739-748. https://doi.org/10.1016/0001-6160(79)90107-X   DOI
39 Simoes, M. and Martinez-Paneda, E. (2021), "Phase field modelling of fracture and fatigue in Shape Memory Alloys", Comput. Methods Appl. Mech. Eng.., 373, 113504. https://doi.org/10.1016/j.cma.2020.113504   DOI
40 Volkov, A.E. and Kukhareva, A.S. (2008), "Calculation of the stress-strain state of a TiNi cylinder subjected to cooling under axial force and unloading", Bull. Russian Acad. Sci.: Phys., 72(9), 1267-1270. https://doi.org/10.3103/S106287380809027X   DOI
41 Yang, S. and Seelecke, S. (2008), "Modeling and analysis of SMA-based adaptive structures", Proceedings of the COMSOL Conference 2008, Boston, MA, USA.
42 Zhang, W., Zhang, Y., Zheng, G., Zhang, R. and Wang, Y. (2013), "A biomechanical research of growth control of spine by shape memory alloy staples", BioMed Res. Int., 384894. https://doi.org/10.1155/2013/384894   DOI