Thanks to high dissipation properties, embedding NiTi Shape Memory Alloys in passive damping devices is effective to mitigate vibrations in building and cable structures. These devices can inconceivably be tested directly on full-scale experimental structures or on structures in service. To predict their effectiveness and optimize the set-up parameters, numerical tools are more and more developed. Most of them consist of Finite Element models representing the structure equipped with the damping device, embedding parts associated with a superelastic behavior. Generally, the implemented behavior laws do not include all the phenomena at the origin of strain energy dissipation, but stress-induced martensitic transformation only. This article presents a thermomechanical behavior law including the following phenomena: (i) intermediate R-phase transformation, (ii) thermal effects and (iii) strain localization. This law was implemented in a commercial Finite Element code to study the dynamic response of a bridge cable equipped with a NiTi wire-based damping device. The numerical results were compared to full-scale experimental ones, by considering the above-mentioned phenomena taken coupled or isolated: it has been shown that it is necessary to take all of these phenomena into account in order to successfully predict the damping capacity of the device.
Citation: Helbert Guillaume, Dieng Lamine, Chirani Shabnam Arbab, Pilvin Philippe. Influence of the thermomechanical behavior of NiTi wires embedded in a damper on its damping capacity: Application to a bridge cable[J]. AIMS Materials Science, 2023, 10(1): 1-25. doi: 10.3934/matersci.2023001
Thanks to high dissipation properties, embedding NiTi Shape Memory Alloys in passive damping devices is effective to mitigate vibrations in building and cable structures. These devices can inconceivably be tested directly on full-scale experimental structures or on structures in service. To predict their effectiveness and optimize the set-up parameters, numerical tools are more and more developed. Most of them consist of Finite Element models representing the structure equipped with the damping device, embedding parts associated with a superelastic behavior. Generally, the implemented behavior laws do not include all the phenomena at the origin of strain energy dissipation, but stress-induced martensitic transformation only. This article presents a thermomechanical behavior law including the following phenomena: (i) intermediate R-phase transformation, (ii) thermal effects and (iii) strain localization. This law was implemented in a commercial Finite Element code to study the dynamic response of a bridge cable equipped with a NiTi wire-based damping device. The numerical results were compared to full-scale experimental ones, by considering the above-mentioned phenomena taken coupled or isolated: it has been shown that it is necessary to take all of these phenomena into account in order to successfully predict the damping capacity of the device.
[1] | Ungar EE, Kerwin EM (1962) Loss factors of viscoelastic systems in terms of energy concepts. J Acoust Soc Am 34: 954–957. https://doi.org/10.1121/1.1918227 doi: 10.1121/1.1918227 |
[2] | Cai J, Mao S, Liu Y, et al. (2022) Nb/NiTi laminate composite with high pseudoelastic energy dissipation capacity. Mater Today Nano 19: 100238. https://doi.org/10.1016/j.mtnano.2022.100238 doi: 10.1016/j.mtnano.2022.100238 |
[3] | Oliveira JP, Zeng Z, Berveiller S, et al. (2018) Laser welding of Cu–Al–Be shape memory alloys: Microstructure and mechanical properties. Mater Design 148: 145–152. https://doi.org/10.1016/j.matdes.2018.03.066 doi: 10.1016/j.matdes.2018.03.066 |
[4] | Patoor E, Berveiller M (1994) Les Alliages à Mémoire de Formes, Hermes. |
[5] | Otsuka K, Wayman C (1998) Shape Memory Materials, Cambridge: Cambridge University Press. |
[6] | Udovenko VA (2003) Damping, In: Brailovski V, Prokoschkin S, Terriault P, et al., Shape Memory Alloys Fundamentals, Modelling and Applications, University of Quebec, Montreal, Canada, 279–309. |
[7] | Orgéas L, Favier D (1998) Stress-induced martensitic transformation of a NiTi alloy in isothermal shear, tension and compression. Acta Mater 46: 5579–5591. |
[8] | Menna C, Auricchio F, Asprone D (2014) Application of shape memory alloys in structural engineering, In: Lecce L, Concilio A, Shape Memory Alloy Engineering: for Aerospace, Structural and Biomedical Applications, Elsevier, 369–403. https://doi.org/10.1016/B978-0-08-099920-3.00013-9 |
[9] | Matsumoto M, Daito Y, Kanamura T, et al. (1998) Wind-induced vibration of cables of cable-stayed bridges. J Wind Eng Ind Aerod 74: 1015–1027. https://doi.org/10.1016/S0167-6105(98)00093-2 doi: 10.1016/S0167-6105(98)00093-2 |
[10] | Dieng L, Helbert G, Arbab Chirani S, et al. (2013) Use of shape memory alloys damper device to mitigate vibration amplitudes of bridge cables. Eng Struct 56: 1547–1556. https://doi.org/10.1016/j.engstruct.2013.07.018 doi: 10.1016/j.engstruct.2013.07.018 |
[11] | Nespoli A, Rigamonti D, Riva M, et al. (2016) Study of pseudoelastic systems for the design of complex passive dampers: static analysis and modeling. Smart Mater Struct 25: 105001. https://doi.org/10.1088/0964-1726/25/10/105001 doi: 10.1088/0964-1726/25/10/105001 |
[12] | Tobushi H, Shimeno Y, Hachisuka T, et al. (1998) Influence of strain rate on superelastic proporties of TiNi shape memory alloys. Mech Mater 30: 141–150. https://doi.org/10.1016/S0167-6636(98)00041-6 doi: 10.1016/S0167-6636(98)00041-6 |
[13] | Liu Y, Favier D (2000) Stabilisation of martensite due to shear deformation via variant reorientation in polycrystalline NiTi. Acta Mater 48: 3489–3499. https://doi.org/10.1016/S1359-6454(00)00129-4 doi: 10.1016/S1359-6454(00)00129-4 |
[14] | Bouvet C, Calloch S, Lexcellent C (2004) A phenomenological model for pseudoelasticity of shape memory alloys under multiaxial proportional and nonproportional loadings. Eur J Mech A-Solid 23: 37–61. https://doi.org/10.1016/j.euromechsol.2003.09.005 doi: 10.1016/j.euromechsol.2003.09.005 |
[15] | Helbert G, Saint-Sulpice L, Arbab Chirani S, et al. (2014) Experimental charaterisation of three-phase NiTi wires under tension. Mech Mater 79: 85–101. https://doi.org/10.1016/j.mechmat.2014.07.020 doi: 10.1016/j.mechmat.2014.07.020 |
[16] | Zhu S, Zhang Y (2007) A thermomechanical constitutive model for superelastic SMA wire with strain-rate dependence. Smart Mater Struct 16: 1696. https://doi.org/10.1088/0964-1726/16/5/023 doi: 10.1088/0964-1726/16/5/023 |
[17] | Heintze O, Seelecke S (2008) A coupled thermomechanical model for shape memory alloys-From single crystal to polycrystal. Mater Sci Eng A-Struct 481–482: 389–394. https://doi.org/10.1016/j.msea.2007.08.028 doi: 10.1016/j.msea.2007.08.028 |
[18] | Shariat BS, Liu Y, Rio G (2012) Thermomechanical modelling of microstructurally graded shape memory alloys. J Alloys Compd 541: 407–414. https://doi.org/10.1016/j.jallcom.2012.06.027 doi: 10.1016/j.jallcom.2012.06.027 |
[19] | Xiao Y, Zeng P, Lei L (2019) Micromechanical modelling on thermomechanical coupling of superelastic NiTi alloy. Int J Mech Sci 153–154: 36–47. https://doi.org/10.1016/j.ijmecsci.2019.01.030 doi: 10.1016/j.ijmecsci.2019.01.030 |
[20] | Otsuka K, Ren X (2005) Physical metallurgy of Ti-Ni-based shape memory alloys. Prog Mater Sci 50: 511–678. https://doi.org/10.1016/j.pmatsci.2004.10.001 doi: 10.1016/j.pmatsci.2004.10.001 |
[21] | Oliveira JP, Mirande RM, Braz Fernandez FM (2017) Welding and joining of NiTi shape memory alloys: A review. Prog Mater Sci 88: 412–466. https://doi.org/10.1016/j.pmatsci.2017.04.008 doi: 10.1016/j.pmatsci.2017.04.008 |
[22] | Šittner P, SedlákP, Landa M, et al. (2006) In situ experimental evidence on R-phase related deformation processes in activated NiTi wires. Mater Sci Eng A-Struct 438–440: 579–584. https://doi.org/10.1016/j.msea.2006.02.200 doi: 10.1016/j.msea.2006.02.200 |
[23] | Sengupta A, Papadopoulos P (2009) Constitutive modeling and finite element approximation of B2-R-B19' phase transformations in Nitinol polycrystals. Comput Method Appl M 198: 3214–3227. https://doi.org/10.1016/j.cma.2009.06.004 doi: 10.1016/j.cma.2009.06.004 |
[24] | Sedlák P, Frost M, Benešová B, et al. (2012) Thermomechanical model for NiTi-based shape memory alloys including R-phase and material anisotropy under multi-axial loadings. Int J Plast 39: 132–151. https://doi.org/10.1016/j.ijplas.2012.06.008 doi: 10.1016/j.ijplas.2012.06.008 |
[25] | Rigamonti D, Nespoli A, Villa E, et al. (2017) Implementation of a constitutive model for different annealed superelastic SMA wires with rhombohedral phase. Mech Mater 112: 88–100. https://doi.org/10.1016/j.mechmat.2017.06.001 doi: 10.1016/j.mechmat.2017.06.001 |
[26] | Zhou T, Yu C, Kang G, et al. (2020) A crystal plasticity based constitutive model accounting for R phase and two-step phase transition of polycrystalline NiTi shape memory alloys. Int J Solids Struct 193–194: 503–526. https://doi.org/10.1016/j.ijsolstr.2020.03.001 doi: 10.1016/j.ijsolstr.2020.03.001 |
[27] | Shaw JA, Kyriakides S (1995) Thermomechanical aspects of NiTi. J Mech Phys Solids 43: 1243–1281. https://doi.org/10.1016/0022-5096(95)00024-D doi: 10.1016/0022-5096(95)00024-D |
[28] | Favier D, Louche H, Schlosser P, et al. (2007) Homogeneous and heterogeneous deformation mechanisms in an austenitic polycrystalline Ti-50.8 at% Ni thin tube under tension. Investigation via temperature and strain fields measurements. Acta Mater 55: 5310–5322. https://doi.org/10.1016/j.actamat.2007.05.027 doi: 10.1016/j.actamat.2007.05.027 |
[29] | Sedmák P, Pilch J, Heller L, et al. (2016) Grain-resolved analysis of localized deformation in nickel-titanium wire under tensile load. Science 353: 559–562. https://doi.org/10.1126/science.aad6700 doi: 10.1126/science.aad6700 |
[30] | He YJ, Sun QP (2010) Rate-dependent domain spacing in a stretched NiTi strip. Int J Solids Struct 47: 2775–2783. https://doi.org/10.1016/j.ijsolstr.2010.06.006 doi: 10.1016/j.ijsolstr.2010.06.006 |
[31] | Shariat BS, Bakhtiari S, Yang H, et al. (2020) Controlled initiation and propagation of stress-induced martensitic transformation in functionally graded NiTi. J Alloys Compd 851: 156103. https://doi.org/10.1016/j.jallcom.2020.156103 doi: 10.1016/j.jallcom.2020.156103 |
[32] | Sun QP, Zhong Z (2000) An inclusion theory for the propagation of martensite band in NiTi shape memory alloy wires under tension. Int J Plast 16: 1169–1187. https://doi.org/10.1016/S0749-6419(00)00006-1 doi: 10.1016/S0749-6419(00)00006-1 |
[33] | Chan CW, Chan SHJ, Man HC, et al. (2012) 1-D constitutive model for evolution of stress-induced R-phase and localized Lüders-like stress-induced martensitic transformation of super-elastic NiTi wires. Int J Plast 32–33: 85–105. https://doi.org/10.1016/j.ijplas.2011.12.003 doi: 10.1016/j.ijplas.2011.12.003 |
[34] | Soul H, Yawny A (2013) Thermomechanical model for evaluation of the superelastic response of NiTi shape memory alloys under dynamic conditions. Smart Mater Struct 22: 035017. https://doi.org/10.1088/0964-1726/22/3/035017 doi: 10.1088/0964-1726/22/3/035017 |
[35] | Xiao Y, Jiang D (2020) Constitutive modelling of transformation pattern in superelastic NiTi shape memory alloy under cyclic loading. Int J Mech Sci 182: 105743. https://doi.org/10.1016/j.ijmecsci.2020.105743 doi: 10.1016/j.ijmecsci.2020.105743 |
[36] | Zuo XB, Li AQ (2011) Numerical and experimental investigation on cable vibration mitigation using shape memory alloy damper. Struct Control Health Monit 18: 20–39. |
[37] | Ben Mekki O, Auricchio F (2011) Performance evaluation of shape-memory-alloy superelastic behavior to control a stay cable in cable-stayed bridges. Int J Non-Linear Mech 46: 470–477. https://doi.org/10.1016/j.ijnonlinmec.2010.12.002 doi: 10.1016/j.ijnonlinmec.2010.12.002 |
[38] | Torra V, Auguet C, Isalgue A, et al. (2013) Built in dampers for stayed cables in bridges via SMA. The SMARTeR-ESF project: A mesoscopic and macroscopic experimental analysis with numerical simulations. Eng Struct 49: 43–57. https://doi.org/10.1016/j.engstruct.2012.11.011 doi: 10.1016/j.engstruct.2012.11.011 |
[39] | Morse P, Ingard K (1968) Theoritical Acoustics, Princeton University Press. |
[40] | MSC (2008) Marc/mentat volume A: Theory and user information. |
[41] | Helbert G, Dieng L, Arbab Chirani S, et al. (2018) Investigation of NiTi based damper effects in bridge cables vibration response: Damping capacity and stiffness changes. Eng Struct 165: 184–197. https://doi.org/10.1016/j.engstruct.2018.02.087 doi: 10.1016/j.engstruct.2018.02.087 |
[42] | Helbert G, Saint-Sulpice L, Arbab Chirani S, et al. (2017) A uniaxial constitutive model for superelastic NiTi SMA including R-phase and martensite transformations and thermal effects. Smart Mater Struct 26: 025007. https://doi.org/10.1088/1361-665X/aa5141 doi: 10.1088/1361-665X/aa5141 |
[43] | Helbert G (2014) Contribution à la durabilité des câbles de Génie Civil vis-à-vis de la fatigue par un dispositif amortisseur à base de fils NiTi, Université de Bretagne Sud. |
[44] | Qian ZQ, Akisanya AR (1999) An investigation of the stress singularity near the free edge of scarf joints. Eur J Mech A-Solid 18: 443–463. https://doi.org/10.1016/S0997-7538(99)00118-7 doi: 10.1016/S0997-7538(99)00118-7 |
[45] | Harvey JF (1974) Theory and Design of Modern Pressure Vessels, Van Nostrand Reinhold. |
[46] | Auger F, Gonçalvès P, Lemoine O, et al. (1996) Time-frequency toolbox: For use with Matlab. Available from: https://tftb.nongnu.org/ |
[47] | Piedboeuf MC, Gauvin R, Thomas M (1998) Damping behaviour of shape memory alloys: strain amplitude, frequency and temperature effects. J Sound Vib 214: 895–901. https://doi.org/10.1006/jsvi.1998.1578 doi: 10.1006/jsvi.1998.1578 |