Modeling of Deformation and Functional Properties of Shape Memory Alloys Based on a Microstructural Approach

Abstract:

This microstructural model of the functional-mechanical behavior of shape memory alloys (SMA) includes a description of the reversible phase deformation, microplastic deformation due to the accommodation of martensite and the evolution of the deformation defects. The laws of these phenomena are formulated in terms of the generalized thermodynamic forces. The microplastic flow rule accounts for isotropic and kinematic hardening, which are related to the accumulation of the deformation defects. The model gives a good description both of reversible and irreversible deformation under one-side or cyclic thermomechanical loading of SMA and opens a way for the fatigue life prediction. The model can be applied for solving of the mechanical problems for SMA parts such as dampers or base isolators used in seismic protection devices.

• Periodical: Materials Science Foundations (Volumes 81-82)
• Pages: 20-37
• DOI: https://doi.org/10.4028/www.scientific.net/MSFo.81-82.20
• Online since: March 2015
• Authors: Aleksandr E. Volkov*, Margarita E. Evard, Fedor S. Belyaev
• Keywords: Irreversible Deformation, Microstructural Model, Modeling, Shape Memory

References

[1] F. Baumgart, J. Jorde, H. -G. Reiss, Memory Legierungen-Eigenschaften, phänomenologische Theorie und Anwendungen, Techn. Mitt. Krupp Forschungsberighte. 34 (1976) 1-16.

[2] D.C. Lagoudas, Z. Bo, M.A. Qidwai, A unified thermodynamic constitutive model for SMA and finite element analysis of active metal matrix composites. Mechanics of composite materials and structures 3 (1996) 153-179.

DOI: 10.1080/10759419608945861

[3] C. Liang, C.A. Rogers, One-dimensional thermomechanical constitutive relations for shape memory materials. J. of Intelligent Materials Systems and Structures 1 (1990) 207-234.

DOI: 10.1177/1045389x9000100205

[4] T.J. Pence, Mathematical modeling of shape memory alloys, Manside Project: Workshop Proc. (1999) II-45-II-57.

[5] F. Trochu, P. Terriault, Nonlinear modeling of hysteresis material laws by dual kriging and application, Comput. Methods Appl. Mech. Eng. 151 (1998) 545-558.

DOI: 10.1016/s0045-7825(97)00165-5

[6] K. Tanaka, A termomechanical sketch of shape memory effect: one-dimensional tensile behavior, Res Mech. 18 (1986) 251-263.

[7] K. Tanaka, S. Nagaki, A thermomechanical description of materials with internal variables in the process of phase transition, Ingenieur-Archiv. 51 (1982) 287-299.

DOI: 10.1007/bf00536655

[8] K. Tanaka, F.D. Fischer, Determination of equation for shape memory alloys. Micromechanical investigations, J. Soc. Mater. Sci. Japan. 39 (1990) 883-887.

[9] K. Tanaka, R, Iwasaki, A phenomenological theory of transformation superplasticity, Eng. Fracture Mech. 21 (1985) 709-720.

DOI: 10.1016/0013-7944(85)90080-3

[10] A.E. Volkov, V. A Likhachev, A.I. Razov, Plasticity mechanics of materials with phase-transitions, Vestnik Leningrad. Uni. Seriya Mat. Mekh. Astronom. 4 (1984) 30-37 [in Russian].

[11] C. Liang, C.A. Rogers, A multi-dimensional constitutive model for shape memory alloys, J. Eng. Math. 26 (1992) 429-443.

DOI: 10.1007/bf00042744

[12] A.A. Movchan, Some manifestations of oriented transform ability of shape-memory alloys, J. App. Mech. and Tech. Phys. 37 (1996) 926-933.

DOI: 10.1007/bf02369274

[13] L.C. Brinson, One-dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with non-constant material functions and redefined martensite internal variable, J. Intelligent Mater. Systems and Structures 4 (1993).

DOI: 10.1177/1045389x9300400213

[14] D.C. Lagoudas, Z. Bo, M.A. Qidwai, A Unified Thermodynamic Constitutive Model for SMA and Finite Element Analysis of Active Metal Matrix Composites, Mech. of Composite Materials and Structures 4 (1996) 153-179.

DOI: 10.1002/(sici)1234-986x(199606)3:2<153::aid-mcm36>3.3.co;2-j

[15] A.C. Souza, E.N. Mamiya, N. Zouain, Three-dimensional model for solids undergoing stress-induced phase transformations, Europ. J. Mech. A / Solids 17 (1998) 789-806.

DOI: 10.1016/s0997-7538(98)80005-3

[16] F. Auricchio, L. Petrini, A three-dimensional model describing stress-temperature induced solid phase transformations: thermomechanical coupling and hybrid composite applications, Int. J. Numerical Methods in Engineering 61 (2004) 716–737.

DOI: 10.1002/nme.1087

[17] J.G. Boyd, D.C. Lagoudas, A thermodynamical constitutive model for shape memory materials. Part 2. The SMA composite material, Int. J. Plasticity 12 (1996) 843-873.

DOI: 10.1016/s0749-6419(96)00031-9

[18] M. Huang, L.C. Brinson, A multivariant model for single crystal shape memory alloy behaviour, J. Mech. Phys. Solids. 46 (1998) 1379-1409.

DOI: 10.1016/s0022-5096(97)00080-x

[19] E. Patoor, A. Eberhardt, M. Berveiller, Micromechanical modelling of superelasticity in shape memory alloys, J. de Physique IV 6 (1996) C1-277-292.

DOI: 10.1051/jp4:1996127

[20] Q. -P. Sun, C. Lexcellent, On the unified micromechanics constitutive description of one-way and two-way shape memory effects, J. de Physique IV 6 (1996) C1-367-375.

DOI: 10.1051/jp4:1996135

[21] M. Huang, X. Gao, L.C. Brinson, A multivariant model for SMAs Part2. Polycrystal model, Int. J. of Plasticity 16 (2000) 1371-1390.

DOI: 10.1016/s0749-6419(00)00014-0

[22] F.A. Nae, Y. Matsuzaki, T. Ikeda, Micromechanical modeling of polycrystalline shape-memory alloys including thermo-mechanical coupling, Smart Materials and Structures 12 (2003) 6-17.

DOI: 10.1088/0964-1726/12/1/302

[23] M.E. Evard, A.E. Volkov, Modeling of martensite accommodation effect on mechanical behaviour of shape memory alloys. J. Eng. Mater. and Technol. 121(1999) 102–104.

DOI: 10.1115/1.2815989

[24] A.E. Volkov, F. Casciati, Simulation of dislocation and transformation plasticity in shape memory alloy polycrystals, in: F. Auricchio, L. Faravelli, G. Magonette and V. Torra (Eds. ) Shape Memory Alloys. Advances in Modelling and Applications, Barcelona, 2001, pp.88-104.

[25] M.E. Evard, A.E. Volkov, A theoretical study of the plastic deformation in titanium-nickel shape memory alloy, in: F. Troshu, V. Brailovski, A. Galibois (Eds. ), Proc. of Int. Symp. on Shape Memory Alloys: Fundamentals, Modelling and Industrial Applications, 1999, p.177.

[26] M.E. Evard, A.E. Volkov, O.V. Bobeleva, An approach for modelling fracture of shape memory alloy parts, Smart Structures and Systems 2 (2006) 357-363.

DOI: 10.12989/sss.2006.2.4.357

[27] S.P. Belyaev, I.V. Inochkina, A.E. Volkov, Modeling of vibration control, damping and isolation by shape memory alloy parts, in: F. Casciati(Ed. ), Proc. 3-rd World Conference on Structural Control, 2003, p.779 – 789.

[28] A.E. Volkov, D.S. Dubilet, Calculation of the efficiency of shape memory alloys application for damping and isolation of structures, J. Composite Mech. and Design 15 (2009) 505-511.

[29] A.E. Volkov, M.E. Evard, A.V. Vikulenkov, E.S. Uspenskiy, Simulation of vibration isolation by shape memory alloy springs using a microstructural model of shape memory alloy, Materials Science Forum 738-739 (2013) 150-154.

DOI: 10.4028/www.scientific.net/msf.738-739.150

[30] A.E. Volkov, M.E. Evard, K.V. Red'kina, A.V. Vikulenkov, V.P. Makarov, A.A. Moisheev, N.A. Makarchev, E.S. Uspenskiy, Simulation of payload vibration protection by shape memory alloy parts, J. Mat. Eng. Perform. 23 (2014) 2719-2726.

DOI: 10.1007/s11665-014-1084-7

[31] A. E. Volkov, A. S. Kukhareva, Calculation of the stress–strain state of a TiNi cylinder subjected to cooling under axial force and unloading, Bulletin of the Russian Academy of Sciences: Physics 72 (2008) 1267–1270.

DOI: 10.3103/s106287380809027x

[32] M. Nishida, T. Nishiura, H. Kawano, T. Imamura, Self-accommodation of B19' martensite in Ti-Ni shape memory alloys – Part I. Morphological and crystallographic studies of variant selection rule, Philosophical. Magazine 92 (2012) 2215–2233.

DOI: 10.1080/14786435.2012.669858

[33] M. Nishida, E. Okunishi, T. Nishiura, H. Kawano, T. Imamura, S. Ii,T. Hara, Self-accommodation of B19' martensite in Ti-Ni shape memory alloys – Part II. Characteristic interface structures between habit plane variants, Philosophical. Magazine 92 (2012).

DOI: 10.1080/14786435.2012.669860

[34] T. Imamura, T. Nishiura, H. Kawano, H. Hosoda, M. Nishida, 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 (2012).

DOI: 10.1080/14786435.2012.669859

[35] K. Madangopal, J. Singh,S. Benerjee. Self-accommodation in Ni-Ti shape memory alloys, Scripta Metallurgica 25 (1991) 2153–2158.

DOI: 10.1016/0956-716x(91)90291-8

[36] R.J. Salzbrenner, M. Cohen, On the thermodynamics of thermoelastic martensitic transformations, Acta Metallurgica 27 (1979) 739–748.

DOI: 10.1016/0001-6160(79)90107-x

[37] K.M. Knowles, D.A. Smith, The crystallography of the martensitic transformation in equiatomic nickel-titanium, Acta Metallurgica 20 (1981) 101-110.

DOI: 10.1016/0001-6160(81)90091-2

[38] S. Miyazaki, K. Otsuka, Y. Suzuki, Transformation pseudoelasticity and deformation behaviour in a Ti-50. 6at. %Ni alloy, Scripta Metallurgica 15 (1981) 287-292.

DOI: 10.1016/0036-9748(81)90346-x

[39] T. Saburi, T. Tatsumi, S. Nenno, Effect of heat treatment on mechanical behaviour of TiNi alloys, J. de Physique 43 (1982) C4-261-266.

DOI: 10.1051/jphyscol:1982435

[40] S. Belyaev, N. Resnina, A. Sibirev, Accumulation of residual strain in TiNi alloy during thermal cycling, J. Mater. Eng. and Perform. 23 (2014) 2339-2342.

DOI: 10.1007/s11665-014-0982-z