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Describing internal subloops due to incomplete phase transformations in shape memory alloys. (English) Zbl 1119.74515

Summary: The hysteretic response of shape memory alloys (SMAs) is one of their essential characteristics and is related to the martensitic phase transformation. The hysteresis loop may be observed either in stress-strain or strain-temperature curves. In brief, it is possible to say that the major (or external) hysteresis loop can be defined as the envelope of all minor (or internal) hysteresis loops, usually denoted as subloops. The macroscopic description of the SMA hysteresis loops, together with their subloops due to incomplete phase transformations, is an important aspect in the phenomenological description of the thermomechanical behavior of SMAs, being of great interest in technological applications. This contribution exploits the description of these internal subloops and employs a constitutive model previously proposed. Numerical investigations of the phenomenon are carried out to show the capability of this model to describe these inner subloops. Comparisons between numerical and experimental results show that they are in close agreement. Moreover, numerical simulations are carried out to elucidate different aspects of this hysteretic behavior.

MSC:

74N30 Problems involving hysteresis in solids
74M05 Control, switches and devices (“smart materials”) in solid mechanics
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[1] Baêta-Neves, A.P., Savi, M.A., Pacheco, P.M.C.L.: On the Fremond’s constitutive model for shape memory alloys. Mech Res Commun 31(6), 677–688 (2004) · Zbl 1098.74519
[2] Benzaqui, H., Lexcellent, C., Chaillet, N., Lang, B., Bourjault, A.: Experimental study and modeling of a TiNi shape memory wire actuator. J Intell Mater Syst Struct 8, 619–629 (1997)
[3] Birman, V.: Theory and comparison of the effect of composite and shape memory alloy stiffeners on stability of composite shells and plates. Int J Mech Sci 39(10), 1139–1149 (1997) · Zbl 0899.73314
[4] Bo, Z.H., Lagoudas, D.C.: Thermomechanical modeling of polycrystalline SMAs under cyclic loading – Part IV: modeling of minor hysteresis loops. Int J Eng Sci 37, 1205–1249 (1999) · Zbl 1210.74051
[5] Brinson, L.C., Huang, M.S.: Simplifications and comparisons of shape memory alloy constitutive models. J Intell Mater Syst Struct 7(1) 108–114 (1996)
[6] Denoyer, K.K., Erwin, R.S., Ninneman, R.R.: Advanced smart structures flight experiments for precision spacecraft. Acta Astronaut 47, 389–397 (2000)
[7] Duerig, T.M., Pelton, A., Stöckel, D.: An overview of nitinol medical applications. Mater Sci Eng A 273–275, 149–160 (1999)
[8] Fremond, M.: Matériaux à mémoire de forme. C.R. Acad Sc Paris Tome. 304, s. II, n. 7, 239–244 (1987)
[9] Fremond, M.: Shape memory alloy: a thermomechanical macroscopic theory. CISM Courses Lect 351, 3–68 (1996)
[10] Garner, L.J., Wilson, L.N., Lagoudas, D.C., Rediniotis, O.K.: Development of a shape memory alloy actuated biomimetic vehicle. Smart Mat Struct 9(5), 673–683 (2001)
[11] Lagoudas, D.C., Rediniotis, O.K., Khan, M.M.: Applications of shape memory alloys to bioengineering and biomedical technology. In: Proceeding of 4th international workshop on mathematical methods in scattering theory and biomedical technology, Perdika, Greece, (1999)
[12] Lemaitre, J., Chaboche, J.-L.: Mech Solid Mat. Cambridge University Press, Cambridge (1990)
[13] Machado, L.G., Savi, M.A.: Medical applications of shape memory alloys. Braz J Med Biol Res 36(6), 683–691 (2003)
[14] Machado, L.G., Savi, M.A.: Odontological applications of shape memory alloys (in portuguese). Rev Brasileira de Odontol 59(5), 302–306 (2002)
[15] Muller, I., Xu, H.: On the pseudo-elastic hysteresis. Acta Metallurgical Mat 39(3), 263–271 (1991)
[16] Ortin, J.: Partial hysteresis cycles in shape memory alloys: experiments and modelling. J. Phys IV 1, C4–65-C4–70 (1991)
[17] Ortin, J., Delaey, L.: Hysteresis in shape memory alloys. Int J Non-Linear Mech 37, 1275–1281 (2002) · Zbl 1346.74029
[18] Ortiz, M., Pinsky, P.M., Taylor, R.L.: Operator split methods for the numerical solution of the elastoplastic dynamic problem. Comp Meth App Mech Eng 39, 137–157 (1983) · Zbl 0501.73077
[19] Pacheco, P.M.C.L., Savi, M.A.: Modeling and simulation of a shape memory release device for aerospace applications. Rev Engenharia e Ciências Aplicadas, (2000)
[20] Paiva, A., Savi, M.A., Braga, A.M.B., Pacheco, P.M.C.L.: A constitutive model for shape memory alloys considering tensile-compressive asymmetry and plasticity. Int J Solids Struct 42 (11–12), 3439–3457 (2005) · Zbl 1127.74027
[21] Paiva, A.: Modeling of thermomechanical behavior of shape memory alloys (in portuguese). PhD Thesis, PUC-Rio, Department of Mechanical Engineering (2004)
[22] Paiva, A., Savi, M.A.: An overview on constitutive models for shape memory alloys. Submitted to Math Problems in Eng (2005) · Zbl 1119.74515
[23] Rockafellar, R.T.: Convex analysis, Princeton Press (1970) · Zbl 0193.18401
[24] Rogers, C.A.: Intelligent materials. Scientific American, 1995, pp. 122–127
[25] Savi, M.A., Paiva, A., Baêta-Neves, A.P., Pacheco, P.M.C.L.: Phenomenological modeling and numerical simulation of shape memory alloys: a thermo-plastic-phase transformation coupled model. J Intell Mater Syst Struct 13(5), 261–273 (2002)
[26] Sittner, P., Hara, Y., Tokuda, M.: Experimental study on the thermoelastic martensitic transformation in shape memory alloy polycrystal induced by combined external forces. Metallurgical Mater Trans A, 26A, 2923–2935 (1995)
[27] Tanaka, K., Nagaki, S.: Thermomechanical description of materials with internal variables in the process of phase transformation. Ingenieur Archiv 51, 287–299 (1982) · Zbl 0495.73098
[28] Tanaka, K., Nishimura, F., Tobushi, H.: Phenomenological analysis on subloops in shape memory alloys due to incomplete transformations. J. Intell Mater Syst Struct 5, 387–493 (1994)
[29] Tanaka, K., Nishimura, F., Hayashi, T., Tobushi, H., Lexcellent, C.: Phenomenological analysis on subloops and cyclic behavior in shape memory alloys under mechanical and/or thermal loads. Mech Mater 19, 281–292 (1995)
[30] Tanaka, K., Nishimura, F., Matsui, M., Tobushi, H., Lin, P.-H.: Phenomenological analysis on plateaus on stress–strain hysteresis in TiNi shape memory alloy wires. Mech Mater 24, 19–30 (1996)
[31] Tobushi, H., Iwanaga, N., Tanaka, K., Hori, T., Sawads, T.: Deformation behavior of Ni-Ti shape memory alloy subjected to variable stress and temperature. Conti Mech Therm 3, 79–93 (1991)
[32] van Humbeeck, J.: Non-medical applications of shape memory alloys. Mater Sci Eng A 273–275, 134–148 (1999)
[33] Webb, G., Wilson, L., Lagoudas, D.C., Rediniotis, O.: Adaptive control of shape memory alloy actuators for underwater biomimetic applications. AIAA J 38(2), 325–334 (2000)
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