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Constitutive modeling and finite element approximation of B2-R-B19\(^{\prime}\) phase transformations in Nitinol polycrystals. (English) Zbl 1230.74146

Summary: A path-dependent constitutive model is proposed for the stress-induced phase transformation of Nitinol single crystals between austenite, rhombohedral and martensite phases. A multi-directional active set strategy is employed to resolve the path and state of the transformation. The resulting algorithm is implemented using a multi-scale finite element-based method which extends the applicability of the model to textured Nitinol polycrystals. Representative numerical simulations are included and show good agreement with experimental results.

MSC:

74N05 Crystals in solids
74S05 Finite element methods applied to problems in solid mechanics

Software:

FEAP; BEARTEX
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References:

[1] Miyazaki, S.; Otsuka, K., Deformation and transition behavior associated with the R-phase in ti – ni alloys, Metall. trans. A, 17A, 53-63, (1986)
[2] Shindo, D.; Murakami, Y.; Ohba, T., Understanding precursor phenomena for the R-phase transformation in ti – ni-based alloys, MRS bull., 27, 2, 121-127, (2002)
[3] Otsuka, K.; Ren, X., Physical metallurgy of ti – ni-based shape memory alloys, Prog. mater. sci., 50, 511-678, (2005)
[4] McNaney, J.M.; Imbeni, V.; Jung, Y.; Papadopoulos, P.; Ritchie, R.O., An experimental study of the superelastic effect in a shape-memory Nitinol alloy under biaxial loading, Mech. mater., 35, 969-986, (2003)
[5] Sittner, P.; Landa, M.; Lukas, P.; Novak, V., R-phase transformation phenomena in thermomechanically loaded niti polycrystals, Mech. mater., 38, 475-492, (2006)
[6] Duerig, T.W., Some unsolved aspects of Nitinol, Mater. sci. engrg. A, 430-440, 69-74, (2006)
[7] Jung, Y.; Papadopoulos, P.; Ritchie, R.O., Constitutive modeling and numerical simulation of multivariant phase transformation in superelastic shape-memory alloys, Int. J. numer. meth. engrg., 60, 429-460, (2004) · Zbl 1060.74579
[8] Ortiz, M.; Repetto, E.A., Nonconvex energy minimization and dislocation structures in ductile single crystals, J. mech. phys. solids, 47, 397-462, (1999) · Zbl 0964.74012
[9] Miehe, C.; Schotte, J.; Lambrecht, M., Homogenization of inelastic solid materials at finite strains based on incremental minimization principles application to the texture analysis of polycrystals, J. mech. phys. solids, 50, 2123-2167, (2002) · Zbl 1151.74403
[10] Sengupta, A.; Papadopoulos, P.; Taylor, R.L., Multiscale finite element modeling of superelasticity in Nitinol polycrystals, Comput. mech., 43, 573-584, (2009)
[11] Ling, H.C.; Karlow, R., Stress-induced shape changes and shape memory in the R and martensite transformations in equiatomic niti, Metall. trans. A, 12A, 2101-2111, (1981)
[12] Miyazaki, S.; Wayman, C.M., The R-phase transition and associated shape memory mechanism in ti – ni single crystals, Acta metall., 36, 1, 181-192, (1988)
[13] Miyazaki, S.; Kimura, S.; Otsuka, S., Shape-memory effect and pseudoelasticity associated with the R-phase transition in ti-50.5 at.
[14] Sittner, P.; Novak, V.; Lukas, P.; Landa, M., Stress – strain – temperature behaviour due to B2-R-B19′ transformation in niti polycrystals, J. engrg. mater. tech., 128, 268-278, (2006)
[15] Hane, K.F.; Shield, T.W., Microstructure in the cubic to monoclinic transition in titanium – nickel shape memory alloys, Acta mater., 47, 2603-2617, (1999)
[16] Hane, K.F.; Shield, T.W., Microstructure in the cubic to trigonal transition, Mater. sci. engrg. A, A291, 147-159, (2000)
[17] Zhang, X.; Sehitoglu, H., Crystallography of the B2-R-B19′ phase transformations in niti, Mater. sci. engrg. A, 374, 292-302, (2004)
[18] Matsumoto, O.; Miyazaki, S.; Otsuka, K.; Tamura, H., Crystallography of martensitic transformation in ti – ni single crystals, Acta metall., 35, 8, 2137-2144, (1987)
[19] Siredey, N.; Patoor, E.; Berveiller, M.; Eberhardt, A., Constitutive equations for polycrystalline thermoelastic shape memory alloys. part I: intragranular interactions and behavior of the grain, Int. J. solids struct., 36, 4289-4315, (1999) · Zbl 0946.74041
[20] Lexcellent, C.; Raniecki, B.; Tanaka, K., Thermodynamic models of pseudoelastic behavior of shape memory alloys, Arch. mech., 44, 261-284, (1992) · Zbl 0825.73044
[21] Wenk, H.-R.; Matthies, S.; Donovan, J.; Chateigner, D., BEARTEX: a windows-based program system for quantitative texture analysis, J. appl. cryst., 31, 262-269, (1998)
[22] R.L. Taylor, FEAP - a finite element analysis program: Users Manual, University of California, Berkeley, 2008. <http://www.ce.berkeley.edu/ rlt>.
[23] Bonet, J.; Bhargava, P., A uniform deformation gradient hexahedron element with artificial hourglass control, Int. J. numer. meth. engrg., 48, 2809-2828, (1995) · Zbl 0835.73069
[24] Luenberger, D.G., Linear and nonlinear programming, (1984), Addison-Wesley Reading · Zbl 0241.90052
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