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Modeling elastic-inelastic processes in shape memory alloys at finite deformations

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Abstract

An equation of state for a shape memory alloy is derived using a formalized approach to the construction of finite-deformation constitutive equations for complex media. The obtained equations were tested for coupled elastic-inelastic boundary-value problems of deformation of a sample of a shape-memory during forward and reverse martensitic transformations.

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References

  1. R. S. Novokshanov and A. A. Rogovoi, “Construction of Evolution Constitutive Relations for Finite Deformations,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 4, 77–95 (2002).

    Google Scholar 

  2. R. S. Novokshanov and A. A. Rogovoi, “Evolution Constitutive Equations for Finite Viscoelastic Deformations,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 4, 122–140 (2005).

    Google Scholar 

  3. A. A. Rogovoi, “Constitutive Relations for Finite Elastic-Inelastic Deformation,” Prikl. Mekh. Tekh. Fiz. 46(5), 138–149 (2005) [Appl. Mech. Tech. Phys. 46 (5), 730–739 (2005)].

    MathSciNet  MATH  Google Scholar 

  4. A. A. Rogovoi, “Thermodynamics of Finite-Strain Elastic-Inelastic Deformation,” Prikl. Mekh. Tekh. Fiz. 48(4), 144–153 (2007) [Appl. Mech. Tech. Phys. 48 (4), 591–598 (2007)].

    MathSciNet  Google Scholar 

  5. A. A. Rogovoi, “Kinematics of Finite-Strain Elastic-Inelastic Deformation,” Prikl. Mekh. Tekh. Fiz. 49(1), 165–172 (2008) [Appl. Mech. Tech. Phys. 49 (1), 136–141 (2008)].

    MathSciNet  Google Scholar 

  6. A. A. Rogovoy, “Formalized Approach to Construction of the State Equations for Complex Media under Finite Deformations,” Contin. Mech. Thermodyn. 24, 81–114 (2012).

    Article  MathSciNet  ADS  Google Scholar 

  7. C. A. Trusdell, A First Course in Rational Continuum Mechanics (J. Hopkins Univ., Baltimore, 1972).

    Google Scholar 

  8. A. A. Movchan, L. G. Sil’chenko, S. A. Kazarina, and Tant Zin Aung, “Constitutive Relations for Shape Memory Alloys: Micromechanics, Phenomenology, and Thermodynamics,” Uch. Zap. Kazan. Univ., Ser. Fiz.-Mat. Nauki 152(4), 180–194 (2010).

    Google Scholar 

  9. J. G. Boyd and D. C. Lagoudas, “A Thermodynamical Constitutive Model for Shape Memory Materials. Part 1. The Monolithic Shape Memory Alloy,” Int. J. Plasticity 12(6), 805–842 (1996).

    Article  MATH  Google Scholar 

  10. M. A. Qidwai and D. C. Lagoudas, “Numerical Implementation of a Shape Memory Alloy Thermomechanical Constitutive Model Using Return Mapping Algorithms,” Int. J. Numer. Methods Eng. 47, 1123–1168 (2000).

    Article  MATH  Google Scholar 

  11. T. J. Lim and D. L. McDowell, “Cyclic Thermomechanical Behavior of a Polycrystalline Pseudoelastic Shape Memory Alloy,” J. Mech. Phys. Solids, 50, 651–676 (2002).

    Article  ADS  MATH  Google Scholar 

  12. F. Auricchio and L. Petrini, “A Three-Dimentional Model Describing Stress-Temperature Induced Solid Phase Transformations: Thermomechanical Coupling and Hybrid Composites Applications,” Int. J. Numer. Methods Eng. 61, 716–737 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  13. F. Auricchio and L. Petrini, “A Three-Dimentional Model Describing Stress-Temperature Induced Solid Phase Transformations: Solution Algorithm and Boundary-Value Problems,” Int. J. Numer. Methods Eng. 61, 807–836 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  14. A. A. Movchan, “Selecting a Phase-Diagram Approximation and a Model of the Disappearance of Martensite for Shape Memory Alloys,” Prikl. Mekh. Tekh. Fiz. 36(2), 173–181 (1995) [Appl. Mech. Tech. Phys. 36 (2), 300–307 (1995)].

    Google Scholar 

  15. A. A. Movchan, P. V. Shelymagin, and S. A. Kazarina, “Constitutive Equations for Two-Step Thermoelastic Phase Transformations,” Prikl. Mekh. Tekh. Fiz. 42(5), 152–160 (2001) [Appl. Mech. Tech. Phys. 42 (5), 864–871 (2001)].

    Google Scholar 

  16. A. A. Movchan and L. G. Sil’chenko, “Analytical Solution of the Coupled Problem of Stability of a Plate of Shape Memory Alloy in the Reverse Martensitic Transformation,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 5, 164–178 (2004).

    Google Scholar 

  17. A. A. Movchan and Tu. Ya. Cho, “Solution of Boundary-Value Problems of the Forward and Reverse Transformation in the Nonlinear Theory of Deformation of Shape Memory Alloys,” Mekh. Kompoz. Mater. Konstr. 13(4) 452–468 (2007).

    Google Scholar 

  18. A. A. Movchan and Tu. Ya. Cho, “Solution of a Coupled Thermoelektromehanical Problem for a Rod of Shape Memory Alloy in the Theory of Nonlinear Deformation of These Materials,” Mekh. Kompoz. Mater. Konstr. 14(3), 443–460 (2008).

    Google Scholar 

  19. A. I. Lur’e, Theory of Elasticity (Nauka, Moscow, 1970) [in Russian].

    Google Scholar 

  20. A. I. Lur’e, Nonlinear Elasticity Theory (Nauka, Moscow, 1980) [in Russian].

    MATH  Google Scholar 

  21. A. A. Movchan, “Accounting for the Variability of the Elastic Moduli and the Effect of Stresses on the Phase Composition in Shape Memory Alloys,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 1, 79–90 (1998).

    Google Scholar 

  22. A. I. Irzhak, V. V. Istomin, V. V. Koledov, et al., “Ordering, Martensitic Transformation, and Shape Memory Effect in Submicron Samples of Rapidly Quenched Ni50Ti25Cu25 alloy,” Izv. Ross. Akad. Nauk, Ser. Fiz. 73(8), 1141–1143 (2009).

    Google Scholar 

  23. B. A. Ass and N. M. Zhukova, Parts and Units of Aircraft Instruments and Their Calculation (Oborongiz, Moscow, 1960) [in Russian].

    Google Scholar 

  24. L. E. Andreeva, Elastic Elements of Instruments (Mashgiz, Moscow, 1962) [in Russian].

    Google Scholar 

  25. A. P. Babichev, N. A. Babushkina, A. M. Bratkovskii, et al., Physical Quantities: Handbook, Ed. by I. S. Grigor’ev and E. Z. Meilikhov (Energoatomizdat, Moscow, 1991) [in Russian].

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Correspondence to A. A. Rogovoi.

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Original Russian Text © A.A. Rogovoi, O.S. Stolbova.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 54, No. 2, pp. 148–162, March–April, 2013.

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Rogovoi, A.A., Stolbova, O.S. Modeling elastic-inelastic processes in shape memory alloys at finite deformations. J Appl Mech Tech Phy 54, 295–307 (2013). https://doi.org/10.1134/S0021894413020156

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  • DOI: https://doi.org/10.1134/S0021894413020156

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