Thermomechanics of martensitic phase transitions in shape memory alloys I: Constitutive theories for small and large deformations

Journal of Mechanics of Materials and Structures

Volumn 2, Issue 1, 2007, Pages 87-112

  Helm, Dirk ^a,b  

^a UNIVERSITY OF KASSEL   (Germany)

^b FRAUNHOFER INSTITUTE FOR MECHANICS OF MATERIALS IWM   (Germany)

Author keywords

Finite deformations; Martensitic phase transitions; Shape memory alloys; Thermomechanical modeling

Indexed keywords

EID: 34548554698     PISSN: 15593959     EISSN: None     Source Type: Journal    
DOI: 10.2140/jomms.2007.2.87     Document Type: Article

References (82)

1. [Achenbach and Müller 1982] M. Achenbach and I. Müller, "A model for shape memory", Journal de Physique, Colleque C4, ICOMAT-82 43 (1982), 163-167.
2. [Anand and Gurtin 2003] L. Anand and M. E. Gurtin, "Thermal effects in the superelasticity of crystalline shape-memory materials", J. Mech. Phys. Solids 51:6 (2003), 1015-1058. MR 2004c:74066
3. [Auricchio and Petrini 2004] F. Auricchio and L. Petrini, "A three-dimensional model describing stress-temperature induced solid phase transformations: solution algorithm and boundary value problems", Internat. J. Numer. Methods Engrg. 61:6 (2004), 807-836. MR 2005d:74032
4. [Auricchio and Stefanelli 2004] F. Auricchio and U. Stefanelli, "Numerical analysis of a three-dimensional super-elastic constitutive model", Internat. J. Numer. Methods Engrg. 61:1 (2004), 142-155. MR 2005b:74100
5. [Auricchio and Taylor 1997] F. Auricchio and R. Taylor, "Shape-memory alloys: modelling and numerical simulations of the finite-strain superelastic behavior", Computer Methods in Applied Mechanics and Engineering 143 (1997), 175-194.
6. [Auricchio et al. 1997] F. Auricchio, R. Taylor, and J. Lubliner, "Shape-memory alloys: macromodelling and numerical simulations of the superelastic behavior", Computer Methods in Applied Mechanics and Engineering 146 (1997), 281-312.
7. [Bertram 1982] A. Bertram, "Thermo-mechanical constitutive equations for the description of shape memory effects in alloys", Nuclear Engineering and Design 74 (1982), 173-182.
8. [Bondaryev and Wayman 1988] E. Bondaryev and C. Wayman, "Some stress-strain-temperature relationships for shape memory alloys", Metallurgical Transactions A 19A (1988), 2407-2413.
9. [Boyd and Lagoudas 1994] J. Boyd and D. Lagoudas, "A constitutive model for simultaneous transformation and reorientation in shape memory materials", pp. 159-177 in Mechanics of phase transformations and shape memory alloys (Chicago, 1994), edited by L. C. Brinson and B. Moran, AMD 189, The American Society of Mechanical Engineers, New York, 1994.
10. [Casey 1985] J. Casey, "Approximate kinematical relations in plasticity", Internat. J. Solids Structures 21:7 (1985), 671-682. MR 88c:73033
11. [Coleman and Gurtin 1967] B. Coleman and M. Gurtin, "Thermodynamics with internal state variables", J. Chem. Phys. 47 (1967), 597-613.
12. [Delobelle and Lexcellent 1996] P. Delobelle and C. Lexcellent, "A phenomenological three dimensional model for pseudoelastic behavior of shape memory", Journal de Physique IV 6 (1996), 293-300.
13. [Dettmer and Reese 2004] W. Dettmer and S. Reese, "On the theoretical and numerical modelling of Armstrong-Frederick kinematic hardening in the finite strain regime", Comput. Methods Appl. Mech. Engrg. 193 (2004), 87-116.
14. [Eckart 1948] C. Eckart, "The thermodynamics of irreversible processes, IV: The theory of elasticity and anelasticity", Physical Rev. (2) 73 (1948), 373-382. MR 9,394a
15. [Eggeler et al. 2004] G. Eggeler, E. Hornbogen, A. Yawny, and M. Wagner, "Structural and functional fatigue of NiTi shape memory alloys", Materials Science and Engineering A 378 (2004), 24-33.
16. [Entchev and Lagoudas 2002] P. Entchev and D. Lagoudas, "Modeling porous shape memory alloys using micromechanical averaging techniques", Mechanics of materials 34:11 (2002), 1-24.
17. [Falk 1983] F. Falk, "One-dimensional model of shape memory", Archives of Mechanics 35 (1983), 63-84.
18. [Flory 1961] P. J. Flory, "Thermodynamic relations for high elastic materials", Trans. Faraday Soc. 57 (1961), 829-838. MR 23 #B1161
19. [Funakubo 1987] H. Funakubo, Shape memory alloys, Gordon and Breach, New York, 1987.
20. [Gall and Sehitoglu 1999] K. Gall and H. Sehitoglu, "The role of texture in tension-compression asymmetry in polycrystalline NiTi", International Journal of Plasticity 15:1 (1999), 69-92. Corrigendum in 15:7, 781.
21. [Graesser and Cozzarelli 1994] E. Graesser and F. Cozzarelli, "A proposed three dimensional constitutive model for shape memory alloys", Journal of Intelligent Material Systems and Structures 5 (1994), 78-89.
22. [Haupt 1985] P. Haupt, "On the concept of an intermediate configuration and its application to a representation of viscoelastic-plastic material behaviour", International Journal of Plasticity 1 (1985), 303-316.
23. [Haupt 2002] P. Haupt, Continuum mechanics and theory of materials, 2nd ed., Advanced Texts in Physics, Springer, Berlin, 2002. MR 2004h:74001
24. [Haupt and Tsakmakis 1989] P. Haupt and C. Tsakmakis, "On the application of dual variables in continuum mechanics", Contin. Mech. Thermodyn. 1:3 (1989), 165-196. MR 91m:73002
25. [Haupt et al. 1992] P. Haupt, M. Kamlah, and C. Tsakmakis, "On the thermodynamics of rate-independent plasticity as an asymptotic limit of viscoplasticity for slow processes", pp. 107-116 in Finite inelastic deformations: Theory and applications (Hannover, 1991), edited by D. Besdo and E. Stein, Berlin, 1992.
26. [Helm 2001] D. Helm, Formgedächtnislegierungen: Experimentelle Untersuchung, phänomenologische Modellierung und numerische Simulation der thermomechanischen Materialeigenschaften, Ph.D. thesis, Institut für Mechanik, Universität Gesamthochschule Kassel, Kassel, 2001.
27. [Helm 2005] D. Helm, "Pseudoelastic behavior of shape memory alloys: Constitutive theory and identification of the material parameters using neural networks", Technische Mechanik 25 (http://www.uni-magdeburg.de/ifme/techmech/2005), 39-58.
28. [Helm 2006] D. Helm, "Stress computation in finite thermoviscoplasticity", International Journal of Plasticity 22 (2006), 1699-1727.
29. [Helm and Haupt 2001] D. Helm and P. Haupt, "Thermomechanical behaviour of shape memory alloys", pp. 302-313 in Smart structures and materials: Active materials, behavior and mechanics (Newport Beach, CA, 2001), edited by C. S. Lynch, Proceedings of SPIE 4333, Internat. Soc. Optical Eng., Bellingham, WA, 2001.
30. [Helm and Haupt 2003] D. Helm and P. Haupt, "Shape memory behaviour: modelling within continuum thermomechanics", International Journal of Solids and Structures 40 (2003), 825-849.
31. [Helm and Schäfers 2006] D. Helm and M. Schäffers, "Thermomechanics of martensitic phase transitions in shape memory alloys, II: numerical treatment", Journal of Mechanics and Materials of Structures (2006), 1-30. prepared.
32. [Hohenemser and Prager 1932] K. Hohenemser and W. Prager, "Über die Ansätze der Mechanik isotroper Kontinua", ZAMM 12 (1932), 216-226.
33. [Huang et al. 2000] M. Huang, X. Gao, and L. C. Brinson, "A multivariant micromechanical model for SMAs, 2: Polycrystal model", International Journal of Plasticity 16 (2000), 1371-1390.
34. [Huo and Müller 1993] Y. Huo and I. Müller, "Nonequilibrium thermodynamics of pseudoelasticity", Contin. Mech. Thermodyn. 5:3 (1993), 163-204. MR 94h:73015
35. [Juhász et al. 2000] L. Juhász, H. Andrä, and O. Hesebeck, "Simulation of the thermomechanical behaviour of shape memory alloys under multi-axial non-proportional loading", pp. 484-495 in Smart structures and materials: Active materials, behavior and mechanics (Newport Beach, CA, 2000), edited by C. S. Lynch, Proceedings of SPIE 3992, Internat. Soc. Optical Eng., Bellingham, WA, 2000.
36. [Jung et al. 2004] Y. Jung, P. Papadopoulos, and R. O. Ritchie, "Constitutive modelling and numerical simulation of multivariant phase transformation in superelastic shape-memory alloys", Internat. J. Numer. Methods Engrg. 60:2 (2004), 429-460. MR 2005a:74076
37. [Khan and Lagoudas 2002] M. Khan and D. Lagoudas, "Modeling of shape memory alloy springs using Preisach model for passive vibration isolation", pp. 336-347 in Smart structures and materials: Modeling, signal processing, and control (San Diego, 2002), edited-by V. Rao, Proceedings of SPIE 4693, Internat. Soc. Optical Eng., Bellingham, WA, 2002.
38. [Kröner 1958] E. Kröner, Kontinuumstheorie der Versetzungen und Eigenspannungen, Ergebnisse der angewandten Mathematik 5, Springer, Berlin, 1958. MR 20 #2117
39. [Kröner 1960] E. Kröner, "Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen", Arch. Rational Mech. Anal. 4 (1960), 273-334. MR 23 #B26
40. [Lagoudas et al. 2006] D. Lagoudas, P. Entchev, P. Popov, E. Patoor, L. Brinson, and X. Gao, "Shape memory alloys, I: Modeling of polycrystals", Mechanics of Materials 38 (2006), 430-462.
41. [Leclercq and Lexcellent 1996] S. Leclercq and C. Lexcellent, "A general macroscopic description of the thermomechanical behavior of shape memory alloys", Journal of the Mechanics and Physics of Solids 44:6 (1996), 953-980.
42. [Lee 1969] E. Lee, "Elastic-plastic deformation at finite strains", Journal of Applied Mechanics 36 (1969), 59-67.
43. [Lee and Liu 1967] E. Lee and D. Liu, "Finite-strain elastic-plastic theory with application to plane-wave analysis". Journal of Applied Physics 38 (1967), 19-27.
44. [Levitas 1998] V. I. Levitas, "Thermomechanical theory of martensitic phase transformations in inelastic materials", Internat. J. Solids Structures 35:9-10 (1998), 889-940. MR 98k:73012
45. [Lexcellent et al. 1996] C. Lexcellent, B. Goo, Q. Sun, and J. Bernardini, "Characterization, Thermomechanical Behaviour and Micromechanical-Based Constitutive Model of Shape-Memory Cu-Zn-Al Single Crystals", Acta Materialia 44 (1996), 3773-3780.
46. [Lexcellent et al. 2006] C. Lexcellent, M. Boubakar, C. Bouvet, and S. Calloch, "About modelling the shape memory alloy behaviour based on the phase transformation surface identification under proportional loading and anisothermal conditions", International Journal of Solids and Structures 43 (2006), 613-626.
47. [Liang and Rogers 1990] C. Liang and C. Rogers, "One dimensional thermomechanical constitutive relations for shape memory materials", Journal of Intelligent Material Systems and Structures 1 (1990), 207-234.
48. [Lim and McDowell 1995] T. Lim and D. McDowell, "Path dependence of shape memory alloys during cyclic loading", Journal of Intelligent Material Systems and Structures 6 (1995), 817-830.
49. [Lim and McDowell 1999] T. Lim and D. McDowell, "Mechanical behavior of an Ni-Ti shape memory alloy under axial-torsional proportional and nonproportional loading", Journal of Engineering Materials and Technology 121 (1999), 9-19.
50. [Lim and McDowell 2002] T. Lim and D. McDowell, "Cyclic thermomechanical behavior of a polycrystalline pseudoelastic shape memory alloy", Journal of the Mechanics and Physics of Solids 50:26 (2002), 651-676.
51. [Lion 2000] A. Lion, "Constitutive modelling in finite thermoviscoplasticity: a physical approach based on nonlinear rheological models", International Journal of Plasticity 16 (2000), 469-494.
52. [Lubliner 1985] J. Lubliner, "A model of rubber viscoelasticity", Mechanics Research Communications 12 (1985), 93-99.
53. [Lubliner 1990] J. Lubliner, Plasticity theory, New York, London, 1990.
54. [Mandel 1972] J. Mandel, Plasticité classique et viscoplasticité, CIMS Courses and Lectures 97, Springer, Vienna, 1972. MR 49 #8463
55. [McNancy et al. 2003] J. McNaney, V. Imbeni, Y. Jung, P. Papadopoulos, and R. O. Ritchie, "An experimental study of the superelastic effect in a shape-memory Nitinol alloy under biaxial loading", Mechanics of Materials 35 (2003), 969-986.
56. [Miyazaki and Otsuka 1989] S. Miyazaki and K. Otsuka, "Development of shape memory alloys". ISIJ International 29:5 (1989), 353-377.
57. [Müller and Bruhns 2004] C. Müller and O. Bruhns, "An Eulerian model for pseudoelastic shape memory alloys", Material Science and Engineering Technology 35 (2004), 260-271.
58. [Novák and Sitner 2004] V, Novák and P. Sittner, "Micromechanical modelling of NiTi polycrystalline aggregates transforming under tension and compression stress", Materials Science and Engineering, A 378 (2004), 490-498.
59. [Otsuka and Ren 1999] K. Otsuka and X. Ren, "Recent developments in the research of shape memory alloys", Intermetallics 7 (1999), 511-528.
60. [Otsuka and Wayman 1998] K. Otsuka and C. Wayman, Shape memory materials, Cambridge University Press, 1998.
61. [Paiva et al. 2005] A. Paiva, M. Savi, A. Braga, and P. Pacheco, "A constitutive model for shape memory alloys considering tensile-compressive asymmetry and plasticity", International Journal of Solids and Structures 42 (2005), 3439-3457.
62. [Patoor et al. 1994] E. Patoor, A. Eberhardt, and M. Berveiller, "Micromechanical modelling of the shape memory behavior", pp. 23-37 in Mechanics of phase transformations and shape memory alloys (Chicago, 1994), edited by L. Brinson and B. Moran, AMD 189, The American Society of Mechanical Engineers, New York, 1994.
63. [Patoor et al. 1996] E. Patoor, A. Eberhardt, and M. Berveiller, "Micromechanical modelling of superelasticity in shape memory alloys", Journal de Physique IV 6 (1996), 277-292.
64. [Patoor et al. 2006] E. Patoor, D. Lagoudas, P. Entchev, L. Brinson, and X., Gao, "Shape memory alloys, Part I: General properties and modeling of single crystals", Mechanics of Materials 38 (2006), 391-429.
65. [Perzyna 1963] P. Perzyna, "The constitutive equations for rate sensitive plastic materials", Quart. Appl. Math. 20 (1963), 321-332. MR 26 #2080
66. [Qidwai and Lagoudas 2000] M. A. Qidwai and D. C. Lagoudas, "On thermomechanics and transformation surfaces of polycrystalline NiTi shape memory alloy material", International Journal of Plasticity 16 (2000), 1309-1343.
67. L- models of pseudoelasticity and their specification for some shape memory solids", European J. Mech. A Solids 13:1 (1994), 21-50. MR 94m:73012
68. [Raniecki et al. 1992] B. Raniecki, C. Lexcellent, and K. Tanaka, "Thermodynamic models of pseudoelastic behaviour of shape memory alloys", Arch. Mech. (Arch. Mech. Stos.) 44:3 (1992), 261-284. MR 94j:73012
69. [Raniecki et al. 2001] B. Raniecki, K. Tanaka, and A. Ziółkowski, "Testing and modeling of NiTi SMA at complex stress state: Selected results of Polish-Japanese research cooperation", Materials Science Research International Special Technical Publication 2 (2001), 327-334.
70. [Rogueda et al. 1996] C. Rogueda, C. Lexcellent, and L. Bocher, "Experimental study of pseudoelastic behaviour of a CuZ-nAl polycrystalline shape memory alloy under tension-torsion proportional and non-proportional loading tests", Archives of Mechanics 48 (1996), 1025-1045.
71. [Seelecke 2002] S. Seelecke, "Modeling the dynamic behavior of shape memory alloys", International Journal of Non-Linear Mechanics 37 (2002), 1363-1374.
72. [Shaw and Kyriakides 1995] J. Shaw and S. Kyriakides, "Thermomechanical aspects of NiTi", Journal of the Mechanics and Physics of Solids 8 (1995), 1243-1281.
73. [Shimizu and Tadaki 1987] K. Shimizu and T. Tadaki, "Shape memory effect: Mechanism", pp. 1-60 in Shape memory alloys, edited by H. Funakubo, Gordon and Breach, New York, 1987.
74. [Simo 1985] J. Simo, "On the computational significance of the intermediate configuration and hyperelastic stress relations in finite deformation elastoplasticity", Mechanics of Materials 4 (1985), 439-451.
75. [Simo 1988] J. C. Simo, "A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition, I: Continuum formulation", Comput. Methods Appl. Mech. Engrg. 66:2 (1988), 199-219. MR 89a:73029
76. [Simo and Pister 1984] J. Simo and K. Pister, "Remarks on rate constitutive equations for finite deformation problems", Computer Methods in Applied Mechanics and Engineering 46 (1984), 201-215.
77. [Souza et al. 1998] A. Souza, E. Mamiya, and N. Zouain, "Three-dimensional model for solids undergoing stress-induced phase transitions", Eur J Mech. A/Solids 17 (1998), 789-806.
78. [Tanaka and Nagaki 1982] K. Tanaka and S. Nagaki, "A thermomechanical description of materials with internal variables in the process of phase transitions", Ingenieur-Archiv 51 (1982), 287-299.
79. [Tanaka et al. 2002] K. Tanaka, D. Ohnami, T. Watanabe, and J. Kosegawa, "Micromechanical simulations of thermomechanical behavior in shape memory alloys: transformation conditions and thermomechanical hystereses", Mechanics of Materials 34 (2002), 279-298.
80. [Thamburaja and Anand 2003] P. Thamburaja and L. Anand, "Thermo-mechanically coupled superelastic repsonse of initially-textured Ti-Ni sheet", Acta Materialia 51 (2003), 325-338.
81. [Tsakmakis 1996] C. Tsakmakis, "Kinematic hardening rules in finite plasticity, I: A constitutive approach", Continuum Mechanics and Thermodynamics 8 (1996), 215-231.
82. [Tsakmakis and Willuweit 2004] C. Tsakmakis and A. Willuweit, "A comparative study of kinematic hardening rules at finite deformations", Int. J. of Non-Linear Mechanics 39 (2004), 539-554.