A 3D finite strain phenomenological constitutive model for shape memory alloys considering martensite reorientation

Continuum Mechanics and Thermodynamics

Volumn 22, Issue 5, 2010, Pages 345-362

  Arghavani, J ^a,b   Auricchio, F ^b,c,d   Naghdabadi, R ^a   Reali, A ^b,d   Sohrabpour, S ^a,e  

^a SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

^b UNIVERSITY OF PAVIA   (Italy)

^c SCUOLA UNIVERSITARIA SUPERIORE IUSS PAVIA   (Italy)

^d EUROPEAN CENTRE FOR TRAINING AND RESEARCH IN EARTHQUAKE ENGINEERING EUCENTRE   (Italy)

^e Academy of Sciences of Islamic Republic of Iran   (Iran)

Author keywords

Constitutive model; Finite strain; Non proportional loading; Phase transformation; Reorientation; Shape memory alloys

Indexed keywords

FINITE STRAIN; NONPROPORTIONAL LOADING; PHASE TRANSFORMATION; REORIENTATION; SHAPE MEMORY ALLOY;

ALLOYS; CONSTITUTIVE MODELS; DEFORMATION; LOADING; MARTENSITE; SHAPE MEMORY EFFECT; THREE DIMENSIONAL;

STRAIN RATE;

EID: 77955768879     PISSN: 09351175     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00161-010-0155-8     Document Type: Article

References (60)

1. Otsuka K., Wayman C.M.: Shape Memory Materials. Cambridge University Press, Cambridge (1998)
2. Duerig T.W., Melton K.N., Stoekel D., Wayman C.M.: Engineering Aspects of Shape Memory Alloys. Butterworth- Heinemann, London (1990)
3. J. Van Humbeeck 1999 Non-medical applications of shape memory alloys Mater. Sci. Eng. A 273 275 134 148 (Pubitemid 30522718)
4. T. Duerig A. Pelton D. Stockel 1999 An overview of nitinol medical applications Mater. Sci. Eng. A 273 275 149 160
5. K. Kuribayashi K. Tsuchiya Z. You D. Tomus M. Umemoto T. Ito M. Sasaki 2006 Self-deployable origami stent grafts as a biomedical application of Ni-rich TiNi shape memory alloy foil Mater. Sci. Eng. A 419 1-2 131 137
6. Funakubo H.: Shape Memory Alloys. Gordon and Breach Science Publishers, New York (1987)
7. T.J. Lim D.L. McDowell 1999 Mechanical behavior of an Ni-Ti shape memory alloy under axial-torsional proportional and nonproportional loading J. Eng. Mater. Technol. 121 9 18 10.1115/1.2816007
8. P. Sittner Y. Hara M. Tokuda 1995 Experimental study on the thermoelastic martensitic transformation in shape memory alloy polycrystal induced by combined external forces Metall. Mater. Trans. A 26 2923 2935 10.1007/BF02669649
9. Helm D.: Formgedächtnislegierungen-experimentelle untersuchung, phänomenologische modellierung und numerische simulation der thermomechanischen materialeigenschaften. Ph.D. thesis, Universitat Gesamthochschule Kassel (2001)
10. Helm D., Haupt P.: Thermomechanical representation of the multiaxial behavior of shape memory alloys. In: Lynch, C.S. (Ed.), Proceedings of SPIE Smart Structures and Materials 2002: Active Materials: Behavior and Mechanics, vol. 4699, pp. 343-354 (2002)
11. C. Bouvet S. Calloch C. Lexcellent 2002 Mechanical behavior of a Cu-Al-Be shape memory alloy under multiaxial proportional and nonproportional loadings J. Eng. Mater. Technol. 124 112 124 10.1115/1.1448324 (Pubitemid 40000933)
12. C. Grabe O. Bruhns 2009 Path dependence and multiaxial behavior of a polycrystalline niti alloy within the pseudoelastic and pseudoplastic temperature regimes Int. J. Plast. 25 513 545 05531242 10.1016/j.ijplas.2008.03. 002
13. E. Patoor D.C. Lagoudas P.B. Entchev L.C. Brinson X. Gao 2006 Shape memory alloys, part I: general properties and modeling of single crystals Mech. Mater. 38 5-6 391 429 10.1016/j.mechmat.2005.05.027 (Pubitemid 43230079)
14. D.C. Lagoudas P.B. Entchev P. Popov E. Patoor L.C. Brinson X. Gao 2006 Shape memory alloys, part II: modeling of polycrystals Mech. Mater. 38 5-6 430 462 10.1016/j.mechmat.2005.08.003 (Pubitemid 43226017)
15. S. Leclercq C. Lexcellent 1996 A general macroscopic description of the thermomechanical behavior of shape memory alloys J. Mech. Phys. Solids 44 6 953 957 10.1016/0022-5096(96)00013-0 1996JMPSo..44..953L (Pubitemid 126359636)
16. A. Bekker L.C. Brinson 1987 Temperature-induced phase transformation in a shape memory alloy: Phase diagram based kinetics approach J. Mech. Phys. Solids 45 6 949 988 10.1016/S0022-5096(96)00111-1 1456084 1997JMPSo..45..949B
17. E.N. Bondaryev C.M. Wayman 1988 Some stress-strain-temperature relationships for shape memory alloys Metall. Trans. A 19A 10 2407 2413 1988MTA....19.2407B
18. Y. Chi T.J. Pence H. Tsai 2005 Axisymmetric plane stress states of an annulus subject to displacive phase transformation J. Appl. Mech. 72 44 53 1111.74365 10.1115/1.1828062 (Pubitemid 40308594)
19. Y. Chi T.J. Pence H. Tsai 2007 Numerical algorithms for cyclic phase transformation hysteresis in a shape memory plate subject to axisymmetric plane stress Int. J. Numer. Methods Eng. 69 1819 1850 10.1002/nme.1829 2292443 (Pubitemid 46344264)
20. B. Raniecki C. Lexcellent 1998 Thermodynamics of isotropic pseudoelasticity in shape memory alloys Eur. J. Mech A/Solids 17 2 185 205 0919.73006 10.1016/S0997-7538(98)80082-X
21. M. Panico L. Brinson 2007 A three-dimensional phenomenological model for martensite reorientation in shape memory alloys J. Mech. Phys. Solids 55 11 2491 2511 1171.74037 10.1016/j.jmps.2007.03.010 2361781 2007JMPSo..55.2491P (Pubitemid 47562464)
22. J. Arghavani F. Auricchio R. Naghdabadi A. Reali S. Sohrabpour 2010 A 3-D phenomenological constitutive model for shape memory alloys under multiaxial loadings Int. J. Plast. 26 976 991 10.1016/j.ijplas.2009.12.003
23. A.C. Souza E.N. Mamiya N. Zouain 1998 Three-dimensional model for solids undergoing stress-induced phase transformations Eur. J. Mech. A/Solids 17 5 789 806 0921.73024 10.1016/S0997-7538(98)80005-3 1998EJMS...17..789S
24. M.A. Qidwai D.C. Lagoudas 2000 Numerical implementation of a shape memory alloy thermomechanical constitutive model using return mapping algorithms Int. J. Numer. Methods Eng. 47 1123 1168 0960.74067 10.1002/(SICI)1097-0207(20000228) 47:6<1123::AID-NME817>3.0.CO;2-N (Pubitemid 30542454)
25. M. Brocca L.C. Brinson Z.P. Bazant 2002 Three-dimensional constitutive model for shape memory alloys based on microplane model J. Mech. Phys. Solids 50 5 1051 1077 1027.74002 10.1016/S0022-5096(01)00112-0 2002JMPSo..50.1051B
26. D. Helm P. Haupt 2003 Shape memory behaviour: modelling within continuum thermomechanics Int. J. Solids Struct 40 4 827 849 1025.74022 10.1016/S0020-7683(02)00621-2 (Pubitemid 36211448)
27. F. Auricchio S. Marfia E. Sacco 2003 Modelling of SMA materials: training and two way memory effects Comput Struct 81 24-25 2301 2317 10.1016/S0045-7949(03)00319-5
28. C. Bouvet S. Calloch C. Lexcellent 2004 A phenomenological model for pseudoelasticity of shape memory alloys under multiaxial proportional and nonproportional loadings Eur. J. Mech. A/Solids 23 1 37 61 1057.74027 10.1016/j.euromechsol.2003.09.005 2034411
29. D.C. Lagoudas P.B. Entchev 2004 Modeling of transformation-induced plasticity and its effect on the behavior of porous shape memory alloys. Part I: constitutive model for fully dense smas Mech. Mater. 36 9 865 892
30. F. Auricchio A. Reali U. Stefanelli 2007 A three-dimensional model describing stress-induced solid phase transformation with permanent inelasticity Int. J. Plast. 23 2 207 226 1105.74031 10.1016/j.ijplas.2006.02.012 (Pubitemid 44636100)
31. P. Popov D.C. Lagoudas 2007 A 3-D constitutive model for shape memory alloys incorporating pseudoelasticity and detwinning of self-accommodated martensite Int. J. Plast. 23 10-11 1679 1720 1127.74008 10.1016/j.ijplas.2007. 03.011 (Pubitemid 47214659)
32. F. Thiebaud C. Lexcellent M. Collet E. Foltete 2007 Implementation of a model taking into account the asymmetry between tension and compression, the temperature effects in a finite element code for shape memory alloys structures calculations Comput. Mater. Sci. 41 2 208 221 10.1016/j.commatsci.2007.04.006 (Pubitemid 350061338)
33. Z. Moumni W. Zaki Q.S. Nguyen 2008 Theoretical and numerical modeling of solid-solid phase change: application to the description of the thermomechanical behavior of shape memory alloys Int. J. Plast. 24 4 614 645 1145.74028 10.1016/j.ijplas.2007.07.007
34. F. Auricchio R.L. Taylor 1997 Shape-memory alloys: modelling and numerical simulations of the finite-strain superelastic behavior Comput. Methods Appl. Mech. Eng. 143 1-2 175 194 0891.73027 10.1016/S0045-7825(96)01147-4 (Pubitemid 127411650)
35. F. Auricchio 2001 A robust integration-algorithm for a finite-strain shape-memory-alloy superelastic model Int. J. Plast. 17 971 990 1107.74338 10.1016/S0749-6419(00)00050-4 (Pubitemid 32543787)
36. A. Pethö 2001 Constitutive modelling of shape memory alloys at finite strain Z. Angew. Math. Mech 81 S2 355 356 1001.74090
37. A. Ziolkowski 2007 Three-dimensional phenomenological thermodynamic model of pseudoelasticity of shape memory alloys at finite strains Contin. Mech. Thermodyn. 19 379 398 1160.74322 10.1007/s00161-007-0060-y 2377798 2007CMT....19..379Z (Pubitemid 350112775)
38. S. Reese D. Christ 2008 Finite deformation pseudo-elasticity of shape memory alloys-constitutive modelling and finite element implementation Int. J. Plast. 24 3 455 482 1145.74005 10.1016/j.ijplas.2007.05.005 (Pubitemid 350251672)
39. D. Christ S. Reese 2009 A finite element model for shape memory alloys considering thermomechanical couplings at large strains Int. J. Solids Struct. 46 20 3694 3709 1183.74265 10.1016/j.ijsolstr.2009.06.017
40. Evangelista V., Marfia S., Sacco E.: A 3D SMA constitutive model in the framework of finite strain. Int. J. Numer. Methods Eng. doi: 10.1002/nme.2717 (2009)
41. Arghavani J., Auricchio F., Naghdabadi R., Reali A., Sohrabpour S.: On the robustness and efficiency of integration algorithms for a 3D finite strain phenomenological SMA constitutive model. Int. J. Numer. Methods Eng. doi: 10.1002/nme.2964
42. C. Müller O. Bruhns 2006 A thermodynamic finite-strain model for pseudoelastic shape memory alloys Int. J. Plast. 22 9 1658 1682 1099.74050 10.1016/j.ijplas.2006.02.010 (Pubitemid 44304445)
43. Bernardini, D., Pence, T.J.: A Multifield Theory for the Modeling of the Macroscopic Behavior of Shape Memory Materials. In: Advances in Multifield Theories for Continua with Substructure. Birkhauser, Boston (2004)
44. L -models of pseudoelasticity and their specifications for some shape memory alloys Eur. J. Mech. A/Solids 13 1 21 50 0795.73010 1268974
45. F. Auricchio L. Petrini 2004 A three-dimensional model describing stress-temperature induced solid phase transformations: thermomechanical coupling and hybrid composite applications Int. J. Numer. Methods Eng. 61 5 716 737 1075.74598 10.1002/nme.1087 2088036 (Pubitemid 39259901)
46. V.I. Levitas 1998 Thermomechanical theory of martensitic phase transformations in inelastic materials Int. J. Solids Struct. 35 889 940 0931.74059 10.1016/S0020-7683(97)00089-9 1608706
47. A.V. Idesman V.I. Levitas E. Stein 1999 Elastoplastic materials with martensitic phase transition and twinning at finite strains: numerical solution with finite element method Comput. Methods Appl. Mech. Eng. 173 71 98 0961.74060 10.1016/S0045-7825(98)00258-8 1694335
48. P. Thamburaja L. Anand 2001 Polycrystalline shape-memory materials: effect of crystallographic texture J. Mech. Phys. Solids 49 709 737 1011.74049 10.1016/S0022-5096(00)00061-2 2001JMPSo..49..709T
49. P. Thamburaja 2005 Constitutive equations for martensitic reorientation and detwinning in shape-memory alloys J. Mech. Phys. Solids 53 825 856 1120.74310 10.1016/j.jmps.2004.11.004 2122487 2005JMPSo..53..825T (Pubitemid 40245176)
50. S. Stupkiewicz H. Petryk 2006 Finite-strain micromechanical model of stress-induced martensitic transformations in shape memory alloys Mater. Sci. Eng. A 438 440 126 130
51. H. Pan P. Thamburaja F.S. Chau 2007 Multi-axial behavior of shape-memory alloys undergoing martensitic reorientation and detwinning Int. J. Plast. 23 4 711 732 1190.74026 10.1016/j.ijplas.2006.08.002 (Pubitemid 46026913)
52. E. Stein G. Sagar 2008 Theory and finite element computation of cyclic martensitic phase transformation with finite strain Int. J. Numer. Methods Eng. 74 1 31 1159.74389 10.1002/nme.2148 2398492 (Pubitemid 351454817)
53. Lubarda V.A.: Elastoplasticity Theory. CRC Press LLC, (2001)
54. Haupt P.: Continuum Mechanics and Theory of Materials. Springer Publication House, New York (2001)
55. Y. Liu Z.L. Xie J. Van Humbeeck L. Delaey 1998 Asymmetry of stress-strain curves under tension and compression for NiTi shape memory alloys Acta Mater. 46 4325 4338 10.1016/S1359-6454(98)00112-8
56. Y. Liu Z.L. Xie J. Van Humbeeck L. Delaey 1999 Effect of texture orientation on the martensite deformation of NiTi shape memory alloy sheet Acta Mater. 47 645 660 10.1016/S1359-6454(98)00376-0
57. Ogden R.W.: Non-linear Elastic Deformations. Ellis Horwood Limited, Chichester (1984)
58. Arghavani J.: Thermomechanical behavior of shape memory alloys under nonproportional loading: constitutive modelling and numerical inplementation in small and finite strains, Ph.d. Thesis, Sharif University of Technology, Iran (2010)
59. Y. Yeganeh R. Naghdabadi 2006 Axial effects investigation in fixed-end circular bars under torsion with a finite deformation model based on logarithmic strain Int. J. Mech. Sci. 48 1 75 84
60. F. Auricchio A. Coda A. Reali M. Urbano 2009 SMA numerical modeling versus experimental results: parameter identification and model prediction capabilities J. Mater. Eng. Perform. 18 5-6 649 654 10.1007/s11665-009-9409-7