Skip to main content
Top
Published in: Meccanica 4-5/2017

28-03-2016

A phenomenological model for the simulation of functional fatigue in shape memory alloy wires

Authors: T. Bartel, M. Osman, A. Menzel

Published in: Meccanica | Issue 4-5/2017

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this contribution, a modelling framework for functional fatigue in shape memory alloy wires is introduced. The approach is in particular designed to reproduce the effective response determined by experiments as published in, e.g., Eggeler et al. (Mat Sci Eng A 378:24–33, 2004). In this context, the decrease of transformation stresses, the increase of irreversible strains, and the occurrence of “characteristic points” with respect to the stress-strain relation is explicitly covered in the model formulation. The modelling approach for the phase transformations itself offers a large potential for further micromechanically well-motivated model extensions.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Footnotes
1
A maximum of two simultaneously occurring discontinuities as this work proceeds.
 
Literature
1.
go back to reference Abeyaratne R, Knowles J (1990) On the driving traction acting on a surface of strain discontinuity in a continuum. J Mech Phys Sol 38:345–360ADSMathSciNetCrossRefMATH Abeyaratne R, Knowles J (1990) On the driving traction acting on a surface of strain discontinuity in a continuum. J Mech Phys Sol 38:345–360ADSMathSciNetCrossRefMATH
2.
go back to reference Auricchio F, Petrini L (2004) A three-dimensional model describing stress-temperature induced solid phase transformations: thermomechanical coupling and hybrid composite applications. Int J Numer Meth Engrg 61:716–737CrossRefMATH Auricchio F, Petrini L (2004) A three-dimensional model describing stress-temperature induced solid phase transformations: thermomechanical coupling and hybrid composite applications. Int J Numer Meth Engrg 61:716–737CrossRefMATH
3.
go back to reference Auricchio F, Reali A, Stefanelli U (2007) A three-dimensional model describing stress-induced solid phase transformation with permanent inelasticity. Int J Plast 23:207–226CrossRefMATH Auricchio F, Reali A, Stefanelli U (2007) A three-dimensional model describing stress-induced solid phase transformation with permanent inelasticity. Int J Plast 23:207–226CrossRefMATH
4.
go back to reference Barrera N, Biscari P, Urbano MF (2014) Macroscopic modeling of functional fatigue in shape memory alloys. Eur J Mech A/Solids 45:101–109CrossRef Barrera N, Biscari P, Urbano MF (2014) Macroscopic modeling of functional fatigue in shape memory alloys. Eur J Mech A/Solids 45:101–109CrossRef
5.
go back to reference Bartel T, Menzel A, Svendsen B (2011) Thermodynamic and relaxation-based modeling of the interaction between martensitic phase transformations and plasticity. J Mech Phys Sol 59:1004–1019ADSMathSciNetCrossRefMATH Bartel T, Menzel A, Svendsen B (2011) Thermodynamic and relaxation-based modeling of the interaction between martensitic phase transformations and plasticity. J Mech Phys Sol 59:1004–1019ADSMathSciNetCrossRefMATH
6.
go back to reference Bertacchini OW, Lagoudas DC, Patoor E (2009) Thermomechanical transformation fatigue of TiNiCu SMA actuators under a corrosive environment-part i: Experimental results. Int J Fatigue 31:1571–1578CrossRef Bertacchini OW, Lagoudas DC, Patoor E (2009) Thermomechanical transformation fatigue of TiNiCu SMA actuators under a corrosive environment-part i: Experimental results. Int J Fatigue 31:1571–1578CrossRef
7.
go back to reference Biot MA (1965) Mechanics of incremental deformations. Wiley, New York Biot MA (1965) Mechanics of incremental deformations. Wiley, New York
8.
go back to reference Casati R, Passaretti F, Tuissi A (2011) Effect of electrical heating conditions on functional fatigue of thin NiTi wire for shape memory actuators. Proc Engrg 10:3423–3428CrossRef Casati R, Passaretti F, Tuissi A (2011) Effect of electrical heating conditions on functional fatigue of thin NiTi wire for shape memory actuators. Proc Engrg 10:3423–3428CrossRef
9.
10.
go back to reference Demersa V, Brailovski V, Prokoshkinb SD, Inaekyana KE (2009) Thermomechanical fatigue of nanostructured Ti-Ni shape memory alloys. Mat Sci Engrg A 513–514:185–196CrossRef Demersa V, Brailovski V, Prokoshkinb SD, Inaekyana KE (2009) Thermomechanical fatigue of nanostructured Ti-Ni shape memory alloys. Mat Sci Engrg A 513–514:185–196CrossRef
12.
go back to reference Eggeler G, Hornbogen E, Yawny A, Heckmann A, Wagner M (2004) Structural and functional fatigue of NiTi shape memory alloys. Mat Sci Eng A 378:24–33CrossRef Eggeler G, Hornbogen E, Yawny A, Heckmann A, Wagner M (2004) Structural and functional fatigue of NiTi shape memory alloys. Mat Sci Eng A 378:24–33CrossRef
13.
go back to reference Grossmann C, Schaefer A, Wagner MFX (2010) A finite element study on localized deformation and functional fatigue in pseudoelastic NiTi strips. Mat Sci Engrg A 527:1172–1178CrossRef Grossmann C, Schaefer A, Wagner MFX (2010) A finite element study on localized deformation and functional fatigue in pseudoelastic NiTi strips. Mat Sci Engrg A 527:1172–1178CrossRef
14.
15.
go back to reference Hartl D, Lagoudas D (2007) Aerospace applications of shape memory alloys. Proc Inst Mech Eng 221:535–552CrossRef Hartl D, Lagoudas D (2007) Aerospace applications of shape memory alloys. Proc Inst Mech Eng 221:535–552CrossRef
16.
go back to reference Hornbogen E (2004) Thermo-mechanical fatigue of shape memory alloys. J Mat Sci 39:385–399ADSCrossRef Hornbogen E (2004) Thermo-mechanical fatigue of shape memory alloys. J Mat Sci 39:385–399ADSCrossRef
17.
go back to reference Jäger P, Steinmann P, Kuhl E (2008) On local tracking algorithms for the simulation of three-dimensional discontinuities. Comput Mech 42:395–406CrossRefMATH Jäger P, Steinmann P, Kuhl E (2008) On local tracking algorithms for the simulation of three-dimensional discontinuities. Comput Mech 42:395–406CrossRefMATH
18.
go back to reference Jani JM, Leary M, Subic A, Gibson MA (2014) A review of shape memory alloy research, applications and opportunities. Mat Design 2014:1078–1113CrossRef Jani JM, Leary M, Subic A, Gibson MA (2014) A review of shape memory alloy research, applications and opportunities. Mat Design 2014:1078–1113CrossRef
19.
go back to reference Kang G, Kan Q, Yu C, Song D, Liu Y (2012) Whole-life transformation ratchetting and fatigue of super-elastic niti alloy under uniaxial stress-controlled cyclic loading. Mat Sci Engrg A 535:228–234CrossRef Kang G, Kan Q, Yu C, Song D, Liu Y (2012) Whole-life transformation ratchetting and fatigue of super-elastic niti alloy under uniaxial stress-controlled cyclic loading. Mat Sci Engrg A 535:228–234CrossRef
20.
go back to reference Lagoudas DC (2008) Shape memory alloys: modeling and engineering applications. Springer, New York Lagoudas DC (2008) Shape memory alloys: modeling and engineering applications. Springer, New York
21.
go back to reference Li YF, Mi XJ, Tan J, Gao BD (2009) Thermo-mechanical cyclic transformation behavior of Ti-Ni shape memory alloy wire. Mat Sci Engrg A 509:8–13CrossRef Li YF, Mi XJ, Tan J, Gao BD (2009) Thermo-mechanical cyclic transformation behavior of Ti-Ni shape memory alloy wire. Mat Sci Engrg A 509:8–13CrossRef
22.
go back to reference McCormick PG, Liu Y (1994) Thermodynamic analysis of the martensitic transformation in NiTi-II. Effect of transformation cycling. Acta Metall Mater 42(7):2407–2413CrossRef McCormick PG, Liu Y (1994) Thermodynamic analysis of the martensitic transformation in NiTi-II. Effect of transformation cycling. Acta Metall Mater 42(7):2407–2413CrossRef
23.
go back to reference Miyazaki S, Igo Y, Otsuka K (1986) Effect of thermal cycling on the transformation temperatures of Ti-Ni alloys. Acta Metal 34(10):2045–2051CrossRef Miyazaki S, Igo Y, Otsuka K (1986) Effect of thermal cycling on the transformation temperatures of Ti-Ni alloys. Acta Metal 34(10):2045–2051CrossRef
25.
go back to reference Nayan N, Buravalla V, Ramamurty U (2009) Effect of mechanical cycling on the stress-strain response of a martensitic Nitinol shape memory alloy. Mat Sci Engrg A 525:60–67CrossRef Nayan N, Buravalla V, Ramamurty U (2009) Effect of mechanical cycling on the stress-strain response of a martensitic Nitinol shape memory alloy. Mat Sci Engrg A 525:60–67CrossRef
26.
go back to reference Olbricht J, Yawny A, Cond’o AM, Lovey FC, Eggeler G (2008) The influence of temperature on the evolution of functional properties during pseudoelastic cycling of ultra fine grained NiTi. Mat Sci Engrg A 481–482:142–145CrossRef Olbricht J, Yawny A, Cond’o AM, Lovey FC, Eggeler G (2008) The influence of temperature on the evolution of functional properties during pseudoelastic cycling of ultra fine grained NiTi. Mat Sci Engrg A 481–482:142–145CrossRef
27.
go back to reference Ostwald R, Bartel T, Menzel A (2012) Phase-transformations interacting with plasticity—a micro-sphere model applied to trip steel. Comput Mat Sci 64:12–16CrossRef Ostwald R, Bartel T, Menzel A (2012) Phase-transformations interacting with plasticity—a micro-sphere model applied to trip steel. Comput Mat Sci 64:12–16CrossRef
28.
go back to reference Ostwald R, Bartel T, Menzel A (2015) An energy-barrier-based computational micro-sphere model for phase-transformations interacting with plasticity. Comput Methods Appl Mech Engrg 293:232–265ADSMathSciNetCrossRef Ostwald R, Bartel T, Menzel A (2015) An energy-barrier-based computational micro-sphere model for phase-transformations interacting with plasticity. Comput Methods Appl Mech Engrg 293:232–265ADSMathSciNetCrossRef
30.
go back to reference Robertson SW, Pelton AR, Ritchie RO (2012) Mechanical fatigue and fracture of nitinol. Int Mat Rev 57(1):1–37CrossRef Robertson SW, Pelton AR, Ritchie RO (2012) Mechanical fatigue and fracture of nitinol. Int Mat Rev 57(1):1–37CrossRef
31.
go back to reference Shaw JA, Kyriakides S (1998) Initiation and propagation of localized deformation in elasto-plastic strips under uniaxial tension. Int J Plast 13(10):837–871CrossRef Shaw JA, Kyriakides S (1998) Initiation and propagation of localized deformation in elasto-plastic strips under uniaxial tension. Int J Plast 13(10):837–871CrossRef
32.
go back to reference Souza AC, Mamiya EN, Zouain N (1998) Three-dimensional model for solids undergoing stress-induced phase transformations. Eur J Mech A/Solids 17:789–806CrossRefMATH Souza AC, Mamiya EN, Zouain N (1998) Three-dimensional model for solids undergoing stress-induced phase transformations. Eur J Mech A/Solids 17:789–806CrossRefMATH
33.
go back to reference Merzouki T, Duval TZ (2012) Finite element analysis of a shape memory alloy actuator for a micropump. Sim Mod Pract Theory 27:112–126 Merzouki T, Duval TZ (2012) Finite element analysis of a shape memory alloy actuator for a micropump. Sim Mod Pract Theory 27:112–126
34.
go back to reference Wagner M (2005) Ein Beitrag zur strukturellen und funktionalen Ermüdung von Drähten und Federn aus NiTi-Formgedächtnislegierungen Wagner M (2005) Ein Beitrag zur strukturellen und funktionalen Ermüdung von Drähten und Federn aus NiTi-Formgedächtnislegierungen
35.
go back to reference Waimann J, Junker P, Hackl K (2016) A coupled dissipation functional for modeling the functional fatigue in polycrystalline shape memory alloys. Eur J Mech A 55:110–121MathSciNetCrossRef Waimann J, Junker P, Hackl K (2016) A coupled dissipation functional for modeling the functional fatigue in polycrystalline shape memory alloys. Eur J Mech A 55:110–121MathSciNetCrossRef
36.
go back to reference Weighardt SC, Maier HJ, Chumlyakov YI (2013) Dependence of functional degradation on crystallographic orientation in NiTi shape memory alloys aged under stress. J Alloys Comp 577:219–221CrossRef Weighardt SC, Maier HJ, Chumlyakov YI (2013) Dependence of functional degradation on crystallographic orientation in NiTi shape memory alloys aged under stress. J Alloys Comp 577:219–221CrossRef
38.
go back to reference Yawny A, Olbricht J, Sade M, Eggeler G (2008) Pseudoelastic cycling and ageing effects at ambient temperatures in nanocrystalline Ni-rich NiTi wire. Mat Sci Engrg A 481–482:86–90CrossRef Yawny A, Olbricht J, Sade M, Eggeler G (2008) Pseudoelastic cycling and ageing effects at ambient temperatures in nanocrystalline Ni-rich NiTi wire. Mat Sci Engrg A 481–482:86–90CrossRef
39.
go back to reference Yin H, He Y, Sun Q (2014) Effect of deformation frequency on temperature and stress oscillations in cyclic phase transition of NiTi shape memory alloy. J Mech Phys Sol 67:100–128ADSCrossRef Yin H, He Y, Sun Q (2014) Effect of deformation frequency on temperature and stress oscillations in cyclic phase transition of NiTi shape memory alloy. J Mech Phys Sol 67:100–128ADSCrossRef
40.
go back to reference Zaki W, Moumni Z (2007) A 3d model of the cyclic thermomechanical behavior of shape memory alloys. J Mech Phys Sol 55:2427–2454ADSCrossRefMATH Zaki W, Moumni Z (2007) A 3d model of the cyclic thermomechanical behavior of shape memory alloys. J Mech Phys Sol 55:2427–2454ADSCrossRefMATH
41.
go back to reference Ziegler H (1963) Some extremum principles in irreversible thermodynamics with application to continuum mechanics. North-Holland, No. IV in Progress in Solid Mechanics Ziegler H (1963) Some extremum principles in irreversible thermodynamics with application to continuum mechanics. North-Holland, No. IV in Progress in Solid Mechanics
Metadata
Title
A phenomenological model for the simulation of functional fatigue in shape memory alloy wires
Authors
T. Bartel
M. Osman
A. Menzel
Publication date
28-03-2016
Publisher
Springer Netherlands
Published in
Meccanica / Issue 4-5/2017
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-016-0419-x

Other articles of this Issue 4-5/2017

Meccanica 4-5/2017 Go to the issue

Premium Partners