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Erschienen in: Journal of Materials Engineering and Performance 7/2014

01.07.2014

Simulations of Mechanical Response of Superelastic NiTi Helical Spring and its Relation to Fatigue Resistance

verfasst von: P. Sedlák, M. Frost, A. Kruisová, K. Hiřmanová, L. Heller, P. Šittner

Erschienen in: Journal of Materials Engineering and Performance | Ausgabe 7/2014

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Abstract

Behavior of NiTi shape memory alloys under complex loading is still a subject of both experimental and theoretical investigations. One of the simplest geometries, in which the material is loaded in combined mode and which has also several practical applications, is a simple helical spring. In this contribution, mechanical response of NiTi superelastic spring is analyzed in detail by numerical simulation and the results are compared to experiments. The simulations show complex stress state, which develops during spring stretching. Analyzing fatigue tests with respect to simulated behavior allowed us to find relation between fatigue resistance and periodic changes in volume fraction of martensite induced by cyclic mechanical loading. The work also underlines an extension of the range of stroke amplitudes guaranteeing enhanced life performance of the spring when material transforms through the R-phase.

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Fußnoten
1
Let us note that there is a direct relation between dissipation function and corresponding yield function through Legendre transformation if some mathematical assumptions are satisfied.
 
2
Anisotropy of elastic properties was experimentally confirmed in Ref 23. However, because of difficulties with complete determination of stiffness tensor (5 independent constants for transverse isotropic material), assumption of elastic isotropy was adopted (similarly to Ref 5-10) and elastic properties were determined only by two constants—Young modulus E and shear modulus G. This simplification can only slightly influence the simulation as only shear and tensile/compressive stress components are significant in loaded spring.
 
Literatur
1.
Zurück zum Zitat D.J. Hartl, D.C. Lagoudas, F.T. Calkins, and J.H. Mabe, Use of a Ni60Ti Shape Memory Alloy for Active Jet Engine Chevron Application: I. Thermomechanical Characterization, Smart Mater. Struct., 2009, 19, p 015020CrossRef D.J. Hartl, D.C. Lagoudas, F.T. Calkins, and J.H. Mabe, Use of a Ni60Ti Shape Memory Alloy for Active Jet Engine Chevron Application: I. Thermomechanical Characterization, Smart Mater. Struct., 2009, 19, p 015020CrossRef
2.
Zurück zum Zitat L.G. Machado and M.A. Savi, Medical Applications of Shape Memory Alloys, Braz. J. Med. Biol. Res., 2003, 36, p 683–691 L.G. Machado and M.A. Savi, Medical Applications of Shape Memory Alloys, Braz. J. Med. Biol. Res., 2003, 36, p 683–691
3.
Zurück zum Zitat D. Vokoun, D. Majtás, M. Frost, P. Sedlák, and P. Šittner, Shape Memory Hooks Employed in Fasteners, J. Mater. Eng. Perform., 2009, 18, p 706–710CrossRef D. Vokoun, D. Majtás, M. Frost, P. Sedlák, and P. Šittner, Shape Memory Hooks Employed in Fasteners, J. Mater. Eng. Perform., 2009, 18, p 706–710CrossRef
4.
Zurück zum Zitat P. Sittner, L. Heller, J. Pilch et al., Roundrobin SMA Modeling, ESOMAT 2009: The 8th European Symposium on Martensitic Transformations, EDP Sciences, P. Sittner, L. Heller, and V. Paidar, Eds., 2009, p 08001 P. Sittner, L. Heller, J. Pilch et al., Roundrobin SMA Modeling, ESOMAT 2009: The 8th European Symposium on Martensitic Transformations, EDP Sciences, P. Sittner, L. Heller, and V. Paidar, Eds., 2009, p 08001
5.
Zurück zum Zitat J. Arghavani, F. Auricchio, R. Naghdabadi, A. Reali, and S. Sohrabpour, A 3-D Phenomenological Constitutive Model for Shape Memory Alloys Under Multiaxial Loadings, Int. J. Plast., 2010, 26, p 976–991CrossRef J. Arghavani, F. Auricchio, R. Naghdabadi, A. Reali, and S. Sohrabpour, A 3-D Phenomenological Constitutive Model for Shape Memory Alloys Under Multiaxial Loadings, Int. J. Plast., 2010, 26, p 976–991CrossRef
6.
Zurück zum Zitat Y. Chemisky, A. Duval, E. Patoor, and T. Ben Zineb, Constitutive Model for Shape Memory Alloys Including Phase Transformation, Martensitic Reorientation and Twins Accommodation, Mech. Mater., 2011, 43, p 361–376CrossRef Y. Chemisky, A. Duval, E. Patoor, and T. Ben Zineb, Constitutive Model for Shape Memory Alloys Including Phase Transformation, Martensitic Reorientation and Twins Accommodation, Mech. Mater., 2011, 43, p 361–376CrossRef
7.
Zurück zum Zitat D.C. Lagoudas, D.J. Hartl, Y. Chemisky, L.G. Machado, and P. Popov, Constitutive Model for the Numerical Analysis of Phase Transformation in Polycrystalline Shape Memory Alloys, Int. J. Plast., 2012, 32–33, p 155–183CrossRef D.C. Lagoudas, D.J. Hartl, Y. Chemisky, L.G. Machado, and P. Popov, Constitutive Model for the Numerical Analysis of Phase Transformation in Polycrystalline Shape Memory Alloys, Int. J. Plast., 2012, 32–33, p 155–183CrossRef
8.
Zurück zum Zitat M. Panico and L.C. Brinson, A Three-Dimensional Phenomenological Model for Martensite Reorientation in Shape Memory Alloys, J. Mech. Phys. Solids, 2007, 55, p 2491–2511CrossRef M. Panico and L.C. Brinson, A Three-Dimensional Phenomenological Model for Martensite Reorientation in Shape Memory Alloys, J. Mech. Phys. Solids, 2007, 55, p 2491–2511CrossRef
9.
Zurück zum Zitat Z. Moumni, W. Zaki, and Q.S. Nguyen, Theoretical and Numerical Modeling of Solid-Solid Phase Change: Application to the Description of the Thermomechanical Behavior of Shape Memory Alloys, Int. J. Plast., 2008, 24, p 614–645CrossRef Z. Moumni, W. Zaki, and Q.S. Nguyen, Theoretical and Numerical Modeling of Solid-Solid Phase Change: Application to the Description of the Thermomechanical Behavior of Shape Memory Alloys, Int. J. Plast., 2008, 24, p 614–645CrossRef
10.
Zurück zum Zitat A.F. Saleeb, S.A. Padula, and A.A. Kumar, A Multi-Axial, Multimechanism Based Constitutive Model for the Comprehensive Representation of the Evolutionary Response of SMAs Under General Thermomechanical Loading Conditions, Int. J. Plast., 2011, 27, p 655–687CrossRef A.F. Saleeb, S.A. Padula, and A.A. Kumar, A Multi-Axial, Multimechanism Based Constitutive Model for the Comprehensive Representation of the Evolutionary Response of SMAs Under General Thermomechanical Loading Conditions, Int. J. Plast., 2011, 27, p 655–687CrossRef
11.
Zurück zum Zitat L. Saint-Sulpice, S. Arbab Chirani, and S. Calloch, A 3D Super-Elastic Model for Shape Memory Alloys Taking into Account Progressive Strain Under Cyclic Loadings, Mech. Mater., 2009, 41, p 12–26CrossRef L. Saint-Sulpice, S. Arbab Chirani, and S. Calloch, A 3D Super-Elastic Model for Shape Memory Alloys Taking into Account Progressive Strain Under Cyclic Loadings, Mech. Mater., 2009, 41, p 12–26CrossRef
12.
Zurück zum Zitat P. Sedlak, M. Frost, B. Benesova, P. Sittner, and T. Ben Zineb, Thermomechanical Model for NiTi-Based Shape Memory Alloys Including R-phase and Material Anisotropy Under Multi-Axial Loadings, Int. J. Plast., 2012, 39, p 132–151CrossRef P. Sedlak, M. Frost, B. Benesova, P. Sittner, and T. Ben Zineb, Thermomechanical Model for NiTi-Based Shape Memory Alloys Including R-phase and Material Anisotropy Under Multi-Axial Loadings, Int. J. Plast., 2012, 39, p 132–151CrossRef
13.
Zurück zum Zitat C. Liang, A Rogers Design of Shape Memory Alloy Actuators, J. Intell. Mater. Syst. Struct., 1997, 8, p 303–313CrossRef C. Liang, A Rogers Design of Shape Memory Alloy Actuators, J. Intell. Mater. Syst. Struct., 1997, 8, p 303–313CrossRef
14.
Zurück zum Zitat Y. Toi, J.-B. Lee, and M. Taya, Finite Element Analysis of Superelastic, Large Deformation Behavior of Shape Memory Alloy Helical Springs, Comput. Struct., 2004, 82, p 1685–1693CrossRef Y. Toi, J.-B. Lee, and M. Taya, Finite Element Analysis of Superelastic, Large Deformation Behavior of Shape Memory Alloy Helical Springs, Comput. Struct., 2004, 82, p 1685–1693CrossRef
15.
Zurück zum Zitat R. Mirzaeifar, R. DesRoches, and A. Yavari, A Combined Analytical, Numerical, and Experimental Study of Shape-Memory-Alloy Helical Springs, Int. J. Solids Struct., 2011, 48, p 611–624CrossRef R. Mirzaeifar, R. DesRoches, and A. Yavari, A Combined Analytical, Numerical, and Experimental Study of Shape-Memory-Alloy Helical Springs, Int. J. Solids Struct., 2011, 48, p 611–624CrossRef
16.
Zurück zum Zitat A.F. Saleeb, B. Dhakal, M.S. Hosseini, and S.A. Padula, Large Scale Simulation of NiTi Helical Spring Actuators Under Repeated Thermomechanical Cycles, Smart Mater. Struct., 2013, 22, p 094006CrossRef A.F. Saleeb, B. Dhakal, M.S. Hosseini, and S.A. Padula, Large Scale Simulation of NiTi Helical Spring Actuators Under Repeated Thermomechanical Cycles, Smart Mater. Struct., 2013, 22, p 094006CrossRef
17.
Zurück zum Zitat K. Hirmanova, J. Pilch, J. Racek, L. Heller, P. Sittner, L. Recman, M. Petrenec, and P. Sedlak, Physical Simulation of the Random Failure of Implanted Braided NiTi Stents, J. Mater. Eng. Perform, accepted in K. Hirmanova, J. Pilch, J. Racek, L. Heller, P. Sittner, L. Recman, M. Petrenec, and P. Sedlak, Physical Simulation of the Random Failure of Implanted Braided NiTi Stents, J. Mater. Eng. Perform, accepted in
18.
Zurück zum Zitat A. Sadjadpour and K. Bhattacharya, A Micromechanics-Inspired Constitutive Model for Shape-Memory Alloys: the One-Dimensional Case, Smart Mater. Struct., 2007, 16, p S51–S62CrossRef A. Sadjadpour and K. Bhattacharya, A Micromechanics-Inspired Constitutive Model for Shape-Memory Alloys: the One-Dimensional Case, Smart Mater. Struct., 2007, 16, p S51–S62CrossRef
19.
Zurück zum Zitat C. Grabe and O.T. Bruhns, On the Viscous and Strain Rate Dependent Behavior of Polycrystalline NiTi, Int. J. Solids Struct., 2008, 45, p 1876–1895CrossRef C. Grabe and O.T. Bruhns, On the Viscous and Strain Rate Dependent Behavior of Polycrystalline NiTi, Int. J. Solids Struct., 2008, 45, p 1876–1895CrossRef
20.
Zurück zum Zitat Q.S. Nguyen, Stability and Nonlinear Solid Mechanics, John Wiley, New York, 2000, p 17–40 Q.S. Nguyen, Stability and Nonlinear Solid Mechanics, John Wiley, New York, 2000, p 17–40
21.
Zurück zum Zitat K. Hackl and F.D. Fischer, On the Relation Between the Principle of Maximum Dissipation and Inelastic Evolution Given by Dissipation Potentials, Proc. R. Soc. A, 2008, 464, p 117–132CrossRef K. Hackl and F.D. Fischer, On the Relation Between the Principle of Maximum Dissipation and Inelastic Evolution Given by Dissipation Potentials, Proc. R. Soc. A, 2008, 464, p 117–132CrossRef
22.
Zurück zum Zitat M. Frost, B. Benesova, and P. Sedlak, A Microscopically Motivated Constitutive Model for Shape Memory Alloys: Formulation, Analysis and Computations, Math. Mech. Solids, accepted in M. Frost, B. Benesova, and P. Sedlak, A Microscopically Motivated Constitutive Model for Shape Memory Alloys: Formulation, Analysis and Computations, Math. Mech. Solids, accepted in
23.
Zurück zum Zitat S. Qiu, B. Clausen, S.A. Padula, R.D. Noebe, and R. Vaidyanathan, On Elastic Moduli and Elastic Anisotropy in Polycrystalline Martensitic NiTi, Acta Mater., 2011, 59, p 5055–5066CrossRef S. Qiu, B. Clausen, S.A. Padula, R.D. Noebe, and R. Vaidyanathan, On Elastic Moduli and Elastic Anisotropy in Polycrystalline Martensitic NiTi, Acta Mater., 2011, 59, p 5055–5066CrossRef
24.
Zurück zum Zitat P. Sittner, M. Landa, P. Lukas, and V. Novak, R-phase Transformation Phenomena in Thermomechanically Loaded NiTi Polycrystals, Mech. Mater., 2006, 38, p 475–492CrossRef P. Sittner, M. Landa, P. Lukas, and V. Novak, R-phase Transformation Phenomena in Thermomechanically Loaded NiTi Polycrystals, Mech. Mater., 2006, 38, p 475–492CrossRef
25.
Zurück zum Zitat K. Gall, H. Sehitoglu, Y.I. Chumlyakov, and I.V. Kireeva, Tension-Compression Asymmetry of the Stress-Strain Response in Aged Single Crystal and Polycrystalline NiTi, Acta Mater., 1999, 43, p 1203–1217CrossRef K. Gall, H. Sehitoglu, Y.I. Chumlyakov, and I.V. Kireeva, Tension-Compression Asymmetry of the Stress-Strain Response in Aged Single Crystal and Polycrystalline NiTi, Acta Mater., 1999, 43, p 1203–1217CrossRef
26.
Zurück zum Zitat V. Grolleau, H. Louche, V. Delobelle, A. Penin, G. Rio, Y. Liu, and D. Favier, Assessment of Tension-Compression Asymmetry of NiTi Using Circular Bulge Testing of Thin Plates, Scr. Mater., 2011, 65, p 347–350CrossRef V. Grolleau, H. Louche, V. Delobelle, A. Penin, G. Rio, Y. Liu, and D. Favier, Assessment of Tension-Compression Asymmetry of NiTi Using Circular Bulge Testing of Thin Plates, Scr. Mater., 2011, 65, p 347–350CrossRef
27.
Zurück zum Zitat S.C. Mao, J.F. Luo, Z. Zhang, M.H. Wub, Y. Liu, and X.D. Han, EBSD Studies of the Stress-Induced B2-B19’ Martensitic Transformation in NiTi Tubes Under Uniaxial Tension and Compression, Acta Mater., 2010, 58, p 3357–3366CrossRef S.C. Mao, J.F. Luo, Z. Zhang, M.H. Wub, Y. Liu, and X.D. Han, EBSD Studies of the Stress-Induced B2-B19’ Martensitic Transformation in NiTi Tubes Under Uniaxial Tension and Compression, Acta Mater., 2010, 58, p 3357–3366CrossRef
28.
Zurück zum Zitat Y.C. Shu and K. Bhattacharya, The Influence of Texture on the Shape-Memory Effect in Polycrystals, Acta Mater., 1998, 46, p 5457–5473CrossRef Y.C. Shu and K. Bhattacharya, The Influence of Texture on the Shape-Memory Effect in Polycrystals, Acta Mater., 1998, 46, p 5457–5473CrossRef
29.
Zurück zum Zitat B. Reedlunn, C.B. Churchill, E.E. Nelson, J.A. Shaw, and S.H. Daly, Tension, Compression, and Bending of Superelastic Shape Memory Alloy Tubes, J. Mech. Phys. Solids, 2014, 63, p 506–537 B. Reedlunn, C.B. Churchill, E.E. Nelson, J.A. Shaw, and S.H. Daly, Tension, Compression, and Bending of Superelastic Shape Memory Alloy Tubes, J. Mech. Phys. Solids, 2014, 63, p 506–537
30.
Zurück zum Zitat S. Miyazaki and K. Otsuka, Deformation and Transition Behavior Associated with the R-phase in Ti-Ni Alloys, Metall. Trans. A, 1986, 17A, p 53–63CrossRef S. Miyazaki and K. Otsuka, Deformation and Transition Behavior Associated with the R-phase in Ti-Ni Alloys, Metall. Trans. A, 1986, 17A, p 53–63CrossRef
31.
Zurück zum Zitat T. Atanacković and M. Achenbach, Moment-Curvature Relations for a Pseudoelastic Beam, Contin. Mech. Thermodyn., 1989, 1(1), p 73–80CrossRef T. Atanacković and M. Achenbach, Moment-Curvature Relations for a Pseudoelastic Beam, Contin. Mech. Thermodyn., 1989, 1(1), p 73–80CrossRef
33.
Zurück zum Zitat R. Mirzaeifar, R. DesRoches, A. Yavari, and K. Gall, Coupled Thermo-Mechanical Analysis of Shape Memory Alloy Circular Bars in Pure Torsion, Int. J. Non-Linear Mech., 2012, 47, p 118–128CrossRef R. Mirzaeifar, R. DesRoches, A. Yavari, and K. Gall, Coupled Thermo-Mechanical Analysis of Shape Memory Alloy Circular Bars in Pure Torsion, Int. J. Non-Linear Mech., 2012, 47, p 118–128CrossRef
34.
Zurück zum Zitat M. Frost, P. Sedlak, A. Kruisova, and M. Landa, Simulations of Self-Expanding Braided Stent Using Macroscopic Model of NiTi Shape Memory Alloys Covering R-Phase, J. Mater. Eng. Perform., submitted to M. Frost, P. Sedlak, A. Kruisova, and M. Landa, Simulations of Self-Expanding Braided Stent Using Macroscopic Model of NiTi Shape Memory Alloys Covering R-Phase, J. Mater. Eng. Perform., submitted to
Metadaten
Titel
Simulations of Mechanical Response of Superelastic NiTi Helical Spring and its Relation to Fatigue Resistance
verfasst von
P. Sedlák
M. Frost
A. Kruisová
K. Hiřmanová
L. Heller
P. Šittner
Publikationsdatum
01.07.2014
Verlag
Springer US
Erschienen in
Journal of Materials Engineering and Performance / Ausgabe 7/2014
Print ISSN: 1059-9495
Elektronische ISSN: 1544-1024
DOI
https://doi.org/10.1007/s11665-014-0906-y

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