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Frontiers of Structural and Civil Engineering

ISSN 2095-2430

ISSN 2095-2449(Online)

CN 10-1023/X

Postal Subscription Code 80-968

2018 Impact Factor: 1.272

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Front. Struct. Civ. Eng.    2015, Vol. 9 Issue (4) : 466-477    https://doi.org/10.1007/s11709-015-0300-3
RESEARCH ARTICLE
An extended thermo-mechanically coupled algorithm for simulation of superelasticity and shape memory effect in shape memory alloys
S. HASHEMI,H. AHMADIAN,S. MOHAMMADI()
High Performance Computing Laboratory (HPC Lab), School of Civil Engineering, University of Tehran, Tehran 1417613131, Iran
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Abstract

Thermo-mechanical coupling in shape memory alloys is a very complicated phenomenon. The heat generation/absorption during forward/reverse transformation can lead to temperature-dependent variation of its mechanical behavior in the forms of superelasticity and shape memory effect. However, unlike the usual assumption, slow loading rate cannot guarantee an isothermal process. A two-dimensional thermo-mechanically coupled algorithm is proposed based on the original model of Lagoudas to efficiently model both superelasticity and shape memory effects and the influence of various strain rates, aspect ratios and boundary conditions. To implement the coupled model into a finite element code, a numerical staggered algorithm is employed. A number of simulations are performed to verify the proposed approach with available experimental and numerical data and to assess its efficiency in solving complex SMA problems.
Keywords shape memory alloy      thermo-mechanical coupling      superplasticity      shape memory effect     
Corresponding Author(s): S. MOHAMMADI   
Online First Date: 19 November 2015    Issue Date: 26 November 2015
 Cite this article:   
S. HASHEMI,H. AHMADIAN,S. MOHAMMADI. An extended thermo-mechanically coupled algorithm for simulation of superelasticity and shape memory effect in shape memory alloys[J]. Front. Struct. Civ. Eng., 2015, 9(4): 466-477.
 URL:  
https://academic.hep.com.cn/fsce/EN/10.1007/s11709-015-0300-3
https://academic.hep.com.cn/fsce/EN/Y2015/V9/I4/466
material parameters value material parameters value
EA 16.5 × 109 Pa a A = a M 22 × 10 − 6   1 / K
EM 16.5 × 109 Pa ρ C A = ρ C M 3.2 × 10 5   J / ( m 3 K )
v A = v M 0.3 s0 − 0.375 × 10 6   J / ( m 3 K )
TMs −30°C Hmax 0.3
TMf −31°C k 18   W / ( m K )
TAs 4°C hair 50   W / ( m K )
TAf 5°C hwater 300   W / ( m K )
Tab.1  SMA material properties
Fig.1  (a) Geometry and boundary conditions; (b) finite element mesh
Fig.2  Comparison of the experimental and numerical simulation for the strain rate of (a) 1.1 × 10−4 s−1, (b) 1.1 × 10−2 s−1; (c) 1.1 × 10−1 s−1
Fig.3  Numerical stress-strain curves in air and water for different strain rates of (a) 1.1 × 10−1 s−1, (b) 3.3 × 10−2 s−1, (c) 2 × 10−2 s−1, (d) 1.1 × 10−2 s−1, (e) 1.1 × 10−4 s−1
Fig.4  Stress-strain curves for different strain rates
Fig.5  Temperature variations vs. time steps for different strain rates
material parameters value material parameters value
EA 55 × 109 Pa v A = v M 0.33
EM 46 × 109 Pa a A = a M 22 × 10 − 6   1 / K
TMs −28°C ρ C A = ρ C M 4.81 × 10 5   J / ( m 3 K )
TMf −43°C s0 0   J / ( m 3 K )
TAs −3°C Hmax 0.056
TAf 7°C k 18   W / ( m K )
Tab.2  SMA material properties [8]
Fig.6  SME and superelasticity paths
Fig.7  Global stress-strain responses of three SMA devices
material parameters value material parameters value
EA 47 × 109 Pa v A = v M 0.3
EM 33 × 109 Pa a A = a M 22 × 10 − 6   1 / K
TMs −52°C ρ C A = ρ C M 6.5 × 10 5   J / ( m 3 K )
TMf −60°C s0 0   J / ( m 3 K )
TAs −30°C Hmax 0.075
TAf −20°C k 18   W / ( m K )
Tab.3  SMA material properties
Fig.8  Geometry and boundary conditions
Fig.9  Force versus displacement of midpoint of the beam in comparison with the experimental and numerical data [12].
Fig.10  Phase transformation (martensite volume fraction distribution) during the forward transformation (The lateral deformation is exaggerated by 100%).
Fig.11  (a) Geometry and boundary; (b) finite element mesh for a quarter of strip
Fig.12  
Fig.13  Temperature contours during forward transformation based on k
Fig.14  Stress (σyy) contours during forward transformation based on MPa
1 Shaw  J, Kyriakides  S. Thermomechanical aspects of NiTi. Journal of the Mechanics and Physics of Solids, 1995, 43(8): 1243–1281
2 Chang  B. Shaw, Iadicola M. Thermodynamics of shape memory alloy wire: Modeling, experiments, and application. Continuum Mechanics and Thermodynamics, 2006, 18(1−2): 83–118
3 Morin  C, Moumni  Z. Thermomechanical coupling in shape memory alloys under cyclic loadings: Experimental analysis and constitutive modeling. International Journal of Plasticity, 2011, 27: 1959–1980
4 Desroches  R, McCormick  J, Delemont  M. Cyclic properties of superelastic shape memory alloy wires and bars. Journal of Structural Engineering, 2004, 130(1): 38–46
5 Mirzaeifar  R, Desroches  R, Yavari  A. Analysis of the rate-dependent coupled thermo-mechanical response of shape memory alloy bars and wires in tension. Continuum Mechanics and Thermodynamics, 2011, 23: 363–385
6 Lagoudas  D C, Bo  Z, Qidwai  M A. A unified thermodynamic constitutive model for SMA and finite element analysis of active metal matrix composites. Mechanics of Composite Materials and Structures, 1996, 3: 153–179
7 Qidwai  M A, Lagoudas  D C. Numerical implementation of shape memory alloy thermomechanical constitutive model using return mapping algorithm. International Journal for Numerical Methods in Engineering, 2000, 47: 1123–1168
8 Lagoudas  D C. Shape Memory Alloys, Modeling and Engineering Applications. Springer, 2008
9 He  Y J, Sun  Q P. On non-monotonic rate dependence of stress hysteresis of superelastic shape memory alloy bars. International Journal of Solids and Structures, 2011, 48: 1688–1695
10 Zhange  X H, Feng  P, He  Y J, Yu  T X, Sun  Q P. Experimental study on rate dependence of macroscopic domain and stress hysteresis in NiTi shape memory alloy strips. International Journal of Mechanical Sciences, 2010, 52: 1660–1670
11 Morin  C, Moumni  Z, Zaki  W. A constitutive model for shape memory alloys accounting for thermomechanical coupling. International Journal of Plasticity, 2011, 27: 748–767
12 Auricchio  F, Taylor  R L, Lubliner  J. Shape-memory alloys: macromodelling and numerical simulations of the superelastic behavior. Computer Methods in Applied Mechanics and Engineering, 1997, 146(3−4): 281–312
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