Numerical Investigation of Preload Process of Bolted Joint with Superelastic Shape Memory Alloy
Abstract
:1. Introduction
2. Constitutive Modeling for NiTi SMA under Cyclic Loading
2.1. Constitutive Equation and Internal Variables
- (i)
- Transformation to martensite phase:If and :
- (ii)
- Transformation to austenite phase:If and :
2.2. Evolution Law of Parameters Governed by Accumulated Martensite Volume Fraction
- (i)
- Evolution equation for residual martensite volume fraction:
- (ii)
- Evolution law of transformation stress
3. FE Modeling for One-Dimensional Bar Element of SMA Ratcheting Behavior
3.1. Numerical Integration Algorithm
3.2. Solving for Incremental Stiffness Matrix
Algorithm 1: Iteration procedure |
Begin Step 1 Initialize variables, assumed at the beginning Step 2 Given and , calculate , , and if , goto Step 5 else if and goto Step 3 else goto Step 5 endif Step 3 Calculate if obtaining , and calculating , , , goto Step 4 endif Step 4 Calculate stiffness matrix and force increment , goto Step 5 Step 5 Calculate , and if , goto Step8 elseif and goto Step 6 else goto Step 8 endif Step 6 Calculate if obtaining , and calculating , , endif Step 7 Calculate stiffness matrix and force increment , goto Step 8 Step 8 Updating status variables End |
4. Numerical Simulation and Model Verification
5. Numerical Examples for the Analyses of Preload Force of SMA Bolted Joint
5.1. FE Modeling for the Preload Process of SMA Bolted Joint
5.2. Simulations and Results
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Material Parameters |
---|
= 48 GPa; = 35 GPa; = 0.3; =0.3; = 0.063; = 295 K; = 285 MPa; = 458 MPa; = 345 MPa; = 164 MPa; = 225 MPa; = 458 MPa; = 310 MPa; = 125 MPa; = 0.05; = 0.05; = 0.05; = 0.05; = 3; = 0.84; = 0.5. |
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Jiang, X.; Wang, Y.; Pan, F.; Jing, Z.; Huang, J.; Li, B. Numerical Investigation of Preload Process of Bolted Joint with Superelastic Shape Memory Alloy. Metals 2018, 8, 730. https://doi.org/10.3390/met8090730
Jiang X, Wang Y, Pan F, Jing Z, Huang J, Li B. Numerical Investigation of Preload Process of Bolted Joint with Superelastic Shape Memory Alloy. Metals. 2018; 8(9):730. https://doi.org/10.3390/met8090730
Chicago/Turabian StyleJiang, Xiangjun, Yongkun Wang, Fengqun Pan, Ze Jing, Jin Huang, and Baotong Li. 2018. "Numerical Investigation of Preload Process of Bolted Joint with Superelastic Shape Memory Alloy" Metals 8, no. 9: 730. https://doi.org/10.3390/met8090730