The Research of the Difference between Small-Strain and Large-Strain Formulations for Shape Memory Alloys

2012 ◽  
Vol 229-231 ◽  
pp. 3-9
Author(s):  
Jie Yao ◽  
Young Hong Zhu ◽  
Yun Zhang Wu
Keyword(s):  
Phase Transformation ◽  
Constitutive Model ◽  
Shape Memory ◽  
Uniaxial Tension ◽  
Driving Force ◽  
Large Strain ◽  
Small Deformation ◽  
Small Strain ◽  
Proportional Loading ◽  
The Difference

Based on thermodynamics and phase transformation driving force, we apply a SMA constitutive model to analyze the large and small deformation of SMA materials. Simulations under different loading, uniaxial tension and shear conditions, illustrate the characteristics of the model in large strain deformation and small strain deformation. The results indicate that the difference between the two methods is small under the uniaxial tension case, while the large deformation and the small deformation results are very different under shear deformation case. It lays a foundation for the further studies of the constitutive model of SMA, especially in the multiaxial non-proportional loading aspects.

The Further Exploration of Applying Small-Strain and Large-Strain Formulations to SMA

2012 ◽  
Vol 529 ◽  
pp. 228-235
Author(s):  
Jie Yao ◽  
Yong Hong Zhu
Keyword(s):  
Phase Transformation ◽  
Constitutive Model ◽  
Uniaxial Tension ◽  
Driving Force ◽  
Research Team ◽  
Large Strain ◽  
Small Deformation ◽  
Small Strain ◽  
Proportional Loading ◽  
The Difference

Recently, our research team has been considering to applying shape memory alloys (SMA) constitutive model to analyze the large and small deformation about the SMA materials because of the thermo-dynamics and phase transformation driving force. Accordingly, our team use simulations method to illustrate the characteristics of the model in large strain deformation and small strain deformation when different loading, uniaxial tension, and shear conditions involve in the situations. Furthermore, the simulation result unveils that the difference is nuance concerning the two method based on the uniaxial tension case, while the large deformation and the small deformation results have huge difference based on shear deformation case. This research gives the way to the further research about the constitutive model of SMA, especially in the multitiaxial non-proportional loading aspects.

Influence of Small-Strain and Large-Strain Methods on Mechanical Behaviors in Shape Memory Alloys

2011 ◽  
Vol 328-330 ◽  
pp. 1556-1559
Author(s):  
Yun Zhang Wu ◽  
Yu Ping Zhu ◽  
Guan Suo Dui
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Shear Deformation ◽  
Uniaxial Tension ◽  
Phenomenological Model ◽  
Large Strain ◽  
Small Strain ◽  
Thermodynamic Theory ◽  
Mechanical Behaviors ◽  
The Difference

Based on thermodynamic theory, a phenomenological model of shape memory alloy is provided. Simulations under different loading illustrate the influence of large-strain deformation and small-strain deformation on the characteristics of the model. The results indicate that the difference between the two methods is small under uniaxial tension case, while the influence is very large under shear deformation case.

scholarly journals One-Dimensional Constitutive Model of Shape Memory Alloy with an Empirical Kinetics Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Lei Li ◽  
Qingbin Li ◽  
Fan Zhang
Keyword(s):  
Plastic Deformation ◽  
Phase Transformation ◽  
Shape Memory Alloy ◽  
Constitutive Model ◽  
Shape Memory ◽  
Uniaxial Tension ◽  
Experimental Results ◽  
Kinetics Equation ◽  
One Dimensional ◽  
Niti Sma

Characteristics of NiTi shape memory alloy (SMA) and its constitutive model with an empirical kinetics equation were investigated in this paper. Firstly, the transformation characters of the NiTi SMA were obtained through a differential scanning calorimetry (DSC) analysis technology, and the properties during incomplete and discontinuous transformation process and the effects of plastic deformation on the transformation were studied. The uniaxial tension, SME, and constrained recovery process of NiTi SMA were examined through an improved 10KN universal material testing machine. Experimental results indicated that the phase transformation characters and the mechanical properties could be affected by the loading process considerably, and the plastic deformation should be taken into account. To simulate the characteristics of NiTi SMA more effectively, a one-dimensional constitutive model derived from the internal variable approach with the consideration of the plastic deformation was constructed based on the DSC and the uniaxial tension experimental results, and a new simple empirical kinetics equation was presented, with the transformation temperature parameters redefined according to the DSC experiment evidence. Comparison between the numerical and experimental results indicated that this constitutive model could simulate the phase transformation characters, the uniaxial tension, SME, and the constrained recovery behavior of NiTi SMA well.

Modeling of Internal Damage Evolution During Actuation Fatigue in Shape Memory Alloys

2018 ◽  
Author(s):  
Francis R. Phillips ◽  
Daniel Martin ◽  
Dimitris C. Lagoudas ◽  
Robert W. Wheeler
Keyword(s):  
Phase Transformation ◽  
Constitutive Model ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Damage Evolution ◽  
Low Cycle Fatigue ◽  
Cycle Fatigue ◽  
Internal Damage ◽  
Functional Fatigue ◽  
Non Linear

Shape memory alloys (SMAs) are unique materials capable of undergoing a thermo-mechanically induced, reversible, crystallographic phase transformation. As SMAs are utilized across a variety of applications, it is necessary to understand the internal changes that occur throughout the lifetime of SMA components. One of the key limitations to the lifetime of a SMA component is the response of SMAs to fatigue. SMAs are subject to two kinds of fatigue, namely structural fatigue due to cyclic mechanical loading which is similar to high cycle fatigue, and functional fatigue due to cyclic phase transformation which typical is limited to the low cycle fatigue regime. In cases where functional fatigue is due to thermally induced phase transformation in contrast to being mechanically induced, this form of fatigue can be further defined as actuation fatigue. Utilizing X-ray computed microtomography, it is shown that during actuation fatigue, internal damage such as cracks or voids, evolves in a non-linear manner. A function is generated to capture this non-linear internal damage evolution and introduced into a SMA constitutive model. Finally, it is shown how the modified SMA constitutive model responds and the ability of the model to predict actuation fatigue lifetime is demonstrated.

A constitutive model for Fe-based shape memory alloy considering martensitic transformation and plastic sliding coupling: Application to a finite element structural analysis

2012 ◽  
Vol 23 (10) ◽  
pp. 1143-1160 ◽  
Author(s):  
Walid Khalil ◽  
Alain Mikolajczak ◽  
Céline Bouby ◽  
Tarak Ben Zineb
Keyword(s):  
Finite Element ◽  
Phase Transformation ◽  
Structural Analysis ◽  
Shape Memory Alloy ◽  
Constitutive Model ◽  
Shape Memory ◽  
Internal Variables ◽  
Thermomechanical Loading ◽  
Proposed Model ◽  
Numerical Tool

In this article, we propose a finite element numerical tool adapted to a Fe-based shape memory alloy structural analysis, based on a developed constitutive model that describes the effect of phase transformation, plastic sliding, and their interactions on the thermomechanical behavior. This model was derived from an assumed expression of the Gibbs free energy taking into account nonlinear interaction quantities related to inter- and intragranular incompatibilities as well as mechanical and chemical quantities. Two scalar internal variables were considered to describe the phase transformation and plastic sliding effects. The hysteretic and specific behavior patterns of Fe-based shape memory alloy during reverse transformation were studied by assuming a dissipation expression. The proposed model effectively describes the complex thermomechanical loading paths. The numerical tool derived from the implicit resolution of the nonlinear partial derivative constitutive equations was implemented into the Abaqus® finite element code via the User MATerial (UMAT) subroutine. After tests to verify the model for homogeneous and heterogeneous thermomechanical loadings, an example of Fe-based shape memory alloy application was studied, which corresponds to a tightening system made up of fishplates for crane rails. The results we obtained were compared to experimental ones.

A large deformation framework for shape memory polymers: Constitutive modeling and finite element implementation

2012 ◽  
Vol 24 (1) ◽  
pp. 21-32 ◽  
Author(s):  
Mostafa Baghani ◽  
Reza Naghdabadi ◽  
Jamal Arghavani
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Shape Memory ◽  
Finite Deformation ◽  
Deformation Gradient ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Shape Memory Polymers ◽  
Small Strain ◽  
Internal Variables

Shape memory polymers commonly experience both finite deformations and arbitrary thermomechanical loading conditions in engineering applications. This motivates the development of three-dimensional constitutive models within the finite deformation regime. In the present study, based on the principles of continuum thermodynamics with internal variables, a three-dimensional finite deformation phenomenological constitutive model is proposed taking its basis from the recent model in the small strain regime proposed by Baghani et al. (2012). In the constitutive model derivation, a multiplicative decomposition of the deformation gradient into elastic and inelastic stored parts (in each phase) is adopted. Moreover, employing the mixture rule, the Green–Lagrange strain tensor is related to the rubbery and glassy parts. In the constitutive model, the evolution laws for internal variables are derived during both cooling and heating thermomechanical loadings. Furthermore, we present the time-discrete form of the proposed constitutive model in the implicit form. Using the finite element method, we solve several boundary value problems, that is, tension and compression of bars and a three-dimensional beam made of shape memory polymers, and investigate the model capabilities as well as its numerical counterpart. The model is validated by comparing the predicted results with experimental data reported in the literature that shows a good agreement.

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