One dimensional constitutive model with transformation surfaces for phase transition in shape memory alloys considering the effect of loading history

A three-phase constitutive model for TiNiNb shape memory alloys (SMAs) is proposed based on the fact that TiNiNb SMAs are dynamically composed of austenite, martensite and -Nb phases. In the considered ranges of stress and temperature, the behaviors of austenite, martensite and -Nb phases are assumed to be elastoplastic, and the behavior of an SMA is regarded as the dynamic combination of the individual behavior of each phase. Then a macroscopic constitutive description for TiNiNb SMAs is obtained by the conventional theory of plasticity, the theory of mixture, the theory of inclusion, and the description of phase transition by Tanaka. The method for determination of the material parameters is given. This constitutive model can describe the main characteristics of SMAs, such as ferrcelasticity, pseudoelasticity and shape memory effect.

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An analytical model for crack monitoring of the shape memory alloy intelligent concrete

Journal of Intelligent Material Systems and Structures ◽

10.1177/1045389x19880010 ◽

2019 ◽

Vol 31 (1) ◽

pp. 100-116 ◽

Cited By ~ 1

Author(s):

Bingfei Liu ◽

Qingfei Wang ◽

Kai Yin ◽

Liwen Wang

Keyword(s):

Shape Memory Alloy ◽

Constitutive Model ◽

Shape Memory Alloys ◽

Shape Memory ◽

Three Dimensional ◽

Three Dimensional Model ◽

One Dimensional ◽

Monitoring Model ◽

Crack Monitoring ◽

The One

A theoretical model for the crack monitoring of the shape memory alloy intelligent concrete is presented in this work. The mechanical properties of shape memory alloy materials are first given by the experimental test. The one-dimensional constitutive model of the shape memory alloys is reviewed by degenerating from a three-dimensional model, and the behaviors of the shape memory alloys under different working conditions are then discussed. By combining the electrical resistivity model and the one-dimensional shape memory alloy constitutive model, the crack monitoring model of the shape memory alloy intelligent concrete is given, and the relationships between the crack width of the concrete and the electrical resistance variation of the shape memory alloy materials for different crack monitoring processes of shape memory alloy intelligent concrete are finally presented. The numerical results of the present model are compared with the published experimental data to verify the correctness of the model.

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Constitutive Model of Shape Memory Alloys: One-Dimensional Phase Transformation Model

Advances in Science and Technology ◽

10.4028/www.scientific.net/ast.56.84 ◽

2008 ◽

Vol 56 ◽

pp. 84-91

Author(s):

Tadashige Ikeda

Keyword(s):

Phase Transformation ◽

Constitutive Model ◽

Shape Memory Alloys ◽

Strain Rate ◽

Shape Memory ◽

Strain Rate Effect ◽

Rate Effect ◽

Reverse Transformation ◽

Stress Strain ◽

One Dimensional

A simple yet accurate macroscopic constitutive model of shape memory alloys has been developed. The features of this model are (1) energy-based phase transformation criterion, (2) one-dimensional phase transformation rule based on a micromechanical viewpoint, (3) dissipated energy with a form of a sum of two exponential functions, (4) duplication of the strain rate effect, and (5) adaptability to multi-phase transformation. This model is further improved to be able to express stress-strain relationships such that the reverse transformation starts at a higher stress than the martensitic transformation starts. Here, the ideal reversible transformation temperature is empirically described by a function of the martensite volume fraction. In this paper, an outline of our model is given, where the improvement is introduced. Then, it is shown that the model can quantitatively duplicate the major and minor hysteresis loops, strain rate effect, and asymmetry in tension and compression on the stress-strain relationship. And that it can also duplicate the stress-strain relationships having the reverse transformation start stress higher than the forward one.

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One-Dimensional Macroscopic Constitutive Model for Ratcheting of Superelastic Shape Memory Alloys

Journal of Engineering Mechanics ◽

10.1061/(asce)em.1943-7889.0001575 ◽

2019 ◽

Vol 145 (3) ◽

pp. 04019007

Author(s):

Xiangjun Jiang ◽

Jingli Du ◽

Yesen Fan ◽

Jin Huang ◽

Fengqun Pan

Keyword(s):

Constitutive Model ◽

Shape Memory Alloys ◽

Shape Memory ◽

One Dimensional

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An Improved Two-Dimensional Constitutive Law for Shape Memory Alloys

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.410-411.429 ◽

2009 ◽

Vol 410-411 ◽

pp. 429-437 ◽

Cited By ~ 1

Author(s):

Wei Wang ◽

Shi Yan ◽

Gang Bing Song ◽

Li Jiao

Keyword(s):

Constitutive Model ◽

Shape Memory Alloys ◽

Shape Memory ◽

Constitutive Law ◽

Two Dimensional ◽

Mechanical Behaviors ◽

Dissipation Energy ◽

One Dimensional ◽

Accurate Expression ◽

Improved Model

An improved two-dimensional constitutive model for shape memory alloys (SMAs), which can describe both the shape memory effect (SME) and super elasticity effect (SE) of the SMAs, is developed in the paper based on the previous work of Boyd and Lagoudas, who used the thermodynamics theories of free energy and dissipation energy to derive the constitutive law of the SMAs. The improved model, which will combine the ideas of Brinsion’s one-dimensional constitutive law and the concepts of Boyd and Lagoudas’ two-dimensional one, has a simple but accurate expression. Two examples are used to numerically validate the efficiency of the improved model and the results of the simulations show that the developed constitutive model can qualitatively describe the thermo-mechanical behaviors of two-dimensional SMAs.

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