scholarly journals Asymptotic Self-Similarity of Minimizers and Local Bounds in a Model of Shape-Memory Alloys

2021 ◽  
Author(s):  
Sergio Conti ◽  
Johannes Diermeier ◽  
Melanie Koser ◽  
Barbara Zwicknagl
Keyword(s):  
Shape Memory Alloys ◽  
Shape Memory ◽  
Volume Fraction ◽  
Self Similarity ◽  
Various Boundary Conditions ◽  
Energy Bounds ◽  
Small Volume Fraction ◽  
The One ◽  
Arbitrary Volume ◽  
Martensitic Variants

AbstractWe prove that microstructures in shape-memory alloys have a self-similar refinement pattern close to austenite-martensite interfaces, working within the scalar Kohn-Müller model. The latter is based on nonlinear elasticity and includes a singular perturbation representing the energy of the interfaces between martensitic variants. Our results include the case of low-hysteresis materials in which one variant has a small volume fraction. Precisely, we prove asymptotic self-similarity in the sense of strong convergence of blow-ups around points at the austenite-martensite interface. Key ingredients in the proof are pointwise estimates and local energy bounds. This generalizes previous results by one of us to various boundary conditions, arbitrary rectangular domains, and arbitrary volume fractions of the martensitic variants, including the regime in which the energy scales as $\varepsilon ^{2/3}$ ε 2 / 3 as well as the one where the energy scales as $\varepsilon ^{1/2}$ ε 1 / 2 .

Martensitic Transformation of High-Entropy and Medium-Entropy Shape Memory Alloys

2021 ◽  
Vol 1016 ◽  
pp. 1802-1810
Author(s):  
Hiromichi Matsuda ◽  
Masayuki Shimojo ◽  
Hideyuki Murakami ◽  
Yoko Yamabe-Mitarai
Keyword(s):  
Solid Solution ◽  
High Temperature ◽  
Martensitic Transformation ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Transformation Temperature ◽  
Solid Solution Hardening ◽  
Solution Hardening ◽  
High Entropy ◽  
The One

As new generation of high-temperature shape memory alloys, high-entropy alloys (HEAs) have been attracted for strong solid-solution hardened alloys due to their severe lattice distortion and sluggish diffusion. TiPd is the one potential high-temperature shape memory alloys because of its high martensitic transformation temperature above 500 °C. As constituent elements, Zr expected solid-solution hardening, Pt expected increase of transformation temperature, Au expected keeping transformation temperature, and Co expected not to form harmful phase. By changing the alloy composition slightly, two HEAs and two medium entropy alloys (MEAs) were prepared. Only two MEAs, Ti45Zr5Pd25Pt20Au5, and Ti45Zr5Pd25Pt20Co5 had the martensitic transformation. The perfect recovery was obtained in Ti45Zr5Pd25Pt20Co5 during the repeated thermal cyclic test, training, under 200 MPa. On the other hand, the small irrecoverable strain was remained in Ti45Zr5Pd25Pt20Au5 during the training under 150 MPa because of the small solid-solution hardening effect. It indicates that Ti45Zr5Pd25Pt20Co5 is the one possible HT-SMA working between 342 and 450 °C.

Optimal Control for Shape Memory Alloys of the One-Dimensional Frémond Model

2020 ◽  
Vol 41 (12) ◽  
pp. 1421-1471
Author(s):  
Pierluigi Colli ◽  
M. Hassan Farshbaf-Shaker ◽  
Ken Shirakawa ◽  
Noriaki Yamazaki
Keyword(s):  
Optimal Control ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
One Dimensional ◽  
The One

Viscoelastic behavior of epoxy resin reinforced with shape-memory-alloy wires

2020 ◽  
pp. 1045389X2097549
Author(s):  
Niloufar Bagheri ◽  
Mahmood M Shokrieh ◽  
Ali Saeedi
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Epoxy Resin ◽  
Volume Fraction ◽  
Niti Alloy ◽  
Micromechanical Model ◽  
Viscoelastic Behavior ◽  
Mechanical Analysis ◽  
Reinforced Polymer ◽  
Small Volume Fraction

The effect of NiTi alloy long wires on the viscoelastic behavior of epoxy resin was investigated by utilizing the dynamic mechanical analysis (DMA) and a novel micromechanical model. The present model is capable of predicting the viscoelastic properties of the shape-memory-alloy (SMA) reinforced polymer as a function of the SMA volume fraction, initial martensite volume fraction, pre-strain level in wires, and the temperature variations. The model was verified by conducting experiments. Good agreement between the theoretical and experimental results was achieved. A parametric study was also performed to investigate the effect of SMA parameters. According to the results, by the addition of a small volume fraction of SMA, the storage modulus of the composite increases significantly, especially at higher temperatures. Moreover, applying a 4% pre-strain caused a 10% increase in the maximum value of the loss factor of the SMA reinforced epoxy in comparison with the 0% pre-strained SMA reinforced epoxy.

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

2019 ◽  
Vol 31 (1) ◽  
pp. 100-116 ◽  
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.

A Constitutive Model for Shape Memory Alloys Involving Transformation, Reorientation and Plasticity

2013 ◽  
Vol 535-536 ◽  
pp. 105-108
Author(s):  
Xiang He Peng ◽  
Min Mei Chen ◽  
Jun Wang
Keyword(s):  
Plastic Deformation ◽  
Constitutive Model ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Shape Memory Effect ◽  
Memory Effect ◽  
Volume Fraction ◽  
Transformation Rule ◽  
Constitutive Behavior ◽  
Plastic Parts

A constitutive model is developed for shape memory alloys (SMAs) based on the concept that an SMA is a mixture composed of austenite and martensite. The deformation of the martensite is separated into elastic, thermal, reorientation and plastic parts, and that of the austenite is separated into elastic, thermal and plastic parts. The volume fraction of each phase is determined with the modified Tanaka’s transformation rule. The typical constitutive behavior of some SMAs, including pseudoelasticity, shape memory effect, plastic deformation as well as its effects, is analyzed.

A Micromechanical Constitutive Model for Porous Shape Memory Alloys

2010 ◽  
Vol 29-32 ◽  
pp. 1855-1861
Author(s):  
Bing Fei Liu ◽  
Guan Suo Dui ◽  
Yu Ping Zhu
Keyword(s):  
Constitutive Model ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Volume Fraction ◽  
Hydrostatic Stress ◽  
General Concept ◽  
Experiment Data ◽  
Critical Stresses ◽  
Elastic Mechanics ◽  
Good Agreement

A micromechanical constitutive model for responding the macroscopic behavior of porous shape memory alloys (SMA) has been proposed in this work. According to the micromechanical method, the stiffness tensor of the porous SMA is obtained. The critical stresses are calculated by elastic mechanics. Based on the general concept of secant moduli method, the effective secant moduli of the porous SMA is given in terms of the secant moduli of dense SMA and the volume fraction of pores. The model takes account of the tensile-compressive asymmetry of SMA materials and the effect of the hydrostatic stress. Only the material parameters of dense SMA are needed for numerical calculation, and can degenerate to dense material. Examples for the uniaxial response of porous SMA materials at constant temperature are then used to illustrate one possible application of the constitutive model. The numerical results have been compared with the experiment data for porous SMA, which show that the modeling results are in good agreement with the experiments.

scholarly journals A low volume-fraction limit for martensic microstructures in shape-memory alloys

PAMM ◽  
2015 ◽  
Vol 15 (1) ◽  
pp. 541-542 ◽  
Author(s):  
Johannes Diermeier
Keyword(s):  
Shape Memory Alloys ◽  
Shape Memory ◽  
Volume Fraction ◽  
Low Volume

Nonlinear Free Vibration of Hybrid Composite Moving Beams Embedded with Shape Memory Alloy Fibers

2016 ◽  
Vol 16 (07) ◽  
pp. 1550032 ◽  
Author(s):  
M. R. Ebrahimi ◽  
A. Moeinfar ◽  
M. Shakeri
Keyword(s):  
Shape Memory Alloy ◽  
Free Vibration ◽  
Shape Memory ◽  
Hybrid Composite ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Parametric Studies ◽  
The One ◽  
Nonlinear Equations Of Motion

The aim of this paper is to investigate the free vibration of hybrid composite moving beams embedded with shape memory alloy (SMA) fibers. The nonlinear equations of motion are derived based on the Euler–Bernoulli beam theory in conjunction with the von Karman type of nonlinearity in strain–displacement relations via the extended Hamilton principle. Also, the recovery stress induced by the SMA fibers is computed by applying the one-dimensional Brinson model and Reuss scheme. Then, an analytical approach in used to solve the nonlinear equation of motion for the simply supported shape memory alloy hybrid composite (SMAHC) moving beams. Based on the analytical solution, several parametric studies are presented to show the effects of various parameters such as volume fraction, pre-strain in the SMA fibers, temperature rise and velocity on the fundamental frequency of the SMAHC moving beams. Due to the lack of similar results in the specialized literature on the subject of interest, this paper is likely to fill a gap in the state of the art of the related research.

An Extended 3D Finite Strain Constitutive Model for Shape Memory Alloys

2021 ◽  
pp. 1-37
Author(s):  
Mengqian Zhang ◽  
Theocharis Baxevanis
Keyword(s):  
Phase Transformation ◽  
Constitutive Model ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Finite Strain ◽  
Volume Fraction ◽  
Internal Variables ◽  
Numerical Implementation ◽  
Deformation Response ◽  
Heat Effects

Abstract A 3D finite-strain constitutive model for shape memory alloys (SMAs) is proposed. The model can efficiently describe reversible phase transformation from austenite to self-accommodated and/or oriented martensite, (re)orientation of martensite variants, minor loops, latent heat effects, and tension–compression asymmetry based on the Eulerian logarithmic strain and the corotational logarithmic objective rate. It further accounts for transformation volume contraction, smooth thermomechanical response, temperature dependence of the critical force required for (re)orientation, temperature and load dependence of the hysteresis width, asymmetry between forward and reverse phase transformation, and is flexible enough to address the deformation response in the concurrent presence of several phases, i.e., when austenite, self-accommodated and oriented martensite co-exist in the microstructure. The ability of the proposed model to describe the aforementioned deformation response characteristics of SMAs under multiaxial, thermomechanical, nonproportional loading relies on the set of three independent internal variables, i.e., the average volume fraction of martensite variants, their preferred direction, and the magnitude of the induced inelastic strain, that further allow for an implicit description of a fourth internal variable, the volume fraction of oriented as opposed to self-accommodated martensite. The calibration of the model and its numerical implementation in an efficient scheme are presented. The model is validated against experimental results associated with complex thermomechanical paths, including tension/compression/torsion experiments and the efficiency of its numerical implementation is verified with simulations of the response of a biomedical superelastic SMA stent and an SMA spring actuator.

Nonlinear dynamics of earthquake-resistant structures using shape memory alloy composites

2020 ◽  
Vol 31 (5) ◽  
pp. 771-787 ◽  
Author(s):  
Lucas L Vignoli ◽  
Marcelo A Savi ◽  
Sami El-Borgi
Keyword(s):  
Energy Dissipation ◽  
Shape Memory Alloy ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Volume Fraction ◽  
Kinematic Hardening ◽  
Frame Structure ◽  
Earthquake Resistant ◽  
Earthquake Resistant Structures ◽  
Residual Strains

Earthquake-resistant structures have been widely investigated in order to produce safe buildings designed to resist seismic activities. The remarkable properties of shape memory alloys, especially pseudoelastic effect, can be exploited in order to promote the essential energy dissipation necessary for earthquake-resistant structures. In this regard, shape memory alloy composite is an idea that can make this application feasible, using shape memory alloy fibers embedded in a matrix. This article investigates the use of shape memory alloy composites in a one-story frame structure subjected to earthquakes. Different kinds of composites are analyzed, comparing the influence of matrix type. Both linear elastic matrix and elastoplastic matrix with isotropic and kinematic hardening are investigated. Results indicate the great energy dissipation capability of shape memory alloy composites. A parametric analysis allows one to conclude that the maximum shape memory alloy volume fraction is not the optimum design condition for none of the cases studied, highlighting the necessity of a proper composite design. Despite the elastoplastic behavior of matrix also dissipates a considerable amount of energy, the associated residual strains are not desirable, showing the advantage of the use of shape memory alloys.

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