scholarly journals Galerkin Weighted Residual Method for Axially Functionally Graded Shape Memory Alloy Beams

2019 ◽  
Vol 36 (3) ◽  
pp. 331-345
Author(s):  
Z. T. Kang ◽  
Z. Y. Wang ◽  
B. Zhou ◽  
S. F. Xue
Keyword(s):  
Elastic Modulus ◽  
Martensitic Transformation ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Geometrical Shape ◽  
Weighted Residual Method ◽  
Concentrated Load ◽  
Residual Method

ABSTRACTThis paper focus on the mechanical and martensitic transformation behaviors of axially functionally graded shape memory alloy (AFG SMA) beams. It is taken into consideration that material properties, such as austenitic elastic modulus, martensitic elastic modulus, critical transformation stresses and maximum transformation strain vary continuously along the longitudinal direction. According to the simplified linear SMA constitutive equations and Bernoulli-Euler beam theory, the formulations of stress, strain, martensitic volume fraction and governing equations of the deflection, height and length of transformed layers are derived. Employing the Galerkin’s weighted residual method, the governing differential equation of the deflection is solved. As an example, the bending behaviors of an AFG SMA cantilever beam subjected to an end concentrated load are numerically analyzed using the developed model. Results show that the mechanical and martensitic transformation behaviors of the AFG SMA beam are complex after the martensitic transformation of SMA occurs. The influences of FG parameter on the mechanical behaviors and geometrical shape of transformed regions are obvious, and should be considered in the design and analysis of AFG SMA beams in the related regions.

Damping capacity in pseudo-elastic and ferro-elastic shape memory alloy-reinforced hybrid composite beam

2019 ◽  
Vol 38 (10) ◽  
pp. 467-477 ◽  
Author(s):  
Yahya Bayat ◽  
Hamid EkhteraeiToussi
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Composite Beam ◽  
Volume Fraction ◽  
Hysteresis Loops ◽  
Beam Theory ◽  
Material Model ◽  
Resonance Phenomenon ◽  
Damping Capacity ◽  
Concentrated Load

Reinforcing a composite beam with shape memory alloy wires may have several benefits such as reduction of buckling risks or elimination of unwanted oscillations. In this paper, the vibration damping of a typical shape memory alloy-reinforced composite or hybrid beam is explored. To formulate the thermo-mechanical behavior of embedded shape memory alloy wires, three-dimensional Panico–Brinson model is employed and tailored to one-dimensional model. This material model can simulate pseudo-elastic and ferro-elastic forms of martensite transformations which occurs in cyclic loadings. Besides, unlike the former studies which rely on classical beam theories, the first-order shear deformation beam theory is used to obtain more accurate estimations of shape memory alloy-wire hysteresis loops and their decaying characteristics. In order to explore the effects of a transient concentrated load applied in the middle of a beam, the governing equations are developed and discretized by differential quadrature–integral quadrature combined method. Incremental time marching solution of the problem is accomplished using the Newmark technique. Results are assessed by comparing with available literature. Considering different types of boundary conditions, the influence of pseudo-elastic and ferro-elastic hysteresis loops on the material damping effects, shape memory alloy volume fraction, and resonance phenomenon is studied in detail.

Nonlinear bending analysis of shape memory alloy beam considering both material and geometric nonlinearity effects

2018 ◽  
Vol 30 (6) ◽  
pp. 823-843 ◽  
Author(s):  
Rasool Zamani Alavije ◽  
Mohsen Botshekanan Dehkordi
Keyword(s):  
Finite Element ◽  
Stress Distribution ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Geometric Nonlinearity ◽  
Volume Fraction ◽  
Virtual Work ◽  
Kinetic Equations ◽  
Weighted Residual Method ◽  
Material And Geometric Nonlinearity

This study examined the nonlinear super-elastic bending of shape memory alloy beam considering the material and geometric nonlinearity effects that coupled together. Shape memory alloy properties change instantaneously at different points in the beam, while they are unknown at the same time. In other words, coupling of the governing and kinetic equations of the shape memory alloy beams together results in a more complicated analysis. In this study, the governing equations were extracted through using the Timoshenko beam theory and applying the principle of virtual work. For achieving this goal, von Karman strains were applied to consider large deflections. The Boyd–Lagoudas three-dimensional constitutive model and return mapping algorithm were also used for shape memory alloy modeling. Furthermore, in order to obtain the characteristics of finite element beam, the Galerkin weighted-residual method was used by developing the iterative nonlinear finite element model. Considering the different supporting conditions and forces for the shape memory alloy beam, this study examined their effects on the distribution of martensitic volume fraction, stress distribution, and changes in the location of the neutral axis. The obtained results revealed that as loading increases, the magnitude of martensitic volume fraction and the level of hysteresis increase, which in turn would result in reduction of the modulus of elasticity and the strength of the material and consequently increases the deflection of shape memory alloy beam. The findings suggested the necessity of nonlinear strain field in this modeling by which the stress distribution and volume fraction become asymmetric along the beam thickness. The results were presented in the forms of loading and unloading diagrams for different support and force conditions, and the martensitic volume fraction along the length and through the thickness of the shape memory alloy beam were also shown. To validate the proposed formulation, the results were compared with other experimental findings in this regard suggesting that there is an acceptable and satisfying level of agreement between them.

On size-dependent bending behaviors of shape memory alloy microbeams via nonlocal strain gradient theory

2021 ◽  
pp. 1045389X2098699
Author(s):  
Bo Zhou ◽  
Zetian Kang ◽  
Xiao Ma ◽  
Shifeng Xue
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Size Dependent ◽  
Material Length Scale Parameter ◽  
Material Length Scale ◽  
Material Length ◽  
Nonlocal Strain Gradient

This paper focuses on the size-dependent behaviors of functionally graded shape memory alloy (FG-SMA) microbeams based on the Bernoulli-Euler beam theory. It is taken into consideration that material properties, such as austenitic elastic modulus, martensitic elastic modulus and critical transformation stresses vary continuously along the longitudinal direction. According to the simplified linear shape memory alloy (SMA) constitutive equations and nonlocal strain gradient theory, the mechanical model was established via the principle of virtual work. Employing the Galerkin method, the governing differential equations were numerically solved. The functionally graded effect, nonlocal effect and size effect of the mechanical behaviors of the FG-SMA microbeam were numerically simulated and discussed. Results indicate that the mechanical behaviors of FG-SMA microbeams are distinctly size-dependent only when the ratio of material length scale parameter to the microbeam height is small enough. Both the increments of material nonlocal parameter and ratio of material length-scale parameter to the microbeam height all make the FG-SMA microbeam become softer. However, the stiffness increases with the increment of FG parameter. The FG parameter plays an important role in controlling the transverse deformation of the FG-SMA microbeam. This work can provide a theoretical basis for the design and application of FG-SMA microstructures.

scholarly journals Experimental and Numerical Analysis of the Mechanical Properties of a Pretreated Shape Memory Alloy Wire in a Self-Centering Steel Brace

Processes ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 80
Author(s):  
Bo Zhang ◽  
Sizhi Zeng ◽  
Fenghua Tang ◽  
Shujun Hu ◽  
Qiang Zhou ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Elastic Modulus ◽  
Energy Dissipation ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Loading Rate ◽  
Effective Elastic Modulus ◽  
Maximum Energy ◽  
Numerical Results ◽  
Energy Dissipation Capacity

As a stimulus-sensitive material, the difference in composition, fabrication process, and influencing factors will have a great effect on the mechanical properties of a superelastic Ni-Ti shape memory alloy (SMA) wire, so the seismic performance of the self-centering steel brace with SMA wires may not be accurately obtained. In this paper, the cyclic tensile tests of a kind of SMA wire with a 1 mm diameter and special element composition were tested under multi-working conditions, which were pretreated by first tensioning to the 0.06 strain amplitude for 40 cycles, so the mechanical properties of the pretreated SMA wires can be simulated in detail. The accuracy of the numerical results with the improved model of Graesser’s theory was verified by a comparison to the experimental results. The experimental results show that the number of cycles has no significant effect on the mechanical properties of SMA wires after a certain number of cyclic tensile training. With the loading rate increasing, the pinch effect of the hysteresis curves will be enlarged, while the effective elastic modulus and slope of the transformation stresses in the process of loading and unloading are also increased, and the maximum energy dissipation capacity of the SMA wires appears at a loading rate of 0.675 mm/s. Moreover, with the initial strain increasing, the slope of the transformation stresses in the process of loading is increased, while the effective elastic modulus and slope of the transformation stresses in the process of unloading are decreased, and the maximum energy dissipation capacity appears at the initial strain of 0.0075. In addition, a good agreement between the test and numerical results is obtained by comparing with the hysteresis curves and energy dissipation values, so the numerical model is useful to predict the stress–strain relations at different stages. The test and numerical results will also provide a basis for the design of corresponding self-centering steel dampers.

Micro and Macromechanical Study of Stress-Induced Martensitic Transformation in a Cu-Al-Be Polycrystalline Shape Memory Alloy

2006 ◽  
Vol 509 ◽  
pp. 87-92 ◽  
Author(s):  
F.M. Sánchez ◽  
G. Pulos
Keyword(s):  
Martensitic Transformation ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Vector Fields ◽  
Displacement Vector ◽  
Optical Microscope ◽  
Image Sequences ◽  
Tension Test ◽  
Loading Device ◽  
Stress States

An experimental investigation of the micro and macromechanical stress-induced martensitic transformation in a Cu-Al-Be polycrystalline shape memory alloy is undertaken using a uniaxial tension test. Digital images are acquired at different stress states. The image sequences are analyzed to estimate the optical flow to get displacement vector fields. The experiments are carried out on a miniature hydraulic loading device mounted under an optical microscope. The stress-strain curves and associated images show stress-induced martensitic transformation in specific grains. Displacement vector fields for the polycrystalline shape memory alloy are obtained. They are inhomogeneous due to the martensitic transformation and inter-granular interactions.

scholarly journals Effect of Nd Addition on the Microstructure and Martensitic Transformation of Ni-Ti Shape Memory Alloys

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
M. Dovchinvanchig ◽  
C. W. Zhao ◽  
S. L. Zhao ◽  
X. K. Meng ◽  
Y. J. Jin ◽  
...  
Keyword(s):  
Rare Earth ◽  
Martensitic Transformation ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Earth Element ◽  
Transformation Behavior ◽  
Nd Addition ◽  
One Step ◽  
Niti Matrix ◽  
Start Temperature

The effect of rare earth element Nd addition on the microstructure and martensitic transformation behavior of Ni50Ti50−xNdx(x=0, 1, 3, 7, 20) shape memory alloy was investigated experimentally. The results showed that the microstructure of Ni-Ti-Nd ternary alloy consists of the NiNd phase and the NiTi matrix. One-step martensitic transformation was observed in all alloys. The martensitic transformation start temperatureMsincreased gradually with increasing Nd content for Ni-Ti-Nd alloys.

Effect of Electroplastic Deformation on Martensitic Transformation in Coarse Grained and Ultrafine Grained Ni-Ti Shape Memory Alloy

2008 ◽  
Vol 584-586 ◽  
pp. 127-132 ◽  
Author(s):  
Anastasia E. Sergeeva ◽  
Daria Setman ◽  
Michael Zehetbauer ◽  
Sergey Prokoshkin ◽  
Vladimir V. Stolyarov
Keyword(s):  
Differential Scanning Calorimetry ◽  
Martensitic Transformation ◽  
Shape Memory Alloy ◽  
Cold Rolling ◽  
Shape Memory ◽  
Coarse Grained ◽  
Scanning Calorimetry ◽  
Structure Relaxation ◽  
Differential Scanning Calorimetry Method ◽  
Ultrafine Grained

The aim of this paper is the investigation of electroplastic deformation (EPD) and subsequent annealing influence on martensitic transformation in the shape memory Ni50.7Ti49.3 alloy. Using differential scanning calorimetry method it was shown that EPD at the low strain stimulates structure relaxation and recovers martensitic transformation in cooling, which is usually suppressed by cold rolling.

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