The shape memory alloy controlled by the sun’s radiation effect

Abstract

The Shape Memory Alloys (SMAs) are smart materials, which have many thermo-mechanical characteristics that can back to their initial strain when they exposed to a definite temperature. They are materials that change their mechanical proprieties in response to stress or heating such as shape, displacement and frequency, which are useful for actuators in many domains such as industry, robotics and engineering. In order to realize thermo-mechanical investigation about Shape Memory Alloy Actuator (SMAA) controlled by the radiation effect, which is useful for renewable energy applications. In this way, numerical simulation simulates shape memory alloy at different temperatures, to show the ability of this materials in various conditions and the parameters are obtained by previous experimental measurements. The first results are pleasing.

Keywords

Shape memory alloys SMA actuator shape memory alloy actuator smart materials radiation effect

1. Introduction

In the last years,the SMAs have been used in many fields such as robotic, engineering, medicine and aeronautic. The special character of this materials advises in two principal macroscopic properties are the Super Elasticity Effect (SE) and the shape memory effect (SME) [1].

The shape memory alloys can be existed in two crystal configurations: first one stable at higher temperatures called Austenite phase, the second one stable at lower temperature called Martensite phase [2].

Figure 1.

Hysteresis the martensitic transformation.

We set four important temperatures in Fig. 1: (M ${}_{\text{s}}$ ) martensitic start temperature, the alloy begins converting from Austenite to Martensite; (M ${}_{\text{f}}$ ) martensitic finish temperature, the alloy is entirely martensitic; (A ${}_{\text{s}}$ ) austenite start, the alloy begins from martensitic to austenite; and (A ${}_{\text{f}}$ ) austenite finish, the alloy is entirely Austenite [2, 3].

The shape memory alloy has been used as a sensor due to its sensibility to temperature and stress, where also can be used as actuator thanks to its ability to recover a large amount of strain against significant stress. This actuator can be made as a spring, ribbon shape or wire. It is able to produce extreme forces from the viewpoint of volume to force ratio [4]. When two-way actuators designed to operate to remember two shapes: one at Martensite and the other at the austenite over many cycles [4] as shown in Fig. 2.

Figure 2.

Two-way shape memory effect (a) austenite phase (b) intermediary phase (c) Martensite phase.

The SMA actuation devices can activate by multiple ways such as exposure to direct temperature, by means of electrical resistance heating and radiation heat. On the one hand the electrical heat and direct temperature are the most used methods in applications, on the other hand the radiation effect is never used even though can be used in many renewable energy applications [3].

In this investigation, we will explore the shape memory alloy for the purpose to create an actuator (tracker) performed the dual functions of sensing and actuating we will study the shape memory alloy which may be useful for thermo-mechanical actuators. For this purpose, we propose a numerical investigation aims to study this material under a solar radiation heatto be able performing the function of trackers and integrate this actuator with the collector to develop a new robotic solar system. The simulations of strain induced by heat under constant compressive stress presented and the parameters had obtained by previous measurements.

2. Modelling

In this section, we propose a numerical model for Shape Memory Alloy aims to study this material under a solar radiation heat, and design ashape memory alloy actuator.

2.1 SMA model

This model is described the mechanism of field-induced large strain of shape memory alloys and their proprieties especially the shape memory effect, the kinetic law that describes the transformation of phase has considered for the phenomenological model. For the purposes of this study, a design objective pursued to optimize the initial configurations and the dimension of the SMA actuator. The fundamental assumptions of this model are as follows [7]:

•
The formalism of small deformations is used
•
The elastic moduli are assumed to be equal for austenite and martensite
•
The transformation deformation is assumed deviatoric
•
The effects of thermal expansion are neglected
•
In the frame of mechanical behavior of Shape Memory Alloys traditionally with the total strain, $\varepsilon_{T}$ , representing the total deformation of the material, a general assumption of additive strain decomposition adopted in the form:

In the frame of macroscopic of mechanical behavior of Shape Memory Alloys (SMA) traditionally with the total strain, $\varepsilon_{T}$ , representing the total deformation of the material, a general assumption of additive strain decomposition adopted in the form [5]:

$\displaystyle\varepsilon_{\textit{tot}}=\varepsilon_{e}+\varepsilon_{Th}+% \varepsilon_{Tr}$ (1)

The elastic strain:

$\displaystyle\varepsilon_{e}=\sigma/E$ (2)

The transformation strain:

$\displaystyle\varepsilon_{tr}=\left(\varkappa-1/2\right)\cdot\gamma_{tw}$ (3)

The transformation strain:

$\displaystyle\varepsilon_{T}=\alpha\cdot\left(\Delta T\right)$ (4)

Where $\alpha$ Thermal Expansion Coefficient, the volume fraction, $\gamma_{tw}$ maximum detwinning strain, $\sigma$ denotes the applied stress $\Delta T$ temperature difference and $E$ denotes the Young modulus, which:

$\displaystyle E=E_{a}+\varkappa(E_{m}-E_{a})$ (5)

The SMA characterize by the martensite transformation, which can initiate with applying stress or varying the temperature, that allocate the fraction of martensite into temperature induced martensite $\varkappa_{T}$ , include of a self-accommodated of martensitic variants and stress-induced $\varkappa_{S}$ , represents the amount of material treatment in the variant of martensite corresponding to the loading direction [5].

Where:

$\displaystyle\varkappa=\varkappa_{T}+\varkappa_{\sigma}$ (6)

The constitutive equation relates the variables of strain $\varepsilon$ , volume fraction of stress induced martensite, and temperature $T$ is:

$\displaystyle\sigma-\sigma_{0}=E\left(\varepsilon-\varepsilon_{{0}}\right)+% \Omega\left(\varkappa-\varkappa_{0}\right)+\theta(T-T_{0})$ (7)

The 0 means the initial condition of the SMA [6], $\theta$ thermal elastic coefficient $\Omega$ is the transformation coefficient as shown in Eq. (2):

$\displaystyle\Omega=-\varepsilon_{L}\cdot E$ (8)

$\varepsilon_{L}$ is the maximum transformation strain of shape memory material and is constant at temperatures under austenite finish temperature $A_{f}$ [8], the transformation from the martensite to austenite can describe by:

$\displaystyle\textit{if}\;T>Ms\textit{ and }\sigma-Cm\left(T-Ms\right)<\sigma<% \sigma-Cm\left(T-Ms\right)$ (9) $\displaystyle x=\frac{1-\varkappa_{0}}{2}\textit{cos}\left\{\frac{\pi}{\sigma-% \sigma}\times\left[\sigma-\sigma_{f}^{cr}-Cm\cdot\left(T-Ms\right)\right]% \right\}+\frac{1+\varkappa_{0}}{2}$ (10)

While the transformation from austenite to martensite describe by:

$\displaystyle\textit{if}\;T>As\textit{ and }C_{A}\left(T-A_{f}\right)<\sigma<C% _{A}\left(T-As\right)$ (11) $\displaystyle x=\frac{\varkappa_{0}}{2}cos\left\{{a}_{A}\times\left[T-As-\frac% {\sigma}{C_{A}}\right]\right\}+1$ (12) $\displaystyle a_{A}=\frac{\pi}{Af-As}$ (13) $\displaystyle a_{A}=\frac{\pi}{Ms-Mf}$ (14)

$C m$ and $C_{A}$ the material properties that describe the relationship of temperature and the critical stress to induce transformation.

The shape memory effect is utilized when SMAs are used as actuators. The helical shape is used, due to the number of parameters that can be arranged, its ease of fabrication and its compactness.
2.2 SMAA model

In this section, the design of the shape memory alloy actuator is a wirehas been designed as springdue to its ability storing energy. In this way, the spring can store energywhen it is compressed after heating and lost energy when it is stretched after cooling.

The stress in the wire and the force on the spring can be connected [6]:

$\displaystyle\sigma=\frac{8FC}{\pi d^{2}}R$ (15)

Where $F$ the external force,and the spring index $C=Ds/d_{w}$ . With $d_{w}$ , the wire diameter and $D s$ , the spring diameter Where $R$ is the shear-stress correction,

$\displaystyle R=\frac{2C+1}{2C}$ (16)

The deflection of the spring, assuming the material to be elastic is given by:

$\displaystyle\delta=\frac{8FD^{3}N}{Gd^{4}}$

Where $N$ number of coil.

Thus, the stiffness ( $S t$ ) calculated as:

$\displaystyle St=\frac{Gd^{4}}{8D^{3}N}$ (17)

The maximum possible stroke ( $S_{m}$ ) denotes:

$\displaystyle S_{m}=\frac{8D^{3}N}{d^{4}}[\alpha_{M}-\alpha_{A}]$ (18)

Where $\alpha=F/G$ the $F$ the load and $G$ the rigidity modulus, $G_{A}$ in austenite and $G_{M}$ in martensite phase.

The load on the spring during heating denoted by $F_{A}$ is the sum of the SMAA driving force ( $F_{M-A}$ ) and the restoring force ( $F_{M}$ ). During cooling the load on the spring, $F_{M}$ is the only restoring force.

We can find the load, $F_{M}$ to be:

$\displaystyle F_{M}=\frac{S_{m}\cdot d^{4}}{8D^{3}N}+G_{M}\cdot\alpha_{A}$ (19)

After the progress of this section of the model and its validation shown in part 3 (simulation) from the geometrical parameters it is then possible to get the thermal parameters (radiation needed for phase transition) to estimate the power needed for activation. To illustrate the result above, a simulation of this model was performed in the next part. Accordingly, from the geometrical parameters it is then possible to get the thermal parameters (radiation needed for phase transition) to estimate the power needed for the activation of the actuator.

By using the geometry of spring and the proprieties of the shape memory alloy, in particular the two-way shape memory effect (Fig. 3). The SMAA designed to operate in two directions over many cycles that the material remembers two shapes: one at high temperature and the other at low temperature [8].

Figure 3.

One-way shape memory effect: (A, C) austenite, (B) Martensite.

It is accepted that the sun provides an important thermal energy which can be able to activate the austenite phase of the shape memory alloy. In this way, the Shape Memory Alloy Actuators can respond to a thermal stimulus to induce a displacement by exerting an important force on a definite weight.

Solar radiation is the exposure of a body to a stream of radiation from the sun. the sunshine refers to the amount of energy received from the sun at one location. Solar electromagnetic radiation is the phenomenon by which energy escapes from the sun at the speed of light in a wave motion. Solar radiation is an undulating form of energy transfer that allows the transfer of heat by means of electromagnetic waves. According to the principle of wave-particle duality, the electromagnetic radiation emitted by the sun can be described in two ways: it is at the same time an electromagnetic wave characterized by a frequency $\nu$ and a wavelength $\lambda$ , but it is also a mass flow of zero mass particles called photons moving in a vacuum at a speed ( $c\approx$ 3 $\times$ 10 ${}^{8}$ ms ${}^{-1}$ ). These two models are linked by the following laws:

$\displaystyle E=h\cdot\frac{c}{\lambda}$ (20)

Where $E$ is photon energy, $h$ is the Planck constant, $c$ is the speed of light in vacuum and $\lambda$ is the photon’s wavelength. on what concerns us, the body at a temperature higher than 0 kelvin emits an electromagnetic radiation called thermal radiation or radiation of the black body. A body that receives electromagnetic radiation can reflect some of it and absorb the rest. The energy absorbed is converted into thermal energy and contributes to the increase of the temperature of this body. The Stefan-Boltzmann Law expresses the heat transfer radiation:

$\displaystyle\frac{P}{A}=\sigma T^{2}(j/m^{2}\cdot s)$ (21)

The work according to the radiation heat is a major energy that can transform the SMA spring from the martensite phase (compressed) to austenite phase (stretched) (Fig. 4).

Figure 4.

Work extraction from SMA.

Figure 5.

Ni-Ti spring respond to a thermal stimulus. a) In martensite phase, b) Intermediate phase, c) In austenite phase.

Thus, The SMAA store the acquired energy from the sun when it is heated by radiant energy. Hence, it releases this energy in the form of mechanical one in the absence of radiation heat [8].

In the first state, the SMAA is stretched in martensitic phase (lower temperature) under the Martensite start after the SMAA is exposed to a thermal stimulus after a little time (a) it can get energy therefore it became compressed (c) with a displacement $\Delta L$ . The heating/cooling process can be repeated as shown in (a) and (c) (Figs 5 and 6).

In this study, we are mainly interested in the ability of the material to alter its state and lift a constant weight by increasing the temperature coming from the sun radiation [9].

Figure 6.

The curves at high and low temperatures of SMA Ni-Ti.

Therefore, we have made an experiment to show how the actuator respond to different temperatures while keeping the same weight.

The design of the open-loop functional model needs based on the following Fig. 7.

Figure 7.

Ni-Ti spring response a constant load and radiation heat.

This feature of shape memory alloys is very interesting and we can use it in many applications (industry, renewable energy and microsystems…).

The actuator proposed consists of spring fixed around a cylindrical beam which keeps it straight and easily moving up and down [5, 8, 9].

Figure 8.

The proposed actuator device with/without heat radiation. a) Position 1: Solar radiation is falling on SMAA (Heating). b) Position 2: Solar radiation is NOT falling on SMAA (cooling).

The ability of shape memory actuator to change the position and lift specific weight depends on the materials used, the weight, the percentage of the sun radiation that can be affected by the seasons and time (the morning or the afternoon). Thus, the SMAA could achieve a good performance if it takes into account these conditions as ingredients in the modelling process [8, 9] (Fig. 8).

Moreover, this actuator can be used to develop a new sun tracker based on shape memory alloy to be like sunflower plants witch performed the dual functions of sensing and actuating. So much that, the collector can follow the sun like the sunflower and face the sun directly during the day to optimize the production of solar energy. the collector has three support made from shape memory alloy actuator (SMAA) in three position. The first one in the east side, the second in south side, and the third in west side. Accordingly, a simple model describes systematically the work of the sun tracker based on shape memory alloy. This smart tracker controlled by the change of temperature and strain that used to apply a load can change the direction of the collector.

Figure 9.

a) the collector I the East-side; b) the collector I the South-side; c) the collector I the West-side.

The sun tracker works like the sunflowers is controlled by temperature created by sunlight and the shadow of the collector (Fig. 9):

•

The collector starts with the sunrises in the east. Meanwhile, the sunlight heats the SMAA in the east side and compressed unlike the others SMAA in the shadow still stretched (martensite). Hence, the collector faces east.

•

As the sun moves, the SMAA faces the sun heats by the sunlight that increase the temperature of the SMA that is why transformed to austenite phase (compressed) when the others eclipsed by the collector’s shadow.

•

Whenever the sun moves from east to west, the SMAA in the front change gradually the form and extend from one side of the tracker to the other.

•

The collector finished the daily cycle faces west side and can repeat the same process in the next day.

3. Simulation and results

In this study, we prepare a simulation by taking a relative value between the minimum temperature and maximum one. We have used the proposed model and used the properties of thematerial for the simulations.

Table 1
Proprieties of the spring actuator used in design calculation [7]

The required stroke (S)
The required stroke (mm)	7
SSTM driving force (N)	1.18
The required stroke (S)
Wire diameter (mm)	0.5
Average spring diameter (mm)	5
The number of coils (n)	20
The maximum allowable shear strain ( )	0.06
Stress-free austenite transformation temperature	40 to 50
Stress-free Martensite transformation temperature	30 to 20
SMAA specifications
Hot test temperature	$\geqslant$ 45
Cold test temperature	$\leqslant$ 25
Maximum allowable force (N)	1 to 10
N ${}^{\circ}$ of actuation/day	24
The hour angle tilting rang	$-$ 60 ${}^{\circ}$ to 60 ${}^{\circ}$
The actuation duration (min)	20

After input the parameter in Matlab the result in (Fig. 10) between the strain and temperature, which is a pleasing result of the shape memory alloys. The Strain-Temperature curve results from the numerical simulation shows in Fig. 10.

Figure 10.

The shape memory effect mechanical behavior of the SMAA.

We also simulate the same actuator in the case of stress Vs strain of spring, in this case, after unloading, the actuator does not recover its initial shape (Fig. 11), but after heating, it can have recovered [8, 9].

Figure 11.

The shape memory effect mechanical behavior of the SMAA.

4. Discussion

It was the main purpose of the paper to draw attention to the shape memory alloys heated by solar radiation and simulates their behavior to perform as actuator (tracker) executed the dual functions of sensing and actuating. In the first phase of the validation process, it has been considered that the wire is heated by the sun radiation. The value of heat is equal to that one employed in the normal days’ temperature. The model output has been observed both in terms of variation of stress and strain and temperature in time.

Figures 10 and 11 curve shows transformation hysteresis. The change of deformation is produced by radiation heat. In this way, the temperature of material increases with increasing of the radiation of the sun over the day or when the sun faces the material or not, therefore, it is essential to define the transformation temperature to determine the radiation of the martensitic and austenitic.

Figure 10 shows the change of strain with the temperature produced by radiation heat. It is observed that the simulation was able to describe the behavior of these materials and it was proved in a normal day. Firstly, the sun faces the material and the temperature increase and reach more than 40 ${}^{\circ}$ C, the SMAA is completely austenitic which is compressed. Secondly, the absence of sun radiation onthe material makes the temperature decrease under 20 ${}^{\circ}$ C, the SMAA is completely martensitic which is stretched.

Figure 11 shows the relationship between stress and strain, in different temperature.This is the reason why the SMA return to its original shape after deformation when is heated by the solar radiation accordingly to get the shape memory effect. Therefore, the strain is about 5%, the SMA is worth mentioning that once the stress increases when the strain increases [7].

5. Conclusion

This paper is a numerical study describes the thermomechanical behavior of shape memory alloy under the effect of sun radiation. The model succeeds in capturing material behavior under complex non-proportional thermomechanical loading, by taking in mind the simultaneous activation of transformation and reorientation. Its validity has evaluated in comparison with experimental results. The simulation in MATLAB was used to study both the shape memory effect and superelasticity features of a SMA wire in different thermal conditions, which can be applicable tool for industrial applications and renewable energy. It can offer a wide deformation and simple heating arrangements which will give opportunities to design many actuators for clean energy.

The proposed actuator satisfy certain has many advantage to the studied application, as: simplicity of movement and fabrication, reduce energy consumption, works under different perturbation conditions (wind, rain, important temperature variations); can work in a water environment and can exert enough force to provide the elongation and shortening of the tracker. Have a fatigue life of more than 100 000 cycles according to manufacturer’s data sheet [12]. In this way, this study validates numerical and that can validate experimental in the next paper to be similar to the sunflowers process for collecting the energy from the sun.

References

Alhamany

Bensalah

M.O.

and Fehri

O.F.

, Couplage dans les alliages à mémoire de forme, Comptes Rendus – Mec. 332(11) (2004), 941–947.

Kumar

and Kumar

, Shape Memory Alloy (SMA) A Multi-Purpose Smart Material, 2014, 282–285.

Pissaloux

E.E.

, MODELLING AND TEMPERATURE CONTROL OF, 13(2) (2012), 1–8.

Ganesh

N.J.

Maniprakash

Chandrasekaran

and Srinivasan

S.M.

, Design and Development of a Sun Tracking Mechanism Using the Direct SMA Actuation, 133(July 2011) (2016), 1–8.

Brinson

L.C.

and Lammering

, Finite element analysis of the behavior of shape memory alloys and their applications, Int. J. Solids Struct. 30(23) (1993), 3261–3280.

Follador

Cianchetti

Arienti

and Laschi

, A general method for the design and fabrication of shape memory alloy active spring actuators, vol. 115029, 2012.

Yates

S.J.

and Kalamkarov

A.L.

, Experimental Study of Helical Shape Memory Alloy Actuators: Effects of Design and Operating Parameters on Thermal Transients and Stroke, 2013, 123–149.

Control

Tension

and Various

A.T.

, TiNi Shape Memory Alloy Tension at Various Temperatures – Infrared Imaging of Shape Memory Effect and Pseudoelasticity, 2011, 20–26.

Panico

and Brinson

L.C.

, A three-dimensional phenomenological model for martensite reorientation in shape memory alloys, J. Mech. Phys. Solids 55(11) (2007), 2491–2511.

10.

Wang

Shi

Liu

and Zhang

, An Accurately Controlled Antagonistic Shape Memory Alloy Actuator with Self-Sensing, 2012, 7682–7700.

11.

Mousazadeh

et al., A Review of Principle and Sun-Tracking Methods for Maximizing Solar Systems Output, Renewable and Sustainable Energy Reviews 13(8) (2009), 1800–1818.

12.

Tobushi

Hachisuka

Yamada

and Lin

P.-H.

, Rotating-bending fatigue of a TiNi shape-memory alloy wire Mech, Mater 26 (1997), 35–42.