Acknowledgement

AbstractShape Memory Alloys (SMAs) have been considered as one of the most promising smart materials. They can provide novel solution in several fields, for various applications (e.g. actuator, biomedical application, clamping systems, ect.). Shape Memory Alloys demonstrate a unique ability to recover their initial shape after deformation through a reversible thermo-elastic phase transformation, it allows Shape Memory Alloys to recover large strains, either spontaneously (pseudoelasticity) or through an increase in temperature (Shape Memory Effect).

The effect of embedded shape memory alloy (SMA) wires on the natural frequency, flutter, limit cycle oscillation (LCO) amplitude and aeroelastic stability margin of a rectangular cantilever wing are investigated.

Wings are modeled in accordance to classical plate theory (CPT) as well as first-order shear deformation plate theory (FSDT) and large deflection Von Karman plate theory. The effects of pre-strain, temperature and number of SMA wires on aeroelastic characteristics are considered.

Significant improvements in aeroelastic behaviors due to the in-plane load of the SMA wires are obtained.

Table of Contents

1. PRELIMINARY: SHAPE MEMORY ALLOY

1.1. History of Shape Memory Alloy:

The first reported steps towards the discovery of the shape memory effect were taken in 1930s. According to Otsuka and Wayman (Otsuka and Wayman 1998), A. Olander discovered the pseudo elastic behavior of the Au-Cd alloy in 1932. Greninger & Mooradian observed the formation and disappearance of a martensitic phase by decreasing and increasing the temperature of a Cu-Zn alloy. The basic Phenomenon of the memory effect governed by the thermo elastic behavior of the martensite phase was widely reported a decade later by Kurdiunov & Khandros. Workers at the U.S. naval Ordnance Laboratory discovered the shape memory effect in an equiatomic alloy of nickel and titanium, which can be considered an alloy named Nitinol (Nickel-Titanium Naval Ordnance Laboratory). Many efforts had been made since then, but not until the mid-1990s, that the first breakthrough in medicine utilizing SMA in commercial stent applications. Nitinols completely new properties of superelaticity and shape memory effect, compare to conventional metal alloys, fascinate many biomaterial scientists. (Harrison and Hodgson 1975)

1.2 Two Main Characteristics of Shape Memory Alloys:

Two main characteristics of Shape Memory Alloys are shape memory effect and pseudo elasticity. SMA is a unique class of alloys which are able to remember their shape and are able to return to that shape even after being deformed. The phenomenon is called Shape Memory Effect. Pseudo elasticity (Super elasticity) refers to the ability of NiTi to return to its original shape upon unloading after a substantial deformation. (Funankubo 1987) The super elastic effect of memory alloys is characterized by the impressive amount of possible elastic strain, which is more than 20 times higher compared to conventional materials; it is beyond elasticity, therefore called super elasticity. The effect is based on an internal transformation of the crystal structure, which is called austenite in the initial condition and which transform to the martensite (this phase is well-known from steel hardening) if external stresses affect the material. The phase transformation is related to the appearance of a pseudo-elastic strain, giving the effect its name super elasticity. After releasing the stress the material recovers the initial shape and temperature changes are not necessary for the occurrence of the effect. (Suzuki 1976; Owen and al. 1979; Delaey and Chandrasekaran 1982; Tamura 1987)

A reversible, solid phase transformation known as mastensitic transformation is the driving force behind shape memory alloys. When nickel and titanium atoms are present in the alloy, in a given proportion, the material forms a crystal structure, which is capable of undergoing a change from one form of crystal structure to another. The transformation from one form of crystalline structure to another creates the mechanism by which the shape change occurs in SMAs. This change involves transition from a monoclinic crystal form (martensite) to an ordered cubic crystal form (Austenite). The Austenite phase is stable at high temperature, and the martensite is stable at lower temperature. In the martensite phase, atoms orient themselves in rows that are tilted left or right. This phenomenon is referred to as twining, as the atoms form mirror images of themselves or twins. The martensite twins are able to flip their orientation, in a simple shearing motion, to the opposite tilt, creating a cooperative movement of the individual twins. The atoms reorient themselves to straight up the lattice when the deformed SMA is heated. Ordinary metals cant reverse the deformation once deformation occurs by dislocation motion and atomic planes sliding over one another, taking on a new crystal position and results in permanent damage to the crystalline order. Unlike regular metals, SMAs deform by detwinning which changes the tilt orientation of twins and doesnt cause any dislocation. Detwinning allows the martensite phase to absorb dislocation to a given extent. Shape recovery only occurs to detwinning, but not to a deformation process involving slip which is not irreversible. (Chu and Tu 1994; Ren and Otsuka 1997) SMA in its Austenite phase exhibits a high elastic behavior. This allows the material to deform up to 7% and then fully recover the resulting strain by simply removing the load. This is psudoelastic effect or pseudo elasticity, it is also referred as super elasticity. Deformed psudoelastic material is in the formation of martensite crystal, it is called stress-induced martensite. Applications using the Shape Memory Effect results of temperature induced transformation. The transformation temperature depends on the composition of the alloy and can vary from 100C down to cryogenic temperatures. (kato and Mori 1976; Otsuka and Shimizu 1982; Pelton, Hodgson et al. 1995)

Fig: 1.1- Microscopic and Macroscopic Views of the Two Phases of Shape Memory Alloys1.3 Temperature Transformation in Shape Memory Alloys:

For almost any use of a Shape Memory Alloy, it is highly desirable knows the Transformation Temperatures (TTRs) of the alloy. The TTRs are those temperatures at which the alloy changes from the higher temperature Austenite to the lower temperature Martensite and vice versa.SMAs do not undergo their phase transformation from martensite to austenite or from austenite to martensite at one specific temperature. The transformations begin at one temperature and stop at another. These start and finish temperatures are different depending on the material is heating or cooling.In order of lowest to highest temperature, are defined: Matensite finish (Mf): Temperature at which the material is completely twinned martensite which does not entail a change in shape if unloaded. Martensite start (Ms): Temperature at which, when austenite is cooled, it begins to change into martensite. Austenite start (As): Temperature at which martensite begins to change in austenite. Austenite finish (Af): The temperature at which the change in austenite is complete.Assume that a strip of SMA begins at an initial temperature where it is completely martensite. Increasing the temperature to as will cause the material to start transforming in austenite. Once the temperature reaches Af, the material is completely in austenite.

Assume that a strip of SMA begins at an initial temperature where it is completely in austenite. Decreasing the temperature to Ms Causes the material to start transforming to martensite. Once the temperature is cooled to Mf, the material is completely twinned martensite.Fig. 2 shows the transformation temperatures and their relation to martensite and austenite in the material.

Fig: 1.2 -Phase Transformation Temperatures of SMA material

Fig: 1.3- Microscopic Diagram of the Shape Memory Effect

1.4 One-way vs. two-way shape memory:

Shape-memory alloys have different shape-memory effects. Two common effects are one-way and two-way shape memory. A schematic of the effects is shown below.

Fig. 1.4: Macroscopically Mechanism of One Way Shape Memory Effect: (a) Martensite, (b) Loaded and Deformed in martensite phase T Mf, (c) Heated above T G As(austenite),(d) Cooling to martensite T Mf.

1.4.1 One-way memory EFFECT:When a shape-memory alloy is in its cold state (below As), the metal can be bent or stretched and will hold those shapes until heated above the transition temperature. Upon heating, the shape changes to its original. When the metal cools again it will remain in the hot shape, until deformed again.With the one-way effect, cooling from high temperatures does not cause a macroscopic shape change. A deformation is necessary to create the low-temperature shape. On heating, transformation starts at As and is completed at Af (typically 2 to 20 C or hotter, depending on the alloy or the loading conditions). As is determined by the alloy type and composition and can vary between 150 C and 200 C.

1.4.2 Two-way memory effect: The two-way shape-memory effect is the effect that the material remembers two different shapes: one at low temperatures, and one at the high-temperature shape. A material that shows a shape-memory effect during both heating and cooling is called two-way shape memory. This can also be obtained without the application of an external force (intrinsic two-way effect). The reason the material behaves so differently in these situations lies in training. Training implies that a shape memory can "learn" to behave in a certain way. Under normal circumstances, a shape-memory alloy "remembers" its high-temperature shape, but upon heating to recover the high-temperature shape, immediately "forgets" the low-temperature shape. However, it can be "trained" to "remember" to leave some reminders of the deformed low-temperature condition in the high-temperature phases. There are several ways of doing this.A shaped, trained object heated beyond a certain point will lose the two-way memory effect; this is known as "amnesia".

1.5 Application of SMA:

Shape memory component can be designed to exert force over a considerable range of motion, often for many cycles. Such an application is the circuit board edge connector made by Beta Phase Inc. (Krumme 1987). In this electrical connector system, the SMA component is used to force open a spring when the connector is heated. This allows force free insertion or withdrawal of a circuit board in the connector. Upon cooling, the NiTi actuator becomes weaker and the spring easily deforms the actuator while it closes tightly on the circuit board and forms the connections. Based on the same principle, CuZnAl shape memory alloys have found several applications in this area. (Waldbusser 1987) Among the SMA force actuator, SMA spring is mostly used. (Baz, Iman et al. 1990; Lee and Lee 2000)

It is possible to use only a part of the shape recovery to accurately position a mechanism by using only a selected portion of the recovery because the transformation occurs over a range of temperature rather than at a single temperature. A device has been developed by Beta Phase Inc. (Hodgson 1988) in which a valve controls the rate of fluid flow by carefully heating a shape-memory alloy component just enough to close the valve the desired amount. A number of products have been brought to market that use the psudoelastic (superelastic) properties of these alloys. Eyeglasses frames use superelastic NiTi to absorb large deformations without damaging the frames are now marketed, and guide wires developed for steering catheters into vessel in the body using NiTi wire, which resists permanent deformation if bent severely. Arch wires for orthodontic correction using NiTi have been used for many years to give greater rapid movement of teeth.