Shape Memory Properties

There are unique properties exhibited by SMAs depending on TTs of the alloy and the operating temperature. If a mechanical load is applied to the SMA at temperature below Mf, it is possible to detwin the twinned martensite by reorienting a certain number of

variants as shown in Figure 1.4. This deformation is therefore different from deformation induced by dislocation motion or deformation twins. The detwinning process results in a macroscopic shape change, where the materials remains in the deformed configuration upon releasing of the load. A subsequent heating of the SMA to a temperature above Af

will result in reverse phase transformation and will lead to complete shape recovery. This process is referred to as the shape memory effect (SME) or one way shape memory effect as illustrated in Figure 1.4a. It is worth to note that cooling back to a temperature below Mf

leads to the formation of twinned martensite again with no associated shape change observed. The reason behind the phenomenon of SME is the formation of self- accommodating martensite structure in order to minimize energy upon cooling under no load. When a force applied in martensite, some favorable martensite variants grow at the expense of others and remain in detwin structure while the load is removed. Furthermore, the detwinned martensite variants transform to austenite phase during heating since it has a higher order of symmetry than martensite, while the self-accommodating martensite structure formed upon cooling in stress free condition, hence, there is no observed shape change. It is worth to mention that the remained strain might not fully recover by heating up above Af if the stress is sufficient to introduce plastic deformation and irrecoverable

strain (ɛir) would present after heating cycle. The total recoverable strain is the combination

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Figure 1.4: Schematic of shape memory effect and superelasticity behavior of SMAs.

In contrast to one way shape memory effect where the material only memorize the structure of parent phase, it is possible that the alloy remember the shape of both low and high temperatures phase. This phenomena is called as two way shape memory effect (TWSME) where material has the ability to generate strain by only thermal cycling in the absence of applied stress. This could be attributed to the development of local stress fields due to presence of defects, such as dislocations, that disrupt self-accommodating structure and favors formation of selective martensite variants upon cooling. It is important to note that the dislocations do not disappear during reverse transformation and they are present in the austenite phase. Thus, the stress fields around the dislocations induce particular martensite variants during cooling and hence a shape change observed during thermal cycling under stress free condition.

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In addition to temperature induced martensitic transformation, SMAs also exhibit stress induced phase transformation. During loading at temperatures slightly above Af,

stress induced transformation leads to formation of detwinned martensite at sufficiently high stress levels and a complete shape recovery is observed upon unloading due to reverse transformation from martensite to austenite phase. This phenomenon is called superelasticity which is schematically shown in Figure 1.4. Superelasticity is represented

in the stress-strain curve as shown in Figure 1.4b. After elastic deformation of austenite, the stress induced martensite transformation initiated at a critical stress level of σMs _{and the}

martensitic transformation end at σMf_{, followed by elastic deformation of martensite phase.}

Upon unloading, the martensite transforms back to austenite and deformation is ideally recovered. The total amount of superelasticity strain that is recovered upon unloading is symbolized by εse in Figure 1.4b and the stress hysteresis mentioned in the plot depicts the

difference in critical stresses for forward and reverse transformation. Young Modulus of elasticity for austenite and martensite phase are represent by EA and EM, respectively.

It can be realized that the SME is a consequence of thermal cycling between Af and

Mf temperatures and superelasticity occurs due to stress induced martensitic transformation

at temperatures above Af. The Clausius-Clapeyron relationship (CC) is a best equation to

describe the stress-temperature dependence of martensitic transformation in SMAs. The relationship for uniaxial stress can be written as follows:

𝑑𝜎 𝑑𝑇 = − ∆𝑆 𝜀𝑡𝑟= − ∆𝐻 𝜀𝑡𝑟𝑇0 (1.3)

where σ is the uniaxial stress, ɛtr is the transformation strain, ∆S is the entropy of

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T0 is the equilibrium temperature of transformation which is determined from the enthalpy

and entropy changes of the transformation. Since ∆S, ∆H and T0 are constant for a given

system, hence the relation between stress and strain is linear. The equilibrium temperature of thermoelastic martensitic transformation can be calculated by the following equation [38, 39]:

𝑇₀ =𝑀𝑠+𝐴𝑓

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The enthalpy changes of the forward and reverse martensitic transformation can be obtained by measuring the area of cooling and heating curves of thermal induce transformation in the absence of stress results. The entropy of martensitic transformation can be express as follows:

∆𝑆 =∆𝐻𝑎𝑣𝑔

𝑇0

Critical stresses for martensite reorientation, martensitic transformation and dislocation slip are strongly testing temperature dependent and are schematized in Figure 1.5. It is noted from Figure 1.5 that SME occurs at temperatures below As and critical stress

for the martensite reorientation decreases with temperature due to increased mobility of internal twins and martensite plates boundaries. The green line in the Figure 1.5 illustrates the critical stress required to induce martensitic transformation which follows the CC relation (Eq. 1.3) and increases with temperature. If the material is in austenite and deformed between Ms and Af, stress induced martensitic transformation during loading and

shape recovery cannot be obtained upon unloading, however, full recovery occurs when the temperature is increased above Af temperature if no plastic deformation formed in the

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desist temperature (Md) where the critical for slip is higher than the stress needed to induce

martensitic transformation. Stress induced martensite cannot be observed above Md and

alloys deform like conventional materials [40]. The intersection of critical stresses of martensitic transformation and dislocation slip can be considered as Md and it is shown in

Figure 1.5. In general, the critical stress for slip (yield stress of austenite) decreases with increasing temperature. If the material is not strong enough or temperature is close to Md,

partial recovery can be observed since martensitic transformation and plastic deformation occur simultaneously. Also, plastic deformation of austenite takes place above Md where

stress induced martensitic transformation is no longer possible and shape recovery cannot be observed during unloading. Thus, superelasticity can only be observed between Af and

Md where the difference between these temperatures is called superelastic window and

shown as a shaded portion in Figure 1.5.

Figure 1.5: Schematic for the critical stresses of various deformation modes as a function

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