1.1 General considerations

When a regular metallic alloy is subjected to an external force greater than its elastic limit, it deforms plastically, i.e. the deformation persists after returning to the unloaded state. The Shape Memory Alloys (SMAs) do not follow this behavior. At low temperatures, an SMA specimen may undergo a plastic deformation of about few percent, and then fully recover its initial shape that had at higher temperature by simple heating above a threshold temperature. Their ability to recover their form when the temperature is raised, makes this class of materials unique. This phenomenon has been discovered in 1938 by researchers working on the gold-cadmium alloys [Gilbertson (1994)]. The shape memory effect remained a laboratory curiosity until 1963, when the first industrial and medical applications appeared.

1.2 Martensitic Transformation

The shape memory effect is based on the existence of a reversible phase transformation of thermoelastic martensitic type [Kurdjumov, Khandros (1949), Kumar, Lagoudas (2008)], between a microstructural state at high temperature (austenite phase) and a microstructural state at low temperature (martensite phase) [Patoor et al. (2006), Lagoudas et al. (2006)]. Austenite has in general a cubic crystal lattice, while martensite is of tetragonal, monoclinic, or orthorhombic crystal lattice. The transformation from one crystal lattice to the other occurs by distortion of the shear lattice does and not by atoms diffusion. This type of transformation is called martensitic transformation [Perkins (1975), Funakubo (1987), Otsuka, Wayman (1999)]. In reality, the matrenitic transformation in SMAs is a phase transformation of the first order, where there is co-existence of several phases, and there is presence of interfaces between the phases [Guénin (1986)].

Historically, the term martensitic transformation describes the transformation of the austenite of steels (iron-carbon alloys) to martensite during a quenching. By extension, this term has been generalized to a large number of alloys whose phase transformations have certain characteristics typical of the transformation of steels [Rosa (2013)].

During martensitic transformation of a SMA, the crystal lattice of the material changes its shape. The microstructure of martensite is characterized by a change in shape and by the difference in volume, which exists between matrensitic and austenitic phase [Duerig et al. (1990)]. Therefore, internal strains arise during the emergence of martensitic areas within the austenite. The internal strains can be partially relaxed by the formation of several areas of self-accommodated martensite crystals that minimize the overall deformation induced. These areas called variants and are oriented in different crystallographic directions [Kumar (2008)].

In the absence of external strains, these variants are equally possible and the distribution of self-accommodated groups allows the material to be transformed in order to retain its original shape. Therefore, the formation of the martensite results in elastic (reversible) deformations [Funakubo (1987)]. At constant temperature, the martensite-austenite interfaces are in steady state. A change in temperature in one direction or the other results in moving these interfaces to the benefit of one or the other phase structure. The interfaces can also move under the action of an imposed strain. A specimen can therefore be distorted not by sliding, which is the usual mechanism of plastic deformation, but by the appearance and disappearance of martensite variants [Kumar (2008)].

Therefore, during martensitic transformation atoms in the structure move on very small distances leading to deformation of the crystal lattice. This causes a small variation in volume with shearing of the structure in a specific direction. During the transformation process, the growth of martensite crystals occur in form of platelets to minimize the energy at the interface.

The martensitic variants can occur in two different types: twinned martensite (formed by combination of self-accommodated martensite variants) and detwinned martensite (reoriented martensite) where a particular variant dominates [Liu, Xie (2007)]. The characteristic behavior of SMAs is based upon the reversible phase transformation from austenitic phase to martensitic phase and the opposite. By cooling under zero loading, the crystal sructure changes from austenitic to martensitic phase (forward transformation to twinned martensitic phase). This transformation is resulting in the development of a number of martensitic variants, which are arranged in a way that the average change in macroscopic shape is insignificant, causing a twinned martensite [Leclercq, Lexcellent (1996)]. When the material is heated at the martensite phase, the crystal structure is transforming to austenite (reverse transformation from detwinned martensitic to austenitic phase), leading to recovery of shape [Saburi, Nenno (1981), Shimizu, Otsuka, Perkins (1975)]. The above process is called Shape Memory Effect (SME) [Schetky (1979), Wayman, Harrison (1989)].

The martensitic transformation is characterized by four temperatures (Figure 2) [Gotthard, Lehnert (2001)]:

• M_S: Temperature below which the martensite appears (martensite start)
• M_F: Temperature below which the entire sample is transformed into martensite (martensite finish)
• A_S: Temperature above which the austenite appears (austenite start)
• A_F: Temperature above which the entire sample is transformed into austenite (austenite finish)

The transformation begins at the cooling to the temperature M_S. This transformation is completed to the temperature M_F. Between these two temperatures, there is coexistence of two phases, which is a characteristic of transformation of the first order. If the cooling is interrupted, the material will not change. To go back to the initial shape, the temperature is increases so that the inverse transformation begins at the temperature A_S and finishes to temperature A_F, which is higher than M_S [Massalski et al. (1990)]. If the trace on a diagram (Figure 1) the volume fraction of material processed as a function of temperature, there is a hysteresis loop, due to the presence of an irreversible energy corresponding to dissipation of mechanical energy transformed into heat [Ortin, Planes, Delaey (2006), Wei,Yang (1988)].

Figure 1 Martensitic transformation temperatures [Gotthard, Lehnert (2001)]

The thermoelastic reversibility of the crystal lattice is certain in the case of an ordered alloy [Otsuka, Shimizu (1977)]. The correlation between the manifestation of martensitic transformation and atomic order was shown experimentally in Fe-Pt SMAs [Dunne, Wayman (1973)]. Nevertheless, in disordered alloys, such as Fe-Pd, Mn-Cu and In-TI, can occur thermoelastic transformation too. The atomic order is, therefore, a sufficient condition for manifestation of thermoelastic transformation, but not necessary [Otsuka, Shimizu (1977)].

1.3 Thermomechanical properties of SMAs

Several effects specific to the SMAs appear through the transformations of the crystal lattice as a function of temperature and of the field of stresses applied on the material [Duerig, Melton, Stöckel (2013)].

1.3.1 Pseudoelastic Effect

In general, by pseudoelasticity we describe both the material’s superelastic behavior, as well as rubble-like behavior. Superelastic behavior is called the reversible phase transformation produced by thermo-mechanical loading. Rubber-like effect refers to the reversible martensitic re-orientation. The stress-strain curve during this process resamples to the superelastic behavior, which is similar to rubber’s nonlinear elastic behavior [Otsuka, Wayman (1999)].

Therefore, a part from inducing phase transformation thermally, martensitic transformation can also be prompt by applying on the material appropriately high mechanical loading, resulting in creating a martensitic phase from austenite. When the temperature of the SMA goes above A_F, shape recovery is resulted while unloading. Such behavior of the material is termed pseudoelastic effect [Kumar (2008)].

Stress-induced martensite, is generally forming from austenite when external stress is present. The process of forming stress-induced martensite can occur through different thermomechanical loading routes [Miyazaki, Otsuka (1986)]. One form of stress-induced martensite is the detwinned martensitic phase formed from austenitic after application of external stress. The material, during the stress-induced martensitic transformation and the reversed process, shows nonlinear elastic behavior described by closed σ-ε curves. This nonlinear elastic behavior is called pseudoelastic transformation [Otsuka, K. and K. Shimizu (1981)]. The shape recovery is due to crystallographic reversibility of transformation, like in the shape memory effect. Hence, the two phenomena, transformation pseudoelasticity and shape memory effect are practically the same except the fact that reverse transformation is produced by warming the specimen to temperature above A_F. In reality, an alloy that undergoes thermoelastic martensitic transformation exhibits both transformation pseudoelasticity and shape memory effect [Otsuka, K. and K. Shimizu (1981)].

Nevertheless, for occurring transformation pseudoelasticity, the necessary stress for slip should be greater than that for stress-induced martensite transformation. As an example, we can refer to equiatomic Ti-Ni alloys which are exposed to slip and do not exhibit any transformation pseudoelasticity, regardless of their Ni content. It was shown, however, that Ni-rich Ti-Ni alloys subjected to annealing after cold working, causing refining of their grain size, leads in raising critical slip stress, which results in any transformation pseudoelasticity [Miyazaki et al. (1982), Saburi, Tatsumi, Nenno (1982), Saburi, Yoshida, Nenno (1984)]. The existence of transformation pseudoelasticity is affected by crystalline orientation, composition of the alloy, and direction of applied stresses [Miyazaki, Otsuka (1986)].

1.3.2 One-Way Shape Memory Effect

Another property of SMAs is the one-way shape memory effect. It takes place in four steps:

(1) The material is cooled to a temperature lower than M_F (the parent austenitic phase) to obtain self-accommodated martensite.

(2) Re-orientation of variants of the martensite is obtained via application of stress.

(3) The stress is released at constant temperature T < M_F. The material remains to a shape depending on the stress field.

(4) The sample is heated at a temperature T > A_F making re-appear the austenitic phase and the material gets its original shape, as shown in Figure 2.

Figure 2 One-way shape memory effect [Miyazaki, Otsuka (1986)]

Two conditions are necessary for occurring shape recovery by shape memory effect. Firstly, the transformation should be reversible, and second, slip should not occur during the entire deformation process. Martensitic transformations in ordered alloys are reversible in nature [Miyazaki, Otsuka (1986), Arbuzova, Khandros (1964)], so the entire shape memory effect mainly occurs in this type of alloys. The second condition is necessary because in the case of high stress and every type of deformation mode (stress-induced martensitic transformation in parent phase, twinning in the martensitic phase) slip can be induced, resulting in plastic strain and, not completed recovery of shape.

In the one-way shape memory effect, the shape in memory by the SMA is the one of the parent phase.

1.3.3 Two-Way Shape Memory Effect

The two-way shape memory effect is the reversible passage of a shape at a high temperature to another shape at low temperature under stress.

The two-way shape memory effect should precede the SMA training [Nagasawa, et al. (1974]. Training of SMAs consists of temperature cycling at constant stress or stress cycling at constant temperature. During training, microstructural defects (i.e. dislocations) lead to internal stresses and therefore promote oriented martensite. A SMA subjected to training can then move from austenitic phase to oriented martensite under zero load by simple change of temperature [Schroeder, Wayman (1977)]. It has then a shape in memory for each of the two phases.

Various methods that cause two-way shape memory effect have been suggested, such as, large deformation in stress-induced martensite transformation at temperatures > M_S [Delaey et al. (1974)], shape memory effect training [Schroeder, Wayman (1977)], stress-induced martensite training [Schroeder, Wayman (1977)], training involving both of shape memory effect as well as stress-induced martensite [Perkins, Sponholz (1984)] remaining in martensite state while heating at a temperature > A_F [Takezawa, Shindo, Sato (1976)], as well as using precipitates [Tadaki, Otsuka, Shimizu (1988)].

1.4 Transformation Induced Plasticity (TRIP)

Several experimental studies have shown the development of nonlinear plastic (irreversible) strain when phase transformations occur [Greenwood, Johnson (1965), Abrassart (1972), Magee (1966), Desalos (1981), Olson, Cohen (1986), Denis et al. (1982)]. This mechanism of deformation is termed Transformation Induced Plasticity (TRIP), resulting from internal stress rising from the change in volume related to the transformation, as well as from the associated change in shape [Marketz, Fischer (1994)]. TRIP differs from classical plasticity. Although plasticity is caused from the applied stress or variation in temperature, TRIP is triggered by phase variations, and occurs even at low and constant stress levels [Gautier et al. (1989), Leblond et al. (1989), Gautier (1998), Tanaka, Sato (1985), Fischer et al. (2000, 1996)]. TRIP takes place because of two separate mechanisms. The first, refers to a process of accommodation of micro-plasticity related to volume change [Greenwood, Johnson (1965)]. The other, refers to an orientation caused by shear internal stresses, favoring the direction of preferred orientation for the formation of martensite when and external stress is present, which involves change in shape [Magee (1966)]. TRIP is caused by the difference in compactness of the lattice structure between the austenite (parent) and the martensite (product) phase [Greenwood, Johnson (1965)]. During martensitic transformation, this difference has produces a change in volume as well as internal stresses causing plasticity in the phase with less yield stress, which is weaker  [Paiva, Savi, Pacheco (2005)].

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