Detailed Introduction to Shape Memory Alloys

Introduction to Shape Memory Alloys

Shape memory alloys (SMAs) are metallic alloys which can recover permanent strains when they are heated above a certain temperature. The key characteristic of all SMAs is the occurrence of a martensitic phase transformation. The martensitic transformation is a shear-dominant diffusionless solid-state phase transformation occurring by nucleation and growth of the martensitic phase from a parent austenitic phase. When an SMA undergoes a martensitic phase transformation, it transforms from its high-symmetry, usually cubic, austenitic phase to a low-symmetry martensitic phase, such as the monoclinic variants of the martensitic phase in a NiTi SMA.

The martensitic transformation possesses well-defined characteristics that distinguish it among other solid state transformations:

• It is associated with an inelastic deformation of the crystal lattice with no diffusive process involved. The phase transformation results from a cooperative and collective motion of atoms on distances smaller than the lattice parameters. The absence of diffusion makes the martensitic phase transformation almost instantaneous.
• Parent and product phases coexist during the phase transformation, since it is a first order transition, and as a result there exists an invariant plane, which separates the parent and product phases. The lattice vectors of the two phases possess well defined mutual orientation relationships (the Bain correspondences), which depend on the nature of the alloy.
• Transformation of a unit cell element produces a volumetric and a shear strain along well-defined planes. The shear strain can be many times larger than the elastic distortion of the unit cell. This transformation is crystallographically reversible.
• Since the crystal lattice of the martensitic phase has lower symmetry than that of the parent austenitic phase, several variants of martensite can be formed from the same parent phase crystal.
• Stress and temperature have a large influence on the martensitic transformation. Transformation takes place when the free energy difference between the two phases reaches a critical value.

The martensitic transformation (austenite-to-martensite) occurs when the free energy of martensite becomes less than the free energy of austenite at a temperature below a critical temperature T₀ at which the free energies of the two phases are equal. However, the transformation does not begin exactly at T₀ but, in the absence of stress, at a temperature M^0s (martensite start), which is less than T₀. The transformation continues to evolve as the temperature is lowered until a temperature denoted M^0f (martensite finish) is reached. This temperature difference M^0s - M^0f is an important factor in characterizing shape memory behavior.

When the SMA is heated from the martensitic phase in the absence of stress, the reverse transformation (martensite-to-austenite) begins at the temperature A^0s (austenite start), and at the temperature A^0f (austenite finish) the material is fully austenite. The equilibrium temperature T₀ is in the neighborhood of (M^0s + A^0f)/2. The spreading of the cycle (A^0f - A^0s) is due to stored elastic energy, whereas the hysteresis (A^0s - M^0f) is associated with the energy dissipated during the transformation.

Due to the displacive character of the martensitic transformation, applied stress plays a very important role. During cooling of the SMA material below temperature M^0s in absence of applied stresses, the variants of the martensitic phase arrange themselves in a self-accommodating manner through twinning, resulting in no observable macroscopic shape change (see the stress-temperature diagram shown in Figure 1). By applying mechanical loading to force martensitic variants to reorient (detwin) into a single variant, large macroscopic inelastic strain is obtained. After heating to a higher temperature, the low-symmetry martensitic phase returns to its high-symmetry austenitic phase, and the inelastic strain is thus recovered. The martensitic phase transformation can also be induced by pure mechanical loading while the material is in the austenitic phase, in which case detwinned martensite is directly produced from austenite by the applied stress (Stress Induced Martensite, SIM) at temperatures above M^0s.

Figure 1. SMA stress-temperature phase diagram.

As a result of the martensitic phase transformation, the stress-strain response of SMAs is strongly non-linear, hysteretic, and a very large reversible strain is exhibited. This behavior is strongly temperature-dependent and very sensitive to the number and sequence of thermomechanical loading cycles. In addition, microstructural aspects have considerable influence on the stress-strain curve and on the strain-temperature curves. In polycrystals, the differences in crystallographical orientation among grains produce different transformation conditions in each grain. The polycrystalline structure also requires the satisfaction of geometric compatibility conditions at grain boundaries, in addition to compatibility between austenite and the different martensitic variants. Thus, the martensitic transformation is progressively induced in the different grains and, as opposed to the single crystal case, no well-defined onset of the transformation is observed. In addition, the hysteresis size increases, and the macroscopic transformation strain decreases.

The key effects of SMAs associated with the martensitic transformation, which are observed according to the loading path and the thermomechanical history of the material are: pseudoelasticity, one-way shape memory effect and two-way shape memory effect. The characteristics associated with these classes of behavior are presented below, and the various strain mechanisms behind these effects are described.

An SMA exhibits the Shape Memory Effect (SME) when it is deformed while in the martensitic phase and then unloaded while still at a temperature below M^0f. If it is subsequently heated above A^0f it will regain its original shape by transforming back into the parent austenitic phase. The nature of the SME can be better understood by following the process described above in a stress-temperature phase diagram schematically shown in Figure 2. The parent austenitic phase (indicated by A in Figure 2) in the absence of applied stress will transform upon cooling to multiple martensitic variants (up to 24 variants for the cubic-to-monoclinic transformation) in a random orientation and in a twinned configuration (indicated by B). As the multivariant martensitic phase is deformed, a detwinning process takes place, as well as growth of certain favorably oriented martensitic variants at the expense of other variants. At the end of the deformation (indicated by C) and after unloading it is possible that only one martensitic variant remains (indicated by D). Upon heating, when temperature reaches A^0s, the reverse transformation begins to take place, and it is completed at temperature A^0f. The highly symmetric parent austenitic phase (usually with a cubic symmetry) forms only one variant, and thus the original shape (before deformation) is regained (indicated by E). Note that subsequent cooling will result in multiple martensitic variants with no substantial shape change (self-accommodated martensite). Also, note in Figure 2 that, in going from A to B many variants will start nucleating from the parent phase, while in going from D to E there is only one variant of the parent phase that nucleates from the single remaining martensitic variant indicated by D.

Figure 2. Schematic representation of the thermomechanical loading path demonstrating the shape memory effect in an SMA.

The stress-free cooling of austenite produces a complex arrangement of several variants of martensite. Self-accommodating growth is obtained such that the average macroscopic transformation strain equals zero , but the multiple interfaces present in the material (boundaries between the martensite variants and twinning interfaces) are very mobile. This great mobility is at the heart of the SME. Movement of these interfaces accompanied by detwinning is obtained at stress levels far lower than the plastic yield limit of martensite. This mode of deformation, called reorientation of variants, dominates at temperatures lower than M^0f.

The above described phenomenon is called one-way shape memory effect (or simply, shape memory effect) because the shape recovery is achieved only during heating. The first step in the loading sequence induces the development of the self-accommodated martensitic structure, and no macroscopic shape change is observed. During the second stage, the mechanical loading in the martensitic phase induces reorientation of the variants and results in a large inelastic strain, which is not recovered upon unloading (Figure 3). Only during the last step the reverse transformation induced by heating recovers the inelastic strain. Since martensite variants have been reoriented by stress, the reversion to austenite produces a large transformation strain having the same amplitude but the opposite direction with the inelastic strain, and the SMA returns to its original shape of the austenitic phase.

Figure 3. Schematic of a stress-strain-temperature curve showing the shape memory effect.

The pseudoelastic behavior of SMAs is associated with recovery of the transformation strain upon unloading and encompasses both superelastic and rubberlike behavior. The superelastic behavior is observed during loading and unloading above A^0s and is associated with stress-induced martensite and reversal to austenite upon unloading. When the loading and unloading of the SMA occurs at a temperature above A^0s, partial transformation strain recovery takes place. When the loading and unloading occurs above A^0f, full recovery upon unloading takes place. Such loading path in the stress-temperature space is schematically shown in Figure&4;. Initially, the material is in the austenitic phase (point A). The simultaneous transformation and detwinning of the martensitic variants starts at point and results in fully transformed and detwinned martensite (point C). Upon unloading, the reverse transformation starts when point D is reached. Finally, at the end of the loading path (point E) the material is again in the austenitic phase.

Figure 4. Schematic of a thermomechanical loading path demonstrating pseudoelastic behavior of SMAs.

If the material is in the martensitic state and detwinning and twinning of the martensitic variants occur upon loading and unloading, respectively, by reversible movement of twin boundaries, this phenomenon is called rubberlike effect . The rubberlike effect is less common, while the superelastic effect is very common in almost all SMAs.

Three distinct stages are observed on the uniaxial stress-strain curve representing the superelastic behavior of an SMA, schematically shown in Figure 5. For stresses below s^Ms, the material behaves in a purely elastic way. As soon as the critical stress is reached, forward transformation (austenite-to-martensite) initiates and stress-induced martensite starts forming. During the formation of SIM large transformation strains are generated (upper plateau of stress-strain curve in Figure 5). When the applied stress reaches the value s^Mf the forward transformation is completed and the SMA is in the martensitic phase. For further loading above s^Mf the elastic behavior of martensite is observed. Upon unloading, the reverse transformation initiates at a stress s^As and completes at a stress s^Af. Due to the difference between s^Mf and s^As and between s^Ms and s^Af a hysteretic loop is obtained in the loading/unloading stress-strain diagram. Increasing the test temperature results in an increase of the values of critical transformation stresses, while the general shape of the hysteresis loop remains the same.

Figure 5. Schematic of the superelastic behavior of SMAs.

Upon cooling under a constant applied stress from a fully austenitic state, it is observed that the transformation is characterized by a martensite start temperature M^ss and a martensite finish temperature M^sf, which are functions of the applied stress. Macroscopic transformation strain obtained in that way (Figure 6) is a result of martensite formation and detwinning of the martensitic variants due to the applied load. The transformation strain is several orders of magnitude greater than the thermal strain corresponding to the same temperature difference required for the phase transformation. A hysteresis loop is observed for the cooling/heating cycle as shown in Figure 6 due to the fact that the reverse transformation begins and ends at different temperatures than the forward transformation does.

Figure 6. Schematic of isobaric thermally induced transformation behavior of SMAs.

The superelastic behavior described above constitutes an approximation to the actual behavior of SMAs under applied stress. In fact, only a partial recovery of the transformation strain induced by the applied stress is observed. A small residual strain remains after each unloading. Further cooling of the material, in the absence of applied stress, is now related to the occurrence of a macroscopic transformation strain contrary to what is observed in the SMA material before cycling. The thermomechanical cycling of the SMA material results in training process. Different training sequences can be used, i.e., by inducing a non-homogeneous plastic strain (torsion, flexion) at a martensitic or austenitic phase; by aging under applied stress, in the austenitic phase, in order to stabilize the parent phase, or in the martensitic phase, in order to create a precipitant phase (Ni-Ti alloys); by thermomechanical, either superelastic or thermal cycles.

The main result of the training process is the development of Two-Way Shape Memory Effect (TWSME). In the case of TWSME, a shape change is obtained both during heating and cooling. The solid exhibits two stable shapes: a high-temperature shape in austenite and a low-temperature shape in martensite. Transition from the high-temperature shape to the low-temperature shape (and reverse) is obtained without any applied stress assistance.

In contrast with the previously discussed properties of SMAs (superelasticity, one-way shape memory) that are intrinsic, the TWSME is an acquired characteristic. In the heart of the TWSME is the generation of internal stresses and creation of permanent defects during training. The process of training leads to the preferential formation and reversal of a particular martensitic variant under the applied load. Generation of permanent defects eventually creates a permanent internal stress state, which allows for the formation of the preferred martensitic variant in the absence of the external load.

Another effect of the training cycle is the development of macroscopically observable plastic strain. The magnitude of this strain is comparable to the magnitude of the recoverable transformation strain. The training also leads to secondary effects, like change in the transformation temperatures, change in the hysteresis size and decrease in the macroscopic transformation strain. These effects are similar to those observed during thermomechanical fatigue tests. It is important to define optimal conditions of training, because an insufficient number of training cycles produces a non-stabilized two-way memory effect and over-training generates unwanted effects that reduce the efficiency of training.

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