2020 Volume 61 Issue 1 Pages 55-60
Cu–Al–Mn single crystals with subgrains were prepared by cyclic heat treatment, and the orientation dependence of superelasticity was investigated using tensile tests, during which the microstructure of the martensite was observed in situ. The transformation strain result basically agrees with the calculation from the shape strain, but the value is lower than the calculation result and the stress hysteresis is abnormally wide in some samples. The stress-induced forward and reverse martensitic transformation takes place by a single variant in the sample with a normal hysteresis but by multiple variants in the sample with wide hysteresis. The wide hysteresis mainly results from an abnormally low stress for the reverse transformation, which is considered to be caused by competition between the variants. The results suggest that multi-variants can be induced when the loading direction is located on the sides of stereo-triangle, such as ⟨001⟩ to ⟨101⟩, ⟨001⟩ to ⟨111⟩, and ⟨101⟩ to ⟨111⟩, based on Schmid’s law.
Superelasticity is a reversible strain response to an applied stress associated with stress-induced forward and reverse martensitic transformations, and the large recoverable strain of superelastic alloys is utilized in engineering and biomedical fields.1,2) In general, a stress-strain curve shows stress hysteresis because a martensite phase is induced by applying stress beyond the equilibrium stress between the parent and martensite phases. In addition, the critical stress for the reverse transformation is lower than the equilibrium stress, due to the friction for the movement of the parent/martensite interface. The hysteresis loop of a stress-strain curve means dissipation energy, which can be used for a damper in anti-seismic devices3,4) or might be a source of functional fatigue.
The most common superelastic alloy system is Ti–Ni, but its use is restricted to shapes resembling a wire or tube in most cases because of its low cold workability. Cu–Al–Mn alloy possesses superior cold workability. The workability is improved by decreasing the degree of order of the L21 phase by lowering the Al content,5) and Cu–Al–Mn alloy with an Al content about 17 at% can be formed into a sheet or complicated shape.6) The superelasticity is poor in Cu–Al–Mn alloys with a fine grain structure relative to the cross-section size7,8) due to the grain constraint.9,10) To overcome this problem, a grain growth technique has been developed for obtaining a bamboo (oligocrystalline) structure or single crystal. It has been found that abnormal grain growth occurs during cyclic heat treatment, consisting of cooling from the β (bcc) singe-phase region (e.g., 900°C) to the α (fcc) + β two-phase region (e.g., 500°C) and subsequent heating to the β single-phase region.11) In this way, a large single crystal, such as a bar 700 mm long, can be obtained with Cu–Al–Mn alloy.12) This technique expands the application range of Cu–Al–Mn to large-scale components, including seismic applications. Recently, a number of studies on superelastic self-centering and/or damping devices have been reported because superelastic alloys can return to their original shape, resulting in suppression of residual deformation of buildings or bridges after strong earthquakes, and they can convert the mechanical energy of oscillation into heat corresponding to a hysteresis loop in the stress-strain curve.3,4,13,14) The Cu–Al–Mn alloys have advantages in terms of workability and machinability against Ti–Ni alloys.15,16)
In Cu–Al–Ni alloys, the superelastic behaviors of single crystals have already been investigated and the recoverable strain and critical stress for martensitic transformation is reported to be strongly dependent on crystalline orientation.17) While the superelasticity of single crystals in Cu–Al–Mn alloys has been reported,12,18) the orientation dependence has hardly been investigated. In this work, we report the orientation dependence in superelasticity and an anomaly in stress hysteresis obtained for five single-crystal samples with different orientations in a Cu–Al–Mn alloy.
Cu–17Al–11.4Mn (at%) alloy was prepared by induction melting. The ingot was hot-rolled at 800°C to 2 mm and then cold-rolled to 1 mm after annealing at 600°C for 30 minutes. The samples were cut and sealed in quartz tubes backfilled with Ar for heat treatment. Single crystals were obtained by repeating the cyclic heat treatment11) 1 or 10 times between 900°C and 500°C with a cooling and heating rate of 3.3 K/min and 10 K/min, respectively. The samples were finally solution-treated in the β single-phase region at 900°C for 3 hours, followed by water quenching, and then aging at 200°C was conducted to stabilize the martensitic transformation temperatures.
The martensitic transformation temperatures were measured by differential scanning calorimetry (DSC) with a cooling and heating rate of 10 K/min. The crystal orientation was determined by the electron backscattering diffraction technique.
Superelasticity was evaluated by a tensile loading/unloading test using the single crystals obtained by ten-cycle heat treatment with 20 mm × 2 mm × 1 mm in the gauge length at room temperature (about 25°C). The surface of the samples was observed by a digital microscope during the tensile test.
Figure 1 shows the DSC cooling and heating curves of the single crystals. It was previously shown that Cu–Al–Mn alloys in this composition range exhibit martensitic transformation between the L21 parent and 6M (18R) martensite phases.5) The martensitic transformation temperatures are determined to be Ms = −41°C, Mf = −43°C, As = −32°C, and Af = −29°C, and the thermal hysteresis is Af − Ms = 12°C and As − Mf = 11°C.
DSC curves of single crystal obtained by the cyclic heat treatment with definition of martensitic transformation temperatures. The transformation temperatures are Ms = −41°C, Mf = −43°C, As = −32°C, and Af = −29°C.
Figure 2(a) and 2(b) shows the grain reference orientation deviation (GROD) maps of the one-cycle and ten-cycle samples, respectively, and subgrains with misorientation up to several degrees are observed only in Fig. 2(b). It has been reported in Cu-based and Fe-based alloys that subgrains form in association with precipitation and remain after heating to a single-phase region, the boundary energy of which is the driving force for abnormal grain growth.11,12,19,20) The present result of the GROD map is similar to the previous reports. Pre-existing grain boundaries migrate out from the subgrains, and thus they are rarely observed in a one-cycle sample. In the ten-cycle sample, subgrains are introduced in abnormally grown grains and remain unless those grains are encroached upon by abnormal grain growth.
Grain reference orientation deviation (GROD) maps of (a) one-cycle and (b) ten-cycle samples. Subgrains are observed only in panel (b).
Five single crystals labeled as A–E with different orientations were prepared, and their stress-strain curves are shown in Fig. 3(a), where the orientations along the loading direction are indicated in Fig. 3(b). Note that the orientations have some spread, which is because the samples contain subgrains with direction differences of several degrees, as shown in Fig. 2. All the samples show a stress-induced martensitic transformation starting at σMs, elastic deformation of martensite beyond the plateau strain εp, and reverse transformation finishing at σAf, with almost full shape recovery in Fig. 3(a). It is found that the plateau strain εp and the critical stresses σMs and σAf are orientation dependent. The plateau strain εp is summarized in Fig. 3(b). The observed plateau strain εp is roughly in agreement with the calculated transformation strain εtr from the shape strain21) except for samples C and E. The lower plateau strain εp in samples C and E is probably due to the induction of the multi-variants, as will be shown later.
(a) Stress-strain curves in single crystals A–E with different crystal orientations. (b) Crystal orientation along the loading direction and plateau strain εp (%) for each single crystal A–E. The size of the circles represents the orientation spread (A: 3.0°, B: 2.6°, C: 2.8°, D: 1.2°, E: 2.9°) due to subgrains and is defined by two standard deviations in misorientation of subgrains versus frequency histogram. Contour lines are transformation strain εtr calculated from the shape strain.21)
Figure 4(a) shows the relation between the plateau strain εp and critical stresses σMs and σAf. In contrast with the smooth stress-strain curves of samples A, B, and D, samples C and E show bumpy curves in Fig. 3(a). Therefore, the σAf-low is also plotted for samples C and E.
Critical stresses σMs and σAf against (a) plateau strain εp and (b) calculated transformation strain εtr with calculation from eqs. (2) and (3). (c) Stress hysteresis σhys = σMs − σAf in the stress-strain curves in Fig. 3(a) as a function of plateau strain εp with calculation from eq. (4). Lower critical stress σAf-low and maximum hysteresis σhys-max are also shown for samples C and E.
The temperature dependence of critical stress for martensitic transformation in the equilibrium state of chemical Gibbs energy σ0 is expressed by the Clausius-Clapeyron relation:22)
| \begin{equation} \frac{d\sigma_{0}}{dT} = - \frac{\Delta S}{\varepsilon_{\textit{tr}} \cdot V_{m}}, \end{equation} | (1) |
| \begin{equation} \sigma_{\textit{Ms}} = \frac{(T - M_{s}) \cdot \Delta S}{\varepsilon_{\textit{tr}} \cdot V_{m}}, \end{equation} | (2) |
| \begin{equation} \sigma_{\textit{Af}} = \frac{(T - A_{f}) \cdot \Delta S}{\varepsilon_{\textit{tr}} \cdot V_{m}}, \end{equation} | (3) |
| \begin{equation} \sigma_{\textit{hys}} = - \frac{\Delta S}{\varepsilon_{\textit{tr}} \cdot V_{m}} \times (A_{f} - M_{s}). \end{equation} | (4) |
The calculated σMs and σAf lines are shown in Fig. 4(a). The σMs and σAf well agree with the calculation in samples A, B, and D, but they are lower than the calculation in samples C and E. Therefore, the critical stresses are plotted as a function of the calculated transformation strain εtr in Fig. 4(b). It is found that the difference in σMs between the experiments and calculation is within several tens of megapascal for all the samples but that the experimental σAf and σAf-low values are much lower than those from the calculation.
Figure 4(c) depicts the stress hysteresis of superelasticity σhys defined as σMs − σAf as a function of the calculated transformation strain εtr with the calculation using eq. (4). The maximum σhys-max and minimum σhys are plotted for samples C and E. Overall, the σhys of Cu–Al–Mn is smaller than that in Ti–Ni alloy24) and Fe-based alloy25–28) but similar to that in Cu–Al–Ni alloy.17,29) The experimental results in samples A, B, and D are close to those from the calculation. It has been reported that the stress hysteresis increases and shape recoverability decreases by subgrains in Fe–Mn–Al–Ni–Ti superelastic alloy,20) but the effect of the subgrains is not obviously observed in the present Cu–Al–Mn alloy. Although the minimum σhys of samples C and E is relatively close to the calculated value, the maximum σhys-max is noticeably larger. This wide hysteresis is mainly caused by the low stress of the reverse transformation during unloading.
3.4 In situ observation of stress-induced martensitic transformationTo reveal the reason for the anomalously wide hysteresis, the microstructure of the martensite of sample D with normal hysteresis and sample C with wide hysteresis was investigated by in situ observation of the surface relief during the tensile tests. The result for sample D with normal hysteresis is shown in Fig. 5. The stress-induced forward martensitic transformation proceeds by formation and growth of a single martensite variant in the loading process and the variant shrinks in the unloading process. In contrast, in sample C with wide hysteresis, three variants are recognized during loading and they reversely transformed to the parent phase during unloading, as shown in Fig. 6. A moderate slope is seen in the stress plateau in the loading process of sample C (Fig. 6). This means the resistance for the movement of the habit plane, which is caused by the fact that the different variants grow and face each other during loading. Dislocations are probably introduced at the variant interfaces in such circumstances. Upon unloading, the dislocations can pin the movement of the interfaces, and the stress is lowered and the stress-strain curve is serrated, as shown in Fig. 6. The induction of the multi-variants may result in a superelastic strain slightly lower than that of the calculated transformation train.
In situ observation of stress-induced forward and reverse martensitic transformation in sample D with normal stress hysteresis.
In situ observation of stress-induced forward and reverse martensitic transformation in sample C with wide stress hysteresis.
Trace analysis was conducted for samples D and C. The habit plane of Cu–Al–Mn has been estimated by the phenomenological theory to be {0.1555 −0.7196 −0.6768}.21) Figure 7(a) and 7(b) shows the normal directions of the possible 24 habit planes of samples D and C, respectively. The habit plane traces are observed in Figs. 5 and 6 and their normal lines are also shown in Figs. 7(a) and 7(b). Here, the Schmid factor m is as follows:
| \begin{equation} m = \cos\chi \cos\lambda, \end{equation} | (5) |
Dependence of the number of variants with the largest Schmid factors on loading direction.
The superelasticity of Cu–17Al–11.4Mn single crystals obtained by cyclic heat treatment was investigated by tensile tests. Basically, the plateau strain is in agreement with the transformation strain calculated from the shape strain and the stress hysteresis also agrees with the estimation from the thermal hysteresis and the Clausius-Clapeyron relationship, but the plateau strain is slightly smaller and the stress hysteresis is abnormally wide due to low reverse transformation stress in some samples. In situ observation of the surface relief showed that one martensite variant grows and shrinks during loading and unloading, in the sample with a normal hysteresis but that three variants are induced in the sample with wide hysteresis. The multi-variant state is considered to be related to the wide hysteresis. The multiple variants inhibit the growth of each variant during loading, and dislocations are probably introduced at the interfaces, which can be obstacles for the shrinkage of the variants during unloading and result in lower stress. Therefore, the stress hysteresis becomes wide. In particular, the reverse transformation during unloading is greatly inhibited. The trace analysis indicates that the induced variants have the largest, second-largest, or large Schmid factors. It is suggested that multi-variants can be induced when the loading direction is on the stereo-triangle sides, such as ⟨001⟩ to ⟨101⟩, ⟨001⟩ to ⟨111⟩, and ⟨101⟩ to ⟨111⟩, based on Schmid’s law. Actually, the samples elongated along orientations on the sides of ⟨001⟩ to ⟨111⟩ and ⟨101⟩ to ⟨111⟩ have a wide hysteresis in this study, and therefore, the multi-variants are induced and the stress hysteresis is anomalously wide.
This work was supported by the Grants-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (Grant Numbers 17H03405 and 15H05766).
