Results of the bending tests are shown in Figure 3. In Figure 3, column (i) indicates the specimens after bending deformation (stage i) while column (ii) suggests the shape recovery of the specimens upon heating (stage ii). Judging from the optical images, an obvious shape recovery was found in the Ti–4Au–20Ta alloy (Figure 3a); on the contrary, the shape recovery rate of the Ti–4Au–30Ta alloy (Figure 3b) was relatively faint. The shape recovery rates of (a) the Ti–4Au–20Ta alloy and (b) the Ti–4Au–30Ta alloy were determined to be 10% and 30%, respectively. Since the apparent phase of the (a) Ti–4Au– 20Ta alloy was determined to be the single parent β–phase via the X–ray diffraction observation (Figure 1a) and the microstructure observation (Figure 2a), it thus could be deduced that the shape recovery behavior of the Ti–4Au–20Ta alloy was brought by the stress–induced martensite transformation (SIMT) during bending deformation (stage i) and followed by its backward transformation upon heating (stage ii). Results of the bending tests are shown in Figure 3. In Figure 3, column (i) indicates the specimens after bending deformation (stage i) while column (ii) suggests the shape recovery of the specimens upon heating (stage ii). Judging from the optical images, an obvious shape recovery was found in the Ti–4Au–20Ta alloy (Figure 3a); on the contrary, the shape recovery rate of the Ti–4Au–30Ta alloy (Figure 3b) was relatively faint. The shape recovery rates of (a) the Ti–4Au–20Ta alloy and (b) the Ti–4Au–30Ta alloy were determined to be 10% and 30%, respectively. Since the apparent phase of the (a) Ti–4Au–20Ta alloy was determined to be the single parent β–phase via the X–ray diffraction observation (Figure 1a) and the microstructure observation (Figure 2a), it thus could be deduced that the shape recovery behavior of the Ti–4Au–20Ta alloy was brought by the stress–induced martensite transformation (SIMT) during bending deformation (stage i) and followed by its backward transformation upon heating (stage ii). Results of the bending tests are shown in Figure 3. In Figure 3, column (i) indicates the specimens after bending deformation (stage i) while column (ii) suggests the shape recovery of the specimens upon heating (stage ii). Judging from the optical images, an obvious shape recovery was found in the Ti–4Au–20Ta alloy (Figure 3a); on the contrary, the shape recovery rate of the Ti–4Au–30Ta alloy (Figure 3b) was relatively faint. The shape recovery rates of (a) the Ti–4Au–20Ta alloy and (b) the Ti–4Au–30Ta alloy were determined to be 10% and 30%, respectively. Since the apparent phase of the (a) Ti–4Au– 20Ta alloy was determined to be the single parent β–phase via the X–ray diffraction observation (Figure 1a) and the microstructure observation (Figure 2a), it thus could be deduced that the shape recovery behavior of the Ti–4Au–20Ta alloy was brought by the stress–induced martensite transformation (SIMT) during bending deformation (stage i) and followed by its backward transformation upon heating (stage ii).

**Figure 3.** Bending tests of the (**a**) Ti–4Au–20Ta alloy and the (**b**) Ti–4Au–30Ta alloy for the examinations of the shape memory effect and shape recovery rates. Stage (**i**) corresponds to after bending deformation while stage (**ii**) indicates shape recovery upon heating process. **Figure 3.** Bending tests of the (**a**) Ti–4Au–20Ta alloy and the (**b**) Ti–4Au–30Ta alloy for the examinations of the shape memory effect and shape recovery rates. Stage (**i**) corresponds to after bending deformation while stage (**ii**) indicates shape recovery upon heating process. **Figure 3.** Bending tests of the (**a**) Ti–4Au–20Ta alloy and the (**b**) Ti–4Au–30Ta alloy for the examinations of the shape memory effect and shape recovery rates. Stage (**i**) corresponds to after bending deformation while stage (**ii**) indicates shape recovery upon heating process.

Similar to the (a) Ti–4Au–20Ta alloy, the apparent phase of the (b) Ti–4Au–30Ta alloy was also the parent β–phase before deformation; however, precipitates of Ti3Au compound was also found in the Ti–4Au–30Ta alloy (Figures 1b and 2b–e). The deteriorated shape recovery rate of the (b) Ti–4Au–30Ta alloy could be attributed to the suppression of the phase transformation by the Ti3Au precipitates during bending deformation and shape

recovery. These results are in accordance with those in the literature [38]. In addition to the inhibition of the phase transformation by the Ti3Au precipitates, the relatively low shape recovery rates (i.e., 10% and 30%) of these two alloys could also be ascribed to the plastic deformation, which was introduced into the alloys during bending deformation. [38]. In addition to the inhibition of the phase transformation by the Ti3Au precipitates, the relatively low shape recovery rates (i.e., 10% and 30%) of these two alloys could also be ascribed to the plastic deformation, which was introduced into the alloys during bending deformation.

Similar to the (a) Ti–4Au–20Ta alloy, the apparent phase of the (b) Ti–4Au–30Ta alloy was also the parent β–phase before deformation; however, precipitates of Ti3Au compound was also found in the Ti–4Au–30Ta alloy (Figure 1(b) and Figure 2(b)–(e)). The deteriorated shape recovery rate of the (b) Ti–4Au–30Ta alloy could be attributed to the suppression of the phase transformation by the Ti3Au precipitates during bending deformation and shape recovery. These results are in accordance with those in the literature

#### *3.5. Continuous Tensile Tests 3.5. Continuous Tensile Tests*

Stress–strain (SS; *σ*–*ε*) curves of the (a) Ti–4Au–20Ta alloy and the (b) Ti–4Au–30Ta alloy by the continuous tensile tests are shown in Figure 4. The cross symbols at the end of the SS curves suggest the fractures of the specimens. The strain until fracture of the (a) Ti–4Au–20Ta alloy was at approximately 17%, which was almost twice larger than that of the (b) Ti–4Au–30Ta alloy (i.e., deformation strain at approximately 9%), showed high elongation. The different ductility of these two alloys could be elaborated through the following reasons. Stress–strain (SS; *σ*–*ε*) curves of the (a) Ti–4Au–20Ta alloy and the (b) Ti–4Au–30Ta alloy by the continuous tensile tests are shown in Figure 4. The cross symbols at the end of the SS curves suggest the fractures of the specimens. The strain until fracture of the (a) Ti–4Au–20Ta alloy was at approximately 17%, which was almost twice larger than that of the (b) Ti–4Au–30Ta alloy (i.e., deformation strain at approximately 9%), showed high elongation. The different ductility of these two alloys could be elaborated through the following reasons.

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**Figure 4.** Stress–strain (SS) curves of the (**a**) Ti–4Au–20Ta alloy and the (**b**) Ti–4Au–30Ta alloy via the continuous tensile tests. The cross symbols at the end of the curves suggest fractures of the specimens. A stress plateau in the (**a**) Ti–4Au–20Ta alloy was indicated by the vertical dashed lines and the horizontal solid arrows. **Figure 4.** Stress–strain (SS) curves of the (**a**) Ti–4Au–20Ta alloy and the (**b**) Ti–4Au–30Ta alloy via the continuous tensile tests. The cross symbols at the end of the curves suggest fractures of the specimens. A stress plateau in the (**a**) Ti–4Au–20Ta alloy was indicated by the vertical dashed lines and the horizontal solid arrows.

Firstly, it was worth noticing that in the (a) Ti–4Au–20Ta alloy, there is a clear stress plateau, which is indicated by the vertical dashed lines and the solid horizontal line with arrows. Given that the apparent phase of the (a) Ti–4Au–20Ta alloy is the parent β–phase at the testing temperature (i.e., RT) (Figure 1(a)), the stress plateau could be attributed to the stress–induced martensitic transformation (SIMT) [38,41,43]. The first yielding could be attributed to the onset of the SIMT, while the second yielding could be ascribed to the commencement of the plastic deformation [38,41,43]. On the other hand, almost no stress plateau was found in the case of the (b) Ti–4Au–30Ta alloy. Therefore, the relatively high elongation of the (a) Ti–4Au–20Ta alloy could be ascribed to the SIMT. It is also worth mentioning that the SIMT found in the Ti–4Au–20Ta alloy in Figure 4(a) corresponds well with the result of the bending test in section 3.4. While the Ti–4Au–30Ta alloy, which had a lower shape recovery rate upon heating (Figure 3b), showed almost no stress plateau in Figure 4b. Firstly, it was worth noticing that in the (a) Ti–4Au–20Ta alloy, there is a clear stress plateau, which is indicated by the vertical dashed lines and the solid horizontal line with arrows. Given that the apparent phase of the (a) Ti–4Au–20Ta alloy is the parent β–phase at the testing temperature (i.e., RT) (Figure 1a), the stress plateau could be attributed to the stress–induced martensitic transformation (SIMT) [38,41,43]. The first yielding could be attributed to the onset of the SIMT, while the second yielding could be ascribed to the commencement of the plastic deformation [38,41,43]. On the other hand, almost no stress plateau was found in the case of the (b) Ti–4Au–30Ta alloy. Therefore, the relatively high elongation of the (a) Ti–4Au–20Ta alloy could be ascribed to the SIMT. It is also worth mentioning that the SIMT found in the Ti–4Au–20Ta alloy in Figure 4a corresponds well with the result of the bending test in Section 3.4. While the Ti–4Au–30Ta alloy, which had a lower shape recovery rate upon heating (Figure 3b), showed almost no stress plateau in Figure 4b.

Secondly, the Ti3Au intermetallic compound, which was merely found in the (b) Ti– 4Au–30Ta alloy (Figures 1b and 2b–e), is known as a brittle phase [44]. The ductility of the (b) Ti–4Au–30Ta alloy was thus deteriorated by the formation of the Ti3Au precipitates. On the contrary, the (a) Ti–4Au–20Ta alloy showed relatively high deformation strain before fracture since no brittle Ti3Au precipitates were found in this alloy (Figures 1a and 2a).

To sum up, the relatively high elongation of the (a) Ti–4Au–20Ta alloy could be attributed to the occurrence of SIMT and lack of Ti3Au precipitates. On the other hand, the relatively low elongation of the (b) Ti–4Au–30Ta alloy was due to the Ti3Au precipitates and almost free of SIMT during deformation. To sum up, the relatively high elongation of the (a) Ti–4Au–20Ta alloy could be attributed to the occurrence of SIMT and lack of Ti3Au precipitates. On the other hand, the relatively low elongation of the (b) Ti–4Au–30Ta alloy was due to the Ti3Au precipitates and almost free of SIMT during deformation.

Secondly, the Ti3Au intermetallic compound, which was merely found in the (b) Ti– 4Au–30Ta alloy (Figures 1b,2b–e), is known as a brittle phase [44]. The ductility of the (b) Ti–4Au–30Ta alloy was thus deteriorated by the formation of the Ti3Au precipitates. On the contrary, the (a) Ti–4Au–20Ta alloy showed relatively high deformation strain before fracture since no brittle Ti3Au precipitates were found in this alloy (Figures 1a,2a).

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However, reverse to the ductility, comparatively high strength was observed in the (b) Ti–4Au–30Ta alloy than that of the (a) Ti–4Au–20Ta alloy in the continuous tensile tests (Figure 4). It was found that the ultimate tensile strength (UTS) was at approximately 737 MPa for the (b) Ti–4Au–30Ta alloy and at approximately 600 MPa for the (a) Ti–4Au– 20Ta alloy. This could be simply explained by the precipitation–hardening effect brought from the precipitates of the Ti3Au compound and also the solution–hardening effect brought by the Ta addition as the third element. However, reverse to the ductility, comparatively high strength was observed in the (b) Ti–4Au–30Ta alloy than that of the (a) Ti–4Au–20Ta alloy in the continuous tensile tests (Figure 4). It was found that the ultimate tensile strength (UTS) was at approximately 737 MPa for the (b) Ti–4Au–30Ta alloy and at approximately 600 MPa for the (a) Ti–4Au– 20Ta alloy. This could be simply explained by the precipitation–hardening effect brought from the precipitates of the Ti3Au compound and also the solution–hardening effect brought by the Ta addition as the third element.

#### *3.6. Functional Mapping 3.6. Functional Mapping*

A functional mapping, which reveals (a) yielding stress (black squares), (b) ultimate tensile strength (UTS) (red circles), and (c) fracture strain (blue triangles) as a function of Ta concentration in the alloys, is shown as Figure 5. It is necessary to mention that for the purposes of completeness and comparison, the binary Ti–4Au alloy was cited from our preliminary research [35] and plotted in Figure 5. It is obvious that both the (a) yielding stress and the (b) UTS increased monotonically with Ta addition concentration. Similar to the explanation in Section 3.5, this enhancement in strength could be attributed to the solid–solution strengthening effect of the introduction of Ta element and the precipitation hardening effect caused by the Ti3Au precipitates. Slip of dislocation (i.e., plastic deformation) was inhibited by the introduction of the Ta impurity and the Ti3Au precipitates. Opposite to the strength, fracture strain (Figure 5c) of the specimens decreased with the introduction of Ta concentration due to the precipitation of the brittle Ti3Au intermetallic compound. A functional mapping, which reveals (a) yielding stress (black squares), (b) ultimate tensile strength (UTS) (red circles), and (c) fracture strain (blue triangles) as a function of Ta concentration in the alloys, is shown as Figure 5. It is necessary to mention that for the purposes of completeness and comparison, the binary Ti–4Au alloy was cited from our preliminary research [35] and plotted in Figure 5. It is obvious that both the (a) yielding stress and the (b) UTS increased monotonically with Ta addition concentration. Similar to the explanation in section 3.5, this enhancement in strength could be attributed to the solid–solution strengthening effect of the introduction of Ta element and the precipitation hardening effect caused by the Ti3Au precipitates. Slip of dislocation (i.e., plastic deformation) was inhibited by the introduction of the Ta impurity and the Ti3Au precipitates. Opposite to the strength, fracture strain (Figure 5c) of the specimens decreased with the introduction of Ta concentration due to the precipitation of the brittle Ti3Au intermetallic compound.

**Figure 5.** Functional mapping of (**a**) yielding stress (black squares), (**b**) ultimate tensile strength (UTS) (red circles), and (**c**) fracture strain (blue triangles) as a function of the Ta addition concentration in the alloys. (Left *y*–axis: stress (MPa); Right *y*–axis: fracture strain (%)) (Note that the results of the binary Ti–4Au alloy was cited from our preliminary research [35]). **Figure 5.** Functional mapping of (**a**) yielding stress (black squares), (**b**) ultimate tensile strength (UTS) (red circles), and (**c**) fracture strain (blue triangles) as a function of the Ta addition concentration in the alloys. (Left *y*–axis: stress (MPa); Right *y*–axis: fracture strain (%)) (Note that the results of the binary Ti–4Au alloy was cited from our preliminary research [35]).

#### *3.7. Cyclic Loading–Unloading Tensile Tests 3.7. Cyclic Loading–Unloading Tensile Tests*

The cyclic loading–unloading tests of the (a) Ti–4Au–20Ta alloy and the (b) Ti–4Au– 30Ta alloy are shown in Figure 6. Overall, it was found that the (a) Ti–4Au–20Ta alloy which exhibited slight pseudoelasticity (PE), showed slight shape recovery during unloading. While the (b) Ti–4Au–30Ta alloy showed almost no shape recovery during unloading in the cyclic loading–unloading tests at RT. Therefore, it could be deduced that the austenite

transformation start temperature (*A*s) is higher than the operation temperature (i.e., RT). In addition, the vanished shape recovery in the (b) Ti–4Au–30Ta alloy could be ascribed to the inhibition of the Ti3Au precipitates. On the other hand, the slight shape recovery in the (a) Ti–4Au–20Ta alloy could be attributed to the pseudoelasticity via the reorientation of martensitic variants, which is commonly observed in the martensite phase [45–47]. Moreover, similar to the results from the continuous tensile tests (Figure 4) in Section 3.5, the (b) Ti–4Au–30Ta alloy showed improved strength than that of the (a) Ti–4Au–20Ta alloy. ture (i.e., RT). In addition, the vanished shape recovery in the (b) Ti–4Au–30Ta alloy could be ascribed to the inhibition of the Ti3Au precipitates. On the other hand, the slight shape recovery in the (a) Ti–4Au–20Ta alloy could be attributed to the pseudoelasticity via the reorientation of martensitic variants, which is commonly observed in the martensite phase [45–47]. Moreover, similar to the results from the continuous tensile tests (Figure 4) in section 3.5, the (b) Ti–4Au–30Ta alloy showed improved strength than that of the (a) Ti– 4Au–20Ta alloy.

The cyclic loading–unloading tests of the (a) Ti–4Au–20Ta alloy and the (b) Ti–4Au– 30Ta alloy are shown in Figure 6. Overall, it was found that the (a) Ti–4Au–20Ta alloy which exhibited slight pseudoelasticity (PE), showed slight shape recovery during unloading. While the (b) Ti–4Au–30Ta alloy showed almost no shape recovery during unloading in the cyclic loading–unloading tests at RT. Therefore, it could be deduced that the austenite transformation start temperature (*A*s) is higher than the operation tempera-

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**Figure 6.** Cyclic loading–unloading tensile tests of the (**a**) Ti–4Au–20Ta alloy and the (**b**) Ti–4Au– 30Ta alloy at RT under ambient. **Figure 6.** Cyclic loading–unloading tensile tests of the (**a**) Ti–4Au–20Ta alloy and the (**b**) Ti–4Au–30Ta alloy at RT under ambient.

For further analysis of the pseudoelasticity, every cycle in the Ti–4Au–20Ta alloy was detached and the stress for SIMT (i.e., first–yielding stress), which is shown in Figure 7a, was read from every cycle of the cyclic loading–unloading tensile test (Figure 6a). During the cyclic tensile test, dislocations, which increased the internal stress, was introduced into the specimen. The martensite phase was stabilized by the elevated internal stress; as a result, the external stress for the SIMT (*σ*SIMT) was reduced accordingly (Figure 7a). This phenomenon was in good agreement with that in the literature [41]. For further analysis of the pseudoelasticity, every cycle in the Ti–4Au–20Ta alloy was detached and the stress for SIMT (i.e., first–yielding stress), which is shown in Figure 7a,was read from every cycle of the cyclic loading–unloading tensile test (Figure 6a). During the cyclic tensile test, dislocations, which increased the internal stress, was introduced into the specimen. The martensite phase was stabilized by the elevated internal stress; as a result, the external stress for the SIMT (*σ*SIMT) was reduced accordingly (Figure 7a). This phenomenon was in good agreement with that in the literature [41].

The ninth cycle in the cyclic loading–unloading tensile test of the Ti–4Au–20Ta specimen is also shown in Figure 7b. It is obvious that during unloading of externally applied stress, there was a slight shape recovery, which is at approximately 0.5%, was brought from the pseudoelasticity. The shape recovery originated from the pseudoelasticity was determined by reading strain difference between the overall recovery strain after fully unloading and the strain produced by the elastic shape recovery. Further explanations for the specific terms are shown and explained by the illustration in Figure 7d.

the specific terms are shown and explained by the illustration in Figure 7d.

**Figure 7.** (**a**) Stress for the first yielding stress (i.e., stress for SIMT) of the Ti–4Au–20Ta alloy, (**b**) the ninth cycle in the cyclic loading–unloading tensile test of the Ti–4Au–20Ta alloy, (**c**) the ninth cycle in the cyclic loading–unloading tensile test of the Ti–4Au–30Ta alloy, and (**d**) the illustration for the explanations of the terms in the SS curve. Where *ε*A indicates the total applied strain, *ε*<sup>E</sup> suggests the elastic shape recovery strain, *ε*PE corresponds to shape recovery strain brought by pseudoelasticity, and *ε*R represents the remaining strain after unloading. **Figure 7.** (**a**) Stress for the first yielding stress (i.e., stress for SIMT) of the Ti–4Au–20Ta alloy, (**b**) the ninth cycle in the cyclic loading–unloading tensile test of the Ti–4Au–20Ta alloy, (**c**) the ninth cycle in the cyclic loading–unloading tensile test of the Ti–4Au–30Ta alloy, and (**d**) the illustration for the explanations of the terms in the SS curve. Where *ε*<sup>A</sup> indicates the total applied strain, *ε*<sup>E</sup> suggests the elastic shape recovery strain, *ε*PE corresponds to shape recovery strain brought by pseudoelasticity, and *ε*<sup>R</sup> represents the remaining strain after unloading.

The ninth cycle in the cyclic loading–unloading tensile test of the Ti–4Au–20Ta specimen is also shown in Figure 7b. It is obvious that during unloading of externally applied stress, there was a slight shape recovery, which is at approximately 0.5%, was brought from the pseudoelasticity. The shape recovery originated from the pseudoelasticity was determined by reading strain difference between the overall recovery strain after fully unloading and the strain produced by the elastic shape recovery. Further explanations for

On the other hand, almost no shape recovery was found in the Ti–4Au–30Ta alloy (Figure 7c) during unloading of the externally applied stress. The aforementioned Ti– 4Au–20Ta alloy and Ti–4Au–30Ta alloy results are in good accordance with those in the bending tests (Figure 3) and the continuous tensile tests (Figure 4). An illustration for the explanations of the specific terms are shown in Figure 7d. In Figure 7d, *ε*A indicates the total applied strain, *ε*E suggests the elastic shape recovery strain, *ε*PE corresponds to shape recovery strain brought by pseudoelasticity, and *ε*R represents the remaining strain after unloading. On the other hand, almost no shape recovery was found in the Ti–4Au–30Ta alloy (Figure 7c) during unloading of the externally applied stress. The aforementioned Ti– 4Au–20Ta alloy and Ti–4Au–30Ta alloy results are in good accordance with those in the bending tests (Figure 3) and the continuous tensile tests (Figure 4). An illustration for the explanations of the specific terms are shown in Figure 7d. In Figure 7d, *ε*<sup>A</sup> indicates the total applied strain, *ε*<sup>E</sup> suggests the elastic shape recovery strain, *ε*PE corresponds to shape recovery strain brought by pseudoelasticity, and *ε*<sup>R</sup> represents the remaining strain after unloading.

This study worked on the Ti–4Au–20Ta alloy and Ti–4Au–30Ta alloy for the preliminary screening of the Ti–Au–Ta–based shape memory alloys. Some of the Ti–Au–based studies have already been carried out by our research group [35,36,38,41,43] while some of the Ti–Au–based studies are now under investigations and preparations. Further results concerning the Ti–Au–based shape memory alloys will be published in the future by our research group. This study worked on the Ti–4Au–20Ta alloy and Ti–4Au–30Ta alloy for the preliminary screening of the Ti–Au–Ta–based shape memory alloys. Some of the Ti–Au–based studies have already been carried out by our research group [35,36,38,41,43] while some of the Ti–Au–based studies are now under investigations and preparations. Further results concerning the Ti–Au–based shape memory alloys will be published in the future by our research group.

#### **4. Conclusions 4. Conclusions**

For the biomedical applications in this work, the Ti–4Au–20Ta and the Ti–4Au–30Ta alloys were prepared by physical metallurgy techniques and their phase constituents, composition analysis, mechanical behaviors, and functional properties, such as shape memory effect (SME) and pseudoelasticity (PE), have been studied. The important findings are listed in the following points. For the biomedical applications in this work, the Ti–4Au–20Ta and the Ti–4Au–30Ta alloys were prepared by physical metallurgy techniques and their phase constituents, composition analysis, mechanical behaviors, and functional properties, such as shape memory effect (SME) and pseudoelasticity (PE), have been studied. The important findings are listed in the following points.

the Ti–4Au–20Ta alloy. On the other hand, no obvious two–stage yielding was found in the Ti–4Au–30Ta alloy due to the inhibition of SIMT from the Ti3Au intermetallic compound.

**Author Contributions:** Conceptualization, T.I. and H.H.; data curation, W.-T.C. and K.F.; formal analysis, W.-T.C., K.F., M.T. and H.H.; funding acquisition, M.T. and H.H.; investigation, W.-T.C., K.F., M.T., T.I. and H.H.; methodology, T.I. and H.H.; project administration, M.T. and H.H.; resources, M.T., T.I. and H.H.; software, W.-T.C. and K.F.; supervision, W.-T.C., Akira Umise, M.T., T.I. and H.H.; validation, W.-T.C., M.T., T.I. and H.H.; visualization, W.-T.C.; writing–original draft, W.-T.C.; writing–review & editing, K.F., M.T. and H.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work is supported by the Tokyo Tech Fund (ASUNARO Grant) and Japan Society for the Promotion of Science (JSPS) (KAKENHI 19H02417 and KAKENHI 20K20544).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** All data contained within the article.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

## *Article* **Strain Rate Effect upon Mechanical Behaviour of Hydrogen-Charged Cycled NiTi Shape Memory Alloy**

**Fehmi Gamaoun 1,2**

**Abstract:** The rate dependence of thermo-mechanical responses of superelastic NiTi with different imposed strain rates after cycling from 1 to 50 cycles under applied 10−<sup>5</sup> s −1 , 10−<sup>4</sup> s <sup>−</sup><sup>1</sup> and 10−<sup>3</sup> s −1 strain rates, immersion for 3 h and ageing has been investigated. The loaded and unloaded as-received NiTi alloy under an imposed strain of 7.1% have shown an increase in the residual deformation at zero stress with an increase in strain rates. It has been found that after 13 cycles and hydrogen charging, the amount of absorbed hydrogen (291 mass ppm) was sufficient to cause the embrittlement of the tensile loaded NiTi alloy with 10−<sup>5</sup> s −1 . However, no premature fracture has been detected for the imposed strain rates of 10−<sup>4</sup> s <sup>−</sup><sup>1</sup> and 10−<sup>3</sup> s −1 . Nevertheless, after 18 cycles and immersion for 3 h, the fracture has occurred in the plateau of the austenite martensite transformation during loading with 10−<sup>4</sup> s −1 . Despite the higher quantity of absorbed hydrogen, the loaded specimen with a higher imposed strain rate of 10−<sup>3</sup> s <sup>−</sup><sup>1</sup> has kept its superelasticity behaviour, even after 20 cycles. We attribute such a behaviour to the interaction between the travelling distance during the growth of the martensitic domains while introducing the martensite phase and the amount of diffused hydrogen.

**Keywords:** shape memory alloys; superelastic; hydrogen; cyclic loading; martensite variants

### **1. Introduction**

NiTi Shape Memory Alloys (SMAs) have been employed on a large scale within various engineering applications such as Micro-Electro-Mechanical Systems (MEMS), aerospace structures [1,2], and biomedical applications [3,4]. The success of these applications hinges on their capability of having an excellent combination of several properties, including superelasticity, corrosion resistance, and biocompatibility. Moreover, due to its larger flexibility, the equiatomic superelastic NiTi archwire turns to be one integral part of orthodontic treatment because of exerting a relatively constant force in the range of tooth movement. However, the NiTi alloy is found to be very sensitive to the hydrogen diffusion caused by adding fluoride to prophylactic agents and toothpaste in the oral cavity [5–7]. In fact, the diffusion of hydrogen is a main environmental cause for premature fractures of the superelastic NiTi alloys [8,9].

We have shown, after immersion, that the NiTi alloy fractures in a brittle manner for different strain rates [10,11] and for varied immersion time [12,13]. In fact, at room temperature and after immersion in a 0.9% NaCl aqueous solution, while utilizing a varied current density of 5, 10, and 20 A/m<sup>2</sup> from 2 to 24 h, embrittlement takes place after ageing at room temperature rather than immediately after hydrogen charging. This behaviour suggests that when hydrogen diffuses to an entire alloy, not concentrated just close to the surface, it can most likely obstruct the stress-induced martensite phase (B19 phase). Ogawa et al. [14] showed by Thermal Desorption Analysis (TDA); i.e., in case the diffused hydrogen exceeded 50–200 mass ppm, that the mechanical SMA characteristics could change, hence the appearance of premature failure. The superelastic NiTi archwire embrittlement, after

**Citation:** Gamaoun, F. Strain Rate Effect upon Mechanical Behaviour of Hydrogen-Charged Cycled NiTi Shape Memory Alloy. *Materials* **2021**, *14*, 4772. https://doi.org/10.3390/ ma14164772

Academic Editor: Carmine Maletta

Received: 6 July 2021 Accepted: 18 August 2021 Published: 23 August 2021

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**Copyright:** © 2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

hydrogen-absorption, was greatly linked to the transformation of stress-induced austenitemartensite [15]. This behaviour was attributed to the accumulation of hydrogen atoms, preferentially within regions that contain continual deficiencies, because of being trapped by retained martensite plates and dislocations, forming an obstacle which would cause fracture when the martensite domains were forced to pass across these boundaries [11]. In several studies [16,17], permanent defects could be obtained by cyclic deformation. In [18], the authors indicated that the pseudo-elastic hysteresis loops would decrease as the number of cycles increased and the strain hardening slope grew. B. Kockar et al. [19] mentioned that the main reason for the cyclic instability of the NiTi SMAs' pseudoelastic response was the local plastic accommodation of incompatibility between the B2 parent phase and the B19 phase during transformation. The authors in [20] indicated that during thermomechanical cycling, the variant interfaces would move backward and forward, while transformationinduced defects such as dislocations would build up and obstruct any interface mobility in the subsequent cycles. As a result, accumulations of retained martensite domains and local residual stresses would eventually affect the macroscopic superelastic behaviour of the NiTi alloy. In addition, we note that the effect of the strain rate on the cyclic deformations of superelastic NiTi alloys was studied by some experimental connotations [21–23]. It was found that rate dependence mainly resulted from the interaction between internal heat production (due to the mechanic dissipation and transformation latent heat) as well as the heat exchange with the external environment. Moreover, during cycling, the higher the strain rate the bigger the number of martensite domains in the austenite-martensite transformation.

Therefore, as the NiTi archwires are subjected to varied mechanical cycling before insertion in the oral cavity, this study aims to determine the hydrogen effect on tensile tests of the superelastic NiTi alloy under different imposed strain rates. The effect of the residual deformation after cycling with 10−<sup>5</sup> s −1 , 10−<sup>4</sup> s <sup>−</sup><sup>1</sup> and 10−<sup>3</sup> s <sup>−</sup><sup>1</sup> before immersion and tensile testing will be discussed.

#### **2. Experimental Procedure**

A commercial superelastic Ni-Ti (50.9 (at.%) Ni–49.1 (at.%) Ti, from Forestdent Co.), is used in this study. We obtained the heat treatment material's transformation temperature from the differential scanning calorimetry test at a scan rate of 10 ◦C/min. The start and finish temperatures of the martensite transformation (M<sup>s</sup> and M<sup>f</sup> ) are equal to −8 and−26 ◦C, respectively; and the start and finish temperatures of the austenite transformation (A<sup>s</sup> and A<sup>f</sup> ) are equal to −11 ◦C and −4 ◦C, respectively. The initial Young's modulus of the austenite and martensite phases were, respectively, 24 GPa and 12 GPa. During the mechanical tensile tests, we used rectangular specimens that had a gage length of 20 mm and across-sectional dimension of 0.64 <sup>×</sup> 0.43 mm<sup>2</sup> .

Cyclic tensile tests, from 1 to 50, and a uniaxial tensile test at room temperature were carried out on a standard Instron screw-driven mechanical testing 5566-type machine (Figure 1a). With the aim of studying the loading rate influence up on the NiTi archwire's superelastic behaviour, we utilized the10−<sup>5</sup> s −1 , 10−<sup>4</sup> s <sup>−</sup><sup>1</sup> and 10−<sup>3</sup> s −1 strain rates. The imposed strain of 7.1% was performed for the applied cyclic tensile test. In order to run the test, 30 mm was cut from the commercial superelastic NiTi archwire (Figure 1b) and clamped between the bottom and top flat grips of the Instron machine (5 mm distance) (Figure 1c). The strain was measured as across-head overall displacement in addition to a 20 mm initial gauge length. A brand-new specimen was used after each monotonic or cyclic test.

**Figure 1.** Loading protocol of the monotonic and cyclic loading: (**a**) Schematic representation of the Instron tensile machine, (**b**) used part of the as-received alloy, and (**c**) clamping method of the NiTi archwire.

Specimens' hydrogen charging was done through the immersion in a 0.9% NaCl solution. This was also performed for 3 h at room temperature at a 10 A/m<sup>2</sup> current density. A Direct-Current (DC) power supply was used for immersion, as shown in Figure 2. Circular platinum and the NiTi archwire were based on the 0.9% NaCl solution as the anode and the cathode, respectively. The current density controlled the generated gaseous hydrogen on the surface of the sample. Before immersion, samples were polished with a No. 600-grit SiC paper. After that, it was ultrasonically washed for 5 min in acetone. To homogeneously distribute the diffused hydrogen after immersion, we would age the specimens for one day in air at room temperature [24,25].

**Figure 2.** (**a**) Scheme of hydrogen charging (**b**) setup by electrolysis.

After immersion for 3 h and ultrasonic cleaning with acetone for 5 min, the amount of desorbed hydrogen was measured by TDA through the use of a gas chromatograph. This latter was actually calibrated under 10−<sup>6</sup> Pa of vacuum with a standard mixture of argon gases and hydrogen. Moreover, we employ the high-purity argon as a carrier gas. TDA was performed on a 20 mm NiTi alloy total length. The sampling time of the carrier gas to the gas chromatograph was 5-min intervals at a heating rate of 100 ◦C/h. All TDA examinations were carried out after 24 h hydrogen charging. The total amount of hydrogen

within the specimen was determined to be the sum of desorbed hydrogen within peaks of a hydrogen desorption rate [26,27]. At least two analyses have been done for each cyclic condition, and the experimental errors of the absorbed-hydrogen amount have been estimated between 5% and 10%.

#### **3. Results and Discussion**

The non-charged and charged specimens' tensile stress–stain curves for 3 h with the current density of 10 A/m<sup>2</sup> besides annealing for 24 hat room temperature are shown in Figure 3. For strain rates of a non-charged hydrogen specimen between 10−<sup>5</sup> and 10−<sup>3</sup> s −1 , the elastic loading of an austenite parent phase is observed, which is followed by "a plateau" during the austenite-martensite transformation. After that, there follows the elastic deformation of a martensite phase until fracture. It can be seen that the martensite start stress goes up from about 430 MPa to 460 as well as 490 MPa for a strain rate of 10−<sup>5</sup> s −1 to 10−<sup>4</sup> s <sup>−</sup><sup>1</sup> and 10−<sup>3</sup> s −1 , respectively. On the other hand, for the 10−<sup>3</sup> s −1 strain rate, the strain hardening effect of the austenite-martensite transformation goes up.

**Figure 3.** Typical engineering stress–strain curves of superelastic Ni-Ti alloy immersed for 3 h and aged for 24 h at different strain rates of 10−<sup>5</sup> s −1 , 10−<sup>4</sup> s <sup>−</sup><sup>1</sup> and 10−<sup>5</sup> s <sup>−</sup><sup>1</sup> and as-received at 10−<sup>5</sup> s −1 .

The strain rate dependency appears in a clear way during the austenite martensite transformation with the growth of the "plateau" slope. After that, it increases in the martensite start stress. Such a rise could be interpreted by the material's viscoelastic behaviour, and this is because of the friction between the martensite interface variants as well as the strain rate dependency that is actually caused by a thermomechanical NiTibehaviour due to the fact that the austenite-martensite transformation was exothermic [28,29]. Indeed, when the strain rate goes up, an internal heat production is as fast as the strain rate and the latent heat of the specimen is confined in the alloy. Consequently, a quantity of heat cannot be transferred outside of the NiTi alloy since the conduct time is shorter. This enhancement in temperature leads to a rise in the necessary applied load for inducing the martensite phase (Figure 4). Thus, both the amount of the required stress inducing the martensite and the slope of the austenite-martensite transformation will increase [17,30,31].

**Figure 4.** Simplified NiTi phase diagram showing the increase in the martensite starting stress from σ1 to σ<sup>2</sup> when the temperature goes up from T<sup>1</sup> to T2, respectively.

After 4 h of immersion with a 10 A/m<sup>2</sup> current density, Figure 3 illustrates a typical tensile curve for the applied 10−<sup>5</sup> s −1 strain rate. This result shows that the material has conserved its superelastic behaviour and that there has not been any fracture detected. However, compared to the non-immersed alloy in the 0.9% NaCl solution, the NiTi archwire indicates arise in the martensite start stress of about 10 MPa. This phenomenon is attributed to the solid-solution hardening during hydrogen charging [18–32].

Figure 5a depicts the tested specimen's stress–strain curves for 50 cycles at the lowest 10−<sup>5</sup> s −1 strain rate under an imposed strain of 7.1%. This latter represents the end of the plateau of the austenite-martensite transformation of the as-received NiTi archwire (Figure 3). The result highlights that the slope of the austenite-martensite transformation increases in a progressive manner during cycling. On the other hand, the martensite start transformation decreases with the growth of the loading and unloading cycles. This martensite start stress decreases from approximately 430 MPa at cycle 1 to about 310 MPa at cycle20. We can attribute this reduction to the introduction of dislocations and to the residual martensite phase during cycling, which is the main cause for establishing the residual stress [20,33]. Therefore, this residual stress assists the stress-induced transformation during the next loading by enabling martensite bands to activate at a lower macroscopic stress. Cyclic loading and unloading with imposed 10−<sup>4</sup> s <sup>−</sup><sup>1</sup> and 10−<sup>3</sup> s −1 strain rates are represented by Figure 5b,c, respectively. It is clear that the slope of the austenite martensite transformation plateau increases steadily with the number of cycles, besides raising the imposed strain rate. In addition, after 10−<sup>4</sup> s <sup>−</sup><sup>1</sup> and 10−<sup>3</sup> s <sup>−</sup><sup>1</sup> of imposed strain rates, the aforementioned yield stress falls approximately by 80 MPa and 110 MPa, respectively, after 20 cycles of loading and unloading. These results show that the internal residual stress becomes more significant with the increase in the imposed strain rate.

Figure 6 depicts the residual strain evolution as a function of the number of cycles for the three various strain rates. This residual strain is significant in the first cycles and goes up progressively according to the number of cycles. Thus, after 20 cycles, for the imposed strain rate of 10−<sup>3</sup> s −1 , the residual deformation at zero stress is almost double of the value obtained with 10−<sup>5</sup> s −1 . According to these results, we can deduce that there is an interaction between the decrease in the martensite start stress and the increment or increase in the residual strain at zero stress, and that there is an imposed strain rate during cycling. The interaction between the critical stress for introducing the martensite and the increase in the residual strain at zero stress was studied previously [20]. In fact, during thermo-mechanical cycling, the phase boundaries propagate forward and backward [34]. Throughout this reversible transformation, defects such as dislocations will form and act as an obstacle for the interface movement for the next cycles. Nevertheless, Chu K et al. [35] showed that during the fatigue tests of NiTi micropillars, the nanosized residual martensite domains, which were in fact blocked by the dislocations, could decrease in a considerable way the overall transformation stress throughout a generated remanent stress and the direct variant increase, and that was without overcoming the martensite nucleation obstacle. Similarly, Kan Q. et al. [36] studied the effect of the strain rates upon loading or unloading the SMA NiTi alloy. They found that the residual strain was accumulated by raising the number of cycles and strain rates. Indeed, after 20 cycles, the residual strain was about 2.04% for a 3.3 10−<sup>4</sup> s −1 strain rate and it reached 4.2% with 3.3 10−<sup>2</sup> s −1 . In addition, they found that the NiTi SMAs' super-elasticity degradation after cycling was caused by interacting between the dislocation slipping and the martensitic transformation. Moreover, they concluded that the super-elastic NiTi SMAs' dislocation slipping could be generated through a high local stress close to the austenite-martensite interfaces. This was in general during the repeated martensitic transformation as well as during its reverse [37–39]. Consequently, during the cyclic deformation, the dislocation density and then the internal stress of NiTi SMAs went up rapidly.

**Figure 5.** Typical strain cycling curve after 50 cycles for deformed specimen until 7.1%, at imposed strain rate of (**a**) 10−<sup>5</sup> s −1 , (**b**) 10−<sup>4</sup> s <sup>−</sup><sup>1</sup> and (**c**) 10−<sup>3</sup> s −1 , showing reduction in phase-transformation yield stress and increase in residual strain.

**Figure 6.** Evolution of residual strain at zero stress as a function of number of cycles for cyclic deformed specimen with 7.1% strain after different imposed strain rates of 10−<sup>5</sup> s −1 , 10−<sup>4</sup> s <sup>−</sup><sup>1</sup> and 10−<sup>3</sup> s −1 (represents the fitting curve).

In our case, a decrease in the martensite start stress and an increase in the residual strain at zero stress can be explained by the rise in the dislocation density and then the internal stress, which acts as an obstacle for the growth of the martensite bands and the nucleation of new variants. In addition, during the reverse transformation, some of the martensite bands can be pinned by dislocations and remain untransformed after unloading [36,40]. During the NiTi specimen's cyclic deformation, the temperature variation is based upon interacting between the heat conduct and the internal heat production. This can greatly depend on the strain rate. In the condition that the strain rate is low, the convected and conducted heat transfer is quicker than the heat production, and this is because of the latent heat and inelastic dissipation. When a strain rate is high, the inelastic-dissipation and latentheat production is quicker than the heat transfer. As the critical stress of the introducing martensite increases linearly with the rising test temperature [24], the required driving force of dislocation slipping will become higher, and then the density of dislocation will build up [34]. As a result, the increase in the residual stress with the strain rates is due to the higher density of dislocation. Additionally, the bigger the number of cycles, the more accentuated the internal stress and the retained martensite by dislocation will be. This is done by raising the dislocation density after the reverse transformation.

The amounts of absorbed hydrogen by the NiTi superelastic alloy obtained by TDA after 3 h of immersion of hydrogen charging within the 0.9% NaCl solution under an imposed current density of 10 A/m<sup>2</sup> at room temperature are illustrated in Figure 7. This quantity of diffused hydrogen is calculated by subtracting the amount of pre-dissolved hydrogen in the as-received NiTi archwire (8 mass ppm). Before mechanical testing and after 3 h of immersion, the as-received specimen shows approximately 96 mass ppm. The maximum peak of desorption is obtained at about 244 ◦C. Moreover, a shoulder of the desorption peak appears at about 142 ◦C. The TDA after loading and unloading from 1 to 20 cycles with 10−<sup>5</sup> s <sup>−</sup><sup>1</sup> and 10−<sup>4</sup> s <sup>−</sup><sup>1</sup> of the imposed strain rate and hydrogen charging is represented in Figure 7a,b, respectively. We can see that after one cycle and immersion, the amount of absorbed hydrogen is about 187 mass ppm with the lower strain rate, and it

grows up to 301 mass ppm after cycling with an imposed deformation of 10−<sup>4</sup> s −1 . Besides, the diffused hydrogen into the NiTi archwire increases progressively with the number of cycles of loading and unloading at the imposed strain of 7.1%. After 20 cycles and 3 h of electrolytic charging in 0.9% NaCl solution for the lower strain rate, this value is about 319 mass ppm, and it becomes 456 mass ppm at 10−<sup>4</sup> s −1 . We can notice that for both strain rates, the primary peak temperature of hydrogen is in the rage of 270–300 ◦C, which is quite higher than the as-received and charged by hydrogen specimen. According to Yokoyama et al. [41], this behaviour is due to the fact that the hydrogen states can vary from a parent phase to a martensite one. Additionally, it is remarkable that the shoulder of the desorption peaks, between 145 and 175 ◦C, is higher than the as-received and charged specimen. Concerning the imposed 10−<sup>3</sup> s −1 strain rate, the quantity of absorbed hydrogen after one cycle and immersion can be about 411 mass ppm (Figure 7c). This value is almost double of the one obtained with an imposed strain rate of 10−<sup>5</sup> s <sup>−</sup><sup>1</sup> and four times higher than the as-received and hydrogen-charged alloy. In addition, after 20 cycles, we notice that the quantity of hydrogen is about 587 mass ppm, which is almost double of the measured value with the lower strain rate obtained after the same number of cycles. Similar to the results obtained with 10−<sup>5</sup> s <sup>−</sup><sup>1</sup> and 10−<sup>4</sup> s −1 , the maximum absorbed peak remains in the same range of temperature, from 270 to 300 ◦C, hence the similarity between hydrogen states and/or trapping. However, a shoulder of the desorption peak is affected by the imposed strain rate. Indeed, this peak is increased and appears in the range 200–230 ◦C. T. Shimada et al. [42] indicated that the shoulder of the hydrogen desorption peak of a superelastic NiTi alloy was lower than that for the specimen charged with an applied stress of 600 MPa. The authors concluded that this phenomenon was due to the formation of the martensite phase under the applied stress where the diffusion distance and hydrogen trapping sites were different from the parent phase. On the other hand, an increase in the shoulder would be in fact detected for the NiTi alloy, which was charged by hydrogen in the martensite phase presence and under a static applied strain [43]. The authors mentioned that the diffused hydrogen tended to form unstable states. After a dynamic cyclic tensile test, carried out under the stress plateau region, the unstable hydrogen states would accumulate, leading to a hydrogen desorption peak shoulder [8]. The latter would increase by raising the strain rate as well as the number of deformation cycles.

The evolution of the mean value of the amount of absorbed hydrogen as a function of cycles number at different imposed strain rates, i.e., 10−<sup>3</sup> s −1 , 10−<sup>4</sup> s −1 , and 10−<sup>5</sup> s −1 , is depicted in Figure 8, respectively. It is seen that there is a direct relation between the amount of absorbed hydrogen, the imposed strain rate, and the number of cycles. Moreover, this behaviour is in coherence with the residual strain evolution at zero stress as a function of the number of cycles observed in Figure 6. In fact, as explained previously, the increase in the residual deformation with the strain rate and the number of cycles is caused by the rise in the internal stress due to the density of dislocations and to the pinned martensite by dislocations after unloading. The dislocations and the retained martensite represent a preferential site for hydrogen diffusion rather than the parent phase. In fact, the diffusion of hydrogen contributes to the stress relaxation of the infinite dislocation strain at the core. Additionally, the amount and diffusion rate of hydrogen are higher in the martensite phase in comparison with those in the austenite phase [41]. Consequently, we can deduce that the amount of absorbed hydrogen goes up with the increase in the residual strain at zero stress, since the density of the dislocation and the quantity of the retained martensite grow after each cycle.

Figure 9a shows the NiTi archwire's stress strain behaviour for the three quasi-static strain rates after 13 cycles with a strain rate of 10−<sup>5</sup> s <sup>−</sup><sup>1</sup> and immersion for 3 h at room temperature. It can be seen that for a lower strain rate of 10−<sup>5</sup> s −1 , the NiTi alloy is embrittled by hydrogen charging. Indeed, the failure stress is detected in the plateau of the martensite start stress; whereas, the tested 10−<sup>4</sup> s <sup>−</sup><sup>1</sup> and 10−<sup>3</sup> s <sup>−</sup><sup>1</sup> NiTi archwires, for the same charging and ageing conditions, present a superelastic behaviour. We notice only an increase in the critical stress for martensite start stress by 50 MPa and 70 MPa, respectively,

compared to the cycled specimen for 13 cycles without immersion. It is important to mention that the tested specimen with different strain rates after 13 cycles with 10−<sup>4</sup> s −1 and 10−<sup>3</sup> s <sup>−</sup><sup>1</sup> and immersion does not show any embrittlement during the tensile tests with different strain rates. The TDA after 13 cycles and immersion with the current density of 10 A/m<sup>2</sup> at different imposed strain rates is represented in Figure 9b. Despite the important amount of absorbed hydrogen of 411 and 543 mass ppm, it is clear that the mechanical behaviour of the NiTi alloy is not remarkably affected during the tensile tests with10−<sup>4</sup> s −1 and 10−<sup>3</sup> s −1 . After 18 cycles of loading and unloading with 10−<sup>3</sup> s <sup>−</sup><sup>1</sup> of the imposed strain rate and hydrogen charging and aging for one day, the tensile test with 10−<sup>5</sup> s −1 and 10−<sup>4</sup> s −1 shows an embrittlement in the Luder-like plateau of the austenite martensite transformation, as depicted in Figure 10a. Nevertheless, the tensile tested NiTi archwire with a higher imposed strain rate of 10−<sup>3</sup> s −1 (corresponding to the shorter time) conserves its superelasticity. This specimen presents a higher martensite start stress and in addition to the lower total strain compared to the non-charged ones. Figure 10a illustrates the TDA after 18 cycles at 10−<sup>3</sup> s <sup>−</sup><sup>1</sup> and hydrogen charging in comparison with loaded specimens at 10−<sup>5</sup> s <sup>−</sup><sup>1</sup> after 13 cycles, where the first embrittlement has happened. It can be seen that the amount of absorbed hydrogen after 18 cycles at 10−<sup>3</sup> s −1 (584 mass ppm) is almost twice the one cycled with 10−<sup>5</sup> s −1 (291 mass ppm), and no fracture has been detected yet (Figure 10b). Table 1 summarizes the results obtained forall performed experimental conditions. It is important to mention that the experimental results obtained after 20 cycles are similar to the ones given with 18 cycles. Accordingly, the hydrogen quantity may not be the only principal factor while considering in particular the studied superelastic NiTi alloy's hydrogen embrittlement mechanism.

**Figure 7.** Hydrogen thermal desorption curves for specimens immersed for 3 h and aged for 24 h at room temperature after 13 cycles with imposed deformation of (**a**) 10−<sup>5</sup> s −1 , (**b**) 10−<sup>4</sup> s <sup>−</sup><sup>1</sup> and (**c**) 10−<sup>3</sup> s −1 , showing an increase in the amount of absorbed hydrogen with stain rates.

**Figure 8.** Amount of absorbed hydrogen vs. number of cycles of loaded and unloaded specimens at imposed 10−<sup>5</sup> s −1 , 10−<sup>4</sup> s −1 , and 10−<sup>3</sup> s −1 strain rates and hydrogen charging for 3 h (represents the fitting curve).

**Figure 9.** (**a**) Tensile curve at 10−<sup>5</sup> s −1 showing fracture after 13 cycles with imposed strain rate of 10−<sup>5</sup> s −1 , and (**b**) amount of absorbed hydrogen after the same number of cycles at 10−<sup>5</sup> s −1 , 10−<sup>4</sup> s −1 , and 10−<sup>3</sup> s −1 .

The strain rate response of the superelastic NiTi alloy can be explained based on a thermo-mechanical phenomenon [44,45]. For a low applied strain rate (10−<sup>5</sup> s <sup>−</sup><sup>1</sup> and 10−<sup>4</sup> s −1 ), once the first variants are generated, the austenite-martensite interfaces move slowly enough in order to enable the latent transformation to be transferred quickly outside. Temperature change in the specimen is eliminated and the transformation is considered under an isothermal process. Consequently, the flat Luder-like plateau of the austenite martensite transformation results from the growth of a few number of martensite bands,

not the nucleation of new martensite variants. In a high strain rate of 10−<sup>3</sup> s −1 , the latent heat cannot be timely convected to the environment since the martensite variants are forced to propagate at a somewhat higher velocity. For the domain-front growth, the domainfronts' localized self-heating raises the stress [46], which becomes more important than the untransformed parent zone's domain-nucleation stress. Therefore, during the phase transformation, the variation in the average sample temperature is significant. The slope of the stress–strain curve goes up and new domains nucleate to fulfill the applied strain, with the continuously changing temperature.

**Figure 10.** (**a**) Tensile curves obtained after 18 cycles and immersion for 3 h showing the embrittlement of loaded specimen with imposed strain rates of 10−<sup>5</sup> s <sup>−</sup><sup>1</sup> and 10−<sup>4</sup> s <sup>−</sup><sup>1</sup> and superelastic behaviour of loaded specimens with 10−<sup>3</sup> s −1 , and (**b**) comparison between critical amount of absorbed hydrogen causing fracture at 10−<sup>5</sup> s <sup>−</sup><sup>1</sup> and quantity of absorbed hydrogen after 18 cycles with 10−<sup>3</sup> s <sup>−</sup><sup>1</sup> and immersion.

**Table 1.** Summary of conducted tensile tests at different strain rates after immersion and cycling with 10−<sup>5</sup> s −1 , 10−<sup>4</sup> s <sup>−</sup><sup>1</sup> and 10−<sup>3</sup> s −1 .

F: Fracture.

The maximum number of martensite variants *nmax* (or the minimum domain spacing) increases as a function of the strain rate. In fact, the maximal number of martensite domains *<sup>n</sup>max* and as well as the strain rate . *ε* canbe fitted into a power-law relationship [47,48]:

$$
\mathfrak{m}\_{\max} = \mathfrak{c} \begin{pmatrix} \dot{\mathfrak{e}} \end{pmatrix}^{\mathfrak{x}}, \tag{1}
$$

where the fitting coefficient *x* is an exponent factor that is around 0.5, and *c* is a fitting coefficient.

Hao Yu et al. [49] showed that during a high strain rate, the precipitation of Ni4Ti<sup>3</sup> is found to increase the NiTi yield strength, which is caused by the impediment of Ni4Ti<sup>3</sup> precipitation to dislocation motion and leading to an increase in the martensite phase nucleation at the interface between the precipitation and the B2 matrix. This indicates that during the tensile tests with the same applied strain rate, the number of martensite variants, obtained in the plateau of austenite martensite transformation, should increase with the imposed strain rate during cycling.

The sensitivity to the strain rate after cycling at different strain rates and after hydrogen charging for 3 h and ageing at room temperature appears to be as follows. After 13 cycles with a 10−<sup>5</sup> s −1 strain rate of, the 291 mass ppm of absorbed hydrogen seems to represent the critical amount to cause fracture during the austenite martensite plateau. Indeed, during tensile loading with 10−<sup>5</sup> s −1 , a few martensite variants tend to grow during the austenite-martensite transformation plateau, since the latent transformation heat is transferred rapidly to ambient media. However, this growth is hindered by the trapped hydrogen into the retained martensite bands and the local dislocation stress field near the austenite-martensite interfaces and this actually happens during the repeated martensitic transformation as well as during its reverse. Thus, the growth of martensite bands cannot overcome the obstacle induced by hydrogen. It is important to point out that during tensile loading with 10−<sup>5</sup> s −1 , the number of martensite variants growing in the plateau for austenite martensite transformation obtained after 13 cycles with an imposed strain rate of 10−<sup>4</sup> s <sup>−</sup><sup>1</sup> and 10−<sup>3</sup> s −1 should be more important than after cycling with 10−<sup>5</sup> s −1 , since we have more local stress near the austenite-martensite interfaces [50]. However, an embrittlement occurs. Thus, it is assumed that the amount of absorbed hydrogen of 543 mass ppm is sufficient to act as an obstacle for the short travelling distance of martensite bands to cause fracture. This points out that there is a competition between the number of martensite variants and the amount of absorbed hydrogen to cause fracture.

With an imposed 10−<sup>3</sup> s −1 strain rate, after 18 cycles, a premature fracture is detected for a loaded tensile NiTi alloy with both 10−<sup>5</sup> s <sup>−</sup><sup>1</sup> and 10−<sup>4</sup> s −1 strain rates. The corresponding amount of absorbed hydrogen, after 3 h of immersion, is about 584 mass ppm, which is considered as the critical value causing earlier fracture during the monotonic tensile test with a 10−<sup>4</sup> s −1 strain rate. The delay of embrittlement with 10−<sup>4</sup> s −1 can be related to a competition between the number of martensite bands in the austenite martensite plateau and the quantity of absorbed hydrogen. In fact, after13 cycles, the number of nucleated variants is higher than 10−<sup>5</sup> s −1 . Consequently, the amount of absorbed hydrogen is not enough to act as an obstacle for the variant growth caused by 10−<sup>4</sup> s −1 , since the travelled distance is less important than the one obtained with 10−<sup>5</sup> s −1 . However, after 18 cycles, despite the increase in nucleated bands, and due to (i) the multiplication of local stress near the austenite-martensite interfaces after cycling with 10−<sup>3</sup> s <sup>−</sup><sup>1</sup> and (ii) the higher applied strain rate during tensile test, the quantity of absorbed hydrogen seems to be sufficient to act as an obstacle for varied growth in the quasi-flat plateau. This explanation seems to be in coherence with the obtained superelastic behaviour after 18 cycles and the tensile test with a higher imposed strain rate. In this case, the time for transferring the latent heat is highly restricted, causing the nucleation of a large number of martensite bands with small domain spacing between them. As a result, the travelled distance of these martensite bands will be very limited and the amount of absorbed hydrogen will have no effect.

#### **4. Conclusions**

We have investigated in this study the effects of the strain rate response after hydrogen charging for 3 h and ageing for one day on pre-cycled superelastic NiTi archwires. Cycling from 1 to 50 loading and unloading at 10−<sup>5</sup> s −1 , 10−<sup>4</sup> s −1 , and 10−<sup>3</sup> s <sup>−</sup><sup>1</sup> has been carried out to generate a gradual rise in the residual strain at zero stress. Moreover, cycling, which is characterized by an increase in the density of dislocation and retained martensite after unloading, represents a preferential site for hydrogen diffusion during immersion. After hydrogen charging with 191 mass ppm of absorbed hydrogen, an embrittlement occurs for the low applied tensile strain rate. In addition, this fracture happens only with a higher quantity of absorbed hydrogen (584 mass ppm) with a 10−<sup>4</sup> s −1 imposed strain rate, and no embrittlement will be detected for the higher strain rate of 10−<sup>3</sup> s −1 . We attribute this behaviour to the interaction between the travelled distance during the increase in martensite bands and the amount of absorbed hydrogen during the step of austenite-martensite transformation.

**Funding:** The author would like to extend his appreciation to the Deanship of Scientific Research at King Khalid University, Saudi Arabia for finding this work through the Reseach Group Program under grant no. RGP.1/14/42.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Conflicts of Interest:** The author declare no conflict of interest.

### **References**

## *Communication* **On the Decrease in Transformation Stress in a Bicrystal Cu-Al-Mn Shape-Memory Alloy during Cyclic Compressive Deformation**

**Tung-Huan Su <sup>1</sup> , Nian-Hu Lu <sup>2</sup> , Chih-Hsuan Chen 2,3,\* and Chuin-Shan Chen 1,3,\***

**Abstract:** The evolution of the inhomogeneous distribution of the transformation stress (*σ*s) and strain fields with an increasing number of cycles in two differently orientated grains is investigated for the first time using a combined technique of digital image correlation and data-driven identification. The theoretical transformation strains (*ε*T) of these two grains with crystal orientations [5 3 26]<sup>β</sup> and [6 5 11]<sup>β</sup> along the loading direction are 10.1% and 7.1%, respectively. The grain with lower *ε*<sup>T</sup> has a higher *σ*<sup>s</sup> initially and a faster decrease in *σ*<sup>s</sup> compared with the grain with higher *ε*T. The results show that the grains with higher *σ*s might trigger more dislocations during the martensite transformation, and thus result in greater residual strain and a larger decrease in *σ*s during subsequent cycles. Grain boundary kinking in bicrystal induces an additional decrease in transformation stress. We conclude that a grain with crystal orientation that has high transformation strain and low transformation stress (with respect to loading direction) will exhibit stable transformation stress, and thus lead to higher functional performance in Cu-based shape memory alloys.

**Keywords:** full-field stress and strain measurements; shape memory alloys; digital image correlation; data-driven identification; superelasticity; functional fatigue

### **1. Introduction**

Superelastic shape-memory alloys (SMAs) are functional materials capable of sustaining a large recoverable deformation strain as a result of a stress-induced martensitic transformation (MT) between austenite and martensite. Among SMAs, Cu-Al-Mn SMAs possess superior features such as low cost, high cold workability, and large transformation strain compared with TiNi-based SMAs [1]. They are considered to be suitable candidate materials for a variety of applications ranging from civil engineering to the space industry, in which the SMAs are subjected to cyclic loading. However, the issue of SMA fatigue and fracture is challenging because fatigue problems in Cu-Al-based SMAs are mainly attributed to the constraints of grain boundaries during MT and its resulting plastic deformation [2]. Several studies have extensively investigated the prevention of intergranular fracture problems caused by high elastic anisotropy in the Cu-Al-Mn alloys with the aim of enhancing the superelasticity of polycrystalline Cu-based shape memory alloys [3–5]. Therefore, treatments of the microstructure designed to increase grain size, such as the introduction of texture and the reduction of triple junctions, significantly improve the functional performance of Cu-Al-Mn SMAs [6–8].

Recently, Cu-Al-Mn single crystals with excellent superelasticity have been fabricated using abnormal grain growth (AGG) induced by a cyclic heat treatment [9,10]. These AGG methods also enable the preparation of large bicrystal samples for mechanical tests,

**Citation:** Su, T.-H.; Lu, N.-H.; Chen, C.-H.; Chen, C.-S. On the Decrease in Transformation Stress in a Bicrystal Cu-Al-Mn Shape-Memory Alloy during Cyclic Compressive Deformation. *Materials* **2021**, *14*, 4439. https://doi.org/10.3390/ma14164439

Academic Editor: Francesco Iacoviello

Received: 9 July 2021 Accepted: 5 August 2021 Published: 8 August 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

providing insight into the inhomogeneous MT phenomenon and the elastocaloric effect of the sample under compression [11]. The experimental results [11] demonstrate the generation of microcracks at the grain and twin boundaries of the bicrystal Cu-Al-Mn sample under cyclic compression. Although compressive deformation is preferred as a deformation mode to delay the fatigue fracture of metallic materials [12,13], much less is known about the compressive fatigue behavior of Cu-Al-Mn SMAs during cyclic phase transformation.

Based on the above-mentioned motivations and the knowledge of large differences in superelasticity properties of the bicrystal Cu-Al-Mn sample [11], it was expected that such differences in superelasticity properties would cause functional instability of the Cu-based bicrsytal sample during cyclic compressive deformation. As Cu-Al-Mn SMAs are regarded as potential candidates of functional materials, the correlations between strain field and transformation stress, and the evolutions of stress and strain distributions during cyclic superelastic deformation, are critical factors for the compressive fatigue behavior of Cu-Al-Mn SMAs. In this study, we investigated the cyclic compressive behavior of the superelasticity of macro-scale Cu-Al-Mn bicrystals using the digital image correlation (DIC) technique and the data-driven identification (DDI) method. Both methods are used to determine the distributions of transformation stress and strain in the bicrystal and near the grain boundary. Based on the full-field measurement results, the correlations between the decrease in transformation stress, accumulation of residual strain, and martensite transformation are determined.

#### **2. Materials and Methods**

Figure 1 illustrates the methods employed to characterize the cyclic behavior of the superelasticity of bicrystal Cu-Al-Mn SMAs. The strain and stress fields of a Cu-Al-Mn shape-memory bicrystal were measured using the DIC technique and DDI method, respectively. In this work, we used the same Cu-Al-Mn bicrystal sample prepared in our previous study [11], with dimensions of 8 mm × 4.2 mm × 4.2 mm. Please note that the specimen was subjected to five compression–unloading tests with a maximum global deformation strain from 1% to 5% in 1% increments for each test (see Figure 1 in the previous study [11]). It was found that some plastic deformation occurred when the global deformation strain was higher than 4%. In this work, we further conducted twenty compression–unloading tests using the same Cu-Al-Mn bicrystal sample, which has already undergone the five compression–unloading tests mentioned above. The grain boundary within the sample is indicated by a dashed line in Figure 1. The crystal orientations of both grains were determined via electron backscatter diffraction (EBSD, Oxford Instruments, Abingdon, UK), as shown in the inset of Figure 2a. The thermal analyses of the sample were conducted in a differential scanning calorimeter (DSC, DSC 25, TA Instrument, New Castle, DE, USA) with cooling and heating rates of 10 ◦C/min. The microstructures were observed by transmission electron microscope (TEM, FEI Tecnai™ G2 F30, Hillsboro, OR, USA) operated at 300 kV. The sample was mechanically ground to a thickness of about 70 µm and then electropolished at −40 ◦C using HNO<sup>3</sup> and CH3OH (2:8 in volume). The preparation procedures for the bicrystal Cu-Al-Mn sample were detailed in the literature [11].

The cyclic compression–unloading test was performed under the strain-controlled mode using a universal tester with a 50 kN load cell (AG-IS 50 KN, Shimadzu, Japan). The strain rate used in the compression–unloading test was about 2.4 <sup>×</sup> <sup>10</sup>−<sup>3</sup> s −1 such that experiments can be considered as quasi-static. Each compression cycle took about 120 s. A speckle pattern was applied on the observed surface (i.e., area of interest, AOI) of the specimen using black and white sprays. The pattern was used for in situ strain tracing and ex post strain field analysis. The deformation strain of the specimen was measured with a virtual strain gauge by optical DIC (VIC-Gauge 3D, Correlated Solutions, Irmo, SC, USA). Three deformation strains (i.e., global gauge strain *ε*<sup>g</sup> as shown in Figure 1 and the local strain gauges at the top and bottom grains *ε*<sup>t</sup> and *ε*<sup>b</sup> as shown in inset of Figure 2b) were measured using the virtual strain gauge technique. Notably, regardless of

the residual strain, a 5% strain (relative to each unloaded state) was applied to the sample during each compression cycle. During the compression test, images of the deformed sample were taken at a rate of 5 Hz using two cameras. Around 600 snapshots were taken for each compression cycle. Because the imaging rate (5 s−<sup>1</sup> ) is higher than the strain rate (2.4 <sup>×</sup> <sup>10</sup>−<sup>3</sup> s −1 ), the deformation behavior of the material can be captured. These snapshots were analyzed ex post in the VIC 3D 8 software to obtain the strain distribution at the surface of the specimen, as shown in the full-field strain measurement in Figure 1. *Materials* **2021**, *14*, x FOR PEER REVIEW 3 of 13

**Figure 1.** The digital image correlation (DIC) technique and data-driven identification (DDI) method were employed to measure the strain and stress distributions, respectively, at the surface of the specimen to characterize the cyclic behavior of the superelasticity of the bicrystal Cu-Al-Mn SMAs. The cyclic compression–unloading test was performed under the strain-controlled mode. The strain fields in the area of interest (AOI) can be obtained using the DIC technique. Based on the experimentally determined strain fields, the stress fields in the AOI can be computed using the DDI **Figure 1.** The digital image correlation (DIC) technique and data-driven identification (DDI) method were employed to measure the strain and stress distributions, respectively, at the surface of the specimen to characterize the cyclic behavior of the superelasticity of the bicrystal Cu-Al-Mn SMAs. The cyclic compression–unloading test was performed under the strain-controlled mode. The strain fields in the area of interest (AOI) can be obtained using the DIC technique. Based on the experimentally determined strain fields, the stress fields in the AOI can be computed using the DDI method. Finally, three parameters (i.e., transformation stress (*σ*s), residual strain (*ε*r), and transformation strain (*ε*tr)) can be computed from the stress–strain responses.

method. Finally, three parameters (i.e., transformation stress (σୱ), residual strain (ε୰), and transformation strain (ε୲୰)) can be computed from the stress–strain responses. Based upon the measured results (i.e., DIC data items) of the strain fields and the applied loads from the full-field strain measurement, the equilibrated stress distribution at the surface of the specimen can be numerically computed using the DDI method [14–16] under a finite-element framework without the use of constitutive modeling, as illustrated in the full-field stress measurement in Figure 1. For a given set of compression–unloading cycle data, the DDI method uses the governing equations (i.e., stress equilibrium equations) to compute the mechanical stresses at the surface of the specimen. Then, the method is used to identify a database of material states that samples the mechanical stress–strain pairs of material to satisfy the criterion of minimum distance between mechanical stress– strain pairs and material database. Mathematically, this process can be formulated as a constrained minimization problem, which was originally proposed in [14]. The DDI method was validated with synthetic data for linear and non-linear elasticity [14] and was further applied experimentally using real experimental data (i.e., DIC measurements) for

The cyclic compression–unloading test was performed under the strain-controlled

mode using a universal tester with a 50 kN load cell (AG-IS 50 KN, Shimadzu, Japan). The strain rate used in the compression–unloading test was about 2.4 × 10−3 s−1 such that experiments can be considered as quasi-static. Each compression cycle took about 120 s. A speckle pattern was applied on the observed surface (i.e., area of interest, AOI) of the specimen using black and white sprays. The pattern was used for in situ strain tracing and ex post strain field analysis. The deformation strain of the specimen was measured with a

**Figure 2.** (**a**) Geometry of the bicrystal Cu-Al-Mn SMA. The loading directions of the top and bottom grains are shown in the inverse pole figure. (**b**) Average stress–strain curves of the top grain (୲), bottom grain (ୠ), and the entire specimen (). The bicrystal sample was loaded to a gauge strain () of 5% during cyclic deformation. Local virtual strain gauges ୲

and ୠ were used to measure the average strains in the top and bottom grains, respectively (inset of (**b**)).

elastomer sheet [15] and Cu-Al-Mn shape memory alloy single crystal [16]. In the DDI method, the only governing equations used to determine the stress components are the stress equilibrium equations. Thus, the bias introduced by the choice and the calibration of a constitutive model was removed. Further details about the full-field stress and strain measurements can be found in the literature [15,16]. specimen to characterize the cyclic behavior of the superelasticity of the bicrystal Cu-Al-Mn SMAs. The cyclic compression–unloading test was performed under the strain-controlled mode. The strain fields in the area of interest (AOI) can be obtained using the DIC technique. Based on the experimentally determined strain fields, the stress fields in the AOI can be computed using the DDI method. Finally, three parameters (i.e., transformation stress (σୱ), residual strain (ε୰), and transformation strain (ε୲୰)) can be computed from the stress–strain responses.

**Figure 1.** The digital image correlation (DIC) technique and data-driven identification (DDI) method were employed to measure the strain and stress distributions, respectively, at the surface of the

*Materials* **2021**, *14*, x FOR PEER REVIEW 3 of 13

**Figure 2.** (**a**) Geometry of the bicrystal Cu-Al-Mn SMA. The loading directions of the top and bottom grains are shown in the inverse pole figure. (**b**) Average stress–strain curves of the top grain (୲), bottom grain (ୠ), and the entire specimen (). The bicrystal sample was loaded to a gauge strain () of 5% during cyclic deformation. Local virtual strain gauges ୲ and ୠ were used to measure the average strains in the top and bottom grains, respectively (inset of (**b**)). **Figure 2.** (**a**) Geometry of the bicrystal Cu-Al-Mn SMA. The loading directions of the top and bottom grains are shown in the inverse pole figure. (**b**) Average stress–strain curves of the top grain (*ε*t), bottom grain (*ε*<sup>b</sup> ), and the entire specimen (*ε*g). The bicrystal sample was loaded to a gauge strain (*ε*g) of 5% during cyclic deformation. Local virtual strain gauges *ε*<sup>t</sup> and *ε*<sup>b</sup> were used to measure the average strains in the top and bottom grains, respectively (inset of (**b**)).

The cyclic compression–unloading test was performed under the strain-controlled mode using a universal tester with a 50 kN load cell (AG-IS 50 KN, Shimadzu, Japan). The strain rate used in the compression–unloading test was about 2.4 × 10−3 s−1 such that experiments can be considered as quasi-static. Each compression cycle took about 120 s. A speckle pattern was applied on the observed surface (i.e., area of interest, AOI) of the specimen using black and white sprays. The pattern was used for in situ strain tracing and ex post strain field analysis. The deformation strain of the specimen was measured with a The mechanically admissible stress–strain pairs, obtained from the full-field stress and strain measurements shown in Figure 1, are stored at each element and are considered to represent the mechanical state (*σ*e,*ε*e), as shown in the stress–strain responses in Figure 1. Using a linear regression analysis of these mechanical states in both the elastic and plateau regions, the distribution of MT stress *σ*<sup>s</sup> can be obtained from the intersection of the two linear stress–strain curves, as illustrated by the stress–strain responses shown in Figure 1. The residual strain *ε*<sup>r</sup> and transformation strain *ε*tr can be obtained readily, as shown in the stress–strain responses of Figure 1.

#### **3. Results**

Figure 2a shows the crystal orientations of the top and bottom grains along the loading direction (LD), as determined using EBSD, which were along [5326]<sup>β</sup> and [6511]<sup>β</sup> , respectively. The theoretical transformation strain (*ε*T) of the transition from the β phase to 6M martensite during compression was calculated based on the Wechsler–Liebermann– Read theory [8,11,17]. The values of *ε*<sup>T</sup> were 10.1% and 7.1% for the top and bottom grains, respectively. Note that the compressive transformation strain of these grains significantly differed in the loading direction.

Figure 2b shows the compressive stress–strain curves of both grains when a gauge strain (*ε*g) of 5% was applied, which covered the entire specimen during deformation, as illustrated in Figure 1. Local virtual strain gauges *ε*<sup>t</sup> and *ε*<sup>b</sup> were used to measure the average strains in the top and bottom grains, respectively (inset of Figure 2b). It can be seen that the stress-induced martensitic transformation (SIMT) of the top grain (blue lines) occurred at transformation stresses of 306 MPa and 297 MPa for the first and twentieth cycles, respectively. By contrast, for the bottom grain (red lines), the transformation stresses of the first and twentieth compression cycles were 398 MPa and 292 MPa, respectively. Both grains exhibited different cyclic behaviors on average, including the decrease in transformation stress, accumulation of irrecoverable strain, and the transformation strain (see Table 1). As shown in Table 1, the properties (i.e., *σ*s, *ε*r, and *ε*tr) of the total curve are between those of the top and bottom grains, which were reported in [11]. Please note that the total stress–strain curve is denoted as "Average" in first column of Table 1. According to the results of residual strain *ε*<sup>r</sup> (sixth column of Table 1), it was found that the plastic

deformation of the entire specimen was mainly contributed from the bottom grain. In short, combinations of crystal orientation in bicrystal SMAs will result in varied mechanical properties of the entire specimen.

**Table 1.** Loading direction (LD), theoretical transformation strain (*ε*T), transformation stress (*σ*s), residual strain (*ε*r), and transformation strain (*ε*tr) of the top grain, bottom grain, and the entire specimen (average) for the first and twentieth compression cycles. Three parameters (i.e., *σ*s, and *ε*tr) were computed from the stress–strain curves of the top grain, bottom grain, and the entire specimen (average) shown in Figure 2b.

Figure 3a shows the evolution of the axial strain field *ε*yy while loading toward and unloading away from a gauge strain *ε*<sup>g</sup> of 5% during the first, tenth, and twentieth compression–unloading cycles. The transformation stress fields are shown in Figure 3b, which illustrates the distribution of transformation stress in the specimen. As shown in the first compression cycle, the top grain underwent most of the deformation during the loading process. By contrast, the bottom grain began its partial MT after an *ε*<sup>g</sup> of 3%. The difference in transformation behavior between the top grain and the bottom grain can be ascribed to differences in the MT stresses required to trigger MT, as shown in Figure 3b. The transformation stress of the top grain was approximately 325 MPa, which was less than that of the bottom grain (approximately 400 MPa), indicating that the top grain was more likely to begin MT earlier until the loading force was high enough to initiate MT in the bottom grain. The transformation stresses of both grains near the grain boundary (indicated by white dashed lines) were smaller than those further away from the grain boundary, as shown in Figure 3b, indicating that the stress state around the grain boundary promoted MT at a lower stress level.

Before the beginning of the tenth compression cycle, some regions in the bottom grain had residual strain. At the tenth deformation, the top grain experienced less deformation relative to the first cycle, whereas the bottom grain began to exhibit increased deformation. As shown in Figure 3b, at the tenth cycle, the transformation stress of the upper part of the bottom grain (near the grain boundary) decreased, bringing the values closer to those of the top grain. This decrease in transformation stress resulted in an increase in regions in which the MT could be triggered in the bottom grain, leading to increased transformation strain in the bottom grain.

At the beginning of the twentieth compression cycle, the band of residual strain at the bottom grain extended, and more residual strain remained. Furthermore, during the loading process, the upper part of the bottom grain showed a level of transformation stress closer to that of the top grain, as shown in Figure 3b. According to Figure 3b, the decrease in transformation stress in the bottom grain was initiated around the grain boundary and then propagated to the lower part of the bottom grain.

**Figure 3.** Distribution of (**a**) axial strain fields ௬௬ during loading toward and unloading away from the gauge strain of 5% and (**b**) transformation stress fields ୱ in the bicrystal Cu-Al-Mn SMA sample for selected compression–unloading cycles: C1, C10, and C20. Points A, B, and C are probing points for recording the local axial stress–strain responses (௬௬, ௬௬) as shown in Figure 4a. (**c**) Transformation stress difference ∆ୱ, which is the difference in transformation stress **Figure 3.** Distribution of (**a**) axial strain fields *ε*yy during loading toward and unloading away from the gauge strain *ε*<sup>g</sup> of 5% and (**b**) transformation stress fields *σ*s in the bicrystal Cu-Al-Mn SMA sample for selected compression–unloading cycles: C1, C10, and C20. Points A, B, and C are probing points for recording the local axial stress–strain responses *σ*yy,*ε*yy as shown in Figure 4a. (**c**) Transformation stress difference ∆*σ*s, which is the difference in transformation stress between cycles 1 and 20, shown in the plot in Figure 3b.

between cycles 1 and 20, shown in the plot in Figure 3b. Before the beginning of the tenth compression cycle, some regions in the bottom grain had residual strain. At the tenth deformation, the top grain experienced less deformation relative to the first cycle, whereas the bottom grain began to exhibit increased deformation. As shown in Figure 3b, at the tenth cycle, the transformation stress of the upper part of the bottom grain (near the grain boundary) decreased, bringing the values closer to those of the top grain. This decrease in transformation stress resulted in an increase in regions in which the MT could be triggered in the bottom grain, leading to increased transformation strain in the bottom grain. By comparing the evolution of the strain distributions during the cyclic deformation, it can be deduced that the region exhibiting a decrease in transformation stress was highly correlated with the region undergoing MT. In the first compression test, the MT band in the bottom grain was clearly identified. During cyclic deformation, the MT in the bottom grain mainly originated from this band, and the residual strain in this region accumulated. This band, which was associated with accumulated permanent deformation, also experienced a more severe decrease in transformation stress than that of the top grain, as shown in Figure 3c, which reveals the decrement in transformation stress after twenty cycles. Because the transformation stress in the top and bottom grains (near the grain boundary) became similar after cyclic deformation, a concurrent MT occurred in the later cycles in these grains, leading to a significantly different deformation behavior from that of the first cycle.

At the beginning of the twentieth compression cycle, the band of residual strain at the bottom grain extended, and more residual strain remained. Furthermore, during the loading process, the upper part of the bottom grain showed a level of transformation stress closer to that of the top grain, as shown in Figure 3b. According to Figure 3b, the decrease in transformation stress in the bottom grain was initiated around the grain boundary and then propagated to the lower part of the bottom grain. By comparing the evolution of the strain distributions during the cyclic deformation, it can be deduced that the region exhibiting a decrease in transformation stress was highly correlated with the region undergoing MT. In the first compression test, the MT band in the bottom grain was clearly identified. During cyclic deformation, the MT in the bottom grain mainly originated from this band, and the residual strain in this region accumulated. To further investigate the relationships between transformation stress (*σ*s) and residual strain (*ε*r), the local axial stress–stain responses (*σ*yy, *ε*yy) at probing points A, B, and C (Figure 3b) are shown in Figure 4a. The evolutions of the transformation stresses and the accumulations of residual strains at these points are shown in Figure 4b,c. Point A was set in the top grain, and points B and C in the bottom grain were placed in the regions that underwent full MT and partial MT, respectively. At point A in the top grain, a stable transformation stress was observed after twenty compression cycles. By contrast, varied mechanical responses in terms of transformation stress and accumulation of irrecoverable strain were observed for points B and C in the bottom grain. The transformation stress and residual strain at these three points were quantified and are presented in Figure 4b,c, respectively. Figure 4b shows a comparison of different grain orientations (points A and B). The transformation stress at point A was observed to have slight decreasing behavior, while at point B, the decrease in transformation stress was more significant (i.e., from 400 MPa to

This band, which was associated with accumulated permanent deformation, also experienced a more severe decrease in transformation stress than that of the top grain, as shown

became similar after cyclic deformation, a concurrent MT occurred in the later cycles in these grains, leading to a significantly different deformation behavior from that of the first

cycle.

311 MPa). The results also show that, for points having the same grain orientation (points B and C), point B, which undergoes more MT (i.e., higher transformation strain, *ε*tr), exhibits faster decreasing behavior than point C, as determined from the stress–strain curve in Figure 4a. In other words, in a single grain, a region that underwent more MT (i.e., high *ε*tr) experienced a greater decrease in transformation stress. Notably, after twenty cycles, the transformation stresses at points A and B became nearly equal, as shown in Figure 4b, which resulted in more MT in the bottom grain. underwent full MT and partial MT, respectively. At point A in the top grain, a stable transformation stress was observed after twenty compression cycles. By contrast, varied mechanical responses in terms of transformation stress and accumulation of irrecoverable strain were observed for points B and C in the bottom grain. The transformation stress and residual strain at these three points were quantified and are presented in Figure 4b,c, respectively. Figure 4b shows a comparison of different grain orientations (points A and B). The transformation stress at point A was observed to have slight decreasing behavior,

To further investigate the relationships between transformation stress (ୱ) and residual strain (୰), the local axial stress–stain responses (௬௬, ௬௬) at probing points A, B, and C (Figure 3b) are shown in Figure 4a. The evolutions of the transformation stresses and the accumulations of residual strains at these points are shown in Figure 4b,c. Point A was set in the top grain, and points B and C in the bottom grain were placed in the regions that

*Materials* **2021**, *14*, x FOR PEER REVIEW 7 of 13

Considering the loading cycles, a region that underwent more MT in the bottom grain also caused a faster accumulation of unrecoverable strain, as shown in Figure 4c. An *ε*<sup>r</sup> of 4% at point B was observed after twenty compression cycles, roughly four times greater when compared with the accumulation at point C. For point A, an *ε*<sup>r</sup> of 0.5% was observed, which is the minimum strain among these points owing to its lower transformation stress. In different grains, the grain requiring a higher stress to induce MT (the bottom grain) showed a larger residual strain and faster decrease in transformation stress. In addition, in the same grain (the bottom grain), the regions with more MT accumulated more residual strain and exhibited a clear decrease in transformation stress. while at point B, the decrease in transformation stress was more significant (i.e., from 400 MPa to 311 MPa). The results also show that, for points having the same grain orientation (points B and C), point B, which undergoes more MT (i.e., higher transformation strain, ε୲୰), exhibits faster decreasing behavior than point C, as determined from the stress–strain curve in Figure 4a. In other words, in a single grain, a region that underwent more MT (i.e., high ୲୰ ) experienced a greater decrease in transformation stress. Notably, after twenty cycles, the transformation stresses at points A and B became nearly equal, as shown in Figure 4b, which resulted in more MT in the bottom grain.

**Figure 4.** (**a**) Local axial stress–strain responses (௬௬, ௬௬) recorded by the probing points (according to Figure 3b) along the axial centerline for several selected compression–unloading cycles (C1, C5, C10, and C20). The evolution of the (**b**) transformation stress ୱ and (**c**) residual strain ୰ with respect to the number of cycles. These values are computed from **Figure 4.** (**a**) Local axial stress–strain responses (*σ*yy, *ε*yy) recorded by the probing points (according to Figure 3b) along the axial centerline for several selected compression–unloading cycles (C1, C5, C10, and C20). The evolution of the (**b**) transformation stress *σ*s and (**c**) residual strain *ε*r with respect to the number of cycles. These values are computed from the local axial stress–strain responses shown in (**a**).

#### the local axial stress–strain responses shown in (**a**). **4. Discussion**

Considering the loading cycles, a region that underwent more MT in the bottom grain also caused a faster accumulation of unrecoverable strain, as shown in Figure 4c. An ୰ of 4% at point B was observed after twenty compression cycles, roughly four times greater when compared with the accumulation at point C. For point A, an ୰ of 0.5% was observed, which is the minimum strain among these points owing to its lower transfor-The difference in transformation stress between the two crystal grains is attributed to the difference of their crystal orientations. According to [18], the habit planes of Cu-Al-Mn martensite are {0.16 −0.72 −0.68} and the shear directions are <0.14 −0.65 0.74>. With these transformation systems, the maximum Schmid factor of the two grains with orientations [5 3 26]<sup>β</sup> (top grain) and [6 5 11]<sup>β</sup> (bottom grain) is determined to be 0.49 and 0.32, respectively. As the Schmid factor of the bottom grain is smaller than that of

mation stress. In different grains, the grain requiring a higher stress to induce MT (the bottom grain) showed a larger residual strain and faster decrease in transformation stress.

the top grain, larger stress is needed to trigger MT in the bottom grain. Therefore, the transformation stress of the bottom grain (398 MPa) is larger than that of the top grain (306 MPa), as shown in Figure 2b and Table 1.

The previous results (Figure 3) show that the decrease in transformation stress in a bicrystal Cu-Al-Mn SMA under a strain-controlled cyclic compression–unloading test was affected by the accumulation of residual strain. These macroscopic residual strains are mainly a result of dislocation slips in the austenite phase [19–24] and accumulated residual martensite phase owing to an incomplete reverse MT [19,25,26]. These dislocation slips, which can be triggered separately during forward and reverse MTs [27], are fostered by localized stress fields between austenite–martensite interfaces during forward and reverse MTs [20,28–30]. Such dislocation slips and residual martensite can also cause mesoscopic residual stress fields within the specimen [31]. Therefore, the mesoscopic residual stress field, which is of the same type as the applied stress, assists in the nucleation of martensite variants [19], and thus leads to a significant reduction in the macroscopic transformation stress required to trigger MT during subsequent cycles [32–36].

In order to provide clear evidence, the bottom grain was cut from the bicrystal sample for thermal analysis. As shown in Figure 5a, after 20 cyclic deformations, the first heat curve shows that the reverse MT occurred at about 140.1 ◦C. The sample was then cooled to −140 ◦C (Step 2), and a forward MT was identified at −87.7 ◦C. During the second heating (Step 3), the reverse transformation occurred at −69.7 ◦C, instead of the 140.1 ◦C in the first heating curve. This feature indicated that the martensite was stabilized during the cyclic compressions. The stabilized martensite needed a higher temperature to transform back to austenite, as shown in the first heating curve. In the successive cooling and heating, the martensite was thermally induced and thus was not stabilized, causing the reverse transformation temperature to be restored to its normal value (−69.7 ◦C). The feature of martensite being stabilized after deformation was also reported in other Cu-based [37] and TiNi-based SMAs [38]. *Materials* **2021**, *14*, x FOR PEER REVIEW 9 of 13

**Figure 5.** (**a**) Thermal analysis of the bottom grain after 20 compression cycles. (**b**,**c**) TEM bright field images of the bottom grain, which show the formation of dislocations and residual martensite after cyclic compression, respectively. **Figure 5.** (**a**) Thermal analysis of the bottom grain after 20 compression cycles. (**b**,**c**) TEM bright field images of the bottom grain, which show the formation of dislocations and residual martensite after cyclic compression, respectively.

As shown in Figure 2b, the higher transformation stress in the bottom grain generates more dislocations in the austenite phase and more residual martensite during the forward and reverse MT. Both mechanisms lead to plasticity formed mainly in the bottom grain. Both the dislocation and stabilized martensite can cause mesoscopic residual stress fields within the specimen. Such residual stress assisted the nucleation of martensite variants and thus led to a significant reduction in the macroscopic transformation stress required TEM analyses were performed on the bottom grain after cyclic compression. Figure 5b shows the TEM bright-field image of the bottom grain, in which entangled dislocations can be observed. Figure 5c shows large amounts of residual martensite in the bottom grain, indicating that martensite was stabilized at room temperature by dislocations after cyclic deformation. The TEM observations confirmed that the residual strain is caused by the dislocation and residual martensite formed during cyclic deformation.

to trigger MT during subsequent cycles. On the other hand, the top grain exhibited smaller residual strain owing to its smaller transformation stress, and thus its transformation stress remained stable. In addition, in the bottom grain, the decreasing behavior varied significantly between regions undergoing different levels of transformation strain (points B and C). As shown in Figure 3c or Figure 4b, point B experienced more MT and associated As shown in Figure 2b, the higher transformation stress in the bottom grain generates more dislocations in the austenite phase and more residual martensite during the forward and reverse MT. Both mechanisms lead to plasticity formed mainly in the bottom grain. Both the dislocation and stabilized martensite can cause mesoscopic residual stress fields within the specimen. Such residual stress assisted the nucleation of martensite variants

residual strain compared with point C. Consequently, point B exhibited a larger decrease in transformation stress than point C. These results support the hypothesis that the

amined to investigate the deformation in the vicinity of the grain boundary. Figure 6a shows the evolution of ௫௫ during loading toward and unloading away from a gauge strain of 5% for the first, tenth, and twentieth compression–unloading cycles. As shown in the unloaded state ( = 0.2%) of the first compression cycle, the bottom grain exhibits an accumulation of residual ௫௫ near the grain boundary (highlighted in the red rectangle), while the remaining part of the grain boundary shows relatively less residual ௫௫. In the tenth and twentieth cycles, this accumulation of residual ௫௫ in the red rectangle kept increasing and expanding toward the remaining part of the grain boundary. Note that, in the right half-part of the grain boundary, the bottom grain accumulated more residual ௫௫ than the top grain. These differences in the accumulation of residual ௫௫ or strain incompatibility in the vicinity of the grain boundary in a bicrystal reveal the relative

movement between the top grain and bottom grain.

and thus led to a significant reduction in the macroscopic transformation stress required to trigger MT during subsequent cycles. On the other hand, the top grain exhibited smaller residual strain owing to its smaller transformation stress, and thus its transformation stress remained stable. In addition, in the bottom grain, the decreasing behavior varied significantly between regions undergoing different levels of transformation strain (points B and C). As shown in Figure 3c or Figure 4b, point B experienced more MT and associated residual strain compared with point C. Consequently, point B exhibited a larger decrease in transformation stress than point C. These results support the hypothesis that the mesoscopic stress field caused by dislocations or residual martensite assisted MT.

In this study, the horizontal strain fields *ε*xx at the surface of the specimen were examined to investigate the deformation in the vicinity of the grain boundary. Figure 6a shows the evolution of *ε*xx during loading toward and unloading away from a gauge strain *ε*<sup>g</sup> of 5% for the first, tenth, and twentieth compression–unloading cycles. As shown in the unloaded state (*ε*<sup>g</sup> = 0.2%) of the first compression cycle, the bottom grain exhibits an accumulation of residual *ε*xx near the grain boundary (highlighted in the red rectangle), while the remaining part of the grain boundary shows relatively less residual *ε*xx. In the tenth and twentieth cycles, this accumulation of residual *ε*xx in the red rectangle kept increasing and expanding toward the remaining part of the grain boundary. Note that, in the right half-part of the grain boundary, the bottom grain accumulated more residual *ε*xx than the top grain. These differences in the accumulation of residual *ε*xx or strain incompatibility in the vicinity of the grain boundary in a bicrystal reveal the relative movement between the top grain and bottom grain. *Materials* **2021**, *14*, x FOR PEER REVIEW 10 of 13

**Figure 6.** (**a**) Distribution of horizontal strain fields ௫௫ during loading toward and unloading away from the gauge strain ε of 5% in the bicrystal Cu-Al-Mn SMA sample for selected compression–unloading cycles: C1, C10, and C20. (**b**) The evolution of average incompatibility strain ∆ε௫௫ ୟ୴ in the regions (R2-R1 and R4-R3) with respect to the number of cycles. These values are computed from the strain fields multiplied by transformation matrix based on the angle between loading direction and normal direction of the grain boundary (inset of (**b**)). **Figure 6.** (**a**) Distribution of horizontal strain fields *ε*xx during loading toward and unloading away from the gauge strain *ε*<sup>g</sup> of 5% in the bicrystal Cu-Al-Mn SMA sample for selected compression–unloading cycles: C1, C10, and C20. (**b**) The evolution of average incompatibility strain ∆*ε* avg xx in the regions (R2-R1 and R4-R3) with respect to the number of cycles. These values are computed from the strain fields multiplied by transformation matrix based on the angle between loading direction and normal direction of the grain boundary (inset of (**b**)).

To further investigate incompatibility conditions of the grain boundary, we quantified the average incompatibility strain ∆ε௫௫ ୟ୴ near the grain boundary. The definition of ∆ε௫௫ ୟ୴ is the average ௫௫ in the selected region of the bottom grain minus the average ௫௫ To further investigate incompatibility conditions of the grain boundary, we quantified the average incompatibility strain ∆*ε* avg xx near the grain boundary. The definition of ∆*ε* avg xx is the average *ε*xx in the selected region of the bottom grain minus the average *ε*xx in the

in the selected region of the top grain. As shown in inset of Figure 6b, we selected four regions near the grain boundary (R1, R2, R3, and R4) and paired the regions (i.e., R2–R1

creased from 0.05% to 0.67%. These results show that the incompatibility of the grain boundary in the region R4-R3 is more severe than that in the region R2-R1. Such a difference between these two regions can be ascribed to the angle between the loading direction and normal direction of the grain boundary. As can be seen in the inset of Figure 6b, the grain boundary in the region R4-R3 deviates from the horizontal plane by approximately 22.5 degrees. This variation in the direction of grain boundary will introduce the major axial deformation ௬௬ as an extra component of tangential movement to the inclined grain boundary (see the right half-part of the grain boundary during the loading process in Figure 3a). Hence, the regions near the inclined grain boundary will experience not only larger axial deformation (Figure 3a), but also larger relative movement (Figure 6a) compared with the regions near the flat grain boundary. Consequently, a significant difference

occurs, as shown in Figure 6b. Additionally, as reported in the previous work [11], the top and bottom grains underwent outward and inward out-of-plane deformations during compression–unloading cycles. This out-of-plane motion was considered for causing generation of microcracks. In this study, we found that the incompatibility along the *x* direction of the bicrystal Cu-Al-Mn sample under cyclic compression could be another mechanism for formation of microcrack at the grain boundary. Thus, even though compressive

ୟ୴ regarding the selected compression–un-

ୟ୴ between the two regions (i.e., R2-R1 and R4-R3)

ୟ୴ in the region R2-R1 in-

ୟ୴ in

the region R4-R3 increased from 0.07% to 1.51%, while the ∆ε௫௫

and R4–R3) to compute their evolution of ∆ε௫௫

in average incompatibility strain ∆ε௫௫

selected region of the top grain. As shown in inset of Figure 6b, we selected four regions near the grain boundary (R1, R2, R3, and R4) and paired the regions (i.e., R2–R1 and R4–R3) to compute their evolution of ∆*ε* avg xx regarding the selected compression–unloading cycles, C1, C10, and C20. In Figure 6b, the average incompatibility strain ∆*ε* avg xx in the region R4–R3 increased from 0.07% to 1.51%, while the ∆*ε* avg xx in the region R2–R1 increased from 0.05% to 0.67%. These results show that the incompatibility of the grain boundary in the region R4–R3 is more severe than that in the region R2–R1. Such a difference between these two regions can be ascribed to the angle between the loading direction and normal direction of the grain boundary. As can be seen in the inset of Figure 6b, the grain boundary in the region R4-R3 deviates from the horizontal plane by approximately 22.5 degrees. This variation in the direction of grain boundary will introduce the major axial deformation *ε*yy as an extra component of tangential movement to the inclined grain boundary (see the right half-part of the grain boundary during the loading process in Figure 3a). Hence, the regions near the inclined grain boundary will experience not only larger axial deformation (Figure 3a), but also larger relative movement (Figure 6a) compared with the regions near the flat grain boundary. Consequently, a significant difference in average incompatibility strain ∆*ε* avg xx between the two regions (i.e., R2–R1 and R4–R3) occurs, as shown in Figure 6b. Additionally, as reported in the previous work [11], the top and bottom grains underwent outward and inward out-of-plane deformations during compression–unloading cycles. This out-of-plane motion was considered for causing generation of microcracks. In this study, we found that the incompatibility along the x direction of the bicrystal Cu-Al-Mn sample under cyclic compression could be another mechanism for formation of microcrack at the grain boundary. Thus, even though compressive deformation is considered a preferred deformation mode to delay fatigue fracture of metallic materials [12,13], the out-of-plane motion and relative deformation near the grain boundary along the x direction in a bicrystal Cu-Al-Mn sample may cause cracking and even fracture in Cu-Al-Mn SMAs.

With the aid of the full-field stress and strain measurements (i.e., DIC and DDI techniques) for revealing strain and transformation stress fields, it was found that grain boundary kinking plays an important role in the decrease in transformation stress near the grain boundary in the bicrystal Cu-Al-Mn sample. As can be seen in Figure 3a, during the loading process, because the right half-part of the grain boundary underwent more MT than the other part of the grain boundary, more residual strain remained near the right half-part of the grain boundary at the end of the cycle (*ε*<sup>g</sup> = 0.2% in Figure 3a). As mentioned above, residual strain causes the decrease in transformation stress. Hence, this additional residual strain near the kink grain boundary will induce an extra decrease in transformation stress. As can be seen in Figure 3c, the transformation stress near the right half-part of the grain boundary degraded faster than other part of the grain boundary. Thus, we concluded that the grain boundary kinking in bicrystal induces an additional decrease in transformation stress.

Furthermore, during the strain-controlled cyclic loading (5% strain for each cycle), the transformation stress of the bottom grain gradually decreased to the values close to those of the top grain (Figure 3b,c). Hence, the bottom grain gradually had more MT, and thus a larger *ε*tr than in its first cycle, as shown in Figure 3a. This explains why the average *ε*tr in the bottom grain increased with the increasing numbers of deformation cycles, as shown in Figure 2b and Table 1. By contrast, because the bottom grain contributed more deformation, the MT and the associated strain contributed by the top grain decreased when the deformation cycles increased, as shown in Figure 2b or Figure 3a. Hence, the average *ε*tr in the top grain decreased with the increasing number of deformation cycles, as shown in Table 1. Therefore, the initially inhomogeneous deformation behavior in the bicrystal sample became slightly more homogeneous after twenty cyclic compressive deformations, as shown in Figure 3a.

The full-field stress and strain measurements provide a promising technique for measuring stress–strain responses in SMAs. This new method offers not only insights into cyclic superelastic deformation, but also the compressive fatigue behavior of Cu-Al-Mn SMAs. With this method, several future research directions could be considered, including the influence of misorientation between two grains on its mechanical properties, the effect of grain boundary geometry on the grain boundary strength [39–41], and the shape memory recoverability between two grains in a bicrystal sample. Furthermore, a direct connection between macroscopic shape memory effects and stress and strain states at the materials' grains could also be elucidated in the future.

### **5. Conclusions**

In summary, this study investigated the distribution of transformation stress and strain fields in a bicrystal Cu-Al-Mn sample under cyclic compression. The decrease in transformation stress in both grains correlated with the accumulation of residual strain. The accumulation of residual strain depends on factors such as grain orientation along the loading directions, transformation strain, and grain boundaries. These experimental results and analyses demonstrated that dislocation slip and residual martensite were triggered more easily when a higher transformation stress was required to trigger MT, thus resulting in greater residual strain and a larger decrease in transformation stress. The decreasing behavior at the grain boundary was related to strain incompatibility and the angle between loading direction and the normal direction of grain boundary. Consequently, microstructures with low-angle grain boundaries or single crystals, which exhibit more homogenous deformation behaviors and less restrictions from grain boundaries, will demonstrate higher functional stability and thus longer lifetimes during their cyclic service lives.

**Author Contributions:** Conceptualization, T.-H.S., C.-H.C. and C.-S.C.; data curation, T.-H.S.; formal analysis, T.-H.S. and N.-H.L.; investigation, T.-H.S. and N.-H.L.; methodology, T.-H.S. and N.-H.L.; software, T.-H.S. and N.-H.L.; visualization, T.-H.S. and N.-H.L.; resources, N.-H.L.; writing—original draft, T.-H.S., N.-H.L. and C.-H.C.; writing—review and editing, T.-H.S., N.-H.L., C.-H.C. and C.-S.C.; funding acquisition, C.-H.C. and C.-S.C.; supervision, C.-H.C. and C.-S.C.; project administration, C.-S.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Ministry of Science and Technology (MOST), Taiwan, under Grant 108-2221-E-002-005-MY3, and by the Young Scholar Fellowship program of MOST, under Grant 109-2636-E-002-031.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.

**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

#### **References**

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