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

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{3}and CH

_{3}OH (2:8 in volume). The preparation procedures for the bicrystal Cu-Al-Mn sample were detailed in the literature [11].

^{−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 virtual strain gauge by optical DIC (VIC-Gauge 3D, Correlated Solutions, Irmo, SC, USA). Three deformation strains (i.e., global gauge strain ${\epsilon}_{\mathrm{g}}$ as shown in Figure 1 and the local strain gauges at the top and bottom grains ${\epsilon}_{\mathrm{t}}$ and ${\epsilon}_{\mathrm{b}}$ 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

^{−1}) is higher than the strain rate (2.4 × 10

^{−3}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.

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**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 (${\sigma}_{\mathrm{s}}$), residual strain (${\epsilon}_{\mathrm{r}}$), and transformation strain (${\epsilon}_{\mathrm{tr}}$)) can be computed from the stress–strain responses.

**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 (${\epsilon}_{\mathrm{t}}$), bottom grain (${\epsilon}_{\mathrm{b}}$), and the entire specimen (${\epsilon}_{\mathrm{g}}$). The bicrystal sample was loaded to a gauge strain (${\epsilon}_{\mathrm{g}}$) of 5% during cyclic deformation. Local virtual strain gauges ${\epsilon}_{\mathrm{t}}$ and ${\epsilon}_{\mathrm{b}}$ were used to measure the average strains in the top and bottom grains, respectively (inset of (

**b**)).

**Figure 3.**Distribution of (

**a**) axial strain fields ${\epsilon}_{\mathrm{yy}}$ during loading toward and unloading away from the gauge strain ${\epsilon}_{\mathrm{g}}$ of 5% and (

**b**) transformation stress fields ${\sigma}_{\mathrm{s}}$ 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 $\left({\sigma}_{\mathrm{yy}},{\epsilon}_{\mathrm{yy}}\right)$ as shown in Figure 4a. (

**c**) Transformation stress difference $\u2206{\sigma}_{\mathrm{s}}$, which is the difference in transformation stress between cycles 1 and 20, shown in the plot in Figure 3b.

**Figure 4.**(

**a**) Local axial stress–strain responses (${\sigma}_{\mathrm{yy}},{\epsilon}_{\mathrm{yy}})$ 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 ${\sigma}_{\mathrm{s}}$ and (

**c**) residual strain ${\epsilon}_{\mathrm{r}}$ with respect to the number of cycles. These values are computed from the local axial stress–strain responses shown in (

**a**).

**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 6.**(

**a**) Distribution of horizontal strain fields ${\epsilon}_{\mathrm{xx}}$ during loading toward and unloading away from the gauge strain ${\epsilon}_{\mathrm{g}}$ 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 $\u2206{\epsilon}_{\mathrm{xx}}^{\mathrm{avg}}$ 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**)).

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

Loading Direction | Theoretical Transformation Strain (%) | Number of Cycles | Transformation Stress (MPa) | Residual Strain (%) | Transformation Strain (%) | |
---|---|---|---|---|---|---|

Top | [5 3 26] | 10.1 | 1st | 306 | 0.12 | 5.7 |

20th | 297 | 0.77 | 5.1 | |||

Bottom | [6 5 11] | 7.1 | 1st | 398 | 0.14 | 2.0 |

20th | 292 | 2.17 | 3.9 | |||

Average | − | − | 1st | 313 | 0.24 | 3.5 |

20th | 290 | 1.78 | 4.0 |

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**MDPI and ACS Style**

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

**AMA Style**

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(16):4439.
https://doi.org/10.3390/ma14164439

**Chicago/Turabian Style**

Su, Tung-Huan, Nian-Hu Lu, Chih-Hsuan Chen, and Chuin-Shan Chen. 2021. "On the Decrease in Transformation Stress in a Bicrystal Cu-Al-Mn Shape-Memory Alloy during Cyclic Compressive Deformation" *Materials* 14, no. 16: 4439.
https://doi.org/10.3390/ma14164439