_{50}Ni

_{50−x}Cu

_{x}

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The damping characteristics of Ti_{50}Ni_{50−x}Cu_{x}_{0}) softening/hardening and the strain variation exhibited in B2↔B19 transformation are all higher than those in B2↔B19’ transformation. The larger _{0} softening/hardening in B2↔B19 can induce higher strain variation in this transformation. It is suggested that the greater mobility of the twin boundaries and the larger magnitude of the strain variation both cause the higher tan δ value exhibited in B2↔B19 transformation, as compared with B2↔B19’ transformation. In comparison with that in B19’ martensite, the _{0} value in B19 martensite is low and not affected so greatly by changes in temperature. Relaxation peaks are observed in B19’ martensite, but not in B19 martensite, because the latter has rare twinned variants. The activation energy of the relaxation peak is calculated and found to increase as the Cu-content increases in these SMAs.

TiNi shape memory alloys (SMAs), which undergo thermoelastic martensitic transformation can exhibit good shape memory effect (SME), pseudoelasticity (PE), and high damping capacity [_{50}Ni_{50−x}Cu_{x}_{0}) softening/hardening and the magnitude of the tan δ value exhibited in TiNiCu SMAs during B2↔B19’ and B2↔B19 martensitic transformations have not been clarified. In addition, a broad peak appears at around −70 °C in the DMA curve of TiNi/TiNiCu SMAs [_{0} softening/hardening, is called the relaxation peak. However, the effect of the Cu-content of Ti_{50}Ni_{50−x}Cu_{x}_{0} softening/hardening associated with B2↔B19’ and B2↔B19 transformations in Ti_{50}Ni_{50−x}Cu_{x}_{50}Ni_{50−x}Cu_{x}_{a}) are also discussed.

As mentioned in _{Tr}) [_{50}Ni_{50−x}Cu_{x}_{50}Ni_{50−x}Cu_{x}_{S}’ − _{S} = 15 °C by _{S}’and _{S} are the starting transformation temperatures of B2→B19 and B19→B19’, respectively. The DSC curves for

_{0}) value is lower in B2↔B19 transformation than in B19↔B19’ transformation. At the same time, the tan δ peak is sharp for B2↔B19 transformation, but it is rather broad for B19↔B19’ transformation. This feature may have resulted from the fact that the difference of the starting and finishing transformation temperatures for B2↔B19 is much smaller than that for B19↔B19’ [

The broad peaks at around −30 °C~−70 °C for _{p} of these broad peaks does not shift to higher temperatures when the applied frequency is increased. Therefore, these broad peaks are not relaxation peaks but B19↔B19’ transformation peaks, for this transformation is an athermal process [

It is well known that the softening of the elastic shear constant occurs in the forward martensitic transformation of SMAs [_{0} _{0} _{0} softening/hardening and the _{0} slope in B19 and B19’ martensites are measured, and they are listed in _{0} softening/hardening and the values of the _{0} slope in B19 and B19’ martensites are defined in the schematic _{0} _{0} softening in B2→B19 transformation is much larger than that in B2→B19’ transformation for _{0} hardening associated with the reverse martensitic transformation. These features demonstrate that the _{0} softening/hardening exhibited in B2↔B19 transformation is more significant than that in B2↔B19’ transformation.

Carefully examining _{0} slope in B2 phase is positive, but those in B19 and B19’ martensites are both negative. As shown in _{50}Ni_{40}Cu_{10} SMA, the value of the _{0} slope in B19 martensite is −85 MPa/°C, and that in B19’ martensite is −329 MPa/°C. This indicates that the absolute value of the _{0} slope in B19’ martensite is much higher than that in B19 martensite. This characteristic may imply that the magnitude of the elastic modulus in B19 martensite is less than that in B19’ martensite. In addition, the _{0} value of B19 martensite does not change much as the temperature decreases, but it changes significantly in B19’ martensite. As also can be seen from _{0} softening is slightly less than that of _{0} hardening in B2↔B19’ transformation, but it is just the reverse in B2↔B19 transformation. This feature may be related to the insignificant _{0} softening/hardening occurred in B2↔B19’ transformation.

The tan δ value and storage modulus (_{0}) curves for Ti_{50}Ni_{50−x}Cu_{x}_{0} slope in B19’ martensite, and the red numbers are the magnitude of _{0} softening and hardening.

The tan δ value and storage modulus (_{0}) curves for Ti_{50}Ni_{50−x}Cu_{x}_{0} slopes in B19’ and B19 martensites, and the red numbers are the magnitude of _{0} softening and hardening.

The tan δ value and storage modulus (_{0}) curves for Ti_{50}Ni_{50−x}Cu_{x}_{0} slope in B19 martensite, and the red numbers are the magnitude of _{0} softening and hardening.

Summary of the storage modulus (_{0}) softening/hardening and the slope of _{0}

Ti_{50}Ni_{50−x}Cu_{x} |
Transformation Sequences | _{0} softening (MPa) |
_{0} hardening (MPa) |
Slope of B19 (MPa/°C) | Slope of B19’ (MPa/°C) |
---|---|---|---|---|---|

0 | B2↔B19’ | 2922 | 1161 | N/A | −166 |

5 | 3216 | 4700 | N/A | −210 | |

7.5 | 3732 | 4632 | N/A | −211 | |

10 | B2↔B19↔B19’ | 20,486 | 19,291 | −85 | −329 |

12.5 | 21,280 | 20,457 | −39 | −254 | |

15 | 18,270 | 16,316 | −53 | −148 | |

20 | B2↔B19 | 13,587 | 13,519 | −40 | N/A |

25 | 28,199 | 26,592 | −81 | N/A | |

30 | 17,766 | 17,560 | −82 | N/A |

The schematic diagram for the definitions of the storage modulus (_{0}) softening/hardening and the slope of _{0}

a: the _{0} slope in B19’ martensite; b: the _{0} slope in B19 martensite; c: the magnitude of _{0} softening; d: the magnitude of _{0} hardening.

_{50}Ni_{50−x}Cu_{x}_{0} softening and hardening, respectively [_{0} softening/hardening is, the larger the strain variation is. From _{0} softening/hardening than the latter during martensitic transformation.

The strain variation curves for Ti_{50}Ni_{50−x}Cu_{x}

It is interesting to clarify why the tan δ peak associated with B2↔B19 transformation is higher than that associated with B2↔B19’ transformation. Although the tan δ values in this study are most contributed from the transitory term (IF_{Tr}), as mentioned in _{PT}) and the intrinsic term (IF_{I}) associated with B2↔B19 transformation are also higher than those associated with B2↔B19’ transformation. The magnitude of the tan δ value exhibited by IF_{PT} term and that by IF_{I} term are closely related to the mobility of the phase interface between the parent phase and martensite and the twin boundary between the martensite variants. It has been reported that the twinning shear exhibited in B2→B19 transformation is smaller than that in B2→B19’ transformation [_{0} softening/hardening during B2↔B19 transformation is greater than that during B2↔B19’ transformation, which can induce higher strain variation in B2↔B19 transformation than in B2↔B19’ transformation, as shown in

As mentioned in _{50}Ni_{50−x}Cu_{x}_{50}Ni_{34}Cu_{16} and Ti_{50}Ni_{30}Cu_{20} SMAs. They found that, in B19 martensite, the twins will be induced to reduce the strain energy if the specimen is slowly cooled from B2 phase. Because, in reference [

_{p} for Ti_{50}Ni_{50−x}Cu_{x}_{a} value is calculated; this value is listed in each plot and also in _{a} values in Ti_{50}Ni_{30}Cu_{15} [_{50}Ni_{34}Cu_{16} [_{50}Ni_{34}Cu_{20} [_{50}Ni_{34}Cu_{25} SMAs [_{a} value is in the range of 0.43~0.69 eV, and it increases as the Cu-content increases, whether in cooling or in heating.

The plots of ln frequency _{50}Ni_{50−x}Cu_{x}

The activation energy (_{a}) values of Ti_{50}Ni_{50−x}Cu_{x}

Ti_{50}Ni_{50−x}Cu_{x} |
0 ^{a} |
5 ^{a} |
7.5 ^{a} |
15 ^{b} |
16 ^{c} |
20 ^{c} |
25 ^{b} |
---|---|---|---|---|---|---|---|

In cooling | 0.43 eV | 0.48 eV | 0.51 eV | N/A | 0.76 eV | 0.67 eV | N/A |

In heating | 0.46 eV | 0.56 eV | 0.69 eV | 0.68 eV | 0.71 eV | 0.64 eV | 0.61 eV |

a: Data from

However, for _{a} value in cooling/heating is in the range of 0.61~0.76 eV and it doesn’t change so much as the Cu-content increases. In addition, the _{a} value for _{a} value shown in

Ti_{50}Ni_{50−x}Cu_{x}^{−4}. For Ti_{50}Ni_{50−x}Cu_{x}_{3}:H_{2}O =1:5:20 in volume ratio. Thereafter, the plates and the ingots were diamond-saw-cut and spark-cut, respectively, into specimens with dimensions of 40.0 × 4.8 × 1.6 mm^{3} for DMA tests. The damping properties of the specimens were measured with a TA 2980 DMA instrument equipped with a single cantilever and a liquid nitrogen cooling apparatus. The continuous cooling/heating rate was 3 °C/min, and the temperature was ranged from −130 °C to 150 °C. The applied strain and frequency were set at 7.1 × 10^{−5} and 1 Hz, respectively. From DMA tests, the curves of the tan δ, storage modulus (_{0}) and the strain variation values _{a}) of the relaxation peak, different frequencies of 0.5, 1, 5, 10, 20 and 100 Hz were employed under a constant strain of 7.1 × 10^{−5}. The _{a} was calculated according to Equation (1):
_{0}·exp(_{a}/R_{p}) = 1
_{0}_{p} is the peak temperature of the relaxation peak in absolute temperature[

DMA tests at low frequency show that Ti_{50}Ni_{50−x}Cu_{x}_{0}) softening/hardening, and strain variation values associated with B2↔B19 transformation are all higher than those with B2↔B19’ transformation. The larger _{0} softening/hardening in B2↔B19 can induce higher strain variation in this transformation. It is suggested that the greater mobility of the twin boundaries and the larger magnitude of the strain variation cause the higher tan δ value exhibited in B2↔B19 transformation than in B2↔B19’ transformation. The _{0} slope in B19’ martensite is much higher than that in B19 martensite, in which the latter is not affected so greatly by changes in temperature, but the former is significantly affected. Relaxation peaks are observed in B19’ martensite for _{a} values of the relaxation peaks are calculated and compared with those reported before, and it is concluded that Ti_{50}Ni_{50−x}Cu_{x}_{a} values.

The authors gratefully acknowledge the financial support for this study provided by the National Science Council (NSC) and National Taiwan University (NTU), Taiwan, under Grants NSC100-2221-E002-100-MY3, NSC 102-2221-E-197-006 and NTU-103R891803 (The Excellence in Research Program, NTU), respectively.

Miss Chen Chien contributes to the sections of the “experimental procedures” and the “results and discussion” of this paper. Shyi-Kaan Wu contributes to the section of “results and discussion”, and he is the principal investigator (PI) of the grants NSC100-2221-E002-100-MY3 and NTU-103R891803. Shih-Hang Chang also contibutes to the section of “results and discussion”, and he is the principal investigator of the grant NSC 102-2221-E-197-006. These grants are also mentioned in the “Acknowledgement” of this paper.

The authors declare no conflict of interest.

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