Schematic illustration showing the roles of internal stress and external stress on stress-induced martensitic transformation in the Ti-Ni SMAs: (a) without internal stress; (b) with internal stress formed by aligned particles of Ti 3 Ni 4 . 

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... the case with a strong internal stress field exerted by aligned coherent particles of Ti 3 Ni 4 , the B2-R trans- formation temperature of V1 is higher than that of V2 because the internal stress selects V1 of the R-phase. This situation is illustrated in Fig. 1(b), where the slope of the phase boundary is assumed to be not influenced by the internal stress. In this case, a stress-induced R(V1) → B2 transformation is possible, as indicated by the arrow in Fig. 1(b). With a further increase in external stress, the B2-phase transforms to the R-phase of the different variant (V2). A thermodynamic explanation of the behavior is given in 19 ...

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... the case with a strong internal stress field exerted by aligned coherent particles of Ti 3 Ni 4 , the B2-R trans- formation temperature of V1 is higher than that of V2 because the internal stress selects V1 of the R-phase. This situation is illustrated in Fig. 1(b), where the slope of the phase boundary is assumed to be not influenced by the internal stress. In this case, a stress-induced R(V1) → B2 transformation is possible, as indicated by the arrow in Fig. 1(b). With a further increase in external stress, the B2-phase transforms to the R-phase of the different variant (V2). A thermodynamic explanation of the behavior is given in 19 ...

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... reason for the stress-induced reverse R-B2 transformation is mainly attributed to the existence of an inter- nal stress and the difference in the stress dependence of the transformation temperature between the different variants as shown in Fig. 1. In the case of the present Ti-51Ni alloy, aligned coherent particles of Ti 3 Ni 4 precipitate is the main cause of internal stress. It has recently been reported that a ribbon of a Ni-Mn-Sn alloy, which does not include coherent precipitates, also shows a stress-induced reverse martensitic transformation due to an internal stress formed in the ribbon through its production 18 . This implies that stress-induced reverse transformation is not a unique case. These transformations may occur in many alloys in which strong internal stresses are ...

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... the difference in stress dependence of the transformation temperature between different variants shown in Fig. 1, we would like to mention a similar behavior in the magnetic field dependence of the transfor- mation temperature of Ni 2 MnGa 22 . The martensite phase of Ni 2 MnGa has strong magnetocrystalline anisotropy. Therefore, a large difference in magnetic energy arises between different variants when a magnetic field is applied. Thus, the magnetic field dependence of the transformation temperature is different between variants: the trans- formation temperature increases with increasing magnetic field when the magnetic field is parallel to the easy axis while it decreases when the magnetic field is perpendicular to the easy axis 22 . ...

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... average temperature of the Age300MPa specimen monitored during the stress-applying and the subse- quent stress-removing is shown in Fig. 3. When the maximum stress is 100 MPa, the temperature decreases by 0.8 K during the stress-applying process (a) and increases by 0.7 K during the stress-removing process (a'). This is due to the stress-induced R(V1) → B2 transformation as mentioned before. When the maximum applied stress is 200 MPa and higher, the temperature decrease is followed by temperature increase. This means that R(V1) → B2 transformation is followed by the B2 → R(V2) transformation in the stress application process. This behavior cor- responds to the vertical arrow shown in Fig. 1(b). In the stress-removing process, the temperature decreases firstly and then increases. This means that R(V2) → B2 transformation is followed by B2 → R(V1) transformation in the stress-removing process. The temperature change caused by the B2 → R(V2) transformation increases as the maximum stress increases. On the other hand, the temperature change caused by the B2-R(V1) transformation is almost independent of stress in the examined stress range, being consistent with the result reported previously 17 ...

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... preparation and characterization. An ingot of Ti-51Ni (at%) alloy was prepared by induction melting and was cast into an iron mold. It was hot rolled into a 1.3 mm thick plate. Tensile test specimens with dimensions of 30 mm in gauge length, 3 mm in width and 0.6 mm in thickness were cut from the rolled plate so that the tensile axis was oriented in the rolling direction. The specimens were solution-treated at 1123 K for 3.6 ks followed by quenching into ice water, then aged at 773 K for 6 ks under an external tensile stress of 300 MPa applied parallel to the tensile axis of the following experiments. We call these specimens Age300MPa. An electron backscattering diffraction analysis revealed that the Age300MPa specimens have a weak (102) <010> texture with an average grain size of 140 μm (Fig. s1 in supplement). For comparison, specimens aged without exter- nal stress were also prepared. We call these specimens Age0MPa. The martensitic transformation temperatures are M s (R) = 315 K, A f (R) = 320 K, M s (B19') = 221 K, and A f (B19') = 297 K for the Age300MPa specimen 17 ; M s (R) = 302 K, A f (R) = 307 K, M s (B19') = 214 K, and A f (B19') = 290 K for Age0MPa specimen 23 . These values were obtained by differential scanning ...

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... intensity of the 211 B2 reflection firstly increases with increasing applied stress then it decreases on fur- ther increasing the applied stress as shown in Fig. 7. The increase of the intensity implies the progress of the stress-induced R(V1) → B2 transformation, and the subsequent decrease implies the stress-induced B2-R(V2) transformation. This behavior corresponds to the vertical arrow shown in Fig. 1(b) and is consistent with the tem- perature change shown in Fig. 3(b). The intensity of the 412 R reflection monotonically decreases as stress increases as shown in Fig. 8. This result also support that the present specimen exhibits stress-induced R(V1) → B2 trans- formation. The intensity of the 114 R reflection is nearly constant below 100 MPa, and it monotonically increases as stress increases as shown in Fig. 9. This result supports stress-induced B2 → R(V2) ...

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... see the change of the diffraction pattern from different aspects, we integrated the 2D pattern within the two sectors indicated by A and B in Fig. 6(a). The angle of these sectors is 20 degrees. The scattering vectors of the reflections within the sector A are close to the loading direction, while those within the sector B are nearly perpendicular to the loading direction. The integrated diffraction patterns in the loading process are presented in Fig. 10(a,b) for the sectors A and B, respectively. These diffraction patterns are essentially composed of the 412 R and 114 R reflections. We may expect the existence of 211 B2 reflection at the position indicated by the dotted red line, but it is almost immersed in the tails of the 412 R ...

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... understand the change in profile we approximate each profile shown in Fig. 10(a) as a single peak contain- ing shoulders. We also approximate each profile shown in Fig. 10(b) as a single peak with an additional small peak of 114 R . Then we evaluate the full width at half maximum (FWHM) value and the d-value of the approximated single peak and the result is shown in Fig. 11(a,b), respectively. The FWHM of sector A first increases and then decreases as the applied stress increases. This increase is probably due to the increase in the intensity of the 211 B2 reflection, which is caused by the stress-induced R(V1)-B2 transformation. The subsequent decrease in FWHM value is due to the decrease in the intensity of the 211 B2 reflection, which is caused by the stress-induced B2-R(V2) transformation. On the other hand, the FWHM of sector B keeps almost ...

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... understand the change in profile we approximate each profile shown in Fig. 10(a) as a single peak contain- ing shoulders. We also approximate each profile shown in Fig. 10(b) as a single peak with an additional small peak of 114 R . Then we evaluate the full width at half maximum (FWHM) value and the d-value of the approximated single peak and the result is shown in Fig. 11(a,b), respectively. The FWHM of sector A first increases and then decreases as the applied stress increases. This increase is probably due to the increase in the intensity of the 211 B2 reflection, which is caused by the stress-induced R(V1)-B2 transformation. The subsequent decrease in FWHM value is due to the decrease in the intensity of the 211 B2 reflection, which is caused by the stress-induced B2-R(V2) transformation. On the other hand, the FWHM of sector B keeps almost ...

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... understand the change in profile we approximate each profile shown in Fig. 10(a) as a single peak contain- ing shoulders. We also approximate each profile shown in Fig. 10(b) as a single peak with an additional small peak of 114 R . Then we evaluate the full width at half maximum (FWHM) value and the d-value of the approximated single peak and the result is shown in Fig. 11(a,b), respectively. The FWHM of sector A first increases and then decreases as the applied stress increases. This increase is probably due to the increase in the intensity of the 211 B2 reflection, which is caused by the stress-induced R(V1)-B2 transformation. The subsequent decrease in FWHM value is due to the decrease in the intensity of the 211 B2 reflection, which is caused by the stress-induced B2-R(V2) transformation. On the other hand, the FWHM of sector B keeps almost ...

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... sector A (Fig. 10(a)), the intensity of the 412 R reflection decreases and that of 114 R reflection increases by the stress application. The behavior is consistent with the results shown in Figs 8(b) and 9(b). In sector B (Fig. 10(b)), on the contrary, the intensity of the 412 R reflection is almost constant while that of 114 R reflec- tion decrease as stress increases. The decrease in the 114 R reflection in sector B is due to the stress induced R(V1) → B2 transformation or rearrangement of variants (V1 → V2). For both sectors, it is difficult to extract the change in the intensity of the 211 B2 ...

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... sector A (Fig. 10(a)), the intensity of the 412 R reflection decreases and that of 114 R reflection increases by the stress application. The behavior is consistent with the results shown in Figs 8(b) and 9(b). In sector B (Fig. 10(b)), on the contrary, the intensity of the 412 R reflection is almost constant while that of 114 R reflec- tion decrease as stress increases. The decrease in the 114 R reflection in sector B is due to the stress induced R(V1) → B2 transformation or rearrangement of variants (V1 → V2). For both sectors, it is difficult to extract the change in the intensity of the 211 B2 ...

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... the following section, we discuss the change in the integrated X-ray profile caused by stress-induced R(V1)-B2-R(V2) transformation. The diffraction pattern shown in Fig. 10 is a mixture of V1 and V2 of the R-phase and the B2-phase. The gradual movement of the reflection from 412 R to 114 R , as seen in Fig. 10(a), occurs because of two events: one is a gradual change in the lattice parameter due to elastic deformation, and the other is a stress-induced successive R(V1)-B2-R(V2) ...

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... the following section, we discuss the change in the integrated X-ray profile caused by stress-induced R(V1)-B2-R(V2) transformation. The diffraction pattern shown in Fig. 10 is a mixture of V1 and V2 of the R-phase and the B2-phase. The gradual movement of the reflection from 412 R to 114 R , as seen in Fig. 10(a), occurs because of two events: one is a gradual change in the lattice parameter due to elastic deformation, and the other is a stress-induced successive R(V1)-B2-R(V2) ...

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... propose that the role of internal stress and external stress on stress-induced transformation can be described by the phase diagram illustrated in Fig. 1. In general, the influence of stress, σ, on the transformation temperature, T, is given by the Clausius-Clapeyron equation (dσ/dT = −ΔS/Δε). Here, ΔS (=S R − S B2 < 0) is the entropy change, and Δε is transformation strain. The sign of Δε is positive for V2 and is negative for V1 of the R-phase; therefore, the slope (dσ/dT) is positive for V2 and negative for V1. We consider the following two cases: with negligible internal stress field; and with an internal stress field exerted by the aligned coherent particles of Ti 3 Ni 4 ...

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... the case with negligible internal stress field, there is no difference in transformation temperature between V1 and V2 of the R-phase unless the external stress is applied. As the external stress increases, the B2-R(V2) transformation temperature increases while the B2 → R(V1) transformation temperature decreases, as shown in Fig. 1(a). The B2 → R(V1) transformation, however, cannot be detected experimentally because V2 is more stable than V1 under stress. In this case, the stress-induced B2-R(V2) transformation occurs as indicated by the arrow in Fig. 1(a), while the stress-induced reverse transformation is ...

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... the case with negligible internal stress field, there is no difference in transformation temperature between V1 and V2 of the R-phase unless the external stress is applied. As the external stress increases, the B2-R(V2) transformation temperature increases while the B2 → R(V1) transformation temperature decreases, as shown in Fig. 1(a). The B2 → R(V1) transformation, however, cannot be detected experimentally because V2 is more stable than V1 under stress. In this case, the stress-induced B2-R(V2) transformation occurs as indicated by the arrow in Fig. 1(a), while the stress-induced reverse transformation is ...