Stress serration and arch-shaped Lüders stress plateau behaviour of Ti–50.8 at% Ni wire prepared by selective electrical resistance over-aging

Figure 1(a) shows a schematic view of the dimensions of the wire samples. The heating length (30 mm) is a middle section of the wire sample defined between the two electrodes used for joule heating. The gauge lengths (GL) indicated are the GL for tensile deformation testing. It is seen that the samples were tested under three different GL conditions (GL = 20 mm, GL = 30 mm and GL = 40 mm), to be within, equal to and wider than the heating length (30 mm), to delineate the contributions of different sections to the mechanical behaviour.

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Figure 1(b) shows the temperature profiles along the heating length as measured by a number of thermocouples attached to the sample at various locations. The temperatures were measured during electrical aging and the values shown in the figure represent the maximum temperatures reached at two different current levels (6 and 7 A). The distance values, denoted x, were measured from the centre of the wire. The temperature profiles showed a bell shape at both 6 and 7 A current levels, with the peak temperature ${T}_{{\rm{p}}}$ being in the middle, indicating the dominant 1D heat dissipation along the length towards the electrodes. It is obvious that the highest temperature gradient occurred at near the ends of the heated section. The sharp gradient originated from the thermal sink effect of the electrodes (two blocks of brass).

Figure 2 shows the deformation behaviour of two NiTi wires after electrical over-aging at 6 and 7 A with a 40 mm deformation GL. The stress–strain curves of an as-received and a solid solution treated sample (at 1123 K for 1.8 Ks) are also shown for comparison. The as-received sample exhibited perfect pseudoelasticity at room temperature, with a forward stress plateau at σ_SIM = 430 MPa and a plateau strain of 7.6% (including the elastic strain). Upon unloading, the sample exhibited a permanent plastic strain of 0.3%. The solid solution treated wire exhibited a shape memory effect at room temperature, with the forward stress plateau at σ_SIM = 317 MPa. For the electrically heated wires (at both 6 and 7 A), the stress-induced martensitic transformation occurred over two stress plateaus. It is obvious that the upper stress plateau was accompanied by pseudoelastic recovery and the low stress plateau showed no pseudoelastic recovery upon unloading.

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It is also evident that the electrically heat treated samples showed a clear upper–lower yielding behaviour at the onset of the first stress plateau, whereas such phenomenon was absent for the solution treated and the as-received samples. This phenomenon is commonly observed in Lüders type deformation of NiTi in tension [9]. The upper yielding is associated with the initiation of the Lüders band due to the stress-induced martensitic transformation. The lower stress level, i.e., the plateau stress, is associated with the propagation of the transformation Lüders band. Its occurrence demonstrates that a higher stress is required to initiate the localised Lüders type deformation band than to propagate it [37, 38]. This upper–lower yielding and flat plateau behaviour is also closely related to the strain rate of the testing. Tobushi et al has reported that when the strain rate is small (≤1%/min), there is enough time for the interface (between martensite and austenite) to move after the creation of the nucleus and therefore the high stress required to move the interface is relaxed. However, in the case of large strain rates, the interface moves quickly after the creation of the nucleus with very little time to relax the stress at the interface. The internal friction resistance against movement of the interface increases, and thus the upper yield at the start point of the transformation does not appear [39]. The strain rate of the current testing is considered very small (3.33 × 10⁻⁵ s⁻¹) thus exhibiting the upper yield point and flat plateau on the stress–strain curve. For the electrically heated samples, the band was nucleated in the middle of the sample, which is much weaker than the unheated sections at the ends of the sample, thus showing the expected upper–lower yielding behaviour. For the as-received and the solution treated samples, which had uniform properties over the entire length of the wire, the stress-induced martensitic transformation had already occurred within the grips during sample mounting prior to the tensile test, thus showing the absence of the upper yielding point but only the lower stress plateau.

For the sample heat treated at 6 A, the first stress plateau occurred at ${\sigma }_{{\rm{S}}{\rm{I}}{\rm{M}}}^{1}=260\,{\rm{MPa}}$ and the second one at ${\sigma }_{{\rm{S}}{\rm{I}}{\rm{M}}}^{2}=420\,{\rm{MPa}}.$ The higher stress plateau was at the same level as that of the as-received sample and was associated with the unheated section (outside the heated section) but within the deformation GL. The deformation over the lower stress plateau did not show any pseudoelastic recovery. This is attributed to over-aging which has led to conversion of the coherent Ti₃Ni₄ precipitates into incoherent precipitates (Ti₂Ni₃, TiNi₃) [18, 40–42]. The stress level of the lower plateau was below that of the solution treated sample. This is attributed to the higher Ni content in the matrix of the solution treated sample, which had been heated to a higher temperature. Higher Ni content implies lower ${M}_{{\rm{s}}}$ temperature, thus higher stress for inducing the martensitic transformation at the room temperature.

After unloading, this sample exhibited a residual strain of ${\varepsilon }_{{\rm{r}}}^{6}=4.6 \% ,$ as seen in figure 2. Assuming a small plastic deformation same as for the as-received sample (ε_plastic = 0.3%), the residual strain associated with unreverted martensite can be estimated to be 4.3%. It is also evident that this sample showed a spontaneous strain recovery of 4.9% upon unloading, which includes both elastic recovery and pseudoelastic recovery. The elastic recovery strain may be estimated using the Young's modulus of the martensite (being estimated as E = 100 GPa) [43–46] as ${\varepsilon }_{{\rm{e}}{\rm{l}}{\rm{a}}{\rm{s}}{\rm{t}}{\rm{i}}{\rm{c}}}\,=\tfrac{{\sigma }_{{\rm{S}}{\rm{I}}{\rm{M}}}^{2}}{E}=\tfrac{420}{100x{10}^{3}}\approx 0.4\, \% .$ This leaves 4.5% as the pseudoelastic recovery strain. Based on this, the effective length of the over-aged section can be estimated as ${L}_{{\rm{o}}{\rm{v}}{\rm{e}}{\rm{r}} \mbox{-} {\rm{a}}{\rm{g}}{\rm{e}}}^{6}=\tfrac{4.3}{\mathrm{4.3+4.5}}\times 40\,\,{\rm{mm}}\approx 19.5\,\,{\rm{mm}},$ or approximately $-9.7\,\,{\rm{mm}}\lt x\lt 9.7\,\,{\rm{mm}}$.

A similar calculation was also applied to the 7 A sample, which gave the effective length of the over-aged section ${L}_{{\rm{o}}{\rm{v}}{\rm{e}}{\rm{r}} \mbox{-} {\rm{a}}{\rm{g}}{\rm{e}}}^{7}=22.2\,{\rm{mm}},$ or $-11.1\,\,{\rm{mm}}\lt x\lt 11.1\,\,{\rm{mm}}.$ Applying these to figure 1(b), the critical temperature for the suppression of pseudoelasticity by over-ageing is estimated to be ${T}_{{\rm{c}}}^{{\rm{o}}}=815\,{\rm{K}}.$ This temperature is consistent with the previously reported values (e.g., 833 K for the Ti–50.8 at% Ni [17]) for over-aging of NiTi. Considering that the section of the sample outside the heated section has a higher (propagation) stress for inducing the martensitic transformation and the heated section has a lower stress for inducing the transformation, the plateau stress profile along the length of the wire can be expected to be as expressed by the black curve, denoted ${\sigma }_{{\rm{p}}}^{6\,{\rm{A}}},$ seen in figure 1(c). The ${\sigma }_{{\rm{p}}}^{6\,{\rm{A}}}$ level within the heated section is 260 MPa and that in close vicinity to the electrodes is 410 MPa, as obtained from the lower and higher plateau stresses of the sample heated at 6 A shown in figure 2.

It is also seen that the sample exhibited an upper yielding stress associated with the initiation of the deformation Lüders band. This stress, denoted ${\sigma }_{{\rm{u}}}^{6\,{\rm{A}}},$ is higher than ${\sigma }_{{\rm{p}}}^{6\,{\rm{A}}},$ and is thus schematically shown as the black dashed curve above ${\sigma }_{{\rm{p}}}^{6\,{\rm{A}}}$ in figure 1(c). The ${\sigma }_{{\rm{u}}}^{6\,{\rm{A}}}$ level within the heated section was 330 MPa as obtained from the upper yielding stress of sample heated at 6 A shown in figure 2. The ${\sigma }_{{\rm{u}}}^{6\,{\rm{A}}}$ of the unaffected regions close to the electrodes was considered higher than 430 MPa which was the plateau stress of the as received sample. Due to the absence of the upper yielding stress during the tensile test of the as received sample (initiation of martensite band had occurred during gripping prior to testing), the maximum value of ${\sigma }_{{\rm{u}}}^{6\,{\rm{A}}}$ was assigned an estimated value of 480 MPa, i.e. 50 MPa above ${\sigma }_{{\rm{p}}}^{6\,{\rm{A}}}$ as for the over-aged section.

For the sample heated at 7 A, the first stress plateau proceeded in an unusual arched shape. This is a common observation of a few samples heated within a narrow current range. The maximum point of the arch was close to that of the solution treated sample. Referring to figure 1(b), it is seen that the middle section of the wire had been heated to higher temperatures, and is thus expected to have higher Ni contents due to the increased dissolution of the Ni-rich precipitates. Higher Ni content implies lower ${{M}}_{{\rm{s}}}$ temperature, thus higher stress to induce the martensitic transformation at the room temperature. Considering this, ${\sigma }_{{\rm{p}}}$ of the 7 A heated sample $({\sigma }_{{\rm{p}}}^{7\,{\rm{A}}})$ can be expressed in the red curve, which exhibits two minimal stress valleys of 260 MPa, as shown in figure 1(b). The red dashed curve shows the initiation stress (upper yielding stress) for the deformation band, ${\sigma }_{{\rm{u}}}^{7\,{\rm{A}}}.$ The ${\sigma }_{{\rm{u}}}^{7\,{\rm{A}}}$at the stress valleys was 330 MPa obtained from the upper yielding stress of the sample heated at 7 A shown in figure 2.

For the sample heated at 6 A, upon loading in tension, the deformation band for stress induced martensitic transformation will nucleate when the stress reaches ${\sigma }_{{\rm{u}}}^{6\,{\rm{A}}}$ within the over-aged section and then propagate across the over-aged length, as shown in figure 1(d). Thus, a stress plateau at ${\sigma }_{{\rm{p}}}^{6\,{\rm{A}}}$ is observed.

For the sample heated at 7 A, upon loading, the deformation band for stress induced martensitic transformation will nucleate when the stress reaches ${\sigma }_{{\rm{u}}}^{7\,{\rm{A}}}.$ The first band will nucleate at either of the two minima on the ${\sigma }_{{\rm{u}}}^{7\,{\rm{A}}}$ curve, and then propagate from low to high along the ${\sigma }_{{\rm{p}}}^{7\,{\rm{A}}}$ curve. It is seen in figure 1(c) that the maximum value of ${\sigma }_{{\rm{p}}}^{7\,{\rm{A}}}$ is below the minimum value of ${\sigma }_{{\rm{u}}}^{7\,{\rm{A}}}.$ That means when the first formed band is propagating, even with increasing stress over the arch, no other band can nucleate. The propagation continues until the band reaches the second minimum on the ${\sigma }_{{\rm{p}}}^{7\,{\rm{A}}}$ curve. Thus, an arch-shaped stress–strain curve is observed over the lower stress plateau associated with the stress induced martensitic transformation within the heated section.

As seen in figure 2, both samples showed serrated stress–strain curves at the transition between the two stress plateaus, as indicated by the arrow. To investigate this phenomenon, several samples were treated at 6 A. The samples were subjected to tensile deformation with different GL symmetrical about the centre of the samples, as schematically illustrated in figure 1(a). The stress–strain curves of the tests are shown in figure 3. It is seen that stress serrations occurred for samples with 30 and 40 mm deformation GL. The sample deformed with 20 mm GL showed only one stress plateau with no stress serration. Therefore, it is evident that the stress serrations were associated with a narrow section along the length of the sample on each side of the over-aged zone. These are the regions where the temperature gradient is the greatest.

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To observe the phenomenon further, the nucleation and propagation of martensite Lüders band during the tensile deformation of the wire was recorded by video. Snapshots at 10 s intervals of the loading process of the 6 A heated sample were extracted and shown in figure 4(a). The dashed curve in the centre across all the snapshots indicates the trajectory of the middle point of the GL. The arrows indicate the fronts of the martensite transformation Lüders band. It is seen that the martensite nucleated at the lower middle section of the wire. The fronts of the transformation band propagated towards both ends of the wire during loading. The total length of the Lüders band, measured as the distance between the two transformation fronts, was determined from the snapshots and shown as a function of time of the tensile deformation in figure 4(b). The time positions of six characteristic moments (1–6) are also indicated on the stress–strain curve shown in figure 3. It is seen that the length of the Lüders band increased linearly initially with the time (for a cross-head speed controlled tensile deformation) before 130 s. This section corresponds to the initiation and propagation of the primary Lüders band within the over-aged section. Upon further loading (time increases from 130 to 160 s), the rate of expansion of the primary Lüders band was reduced, displaying a small plateau on the curve. Under the condition of constant strain rate tension, the reduced strain contribution from the slower expansion of the primary Lüders band was compensated by the increase of elastic strain throughout the wire sample due to the increase of stress between points (3) and (4) on the stress–strain curve of 6 A sample (black curve in figure 3). The continuous but slower propagation of the primary Lüders band proceeded for a short distance beyond the over-aged section with the rapid increase of ${\sigma }_{{\rm{p}}}^{6\,{\rm{A}}}$ and stopped until ${\sigma }_{{\rm{u}}}^{6\,{\rm{A}}}$ was reached, which triggered the nucleation of a new Lüders band just in front of the primary band and caused the first stress serration on the stress–strain curve (figure 3, point (4)). At this moment the total length of the Lüders bands suddenly increased again upon loading. Due to the fact that this region where the new Lüders band was formed had a very high anneal temperature gradient (figure 1(b)), the newly formed Lüders band had a very limited space to propagate before the stress was becoming too high again and a second new Lüders band was nucleated on the other side of the primary Lüders band, causing the formation of the second stress serration (figure 3, point (5)). Such process may continue as seen from 170 to 210 s on the stress–strain curve until the Lüders band deformation has reached the original portion of the wire sample outside the heated section. It is also visually evident in figure 4(a) that at the moments of stress serration, new Lüders bands had nucleated and propagated for a very short distance within the narrow sections close to the electrodes. Referring to figure 1(b), these sections have the highest temperature gradient. The inset of figure 4(a) shows an enlarged image of the new Lüders band (from the lower end of the wire) emerging and propagating within this high temperature gradient region.

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Given the above evidences, it is easy to understand the occurrence of the stress serrations and the arched stress plateau phenomena. As discussed above, transformation Lüders band nucleates within the heated zone in the middle of the sample and propagates towards both ends. With the decrease of the heating temperature towards the electrodes, as seen in figure 1(b), the stress for transformation band propagation, ${\sigma }_{{\rm{p}}}^{6\,{\rm{A}}},$ increases, till reaches ${\sigma }_{{\rm{u}}}^{6\,{\rm{A}}}$ when the propagation of the current Lüders band is stopped and a new Lüders band nucleates. The serrated stress–strain behaviour seen in figures 2 and 3 is in fact the upper–lower yielding behaviour of the new Lüders band nucleation.