Effect of training on the cyclic behaviour of SMA wire

Shape memory alloys (SMAs) are a new generation of smart metallic materials with numerous unique and widely applicable characteristics. With their superelasticity and ability to dissipate energy under cyclic loading, SMAs are an excellent choice for passive vibration energy dissipation systems. However, due to functional fatigue, the energy dissipation and re-centring capacity of virgin SMA dwindles at a decreasing rate during cyclic loading and eventually reaches a stable level. Since for vibration control applications stable mechanical properties with predictable responses to vibrational forces are preferred, preloading SMA wires for mechanical training is proposed to overcome this drawback. Nevertheless, the effect of training conditions on the mechanical behaviour of SMA wires has only been investigated in a few studies. To fill this research gap, the influence of different training parameters, such as strain amplitude, frequency, number of cycles and prestrain, on the mechanical behaviour of SMA wires is examined. The results show that while a sufficient number of cycles and certain level of strain amplitude are required to reach a stable stress–strain relation, training frequency is the most important parameter for eliminating residual strain.


Introduction
Shape memory alloys (SMAs) are a new generation of smart metallic materials with numerous unique characteristics, making them applicable in various fields, including biomedical, aerospace, and vibration control devices. Nickel and titanium alloy (Nitinol-NiTi) is the most common type of SMA currently used in industry due to its * Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. high strength, superior fatigue and corrosion resistance, large damping capacity, ability to experience large recoverable deformations, and availability in many possible shapes and configurations [1,2].
Two particularly interesting and appealing characteristics of SMAs are superelasticity (SE) and shape memory effect. The former, which is also known as pseudoelasticity, allows SMAs to deform to large strains (up to 8%-10%) and regain their original shape after unloading with negligible residual strain [1]. SMAs can also recover from large deformations via heating, which is known as the shape memory effect. These characteristic behaviours are a result of reversible phase transformations between the austenitic and martensitic crystal phases that can be induced by either a stress or a temperature change. Typically, martensite is stable at high stress and low temperature, whereas austenite is stable at low stress and high temperature.
SMA's unique capacity to dissipate energy under cyclic loading and their exceptional SE make them an excellent material choice for passive vibration energy dissipation systems [3]. For vibration control applications, due to the cyclic nature of loads, it is imperative to investigate the behaviour of SMAs under such loading conditions. Although martensitic phase transformation is a time-independent phenomena, results of previous experimental studies have shown that NiTi's mechanical behaviour varies greatly with strain rate [1]. Unlike typical viscoelastic effects, this rate dependent effect originates from the complex coupling among stress, wire temperature, ambient temperature, and the heat transfer condition of the SMA specimen during stress-induced phase transformations [4]. Since a wide range of vibration control applications use or can use superelastic SMAs, the sensitivity of various mechanical properties of SMAs to cyclic loadings with different amplitude and frequency, as well as temperature have been extensively studied [5][6][7][8].
The effect of the number of loading cycles on the mechanical behaviour of SMA wires has been studied by some researchers [6,8,9]. Experimental results show that when a SMA wire experiences more cycles of loading, the forward transformation stress level shifts down, especially within the first two cycles [6,8,9]. This phenomenon is primarily due to transformation-induced plasticity (TRIP) where dislocations created in subsequent cycles result in internal stress fields after complete unloading. Such high local stress fields facilitate the localized dislocation slip in subsequent cycles, leading to a significant reduction in the stress needed for forward phase transformation [6,10]. The stress levels corresponding to the reverse transformation vary only slightly compared to those of the forward transformation. Therefore, the amount of dissipated energy per cycle reduces as the wire undergoes a greater number of cycles.
The residual strain also increases during cyclic loading until it reaches a stable level after a certain number of cycles [8]. This residual strain is the direct consequence of dislocations caused by TRIP. A higher loading stress triggers larger TRIP resulting in more dislocations in the material body, i.e. greater residual deformation. This phenomenon, also known as functional fatigue, causes the energy dissipation capacity and recentring capability of SMAs to gradually decline and approach a stable level. This type of fatigue differs from conventional structural fatigue, which typically leads to the failure of specimen after a large number of cycles.
The strain rate is another important parameter that has been studied by numerous researchers [6,9,[11][12][13][14]. Unlike the effect of number of cycles, there is no consensus on the effect of strain rate on the forward and reverse transformation stress levels and dissipated energy [1]. While some experimental studies, such as DesRoches et al [6] and Dolce et al [9], detected an increase in both forward and reverse transformation stress levels with increasing strain rates, others, such as Wolons et al [13] and Ren et al [15], reported an increase in the reverse transformation stress with no significant variation in the forward transformation stress. Furthermore, some observed a decrease in the reverse transformation stress but an increase in the forward transformation stress [12]. The inconsistency in the existing results regarding strain rate effects may arise from differences in the chemical composition of the SMA wires, tested strain ranges, and experimental conditions [1]. As a result, contradictory findings in energy dissipation have been reported, e.g. when the strain rate increases, both a reduction [6,13,15,16] and an increase [12] in dissipated energy have been observed.
Stable mechanical properties are preferred for vibration control applications to provide a predictable response to vibrational forces. To obtain stable mechanical behaviour and reduce the functional fatigue effect, Miyazaki et al [17] and Zhang et al [18] proposed to preload SMA for training. Training generally refers to any complex thermomechanical treatments applied to improve or stabilize material properties. Such improvement is of interest to practical applications, especially for SMA wires experiencing long term cyclic loading in vibration control applications. For example, results from Chen et al [19] showed that applying heat treatment can improve fatigue behaviour of NiTi SMA wires by increasing material grain size and also result in a higher critical stress to trigger stress-induced martensitic transformation with less residual strain.
Unlike heat treatment, which has been extensively studied by many researchers, e.g. [19,20], research on the effects of mechanical training on SMA properties is scarce and there is no consistency for the training conditions used in existing studies. For example, as part of their study of the fatigue behaviour of SMA, Yang et al [8] used a 4% strain amplitude for 20 cycles in the training step. During their study on the loading frequency and size effect on the damping capacity of SMA, Soul et al [11] trained wire specimens for 100 cycles at 0.01 Hz and an 8% strain amplitude. Dolce and Cardone [9] investigated seismic applications of SMA and used ten cycles of a 7% strain amplitude as the training condition. Wolons et al [13] observed that SMA wires require significant mechanical cycling to achieve stable hysteresis loops. They proposed to use at least 100 cycles in training to ensure the stability of the material behaviour.
McCormick et al [21] conducted a two-level factorial experimental design to explore the optimal number of cycles, loading frequency and ultimate strain to minimize the functional fatigue effect in terms of the equivalent linear viscous damping (henceforth referred to as damping for brevity), residual strain and loading stress plateau. They reported that performing mechanical training could reduce the hysteresis loop area and obscure the forward transformation plateau. An increase in the training strain level was found to decrease the loading plateau stress and the damping. In addition, the number of training cycles had a negligible effect on damping, residual strain and loading stress plateau, while the loading rate after training played a significant role in all of them. It was concluded that applying higher loading rates to SMAs would decrease degradation in the loading stress plateau and reduce residual strain, which implied the viability of SMAs for seismic retrofit and design application [21]. Nevertheless, McCormick et al [21] did not consider the effects of larger number of cycles, higher training frequency, larger strain levels and specimen size on training, as well as the long-term effects of training. No comparison has been made between the mechanically trained and untrained wires to evaluate the impact of mechanical training on the SMA mechanical properties and the potential benefits. To address the long-term effect of mechanical training on SMA behaviour, Zhang et al [10] conducted an experimental study to investigate the effect of the amplitude of the training stress on the fatigue life of NiTi. They reported that the fatigue behaviour of SMA improves after mechanical training. This improvement was due to the presence of dislocation-induced local residual stress fields which assisted the phase transformation [10].
Despite the importance of mechanical training of SMAs, there is a lack of comprehensive research investigating the effect of different training parameters, i.e. the number of cycles, frequency, strain amplitude, pre-strain and wire size on the cyclic behaviour of SMA wire. The current paper will study the effect of these training parameters on SMA wire's cyclic behaviour. The remaining content of this paper is organized as follows: section 2 presents information about the studied SMA wires, experimental setup, and detailed information of all the testing and training conditions. The general behaviour of SMA wires observed in all tests under cyclic loading is discussed in section 3. The assumptions made for stress and strain calculations are also described. This section is followed by test results and discussion in section 4. Section 5 summarizes the main findings of this study.

Experimental setup and specimens
The Nitinol SMA wire specimens of diameters D = 0.5 mm, 0.8 mm, and 1.2 mm were supplied by Lumenous Peiertech. The chemical composition of the NiTi SMA wires is Ni 57% and Ti 42.77%. The austenite finish temperature (A f ), which refers to the temperature the material is entirely in the austenite phase, is 10 ± 7 • C.
An MTS Criterion testing apparatus (Model No. C45.305) was used to perform cyclic tests on the wire specimens. All experimental tests were conducted using displacement control at room temperature (23 • C). The force applied to the specimen and the specimen's elongation were recorded during the tests. To measure the load, an external load cell (Omega LCH-1K) with a capacity of 4.4 kN was used. MTS clamps with two wedges were used to secure the wires at both ends. To prevent slippage, an anchorage length of 5 cm was used to hold the wire between the plates. The total length of the wire specimens was 25 cm (i.e. 15 cm gauge length). The stress was calculated based on the nominal cross-sectional area of the virgin wire whereas the strain was obtained by dividing the axial elongation by the initial gauge length of the specimen. Figure 1 shows the experimental setup and securing method at the ends.
Additional discussion on the stress and strain is provided in section 3.

Test cases
To examine the effect of the training conditions on the cyclic behaviour of SMA wires, five sets of tests were conducted, each set consisted of three specimens. Set 1 (Wire 1 to Wire 3), Set 2 (Wire 4 to Wire 6), Set 3 (Wire 7 to Wire 9), Set 4 (Wire 10 to Wire 12) and Set 5 (Wire 13 to Wire 15) investigated the effects of the number of training cycles, training strain amplitude, training frequency, training pre-strain, and wire size, respectively. The cyclic testing and training conditions are listed in table 1. An ID with the form of 'T/S#F#A#(E#)' will be used to refer to each case herein. It begins with either T or S to indicate either a training or a testing condition, respectively. This letter is followed by the number of cycles applied under the specified condition. The numbers after F and A indicate respectively the frequency and strain amplitude. For convenience, F200, F020 and F002 are used to represent a frequency of 0.2 Hz, 0.02 Hz and 0.002 Hz, respectively. If pre-strain exists in the wire, the amplitude of pre-strain comes after the letter E (optional). For example, T100F002A8E6 refers to a training condition with a frequency of 0.002 Hz, strain amplitude of 8% and 100 loading cycles for a SMA wire with a 6% pre-strain, i.e. the strain amplitude of the SMA wire varies between 6% and 8% during training. The first few cycles of the strain amplitude time history of a SMA wire under such a training condition is shown in figure 2 to illustrate the definition of strain amplitude and pre-strain. In the discussion, C is used to refer to the cycle number. For example, C1 indicates the first cycle in either training or testing. If the training condition of a wire listed in table 1 is not given, such as Wire 1, Wire 4 and Wire 10, it indicates that the test was conducted on a virgin wire.

Stress-strain curve of SMA wire under cyclic loading
The experimental program revealed that all the considered SMA wires exhibit certain behaviours regardless of the characteristics of the cyclic loading. Figure 3 shows a typical stressstrain curve of Wire 1, which is a 1.2 mm virgin SMA wire tested under a cyclic load with a frequency of 0.02 Hz and strain amplitude of 8% for 300 cycles. As shown in figure 3, a downward shift in the hysteresis loops occurs in subsequent cycles, but as the number of cycles increases, the magnitude of the shift decreases. The shift in the forward phase transformation stress plateaus is more pronounced than the reverse transformation plateaus, resulting in narrower hysteresis loops at higher cycles. The reverse transformation plateaus almost overlap with each other after 100 cycles and there is no visibly noticeable change in the subsequent cycles. Therefore, the area enclosed by a force-displacement loop, which represents the  amount of dissipated energy per cycle, reduces at a decreasing rate and gradually approaches a stable value. Significant stress drops are usually visible in the forward phase transformation stress plateaus, especially during the first few cycles, while the reverse transformation plateau rarely shows similar sudden changes. This behaviour was more noticeable for the intermediate level of training frequency (0.02 Hz). During testing, these significant stress drops were accompanied by a sudden colour change in the wires, as shown in figure 4(c), and click-like noises, indicative of sudden and localized material phase transformation in a wire. The thermal images in figure 4(b) show that stress drops occur when there is an abrupt increase in the wire temperature at the locations where the colour changes. The non-uniform temperature field during phase transformation was also observed by Zhang et al [22]. Such jagged curves in the loading plateau have been observed by Wolons et al [13], Yang et al [8] and Zhang et al [22]. While Yang et al [8] suggested that this phenomenon may be related to the loading rate, other studies, e.g. Zhang et al [22], attributed this phenomenon to the discontinuous  evolution of local stress at the grain scale during the stressinduced transformation. They indicated that this local stress came from the incompatible deformation field formed during phase transformation at the austenite-martensite interface. This incident was also found to be accompanied by slipping of dislocations that occurred at the austenite-martensite interface [22]. These stress drops gradually disappear with increasing cycles and after 50 cycles almost no significant stress drops were observed on the loading plateau.
In addition to the narrower hysteresis loops, another characteristic that differentiates the hysteresis loops of higher cycles from the first few cycles is the increase of tangential stiffness at the end of the loading plateau. As shown in figure 3, such a tangential stiffness increase is not present in the first 5 cycles. It starts to develop afterwards, and the end of the loading plateau becomes sharper as the number of cycles increases. Shi et al [7] postulated that linear hardening at the end of the loading plateau represents the completion of the stress-induced martensitic transformation and the involvement of elastic/plastic deformation of the martensite phase. Figure 3 highlights that a significant portion of the ultimate residual strain occurs during the first few cycles, and it increases at a lower rate as the number of cycles increases. In all tests, it was observed that the wires gradually recover a portion of their ultimate residual strain after the test. At the end of the test, the wire's temperature is lower than the ambient temperature. Therefore, it takes some time for the wire to warm up and reach the ambient temperature. The increasing wire temperature increases its SE and recentring capability, which may cause the partial recovery of the residual strain. This observation goes against the typical expectation of elongation of the wire length as a result of thermal expansion. It is worth mentioning that since a wire experienced elongation during loading stage, when the displacement returned to zero at the end of unloading stage in the displacement-control mode, buckling occurred in the wire. The level of buckling and the resulting impact depends on the free length and the diameter of the wire. In the current study, due to a relatively long free span length of the wire, which was 15 cm, and the low compressive stress at the end of the unloading stage, the magnitude of the buckling-induced bending stress in the wire was negligible.

Strain uniformity
An MTS DIC video extensometer (Model No. Nano-M1450) was employed to monitor the strain along the wire length during two cyclic loading tests performed in this section. The gauge length of the wire was divided into four equal segments. The average strain time history corresponding to the upper first and second quarters of the wire length (L 1 and L 2 ) and upper half (L 3 ) of the wire, as shown in figure 4(a), respectively named Strain 1, Strain 2 and Strain 3, were calculated and compared with the overall average strain time history, Strain 4. Two separate tests were conducted: one on a virgin wire and one on a trained wire (T100F200A6E2). The strain time histories for the virgin and trained wire are shown in figure 5. The thermal contours along the wire during the loading process was recorded using a thermal camera (Model No. FLIR ONE 435-0004-03-NA). Additionally, two thermometers (Model No. Omega HH502) were used to measure temperature changes of two arbitrary points within L 1 and L 2 . Figure 5 shows that the strain is non-uniform along the wire length and that the middle segment, L 2 , undergoes smaller strain comparing to the overall strain, Strain 4, in both wires. The thermal contours shown in figure 4(b) reveals that the phase transformation, which translates into heat generation in loading and cooling of the wire in unloading, is more concentrated in L 1 than in L 2 . This explains the higher strain in L 1 . Table 2 lists the highest and lowest temperatures of the two selected points in L 1 and L 2 during loading and unloading, respectively. As shown in table 2, for the trained wire, when the highest temperature of 30.6 • C in L 1 is reached, the temperature in L 2 is 29.8 • C. The difference is more noticeable for the virgin wire, 29.3 • C and 23.8 • C for L 1 and L 2 , respectively. The same pattern is observed in the lowest temperatures, which suggests that the temperature gradient is smaller in trained wires. Such findings may provide explanations for Zhou et al [14] observation that wires broke near clamping devices before they reached their fatigue life. Moreover, figure 5 also shows that the strain is not symmetric (i.e. otherwise Strain 3 would match Strain 4). This observation further emphasizes the need of training in stabilizing the material behaviour. Despite this fact, in the rest of the paper, the overall average strain of the wire, L 4 , is always used when discussing material behaviour.

Effect of number of training cycles
Cyclic tests have been performed on three wires in Set 1 to examine the effect of the number of training cycles. This set includes a virgin wire (Wire 1) and two trained wires, i.e. Wire 2 (T300F020A8) and Wire 3 (T600F020A8). The testing condition is S300F020A8. Figure 6 compares the stress-strain curves of the three wires at selected cycles. The stress-strain curves of the three wires display different characteristics in the first few cycles. While Wire 1 shows significant stress drops and a higher stress plateau, Wire 2 and Wire 3 show smoother curves with a lower loading stress plateau. The shift in the stress plateau for the virgin wire is more significant compared to Wire 2 and Wire 3, especially in the first 150 cycles. The forward phase transformation stress plateaus of all three wires converge as the number of cycles increases. Unlike the virgin wire, Wire 2 and Wire 3 have linear hardening after the stress plateau at early cycles, whereas the same does not occur in the virgin wire. The hardening appears as the virgin wire undergoes more cycles, and gradually becomes distinct as the number of cycles increases. Figures 7(a) and (b) shows the variation of dissipated energy per volume and residual strain of all three wires with respect to the number of loading cycles. All the curves in these two plots are smoothed by averaging the value of ten adjacent cycles, i.e. a moving average. The same technique is applied to all subsequent similar plots to show trends as a function of cycle number. A sudden drop in dissipated energy after the first few cycles can be observed in figure 7(a) in all cases. The virgin wire can dissipate more energy after the initial sudden drop. This could be attributed to two possible reasons. According to figure 3, in the first few cycles, the loading plateau of a virgin wire shifts down significantly and the initial elastic curve, i.e. the loading curve before the loading stress plateau, moves to the right due to the residual strain. Following that, the dissipated energy reduces gradually until it reaches a stable level because of the same reasons, but with less intensity. For the virgin wire the reduction rate for dissipated energy in subsequent cycles is higher, so the amount of dissipated energy in the virgin wire converges to that of Wire 2 and Wire 3 and after 150 loading cycles they almost overlap. Figure 7(b) shows in all wires that the residual strain increases with an increasing number of loading cycles. It also reveals that regardless of the training condition, more than 60% of the ultimate residual strain occurred within the first 5 cycles. In the subsequent cycles, the residual strain increases at a slower rate. This rate decreases as the wire undergoes more training cycles, so the ultimate residual strain, i.e. the residual strain of C300, is less for the wires which experienced a greater number of training cycles.
In addition, the results in figure 7(a) show that although in terms of energy dissipation, there is no significant difference between Wire 2 (T300F020A8) and Wire 3 (T600F020A8), these two trained wires have a smaller residual strain than Wire 1 (virgin). Therefore, they dissipate less energy because of lower stress plateaus and also reach a stable value in fewer cycles.

Effect of training strain amplitude
Set 2, which includes Wire 4 to Wire 6, was tested to study the effect of training strain amplitude on the cyclic behaviour of trained SMA wires. In Set 2, two wires, Wire 5 and Wire 6, were trained under the condition T50F020A4 and T50F020A8, respectively. They were then tested under the condition S50F020A6. Figure 8 shows the stress-strain curves of Wire 5 and Wire 6. For comparison, the results of the virgin wire, Wire 4, under the same testing condition are also plotted. Compared to Wire 4 and Wire 5, the wire trained under 8% strain amplitude, Wire 6, shows more consistent stressstrain loops, less residual strain and almost no sudden stress drops on the loading plateau. In addition, it is observed in figure 8 that at the beginning of loading plateau, Wire 5, the wire trained under a 4% strain amplitude, follows the same path as Wire 6, which was trained under 8%. The Wire 5 curve then diverges and reaches the loading plateau of virgin wire as strain increases and follows its path. This pattern is similar in every cycle, and the forward phase transformation stress plateaus of both Wire 4 and Wire 5 approach that of Wire 6 as the number of cycles increases. Figure 9(a) shows a comparison of the energy dissipated per cycle as a function of cycle number for Wire 4 to Wire 6. In terms of stability of energy dissipation, if the strain amplitude used in training is lower than that experienced by the wire in the subsequent tests, the energy dissipation capacity of the wire in the first few cycles remains more or less the same as the virgin wire. But as the number of cycles increases the virgin wire dissipates less energy, likely because the residual strain is larger. Figure 9(b) shows a comparison of the residual strain as a function of cycle number for Wire 4 to Wire 6. In the first two cycles the residual strain of the wire trained under 4% strain amplitude increases faster than the wire trained under 8% strain amplitude and slower than the virgin wire. This leads to a higher ultimate residual strain for Wire 4 and Wire 5 compared to Wire 6. Figure 10(b) indicates that residual strain in wires that have undergone training is significantly reduced even in the case that the training strain amplitudes is lower than that of testing.
The results reveal that using an appropriate strain amplitude in training is crucial for ensuring consistent behaviour in terms of loading plateaus and residual strain or in other words, to be better trained. Particularly, the training strain amplitude should exceed the applied strain amplitude. Nevertheless, even using a lower strain amplitude in training can still significantly reduce residual strain.

Effects of training frequency
The tests of Set 3, which includes Wire 7 to Wire 9, were performed to study the effect of training frequency   on the cyclic behaviour of trained SMA wires. The training conditions for Wire 7 to Wire 9 were T100F200A6, T100F020A6 and T100F002A6, respectively, and the testing condition was S100F002A6. The stress-strain curves of these wires are presented in figure 10. Results show that the wires trained at 0.2 Hz, Wire 7, and 0.02 Hz, Wire 8, experience sudden stress drops with lower amplitudes on the loading plateau. The stress-strain loops of Wire 9 have  higher forward phase transformation stress plateaus and lower reverse transformation stress plateaus, i.e. a larger hysteresis loop area. It also shows that hardening after the loading plateau appears at earlier cycles in Wire 7 and Wire 8 than in Wire 9. Figure 11(a) confirms that, despite the presence of a larger residual strain, the energy dissipated by Wire 9 is more than Wire 7 and Wire 8. Compared to Wire 7, the energy dissipated by Wire 8 is less in early cycles, but starts to increase around cycle 45 and becomes the same as Wire 7 after cycle 60. Figure 11(b) shows that the residual strain of Wire 7 and Wire 8 are substantially lower than Wire 9. This is mainly because of the significant reduction of residual strain accumulated during the first few cycles. This part of strain usually contributes the majority of ultimate residual strain. A flatter forward stress plateau can be observed in figure 10 when the training frequency is increased, which suggests more homogeneous distribution of dislocations. This may possibly cause an improvement in fatigue life [11]. However, the frequency of loading and fatigue life have not been distinctly correlated in previous studies [10,23].

Effects of pre-strain
The purpose of Set 4 is to investigate the effect of pre-strain applied in training on the cyclic behaviour of trained SMA wire. This set includes a virgin wire (Wire 10) and two trained wires, Wire 11 (T100F002A8E6) and Wire 12 (T100F002A8). To observe the effect of pre-strain in SMA wire training more clearly, a relatively large value of 6% was selected for the prestrain in case T100F002A8E6 such that the wire was trained over a strain range of 6%-8%. Therefore, when subjected to the subsequent cyclic load with the strain varying between 0% and 8%, the wire was only trained over the higher quarter of the loading strain range, i.e. from 6% to 8%, but had not experienced lower strain of 0%-6%. The stress-strain curves of these three wires are compared in figure 12. The results reveal that in the first few cycles, e.g. C5 and C10, the loading stress plateau  of Wire 11 falls between those of the virgin wire and Wire 12. The stress-strain curves of Wire 11 follow the path of the virgin wire, Wire 10, very closely at the beginning of the loading plateau. Then it diverges from Wire 10 and approaches the plateau of Wire 12 (trained without pre-strain). In C50 to C100, Wire 11 reaches a plateau similar to Wire 12's at around 6% strain, and then falls below Wire 12 afterwards. Wire 12 is trained with no pre-strain. It displays a small shift in the forward transformation plateau level and unloading stress plateaus compared to Wire 10 and Wire 11. All curves converge as more cycles are completed and after 100 cycles almost overlap with each other. Figure 12 shows that the wire which has no pre-strain, Wire 12, has the most consistent behaviour in its stress-strain curve, along with a uniform shift of the loading plateau. This figure also indicates that compared to Wire 12, the downward shift in the loading plateau of Wire 11 is not monotonic across the loading strain range. Wire 11 experiences larger plateau shifts at higher levels of strain than lower levels. As a result, a larger portion of the ending loading plateau of Wire 11 is positioned below that of Wire 12 when the number of cycles increases. Specifically, while in C5 only a small ending portion of Wire 11 loading plateau falls below  Wire 12, in C50 the portion of the loading plateau corresponding to strains higher than 6% all falls below Wire 12. These trends are not as distinct as observed in other sections. Figures 13(a) and (b) show respectively the variation of dissipated energy per volume and residual strain as a function of cycle number, of which Wire 11 is seen to have a residual strain and dissipated energy between those of Wire 10 and Wire 12. Wire 12 shows a more consistent behaviour, i.e. less residual strain and a more stable amount of dissipated energy, than Wire 11. These observations imply that it is advisable to train the wire using the full strain range induced by the anticipated loading condition and avoid applying pre-straining.

Effects of wire size
To investigate the effect of wire size on the cyclic behaviour of trained SMA wires, Set 5 tests, including Wire 13 to Wire 15, were conducted. The three wires in this set have diameters of 0.5 mm (Wire 13), 0.8 mm (Wire 14) and 1.2 mm (Wire 15), respectively. They were all trained under the condition of T100F020A6 and then subjected to cyclic loading S100F020A6. Figure 14 presents a comparison of the stress-strain curves of Wires 13 to Wire 15. The first cycle stress-strain curves of the corresponding virgin SMA wires are also shown in the figure in dashed lines to better distinguish the differences caused by the effect of wire size and number of training cycles. According to figure 14, as the wire size increases there is an increase in the residual strain. However, no apparent direct relationship between the loading stress plateau and the wire size is observed. Note that the key parameters of the stress-strain curve, such as the residual strain, the loading plateau stress, and the dissipated energy, are all functions of wire size. Hence, to eliminate the size effect, the training effect is evaluated based on the ratios of the residual strain and dissipated energy of the trained wires and the corresponding virgin wires. These ratios are calculated for each cycle. Figures 15(a) and (b) illustrate the variation of the dissipated energy ratio and residual strain ratio with respect to the number of cycles for Wire 13 to Wire 15, respectively. Results in figure 15(a) show that Wire 13 initially has a higher dissipated energy ratio than the other two wires, suggesting that the same training conditions has more considerable impact on the behaviour of small diameter wires than on large diameter ones. Figure 15(b) shows that the residual strain ratio decreases as the wire diameter increases. This implies that the impact of training on Wire 13 is more significant, as there is a larger discrepancy between the material behaviour of the trained wire and the virgin wire. According to this figure, effect of training improves with decreasing wire diameter. It is worth mentioning that as frequency increases, wires having different sizes will have different heat transfer efficiency with the ambient medium, of which the wire temperature may play a more important role.

Conclusion
An experimental study was conducted to examine the effect of training conditions on the cyclic behaviour of SMA wires. The influence of the number of cycles, frequency, strain amplitude, pre-strain used in training, as well as the wire size were investigated. Based on the test results, the following conclusions can be drawn: (1) Regardless of the training condition, the stress-strain curve of SMA always displays a noticeable downward shift in the forward transformation stress plateau and accumulates a majority of the residual strain in the first few cycles. (2) The sudden stress drops observed on the loading plateau of a virgin wire diminish gradually as the wire undergoes more cycles and vanish almost completely after 50 cycles. The stress drops do not occur in a trained wire provided the loading strain does not exceed the training strain. (3) It is speculated that the stress drops in the loading plateau could be caused by a sudden phase transformation within specific regions of the wire which are accompanied by sudden heat release. This is believed to be the main reason for the strain non-uniformity along the wire. (4) More training cycles results in a reduced shift in the loading plateau and less residual strain. By increasing the number of training cycles, both loading and unloading plateaus and residual strain approach to stable levels within a smaller number of testing cycles. (5) In general, residual strain, loading plateau shift, and energy dissipation behaviour are more stable in wires that have been trained under larger strain amplitudes. However, the results suggest that provided the strain amplitude used in training is lower than that in testing, it can effectively limit residual strain during testing, though it has a negligible effect in reducing stress drops in the loading plateau and the loading plateau downward shift in the first few cycles. For real applications, it is recommended that the strain amplitude should be greater than that induced by the anticipated loading strain amplitude. (6) Employing a higher frequency in training is beneficial. A flatter forward stress plateau can be observed as the training frequency increases. This indicates a more homogeneous distribution of dislocations which is preferred. The experimental results indicate that using a higher frequency in training than in testing can reduce the residual strain. (7) Although pre-strained wires exhibit a flatter forward stress plateau, wires trained without pre-strain exhibit more consistent behaviour in terms of loading plateau shift, residual strain, and stress drops on loading plateau. For this reason, it is recommended to use the full range of anticipated loading strains in training. (8) The required training conditions depend on specimen size.
Larger size wires require a greater number of training cycles. Under the same training condition, specimens with smaller size experience greater changes in material behaviour.

Data availability statement
The data cannot be made publicly available upon publication because they are not available in a format that is sufficiently accessible or reusable by other researchers. The data that support the findings of this study are available upon reasonable request from the authors.