In situ observation on temperature dependence of

Materials and Design 134 (2017) 111–120

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In situ observation on temperature dependence of martensitic transformation and plastic deformation in superelastic NiTi shape memory alloy Yao Xiao a, Pan Zeng a,⁎, Liping Lei a, Yanzhi Zhang b a b

Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China Institute of Materials, China Academy of Engineering Physics, Mianyang 621900, China

H I G H L I G H T S

G R A P H I C A L

A B S T R A C T

• The deformation mode of NiTi transits from localization to delocalization as temperature increases. • Plasticity occurs together with martensitic transformation at the band front and its amount increases with temperature. • Plastic deformation dominates over residual martensite as the source of strain irreversibility in superelastic NiTi.

a r t i c l e

i n f o

Article history: Received 3 May 2017 Received in revised form 30 July 2017 Accepted 17 August 2017 Available online 18 August 2017 Keywords: NiTi shape memory alloy Phase transformation Plasticity Localized deformation

a b s t r a c t In situ digital image correlation (DIC) and in situ X-ray diffraction (XRD) are applied to investigate the effect of temperature on martensitic transformation and plastic deformation in superelastic NiTi shape memory alloy. Via in situ DIC, two well-known deformation modes of NiTi are identified at various temperatures: (A) localized forward and reverse transformations with little residual strain (b1%); (B) localized forward transformation and homogenous reverse transformation with considerable residual strain (N 1%). As temperature increases from 25 °C to 120 °C, the mechanical response of NiTi gradually transits from Type A to Type B. We verify that plastic strain accumulates concurrently as the traverse of the front of localized deformation band. Via in situ XRD observation, we conclude that it is material plasticity rather than retained martensite that plays a dominant role in the irreversibility of NiTi. The experimental results provide both macroscopic and lattice level scenarios to understand the temperature dependence of complicated thermomechanical coupling and plasticity in superelastic NiTi. © 2017 Elsevier Ltd. All rights reserved.

1. Introduction Near-equiatomic NiTi shape memory alloy (SMA) holds great potential for a broad range of applications in engineering, aeronautics, ⁎ Corresponding author. E-mail address: [email protected] (P. Zeng).

http://dx.doi.org/10.1016/j.matdes.2017.08.037 0264-1275/© 2017 Elsevier Ltd. All rights reserved.

dentistry and medical fields [1] due to the unique shape memory effect (SME) and superelasticity (SE) originating from thermoelastic phase transformation between austenite (cubic structure, B2) and martensite (monoclinic structure, B19′) [2–4]. It is well established that under tension, stress-induced transformation of superelastic NiTi leads to localized deformation, featured by the coexistence of several localized deformation bands (LDBs) [5–19]. More recently, Zheng et al. [20]

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Y. Xiao et al. / Materials and Design 134 (2017) 111–120

reported that cyclic band nucleation/annihilation accelerates the microstructure degradation of NiTi and deteriorates the fatigue performance. These findings further emphasize the importance of understanding the localized deformation of superelastic NiTi. Apart from macroscopic investigation, substantial efforts have also been made to elucidate the underlying microstructural mechanisms of localized deformation in superelastic NiTi through optical microscopy [21], electron backscattered diffraction (EBSD) [22,23] and X-ray diffraction (XRD) [24–27]. Despite of the abundant investigation on superelastic NiTi at room temperature, the temperature dependence of the mechanical behavior of superelastic NiTi, however, has not been studied in sufficient detail. At the temperature above martensite desist temperature (Md), stressinduced martensite is suppressed. Twinning and dislocation slip dominate in the deformation of NiTi, leading to the accumulation of plasticity [28]. At the temperature between autensite finish temperature (Af) and Md, our recent studies [12,13] have shown that the deformation mode of superelastic NiTi undergoes significant change with the elevating temperature. NiTi exhibits well-known localized deformation and superior reversibility in the relatively low temperature regime, nevertheless NiTi demonstrates localized forward transformation and homogenous reverse transformation with considerable residual strain in the relatively high temperature regime. It is widely accepted that the reversible strain is due to elastic deformation and stress-induced transformation, while the irreversible mechanisms are commonly attributed to plastic deformation and the formation of retained martensite [28–32]. Šittner et al. [33] pointed out that the concurrence of plastic deformation and stress-induced transformation leads to the elimination of localized deformation, whereas the systematic microscopic investigation is missing. The objective of this work is to examine the mechanical behavior of superelastic NiTi between Af and Md. The study presents an in-depth insight into the unusual thermomechanical properties of superelastic NiTi. By employing in situ digital image correlation (DIC) and in situ X-ray diffraction (XRD), we acquired the local strain profile, the evolution of LDB and the lattice-level data from macroscopic and microscopic perspectives. Another contribution of the work is to provide dependable data which can be used to calibrate and establish the constitutive model accounting for the temperature dependence of mechanical response of NiTi, hitherto limited at room temperature and without considering the interaction between transformation and plastic deformation in NiTi [34–38]. In the following, the material properties and experimental methods are introduced in Section 2. Macroscopic DIC observation, microscopic XRD observation and discussions are provided in Section 3. Conclusions are drawn in Section 4.

heating stage was installed on the Empyrean diffractometer (PANalytical Inc.) equipped with PIXcel3D detector and with CuKα radiation at 40 kV and 40 mA. The X-ray was focused on the gauge section of the sample by laser positioning. The projection of the X-ray on the specimen's surface was a rectangle with width of about 1 mm and length of about 12 mm. The specimen was quasi-statically loaded at the strain rate of 1.8 × 10−4 s−1 with loading axis perpendicular to the direction of the incident beam. During X-ray scanning, the grip displacement was fixed. The scanning range of the specimen was 35° b 2θ b 50° or 35° b 2θ b 95°, and the step size was 0.013°. 3. Experimental results and discussion 3.1. Overview of in situ DIC observation Fig. 1 shows the applied stress-applied strain response of NiTi at various temperatures. The applied stress is calculated from the ratio between the applied force and the original cross section area. The applied strain represents the spatial average of the strain in the gauge section from DIC results. Fig. 2 presents the temperature dependence of residual strain, nucleation stress and austenitic elastic modulus. The nucleation stress of LDB is defined as the maximum stress prior to the onset of the first LDB, and it is linearly fitted with respect to temperature in Fig. 2(b). The temperature dependence of the nucleation stress is 5.60 MPa/°C, in good accordance with the reported results ranging from 5.3 MPa/°C to 8.5 MPa/°C [34,39–43]. The elastic modulus of austenite, defined as the initial stiffness by fitting the first 0.5% linear response, is shown in Fig. 2(c). Basically, the elastic modulus of austenite displays increasing trend with elevating temperature, i.e. from 66 GPa at 25 °C to 95 GPa at 120 °C, and gradually gets saturated. Figs. 3 to 5 and Figs. S1 to S7 in Supplementary material illustrate sets of full-field DIC contours and the corresponding central line longitudinal strain profile at the representative applied strains. In light of the previous research [12,13], two typical deformation modes of NiTi are identified: (A) both forward and reverse transformations are localized and with little residual strain (b 1%); (B) forward transformation is localized while reverse transformation is homogeneous and with considerable residual strain (N 1%). At temperatures between 25 °C and 55 °C, NiTi exhibits Type A mechanical response. The specimen

2. Materials and experiments The material used in this study was commercially available NiTi polycrystalline sheets (0.5 mm thickness, 55.82 wt% Ni, Memry Corp.). The austenite finish temperature Af is 3.3 °C [13], which means that the specimen is austenitic at and above room temperature. For in situ DIC observation, the sheet was electro-discharge machined into dogbone shape with gauge width of 7 mm and gauge length of 40 mm. Before the tensile test, a random speckle pattern was painted by spraying white background and black spot on the surface of the specimen. The specimen was placed in the environmental chamber and was strained/unloaded by the testing machine (Shimazu AG-X universal testing machine) at the strain rate of 2 × 10−4 s−1 to ensure isothermal condition. A digital camera (Daheng Image, DHSV1410FM) was used to record the surface morphology with the frequency of 1 Hz and the spatial resolution of captured images was 1392 × 1040 pixels. The spatial accuracy of DIC results is up to 1 μm, which can meet the requirement of the experiment [12,13]. For the in situ XRD experiment, the dog-bone tensile specimen with gauge width of 1.8 mm and gauge length of 14 mm was electrodischarge machined from the sheet. A custom-made mini-tensile/

Fig. 1. Applied stress-applied strain response of NiTi. The onset points of LDB are marked by arrows.


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Fig. 2. Temperature dependence of (a) residual strain, (b) nucleation stress of LDB (the dashed line is the linearly fitted curve) and (c) elastic modulus of austenite.

undergoes an initial stiff and nearly linear branch during which austenite deforms elastically and homogeneously. At the end of the linear branch, local maximum stress is reached in the applied stress-applied strain curve and LDB tends to nucleate at one of the end parts of the gauge section. Following the stress drop, the stress plateau enables LDB to propagate at essentially constant load and another LDB may initiate at the other end part of the gauge section. When LDB covers the whole gauge section, the applied stress takes an abrupt upturn. During unloading, the material is subjected to the mechanical evolution reverse

to loading. As can be seen in the strain profiles in Fig. 3 and Figs. S1 to S3, significant strain jump at the LDB front is clearly noticed. For the cases tested at and above 75 °C, NiTi demonstrates Type B mechanical response. The specimen undergoes localized deformation during loading, characterized by the nucleation and propagation of LDB. During unloading, the material undergoes homogenous deformation. For the tests at 75 °C and 85 °C, the lower stress plateau and the transition knee associated with reverse transformation are less distinct, compared with the tests at and below 55 °C. When the temperature

Fig. 3. Representative full-field DIC contours and the corresponding central line longitudinal strain profile at various applied strains at 25 °C.


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3.2. Overview of in situ XRD observation


exceeds 85 °C, reverse transformation plateau eventually vanishes and the unloading branch becomes linear, similar to the performance of ordinary elastic-plastic metal. It should be noted that the LDB evolution of NiTi at 65 °C differs from that of NiTi at other temperatures. During loading, the LDB front gradually gets bent with the ongoing deformation, which is a salient feature of Type B mechanical response; during unloading, although LDB can be recognized, the strain gradient at the LDB front is much less than the cases with Type A mechanical response, manifesting more homogenous deformation. Therefore, the mechanical response at 65 °C is the transient response between Type A and Type B.

In the in situ XRD test, the deformation of the specimen is under displacement control. The applied strain value is the nominal strain calculated from the ratio between the grip displacement and the gauge length. Upon loading, the strains at which the XRD measurements are done are selected as: 0% (the reference state), 0.7% (the elastically deformed state), 1.5%, 3%, 5% or 6% (within upper stress plateau), 7.5% or 8% (after the termination of the upper stress plateau). Upon unloading, the strain at which XRD measurement is performed decreases from 6.5% to the residual strain, with the interval of 1.5% or 1%. The XRD profiles at 25 °C, 45 °C, 65 °C, 85 °C and 105 °C are shown in Figs. 6 to 8. The diffraction pattern is smoothed by B-spline and indexed by austenitic B2 phase (a0 = 3.015 Å) and martensitic B19′ phase (a = 2.882 Å, b = 4.123 Å, c = 4.626 Å, β = 97°) [2,44]. The diffraction pattern is further normalized by the peak intensity of B2(110) at the reference state under the given temperature. Upon loading, NiTi first undergoes austenitic elastic deformation with the decrease of B2(110) peak intensity. When the strain exceeds 0.7%, the commencement of forward transformation is evidenced by the emergence of B19′ peaks. Basically, martensite with lower symmetry possesses lower structure factors than austenite with higher symmetry [2,45]. Due to the weak diffraction of martensite, the B19′ peaks at 2θ N 50° are not remarkable and even cannot be accurately indexed at temperatures higher than 45 °C. Therefore, in this paper, primary attention is paid to the XRD profile with 2θ ranging from 35° to 50°. For tests at 25 °C and 45 °C, B2 (110) peak splits into three B19′ peaks, i.e. B19′ (110), B19′ (020) and B19′ (111). B19′ (020) peak undergoes rapid increment since the beginning of transformation, while B19′ (110) peak or B19′ (111) peak does not become distinct until the elongation increases to 5%. For tests at 65 °C, B2 (110) peak splits into two B19′ peaks, i.e. B19′ (110) and B19′ (020). For tests at 85 °C and 105 °C, only the transition between B2 (110) and B19′ (020) can be witnessed. When the highest applied strain is reached, for test at 25 °C, only B19′ peaks are detectable, which is a signature of the completion of transformation, nevertheless, for tests at and above 45 °C, B2(110) peak and B19′ peaks coexist, which is an indicator of partial transformation. Upon unloading, for test at 25 °C, NiTi initially deforms in martensitic phase. When the applied strain is below 5%, reverse transformation initiates accompanied with the emergence of B2 peak. As unloading

Fig. 6. Representative XRD profiles at various applied strains at 25 °C. Left column: normalized XRD profile within 35° b 2θ b 50°; Right column: selected XRD profile within 35° b 2θ b 95°.


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Fig. 7. Representative XRD profiles at various applied strains at 45 °C. Left column: Normalized XRD profile within 35° b 2θ b 50°; Right column: Selected XRD profile within 35° b 2θ b 95°.

progresses, B19′ (110) peak first disappears, followed by B19′ (111) peak, and finally B19′ (020) peak vanishes. For tests at and above 45 °C, unloading gives rise to simultaneous reverse transformation, evidenced by the sharp increment of B2 (110) peak and the decrement of B19′ peaks. The difference of the XRD profile evolution results from different deformation modes and transformation mechanisms at various temperatures [27]. After complete unloading, all B19′ peaks, regardless of testing temperature, revert back to original B2 peaks, i.e. B2 (110), B2 (211) and B2 (220), and no residual B19′ can be figured out in the profile. 3.3. Evolutions of LDB and plastic deformation At temperatures between 25 °C and 65 °C (Figs. 3 and S1 to S3), straight LDB front and nearly constant band inclination ranging from 52° to 57° are observed in the strain map throughout the loading-

unloading process, which is consistent with the previous observation at room temperature [5,7,9]. For the cases tested above 75 °C, the band angle varies with elongation. At first the band inclination obtained from the strain map lies between 55° and 60°. As elongation increases to 3%, the increasing band inclination makes LDB front get more and more horizontal. Eventually, LDB front becomes horizontally arc-shape at relatively high applied strains, e.g. frames 4 in Fig. 4 and Figs. S4 to S7. From the view of continuum mechanics, the inclination angle of LDB can be related to the transformation surface and the associative flow rule (See Supplementary material). At temperatures between 25 °C and 65 °C, von Mises criterion can be applied to predict the band angle with theoretical value (θvM) of 54.74° [5,11]. At temperatures above 75 °C, the deviation from θvM implies the variation of the principal strain rates, stemming from the complicated stress state [11] and the severe plastic accumulation upon deformation.

Fig. 8. Representative normalized XRD profiles at various applied strains at (a) 65 °C, (b) 85 °C and (c) 105 °C.

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Additional experiments were conducted to check the interaction between LDB evolution and plastic deformation at three typical temperatures, i.e. 75 °C, 95 °C and 120 °C. The specimens were unloaded as the length of LDB was about half of the gauge length. Fig. 9 displays sets of full-field DIC contours and the corresponding central line longitudinal strain profile at the representative applied strains. Frame 2 corresponds to the largest deformation state of the specimen, so its strain profile is identical to the maximum strain distribution. LDB separates NiTi into Zone I (the region once covered by LDB and with maximum strain around 7.5%), Zone II (the region without being covered by LDB), and Zone III (the transient region between Zone I and Zone II). As shown in Fig. 9, Zone I broadens while Zone II shrinks with increasing deformation. Zone III shifts along the loading axis and its width keeps nearly unchanged. The strain variation in residual strain profile (frame 4) indicates the concurrence of transformation and plastic deformation. The relation between the maximum strain (ɛmax) and residual strain (ɛres) is illustrated in Fig. 10. All the correlation coefficients (R2) are well above 0.95. Although we cannot confirm the interdependency of ɛmax and ɛres, we can at least conclude that ɛmax and ɛres are positively related variables. Furthermore, we verify that higher temperature elicits more severe superelasticity degradation. On one hand, as elucidated in Fig. 10, the fitted slope of dɛres/dɛmax increases sharply from 0.142 to 0.412 as temperature increases from 75 °C to 120 °C. On the other hand, as plotted in Fig. 2(a), more drastic residual strain accumulation is clearly identified with elevating temperature, increasing from 0.1% (25 °C) to 3.3% (120 °C), which is in agreement with the previous observation [41]. At temperatures higher than 75 °C, the nucleation and propagation of LDB are witnessed during forward transformation with the absence of stress plateau, which contradicts common perception of the mechanics of LDB propagation [5,8,9,17,33]. We infer that the intense difference of the mechanical responses within and out of LDB leads to the disappearance of the stress plateau. Further investigation is desired to

Fig. 10. Relation between the maximum strain (data from frames 2 in Fig. 9) and residual strain (data from frames 4 in Fig. 9) at 75 °C, 95 °C and 120 °C.

uncover the underlying mechanism. In this temperature regime, we also note that forward transformation is localized while reverse transformation is homogeneous. It can be attributed to the fact that LDB front moves through the virgin microstructure during loading while it moves through the plastically deformed microstructure during unloading. 3.4. Interaction between the defect and plastic deformation Since the unloaded specimen may only contain little retained martensite which X-ray diffractometer fails to resolve, the primary source of irreversibility is the accumulation of material plasticity [25,27,29].

Fig. 9. Representative full-field DIC contours and the corresponding central line longitudinal strain profile at various applied strains at 75 °C, 95 °C and 120 °C. The gauge sections are separated into Zone I (the region once covered by LDB and with maximum strain around 7.5%), Zone II (the region without being covered by LDB), and Zone III (the transient region between Zone I and Zone II). The specimens are unloaded at about 4% (frame 2) when LDB covers about half of the gauge section.


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from the XRD profile. D and ɛm are obtained by linearly fitting B2(110), B2(211) and B2(220) peaks with Eq. (1). The approximate estimation of the dislocation density ρ holds [47]: ρ¼

Fig. 11. The evolution of FWHM with respect to temperature. The data obtained from virgin NiTi and deformed NiTi are symbolled with up triangle and down triangle, respectively. Error bars are included, but are usually smaller than the symbol size.

The evolution of full width half maximum (FWHM), which scales with the density of defects introduced by plastic deformation in grain domains [46,47], is shown in Fig. 11. For all the virgin specimens, FWHM of a particular crystallographic plane keeps at a constant level. A single loading-unloading procedure at 25 °C has limited effect on the accumulation of defects, which is in accordance with little plastic deformation at 25 °C. Deforming at elevating temperature leads to the increment of FWHM, indicating the accumulation of defects or residual strain occurs in NiTi. The concurrence of localized transformation and plastic deformation, which is shown in Fig. 9, is further discussed from the microscopic view. As proposed by Benafan et al. [28,32] and Ezaz et al. [30], the transformation-induced plasticity is more ready to be triggered in austenite. The nucleation and build-up of slip in austenite are required to accommodate the rather high transformation strain upon traversing martensite interfaces [2,28,30]. Elevating temperature gives rise to lower yield stress [2] while higher transformation stress due to Clausius-Clapeyron relation [40], which will greatly facilitate the defect generation in NiTi. Several dislocation systems of austenite, such as ⟨100⟩{011} system [29], ⟨100⟩{001}system [30], {114} compound twinning [28,29] etc., have been experimentally observed. As calculated by Ezaz et al. [30], ⟨100⟩{011} system will be activated at 2.6 GPa, and ⟨111⟩ type slip is expected to be activated over 5 GPa. It is worth noting that the maximum applied stress in the experiments is no N1 GPa, let alone the resolved shear stress. Therefore, without extra stress, the intense accumulation of defects or plasticity cannot be triggered, just as what happens in Zone II in Fig. 9. For material within Zone III, the strain gradient at the front of macroscopic LDB and the misfit at microscopic austenite-martensite interface provides additional stress concentration. Therefore, intense plastic accumulation occurs concurrently with the traverse of LDB front. For material within Zone I, the vanishing of LDB front weakens the extent of stress concentration. Hence the dislocation defect will not experience drastic increment and a relatively constant plastic strain is attained within Zone I. Williamson-Hall equation is applied to analyze the diffraction linebroadening [46]: β cosθ=λ ¼ 1=D þ Cεm sinθ=λ

ð1Þ

β is the integral width, θ is the diffraction angle, λ is the wavelength of the X-ray, D is the average crystallite size, ɛm is the micro strain, and C is the constant concerning the nature of inhomogeneous micro strain. In the paper, C is set as 4 [27] and λ equals to 1.5418 Å. β and θ are obtained

pffiffiffiffiffiffi 6π εm =bD

ð2Þ

where b is the length of the Burgers vector. For body-centered cubic austenite, b equals to 1/2a0 ⟨111⟩ [27]. Generally, the calculated value of dislocation density obtained from XRD method is not strictly precise. In the XRD method, theoretical concepts, instrumental parameters, crystallographic defects and textural effects will affect the calculated dislocation density [48]. Nevertheless, comparisons of XRD method with other alternative methods for measuring dislocation densities indicate that the results obtained from XRD are fairly reasonable [47, 48], so the calculated value of dislocation density is used for qualitative analysis. At 25 °C, the dislocation density before deformation (ρo) and that after deformation (ρd ) are essentially identical at about 1.5 × 1014 m− 2. At 105 °C, ρd is 1.12 ± 0.02 × 1015 m− 2, an order of magnitude higher than ρd at 25 °C. The reported ρd required for delocalization of cyclically deformed NiTi ranges from 8.2 × 1014 m−2 to 2.1 × 1015 m−2 [25,27]. In the paper, ρd of the transient case (tested at 65 °C) is 6.55 ± 0.17 × 1014 m− 2, in general agreement with the previous results. 3.5. Evolution of microstructure Since the penetration depth of X-ray is around tens of micrometers and the deformation of the specimen may be heterogeneous, the lattice strain obtained from the XRD profile is the average lattice strain of the surface, and we are able to analyze the evolution of the microstructure qualitatively. In some macroscopic studies, martensite volume fraction (MVF, fM) yields the ratio between local strain and the strain jump at LDB front, presuming that material undergoes complete transformation within Zone I and transformation does not occur within Zone II [49]. This hypothesis, however, is quite controversial since microscopic observations have shown that fM within LDB ranges from 60% to 100%, depending on loading condition as well as loading history [21,24,25,50]. Besides, the strain jump at LDB front consists of both plastic strain and transformation strain. Therefore, in this work, fM is calculated from the XRD results [25,27,50]: P

fM ¼ P

I HKL;M P I HKL;M þ Ihkl;A

ð3Þ

where IHKL,M and Ihkl,A denote the integrated intensities of martensite with plane HKL and austenite with plane hkl, respectively. XRD profiles are deconvoluted with Lorentz function to separate the diffraction peaks. Due to the weak diffraction of martensite at 2θ N 50°, only B2 (110), B19′ (110), B19′ (020) and B19′ (111) are taken into account in Eq. (3). The maximum fM (denoted as fM,max) tends to decrease with increasing temperature. At 25 °C, NiTi is subjected to complete transformation, i.e. fM,max = 1. At temperatures higher than 25 °C, the density of defects increases with elevating temperature and the accompanying internal stress impedes NiTi undergoing complete transformation even at the end of the upper stress plateau, e.g. fM,max is only 0.37 at 105 °C. From DIC results, the end of the upper stress plateau is the signature that LDB fully covers the gauge section. Therefore, transformation within the propagating LDB is not completed except for the case at 25 °C. Furthermore, it is straightforward for us to extrapolate that other loading conditions associated with significant defect generation, such as mechanical training and thermal cycling, will also induce incomplete martensitic transformation and eventually originates in the decrease of reversible transformation strain and superelasticity deterioration [25,29,50].

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The lattice strain of a particular crystallographic plane hkl is denoted as ɛhkl and is obtained from the following formula: εhkl ¼

dhkl −d0;hkl d0;hkl

ð4Þ

where d0,hkl and dhkl are the d-spacings of the plane hkl before loading and under applied stress, respectively. The lattice strain of austenitic B2(110) is denoted as ɛB2(110). One should note that ɛB2(110) decreases with elongation because the diffraction plane is perpendicular to the tensile direction and the lattice contracts in the transverse direction owing to Poisson's effect.

The evolution of ɛB2(110) is shown in Fig. 12. At 25 °C, the lattice strain keeps nearly unchanged during transformation. As temperature increases, the evolution of ɛB2(110) traces a nearly closed hysteresis. Upon loading, B2(110) first undergoes elastic deformation when MVF equals to zero. After the commencement of forward transformation, the lattice strain decreases mildly with increasing applied strain. A sharp turn is noticeable at the end of loading. At temperatures lower than 65 °C, the evolution of the lattice strain upon unloading is characterized with the transition knee, and the overall evolution is reverse to that upon loading. At temperatures higher than 65 °C, the lattice response is submitted to linearly unloading. The change of the lattice response implies the transition of the deformation mode in NiTi. The residual lattice strain is b 0.05%,

Fig. 12. The evolution of ɛB2(110) at (a) 25 °C, (b) 45 °C, (c) 65 °C, (d) 85 °C and (e) 105 °C. Error bars are included, but are usually smaller than the symbol size.


indicating NiTi essentially transforms back to its original lattice state after complete unloading. 4. Conclusions In situ digital image correlation and in situ X-ray diffraction are applied to investigate the effect of temperature on martensitic transformation and plastic deformation in superelastic NiTi shape memory alloy. From the results obtained in the present study, several conclusions can be made. (1) Two typical deformation modes of NiTi are identified: (A) both forward and reverse transformations are localized and with little residual strain (b1%); (B) forward transformation is localized while reverse transformation is homogeneous and with considerable residual strain (N 1%). As temperature increases from 25 °C to 120 °C, the mechanical response of NiTi gradually transits from Type A to Type B. (2) Type A deformation is realized mainly by reversible martensitic transformation, while Type B deformation is accomplished by martensitic transformation alongside drastic plastic deformation. Plastic deformation occurs together with martensitic transformation at the propagating LDB front and its amount increases with increasing temperature. (3) The density of defects remaining in superelastic NiTi after a single loading-unloading procedure increases with increasing temperature. Plastic deformation dominates over residual martensite as the source of strain irreversibility in superelastic NiTi. Acknowledgements The work is supported by National Natural Science Foundation of China (No. 51671176). Appendix A. Supplementary data Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.matdes.2017.08.037. References [1] J. Mohd Jani, M. Leary, A. Subic, M.A. Gibson, A review of shape memory alloy research, applications and opportunities, Mater. Des. 56 (2014) 1078–1113. [2] K. Otsuka, X. Ren, Physical metallurgy of Ti-Ni-based shape memory alloys, Prog. Mater. Sci. 50 (2005) 511–678. [3] C. Cisse, W. Zaki, T.B. Zineb, A review of constitutive models and modeling techniques for shape memory alloys, Int. J. Plast. 76 (2016) 244–284. [4] P. Chowdhury, H. Sehitoglu, A revisit to atomistic rationale for slip in shape memory alloys, Prog. Mater. Sci. 85 (2017) 1–42. [5] J.A. Shaw, S. Kyriakides, On the nucleation and propagation of phase transformation fronts in a NiTi alloy, Acta Mater. 45 (1997) 683–700. [6] Z.Q. Li, Q.P. Sun, Phase transformation in superelastic NiTi polycrystalline microtubes under tension and torsion from localization to homogeneous deformation, Int. J. Solids Struct. 39 (2002) 3797–3809. [7] M.A. Iadicola, J.A. Shaw, Rate and thermal sensitivities of unstable transformation behavior in a shape memory alloy, Int. J. Plast. 20 (2004) 577–605. [8] S. Daly, G. Ravichandran, K. Bhattacharya, Stress-induced martensitic phase transformation in thin sheets of Nitinol, Acta Mater. 55 (2007) 3593–3600. [9] J.F. Hallai, S. Kyriakides, Underlying material response for Lüders-like instabilities, Int. J. Plast. 47 (2013) 1–12. [10] B. Reedlunn, C.B. Churchill, E.E. Nelson, J.A. Shaw, S.H. Daly, Tension, compression and bending of superelastic shape memory tubes, J. Mech. Phys. Solids 63 (2014) 506–537. [11] N.J. Bechle, S. Kyriakides, Evolution of localization in pseudoelastic NiTi tubes under biaxial stress states, Int. J. Plast. 82 (2016) 1–31. [12] Y. Xiao, P. Zeng, L. Lei, H. Du, Local mechanical response of superelastic NiTi shapememory alloy under uniaxial loading, Shape Mem. Superelasticity 1 (2015) 468–478. [13] Y. Xiao, P. Zeng, L. Lei, Experimental investigation on local mechanical response of superelastic NiTi shape memory alloy, Smart Mater. Struct. 25 (2016), 017002. [14] Y. Xiao, P. Zeng, L. Lei, Experimental observations on mechanical response of threephase NiTi shape memory alloy under uniaxial tension, Mater. Res. Express 3 (2016) 105701.

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