Cyclic phase transformation behavior of nanocrystalline NiTi at microscale

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Cyclic phase transformation behavior of nanocrystalline NiTi at microscale Peng Hua , Kangjie Chu , Fuzeng Ren , Qingping Sun PII: DOI: Reference:

S1359-6454(19)30848-1 https://doi.org/10.1016/j.actamat.2019.12.019 AM 15715

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Acta Materialia

Received date: Revised date: Accepted date:

9 August 2019 21 November 2019 9 December 2019

Please cite this article as: Peng Hua , Kangjie Chu , Fuzeng Ren , Qingping Sun , Cyclic phase transformation behavior of nanocrystalline NiTi at microscale, Acta Materialia (2019), doi: https://doi.org/10.1016/j.actamat.2019.12.019

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Cyclic phase transformation behavior of nanocrystalline NiTi at microscale Peng Hua a, Kangjie Chu a, Fuzeng Ren b, Qingping Sun a, * a

Department of Mechanical and Aerospace Engineering, The Hong Kong University of

Science and Technology, Clear Water Bay, Hong Kong, China b

Department of Materials Science and Engineering, Southern University of Science and

Technology, Shenzhen, Guangdong 518055, China

Abstract Cuboidal micropillars of nanocrystalline superelastic NiTi shape memory alloys with an average grain size of 65 nm were fabricated by focused ion beam and then subjected to cyclic compression. It is found that the micropillars have maintained superelasticity for over

full-transformation cycles under a maximum compressive stress of 1.2 GPa.

Functional degradation of the micropillars mainly occurs in the first

cycles where

hysteresis loop area and forward transformation stress rapidly decrease from initial 11 MPa (

) and 586 MPa to 6 MPa and 271 MPa. In the

cycles, stress-strain

responses of the micropillars show asymptotic stabilization. Residual strain is accumulated to 3.3% and multiple ~50 nm wide extrusions are found at the surface of the micropillars after

cycles. SEM and TEM studies indicate that cyclic phase transformation results in

formation and glide of transformation-induced dislocations that create surface steps and the

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extrusions. The dislocations inhibit reverse transformation and result in residual martensite and residual stresses. The dislocations and the residual martensite lead to the functional degradation. The role of the residual martensite in the functional degradation is further verified by 21% recovery of the residual strain and an increase of 278 MPa in the forward transformation stress after heating up the cyclically deformed micropillars to 100 ℃. The recorded over

phase transformation cycles under a maximum stress of 1.2 GPa of the

NiTi shape memory alloys at microscale open up new avenues for applications of the material in microscale devices and engineering.

Keywords: Functional degradation; NiTi; Cyclic response; Dislocations; Martensitic phase transformation.



Corresponding author. Tel.: +852 23588655; fax: +852 23581543. E-mail address: [email protected] (Q. Sun).

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1. Introduction Bulk NiTi superelastic shape memory alloys (SMAs) under cyclic deformation show functional degradation (i.e. training effect) that is characterized by a gradual increase in residual strain and decreases in martensitic transformation stress and hysteresis loop area as the cycle number increases. Before the NiTi SMAs completely lose superelasticity (i.e. functional fatigue), the functional degradation usually tends to saturate as the cycle number further increases, leading to asymptotic stabilization in stress-strain responses [1–4]. However, this process is often interfered by nucleation and propagation of cracks from preexisting defects that can lead to structural fatigue failure of the materials [3,5,6]. The functional degradation and the structural fatigue are major obstacles to applications of the NiTi SMAs in solid-state cooling technology [7–9], bio-medical implants [10,11], and micro-electro-mechanical systems (MEMS) [12,13]. Therefore, it is essential to investigate the cyclic deformation behavior of the NiTi SMAs at both macro- and microscopic levels. Existing research shows that the functional degradation of the NiTi SMAs is mainly caused by the microscopic-level strain incompatibility between austenite phase (B2 cubic) and martensite phase (B19′ monoclinic [14]). Such lattice-level incompatibility leads to localized high stress concentration (much higher than the externally applied stress) and formation of dislocations at the habit planes, i.e. austenite-martensite interfaces [15–18]. The most-frequently observed dislocation slip system in the NiTi SMAs under cyclic phase transformation (PT) is the <100>{110} austenite slip system that has the smallest energy barrier and therefore requires the lowest resolved shear stress to activate [19–21]. A single dislocation loop can be multiplicated into arrays of dislocations during the reciprocating

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motion of the habit planes [22]. In return, the created dislocations can block the reverse motion of the habit planes during unloading, resulting in residual martensite and the associated significant residual stress [23–26]. The combined effects of the transformationinduced dislocations and the residual martensite lead to the functional degradation which manifests as monotonic increases in residual strain, and monotonic decreases in both transformation stresses (especially the forward transformation stress) and hysteresis loop area. The existence of the residual martensite can be examined by its partial recovery via reverse transformation during heating [23,25]. In the later stage of the cyclic deformation of NiTi, the functional degradation is no longer significant as the dislocations and the residual martensite tend to saturate with the increase in cycle number [1] and the structural fatigue become the dominating failing mechanism. The bulk superelastic NiTi under cyclic tension fails by nucleation and fast propagation of cracks that are perpendicular to the applied tension [5]. In contrast to the short fatigue life of the bulk NiTi under cyclic tension, the fatigue life of NiTi under cyclic compression can reach 70 million reversible PT cycles (depending on the stress level), due to the extremely low stress intensity factor of compression-parallel cracks and the resulting slow crack propagation [6,27]. Compared with the bulk SMAs of large grain sizes (GS), SMAs with small (microscale and nanoscale) sample sizes [15,28–31] and nanoscale GS [32,33] demonstrate different mechanical behaviors. The sample size affects the transformation stresses [28] and the functional degradation of SMAs, including NiTi [34] and CuAlNi [35,36]. Transformationinduced dislocations which are main sources of the functional degradation are significant in single crystal NiTi micropillars subjected to just a few superelastic cycles [15]. Reducing

4

Ni content and adding a third or more chemical elements, such as Cu, Co and Pd, may improve strain compatibility at habit planes and reduce the transformation-induced dislocations, and therefore improve the resistance to functional degradation of NiTi-based SMAs [37,38]. Nanocrystallization is also an efficient method to improve functional fatigue performance of bulk NiTi [39,40]. Whether the established mechanisms of functional degradation of bulk coarse-grained and single crystal NiTi are still valid for nanocrystalline (NC) NiTi at microscale remains to be unveiled by systematic study. In this work, we perform an experimental study of the cyclic PT behavior and the underlying mechanisms of functional degradation of NC NiTi at microscale. Cuboidal superelastic NiTi micropillars with an average GS of 65 nm are manufactured and compressed under a maximum stress of 1.2 GPa for over

full-PT cycles. Evolutions of

cyclic stress-strain responses, surface morphology and microstructural changes are measured by a nanoindenter, SEM and TEM. The effects of transformation-induced dislocations and residual martensite on the cyclic stress-strain responses are investigated. 2. Materials and methods 2.1 Materials The raw material was a bulk NC NiTi sheet with a chemical composition of 50.9 at.% Ni-49.1 at.% Ti from Johnson Matthey Incorporation (USA). The slightly Ni-rich NiTi was selected as it is mass-produced in industry and widely-used in medical devices [32,38,40]. The austenite finish temperature T1000 at a scanning rate of

of the NC NiTi was 14 ℃ (measured by a DSC QA ), which ensured a superelastic behavior at a room

temperature of 25 ℃. The bright-field TEM (JEOL JEM 2010) image and the selected area 5

electron diffraction (SAED) in Fig. 1 show that the undeformed NiTi sample is composed of fully crystallized austenite grains with an average GS of 65 nm. There is no martensite phase and precipitates in the original sample, as shown by the TEM image and XRD diffraction pattern (see Supplementary data). 2.2 Fabrication of cuboidal micropillars columns were wire-cut from the NC NiTi sheet and were rough polished with silicon carbide sandpapers (from 600 grit to 1200 grit) and fine polished with alumina suspension (with particle sizes from 1 micropillars (

to 0.05

). Cuboidal

as shown in Fig. 2) were fabricated at the

polished surface of the columns by focused ion beam (FIB) in a FEI Helios NanoLab 600i system (Thermo Fisher Scientific) via the method of Chu et al. [41,42]. Compared with the widely used tapered cylindrical pillars, the cuboidal micropillars with uniform crosssectional area have the advantages of more uniform stress and more convenient observation of the surface morphology in SEM. 2.3 Mechanical testing of micropillars

The cyclic compression of micropillars was conducted in a nanoindenter (Hysitron TI 950, Bruker Inc.) equipped with a 10 and strain and

-diameter flat end diamond tip. Engineering stress |

were calculated by equations:

| and

|

|, where ,

,

,

were the compressive load, the original height, the original cross-sectional area of

the micropillars and the tip displacement respectively. The transformation stresses (including forward

and reverse

) were measured at the intersection of the elastic

6

deformation stage of austenite and the transformation stages of the stress-strain curves. The transformation strain (

) is calculated by fitting the initial elastic unloading curve of

martensite with a linear line to intersect with the axis of strain [43]. The hysteresis loop area

was calculated by integrating the stress with respect to the strain. To measure the

yield strength of martensite phase at the room temperature, micropillar #1 was subjected to displacement-controlled single cycle compression with a maximum nominal strain of 19% and a nominal strain rate of

. The yield strength of austenite phase was

measured at a temperature of 150 ℃ without changing other parameters. The martensitic transformation stress increases with the temperature

(see Fig. F4 of

Supplementary data) according to Clausius-Clapeyron relationship. At 150 ℃, the martensitic transformation stress (~2100 MPa) is much higher than the plastic yield stress of austenite, therefore plastic deformation of austenite will take place without martensitic transformation and the yield strength of austenite can be measured as a material property. To study the cyclic compressive PT behavior, micropillar #2 was cyclically compressed under load-control mode for over

cycles with a maximum stress (

) of 1.2 GPa and

a minimum stress of 25 MPa at a frequency of 5 Hz. To check repeatability of the experimental results, micropillars #S1 and #S2 (see Supplementary data) were manufactured and tested under the same conditions as the micropillar #2. All cyclic compression of micropillars were conducted at a room temperature of 25 ℃. To study the cyclic deformation behavior without PT, micropillar #3 with a size of 2.5

was

cyclically compressed at a frequency of 5 Hz at the room temperature and under which was just below

(~600 MPa) of the micropillars. After the cyclic

7

tests, the micropillars #2, #S1 and #3 were heated to 100 ℃, held at the temperature for ten minutes and then cooled to the room temperature to examine the existence of residual martensite and its effects on the stress-strain responses [23,25,44]. The micropillars were then cyclically compressed for several hundred cycles at the room temperature under the same loading conditions. The heating-cooling and the following cyclic compression tests were done twice on the micropillar #2 to check the repeatability of the effect of heating on the stress-strain responses. The measurement of load-displacement responses of the micropillars is not affected by the thermal drift of the nanoindenter, as the loading and the unloading times of the cyclic compression are small (0.1 s). However, the thermal drift strongly affects the measurement of residual deformation of the micropillars under the long-time cyclic compression with the intermittent heating and cooling. To solve this issue, a non-contact Bruker NPFLEX 3D surface metrology system was used to measure the height changes of the micropillars after certain cycles of compression and after each heating and cooling (see Supplementary data). TEM samples with thicknesses of ~60 nm were milled from the micropillars by FIB and lifted out by a nanomanipulator to observe microstructure changes after the mechanical tests. High-resolution TEM (HRTEM) images were taken by a JEOL JEM 2010F TEM.

3. Results 3.1 Martensitic transformation stress and yield strength at microscale Fig. 3a shows the superelastic stress-strain response of the NC NiTi at microscale. The NC NiTi micropillars have average forward transformation stress (

) of 599 MPa,

reverse transformation stress ( ) of 315 MPa, initial hysteresis loop area ( ) of 11.7 MPa,

8

and martensitic transformation strain (

) of 3.5%. During the compression of the

micropillars, the non-uniform deformations of the micropillars’ top and bottom part (including substrate) under the applied stress increased the measured indenter displacement, which can result in an overestimation of strains and an underestimation of elastic modulus of the micropillars. To eliminate the non-uniform deformations, a recently developed dualpillar method (see Supplementary data and reference [41]) was used to correct all stressstrain responses and the corrected room-temperature elastic modulus of the initial austenite phase is 57 GPa which is the same as that of the literature [45]. It is noticed that the errors in the measured transformation stresses and transformation strain are still negligible [41].

The yield strength

of the martensite phase was about 2 GPa, measured at the room

temperature (blue curve in Fig. 3b). The yield strength of the austenite phase was 1.3 GPa, measured at 150 ℃ where there was only elastic and plastic deformation of austenite (see Methods and the red curve in Fig. 3b). The plastic deformation of both the austenite and the martensite demonstrated strain hardening behavior.

3.2 Functional degradation of the NC NiTi at microscale Fig. 4a shows the cyclic stress-strain responses of the micropillar #2 under a maximum stress of 1.2 GPa. It should be noted that the maximum applied stress of 1.2 GPa was lower than the plastic yield strength of martensite (2 GPa) and austenite (1.3 GPa), ensuring superelastic responses. Average values and standard deviations of residual strain ( hysteresis loop area (

in Fig. 4c),

and

(Fig. 4d),

(Fig. 4b), rate of (Fig. 4e) and rate of

in Fig. 4f) of micropillars #2, #S1 and #S2 (Supplementary

9

data) were shown in Fig. 4b-f. ,

,

and

of the micropillar #2 was increased to 3.3% while

gradually decreased from 586 MPa, 285 MPa, 3.3% and 11.4 MPa

in the first cycle to 265 MPa, 99 MPa, 2.3% and 4.9 MPa after The decrease in

(by 186 MPa) was smaller than the decrease in

Decreases in the gap ( decreases in |

. In the first

| decreased from 0.24

and

cycles of compression.

) between

and

(by 321 MPa). contributed to the

cycles, the magnitudes of the rates |

| (Fig. 4c) and

and 0.9 MPa/cycle to the order of

MPa/cycle. This demonstrated that the functional degradation was most

significant in the initial stage of the cyclic compression and the stress-strain responses show asymptotic stabilization after ,

and

cycles of compression. The experimental data of

,

in Fig. 4 can be fitted by power law functions which are further

discussed in section 4.3. The above results were repeatable on the micropillar #S1 and #S2 (see Supplementary data). 3.3 Thermally induced partial recovery of functional degradation The functional degradation can be partially recovered via a simple heating process. Significant changes in the stress-strain responses of the micropillar #2 after the heating were observed, as shown in Fig. 5 where all stress-strain curves were measured at the room temperature (25 ℃). Before the heating,

,

(Fig. 5c) and

(Fig. 5d) were 265

MPa, 99 MPa and 4.9 MPa. After the heating, they were drastically increased to 543 MPa, 288 MPa and 7.2 MPa. of and

increased by 278 MPa that was much more significant that

(increased by 189 MPa), leading to the increase in

. The changes in

,

were caused by partial reverse transformation of the residual martensite during the 10

heating (up to 100 ℃ that is well above temperature (>300 ℃)). About 21% of

(14 ℃) and below the recrystallization

was recovered after the heating (see Methods

and Supplementary data), showing that a significant part of martensite.

was due to the residual

was also increased from 2.3% (before the heating) to 2.9% (after the

heating), as shown in Fig. 5a. In the following 2104 cycles after the heating, functional degradation of the micropillar proceeded in a similar way but at a lower rate than the first the heating.

superelastic cycles before

only decreased by 123 MPa in the 2104 cycles (with an average rate

of 0.06 MPa/cycle), much smaller than the decrease of 273 MPa in

of the first

cycles before the heating (with an average rate of 0.27 MPa/cycle). Compared with the decrease in

(by 123 MPa),

compression, leading to a decrease in

only decreased by 36 MPa in the 2104 cycles of . Like the

cycles of compression before the

heating, power law fitting functions can be applied to fit the data of the 2104 cycles of compression in Fig. 5c-d, if the first cycle after the heating process was set to be cycle one. The thermally induced recovery of the functional degradation is repeatable. After the 2104 cycles of compression, a second heating increased

(Fig. 5c) and

(Fig. 5d) from

420 MPa and 6.0 MPa to 480 MPa and 6.3 MPa while

was reduced from 3.2% before

the second heating to 2.9% after the second heating. Similar results were observed in the micropillar #S1 (see Supplementary data).

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3.4 Cyclic deformation of the NC NiTi micropillars under Functional degradation is no longer prominent if the amount of martensitic transformation in each cycle is small. This is shown in the cyclic stress-strain responses of the micropillar #3 under

(Fig. 6). The stress-strain response of the

micropillar #3 in the first cycle was almost linear with a small was just below

of 0.49 MPa, because

. There was a only trivial amount of martensitic

transformation in each cycle, as grains with <110> and <001> orientations have much lower

in compression than grains with other orientations [23]. In the 100503rd

cycle shown in Fig. 6,

only accumulated to 1.06%, while the stress-strain curve

became nonlinear with a decreased

of 0.33 MPa. The nonlinearity was a sign of

martensitic transformation at a low-stress level, as

was reduced with the increase

in cycle number. After the heating process, the stress-strain curve became linear again with an increased

of 0.44 MPa and a reduction in

from 1.06% to 0.58%, showing that the

residual martensite still played an important role in the low-stress cyclic deformation. In the following 1200 cycles after the heating process,

increased slightly to 0.64%, while

decreased slightly to 0.33 MPa in the 101703rd circle. 3.5 Surface morphology and microstructure changes after cyclic deformation The surface of the micropillar #2 remained smooth in the first compression (Fig. 7a). After

cycles of

cycles of compression, stochastically distributed surface

extrusions (see Fig. 7b & 7c) appeared at the micropillar surface. The extrusions were around 20 nm wide (from the peak of extrusions to the micropillar surface). After cycles, the number of extrusions almost doubled (Fig. 7d) and the extrusions’ width

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increased to 30 nm (Fig. 7e). A nanoscale crack was observed at the bottom of the edge, spanning across the face 1 (F1) and face 2 (F2) of the micropillar #2 (Fig. 7d). After cycles, the number of extrusions remained the same as that of the

cycle and the width

of extrusions saturated at around 50 nm (Fig. 7f & Fig. 7g). Further cyclic compression up to

cycles did not increase the number and the size of the extrusions (Fig. 7h). The

extrusions did not disappear after the heating (Fig. 7i), indicating that they were not caused by residual martensite but related to plastic deformation. In correspondence to the observation in Fig. 7, extrusions and surface shear cracks were frequently observed at the surface of the micropillar #2 in the bright-field TEM image in Fig. 8a (the edges of the TEM samples are the surface of the micropillars). Shear displacement and steps at the surface of the micropillar are essential components of an extrusion (Fig. 8b). The extrusions were also found in the micropillar #S1 (see Supplementary data) that had the same size and was subjected to the same loading as the micropillar #2. The observed shear displacement ranged from several nanometers to 25 nm and the sheared zone was about 55 nm thick. The estimated local plastic shear strain (shear displacement divided by thickness of the sheared zone) ranged from 9% to 40% [42]. The shear displacement measured in the TEM images was smaller than that of the SEM images (Fig. 7), as the extrusions were partly removed by FIB during preparation of the TEM sample. Therefore, the actual plastic shear strain was in the range of 19% to 60%, based on measured shear displacement from the SEM images (Fig. 7). The deformed grains in Fig. 8b contained dense contours of local lattice distortion, indicating high internal stress fields from high-density dislocations which have a Burgers vector of

13

validated by the

HRTEM image of a deformed austenite grain (Fig. 8c) and its corresponding inverse fast Fourier transform (IFFT) image (Fig. 8d). The

dislocations were the most

common line defects in cyclically-deformed austenite phase of NiTi [15,40]. Weak diffraction spots of residual martensite were observed in the SAED in Fig. 8a where the strong diffraction spots belong to austenite, showing that most of the cyclically deformed grains remained in austenite phase. HRTEM, fast Fourier transform (FFT) and its IFFT of a residual martensite grain in the near-surface region were shown in Fig. 8e-f. Like the deformed austenite grains, the residual martensite grain contained dislocations (Burgers vector

̅

) (Fig. 8f) which inhibited reverse transformation of the residual

martensite. The cracks in Fig. 8b were mainly mode II shear cracks that were similar to those found in the metallic glasses under compression [46]. The cracks were shallow and constrained to the surface region of the micropillars, due to the crack closing force from the cyclic compression [47]. For the micropillar #3 under the low-stress cyclic compression, there was no extrusion appearing at the surface of the micropillar after

cycles of compression (Fig. 9a), nor

was there any surface crack observed in the TEM image of Fig. 9b. The microstructure (Fig. 9b) was the same as the original sample (Fig. 1a). Fig. 9c-d show a defect-free austenite grain in the micropillar #3. It is seen that the microstructure was not strongly affected by the limited PT and the low stress level.

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4. Discussion 4.1 Combined effects of dislocations, residual martensite and the residual stress on the functional degradation of the micropillar #2 was composed of two parts: plastic strain (~79% of total due to dislocations (Fig. 8b-f) and reversible

)

due to residual martensite (~21%,

estimated by the recovered strain after heating as shown in Fig. 5a). The dislocations were mainly cyclic transformation-induced, because the maximum applied cyclic stress on the micropillar #2 was below the yield strength of austenite and martensite (Fig. 3b) and the dislocations were observed in the micropillar #2 (Fig. 8b-f) under full-PT cyclic compression but not in the micropillar #3 (Fig. 9) under elastic cyclic compression. Local stresses that exceed the yield strength of austenite can lead to transformation-induced dislocations at the incompatible habit planes during the cyclic PT [15,16,18]. Martensite that formed during the loading of cyclic deformation was pinned by the dislocations and cannot reverse transform into austenite during the unloading. As a result, it became residual martensite (Fig. 8e-f) [1], which was further evidenced by the recovery of residual strain after the heating (Fig. 5). The transformation-induced dislocations, the resulting residual martensite and the associated residual stress are the physical origins of the functional degradation of the micropillar #2 [1,3,23].

of the micropillar #2 decreased with

the increase in cycle number, as a result of the increases in the dislocation density, the accumulation of residual martensite and residual stress. Direct growth of the residual martensite without the nucleation process further decreased

. As the decrease in

was larger than the decrease in the reverse transformation stress

15

(Fig. 4d), the

mechanical dissipation decreases in

was decreased. Reduction of

in each cycle also led to

. The role of residual martensite in the functional degradation was further

verified by increases in

,

(increased for a lower value than

(Fig. 5) after heating the deformed micropillar #2 well above

),

and

(but below

recrystallization temperature) to trigger reverse transformation of the residual martensite, which partially relieved the residual stress. With an increase in

after the heating, the

functional degradation was reactivated in the following superelastic cyclic compression (Fig. 5b-d). The coupling of the cyclic-transformation-induced dislocations and the residual martensite made the cyclic deformation behavior of the NC NiTi distinct from that of traditional metals and alloys [48,49]. 4.2 Nanoscale extrusions resulted from cyclic PT Fatigue crack initiation in metals and alloys under cyclic deformation are often attributed to the development of persistent slip bands (PSBs) that are manifested by extrusions and intrusions at surface of the metallic materials. The extrusions and intrusions are results of combined nucleation, glide and annihilation of dislocations [48,50,51]. The extrusions observed at the surface of the NiTi micropillars (Fig. 7, Fig. 8a-b & Fig. 10a) under cyclic PT are attributed to the transformation-induced dislocations (Fig. 8c-f) which glided on local shear planes and created steps at the surface of micropillars, as shown in Fig. 8b. Such extrusions were not observed in the micropillar #3 that was cyclically compressed below the martensitic transformation stress, indicating that the transformation-induced dislocations are essential sources of the extrusions in the NiTi micropillars.

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Although the applied forces on the micropillar #2 were compressive, shallow shear cracks were formed at the surface of the micropillar under cyclic PT, as shown in Fig. 8b. As tensile stress is essential for crack nucleation [47], it is conjectured that the observed shear cracks nucleated under local tensile stresses in the near-surface region of the micropillar under overall cyclic compressive stress, because the deformation (here it is plastic shear band) of the micropillar was non-uniform. The SEM and TEM observations of surface extrusions and shear cracks (Fig. 7 & Fig. 8) confirmed that the plastic shear deformation in the cyclically deformed micropillar was localized in the near-surface region of the micropillars while the rest part of the micropillar remained undamaged. This is significantly different from the case of large shear planes that can penetrate the whole cross-section of the micropillar (Fig. 10b) and create circumferential steps at the surface of micropillar under a large plastic strain [29,42,52]. During the unloading process, the undamaged superelastic region tends to recover to its original shape while the locally sheared region has permanent deformation and cannot fully recover. This creates a local tensile stress in the sheared region (Fig. 10c). Under such local tension, a separate shear plane formed and served as a potential site for crack nucleation near the existing shear plane. The extrusions were mainly formed in the first saturate after

cycles of compression and tended to

cycles (Fig. 7), as a result of the cyclic hardening [47].

was the

largest in the first cycle (0.24%/cycle) and rapidly decreased to less than 0.005%/cycle after 20 compressive cycles. The behavior was consistent with the strain hardening of austenite

17

phase during plastic deformation (Fig. 3b) [15]. Similar strain hardening behavior was frequently observed in NC Ni and Ni alloy [52,53]. Extrusions at surface have not been observed in the macroscale NC NiTi pillars under cyclic compression where splitting and chipping via crack nucleation from the existing defects (such as microscale voids) and slow propagation of the compression-parallel cracks become the dominant mode of structural fatigue failure [6,27]. The compression-parallel cracks were not found in the cyclically deformed micropillars, as the latter has much less defects than the macroscale pillars. Therefore, the fatigue life of the NC NiTi micropillars is expected to be much higher than the macroscale counterparts. 4.3 Power-law trend in functional degradation As shown in Fig. 4 and Fig. 5, (Eq. (1-3)) with the cycle number

,

,

and

follow power law relationship

. (1) (2) (3)

The scaling factors

,

,

and

in Eq. (1-3) are values of

in the first cycle of the cyclic deformation. Exponents

,

,

,

,

and

and

are positive

constants that reflect the resistance of the material to the functional degradation. The transformation stresses

and

of the micropillar #2 was stable after

superelastic compression, and no longer followed the power law trend.

18

-

cycles of curve (Fig.

4b) and

-

curve (Fig. 4e) can be fitted with power law functions in the full range of the

superelastic cycles. The power law trend indicated that the functional degradation of the micropillar #2 was only significant at the beginning of the cyclic deformation and tended to saturate as the cycle number increased [1,54]. The repulsive force of existing dislocations increased the required shear stress to generate new dislocations [47], leading to the saturation of transformation-induced dislocations. Therefore, the stress-strain response of the micropillar #2 became stable; and the functional degradation was no longer significant after

cycles

of superelastic compression which was reflected in the stable transformation stresses (Fig. 4d), extremely small

(Fig. 4c) and

(Fig. 4f).

The heating process partially recovered the functional degradation by reverse transformation of the residual martensite (Fig. 5). It reset the scaling factor ( , ) and the exponents (

,

,

and

,

and

) in Eq. (1-3), revitalizing the already saturated

functional degradation. The power law relationship has been checked to be reproducible in the NC NiTi micropillars (Supplementary data). Similar trend has also been observed in the thermal cycling of NiTi [55]. 5. Conclusions Cuboidal micropillars with uniform cross-section have been fabricated by FIB from a bulk NC NiTi sample with an average GS of 65 nm. The cyclic deformation behavior of the material at the microscale is investigated via superelastic cyclic compression of the micropillars below the plastic yield strength of austenite and martensite. SEM and TEM

19

observation of the micropillars are conducted to provide the surface morphology evolution and the microstructure changes due to the cyclic PT. The followings are the main conclusions of this research. 1. The cyclic compression experiments show that the NC NiTi micropillars remain superelastic for over

full-transformation cycles without structural fatigue failure. The

functional degradation mainly take place within the first monotonically decrease, and the rest of the cycles (

~

cycles where

,

monotonically increases with the cycle number ( ), the rates of

,

,

and

and . In

become very small

and negligible, demonstrating an asymptotic saturating trend of the cyclic responses. 2. Different from the bulk NiTi that fails by splitting and chipping under cyclic compression [6], the damage of the micropillars under full-transformation cyclic compression is manifested by nanoscale local extrusions and shallow shear cracks at the surface of the micropillars. The cyclic martensitic transformation-induced dislocations, the resulting residual martensite and the associated residual stress are the main sources of the observed functional degradation, the extrusions and the shear cracks. 3. The functional degradation can be partially recovered by heating the cyclically deformed micropillars to 100 ℃ which triggers partial reverse transformation of the residual martensite. The partial removal of the residual martensite leads to decreases in both the residual strain and the residual stress, which result in the increases in the externally applied transformation stresses and the overall transformation strain. Therefore, the heating can be repeatedly used to partially eliminate the functional degradation of NiTi.

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Acknowledgement This work was financially supported by Hong Kong Research Grant Council (GRF Project No. 16206119) and the Shenzhen Municipal Government SZSTI (Project No. SGDX2019081623360564 and Project No. JCYJ20170412153039309). The research work was carried out in the DSMF and MCPF of HKUST, and the Pico Center of SUSTech that receives support from Presidential fund and Development and Reform Commission of Shenzhen Municipality.

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Fig. 1 (a) Bright-field TEM image and SAED of the region in the dashed red circle of the original NiTi sample and (b) grain size distribution.

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Fig. 2 Just fabricated cuboidal micropillars viewed at 45 tilting in SEM.

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Fig. 3 (a) The superelastic stress-strain response with a maximum strain of 5.6% at a room temperature of 25 ℃ and (b) the stress-strain response with a maximum strain of 19% at the room temperature (blue curve) and at a high temperature of 150 ℃ (red curve where (~2.1 GPa) is higher than the plastic yield strength of austenite (1.3 GPa)).

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Fig. 4 (a) Stress-strain curves of the micropillar #2 that has been compressed for superelastic cycles, the evolutions of (b) residual strain, (c) rate of residual strain ( ), (d) forward and reverse transformation stresses, (e) hysteresis loop area, and (f) rate of hysteresis loop area (

) against the cycle number (N) plotted in logarithm scale.

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Fig. 5 (a) Stress-strain curves of the micropillar #2 before and after the first heating, (b) after the first heating (AH1), after 2104 more superelastic cycles of compression and after the second heating (AH2), (c) the evolution of forward and reverse transformation stresses, and (d) hysteresis loop area against the cycle number (N).

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Fig. 6 Stress-strain curves of the micropillar #3 subjected to

cycles of compression

under a maximum stress of 550 MPa which is slightly lower than the forward transformation stress of 600 MPa.

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Fig. 7 SEM images showing the surface morphology of the micropillar #2 after (a) (b-c)

, (d-e)

, (f-g)

, (h)

,

cycles of compression, and (i) after the first heating.

The images were taken at 45⁰ tilting of the micropillar in SEM. F1-F4 represent the corresponding faces of the cuboidal micropillar.

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Fig. 8 (a) A bright-field TEM image where multiple extrusions and shear cracks are observed at the right edge (surface) of the micropillar #2. The SAED shows both austenite and martensite phases. (b) A magnified bright-field TEM image of an extrusion and a shear crack, (c) high-resolution TEM (HRTEM) image, fast Fourier transform (FFT) and (d) the corresponding inverse fast Fourier transform (IFFT) image of an austenite grain with dislocations, (e) HRTEM, FFT and (f) IFFT of residual martensite with dislocations.

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Fig. 9 (a) SEM image taken at 45⁰ tilting of the micropillar #3, (b) bright-field TEM image of the micropillar #3 compressed below the forward transformation stress for cycles, (c) HRTEM, FFT and (d) IFFT of a defect-free austenite grain in the cyclicallydeformed micropillar #3.

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Fig. 10 (a) SEM images of extrusions on the micropillar #S1 subjected to cyclic deformation under a maximum stress of 1.2 GPa for

cycles (F1-F4 represent the

corresponding faces of the cuboidal micropillar), (b) shear planes that penetrate through the whole micropillar, and (c) evolution of extrusions at the surface the micropillar due to local shear during the loading and non-uniform recovery during the unloading of cyclic compression.

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Graphical Abstract

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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