transmission electron microscopy investigation of ... · dislocation slip nanograins abstract...

International Journal of Plasticity xxx (2010) xxx–xxx

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International Journal of Plasticity

journal homepage: www.elsevier .com/locate / i jp las

Transmission electron microscopy investigation of dislocation slip duringsuperelastic cycling of Ni–Ti wires

R. Delville a,*, B. Malard b,1, J. Pilch b, P. Sittner b, D. Schryvers a

a EMAT, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgiumb Institute of Physics of the ASCR, Na Slovance 2, 182 21, Prague, Czech Republic

a r t i c l e i n f o

Article history:Received 13 January 2010Received in final revised form 9 May 2010Available online xxxx

Keywords:Transmission electron microscopyShape memory alloyMartensitic transformationDislocation slipNanograins

0749-6419/$ - see front matter � 2010 Elsevier Ltddoi:10.1016/j.ijplas.2010.05.005

* Corresponding author. Tel.: +32497946591.E-mail address: [email protected] (R. Delvill

1 Present address: SIMaP, 1130 rue de la piscine, 3

Please cite this article in press as: Delville, R.,cycling of Ni–Ti wires. Int. J. Plasticity (2010),

a b s t r a c t

Superelastic deformation of thin Ni–Ti wires containing various nanograined microstruc-tures was investigated by tensile cyclic loading with in situ evaluation of electric resistivity.Defects created by the superelastic cycling in these wires were analyzed by transmissionelectron microscopy. The role of dislocation slip in superelastic deformation is discussed.Ni–Ti wires having finest microstructures (grain diameter

2 R. Delville et al. / International Journal of Plasticity xxx (2010) xxx–xxx

is not exactly the case, particularly if larger transformation strains are needed and many of the considered promising engi-neering applications of SMAs have never been realized due to the degradation of Ni–Ti functional properties and fatigue fail-ure with increasing number of cycles. In this respect, the repetitive stress-induced transformations during pseudoelasticcycling have always been used as a standard experiment, although the cyclic instability is characteristic for any thermome-chanical load due to reversible martensitic transformation. After the pioneering works of Melton and Mercier (1979) andMiyazaki et al. (1986), a large number of experimental investigations dealing with the effects of pseudoelastic cycling onthe functional and structural properties of Ni–Ti was published (e.g. Brinson et al., 2004; Gall et al., 1999; Gall and Maier,2002; Hamilton et al., 2004; Kang et al., 2009; Kockar et al., 2008; Liu et al., 1999; McCormick and Liu, 1994; Nayanet al., 2008; Nemat-Nasser and Guo, 2006; Sehitoglu et al., 2001; Shaw and Kyriakides, 1995; Strnadel et al., 1995; Wanget al., 2010; Yawny et al., 2005). Studies on fatigue crack growth in Ni–Ti (McKelvey and Ritchie, 2001; Eggeler et al.,2004; Gall et al., 2008) have shown that fatigue limit of Ni–Ti is related to the degradation of functional properties and de-pends significantly on the microstructures achieved by various heat treatments of cold worked Ni–Ti alloys. Main character-istics of the degradation of functional properties during pseudoelastic cycling are: (i) decrease of the transformation plateaustress, (ii) accumulation of residual strain, and (iii) decrease of the stress hysteresis and change of the shape of the stress–strain curve from ‘‘plateau type” to ‘‘hardening type”. These changes have been frequently ascribed to the build-up of aninternal stress in the microstructure upon pseudoelastic cycling. Since the decrease of the unloading plateau is always smal-ler that the decrease of the forward loading plateau, the stress hysteresis width decreases upon cycling. This means that theenergy dissipated in a single cycle decreases. The accumulation of residual strain was generally attributed to plastic defor-mation (dislocations) and retained martensite stabilized by the dislocation strain fields. Both have been experimentally ob-served (Gall and Maier, 2002; Hamilton et al., 2004), nevertheless, it still remains unclear how much of the accumulatedstrain is due to the accumulation of dislocations in the austenite and how much is related to the formation of stabilized mar-tensite. All these effects tend to stabilize after a certain number of cycles due to saturation of plastic deformation.

An important aspect of the superelastic cycling of Ni–Ti in tension is the tendency for localization of stress-induced mar-tensite transformation in shear bands (Lüders-type deformation) in contrast with a homogeneous mode (Miyazaki et al.,1981; Shaw and Kyriakides, 1997a,b; Liu and Van Humbeeck, 1998; Tan et al., 2004; Sittner et al., 2005). Whether the super-elastic deformation of Ni–Ti proceeds in a homogeneous or localized manner depends on a number of factors, including theapplied stress, texture, heat treatment conditions, deformation history and test temperature. The localized deformationmode of superelastically cycled Ni–Ti gradually changes to the homogeneous deformation mode with increasing numberof cycles (Sittner et al., 2005).

Another interesting feature of superelastic cycling is the memory of maximal reached strain. When a Ni–Ti wire is cycledsuch that the strain is incrementally increased, each additional cycle starts at a lower plateau stress but once the maximumstrain from the previous cycle is reached, it goes back to the previous plateau stress level and continues exactly where it wasunloaded (Yawny et al, 2005). This apparent memory of the loading history was explained by considering the gradual ad-vance of the martensite front (both in Lüders band or homogeneous deformation modes) in each subsequent cycle, leavingbehind slip dislocations marking the loading path. No direct proof was, however, given.

Experimental studies on single Ni–Ti crystals have shown a strong orientation dependence of superelastic deformation(Chumlyakov et al., 1996; Gall and Maier, 2002). Single crystals oriented with certain crystallographic orientations alongthe tensile axis such as h1 1 1i show large transformation strain but low resistance to slip whereas other orientations suchas h1 0 0i show a small transformation strain and high resistance to slip. This means that the individual grains of a Ni–Tipolycrystal might respond in a different way to superelastic cycling and texture plays a significant role (Gall et al., 2000;Sittner et al., 2005).

Slip dislocations have been experimentally observed in superelastically deformed Ni–Ti by TEM (Gall and Maier, 2002;Hurley et al., 2003; Hamilton et al., 2004). Very recently generation of dislocation defects during thermal cycling of Ni–Tisingle crystal was investigated by Simon et al. (2010) using in situ TEM. A mechanism for generation of h1 0 0i/{0 1 1} dis-location loops by propagating austenite/martensite interface was proposed. Norfleet et al. (2009), who carried out STEMobservation of defects created by stress-induced martensitic transformation in Ni–Ti micropillars deformed in compression,observed bands of h1 0 0i/{0 1 1} dislocation loops aligned with internal twins plane of a martensite plate but not along themost favored slip plane. They concluded that the dislocation loops are created by propagating austenite/martensite inter-faces. Interestingly, no retained martensite phase was observed after unloading the micropillars.

It thus appears very likely that the mechanism responsible for the accumulation of plastic strains and evolution of super-elastic stress–strain behavior of Ni–Ti in tension is related to the coupling between martensitic transformation and disloca-tion plasticity. The mechanism is, however, not yet fully understood. What defects responsible for accumulation ofirreversible strain are created during superelastic cycling of polycrystalline wires? The yield stress for plasticity in martens-ite or austenite is commonly twice as large as the upper plateau stress (>1.3 GPa). Upon loading at high temperatures(�100 �C), the critical stress for yielding of austenite frequently raises above 900 MPa. So why does dislocation slip occurduring superelastic deformation of Ni–Ti at room temperature below 500 MPa? Does the dislocation slip occur in martensiteor austenite? Can it be that the dislocation slip only accompanies the propagation of the austenite/martensite interface onthe local level of individual habit planes as Norfleet et al. (2009) suggest? These questions have motivated our research.

Researchers have always tried to promote the phase transformation and prevent the plasticity in Ni–Ti in order to sup-press the degradation of the superelastic response by applying suitable thermomechanical treatment to the alloy. There arebasically two ways to deal with the problem of degradation of functional properties of Ni–Ti upon cycling. One is to try to

Please cite this article in press as: Delville, R., et al. Transmission electron microscopy investigation of dislocation slip during superelasticcycling of Ni–Ti wires. Int. J. Plasticity (2010), doi:10.1016/j.ijplas.2010.05.005

http://dx.doi.org/10.1016/j.ijplas.2010.05.005

R. Delville et al. / International Journal of Plasticity xxx (2010) xxx–xxx 3

optimize the alloy microstructure (grain size, defects, precipitates, internal stress) in such a way that the dislocation slipactivity is minimized. This includes application of strain hardening (Miyazaki et al., 1982), precipitation hardening (Saburiet al., 1982; Gall and Maier, 2002), grain refinement (Kockar et al., 2008; Malard et al., 2009), texturing (Gall et al., 2000) andphase compatibility (Delville et al., 2009, 2010a). Nevertheless, even the best performing superelastic medical grade Ni–Tiwires and tubes still show significant accumulation of residual strains to some extent. So an alternative approach wouldbe to accept the inevitable presence of dislocation activity accompanying stress-induced transformation in Ni–Ti, train itby superelastic cycling prior the use to minimize the degradation and predict the further degradation including its conse-quences for practical applications through mechanics modeling. This second modeling based approach has recently attractedsignificant attention in the literature (Table 1).

The approaches used to model the simultaneous transformation and plasticity are not discussed here since this is anexperimental paper. Nevertheless, it seems that the main obstacle hindering successful and reliable modeling of the degra-dation of cyclic superelasticity (evolution of stress–strain curves upon cycling) is the yet insufficient knowledge of the defor-mation mechanism involving coexistence of slip deformation and martensitic transformation. In particular, reliableidentification of defects (slip dislocations, deformation twins, residual martensite, internal stress) created by the tensile cy-cling of commercial superelastic wires seems to be needed.

In this experimental work, we have taken advantage of the opportunity of having Ni–Ti wires featuring a wide range ofdifferent microstructures with grain sizes ranging from �10 nm up to �1 lm and different levels of recrystallization/recov-ery. Such wires were prepared using a recently developed method of non-conventional heat treatment by controlled elec-trical current (Patent, 2009; Pilch et al., 2009; Malard et al., 2009) called ‘‘Final Thermo Mechanical Treatment by ElectricCurrent” (FTMT-EC). Compared to conventional heat treatments in environmental furnace, FTMT-EC enables a finer controlof microstructures (Delville et al., 2010b), internal stress and texture (Malard et al., 2009) and functional mechanical prop-erties (Pilch et al., 2009) of thin Ni–Ti filaments. We have performed 10 superelastic cycles on variously treated Ni–Ti wires,prepared TEM foils from wires before and after tensile cycling and analyzed the dislocation defects created by the superelas-tic cycling. In this way, we could investigate the stability of the various nanosized microstructures present in the wiresagainst dislocation slip occurring during superelastic cycling. In addition, superelastic deformation of Ni–Ti wires havingvery well-defined microstructures (fully recrystallized grains free of defects, no internal stress) was investigated in a moredetailed manner. Dedicated tensile tests were performed in a wide temperature range involving in situ electrical resistancestudies during superelastic cycling with the aim to shed more light on the evolution of stress–strain response and accumu-lation of residual strain. The results help to better understand the deformation mechanism of simultaneous dislocation slipand stress-induced transformation in Ni–Ti concerned by the modeling work summarized in Table 1.

2. Experimental procedures

Cold worked Ni–Ti wires with a diameter d = 100 lm were obtained from Fort Wayne Metals (Ni–Ti#1–CW (Fort WayneMetals, 2009)). The composition of wires as determined by atomic absorption spectroscopy is 50.8 at.%Ni–49.2 at.%Ti whichis in good agreement with the composition given by the manufacturer (50.9 at.%Ni–49.1 at.%Ti). The wires were heat-treatedby sequences of DC electric power pulses using P = 125 W. For example, the ‘18 ms wire’ was treated by 18 subsequentpulses 1 + 2 + 3 + �� + 18 ms long. Although in this interrupted treatment the wire is exposed to high temperatures for a much

Table 1SMA modeling of the effect of plastic deformation on transformation superelasticity.

Source Feature

Tanaka et al. (1995) Phenomenological modeling of cyclic loading instabilities of SMAsAbeyaratne and Kim (1997) Modeling of cyclic effects in shape memory alloys: a one-dimensional continuum modelBo and Lagoudas (1999) One of the first attempts to simulate the evolution of plastic strains during superelasticity in micromechanics modelLagoudas and Entchev

(2004)SMA model incorporating plastic deformation

Paiva et al. (2005) A constitutive model for shape memory alloys considering phase transformation and plasticityAuricchio et al. (2007) A 3D model describing stress-induced solid phase transformation with permanent inelasticityZaki and Moumni (2007) A 3D model of the cyclic thermomechanical behavior of shape memory alloys; detailed simulations for Ni–Ti wire in

cyclic tensionWang et al. (2007) Micromechanical constitutive model for pseudoelastic Ni–Ti modified to include plastic deformationNovak et al. (2009) An adaptation of crystallographically based micromechanics 1D model of SMAs for concurrent plastic deformation.

Considering anisotropies of elasticity, transformation and plastic slip in both austenite and martensite phases, thismodel firstly predicts the redistribution of stresses and strains in transforming textured Ni–Ti polycrystals. Simulationof responses of Ni–Ti wire in various thermomechanical loads are presented

Saint-Sulpice et al. (2009) Experiment and 3D superelastic modeling of strain accumulation under cyclic loadings, internal loops, CuAlBepolycrystal

Manchiraju and Anderson(in press)

A microstructural finite element (MFE) model treating the interaction between martensitic transformations andplasticity through the grain-to-grain redistribution of stress caused by both deformation processes modeled at acrystallographic level and operating simultaneously

Kan and Kang (2010) Constitutive model for uniaxial transformation ratcheting of superelastic Ni–Ti shape memory alloy



Fig. 1. FIB extraction of a longitudinal slab from the microwire.


longer time than in a direct annealing, it was shown (Delville et al., 2010b; Malard et al., 2009) that the resulting microstruc-ture and functional properties are similar. This is because the effects of individual pulses are not simply additive but the finalpulse with the longest time, in which the highest temperature is reached (Malard et al., 2009), has the most decisive influ-ence on the resulting microstructure in the wire. Hence, the presented TEM results can be considered representative also fordirect FTMT-EC pulse treatments. This stepwise annealing method was employed to allow for precise X-ray synchrotronmeasurements after each annealing step on the same wire (Malard et al., 2009). The step-annealing experiments were sub-sequently reproduced in order to perform TEM investigation of the microstructures.

The functional superelastic responses of the Ni–Ti wires treated 4 ms, 6 ms, 8 ms, 10 ms, 12 ms, 14 ms, 16 ms and 18 mswere evaluated by performing 10 tensile stress–strain cycles up to 1500 MPa or 8% of total strain at room temperature inposition control. The 16 ms and 18 ms treated wires were subjected to tensile tests in temperature range from �40 to80 �C. The variation of electrical resistivity of the wire was monitored during straining in all tests.

Thin foil specimens for TEM investigations of microstructures were prepared from the heat-treated non-cycled wire aswell as from the heat-treated and mechanically cycled wires (after 10 superelastic cycles). A cross-sectional surface of thecut wire was carefully polished. Longitudinal slabs were extracted from the center of the wire using the focused ion beam(FIB) technique (Fig. 1) and subsequently thinned to electron transparency. TEM observations were carried out in a FEG TEC-NAI F20-ST and CM30 Ultra-Twin operated at 200 kV and 300 kV, respectively.

3. Results and discussion

3.1. Effect of microstructure on involvement of dislocation slip in superelasticity

Fig. 2 summarizes the key experimental results. It shows superelastic stress–strain curves (Fig. 2a–h) of the Ni–Ti wire atroom temperature (10 cycles) having eight very different microstructures obtained by the FTMT-EC treatments with differ-ent pulse times (Fig. 2i–n, the 4 and 6 ms annealed wires are not presented here). The microstructures were observed in TEMfoils prepared from the Ni–Ti wires which were exposed to 10 superelastic cycles. Fig. 2 provides the essential informationabout the microstructure–property relationship for superelastic Ni–Ti wires. Since this was already discussed in detail in therelated paper (Delville et al., 2010b), the details of the microstructure–property relationship will not be covered in the pres-ent paper. Instead, this work focuses on the evidences for plastic deformation due to dislocation slip taking place during thesuperelastic cycling, particularly the evolution of the shapes of superelastic curves, electric resistivity–strain curves andaccumulation of non-recovered strain shown in Fig. 2a–h and how it relates to the dislocation defects found in the micro-structures after the superelastic cycling (Fig. 2i–n).

The 6–10 ms treated wires do not yet show fully developed superelastic responses (transformation strains 1–4% (Fig. 2b–d)) and their respective microstructures (Fig. 2i and j for 8 ms and 10 ms) are characterized by an increasing degree of recov-ery but no significant recrystallization. No evidence of plastic deformation such as dislocation slip or internal strain inducedby the mechanical cycling could be identified in these microstructures. Plateau type stress–strain superelastic curve showingstress-induced B2–R-phase transformation (as evidenced by the hysteretic electric resistivity–strain curve) preceding themartensitic transformation appears first after the 10 ms treatment (Fig. 2e).



Fig. 2. (a)–(h) Superelastic functional responses (10 tensile cycles till 8% strain or 1500 MPa stress at room temperature) of 0.1 mm thin Ni–Ti wires heat-treated by pulsed electric current (FTMT-EC, 125 W/4–6–8–10–12–14–16–18 ms DC pulse times). Red curves denote the in situ measured electric resistanceof the wire. (i)–(n) BF images of microstructures observed in the FTMT-EC treated (8–10–12–14–16–18 ms DC pulse times) wires subjected to 10superelastic cycles. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)


The 12 ms treated wire shows the best functional properties of all treated wires (Fig. 2e) with a plateau type stress–straincurve and sharp yield point, 6% transformation strain, stress-induced R-phase transformation, high strength �1.6 GPa andexceptional stability upon cyclic loading. The partially polygonized and recrystallized microstructure (Fig. 2k) responsiblefor these remarkable functional properties consists of nano-grains with sizes ranging from 20 to 50 nm. This dual micro-structure is believed to be the reason for the exceptional cyclic mechanical stability of the 12 ms treated wire (Delvilleet al., 2010b). In order to visualize the effect of cycling of the 12 ms microstructure, the foils of the 12 ms cycled andnon-cycled wires were further thinned below 20 nm thickness. The goal was to minimize contrasts due to the overlappingof nano-grains which can lead to misinterpretation (Rentenberger et al., 2004). However, some Moiré contrasts in the formof parallel dark fringes of are still visible. The microstructures before and after cycling are presented in Fig. 3a and b,



Fig. 3. Nano-grained microstructures in the 12 ms annealed wire (a) before and (b) after cycling. Both microstructures reveal the same kind of partiallypolygonized and recrystallized grains. No evidence of slip deformation during superelastic cycling is observed.

Fig. 4. 14 ms FTMT-EC treated wire (a) before cycling (b) after cycling. (c) Slip dislocations observed in one of the largest recrystallized grains occurringduring cycling as shown in the bright field (BF) image taken in two-beam orientation.


respectively. No clear differences which would evidence slip deformation during superelastic cycling could be found. This isin agreement with the negligible build-up of residual strain upon cycling (

Fig. 5. Microstructure of 16 ms FTMT-EC treated Ni–Ti wire prior (a) and after (b) 10 superelastic cycles till 8% deformation. Multiple slip dislocations areclearly visible inside most of the grains in the fully recrystallized microstructure.

Fig. 6. 16 ms FTMT-EC treated Ni–Ti wire after 10 superelastic cycles till 8% deformation. BF images in various two-beam conditions used for conventionaldislocation analysis. (a) Near the h1 1 1i zone orientation three slip planes are visible. (b)–(d) By selecting one of the g ¼ h�110i vectors for two-beamanalysis, the corresponding f�110g slip planes become invisible. The vanishing contrast condition g � b = 0 yields a Burgers vector b = ah1 0 0i, where a is theaustenite lattice parameter.


microstructure of the mechanically cycled wire (Figs. 2m and 5b). If proper contrast conditions are set, dislocation lines areclearly visible in all grains larger than 300 nm, irrespective of their orientation. Note that because of the random orientationof the recrystallized grains, it is not possible to have all the grains correctly oriented to show dislocation contrast in a singlepicture (see Fig. 5b). For grains smaller than 300 nm, overlapping with surrounding grains within the foil thickness and inter-nal contrast render the study of dislocation slip difficult. However, it appears that the smallest grains do not show much dis-location activity, while the largest grains (600–700 nm) (Fig. 6) show a slightly higher dislocation density than mid-sizegrains (400–500 nm). Grain boundaries in microstructures of the cycled wires appear less well-defined and uneven diffrac-tion contrast originating from newly induced local strain fields is clearly visible. No residual B190 martensite phase wasfound in the microstructure after cycling.

The results of the two-beam analysis of the slip systems activated in the 16 ms treated wire are shown in Fig. 6. Thefirst image is a BF image of one of the largest grains oriented near a h1 1 1i zone showing three activated {1 1 0} slipplanes. Fig. 6b–d shows the same grain orientated in different two-beam conditions for which the defect contrast ofone of three slip plane vanishes. The g-vectors responsible for different contrasts are marked with a black arrow. Theextinction rule g � b = 0 gives a Burgers vector b = ah1 0 0i. This is the commonly observed Burgers vector of dislocationsin Ti–Ni and more generally in ordered B2 crystals since it is the shortest Burgers vector for perfect dislocations. Straightdislocation segments are unequally distributed among the grains. Largest grains show highest density of dislocationlines. Within one grain, the activity is frequently concentrated near grain boundaries.

The recrystallized grains in the microstructure of the 18 ms treated wire (Figs. 2n and 7) are micrometer-sized. Thestress–strain response (Fig. 2h) shows a very fast build-up of residual strains during tensile cycling – 5% in the first threecycles. A much higher density of dislocations than in the 16 ms treated samples was observed after cycling in all the grains,irrespective of their orientation (Fig. 7b–d). Individual dislocation lines were not easily resolved. Fig. 7c shows a BF imagetaken near a h1 1 1i zone axis revealing the very high density of slip dislocations. When the sample was tilted away toset the invisibility condition to the slip planes closest to the wire axis which contains the highest density of dislocation lines,dislocation lines belonging to the two other activated slip systems become visible (Fig. 7d). No retained B190 martensite wasfound.



Fig. 7. Microstructure of 18 ms FTMT-EC treated Ni–Ti wire (a) prior and (b)–(f) after 10 superelastic cycles till 8% deformation. (b) Very dense dislocationtangles and strain contrast after cyclic deformation, (c) high density of entangled dislocations in general diffraction orientation (h1 1 1i zone), (d) the samegrain in two-beam condition in which part of the dislocations in tangles satisfy the invisibility condition for g ¼ h0 �11i. (e) BF image showing parallel darkbands oriented along a {1 1 0}B2 slip plane due to the accumulation of dislocations at specific locations in a grain of the 18 ms treated wire. (f) BF imageshowing bands of dislocations (indicated by white arrows) crossing over a grain boundary (indicated by a dashed line).


An additional feature visible in the grains of the 18 ms treated sample when proper diffraction conditions are set for BFimaging is the arrangement of dislocations in parallel macroscopic bands. As seen in the BF pictures in Fig. 7e and f taken attwo different locations, the regularly spaced bands present a dark contrast indicating a high density of dislocations. They areoriented along one of the {1 1 0}B2 planes and are sometimes observed to cross grain boundary (Fig. 7e). Note that such bandswhich result from the accumulation of dislocations at certain location are not visible in 16 ms treated wire having much low-er density of dislocations.

An additional deformation mode was observed in the microstructure of the 18 ms treated wire. Fig. 8a is a BF imageshowing planar defects which have developed from the grain boundaries and grown into the grain interiors. The selected



Fig. 8. Analysis of a {1 1 4} compound twin found frequently in the microstructure of 18 ms FTMT-EC treated Ni–Ti wire after 10 superelastic cycles till 8%deformation – BF pictures (a and d), experimental and simulated diffraction patterns from the matrix and twins (b, e, c, and f). The respectivecrystallographic axes are indicated in panels (c) and (f).


area diffraction pattern (SADP) taken over the circled area is shown in Fig. 8b and is reproduced in Fig. 8c. It is composed oftwo sets of reflections in {1 1 0} orientations, one originating from the grain matrix (circular red2 dot) and one from the planardefect (blue dots with bar). They are in mirror orientation along the {1 1 4}B2 twinning plane suggesting {1 1 4} compoundtwins. Another example in Fig. 8d shows the BF image of V-shaped defect in another grain. The grain boundaries are highlightedwith fine dashed lines. From the SADP taken over the circled area (Fig. 8e), three sets of reflections were recognized as detailedin Fig. 8f. The reflections from the planar defect corresponding to the largest and smallest branches of the V are in {1 1 4}B2 andf�1 �14gB2 twin orientation with the matrix, respectively. The {1 1 4} compound twins were found repeatedly in the microstruc-ture of the 18 ms treated wire.

The experimental evidences presented above clearly support the view that the accumulated plastic strain during super-elastic cycling of Ni–Ti wires is due to dislocation slip coupled with the martensitic transformation This supports the recentlyreported TEM evidences (Norfleet et al., 2009; Simon et al., 2010) describing how dislocation defects might be created duringmartensitic transformation in Ni–Ti. It still, however, remains to be found whether such dislocations can provide the basis fordeformation mechanism leading to large plastic strain accumulation observed in experiments and whether and how it de-pends on grain size, temperature or strain rate.

3.2. Stability of microstructures with respect to dislocation slip

It shall be noticed that, for annealing times greater or equal to 10 ms, the forward plateau stress of the superelastic curvesin Fig. 2d–h practically does not depend on the microstructure, even if the grain size changes two orders of magnitude from10 to 1000 nm. This suggests that the thermodynamic properties of the alloy are stable with respect to the FTMT-EC treat-ment and that the inverse relationship between the yield stress and grain size typical for plastic deformation of metals (Hall–Petch relation) fails for polycrystal superelasticity governed by the stress-induced martensitic transformation. The heattreatment time in the ms range probably does not allow for any diffusional processes, which would lead to a variation ofthe chemical composition of the matrix including the formation of precipitates and hence to a change of the T0 equilibriumtemperature for the B2–B190 transformation. The Ms0 temperature (temperature at which the forward transformation line

2 For interpretation of the references to color in Fig. 8, the reader is referred to the web version of this paper.



Fig. 9. Electrical resistivity–strain in situ responses of the FTMT-EC treated Ni–Ti wires reproduced from Fig. 2a–h.


drF/dT in the stress–temperature diagram meets the temperature axis) seems not to be affected by the heat treatment. Otherparameters such as transformation strain, hysteresis, elastic moduli, etc., however, depend significantly on the FTMT-ECtreatment (i.e. on the microstructure).

For FTMT-EC treatments with pulse times

Fig. 10. (a and b) Superelastic stress–strain cycling of 16 ms (left) and 18 ms (right) until the end of the plateau (red curve) followed by cycling to 20% (bluecurve) treated Ni–Ti wires with in situ electric resistance as a function of strain (top curve), and (c and d) stress–electric resistivity record evolving duringcycling due to accumulation of defects r and decrease of martensite fraction at the peak stress s. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this paper.)

Fig. 11. Superelasticity of a 16 ms treated wire in temperature range from 0 �C to +80 �C (a) strain and electrical resistivity as a function of stress at 40 �C,50 �C and 60 �C, (b) temperature dependence of characteristics of superelastic responses: 1 – electrical resistivity after unloading, 2 – electrical resistivity atthe peak strain 10%, 3 – non-recovered strain, 4 – upper plateau maximum strain, 5 – real transformation strain = upper plateau maximum strain minusnon-recovered strain, and 6 – upper plateau stress.


treated wires drifts upon cycling (Figs. 2, 9, and 10). The electrical resistivity at zero stress increases with number of cyclesdue to the accumulation of dislocation defects and/or retained martensite. There is, however, also a downward drift of thevalue of electric resistivity at maximum strain during the tensile cycling of the 14–18 ms treated wires (Figs. 9 and 10) whichmust be explained. This will be discussed below with the help of Fig. 10. The larger is the grain size, the more pronounced isthe accumulation of defects during the superelastic straining and the resultant drift of the electric resistivity (Fig. 9).

The in situ measurement of electrical resistivity can hence be beneficially used to investigate the deformation mechanismof Ni–Ti involving simultaneous transformation and dislocation slip. Supplemental experiments were performed on the16 ms and 18 ms treated wires. The reason why these wires were selected is that the interaction between the transformationand plasticity is strong, the microstructure is fully recrystallized (free of dislocation defects and internal strains) and we havedetailed TEM information about defects created by superelastic cycling. From practical point of view, these wires are over-treated, the really interesting wires would be the 10–12 ms treated wires showing much better superelasticity. The 16 msand 18 ms treated wires were exposed to tensile cycling at room temperature till the end of the stress plateaus and addition-ally up to 20%, 30% and 40% strain. Fig. 10a and b shows the strain–stress curves and specific electrical resistance–straincurves measured during cycling till to the end of the stress plateau (red curves) followed by cycling till 20% deformation(blue curves). Fig. 10c and d shows the stress against specific resistance recorded in these experiments. Note that microstruc-tures of the wires deformed beyond the end of the plateau were not investigated with TEM.

We did not consider so far the fact that the tensile deformation of Ni–Ti wires proceeds by nucleation and propagation oflocalized deformation bands as clearly evidenced by the stress plateau and sharp yield points of the stress–strain curves in




Figs. 2d–h, 10 and 11. Strain localization in superelastic Ni–Ti is commonly believed to be due to stress-induced martensitictransformation (Shaw and Kyriakides, 1997b; Sittner et al., 2005). The present results, however, suggest that dislocation slipmight be involved in strain localization too, so the question arises whether it has an effect on this phenomenon. Interestingly,the forward stress plateaus in the first cycles on the 16 ms and 18 ms treated wires are indeed significantly longer (7.3% and7.5%, respectively, see stress–strain curves in Fig. 10a and b) compared to �6% observed in case of the 12 ms treated wire(Fig. 2e). This means that the strains localized in shear bands of the wires with fully recrystallized microstructures are sig-nificantly larger. It could be that there is a larger martensite fraction or more suitably oriented martensite variants in thewires with larger grain size, but it is equally possible that the plateau strains are not purely transformation strains but strainsdue to dislocation slip are also partially involved. The common feature of the evolution of the superelastic stress–strain curveupon tensile cycling is that the forward plateau stress decreases in small decrements in every subsequent cycle (see 8 ms–14 ms curves in Fig. 2c–f). This has been frequently associated in the modeling literature with the retained martensite (e.g.Lagoudas and Entchev, 2004; Wang et al., 2007; Kang et al., 2009) or internal stresses (e.g. Novak et al., 2009) induced duringsuperelastic cycling of Ni–Ti.

In this work, however, no martensite particles were found with TEM in the microstructures of the wires cycled within thesuperelastic plateau range. Hence, we assume that all non-recovered strain after cycling is due to dislocation slip or {1 1 4}austenite twinning. In other words, it is assumed that all martensite retransforms back to austenite upon unloading in eachcycle. The unrecovered strain which accumulates during cycling is thus due to dislocation slip. Of course we cannot com-pletely exclude the possibility that the retained martensite disappeared from the microstructure during thin foil preparationor long time relaxation. There is, however, additional argument which leads us to the above assumption. If the accumulatedstrains were due to residual martensite only, the electric resistivity measured at the maximum strain during cycling wouldhave to remain constant, but it markedly decreases (see Fig. 9 for the 14–16–18 ms treated wires and Fig. 10a and b, topcurves, for the 16 ms and 18 ms treated wires).

The dislocation slip taking place during forward loading increases the density of dislocation defects which are not recov-ered upon unloading. Consequently plastic strains and internal stress accumulate in the wire with increasing number of cy-cles. Since we assume that the dislocation slip is responsible for the accumulation of irreversible strain after unloading, theremust be less and less martensite phase in the fully stretched wire with increasing number of cycles. The martensite volumefraction in the wire at the peak stress thus decreases in each subsequent cycle due to dislocation slip taking place duringforward loading instead of stress-induced transformation. The accumulation of dislocation defects during cycling thus ex-plains the evolution of minimum and maximum of the electric resistance (drift of the electric resistance–strain response)during superelastic cycling of the Ni–Ti wires. No retained martensite is necessary to explain the accumulation of irreversiblestrains during superelasticity. This argument, however, does not exclude the possible occurrence of very small amount ofretained martensite, particularly in 18 ms treated wires. Since we are aware of the fact that this concept might be difficultto understand, the stress–electric resistance records for the 16 ms and 18 ms treated wires, respectively, are shown inFig. 10c and d. It is clearly seen how the accumulating slip deformation ðrÞ and related decreasing martensite fraction atthe peak stress ðsÞ quickly lead to the reduction of the stress hysteresis during superelastic cycling. The in situ electricalresistivity results thus seem to support the assumption that the dislocation slip takes place during forward loading andno or very small amount of residual martensite has been induced by the superelastic cycling of the 16 ms and 18 ms treatedwires.

When the 16 ms treated wire subjected to 10 superelastic cycles (5% accumulated strain Fig. 10a) was heated to 120 �C instress-free conditions, the strain decreased (�0.5%) and was not restored upon cooling. This suggests that only �10% of thenon-recovered strains accumulated in 10 tensile cycles can be possibly ascribed to the retained martensite. If the retainedmartensite remains in the microstructure after cycling (which is likely particularly for the 16 and 18 ms treated wires whichhave lower yield stress for plasticity) it is in a very small volume fraction. The small amount of residual martensite left in themicrostructure after superelastic cycling is surprising since most of experimental studies reported so far (see the referencescited in Section 1) as well as mechanical models of superelasticity listed in Table 1 consider that the unrecovered strain uponcycling is to large extent due to the residual martensite. Hence further thermomechanical experiments including dedicatedsynchrotron X-ray studies focusing on the evidence for internal stresses and residual martensite in cycled 12–18 ms wireshave been made. The results, suggest that the accumulated residual strains can be indeed ascribed to the generation of dis-locations observed in this work and that the evolution of superelastic stress–strain response is more related to the associatedinternal strains in the microstructure. These are better seen by X-rays than TEM. Since this, however, exceeds the scope ofthis paper, it will be published elsewhere (Sittner et al., in preparation).

Upon loading the 16 ms and 18 ms wires beyond the plateau level (stress–strain curves Fig. 10a and b), the electricalresistivity increases linearly with strain up to about 12% (Fig. 10a and b, top curves), where the slope gradually decreases.This is believed to be due to the fact that the stress-induced transformation is completed and that the dislocation slip inthe martensite takes over as the main deformation mechanism in addition to elasticity. If the 16 ms and 18 ms treated wiresare deformed and cycled with maximum strains 20%, 30% or 40%, superelastic deformation still proceeds but always inhomogeneous deformation mode (Fig. 10c and d in the case of 20% deformation). Note that the recoverable inelastic defor-mation in the first superelastic cycle is 7.3% (cycling till 9% strain) and 6.3% when cycled till 20% strain. Comparing the evo-lution of ‘‘stabilized” transformation strain, etr, with increasing maximum strain during cycling, it even increases from �2.9%(cycling till 9% strain) to �4.1% (cycling till 20% strain). This means that the accumulation of dislocation defects during ten-sile cycling does not prevent the superelasticity. The stabilized superelasticity may even improve (narrower stress hysteresis,




larger transformation strains). The dislocation slip accompanying the transformation, however, changes the shape of thestress–strain curve, makes it unstable upon cycling and changes the localized deformation mode into the homogeneousmode. This does not, however, automatically imply that there will be no residual martensite left in the heavily deformedwires (e.g. blue curves in Fig. 10). We know from supplemental X-ray studies (Sittner et al., in preparation) that there is asmall amount of residual martensite left after superelastic cycling of the 18 ms treated wire (but not detected in TEM andnot enough to account for the large build-up of residual strain) and a significant amount in the heavily deformed (�40%)16 ms treated wires. Further research is ongoing concerning the superelasticity and microstructures of the heavily deformedNi–Ti wires.

3.4. Superelasticity at various test temperatures

The dislocation slip activity during superelastic cycling is expected to increase with increasing test temperature since thetransformation stress is approaching the yield stress for dislocation slip. In order to verify this, a series of supplemental ten-sile tests was performed on the 16 ms treated wire at different temperatures in the range from �30 �C to +80 �C. First super-elastic stress–strain curves at T = 40 �C, 50 �C and 60 �C and superimposed in situ electric resistance measurement are shownin Fig. 11a. With increasing temperature, the plateau strain increases, residual strain after unloading increases and the elec-tric resistivity at the peak stress decreases. This is again interpreted as being due to the increasing involvement of dislocationslip during superelastic straining with increasing test temperature. Fig. 11b shows the evolution of particular characteristicsof the superelastic stress–strain curves with test temperature. One can see that, the upper plateau stress (curve 6) andmaximum strain (curve 4) continuously increase with increasing temperature, the real transformation strain (curve 5) (equalto the upper plateau maximum strain (curve 4) minus the non-recovered strain (curve 3) in that cycle), however, starts todecrease significantly with increasing test temperature above 40 �C, where the deformation due to dislocation slip becomesmore and more pronounced. The electric resistivity at the peak strain 10% (curve 2) accordingly decreases with increasingtest temperature above 40 �C. The fact that the electric resistivity at the peak strain 10% (curve 2) shows maximum at40 �C, can be explained by assuming two different mechanisms influencing the electrical resistivity of the wire at the peakstrain 10%. On the one hand, we assume that, as the plateau stress increases with increasing temperature, a larger volume ofaustenite grains transforms to martensite in the shear band. This leads to the increase of the electrical resistivity measured atthe peak strain of 10% with increasing temperature (Fig. 11b). This mechanism dominates at temperatures below 40 �C (thestress–strain curves are not shown in Fig. 11a). On the other hand, for test temperatures above 40 �C, as the transformationplateau stress approaches closer to the yield stress for dislocation slip (�1000 MPa for 16 ms treated wire (Sittner et al., inpreparation)), there is more slip deformation and less martensite transformation in propagating shear bands as evidenced bythe decrease of the electrical resistivity at the peak stress with increasing temperature (Fig. 11b). This latter mechanismdominates at temperatures above 40 �C, where the amount of slip deformation (and hence non-recovered strain) dramati-cally increases with increasing test temperature. Both mechanisms are, however, thought to be active in the whole temper-ature range of Fig. 11. The slope of the electric resistivity–strain dependence (Fig. 11a) clearly decreases with increasing testtemperature for the very same reason. Considering this together with the above discussion of the in situ measured electricalresistance in Figs. 9 and 10, it appears that the in situ electrical resistance measurement can be beneficially used to distin-guish the deformation due to dislocation slip from the martensitic transformation during continuous tensile straining of Ni–Ti.

In spite of the increasing involvement of dislocation slip with increasing temperature, the upper plateau stress increasesfrom 350 MPa at 0 �C to 830 MPa at 70 �C (drF/dT = �7 MPa/�C) as typical for Ni–Ti. It implies that the dislocation slip is cou-pled with the martensitic transformation – i.e. it does not proceed in the austenite phase without the martensitic transfor-mation even if the temperature and stress increase significantly. When the stress-induced transformation starts at elevatedtemperature – e.g. 60 �C (Fig. 11a), however, the dislocation slip proceeds simultaneously with the transformation in a largeextent. The low true transformation strain localized in the shear band (curve 5 in Fig. 11b) is due to the significant involve-ment of dislocation slip which substitutes for the transformation strain. In fact, at test temperature 60 �C, the part of the pla-teau strain due to slip becomes comparable to that due to martensitic transformation (Fig. 11a,b). Under such circumstances,the reverse superelastic plateau upon unloading is largely suppressed (Fig. 11a) and the wire fails to exhibit superelasticity atthis temperature and above.

Since the presented evidences seem to suggest that the observed slip dislocations might have been created by a mecha-nism related to the propagation of austenite/martensite interface such as proposed by Simon et al. (2010) or Norfleet et al.(2009) (the observed dislocation defects lie in the same h1 0 0i/{0 1 1} slip system (Figs. 6 and 8d) and their density increaseswith number of transformation cycles (Fig. 10)), we may consider such mechanism to be responsible also for the accumu-lation of dislocation defects and residual strains during superelastic cycling of Ni–Ti (compare the dislocation bands in Fig. 7eand f with Fig. 6 in Norfleet et al. (2009) showing dislocation loops aligned in very similar bands after just one compressionloading unloading cycle on Ni–Ti microcrystal). Even if we accept that the mechanism generating the dislocation loops bystress concentration at propagating phase interface proposed by Norfleet et al. (2009) is responsible for dislocations observedin this work, there still remains to be found out why the activity of this mechanism (i) is suppressed by decreasing grain size(dislocations were not observed for wires having grains size


wires are responsible for the accumulated strain (Figs. 2 and 5–7), we still do not know, whether the slip happened in theaustenite or martensite state. Further ongoing research suggests that the latter is more likely.

So far the role of {1 1 4}B2 deformation twins observed in the superelastically cycled 18 ms wire has been omitted. How-ever, given the fact that they were observed quite frequently, their role should not be neglected. We propose that the{1 1 4}B2 compound twins observed in the heavily dislocated 18 ms austenite microstructure have formed upon unloadingfrom the highly deformed and twinned martensite phase. Critical stress for twinning in martensite is several times smallercompared to the stress required for twinning in austenite (Miyazaki et al., 1982). According to Ii et al. (2003), there is a directcorrelation between f20 �1gB190 and {1 1 4}B2 deformation twins in Ti–50.6 at.%Ni. Deformation twinning occurs in the B190martensite along the f20 �1gB190 plane, which, upon reverse transformation, is retained into austenite as the corresponding{1 1 4}B2. Ii et al. (2003) claim that the high ductility of the B190 martensite can be attributed to the deformation byf20 �1gB190 compound twinning with a large twinning shear of 0.425. Such ‘‘two phase twinning” would represent a yet an-other deformation mechanism yielding residual irrecoverable strains, additional to dislocation slip. Three f20 �1gB190 com-pound twins supplement the three independent h1 0 0i/{0 1 1} slip systems (and/or their corresponding B190 martensiteslip) as active deformation systems (5 is commonly assumed to be required for compatible plastic deformation of a polycrys-talline material (Moberly et al., 1990)). Since the austenite deformation twins were not found in 16 ms treated Ni–Ti wiresshowing less dislocation density, we can anticipate that the activity of this additional deformation mechanism is more pro-nounced with increasing slip activity – i.e. with increasing grain size, upon loading further beyond the end of plateau and/orpossibly at higher test temperatures. That, however, remains to be confirmed experimentally.

4. Conclusions

As-drawn Ni–Ti wires were heat-treated by non-conventional pulsed electric current method yielding various micro-structures and functional superelastic properties depending on the applied heat treatment. The heat-treated wires were sub-jected to 10 tensile cycles at room temperature with in situ measurement of electrical resistivity. Microstructures in thewires before and after superelastic cycling were investigated by TEM and dislocation defects created during cycling wereanalyzed. The involvement of dislocation slip in superelasticity is discussed based on the results.

The heat-treated Ni–Ti wires having microstructures recovered through polygonization and/or recrystallization showsuperelasticity at room temperature. The wires having polygonized/partially recrystallized nanosized microstructures(125 W/6–12 ms pulse time) are highly resistant against dislocation slip, while those with fully recrystallized microstruc-tures (125 W/12–18 ms pulse time) are prone to dislocation slip (slip dislocations found in the microstructure of cycledwires, unstable stress–strain response), particularly as the grain size exceeds 200 nm.

Slip dislocations created during superelastic cycling of 14–16–18 ms treated wires were found only in relatively largerecrystallized grains (>200 nm), never in areas recovered only through polygonization or in small recrystallized grains below200 nm. The density of dislocation defects created by cycling in 14–16–18 ms treated wires (mean grain size�150,�500 and�1000 nm, respectively) increased significantly with increasing grain size. Dislocations in three austenite slip systemsh1 0 0i/{0 1 1} were identified in cycled wires. The involvement of dislocation slip in superelastic deformation at room tem-perature thus decreases with decreasing grain size and becomes essentially suppressed in wires having nanograin micro-structures (d < 200 nm).

The upper plateau stress of the superelastic stress–strain curve does not depend on the grain size in 10–1000 nm range.This suggests that the inverse relationship between the yield stress and grain size (Hall–Petch relation) does not apply for thestress-induced martensitic transformation in that range of grain size.

It is proposed that dislocation slip in superelastic cycling occurs alongside with the stress-induced martensitic transfor-mation during forward loading. Since the activity of dislocation slip increases with increasing grain size, the length of theforward transformation plateau of 14–18 ms treated wires increases as well. The dislocation defects and related internalstress remain in the microstructure after unloading. This results in accumulation of irreversible strain upon cycling andmakes the cyclic superelastic stress–strain response more unstable with increasing grain size.

No residual martensite was found in the microstructures of superelastically cycled Ni–Ti wires (10 cycles till the end ofplateau) by TEM. The results of the in situ electric resistance measurements (evolution of electric resistance–strain responsewith cycling) could be interpreted assuming accumulation of dislocation defects only. Hence, it is concluded that none orvery little retained martensite is created by tensile cycling of superelastic Ni–Ti till the end of plateau.

The accumulation of dislocation defects, however, does not prevent the superelasticity but merely affects the shape of thesuperelastic stress–strain curve, makes the superelastic behavior unstable upon cycling and changes the deformation modefrom localized to homogeneous. If the wire is ductile enough, it shows �4% of reversible superelastic strain upon tensile cy-cling even if it is deformed as much as 40%.

Based on the results of in situ electric resistance measurements, it is claimed that the involvement of dislocation slip insuperelastic deformation of Ni–Ti significantly increases with increasing temperature, as the plateau stress approaches theyield stress for dislocation slip. Although the forward plateau strain increases with increasing temperature, the true trans-formation strain decreases. The missing transformation strain is substituted by the irreversible strain due to dislocation slipwhose amount increases with test temperature. When it increases to the point that it becomes comparable to the reversible




strain due to martensitic transformation, the reverse superelastic plateau is suppressed and the wire does not show super-elasticity anymore.

Experimental evidence for {1 1 4} compound austenite twinning as a mode of plastic deformation additional to slip wasobserved in the largest grains of the fully recrystallized microstructures. Based on the earlier literature evidence, it is pro-posed that the {1 1 4} austenite compound twins formed upon unloading from the highly deformed and twinned martensitephase. The deformation twinning is assumed to occur in the B190 martensite along the f20 �1gB190 plane, which upon reversetransformation is retained into austenite as the corresponding {1 1 4}B2 plane. Such twinning would represent an additionaldeformation mechanism of Ni–Ti yielding residual irrecoverable strains.

Acknowledgements

Part of this work was performed in the framework of a European FP6 project ‘‘Multi-scale modeling and characterizationfor phase transformations in advanced materials” (MRTN-CT-2004-505226). Support was also provided by the FWO projectsG.0465.05 ‘‘The functional properties of SMA: a fundamental approach” and G.0180.08 ‘‘Optimization of Focused Ion Beam(FIB) sample preparation for transmission electron microscopy of alloys for TEM” and the IAP program of the Belgian StateFederal Office for Scientific, Technical and Cultural Affairs, ‘‘Physics based multilevel mechanics of metals” under ContractNo. P6/24. Additional support was also provided from projects AV0Z10100520 and IAA200100627.

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http://www.esomat.orghttp://dx.doi.org/10.1051/esomat/200903009http://www.esomat.orghttp://dx.doi.org/10.1051/esomat/200905024http://dx.doi.org/10.1016/j.ijplas.2010.05.005

Transmission electron microscopy investigation of dislocation slip during superelastic cycling of Ni–Ti wiresIntroductionExperimental proceduresResults and discussionEffect of microstructure on involvement of dislocation slip in superelasticityStability of microstructures with respect to dislocation slipIn situ electrical resistance measurements during cyclingSuperelasticity at various test temperatures

ConclusionsAcknowledgementsReferences

transmission electron microscopy investigation of ... · dislocation slip nanograins abstract...

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