Impurity levels and fatigue lives of pseudoelastic NiTi shape memory alloys

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Acta Materialia 61 (2013) 3667–3686

Impurity levels and fatigue lives of pseudoelastic NiTi shapememory alloys

M. Rahim a,⇑, J. Frenzel a, M. Frotscher a,1, J. Pfetzing-Micklich a, R. Steegmuller b,M. Wohlschlogel c, H. Mughrabi c, G. Eggeler a

a Institut fur Werkstoffe, Ruhr-Universitat Bochum, 44801 Bochum, Germanyb ADMEDES Schuessler GmbH, 75179 Pforzheim, Germany

c Department Werkstoffwissenschaften, Friedrich-Alexander-Universitat Erlangen-Nurnberg, 91058 Erlangen, Germany

Received 8 January 2013; received in revised form 28 February 2013; accepted 28 February 2013Available online 29 March 2013

Abstract

In the present work we show how different oxygen (O) and carbon (C) levels affect fatigue lives of pseudoelastic NiTi shape memoryalloys. We compare three alloys, one with an ultrahigh purity and two which contain the maximum accepted levels of C and O. We usebending rotation fatigue (up to cycle numbers >108) and scanning electron microscopy (for investigating microstructural details of crackinitiation and growth) to study fatigue behavior. High cycle fatigue (HCF) life is governed by the number of cycles required for crackinitiation. In the low cycle fatigue (LCF) regime, the high-purity alloy outperforms the materials with higher number densities of carbidesand oxides. In the HCF regime, on the other hand, the high-purity and C-containing alloys show higher fatigue lives than the alloy withoxide particles. There is high experimental scatter in the HCF regime where fatigue cracks preferentially nucleate at particle/void assem-blies (PVAs) which form during processing. Cyclic crack growth follows the Paris law and does not depend on impurity levels. The resultspresented in the present work contribute to a better understanding of structural fatigue of pseudoelastic NiTi shape memory alloys.� 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: NiTi shape memory alloys; Fatigue; Pseudoelasticity; Inclusions; Crack initiation and propagation

1. Introduction and objectives

NiTi shape memory alloys (SMAs) are fascinating mate-rials with unique properties which are exploited in engi-neering [1–5] and medical technology [6–8]. The one-wayeffect (1WE) describes a shape recovery, where a deformedmaterial can return into its original shape upon heating [9–12]. Many different kinds of actuator applications whichhelp to connect, couple, switch, release, adjust, etc. exploitthis type of thermal memory [1,4,13,14]. In the presentstudy we focus on the fatigue life of pseudoelastic NiTi.Pseudoelasticity (PE) represents a mechanical memory. A

1359-6454/$36.00 � 2013 Acta Materialia Inc. Published by Elsevier Ltd. All

http://dx.doi.org/10.1016/j.actamat.2013.02.054

⇑ Corresponding author. Tel.: +49 234 3222040; fax: +49 234 3214235.E-mail address: [email protected] (M. Rahim).

1 Present address: Cortronik GmbH, 18119 Rostock Warnemunde,Germany.

pseudoelastic specimen which is deformed to strains as highas 8% can almost fully recover its shape upon unloading[15]. This strain reversibility largely exceeds recoverablestrains associated with conventional elasticity. PE is relatedto the stress-induced formation of martensite upon loadingand its back transformation to austenite upon unloading[6,9–11]. pseudoelastic NiTi is used in applications wherehigh flexibility is required, like in unbreakable eye glassframes, portable phone antennas, medical implants andinstruments, etc.

The cyclic mechanical behavior of NiTi components hasreceived considerable attention in the last decade, and theimportance of functional and structural fatigue of 1WEand PE applications for the ultimate success of SMA appli-cations has been highlighted [16–18]. The present study isrelated to the fatigue loading of medical stents [19–23].Stents are small tubular implants which stabilize blood ves-

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3668 M. Rahim et al. / Acta Materialia 61 (2013) 3667–3686

sels in the human body. NiTi stents nowadays represent thecommercially most successful SMA application; an exam-ple of a generic NiTi stent is shown in Fig. 1. pseudoelasticNiTi stents are produced from small NiTi tubes by lasercutting and subsequent shape setting and surface treat-ments. Their PE allows for a radial compression which issufficient to push the stent through a guiding catheter tothe target position by means of a guide wire. When emerg-ing at the end of the catheter, a NiTi stent self-expandswithout the need for balloon expansion like in the case ofsteel stents [24]. Electropolished and/or passivated NiTistents exhibit good biocompatibility. This is generallyattributed to the presence of a protective titanium oxidelayer preventing the release of Ni atoms [6,25,26]. Oncepositioned, a pseudoelastic stent can easily withstand thestatic loading associated with the mechanical constraintsimposed by the surrounding vessel. But there is concernabout pulsatile fatigue, which is related to diametricchanges (widening and contraction) of the order of 3–10% associated with the blood pressure, which varies withthe pulse frequency [27,28]. A stent is expected to keep itsmechanical integrity for at least ten years, which, at anaverage pulse of 70 min�1, corresponds to 3.7 � 108 loadcycles. Stents therefore have to withstand high cycle fatigueconditions, with cycle numbers in excess of 108 load cycles[29–31]. A laser-cut stent can be considered as an assemblyof strut elements which form a tubular grid with notcheswhere struts connect. When positioned in a blood vessel(Fig. 2a) the stent is never fully expanded, and thus com-pressive (position 1 in Fig. 2b) and tensile stresses (position2 in Fig. 2b) are present. Cyclic widening and contractionof the blood vessel result in a relatively large loading ampli-tude, which gives rise to pulsatile fatigue [19]. Therefore itis important to base advanced stent design and stent lifeassessments on a reliable high cycle fatigue data base. Likein many other technological fields, however, high cycle fati-gue data are not readily available.

In early NiTi SMA research, material scientists wereinterested in the chemical, physical and crystallographicaspects of the binary NiTi system [3,32,33]. It was realizedthat processing of NiTi alloys is unavoidably associated

Fig. 1. Example of a coronary stent produced by laser cutting.

with an uptake of small amounts of carbon (C) and oxygen(O) [34–38]. Recently the effects of small C and O levels onthe elementary processes which govern the martensitictransformation have been explored [39]. Thus it is wellknown that the presence of C in NiTi leads to the forma-tion of TiC, which results in a local Ti depletion of thematrix surrounding the carbide. This, in turn, results in alower local martensite start temperature close to the car-bide, because the martensite start temperature MS stronglydepends on the Ni concentration of the matrix[34,35,38,39]. But the formation of Ti-rich carbides andoxides not only modifies phase transition temperatures;the presence of small particles can also affect fatigue lives[31,40–53]. Therefore, C and O contents in NiTi alloysfor medical applications were both limited to 0.05 wt.%,and it was suggested to keep the maximum size of inclu-sions below 39 lm [54]. There was little experimental evi-dence to justify these limits, though it is widely knownthat particles can act as crack starters during structuralfatigue. Morgan et al. [55] showed that a NiTi SMA withlower impurity contents (“ELI alloys”, ELI standing forextra-low inclusion content) showed superior low cyclefatigue lives and that fewer inclusions appear to increasethe strain limit below which fatigue lives greater than 107

cycles can be achieved [55].The growing awareness of the importance of structural

fatigue and of the detrimental role of particles in shorten-ing high cyclic lives represent driving forces for the devel-opment of cleaner alloys. However, so far, no hardexperimental evidence exists which proves that loweringcarbon and oxygen levels far below the accepted levels[55–57] is beneficial. This question is interesting from a sci-entific point of view, because it is not clear how particlesaffect fatigue lives in a matrix which can undergo stress-induced martensitic transformations. From a technologicalpoint of view, moving towards a cleaner processing tech-nology generally increases costs. The objective of the pres-ent work is to study structural fatigue in pseudoelasticNiTi, placing special emphasis on the role of C and O levelsin the alloy. Data from fatigue experiments which failedafter up to 6 � 108 cycles are presented and a quantitativemetallographic analysis of fatigue crack initiation andgrowth is performed, paying special attention to the roleof oxides and carbides. We discuss our findings in lightof what is generally known about the role of particles inlow and high cycle fatigue (LCF and HCF) and withrespect to the special structural and functional propertiesof PE SMAs.

2. Materials, experiments and procedures

2.1. Materials processing and chemistry

In the present study we investigate NiTi wires, which areproduced by vacuum arc melting (VAM) followed by dropcasting, homogenization annealing, swaging, rolling, wiredrawing and a final electrochemical surface treatment.

Fig. 2. Schematic illustration of pulsatile fatigue. (a) Pulsatile loading of a stent in a vessel. (b) Arrows 1 and 2, locations with different stress states.

M. Rahim et al. / Acta Materialia 61 (2013) 3667–3686 3669

Details describing the ingot metallurgy processing route arereported elsewhere [17,38,58,59]. Fig. 3 presents differentstages in the processing chain of one of the NiTi materialsinvestigated in the present study. In order to produce high-purity alloys (HP material), high-purity Ni (Ni > 99.995wt.%; Al, 1.6 ppm; Co, 0.1 ppm; Cr, 0.24 ppm; Cu,0.26 ppm; Fe, 11 ppm; Si, 0.22 ppm; Ti, 10 ppm; V,1.3 ppm) and Ti (Ti > 99.995 wt.%; Al, 7.3 ppm; Cr,2.9 ppm; Cu, 1.2 ppm; Fe, 8.5 ppm; N, 15 ppm; C,70 ppm; O, 270 ppm) were used (supplied by ChemPurFeinchemikalien und Forschungsbedarf GmbH, Kar-lsruhe, Germany and Hauner Metallische Werkstoffe, Rot-tenbach, Germany, respectively). Melting of 70 g ingots(Fig. 3:1) was performed under a protective atmosphereof 99.9999 vol.% argon at a pressure of 700 mbar. After10 VAM remelting cycles excellent chemical homogeneityof the ingots was obtained. Drop casting after the finalremelting step yielded cylindrical ingots (Fig. 3:2), whichwere encapsulated in evacuated quartz tubes and subjectedto a homogenization treatment at 1000 �C for 16 h(Fig. 3:3). Subsequently, the material was swaged androlled at 800 �C (Fig. 3:4 and 5). Wires with a diameter

Fig. 3. Ingot metallurgy processing route: (1) 70 g NiTi button-shapedingot, (2) ingot after drop casting, (3) drop-cast ingot after homogeniza-tion, (4) NiTi rod after rotary swaging, (5) hot-rolled rod and (6) NiTi wireafter final annealing and electropolishing.

of 0.85 mm were produced by wire drawing. Finally, anelectrochemical surface treatment was used to remove a50 lm surface layer in order to establish high-quality wiresurfaces (Fig. 3:6). A Ti–O prealloy obtained from S + DSpezialstahl Handelsgesellschaft mbH (Stelle, Germany)was used in the feedstock for melting alloys with higheroxygen levels (O-rich material). An Ni–C prealloy(obtained as outlined in Refs. [37,60]) was used in the feed-stock to obtain materials with higher C levels. The O (usingthe inert gas fusion infrared method [61]) and C levels(using the combustion infrared absorption method [61])in the alloys were analyzed by Revierlabor (Essen, Ger-many). The chemical compositions of the materials investi-gated in the present study are given in Table 1. For theobjectives of the present work it was important to producematerials which vary in the number and volume fraction ofcarbides and oxides, but which have the same Ni concen-tration in the matrix.

2.2. Microstructure prior to fatigue loading

Materials processing establishes an ultrafine-grainedmicrostructure in all three materials. The microstructureof the carbon-rich material can be seen in the transmissionelectron microscopy (TEM) micrograph of Fig. 4a. Such amicrostructure shows a superior functional behavior[62,63]. All details describing the TEM procedure are pub-lished elsewhere [64,65]. The microstructures of the othertwo materials look very similar. A line intersection methodwas used to determine the size distribution of the ultrafinegrains (UFGs) in the three materials, considering a mini-mum of 120 grains in each case. The sizes of the UFGs fol-low very similar log-normal distributions, as can be seen inthe probability net [66] of Fig. 4b. In Fig. 5 we presentback-scatter scanning electron microscopy (SEM) micro-graphs from the three materials. SEM investigations wereperformed using a FEI Quanta FEG 650 scanning electronmicroscope. The C- and O-rich materials shown in Fig. 5aand b contain significantly more particles than the high-purity material in Fig. 5c. The particles shown in Fig. 5a(oxygen-rich material) are mainly oxides, while the parti-cles shown in Fig. 5b (carbon-rich material) represent

Fig. 4. UFG microstructure: (a) TEM bright-field image of the C-rich material, (b) probability net showing three very similar log-normal size distributionsof ultrafine grains in the three material states investigated.

Table 1Targeted and actual chemical composition of the three pseudoelastic materials investigated in the present study.

Targeted compositions Compositions of experimental alloys

cO/wt.% cC/wt.% xNi/at.% cO/wt.% cC/wt.%

HP (high purity) As low as possible As low as possible 51.20 0.004 (±0.001) <0.002O-rich 0.05 As low as possible 51.00 0.048 (±0.003) <0.002C-rich As low as possible 0.05 51.08 0.004 (±0.001) 0.05 (±0.003)


mainly carbides [38]. It has been previously discussed thatwhile particles of the type shown in Fig. 5a are commonlyviewed as oxides, their true physical nature is closer to aTi2NiO1/2 intermetallic with oxygen in solid solution [38].For the objectives of the present paper this is not importantand we simply address these particles as oxides. The parti-cles found in the high-purity material represent mostly thistype of oxide. Fig. 6 shows back-scatter SEM micrographsof particles taken at a higher magnification. In our materi-als carbides (Fig. 6a) are typically smaller than oxides(Fig. 6b). And both types of particles are often associatedwith voids, as can be seen in Fig. 6c (carbide and elongatedvoid) and Fig. 6d (oxide and elongated void). The voidshave an elongated shape and are aligned in the wire draw-ing directions, which are indicated by black double arrows.The defects shown in Fig. 6c and d are absent in the as-castmaterial state and originate from processing [38,39]. Amicromechanical view of how such voids form during pro-cessing has been published [67]. We refer to the types ofdefects shown in Fig. 6c and d as particle/void assemblies(PVAs). It appears that the PVA shown in Fig. 6d origi-nated during wire drawing, when a larger oxide inclusionbroke into smaller pieces.

Particle densities (number of particles per area) and par-ticle sizes (particle areas on SEM micrographs) were mea-sured. Particle shapes were obtained from the ratiobetween the longest and the smallest particle dimension

detected between two parallel tangents (in stereologicalstudies often referred to as Feret parameters: fmax is themaximum particle size and fmin is the minimum particlesize) from elongated sampling fields of 68940 lm2. Quanti-tative metallographic results obtained in the present studyare presented in Table 2 and Fig. 7. Table 2 shows thatthe number of particles in the sampling fields is almostten times higher in the O- and C-rich materials than inthe high-purity material. The particles in the O-rich mate-rial are oxides, and in the C-rich material carbides. Thehigh-purity material contains both oxides and carbides,but the relative number of oxides is more than 20 timeshigher than the number of carbides. The number of PVAsin the sampling fields is significantly higher in the O-richmaterial (158 PVAs in sampling field) than in the two othermaterials (29 in the carbon-rich and 14 in the high-puritymaterial). 7% of the oxides in the oxygen-rich materialare associated with voids and thus represent PVAs. Only1% of the carbides in the C-rich materials are associatedwith PVAs. In the high-purity material, 6% of the inclu-sions can be attributed to PVAs. Fig. 7 shows size distribu-tions of projected particle areas and of the form factors ofthe particles in the sampling fields of all three materials.Fig. 7a shows that the particle sizes within one materialare distributed quantities (small particles can be ten timessmaller than larger particles). Fig. 7b shows that all parti-cles have slightly elongated shapes.

Fig. 5. SEM back-scatter micrographs of particles: (a) O-rich material; (b)C-rich material; (c) high-purity alloy. Arrows indicate the wire drawingdirection.


2.3. Differential scanning calorimetry (DSC) and

mechanical behavior

DSC was used to characterize transformation behavior.DSC charts were recorded between ±150 �C. All detailsdescribing our DSC procedure are published elsewhere[65,68]. Fig. 8a shows how different levels of C and O affect

the martensite start temperature MS. Adding C and O leadsto the formation of Ti-rich carbides and oxides. This resultsin a decrease of the Ti concentration and in an equivalentincrease of the Ni concentration next to the carbides. Asa consequence, MS temperatures decrease, which in turnexplains the behavior shown in Fig. 8a (for a detailedexplanation see Ref. [38]). In the present study we haveproduced materials which vary in the number and volumefractions of carbides and oxides, but which neverthelesshave the same matrix Ni concentrations. Thus they showthe same values for the austenite finish temperature AF

close to 30 �C. Consequently, equal superimposed strainsresult in similar plateau stresses required for the forwardtransformation from austenite to martensite during tensileloading [69,70]. Similar Ni concentrations in the matrixwere achieved following the procedure outlined in Ref.[38], which allows the calculation of the decrease of Ti(and the related increase of Ni) in the alloy as Ti-rich oxi-des and carbides form. Table 1 shows the chemical compo-sitions of the materials, which were subjected to fatiguetesting. On the left side of Table 1 we show the target com-positions. The right side of Table 1 shows the actual alloycompositions. Fig. 8b shows that the three materials (afterdrop casting and homogenization, Fig. 3:3) show coincid-ing DSC charts. Fig. 8c shows how the DSC charts ofour materials are affected by swaging, rolling and wiredrawing. The evolution of DSC chart features (fromFig. 8b and c) reflects the evolution of microstructure dur-ing thermomechanical processing [58,59]. The three materi-als show the same values for the austenite finishtemperature AF close to 30 �C (black arrow in Fig. 8c).

The stress–strain curves shown in Fig. 9 document thatthis also holds for the martensitic forward and reversetransformations during loading and unloading at 37 �C(above AF, Fig. 8c). The stress–strain curves in Fig. 9 alsoshow that the three materials show excellent shape recoveryduring PE cycling. All details describing pseudoelasticloading/unloading are described elsewhere [71,72]. So farwe have established that the three materials investigatedin the present study show very similar functional (phasetransition temperatures, Fig. 8) and structural (pseudoelas-tic plateau stresses, Fig. 9) properties. In the present studythe stiffness of oxides in NiTi was assessed through nanoin-dentation measurements using the Oliver–Pharr method[73]. For statistical accuracy, 20 indentation tests were per-formed and the Young’s modulus was determined as151.1 ± 3.6 MPa, which is one third of the elastic modulusof TiC [74].

2.4. Bending rotation fatigue (BRF) testing and SEM

In the present study we use bending rotation fatigue tostudy fatigue failure of NiTi wires of 0.75 mm diameter.All experimental and mechanical aspects of BRF testingare described elsewhere [16,75–80]. It is important to high-light that BRF testing represents a loading condition whichis displacement controlled. A wire is bent into a half circle

Fig. 6. SEM back-scatter micrographs of particles/inclusions and pre-existing voids. (a) carbide in C-rich material. (b) oxide in O-rich material. (c) PVA(carbide with crack-like void highlighted by white arrow) in C-rich material. (d) PVA (three oxides with crack-like void highlighted by white arrows) in O-rich material. Black arrows indicate the wire drawing direction.

Fig. 7. Probability nets with results for particle sizes and particle shapes: (a) distribution of projected particle areas, (b) distribution of particle shapefactors.


with radius R. The maximum tensile strain in the surface ofthe bent wire, eS, is related to its diameter d and to its bend-ing radius R:

es ¼ d=2R ð1ÞDuring a full rotation of the wire, each surface element

passes through tensile and compressive stages [76,77]. Thebasic elements of an appropriate test rig have beendescribed previously [16,75–78,80]. The objective of thepresent study was to provide high cycle fatigue data. There-fore it was necessary to design two new test rigs, each ofwhich integrates five single wire test instruments of the typewhich we have described earlier [16,75–78,80]. Details onthese two multispecimen BRF systems are described else-

where [81]. To avoid self-heating [75,82], the rotating wirespecimens were tested in water kept at 37 �C. At a rota-tional speed of 20 Hz it takes 57.9 days to accumulate 108

fatigue cycles, and several specimens reached an evenhigher number of BRF cycles. One BRF fracture datapoint is associated with a bending radius R which yieldsthe imposed surface strain eS. This imposed strain resultsin a number of cycles to failure NF.

2.5. Fractography

After fatigue failure, BRF specimens were thoroughlyexamined by SEM. Emphasis was placed on both fractureand outer wire surfaces. An effort was made to identify

Table 2Results of an extended quantitative metallographic evaluation character-izing the parameters of the particle populations as determined fromsampling fields with a width of 125 lm and a length of close to 551 lm (sixSEM micrographs taken at a magnification of 1000 � and arranged suchthat a perfect overlap was obtained).

O-rich C-rich High purity

Sampling field area/lm2 68940 68940 68940Number of inclusions 2410 2005 246Number of inclusions per mm2 34958 29083 3568Ratio Ti2NiO1/2:TiC �100:0 �0:100 �96:4Mean area of inclusions/lm2 0.7 0.4 0.5Number of PVAs 158 29 14Number of PVAs per mm2 2292 421 203Fraction of PVAs 7% 1% 6%

Fig. 8. Results from DSC measurements: (a) dependence of the Ms

temperature on C and O levels (when changing Ni/Ti ratios are notanticipated), (b) DSC charts of the three materials after a homogenization(1000 �C, 16 h), (c) DSC charts of the three materials after processing.


crack initiation sites and to study fatigue striations. Fig. 10shows examples for different crack initiation sites. Thedirections of the superimposed total strains (parallel tothe drawing direction of the wire) are indicated by blackdouble arrows in Fig. 10a, e and f. Fig. 10b–d shows frac-ture surfaces which are perpendicular to the direction ofthe superimposed total strain. Fig. 10a shows a large crackresulting from wire drawing (arrow 1), which was not elim-inated by the electrochemical surface treatment. Suchdefects are rare. Arrow 2 in Fig. 10a shows a small PVA,right next to this large crack. It is clear that a detrimentaleffect of this small PVA (at arrow 2) cannot manifest itselfclose to the much larger defect (at arrow 1). Fig. 10b showsa BRF fracture surface at two magnifications. Crack initi-ation occurred at a die mark on the specimen surface. Inthe present study we differentiate between BRF failuresassociated with processing defects and with inclusions.Fig. 10c and d shows cases where BRF fracture initiatedat oxides and carbides, respectively. Examples for BRFsurface cracks are presented in Fig. 10e and f. Fig. 10eshows a typical microstructural feature which consists ofa particle embedded into a crack-like horizontal void(PVA). A close inspection of Fig. 10e reveals the presenceof two tiny BRF fatigue cracks emanating from both sidesof the particle at or close to the particle/void interfaces.Fig. 10f provides evidence for the linking up of microcracksduring fatigue loading.

Fig. 11 compiles SEM micrographs which illustrate thetype of information which can be obtained by fractography[83]. Fig. 11a gives an overview of an entire BRF fracturesurface. The crack initiation site is highlighted by a blackarrow pointing down. The black and gray areas in the sche-matic insert at the lower left indicate the parts of the rup-ture surface which were associated with crack growth(black) and final rupture (gray), respectively. SEM micro-graphs taken at higher magnifications are shown in theright part of Fig. 11a. In the SEM micrograph taken atlocation 1 we see fine fatigue striations. A mean fatigue stri-ation width (here: �w ¼ 0:17 lm) can be determined bydividing the length of a reference line perpendicular tothe fatigue striations (here: Da = 1.71 lm) by the numberof fatigue striations (here: n = 10). As can be seen from

the SEM micrograph taken at position 2, the striationwidth increases, because with increasing crack length, thecyclic stress intensity factor range DK increases. The higher

Fig. 9. Stress–strain curves of the three materials.


magnification SEM micrograph taken at position 3 illus-trates the presence of characteristic dimples [83] and thefractal nature [84,85] of the residual fracture surface. TheSEM micrograph shown in Fig. 11b was taken at a locationwhere the imposed BRF strain eS was reduced from 1.5%to 0.8%. 100 BRF cycles were then imposed at this lowerstrain amplitude. These 100 mechanical cycles lead to pre-cisely 100 fatigue striations on the rupture surface, as indi-cated by the reference line where the number of fatiguestriations is indicated (difficult to recognize in the low mag-nification micrograph of Fig. 11b). This proves that thefinal stages of BRF cycling are governed by a cycle-by-cyclecrack growth which has been described in the fatigue liter-ature [86–92]. This allows us to use SEM fractography toassess crack propagation.

2.6. Evaluation of crack propagation

In the present study an attempt was made to study theinfluence of cycle number N, crack length a, imposed max-imum surface strain eS and alloy purity (high purity, C-richand O-rich) on cyclic crack growth. It is straightforward toobtain da/dN = f(NP) curves (da/dN represents the crackextension per cycle, NP corresponds to the number of cyclesassociated with crack propagation) from w = f(a) raw data(w is the fatigue striation width as shown in Fig. 11a and a

is the crack length).In a first step the experimental data were plotted as fati-

gue striation width w vs. crack length a. A good fit of thedata was obtained using a polynomial of third degree:

wðaÞ ¼ c1 � a3 þ c2 � a2 þ c3 � aþ c4 ð2ÞOne fatigue striation spacing w(a) directly represents the

associated crack extension per cycle; we therefore can write

da=dN ¼ wðaÞ ð3ÞWe rearrange and obtain

dN ¼ da=wðaÞ ð4Þ

We use NI and NF for the numbers of cycles to crack ini-tiation and to failure, respectively. Eq. (4) can then beintegrated:Z NF

N¼NI

dN ¼Z a�

a¼0

dawðaÞ ð5Þ

This finally yields the number of cycles NP associatedwith crack propagation:

NF � NI ¼ NP ð6ÞThis type of data assessment allows us to obtain da/

dN = f(NP) curves from w = f(a) raw data.

3. Fatigue lives and mechanisms of crack initiation

In Fig. 12 we present all mechanical results obtainedfrom BRF testing. Fig. 12a and b shows imposed surfacestrains (on the y-axis) and associated logarithmic cyclenumbers (on the x-axis). In most cases, the number Ntot

represents the numbers of cycles to failure (NF). In only afew cases (symbols with small arrows pointing to the right)BRF tests did not yet fail. Fig. 12a and b shows the typicalshape of pseudoelastic NiTi strain controlled rupturecurves, where steep and flat eS(logN) lines characterizethe LCF and the HCF regimes. Fig. 12a compiles the fati-gue data of all experiments which were performed. Afterfatigue fracture, all specimens were inspected in the SEM.A special effort was made to identify crack initiation sites.Table 3 summarizes the results. It indicates the number oftests which were performed for the three materials andhighlights how many were performed at imposed surfacestrains above 1.2% (the strain limit above which stress-induced martensite forms in uniaxial tension, see Fig. 9).In addition, Table 3 differentiates between the number ofexperiments where crack initiation occurred at inclusions,at drawing defects, at die marks and the number of exper-iments where the crack initiation site could not be identified(“other locations”). Table 3 shows that a significant num-ber of experiments showed fatigue crack initiation at draw-ing defects and die marks. In only a few cases, the crackinitiation sites could not be identified. Fig. 12b representsa refined compilation of the fatigue fracture data presentedin Fig. 12a. In Fig. 12b, all fracture data were taken outwhere either crack initiation occurred at drawing defectsand die marks or where crack initiation sites could not beidentified. Comparing Fig. 12a and b one can see that mostof the early failures represent cases where cracks initiatedat drawing defects and die marks. The results of 30 highstrain experiments (eS = 1.88%, rectangle in Fig. 12b) arepresented at a higher resolution in Fig. 12c. The x-axis ofFig. 12c is subdivided into three regimes, each of whichshows results from ten BRF fracture tests. The arbitrarynumbers from 1 to 30 represent reference numbers of wirespecimens tested in the three material groups (O-rich mate-rial: wires 1–10; C-rich material: wires 11–20; high-puritymaterial: wires 21–30). For each regime a horizontal lineindicates the average number of cycles to failure. Fig. 12c

Fig. 10. SEM assessment of crack initiation sites. The double-tip arrows in (a, e, f) and the little circles with central point (b, c, d) indicate the longitudinalwire direction. Crack initiation at: (a) a large crack-like surface defect (view onto wire surface), (b) a die mark (rupture surface view), (c) a large oxide(rupture surface view), (d) a small carbide (rupture surface view), (e) carbide associated with a crack-like void (view onto wire surface) and (f) oxidesassociated with crack-like voids (view onto wire surface).


clearly shows that on average, under high strain conditions,the O-rich material shows the shortest fatigue failure life,the C-rich material shows an intermediate performance

and the high-purity material exhibits the highest resistanceagainst fatigue failure. Fig. 12c also shows that the O-richspecimens fail within a narrow scatter band of numbers of

Fig. 11. SEM fractographs. Little circle with central point indicates longitudinal wire direction. (a) Fracture surface with regions marked by cyclic crackgrowth and final fracture. Locations marked with 1, 2 and 3 are shown at higher magnifications. (b) Fatigue striations on fracture surface.


cycles to failure NF (1981 < NF < 2610), while the high-pur-ity material with the longest fatigue rupture lives shows thelargest scatter (2705 < NF < 7865).

An attempt was made to determine the number of caseswhere small fatigue cracks, as shown in Fig. 10e and f, canbe detected. Fig. 10e shows how fatigue cracks initiate at aPVA in the C-rich material. Fig. 10f shows a scenariowhere two cracks emanating from two PVAs are just aboutto interlink. For this purpose high strain experiments(eS = 1.88%) with a total number of 2400 cycles were per-formed for all three materials. Large sampling fields withdimensions between 145000 and 370000 lm2 were evalu-ated. Fig. 13 shows a small part of the sampling field eval-uated for the material with an elevated oxygen content.Sites at which small cracks emanate from inclusions arehighlighted. At locations of type 1, cracks emanate fromfully embedded particles. At locations of type 2, cracksform at PVAs. In the upper right part of Fig. 13, micro-cracks from several PVAs have started to interlink (high-lighted by white arrow).

The results of a quantitative SEM evaluation are pre-sented in Table 4. It shows the sizes of the sampling fieldsand the total number of inclusions. Table 4 lists the totalnumber of fatigue cracks observed in the sampling fieldsand the number of fatigue cracks per mm2. It shows whichfractions of all oxides and carbides (irrespective of whetheror not they are associated with voids) act as initiation sitesfor microcracks. And it reports the average crack lengthsobserved in the three materials. Table 4 clearly shows thatthe O- and C-rich materials contain a higher number ofpotential fatigue crack initiation sites than the high-puritymaterial. Table 4 also shows that the O-rich inclusions aremore efficient in promoting BRF fatigue crack initiationthan C-rich inclusions. We found almost 300 small fatiguecracks per mm2 in the O-rich material, while there wereonly 89 and 35 per mm2 in the C-rich and high-purity mate-rials, respectively.

Table 4 shows that when all inclusions are considered,1% act as fatigue crack initiation sites in the O-rich andthe high-purity material (which contains significantly more

Fig. 12. BRF fatigue rupture data. (a) All data. (b) rupture data where fatigue failure initiated at carbides, oxides and PVAs (data of ongoing experimentsindicated by arrows pointing to the right). (c) fracture data from 30 high strain experiments.


oxides than carbides, Table 2). In contrast, only 0.3% ofcarbides represent crack initiation sites. This seems to sug-gest that oxides are more efficient crack nucleation sitesthan carbides. Table 4 also shows that the average micro-crack length detected at oxides is almost an order of mag-nitude larger than in the case of carbides. In Fig. 6c and dwe show SEM micrographs of inclusions which are part ofPVAs. An attempt was made to differentiate between crackinitiation from PVAs (as documented in the SEM micro-graphs of Fig. 10e and f) and crack initiation from inclu-sions which are fully embedded in the matrix. The resultsare presented in Fig. 14a and Table 5, where it can be seenthat in all three materials, fatigue cracks preferably initiateat PVAs. Table 5 lists the total numbers of fully embeddedinclusions and PVAs observed in the sampling fields in thedifferent wires. Table 5 shows the numbers and fractions offatigue cracks starting from these types of defects. Table 5shows that less than 0.1% of all cracks initiated from fullyembedded inclusions. However, as soon as PVAs are con-sidered the situation changes. About 12% of all PVAs in

the O-rich, 18% of the PVAs in the C-rich wire, and 16%of all PVAs in the high-purity material act as crack initia-tion sites. Fig. 14b shows that there is no clear correlationbetween the size of a microcrack close to a particle and themaximum size fmax of this particle. In Fig. 14c, the numberof fatigue cracks is plotted as a function of the number ofPVAs per mm2. It can be seen that the number of fatiguecracks per surface area decreases with decreasing numberof PVAs. We note that the data can be rationalized by astraight line through zero, which suggests that in theabsence of PVAs no fatigue crack would be observed.

In our BRF experiments, the formation of fatigue cracksoccurs at PVAs, as shown in Fig. 10e and f. Once a macro-scopic crack has formed, one can study its growth. In thepresent study, crack growth was evaluated performing anextensive post-mortem SEM assessment of fracture sur-faces with a focus on fatigue striations like those shownin Fig. 11a. Fig. 15a shows a plot of the fatigue striationwidth w as a function of crack length a. During displace-ment controlled BRF testing, a growing crack experiences

Table 3Total numbers of tests performed on wire specimens from the three material states, considering high (>1.2%) and low strain (<1.2%) BRF loading.

Alloys e (%) Total number of experiments Crack initiation at

Inclusions Drawing defects Die marks Other locations

High purity >1.2 23 18 4 0 0<1.2 22 6 10 1 6

O-rich >1.2 23 19 2 2 0<1.2 10 7 1 2 0

C-rich >1.2 21 14 2 2 2<1.2 14 4 4 2 4

The number of experiments with cracks initiating at inclusions (carbides and oxides), at drawing defects, at die marks and at other locations (notidentified) are given.

Fig. 13. Part of the sampling field of the O-rich material (eS = 1.88%, NF = 2400). Crack nucleate at fully embedded particle and at PVAs. White arrowhighlights microcracks from several PVAs that have interlinked.

Table 4Compilation of quantitative SEM results from montages of SEMmicrographs.


Sampling field area/lm2 145000 145000 370000Number of inclusions 5069 4218 1320Number of fatigue cracks 41 13 13Number of fatigue cracks per mm2 283 89 35Inclusions with fatigue cracks 0.81% 0.31% 0.98%Mean length of fatigue cracks/lm 6.74 0.77 3.94

SEM micrographs were taken at a magnification of �1000. The montagesconsisted of 12 (O-rich and C-rich material) and 32 (high-purity material)individual micrographs.


an increasing driving force. This explains the increase offatigue striation width w with increasing crack length a,Fig. 15a. Fig. 15a shows the increase of fatigue striationwidth w with crack length a for two experiments performed

on oxygen-rich material, where the maximum imposed sur-face strain was 0.94%. In one experiment, failure occurredafter 6.3 � 104 cycles, while in the other experiment a muchhigher number of cycles to failure of 48.5 � 106 cycles wasobserved. In spite of these differences, Fig. 15a clearlyshows that both samples exhibited the same crack growthbehavior. Final rupture occurs when the fatigue cracklength has reached 300 lm. From experimental data likethose shown in Fig. 15a, one can calculate how the cracklength a increases per cycle N as outlined above. InFig. 15b we plot the macroscopic fatigue crack growth rateda/dN data as a function of the crack propagation cyclenumber NP. Fig. 15b shows five data sets, where the max-imum imposed BRF surface strain increases from 0.94% to1.88%. Fig. 15b clearly shows that higher maximumimposed BRF surface strains result in faster crack propaga-tion as well as lower maximum crack lengths. Fig. 15cshows the influence of alloy purity on crack growth. It

Fig. 14. Graphic presentation of parameters characterizing fatigue crackinitiation. (a) Number of fatigue microcracks starting from PVAs andfrom fully embedded particles in sampling fields of 145,000 lm2 in size. (b)No correlation of microcrack length with the maximum size fmax ofinclusions. (c) Correlation of PVAs with the number fatigue cracks on wiresurface.


shows data sets with two imposed surface strains eS of 0.94and 1.88%. Fig. 15c clearly shows that crack growth does

not depend on whether our alloy contains inclusions ornot and it does not play a role whether carbides or oxidesare present.

Fatigue crack growth is usually described by the Parislaw:

da=dN ¼ C � DKm ð7Þ

where DK represents the stress intensity factor range, and C

and m are constants. The constant m typically has values inthe range between 2 and 4 [31]. The stress intensity factorrange DK is proportional to Dr�pa, where Dr is the stressrange. Assuming that Dr remains constant, Eq. (7) can berewritten as

da=dN �ffiffiffiap m ð8Þ

Fig. 15d presents a log–log plot of crack extension percycle da/dN vs. the square root of crack length a. Two datasets for the O-rich material are presented, one from theLCF (high imposed surface strains) and another from theHCF regime (low imposed surface strains). The stressesin front of the crack tips should be similar in both cases,because they are limited by the stress which characterizesthe loading plateau (Fig. 9). However, for a given cracklength, higher fatigue crack growth rates are observed forLCF than for HCF loading. The Paris law constant C

depends on the amount of superimposed strain. Fatiguecrack extension rates are not well described by the Parislaw for crack lengths smaller than 36 lm.

We finally compare the numbers of cycles required forfatigue crack initiation NI and the numbers of cycles spentin fatigue crack propagation NP (Fig. 16). Fig. 16 compilesrepresentative data from fractured specimens from thewhole imposed surface strain amplitude range. Verticaldashed lines at 1.2% in Fig. 16a–c mark the transitionsfrom LCF to HCF. Fig. 16a shows that for imposed max-imum BRF strains eS smaller than 1.2% (HCF regime),high numbers of fatigue cycles are required for crack initi-ation. But the HCF results also show large scatter and twovery early initiation events are observed for the O-richmaterial. At imposed maximum BRF strains larger than1.2%, the initiation of a crack requires fewer cycles. In thisloading range the number of cycles required for fatiguecrack initiation fall in a narrow scatter band. The dottedtrend line shown in Fig. 16a represents a best fit to all data.In Fig. 16b we present the numbers of cycles NP of macro-scopic fatigue crack propagation prior to fracture. NP

depends on the imposed surface strain and all three mate-rials (high purity, O-rich and C-rich) yield very similarresults. The number of cycles spent for macroscopic fatiguecrack propagation shows an increase below imposed sur-face strains of 1.2%. But it never exceeds 3000 cycles.Therefore fatigue crack propagation does not play a signif-icant role in HCF fatigue rupture lives. In the technologicalrelevant HCF range, fatigue lives of pseudoelastic NiTishape memory alloys are crack initiation controlled. Theplot presented in Fig. 16c highlights these findings.

Table 5Quantitative evaluation of fatigue crack initiation from fully embedded inclusions and PVAs.


Number of fully embedded inclusions 4737 4157 1245Number of PVAs 332 61 75Number of fatigue cracks at fully embedded inclusions 1 2 1Number of fatigue cracks at PVAs 40 11 12Fraction of fully embedded inclusions with fatigue cracks 0.02% 0.05% 0.08%Fraction of PVAs with fatigue cracks 12% 18% 16%

The results were obtained from the same experiments and the same sampling fields as in case of Table 4.

Fig. 15. Characterization of crack growth behavior during BRF testing. (a) Evolution of striation widths (w) as a function of crack length. (b) Effect ofstrain amplitude. (c) Effect of alloy purity. (d) Paris law plot (for cracks longer than 36 lm).


Fig. 16c shows the ratio of the numbers of cycles requiredfor crack initiation NI and the number of cycles to failureNF plotted as a function of eS. NI/NF ratios close to 1 indi-cate that the total fatigue life is dominated by the numberof cycles required for crack initiation. As can be seen inFig. 16c, this is the case for imposed strains <1.2%, i.e.for all experiments from the HCF regime. Only when fati-gue failure occurs after less than 104 cycles, half of the fati-

gue life is required to nucleate a crack. These findings are inline with the view that the period of crack initiation dom-inates most of the cyclic life in the HCF and UHCF (ultra-high-cycle fatigue) regimes [93]. To highlight theimportance of surface quality, we have included one datapoint for the high-purity material with a surface defect(in the lower right corner of Fig. 16c), where the crackstarts to propagate at the beginning of cyclic loading.

Fig. 16. Parameters which characterize the relative importance of crackinitiation NI and crack propagation NP in the total cyclic fatigue life NF.All results show data from experiments where cracks nucleated atinclusions or PVAs. (a) NI as a function of imposed surface strain eS,(b) NP as a function of function of imposed surface strain eS, (c) ratio of NI

to NF crack propagation as a function of imposed surface strain eS. Thearrow highlights a data point which falls short due to poor surface quality.


The corresponding fracture result falls short when com-pared to results from specimens with high surface quality.

4. Discussion

4.1. Fatigue testing

The objective of the present study was to gain insightinto the role of carbides and oxides in structural fatigueof pseudoelastic NiTi SMAs. For this purpose we havecompared alloys with different C and O levels, but whichshow the same phase transition temperatures and the samecritical stresses for the formation of stress-induced mar-tensite (Figs. 8 and 9). As can be seen in Fig. 9, the criticalstress to induce martensite in our high-purity alloy is a littlehigher than for the two other alloys. This implies that thedisplacement controlled experiments performed for thehigh-purity alloy were associated with slightly higher stres-ses in each cycle. Therefore, when a high-purity alloy spec-imen fails after the same cycle number as a specimen fromone of the two other alloys, its fatigue resistance is actuallya little higher. It is equally important to perform fatigueexperiments at a constant temperature because otherwiseself-heating during pseudoelastic cycling results in an unde-fined increase of the plateau stress as rationalized by theClausius–Clapeyron equation [94]. Self-heating can resultin frequency dependencies which are not observed whenthe temperature is kept constant. A good surface qualityis of utmost importance. When surface defects like diemarks or other defects associated with metal forming arepresent, they act as crack initiation sites where microcrackscan nucleate early (see Table 3 and Fig. 10a and b). Whensurface defects are not removed, higher alloy purities donot result in longer fatigue lives. Our earlier bending rota-tion fatigue results on pseudoelastic NiTi wires [16,80]show significantly shorter fatigue lives than observed inthe present study. This is related to the inferior surfacequality of the material used in these previous studies (seeFig. 9 in Ref. [80] and Fig. 4a in Ref. [16]).

4.2. Low cycle fatigue vs. high cycle fatigue

When discussing our results it must be borne in mind thatmechanical loading can result in the formation of stress-induced martensite. In the LCF regime (eS > 1.2%) the wiresurface transforms into martensite. Wagner et al. haveshown [76] that during BRF testing in the LCF regime, thestress-induced formation of martensite does not occur in alocalized manner like during uniaxial tensile loading [95].In HCF (eS < 1.2%), the stress-induced formation of mar-tensite requires local stress concentrations at particles orPVAs. The stress-induced formation of martensite limitsstresses to the levels of the plateau stresses observed inFig. 9. The stress-induced formation of martensite is revers-ible. Austenite transforms to martensite on loading, andstress-induced martensite transforms back to austenite onunloading. Under the present test conditions, this reversiblestress-induced forward and reverse transformation appearsto provide some damage tolerance, which accounts for thegood fatigue performance of pseudoelastic NiTi as


compared to other engineering materials tested under similarconditions in a similar strain range [30,31]. In addition, it hasbeen reported that the cyclic martensitic transformation infront of a crack tip improves crack growth resistance duringcrack advance [96,97]. In the LCF regime (eS > 1.2%,NF < 104), the behavior of the three materials can be clearlydifferentiated (Fig. 12c). The O-rich material fails after theshortest number of cycles, followed by the C-rich material.The high-purity material shows the highest fatigue fracturelives. Note that there is very little scatter in fatigue rupturefor O-rich materials. The scatter increases for C-rich mate-rial, and is largest for the high-purity alloy. As one wouldexpect, the scatter in fatigue rupture lives increases as thenumber of critical defects (PVAs) per volume decreases[98] (Fig. 12c). In the LCF range, fatigue crack growth ratesdo not increase with increasing imposed strain amplitude. Ascan be seen in Fig. 15b, imposed surface strains of 1.5% and1.88% yield very similar macroscopic crack propagationdata. In both cases, cracks are driven by the same maximumload, which is governed by the upper plateau stress of thestress–strain curve of Fig. 9.

In the HCF regime, the O-rich material shows the lowestrupture lives (Fig. 12b). There is no significant differencebetween the HCF rupture lives of the high-purity materialand the C-rich material (Fig. 12b). The HCF regime is char-acterized by a high scatter in fatigue fracture lives for thehigh-purity material (Fig. 12a). The scatter in fatigue rupturelives increases, as the number fraction of PVAs per volumedecreases. As can be clearly seen from a comparison betweenFig. 16a and b, this scatter is governed by the elementary pro-cesses which govern fatigue crack initiation. It seems reason-able to assume that this is related to the intrinsic stochasticnature of microstructural damage accumulation which pre-cedes the formation of a macrocrack. This stochastic natureof the nucleation of a macroscopic crack has been discussedfor the formation of cracks as a result of a micromechanicalinteraction of damaged grain boundaries during creep of aferritic steel [99] and for the formation of critical cracks ina population of statistically distributed microcracks bymicrocrack coalescence during multiaxial fatigue loadingof an austenitic steel [100]. In our case, this high scatter inthe HCF regime is probably not only related to the spatialdistribution of PVAs and their presence/absence in surfaceregions. Other distributed local properties, the detailedgeometry of PVAs, the mechanical properties of the particlesand the crystallographic and chemical nature of particle/matrix interfaces can also contribute to the observed scatter.It should also be mentioned that while our number of cyclesfor HCF rupture approach the ultrahigh cycle fatigue(UHCF) regime, we do not observe damage which initiatesbelow the surface, as was reported for ultrahigh-strengthsteels (fish-eye fractures, e.g. Refs. [52,53]).

4.3. Crack initiation from particle/void-assemblies

There is a good understanding of the role of inclusionson fatigue lives (e.g. Refs. [31,40–50,52,53]). In the intro-

duction to their numerical research paper on fatigue cracknucleation at inclusions and voids, Gall et al. [41] providean excellent short review on elementary mechanisms offatigue crack initiation. They point out that, in many cases,the time spent nucleating a crack accounts for most of thefatigue life. This is fully in line with our results obtained forthe HCF range, where the comparatively small period ofcrack propagation can almost be ignored (Fig. 16c). Itwas also pointed out [41] that elementary crack initiationprocesses at extrusions and grain boundaries are notalways helpful to rationalize the behavior of engineeringmaterials with inclusions. There are several comprehensivereviews which emphasize the importance of fatigue crackinitiation at particles [31,45–48], and one observation iscentral to nearly all materials studied [41,47,48]: if a fatiguecrack nucleates at a second phase inclusion, the crackalmost always originates at a partially debonded particle.In Fig. 3 of their paper, Gall et al. [41] consider a numberof different configurations like fully embedded particles,cracked particles, voids and partially debonded particles.In their finite element study they show that local stressesare highest at partially debonded particles. These numericalresults are in good qualitative agreement with our findingthat PVAs like those shown in Fig. 6c and d are efficientcrack initiation sites. Schaffer et al. [51] also providedmicrostructural evidence for crack initiation at PVAs inNiTi. Their Fig. 8 shows two SEM images of both fracturesurfaces of a failed sample: one shows the inclusion and theother shows the associated void. This result is in goodagreement with our conclusion that cracks emanate fromPVAs. Fig. 14c clearly shows that the number of fatiguecracks per surface area decreases with decreasing numberof PVAs. We note that the data can be rationalized by astraight line through zero, which suggests that in theabsence of PVAs no fatigue cracks would form and thatit is well worth the effort to keep inclusion levels low. Itshould be highlighted that the PVAs observed in the pres-ent study do not simply form when a fully embedded par-ticle debonds. PVAs originate from forming processeswhich may well trigger fragmentation of particles, as sug-gested by the SEM micrograph in Fig. 6d.

4.4. Oxides, carbides and PVAs

The results obtained in the present study have shownthat the alloy with higher oxygen contents shows the short-est fatigue lives in both the LCF and HCF regimes(Fig. 12b and c). This seems to suggest that oxides are moreeffective in promoting fatigue crack initiation than car-bides. Oxides are more often associated with PVAs, andthis type of defect is more detrimental than an isolated par-ticle (Fig. 14c). As can be seen from the quantitative data inTable 2, 7% of the particles in the O-rich material representPVAs, while only 1% of the particles in the C-rich materialare associated with voids. The high-purity material con-tains considerably fewer oxides than the oxygen-rich mate-rial. But the number of oxides is still high enough to


provide a sufficient number of locations for fatigue crackinitiation. It should be kept in mind that NiTi SMAs haveno solubility for O and C in the solid state [35,101]. C andO affect fatigue behavior through the formation of oxidesand carbides (Fig. 10c–f). Before concluding that oxide-related PVAs are generally more detrimental than PVAswith carbides (more fatigue cracks in O-rich wires(Fig. 14a, Table 4) and larger oxide than carbide sizes(Table 2, Fig. 7a)) one must take a closer look at crack ini-tiation from PVAs. The probability that a fatigue crack ini-tiates from a carbide related PVA is larger (18%) than incase of a PVA with an oxide (12%), Table 5. This may berelated to the higher Young’s modulus of carbides [74],which can result in higher stresses at PVA/matrix inter-faces. However, crack initiation at oxide related PVAsoccurs earlier during cyclic loading. This can be concludedfrom higher microcrack lengths of oxide related PVAs(Table 4, Fig. 14b). The tendency for earlier crack initiation(Table 4, Fig. 14b) in combination with the higher numberfraction of PVAs per volume (Table 2) results in shorterfatigue lives of O-rich NiTi wires. Oxides were oftenobserved to be larger than carbides (Table 2 and Fig. 7a),which is in line with what was reported in the literature[102–104]. Oxides are larger than carbides in the as-castmaterial, prior to any forming operations [38,105]. This lar-ger size of oxides may promote the formation of a largernumber of PVAs during thermomechanical processing (inour case: swaging, rolling and wire drawing). Larger parti-cles have a stronger tendency to break during forming(Fig. 6d), and each fracture event can result in the forma-tion of a PVA. Commercial NiTi melting procedures arenot openly disclosed and it is therefore difficult to drawgeneral conclusions on sizes of oxides and carbides. Itmay be that the thermodynamic and kinetic conditionswhich govern the formation of oxides and carbides duringsolidification are such that oxides which form in a peritecticreaction [38] grow larger than carbides which result froman eutectic reaction [39,101]. Peritectic reactions are oftenthought of as being sluggish [106,107]. This suggests thatnucleation rates are lower for oxides than for carbides.The high affinity of oxygen to titanium may then resultin a stronger growth of a smaller number of oxide nuclei.Another reason for the low tendency to form PVAs in C-rich NiTi could be the presence of certain orientation rela-tionships between carbides and the NiTi matrix [108],which may result in interfaces with better cohesion. Itseems worthwhile to clarify these points in order to providea basis for establishing processing routes which allow to uskeep oxide sizes at a minimum. Alloy manufacturers mayalso benefit from a better understanding of the factorswhich govern the formation of PVAs during thermome-chanical processing. Fig. 14c clearly suggests that it is wellworth the effort to keep the number density of PVAs at aminimum. It may be possible to identify suitable thermo-mechanical processing routes, where an appropriate hydro-static stress state helps to suppress the formation of PVAs.Further work is required to clarify this point.

It should be noted that the carbides and oxides whichcharacterize the materials investigated in the present studyare smaller (between 0.5 and 4 lm) than in commercialalloys (between 2 and 18 lm [102,103,109,110]). ASTMstandard 2063–05 [54] even considers particles of 39 lmsize as acceptable. The fact that our particles are very muchsmaller is probably related to the fact that our small meltvolumes (masses of ingot after solidification: 70 g) can cooldown quickly, so there is only a limited time for particlegrowth [106,107]. Even when particles are small, however,they form PVAs and act as crack nucleation sites. Furtherwork is required to find out whether large particles aremore effective in nucleating fatigue cracks than smallparticles.

4.5. Crack initiation and crack growth

Fatigue lives can be subdivided into periods of crack ini-tiation NI and crack propagation NP. The results compiledin Fig. 15c show that crack propagation does not dependon the O- and C-levels in the alloys and that crack exten-sions per cycle increase with increasing imposed surfacestrains eS. For cracks longer than 36 lm crack growthcan be rationalized by the phenomenological Paris law(Fig. 15d). LCF and HCF data yield Paris law stress expo-nents close to m = 2.5. LCF tests yield higher crack growthrates and therefore the Paris law constant C increases withincreasing imposed surface strain. It must be kept in mindthat our tests are no fracture mechanics tests and the x-axisof Fig. 15d reflects the uncertainty concerning the precisevalue of Dr in our experiments. For a discussion of crackgrowth behavior in NiTi we refer to the seminal overviewarticle of Robertson et al. [20], who give an excellentaccount of all previous work. Our m-value of 2.5 (deter-mined from post-fracture SEM analysis of fracture surfacesassuming that Dr is constant) is smaller than the m valuesthey report (between 2.8 and 4.1). The fact that the growthof small cracks (a < 36 lm) cannot be rationalized by theParis law has probably to do with the fact that a zone ofstress-induced martensite forms at the crack tip [111] andthat for short cracks the loading conditions do not fulfillthe conditions which need to be met when applying linearelastic fracture mechanics. It is well known that there aredifferences in the growth behavior of small and large cracks[112,113]. On the other hand the results presented inFig. 15d suggest that in spite of the continuously trans-forming/retransforming process zone in front of the cracktip, far field elastic stress fields govern fatigue crack growthfor cracks longer than 36 lm. Crack growth is important inthe LCF regime. HCF, on the other hand, is crack initia-tion controlled. Under HCF conditions, the relatively shortperiods of crack growth (NP: several thousand cycles) arealmost negligible when considering the high numbers oftotal cycles to failure (NF: hundred million cycles). Furtherwork is required to study elementary mechanical andmicrostructural aspects of fatigue crack initiation underHCF conditions.


4.6. Size effects

Finally, it should be mentioned that the diameters of ourwires (0.75 mm) were much larger than the typical dimen-sion of a PVA (1–4 lm). Size effects can be expected for sig-nificantly smaller dimensions of SMA components.Further work is required to clarify this point.

5. Summary and conclusions

In the present study we investigate LCF and HCF ofpseudoelastic NiTi wires of 0.75 mm diameter subjectedto isothermal BRF testing at 37 �C. We compare threealloys with similar austenitic nanograin sizes, similar AF

temperatures and similar critical stresses for the stress-induced formation of martensite. One alloy was of highpurity, while the other two alloys contained maximumaccepted levels of O and C. These two alloys contained ahigher number density and volume fraction of oxides andcarbides, respectively. From the results obtained in thepresent study the following conclusions can be drawn:

(1) For good fatigue resistance, surface quality is ofutmost importance. If processing defects (like draw-ing defects and die marks) are not fully removed,fatigue crack initiation will occur there and lowerC and O contents will not result in higher fatiguelives.

(2) In the absence of surface defects, particle/void assem-blies (PVAs) which originate during thermomechani-cal processing represent the relevant crack initiationsites. Crack initiation from PVAs was found to bemore effective than crack initiation from fully embed-ded particles. Other crack initiation processes (forma-tion of extrusions, evolution of microcracks fromgrain boundaries intersecting the specimen surface)are less important. Further work is required to inves-tigate how cracks initiate from PVAs.

(3) In both the LCF and HCF regimes, the alloy with thehigher O content shows the lowest fatigue lives. Oxi-des which form during a peritectic reaction duringsolidification of a NiTi melt may grow larger thaneutectic carbides. Subsequently, larger oxides give riseto the formation of more and larger PVAs duringthermomechanical processing. This may be moreimportant for fatigue crack nucleation than other fac-tors, like differences in the elastic properties of parti-cles and matrix or the physical nature of particle/matrix interfaces. Further work is required to clarifythis point.

(4) The number density of particles in the high-purityalloy was significantly smaller than in the case ofthe C- and O-rich materials. But the impurity levelin the high-purity alloy was still high enough to formcarbides and oxides. It was found that fatigue crackinitiation in the high-purity alloy mainly occurredat oxides associated with PVAs in both the LCF

and HCF regimes. Clean processing decreases theprobability for fatigue crack initiation, but it cannotsuppress it completely.

(5) Fatigue crack growth can be resolved on a cycle-by-cycle basis. Cyclic fatigue crack propagation ratesdo not depend on alloy purity. Crack growth ratesin the LCF regime are higher than in the HCFregime. For crack length larger than 36 lm, the fati-gue crack growth data can be rationalized by a Paristype of law, with a Paris law exponent m of 2.5.

(6) The results obtained in the present study show thatthe fatigue lives in the technologically relevant HCFand UHCF regimes are crack initiation controlled.The propagation of a macroscopic fatigue crack priorto final fracture is important under LCF conditions,but can be ignored under HCF and UHCF condi-tions. The stochastic nature of the interaction of ele-mentary damage processes required for fatigue cracknucleation results in the high experimental scatter inHCF lives observed in the present study. From botha basic and an engineering point of view, there is aneed for further probabilistic assessments of struc-tural fatigue.

Acknowledgements

The authors acknowledge funding by the DeutscheForschungsgemeinschaft (DFG) through projects C7 andT3 of the Collaborative Research Centre SFB 459 onShape Memory Technology. MR acknowledges fundingfrom the Interdisciplinary Centre for Advanced MaterialsSimulation (ICAMS).

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Impurity levels and fatigue lives of pseudoelastic NiTi shape memory alloys