www.elsevier.com/locate/actamat

Acta Materialia 55 (2007) 3437–3451

Pore formation mechanism and characterization of porous NiTishape memory alloys synthesized by capsule-free hot isostatic pressing

Shuilin Wu a, C.Y. Chung a,*, Xiangmei Liu a, Paul K. Chu a,*, J.P.Y. Ho a, C.L. Chu a,b,Y.L. Chan c, K.W.K. Yeung c, W.W. Lu c, K.M.C. Cheung c, K.D.K. Luk c

a Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, Chinab School of Materials Science and Engineering, Southeast University, Nanjing 211189, China

c Division of Spine Surgery, Department of Orthopaedics and Traumatology, The University of Hong Kong, Pokfulam, Hong Kong

Received 8 June 2006; received in revised form 26 January 2007; accepted 28 January 2007Available online 23 March 2007

Abstract

Porous NiTi alloys with different porosities were fabricated by capsule-free hot isostatic pressing (CF-HIP) with ammonium acid car-bonate (NH4HCO3) as a space-holder. The microstructure and porosity of porous NiTi produced with different NH4HCO3 contents andsintering temperatures were determined. Two different creep expansion models are used to explain the pore expansion mechanism duringthe sintering process, which involves slow and continuous reduction of the argon pressure at high temperatures. When the NH4HCO3

content is 30 wt.% and the sintering temperature is 1050 �C, an ideal porous NiTi alloy with 48 vol.% porosity and circular pores (50–800 lm) is obtained. Compression tests indicate that the porous NiTi alloys with 21–48% porosity possess not only lower Young’s mod-uli of 6–11 GPa (close to that of human bones) but also higher compression strength and excellent superelasticity. Cell cultures revealthat the porous NiTi prepared here has no apparent cytotoxicity. The porous materials are thus promising biomaterials in hard tissuereplacements.� 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Porous NiTi; Creep expansion; Hot isostatic pressing; Sintering; Shape memory alloy

1. Introduction

Biometals such as Ti-based alloys and NiTi shape mem-ory alloys (SMAs) have had commercial success thanks totheir higher strength and excellent biocompatibility [1–4].However, the Young’s moduli of these biometals, e.g.105 GPa for Ti alloys (a + b) and 80 GPa for NiTi (austen-ite) [5], are much higher than those of human bones (1–2 GPa for cancellous and 17.0–18.9 GPa for compactbones) [6]. This mismatch has hampered wider commercialapplications such as surgical implants because only a low

1359-6454/$30.00 � 2007 Acta Materialia Inc. Published by Elsevier Ltd. All

doi:10.1016/j.actamat.2007.01.045

* Corresponding authors. Tel.: +852 27887724; fax: +852 27889549(P.K. Chu); tel.: +852 27887835; fax: +852 27887830 (C.Y. Chung).

E-mail addresses: appchung@cityu.edu.hk (C.Y. Chung), paul.chu@cityu.edu.hk (P.K. Chu).

stiffness, close to that of bones, can provide a good loadtransfer whereby effective new bone formation can be real-ized. It is possible to decrease the Young’s moduli (stiff-ness) of these biometals by increasing their porosity viathe proper powder metallurgical (PM) processes. Murrayet al. [7] successfully fabricated porous titanium with amaximum porosity of 44% by expanding pressurizedtrapped argon gas at high temperature. Kearns et al. [8]obtained porous Ti–6Al–4V with 40% porosity using a sim-ilar method conducted at 1240 �C for several days. Bobynet al. fabricated porous tantalum by chemical vapor depo-sition/infiltration (CVD/CVI) [9]. Among these porousmetals, porous NiTi alloys have attracted the most interestfrom materials researchers because their unique shapememory effect (SME) [10–13], biocompatibility [10,14–16], lower stiffness, and higher strength combined with

rights reserved.

3438 S. Wu et al. / Acta Materialia 55 (2007) 3437–3451

porous structure [10,13] make them suitable for surgicalimplants as well as high-energy absorbing materials[11,14–17].

In recent years, many different PM methods have beenused to fabricate porous NiTi SMAs. Traditional elemen-tal powder sintering (EPS) in an argon ambient is thesimplest method. However, the compressive curves ofporous NiTi produced by this process do not exhibitthe obvious stress–strain plateau and have larger recoverystrains [18,19]. Chu and Li prepared porous NiTi alloy bycombustion synthesis (CS), but their materials still pos-sessed low compression strength [20,21]. Self-propagatinghigh-temperature synthesis (SHS) processes can be usedto synthesize porous NiTi with larger porosity and linearchannels [22]. However, Kim’s research showed that por-ous NiTi alloys made by SHS were brittle and their ten-sile strength was in the range of 15–25 MPa [23], possiblyas a result of the large porosity and unidirectional porouschannels. A recent report [24] shows that a proper post-reaction heat treatment process can induce a single NiTiphase that can slightly improve the superelasticity of por-ous NiTi. Zhao et al. fabricated porous NiTi alloys oftwo different porosities by spark plasma sintering (SPS).Their results showed that porous NiTi with 13% porosityhad higher compression strength and excellent superelas-ticity, similar to those of dense NiTi alloys, while the25% porosity sample exhibited lower compressionstrength [11]. Lagoudas et al. prepared porous NiTi frommixed NiTi powders filled with argon gas by hot isostaticpressing (HIP), but their porous samples also showed lowcompression strength, possibly due to their irregular poreshape and distribution [25]. Greiner et al. fabricated por-ous NiTi alloys from mixed pre-alloyed martensitic NiTipowders and small quantities of elemental Ni powdersfilled with argon by HIP [13]. They were able to obtainporous NiTi by long-term creep expansion under highvacuum at high temperature, and their porous productsshowed excellent superelasticity and higher compressionstrength. Unfortunately, the porosity of the porous NiTiprepared by this method cannot exceed 20% despiteexpansion for 100 h, and the long expansion time coupledwith the high temperature are not economically attrac-tive. In addition, the pores obtained by this process aretoo small, in the range of 10–20 lm, compared to theconventional pore size of 50–500 lm suitable for tissueintegration [26].

Capsule-free hot isostatic pressing (CF-HIP) is quite dif-ferent from traditional HIP and has been used to improvethe mechanical properties of ceramic materials whileretaining adequate porosity [27,28]. Using this method,Yuan et al. fabricated porous NiTi SMAs with a porosityof 40% and a pore size ranging from 50 to 200 lm [29].Although their porous materials had good mechanicalproperties, it was difficult to adjust the pore size, distribu-tion and porosity by this method. One of the most promis-ing methods to produce adjustable porous titaniummaterials is by sintering of compacted or extruded powder

mixtures that contain removable space-holder materialssuch as ammonium acid carbonate (NH4HCO3). Somereports have revealed that 25–80% porosity can be achievedin titanium by this method [30,31]. In the work reportedhere, we for the first time used NH4HCO3 as a space-holderto produce porous NiTi and investigated the pore forma-tion mechanism by monitoring the evolution of the micro-structures during the CF-HIP process. Furthermore, westudied the effects of the porosity on the mechanical prop-erties and phase transformation temperatures of the porousNiTi alloys. In addition, the cytocompatibility of thesematerials was evaluated by osteoblast cultures.

2. Materials and methods

Titanium and nickel powders (from Shanghai ReagentCorporation) with an average particle size of about75 lm (purity >99.5%) were weighed using an FR-300MKI electronic balance with a precision of 0.1 mg andput into a polymer can in equiatomic proportion togetherwith some stainless steel balls. The powder-to-ball ratiowas 1:2 by weight. Before mixing, the can with the powdermixture was purged with argon gas for 2 h in order to min-imize oxidation of the powders during mixing. The materi-als were mixed in a horizontal universal ball mill (ModelUBM-4) at a speed of 100 rpm for 12 h. The purpose ofmixing the powders with steel balls in the polymer can ata low speed was to produce a homogeneous mixture ofthe elemental powders and to minimize pre-alloying andoxidation of nickel and titanium powders during mixing.Afterwards, the mixed powders were divided into four por-tions and then mixed with NH4HCO3 powders (Specifica-tion of Ph. Eur., BP, E503, purity >99.5%) at ratios of1:10, 1.5:10, 2:10; 3:10 (NH4HCO3 powders: mixing pow-ders) by weight and labeled A, B, C, D, respectively. Thesemixtures were then pressed into green compacts in a steelmold with a diameter of 16 mm using a hydraulic pressat a cold compaction pressure of 200 MPa. The green com-pacts A–D were heated to 200 �C for 2 h in a tube furnaceunder a continuous flow of 99.995% pure argon at atmo-spheric pressure to remove the NH4HCO3. The pretreatedgreen compacts were subsequently put into capsule-freestainless steel canisters and sintered in the HIP unit (ABBCo.). The HIP chamber was vacuum purged and backfilledwith 99.995% pure argon gas before the pressure was raisedto 100 MPa. The temperature in the HIP chamber was thenincreased. The argon pressure and temperature reached150 MPa and 1050 �C at the same time.

The sintering and pore expansion processes took placeduring stages 1 and 2 (shown in Fig. 1). In stage 1, the NiTialloy ‘‘wall’’ produced by the diffusion reaction of nickeland titanium enclosed the original closed pores in the greencompacts. Local melting inside the compacts caused by thelocalized overheating reaction of nickel and titanium alsopossibly obstructed the originally interconnected openpores. These two conditions induced the formation of alarge number of closed pores filled with argon gas at ele-

0 40 80 160 200 240 280 320 3600

200

400

600

800

1000

1200

0

20

40

60

80

100

120

140

160

180

200

220

Stage 2

Tem

pera

ture

( ° C

)

Time (min)

1050 °C

150MPa

line cline bline a

Stage 1

Arg

on p

ress

ure

(MP

a)

120

Fig. 1. Sintering parameters during the CF-HIP process.

S. Wu et al. / Acta Materialia 55 (2007) 3437–3451 3439

vated pressure. In stage 2, the external argon pressure wasslightly lowered from 150 to 140 MPa at a rate of1.67 atm min�1 at 1050 �C. This evoked slow expansionof these closed pores.

After HIP, the porous NiTi SMAs were annealed at450 �C in a tube furnace under flowing 99.995% pure argonat atmospheric pressure for 0.5 h. The phase compositionof the porous NiTi was determined by X-ray diffraction(XRD; Siemens D500). The martensitic transformationtemperature was determined using a differential scanningcalorimetry (DSC) thermal analyzer (TA; 2910 Instrument)with the specimen weights between 10 and 20 mg. In theDSC thermal analysis, the specimens were heated to100 �C and kept isothermally for 2 min to establish thermalequilibrium, cooled down to �50 �C, kept isothermally foranother 2 min, and then heated to 100 �C again. The heat-ing and cooling rates were 5 �C min�1. The surface mor-phology and microstructure of the porous specimens wereevaluated by scanning electron microscopy (SEM;JSM5200) and optical microscopy (Olympus BH2-UMA).The NH4HCO3 powders coated with a thin layer of goldwere observed by SEM (JSM820). The pore size and distri-bution were determined using a Leica Qwin V3 image anal-ysis system. In order to investigate whether NH4HCO3 hadbeen completely removed from the compacts, high-resolu-tion small-area (120 lm) X-ray photoelectron spectroscopy(XPS; Physical Electronics PHI 5802, Minnesota, MN)analysis was performed on the wall of one of the internalbig pores to determine the chemical composition of theinternal surface of the pores. The take-off angle was 45�and base vacuum was 2 · 10�8 Pa. Survey scans spanninga binding energy range of 0–1200 eV with a pass energyof 187.85 eV and 0.8 eV step�1 were first acquired to iden-tify the elemental species. High-resolution scans were sub-sequently obtained with a pass energy of 11.75 eV and0.1 eV step�1. A Gaussian–Lorentzian peak-fitting modelwas used to deconvolute the spectra.

The general porosity, p, of the porous samples was cal-culated by the formula:

p ¼ 1� mqV

� �� 100ð%Þ;

where m and V are the mass and volume of the porous sam-ples, respectively, and q is the theoretical density of NiTi(6.45 g cm�3 for bulk equiatomic NiTi SMA). The samplesfor the compression test were machined into cylindricalbars 6 mm in diameter and 12 mm thick. They wereannealed in a tube furnace at 450 �C for 0.5 h under flow-ing 99.995% pure argon at atmospheric pressure. The uni-axial compression tests were carried out in accordance withthe ASTM standard E9-89a protocol [32] at a constant rateof 0.06 mm min�1 at room temperature (about 22 �C) usingan Instron 4206 to investigate the compression strengthand superelastic behavior of the porous NiTi SMAs.

In order to investigate the biocompatibility of the NiTialloy produced by CF-HIP with NH4HCO3 as the space-holder, osteoblasts isolated from calvarial bones of 2-day-old mice that ubiquitously expressed an enhancedgreen fluorescent protein (EGFP) were cultured in a Dul-becco’s modified eagle medium (DMEM) (Invitrogen) sup-plemented with 10% (v/v) fetal bovine serum (Biowest,France), antibiotics (100 U ml�1 of penicillin and100 lg ml�1 of streptomycin), and 2 mM L-glutamine at37�C in an atmosphere of 5% CO2 and 95% air. The spec-imens (2 mm thick and 5 mm in diameter) were fixed ontothe bottom of a 24-well tissue culture plate (Falcon) using1% (w/v) agarose. A cell suspension consisting of 15,000cells in 100 ll of medium was seeded onto the surface ofthe porous NiTi samples, and wells without any metal disksserved as the control for normal culturing conditions. Thecells were allowed to settle and attach to the surface of thediscs for 4 h. One milliliter of the medium was then addedto the wells and changed every 3 days. Four identical sam-ples were used and cell proliferation was examined after 8days of culturing. In this study, the cells were allowed toreach confluence during the examination period. The mor-phology of the attached living EGFP-expressing osteo-blasts was examined using a scanning electronmicroscope (Cambridge Stereoscan S440) and fluorescentmicroscope (Axioplan 2, Carl Zeiss, Germany). To preparefor the SEM observation, the disks together with theattached cells were washed gently in PBS before fixationin 2.5% glutaraldehyde buffered at pH 7.42 with 0.1 Msodium cacodylate for 24 h at 4 �C. Excess fixatives wereremoved by washing in 0.1 M sucrose in cacodylate bufferand dehydration was carried out in graded series of bathsof ethanol–water to 100% ethanol. The cells were then crit-ical point dried and sputter coated with gold before exam-ination by SEM.

3. Results and discussion

3.1. Characteristics of powders and green compacts

Fig. 2 shows the shape and size of the NH4HCO3 pow-ders used as space-holders in our experiments. The particle

Fig. 2. SEM image of NH4HCO3 powders.

3440 S. Wu et al. / Acta Materialia 55 (2007) 3437–3451

size ranges from 20 to 100 lm and the average particle sizeis about 55 ± 5 lm. Fig. 3a and b depicts the XRD patternsof the mixtures composed of Ni, Ti and NH4HCO3 pow-

10 20 30 40 50 60 70 80

∇

∇:NH4HCO3

♦:Ni •:Ti

•••

♦

•∇∇

∇∇

∇

∇∇

∇ ♦

♦

∇

∇

∇

•

•

Inte

nsity

(a.

u.)

2 Theta (degree)

10 20 30 40 50 60 70 80

••••••

•

♦

♦

♦

Inte

nsity

(a.

u.)

2 Theta (degree)

♦: Ni•: Ti

b

Fig. 3. XRD patterns acquired from Ni, Ti and NH4HCO3 mixingpowders: (a) before heat treatment; (b) after heat treatment at 200 �C.

ders before and after heat treatment, respectively. It isapparent that NH4HCO3 is removed after heat treatmentat 200 �C for 2 h and that the heat treatment process doesnot introduce any new substances into the green compacts.Fig. 4 shows the evolution of the surface morphologies ofthe pretreated green compacts with different NH4HCO3

contents. It can be found that both the number and sizeof the pores in the green compacts increase with higherNH4HCO3 contents after heat treatment due to the follow-ing decomposition reaction:

NH4HCO3 ! NH3 " þ H2O " þ CO2 " : ð1ÞThe pores are almost evenly distributed in the green com-pacts. This can be ascribed to the relatively uniform distri-bution of NH4HCO3 in the mixtures during mixing.

3.2. Characteristics of the pore surface

Since the decomposition of NH4HCO3 releases NH3

(Reaction (1)), which is harmful to human beings [33], itis very important to remove all the NH4HCO3 from theas-sintered porous NiTi alloy. Although the XRD patterns(Fig. 3b) indicate that NH4HCO3 has been removed fromthe green compacts after the heat treatment, it is difficultto confirm that all the NH4HCO3 has been totally removedas a small amount of decomposed gas molecules such asH2O, NH3 and CO2 can still be retained in some of thepores in the compacts due to the relatively short diffusiontime and low temperature (200 �C). Therefore, it is neces-sary to measure the chemical composition of the exposedsurface of the internal pores of the as-sintered NiTi alloy.High-resolution small-area XPS spectra acquired fromthe wall of an internal pore (shown in Fig. 5) are displayedin Fig. 6. The typical survey spectrum (Fig. 6a) indicatesthat the pore surface is composed of mainly C and O witha small amount of Ni, Ti and N (curve 1). After the top5 nm has been removed by Ar sputtering, Ni, Ti, C andO become the dominant species and N can no longer bedetected (curve 2). Fig. 6b–f shows the high-resolutionspectra of Ti 2p, Ni 2p, C 1s, O 1s and N 1s together withthe corresponding fitted components. As shown in Fig. 6b,the main species on the surface of the pore is TiO2 andtraces of NiTi and TiO are detected (curve 1). After thetop 5 nm has been sputtered off, the TiO2 contentdecreases, whereas the amounts of TiNi, TiO and Ti2O3

increase (curve 2). It can also be found from Fig. 6c thatsome nickel oxides such as Ni2O3 and NiO and a smallamount of NiTi exist on the surface of the pore. Metal oxi-des appear on the pore surface due to oxidation of NiTiduring high-temperature sintering. There is a small amountof trapped O2 in the closed pore, possibly originating fromair or decomposed NH4HCO3 The high-resolution O 1sXPS spectrum in Fig. 6d shows three peaks at 530.8,532.2 and 534.2 eV that are associated with the metal oxidebonds, the carbonyl bond (C@O) and the carbon–oxygensingle bond (C–O), respectively [34,35]. Fig. 6e reveals thatthe dominant peak at 285.6 eV corresponds to C–C bonds.

Fig. 4. Macro-morphologies of green compacts after treatment at 200 �C in a tube furnace: (a) green compact A; (b) green compact B; (c) green compactC; (d) green compact D. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 5. Typical surface morphology of porous NiTi used in XPS analysis.

S. Wu et al. / Acta Materialia 55 (2007) 3437–3451 3441

Two other peaks located at 286.8 and 289.2 eV are associ-ated with the C–N bond and carbonyl bond (C@O), respec-tively [34–36]. According to the high-resolution N 1sspectrum (Fig. 6f), the N 1s binding energy is 399.8 eV,which corresponds to the organic matrix (C–N) [34–37].Tan and Torkar [34,37] attribute these carbon and nitrogenbonds to organic surface contamination from the cleaningsolvents. On the exposed surface of the internal pores here,some carbon and nitrogen bonds probably originate fromthe complex reaction involving NH3, CO2 and H2O duringhigh-temperature and high-pressure sintering. These gases

are products of decomposition of NH4HCO3 remainingin some of the closed pores. Wu et al. [38] reported thatNH3 could be decomposed above 600 �C and nitride thesurface of NiTi alloy. Our XPS analysis failed to detectany metal nitrides perhaps because of the low nitrogen con-tent on the pore surface. In summary, our results do notshow the existence of NH3 in the closed pores of the as-sin-tered porous NiTi. It should be mentioned that althoughthe titanium oxide layer formed on the exposed surfaceof the pores is thin, Chu and Yeung’s works [39,40] haveshown that the formation of surface titanium oxide ornitride can improve the biocompatibility of NiTi alloys.

3.3. Synthesis by CF-HIP

The green compacts A–D were put into the HIP cham-ber simultaneously and highly pressurized argon gas wasused during sintering. The procedures favor the formationof open pores, resulting in adequate porosity in the as-pressed powders [27,28] because the argon gas under highpressure can readily penetrate the green compacts throughthe original pores. Argon can also minimize oxidation oftitanium and nickel powders so that the more desirableNiTi alloy can form from the diffusion reaction of nickeland titanium during the sintering process at high tempera-ture. Local oxidation can result in the composition fluctu-ation in the compacts inducing the formation of differentsecondary phases such as Ni3Ti, Ti2Ni and Ni4Ti3 [22],

470 465 460 455

1

Max. acounts= 474

TiO2Ti2O3 TiO

NiTi

TiO2

Inte

nsity

(a.

u.)

Binding energy (eV)

NiTiTiO

Max. acounts= 450

2

890 885 880 875 870 865 860 855 850 845

2p3/2

2p1/2

Max. acounts=988

inte

nsity

(a.

u.)

Binding energy (eV)

NiTiNiO

Ni2O

3

NiTi

Max. acounts=137

2

1

c

295 290 285 280

1

2

Max. acounts= 408

Max. acounts= 165

C=O C-N

C-C

C=O

C-N

Inte

nsity

(a.

u.)

Binding energy (eV)

C-C

405 400 395

1

Max. acounts= 107

Inte

nsity

(a.

u.)

Binding energy (eV)

C-N

540 535 530 525

O-C

O-C

O=C

O=C

O-Metal

O-Metal

1

2

Max. acounts=816

Max. acounts=964

Inte

nsity

(a.

u.)

Binding energy (eV)

e

f

Fig. 6. Small area XPS results acquired from the wall of an internal pore of porous NiTi: (a) survey spectra; (b) high-resolution Ti 2p spectra; (c) high-resolution Ni 2p spectra; (d) high-resolution O 1s spectra; (e) high-resolution C 1s spectra; (f) high-resolution N 1s spectra.

3442 S. Wu et al. / Acta Materialia 55 (2007) 3437–3451

and Biswas’ results indicate that these secondary phasesimpair the mechanical properties and superelasticity ofporous NiTi alloys [24]. As shown in Fig. 1, the argon pres-sure is elevated to 100 MPa before raising the temperatureso that the original spaces in the green compacts can be

completely filled with argon. The faster heating rate canspur the exothermic reactions, inducing collapse of thesamples during sintering [24]. A slow heating rate of about10 �C min�1 is employed subsequently because it can pro-vide a slow pressurizing rate (about 5 atm min�1) to keep

Fig. 7. SEM micrographs of as-sintered samples produced using mixed powders A–D: (a) sample A; (b) sample B; (c) sample C; (d) sample D; (e) high-magnification image of (d); (f) stereo SEM image of sample D; (g) longitudinal SEM image of sample D (without grinding).

S. Wu et al. / Acta Materialia 55 (2007) 3437–3451 3443

3444 S. Wu et al. / Acta Materialia 55 (2007) 3437–3451

the dynamic argon pressure equilibrium between the inte-rior and exterior of the pores in the green compacts. Thehigh sintering temperature is maintained for 180 min toensure that the Ni and Ti diffusion reaction can take placefor a sufficiently long time. The slight drop in the argonpressure (between line b and line c, shown in Fig. 1) inducesslow expansion of the argon pores.

3.3.1. Effects of NH4HCO3 contents on the porous structure

Fig. 7 shows the evolution of the porous structure pro-duced from the green compacts containing differentNH4HCO3 contents. The average pore sizes of samplesA–D are 57 ± 5, 73 ± 5, 93 ± 5 and 128 ± 5 lm, respec-tively. In sample A, 50% of the pores have sizes below50 lm, with the remaining 41% and 9% have sizes of50–100 and 100–200 lm, respectively. A typical micro-graph of sample A is shown in Fig. 7a. Similarly, poreswith sizes smaller than 50, 50–100 and 100–300 lmaccount for 43%, 38% and 19% of the total pores in sam-ple B, as shown in Fig. 7b. As the NH4HCO3 contents inthe green compacts increase, the number of big pores inthe final sintered products increases significantly. Forexample, as shown in Fig. 7c, 18% of the pores in sampleC are smaller than 50 lm and 34% of the pores are largerthan 100 lm. When the NH4HCO3 concentration in themixed powders goes up to 30%, 11% of the pores aresmaller than 50 lm, 41.5% of the pores are larger than100 lm, and 9% of the pores are 300–800 lm. The repre-sentative transverse surface morphology of the sampledepicted in Fig. 7d indicates that most of the pores arealmost circular. Fig. 7f and g exhibits the stereo and lon-gitudinal SEM images of the same sample, respectively,disclosing that the pores in these as-sintered porous NiTialloy are nearly spherical.

Fig. 8 shows the changes in the porosity with differentNH4HCO3 concentrations in the mixed powders. Both theporosity of the green compacts and as-sintered porous

10 15 20 25 30

16

20

24

28

32

36

40

44

48

52

56

60

64

68

Green compacts after treatment at 200 °C

As HIPed

Por

osity

( v

ol%

)

Content of NH4HCO3 (wt %)

Fig. 8. Porosity evolution vs. NH4HCO3 concentration in the mixedpowders.

NiTi samples increase with larger NH4HCO3 contents inthe mixed powders. In the green compacts with a higherNH4HCO3 content, more space remains after the heattreatment, leading to a higher density of pores and smal-ler average distance between neighboring spaces. Duringsubsequent CF-HIP, expansion of the argon-filled poresleads to merging of adjacent pores. This is one of the rea-sons why the number of big pores increases, whereas thatof small pores decreases with increasing NH4HCO3 con-tents in the mixed powders. The results are confirmedby Fig. 7e, which shows that pores 1 and 2 merge whenthe wall between them is pierced during expansion (illus-trated by the circle). A similar phenomenon occursbetween pores 2 and 3. It can be observed that some smallpores exist in the wall of the big pores (indicated by thewhite arrows in Fig. 7e), as manifested by the intercon-nection between these pores. In fact, the open porositiesmeasured from samples A and D using the ASTM stan-dard B328-96 protocol [41] are about 40% and 70%,respectively.

3.3.2. Effects of sintering temperature on the porousstructure

Considering that samples made from mixed powders Cand D have the high porosity and big pore size that aresuitable for tissue ingrowth [26], we use two types ofpowders to investigate the influence of the sintering tem-perature on the porous structure of the NiTi alloys byaltering the sintering temperature from 1050 �C (shownin Fig. 1) to 1060 �C. It can be observed that the poresizes in the sample made from powders C change from50 lm to 2.3 mm (Fig. 9a). In comparison, most of thepores in the sample sintered from mixed powders Dmerge into one big pore (Fig. 9b). When the sinteringtemperature is reduced to about 1055 �C, several bigpores appear in the sample made from powders D(Fig. 9c) in lieu of one big pore as in the case of1060 �C. These phenomena are probably caused by theexpansion of the argon-filled pores between lines a andc (Fig. 1). During the CF-HIP process, NiTi forms ini-tially in the ectotheca of the sample because the outsidereaches the sintering temperature before the inside, andlocal melting or collapse does not occur easily due todirect contact with the high-pressure argon atmosphere.However, the elevated sintering temperature expeditesthe following exothermic reactions of Ni and Ti in theinterior of the sample [19]:

Niþ Ti! NiTiþ 67 kJ=mol; ð2ÞNiþ Ti! Ti2Niþ 83 kJ=mol; and ð3ÞNiþ Ti! Ni3Tiþ 140 kJ=mol: ð4Þ

The reactions lead to local overheating, and subsequentlylocal melting occurs in these regions. As a result, expansionand coalescence of the pores occur and the inner smallpores evolve into one or several big pores as the sinteringtemperature is increased.

Fig. 9. Surface morphology of porous NiTi produced from mixedpowders C and D: (a) sample C at 1060 �C; (b) sample D at 1060 �C; (c)sample D at 1055 �C.

20 30 40 50 60 70 80

∇: B2 (NiTi)♦: B19' (NiTi)Ο: Ni3Ti

♥: Ti2Ni

♣: Ni4Ti3

♥ ♣♣♣

♣

♥

♥

♥♥

ΟΟ

Ο

♦♦Ο

Ο

♦

♦

∇∇∇

∇

Inte

nsity

(a.

u.)

2 Theta (degree)

1: annealed at 450 °C for 0.5 hr2: as HIPed

1

2

Fig. 10. XRD patterns of porous NiTi alloy produced using mixedpowders D.

-60 -40 -20 0 20 40 60 80 100

-0.5

0.0

0.5

1.0

1.5

Hea

t flo

w (

W/g

)

Temperature ( °C)

21% porosity 36% porosity 42% porosity 48% porosityheating

cooling

Fig. 11. DSC curves for porous NiTi with different porosities annealed at450 �C for 0.5 h.

S. Wu et al. / Acta Materialia 55 (2007) 3437–3451 3445

3.3.3. Phase composition of porous NiTi

Fig. 10 shows the phase composition of the porous NiTiSMAs produced by CF-HIP. Similar to NiTi alloys fabri-cated by other PM methods such as EPS [18], CS [20],SHS [22], HIP [42] and SPS [43], several intermetallic com-pounds are formed during the CF-HIP process. These aremainly composed of the desirable B2 (austenite NiTi),B19 0 (monoclinic martensite NiTi) and minor secondphases such as Ni3Ti, Ti2Ni and Ni4Ti3. NiTi is the majorphase due to the equiatomic Ni–Ti composition of thegreen compacts before sintering according to the Ni–Ti

binary diagram [44]. Emergence of the second phases is acommon phenomenon in PM processing of NiTi alloys.The Ni–Ti binary diagram [44] indicates that Ni3Ti andTi2Ni are stable phases, and slight fluctuations in the localcomposition will cause the formation of these phases. Liet al. [22] ascribe the fluctuations to insufficient mixing ofthe raw powders as well as their large particle size.Recently, Biswas has proposed that these second phasescan be eliminated completely by a post-reaction heat treat-ment [24]. This is based on the fact that the eutectic temper-atures of Ti2Ni and Ni3Ti are 984 and 1118 �C,respectively, and that the higher post-treatment tempera-ture of 1150 �C will induce the dissolution of these phases.

3.4. DSC analysis

Fig. 11 shows the DSC curves acquired from the porousNiTi alloys with different porosities annealed at 450 �C for

0 1 2 3 4 50

100

200

300

400

500 21% porosity 1st cycle

2nd cycle 3rd cycle 4th cycle 5th cycle

Str

ess

(MP

a)Strain (%)

0 1 2 3 40

50

100

150

200

250

300

350

400 1st cycle 2nd cycle 3rd cycle 4th cycle 5th cycle

36% porosity

Str

ess

(MP

a)

b

3446 S. Wu et al. / Acta Materialia 55 (2007) 3437–3451

0.5 h. The temperatures of endothermic peaks in the heat-ing curves of the samples with porosities of 21%, 36%, 42%and 48% are 26.7, 24.4, 27.4 and 18.1 �C, respectively, all ofwhich are below the human body temperature. The corre-sponding As values (the onset point of transformation frommartensite to austenite) are 11.4, 7.7, 10.5 and 5.7 �C,respectively, which are below room temperature. There-fore, these porous materials can exhibit superelastic behav-ior even at room temperature due to the stress-inducedmartensite transformation.

3.5. Compression behavior

The samples with porosities of 21%, 36% and 48% wereused in the compression tests. The compressive stress–strain results are shown in Fig. 12. All the curves showan obvious stress plateau similar to dense NiTi. The stressplateau of the NiTi sample with nearly spherical sporesarises from the cellular structure of the sample. Gibsonand Degischer [45,46] reported that the compressivestress–strain curves of cellular materials such as wet cancel-lous bones, mullites, polymers and Al-based alloys exhib-ited an obvious plateau. Gibson and Ashby [45]attributed the plateau to the collapse of the cells duringcompression. This collapse of different cellular materialshas different mechanisms, e.g. elastic buckling in elasto-meric porous polymers, brittle crushing in brittle ceramics,or formation of plastic hinges in cellular metals. On theother hand, the plateau of porous NiTi SMA can be par-tially induced by the stress-induced martensite transforma-tion [5]. This stress plateau with a hysteresis loop duringloading and unloading indicates that porous NiTi preparedby CF-HIP has good superelasticity and it bodes well forthe use of NiTi in medical implants [47]. In fact, the super-elastic behavior is often accompanied by a hysteresis loop,which is a common phenomenon in biological materials.Deformation characteristics such as high elasticity, low

0 1 2 3 4 50

50

100

150

200

250

300

350

400

450

48% porosity

Ste

ss (

MP

a)

Strain (%)

21% porosity

36% porosity

Fig. 12. Compressive stress–strain curves of porous NiTi at roomtemperature.

deformation forces and constant force over wide rangesof strain are common in human tissues as well as NiTi[48]. The human bone also exhibits a large recoverablestrain up to 2% [45], which is achievable with the superelas-

Strain (%)

0.0 0.5 1.0 1.5 2.0 2.5 3.00

20

40

60

80

100

120

140

160 1st cycle 2nd cycle 3rd cycle 4th cycle 5th cycle

48% porosity

Ste

ss (

MP

a)

Strain (%)

c

Fig. 13. Comparison of compressive stress–strain curves with differentstress cycles of porous NiTi at room temperature: (a) 21% porosity; (b)36% porosity; (c) 48% porosity.

S. Wu et al. / Acta Materialia 55 (2007) 3437–3451 3447

tic NiTi. The mechanical mismatch between bones andNiTi is therefore likely to be smaller in comparison withother common surgical materials such as 316L stainlesssteels. It can be found in Fig. 12 that the plateau inducedby the critical stress decreases slightly with increasingporosities. In the NiTi with a higher porosity, the quantityof austenite transformed into martensite per unit volume isless than that in samples with lower porosities. Hence, alower critical stress can induce martensite transformationin samples with higher porosities. Generally, the criticalstress in porous samples diminishes with decreasing relativedensity [45]. Although porous samples prepared by othermethods have higher compression strength [11,13], goodmechanical properties can be achieved only from sampleswith low porosities. For example, the sample with 25%porosity made by SPS [11] has a compression strength ofabout 120 MPa when strained to about 2.2%, while thespecimen with a porosity of 48% fabricated by CF-HIPin this work displays a similar compression strength ofabout 130 MPa when strained to 2.8%. In addition, thecompression strengths of the samples with 36% and 21%porosities are 340 and 410 MPa when strained to 4.2%and 4.7%, respectively. In contrast, although the porousNiTi alloys prepared via SHS have high porosity, theyare not superelastic and have low compression strength[15,23].

Fig. 13 illustrates the compression behavior of theporous NiTi alloys with different cycles. The Young’smoduli of the porous samples can be calculated in thenear-linear region by Hooke’s law [49] and the resultsare shown in Fig. 14. It can be found that the Young’smoduli of the porous NiTi alloys prepared by CF-HIPdecrease with increasing porosities, and the trend is con-sistent with that observed in porous materials by Ond-racek and Gibson [50,45]. The Young’s moduli of thesamples with 21–48% porosities range from 6 to11 GPa, which are close to those of wet compact human

18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 506.0

6.5

7.0

7.5

8.0

8.5

9.0

9.5

10.0

10.5

11.0 1st cycle 2nd cycle

You

ng's

Mod

ulus

(G

Pa)

Porosity (%)

Fig. 14. Evolution of Young’s moduli with respect to the porosity ofporous NiTi.

bones of about 11.5–17.0 GPa [45]. Greiner et al. [13]reported that the apparent Young’s modulus of theirsample with 16% porosity was about 15 ± 1 GPa whichis slightly higher than that of our sample. This differenceis perhaps due to the lower porosity. The Young’s

Fig. 15. Cell (mice osteoblasts) morphologies on porous NiTi alloys afterculturing for 8 days: (a) EGFP-expressing image of the entire surface; (b)SEM image of the entire surface; (c) SEM image of the pore of the sample.

3448 S. Wu et al. / Acta Materialia 55 (2007) 3437–3451

moduli determined from the second cycle are slightly bet-ter than those calculated from the first cycle in all thesamples, and this is believed to be due to work harden-ing and the internal stress produced during the firstcycle. In the subsequent third, fourth and fifth cycles,the Young’s moduli and compression strength do notchange significantly.

3.6. Cytocompatibility

Fig. 15 shows the cell morphologies on the porous NiTiafter 8 days of cell culturing. As shown in Fig. 15a and b,the cells can clearly adhere and proliferate on the entiresurface of the porous NiTi fabricated by CF-HIP.Fig. 15c indicates that osteoblasts can also adhere and pro-liferate well on the internal surface of the pores. Theseresults suggest that the porous surfaces of NiTi preparedby CF-HIP with NH4HCO3 as a space-holder in the greencompacts are biologically friendly to osteoblasts. We areconducting bone implants experiments in rabbits usingporous NiTi prepared by CF-HIP to examine the long-term bone in-growth effects and will report our findingsin due course.

4. Pore formation mechanism

Fig. 16 illustrates the formation process of the pores inthe porous NiTi during CF-HIP. The original poresinclude the intraparticle voids as well as spaces createdby the removal of NH4HCO3 in the green compacts.After evacuation and subsequent argon backfilling, these

Fig. 16. Schematic of pore

pores are filled with pressurized argon gas. In stage 1(illustrated by lines a and b in Fig. 1), the pores evolveinto closed pores, open pores and interconnected openpores. Some of the original open, interconnected andclosed pores are retained due to the pressure equilibrium.At the same time, some of the open pores are blocked bylocal melting arising from the exothermic reactionsdescribed previously, leading to the formation of closedpores. Furthermore, both the sample and pores shrinkin stage 1 due to the aforementioned diffusion reactions(2)–(4) at high temperature and high pressure. Hence,the porosities of the as-sintered samples are lower thanthose of the corresponding green compacts (Fig. 8). Dur-ing stage 2 (indicated by line b and line c in Fig. 1), theclosed pores expand in the soft medium due to the pres-sure differential across the pore wall as a result of thegradual reduction of the external argon pressure. In thisstage, two types of creep expansion kinetics occursimultaneously.

4.1. Expansion of closed pores

During expansion of the closed pores, the densificationmodel proposed by Wilkinson and Ashby [51] (Fig. 17)can be adopted because the expansion is the reverse ofthe densification when the internal pressure, pi, is higherthan the external pressure, pe, i.e. pi > pe. Assuming thatthe thick shell around the closed pores flows by thepower-law creep, then the strain-rate _e can be given bythe following relationship:

_e ¼ Arn; ð5Þ

formation during HIP.

Fig. 18. Porous NiTi sample sintered from green compact D at 1060 �C:(a) macro-image; (b) longitudinal-image; (c) high-magnification image ofcrack in (b).

Fig. 17. Schematic of single isolated closed-pore model.

Fig. 19. Model used for analysis of pore merging in the solid state.

S. Wu et al. / Acta Materialia 55 (2007) 3437–3451 3449

where A and n are the constants of the special materialsand r is the applied stress during deformation. Under theideal condition that the materials are isotropic and theflow-field has a spherical symmetry, the expansion ratecan be expressed by the following equation:

_q ¼ 3nþ1SA

2nþ1

qð1� qÞ½1� ð1� qÞ1=n�n

Dpn

� �n

; ð6Þ

where S = sign (Dp), q is the relative density after deforma-tion, and Dp = pi � pe. In this case, pi is the backfilled argonpressure of 150 MPa and pe is the instantaneous argon pres-sure, which is continuously reducing from 150 MPa at aconstant rate of 1.67 atm min�1. This expansion modelcan be used to explain the increase in the average pore sizein the as-sintered samples relative to that of the space-holderin the green compacts. The average pore sizes of the as-sin-tered samples produced using green compacts A–D are 57,73, 93 and 128 lm, respectively, whereas the averagespace-holder size is 55 lm. Fig. 18a shows the porous sam-ple sintered from green compact D at 1060 �C. It can be seenfrom the longitudinal image (Fig. 18b) that there is one bigpore in this sample, thereby corroborating that pores ex-pand during stage 2 in the CF-HIP process. In addition toexpansion, Fig. 18b reveals that pores merge in stage 2and the schematic of pores merging is illustrated in Fig. 16.

4.2. Pores merging and expansion in the melted local region

The green compact porosity is above 60% after remov-ing NH4HCO3 when the NH4HCO3 content is over20 wt.%. Hence, some walls between two neighboring poresare much thinner than the above assumed shell. As shownin Fig. 16, some pores merge with each other when theadjacent walls are pierced during expansion. The phenom-enon is verified by our experimental results shown in Figs.7e, 9c and 18b. Elzey and Wadley [52] proposed a modelfor the progression of crack (pore) wall rupture in orderto analyze pore merging. There is a stress field at the poretip region, namely the Hutchinson–Rice–Rosengren(HRR) field [53], as shown in Fig. 19. In our case, the stressfield is induced by the high-pressure argon in the closedpores. Fig. 18c clearly reveals that some closed poresexpanded and emerged by the crack progression. In fact,

with regard to the formation of the porous structure duringCF-HIP, the internal interactive exothermic reactionbetween Ni and Ti plays an important role. Local overheat-ing induces local melting. The pore growth in these regionscan be explained using the semi-solid regime (SSR) pro-posed by Elzey and Wadley [52]. In this case, w, a dimen-sionless ratio, can be utilized to measure the ability of thesurface tension to eliminate ligament curvature and neck-ing between two neighboring pores. w is given by:

w ¼ c4Rl

1

_c

� �; ð7Þ

3450 S. Wu et al. / Acta Materialia 55 (2007) 3437–3451

where c is the surface energy, _c is the shear strain rate, R isthe average pore radius and l is the temperature-dependentviscosity. When w > 106, necking does not occur duringsemi-solid expansion. During the evolution of the porousstructure, the surface tension overcomes the resistance toflow and eliminates the curvature between the neighboringpores. Hence, formation of spherical pores is favored asshown in Figs. 7d and 9a. As the sintering temperature in-creases, the pores expand more effectively and merge by theSSR expansion mechanism because a higher temperature ismore favorable to the exothermic reaction that causes morelocal melting. For example, in the porous NiTi sinteredfrom the green compact D, many circular pores can be ob-served when sintering temperature was 1050 �C (Fig. 7d),and when the temperature is raised to 1060 �C, the exis-tence of a big pore can be observed, as shown in Fig. 18b.

5. Conclusion

Porous NiTi SMAs with different porosities have beenfabricated by CF-HIP with NH4HCO3 as a space-holder.The evolution of the microstructure and porosity of theporous NiTi has been investigated by varying theNH4HCO3 contents and sintering temperature. Two differ-ent creep expansion models are used to analyze the expan-sion kinetics during stage 2 of CF-HIP. When theNH4HCO3 concentration exceeds 30 wt.% and the HIP sin-tering temperature is 1050 �C, porous NiTi with 48%porosity and virtually spherical pores is obtained, and thepore sizes range from about 50 to 800 lm. Compressiontests reveal that the porous NiTi samples with porositiesbetween 21% and 48% have lower Young’s moduli of 6–11 GPa (very close to moduli of human bones), highercompression strength and excellent superelasticity. Thegood mechanical properties and round porous structuresin NiTi with higher porosities arise from the special sinter-ing process during CF-HIP. XRD and high-resolutionsmall area XPS indicate that no space-holder remains inthe as-sintered NiTi samples and on the surface of theinternal pores. Cell cultures reveal that the porous NiTiprepared by CF-HIP with NH4HCO3 as a space-holderhas no apparent cytotoxicity.

Acknowledgements

This work was jointly supported by Hong Kong Re-search Grants Council (RGG) Central Allocation GroupResearch Grant No. CityU 1/04C, City University of HongKong Applied Research Grant (ARG) No. 9667002, andCity University of Hong Kong Strategic Research Grant(SRG) No. 7001999.

References

[1] Hench LL, Ethridge EC. Biomaterials. an interfacial approach. NewYork: Academic Press; 1982.

[2] Hench LL. J Am Ceram Soc 1991;74:1487.

[3] Castleman LS, Motzkin SM, Alicandri FP, Bonawit VL, JohnsonAA. J Biomed Mater Res 1976;10:695.

[4] Sachdeva R, Oshida Y, Fukuyo S, Miyazaki S. In: Ling JJ, editor.Proceedings of the international conference on medical applicationsof shape memory alloys. Shanghai: Shanghai Ion and Steel ResearchInstitute; 1990. p. 98.

[5] Helsen JA, Jurgen Breme H. Metals as biomaterials. New York: -Wiley; 1998.

[6] Suchanek W, Yoshimura M. J Mater Res 1998;13:94.[7] Murray NGD, Dunand DC. Acta Mater 2004;52:2279.[8] Kearns MW, Blenkinsop PA, Barber AC, Farthing TW. Int J Powder

Metall 1988;24:59.[9] Bobyn JD, Stackpool GJ, Hacking SA, Tanzer M, Krygier JJ. J Bone

Joint Surg Br 1999;81B:907.[10] Wu SL, Chu PK, Liu XM, Chung CY, Ho JPY, Chu CL, et al. J

Biomed Mater Res A 2006;79:139–46.[11] Zhao Y, Taya M, Kang YS, Kawasaki A. Acta Mater 2005;53:337.[12] Itin VI, Gyunter VE, Shabalovskaya SA, Sachdeva RLC. Mater

Charact 1994;32:179.[13] Greiner C, Oppenheimer SM, Dunand DC. Acta Biomater

2005;1:705.[14] Assad M, Jarzem P, Leroux MA, Coillard C, Chernyshov AV,

Charette S, et al. J Biomed Mater Res B 2003;64:107.[15] Prymak O, Bogdanski D, Koller M, Esenwein SA, Muhr G,

Beckmann F, et al. Biomaterials 2005;26:5801.[16] Bertheville B. Biomaterials 2006;27:1246.[17] Zhao Y, Taya M, Izui H. Int J Solids Struct 2006;43:2497.[18] Zhu SL, Yang XJ, Hu F, Deng SH, Cui ZD. Mater Lett 2004;58:

2369.[19] Li BY, Rong LJ, Li YY. Intermetallics 2000;8:643.[20] Chu CL, Chung CY, Lin PH, Wang SD. Mater Sci Eng A

2004;366:114.[21] Li YH, Rong LJ, Li YY. J Alloys Compd 2002;345:271.[22] Li BY, Rong LJ, Li YY, Gjunter VE. Acta Mater 2000;48:3895.[23] Kim JS, Kang JH, Kang SB, Yoon KS, Kwon YS. Adv Eng Mater

2004;6:403.[24] Biswas A. Acta Mater 2005;53:1415.[25] Lagoudas DC, Vandygriff EL. J Intel Mat Syst Str 2002;13:837.[26] Tadic D, Beckmann F, Donath T, Epple M. Materialwiss Werkst

2004;35:240.[27] Hayashi T, Sugihara S, Okazaki K. Ferroelectrics 1992;131:75.[28] Tamai M, Miki S, Pezzotti G. J Ceram Soc Jpn 2000;108:915.[29] Yuan B, Chung CY, Zhu M. Mater Sci Eng A 2004;382:181.[30] Dunand DC. Adv Eng Mater 2004;6:369.[31] Degischer HP, Kriszt B. Handbook of cellular metals: production,

processing, applications. Weinheim: Wiley–VCH; 2002.[32] ASTM Standard E9-89a (Reapproved 2000). Philadelphia (PA):

American Society for Testing and Materials; 2000.[33] Ammonia toxicity: a report of the major hazards assessment panel

toxicity working party. Rugby, UK: Institution of Chemical Engi-neers; 1988.

[34] Tan L, Crone WC. Acta Mater 2002;50:4449.[35] Moulder JF, Stickle WF, Sobol PE, Bomben KD, Chastain J.

Handbook of X-ray photoelectron spectroscopy: a reference bookof standard spectra for identification and interpretation of XPSData. Minnesota: Perkin–Elmer, Physical Electronics Division;1992.

[36] Denton DD, Buncick MC, Pranjoto H. J Mater Res 1991;6:2747.[37] Torkar M, Mandrino D, Rosenband V. Vacuum 2005;80:35.[38] Wu SK, Lin HC, Lee CY. Surf Coat Technol 1999;113:17.[39] Chu PK. Nucl Instrum Meth B 2006;242:1.[40] Yeung KWK, Poon RWY, Liu XY, Ho JPY, Chung CY, Chu PK,

et al. J Biomed Mater Res A 2005;75:256.[41] ASTM Standard B328-96 (Reapproved 2003). Philadephia, PA:

American Society for Testing and Materials; 2003.[42] Schuller E, Hamed OA, Bram M, Sebold D, Buchkremer HP, Stover

D. Adv Eng Mater 2003;5:918.[43] Shearwood C, Fu YQ, Yu L, Khor KA. Scripta Mater 2005;52:455.

S. Wu et al. / Acta Materialia 55 (2007) 3437–3451 3451

[44] Massalski TB, Okamoto H, Subramanian PR, Kacprzak L. Binaryalloy phase diagrams. Materials Park (OH): ASM International;1990. p. 2874.

[45] Gibson LJ, Ashby MF. Cellular solids. Cambridge: CambridgePress; 1997. p. 176, 435, 439.

[46] Degischer HP, Kriszt B. Handbook of cellular metals. Wein-heim: Wiley–VCH; 2002. p. 51.

[47] Duerig TW. MRS Bull 2002;27:101.

[48] Morgan NB. Mater Sci Eng A 2004;378:16.[49] Hibbeler RC. Mechanics of materials. 3rd ed. Upper Saddle River

(NJ): Prentice Hall; 1997. p. 94.[50] Ondracek G. Proceedings of the colloquium interfaces in materi-

als. Brussels: KAW; 1988. p. 113.[51] Wilkinson DS, Ashby MF. Acta Metall 1975;23:1277.[52] Elzey DM, Wadley HNG. Acta Mater 2001;49:849.[53] Hutchinson JW. J Mech Phys Sol 1968;16:13.