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ContentslistsavailableatScienceDirect

Acta Biomaterialia

journalhomepage:www.elsevier.com/locate/actbio

Full length article

Microtensile properties and failure mechanisms of cortical bone at the lamellar level R

Daniele Casari

a,

, Johann Michler

a

, Philippe Zysset

b

, Jakob Schwiedrzik

a,

aEmpa, Swiss Federal Laboratories for Materials Science and Technology, Laboratory for Mechanics of Materials and Nanostructures, Feuerwerkerstrasse 39, CH-3602 Thun, Switzerland

bARTORG Centre for Biomedical Engineering Research, University of Bern, Freiburgstrasse 3, CH-3010 Bern, Switzerland

a rt i c l e i n f o

Article history:

Received 10 January 2020 Revised 9 April 2020 Accepted 16 April 2020 Available online xxx Keywords:

Bone

Microtensile strength Lamellar level Failure mechanisms Composite modeling

a b s t r a c t

Bonefeaturesaremarkablecombinationoftoughnessand strengthwhichoriginates fromitscomplex hierarchicalstructureandmotivatesitsinvestigationonmultiplelengthscales.Here,insitumicrotensile experimentswereperformedondryovineosteonalboneforthefirsttimeatthelengthscaleofasingle lamella.Themicromechanicalresponsewasbrittleandrevealedlargerultimatetensilestrengthcompared tothemacroscale (factorof2.3). Ultimatetensilestrengthforaxialandtransversespecimenswas0.35

±0.05GPaand0.13±0.02GPa,respectively.Asignificantlygreaterstrengthanisotropyrelativetocom- pressionwasobserved(axialtotransversestrengthratioof2.7:1fortension,1.3:1forcompression).Frac- turesurfaceandtransmissionelectronmicroscopicanalysissuggestedthatthismayberationalizedbya changeinfailuremodefromfibril-matrixinterfacialshearingforaxialspecimenstofibril-matrixdebond- inginthetransversedirection.AnimprovedversionoftheclassicHashin’scompositefailuremodelwas appliedtodescribelamellarbonestrengthasafunctionoffibrilorientation.Togetherwithourexperi- mentalobservations,themodelsuggeststhatcorticalbonestrengthatthelamellarlevelisremarkably toleranttovariationsoffibrilsorientationofabout±30°.Thisstudyhighlightstheimportanceofinvesti- gatingbone’shierarchicalorganizationatseverallengthscalesforgainingadeeperunderstandingofits macroscopicfracturebehavior.

StatementofSignificance

Understandingbonedeformationandfailurebehavioratdifferentlengthscalesofitshierarchicalstruc- tureisfundamentalfortheimprovementofbonefractureprevention,aswellasforthedevelopmentof multifunctionalbio-inspiredmaterialscombiningtoughnessandstrength. Theexperimentsreportedin thisstudyshedlightonthemicrotensilepropertiesofdryprimaryosteonalboneandestablishabase- linefromwhichtostartfurtherinvestigationsinmorephysiologicalconditions.Microtensilespecimens werestrongerthantheirmacroscopiccounterpartsbyafactorof2.3.Lamellarbonestrengthseemsre- markablytoleranttovariationsofthesub-lamellarfibrilorientationwithrespecttotheloadingdirection (±30°). Thisstudyunderlines theimportanceofstudying boneonall lengthscalesfor improvingour understandingofbone’smacroscopicmechanicalresponse.

© 2020ActaMaterialiaInc.PublishedbyElsevierLtd.

ThisisanopenaccessarticleundertheCCBYlicense.(http://creativecommons.org/licenses/by/4.0/)

Abbreviations: MCF, mineralized collagen fibril; EFM, extrafibrillar matrix; ECM, extracellular matrix; FIB, focused ion beam; SEM, scanning electron microscope;

STEM, scanning transmission electron microscopy; HR-SEM, high-resolution SEM;

BF-STEM, bright-field STEM.

R Part of the Special Issue on Biomineralization: From Cells to Biomaterials, as- sociated with the BIOMIN XV: 15th International Symposium on Biomineralization, held at the Ludwig Maximilian University, Sept 9-13, 2019, organized by Wolfgang Schmahl and Erika Griesshaber.

Corresponding authors. Empa Swiss Federal Laboratory for Material Science and Technology, Laboratory of Mechanics of Materials and Nanostructures, Feuerwerker-

1. Introduction

Bone is a hierarchically structured connective tissue with re- markable mechanical properties.Its primary functions are struc- tural support, locomotion, organ protection, mineral storage and

strasse 39, 3602 Thun, Switzerland. Phone: Tel: + 41 58 765 62 31; Fax: + 41 58 765 69 90.

E-mail addresses: daniele.casari@empa.ch (D. Casari), jakob.schwiedrzik@empa.

ch (J. Schwiedrzik).

https://doi.org/10.1016/j.actbio.2020.04.030

1742-7061/© 2020 Acta Materialia Inc. Published by Elsevier Ltd. This is an open access article under the CC BY license. ( http://creativecommons.org/licenses/by/4.0/ )

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bloodcellproduction[1].Formed andcontinuously remodeledby a cell-mediated process, bone can self-repair and adapt accord- ingtophysiologicalloadsthroughoutlife[2,3].Onthemacroscale, itconsists ofa dense andhard cortex incorporating a trabecular (spongy) structure.Cortical bone accountsfor approximately80%

oftheskeletalmass[1]andhasaprominentrole indefining the overall tissue mechanical properties [4]. In humans, it is largely composed of osteons, cylindrical structures made of concentric lamellaeencompassingcentralbloodvessels(Haversiancanals).In- dividuallamellaeare 3-7μm thick andare composedof bundles of parallel mineralized collagen fibrils (MCFs), typically arranged inplywood-likemotifs[5–8].Embeddedintoanextrafibrillarma- trix(EFM)ofnon-collagenous proteins,extrafibrillar mineralsand water,MCFsmake up the nanostructural buildingblocks ofbone extracellularmatrix(ECM)[9–11].

Byeffectivelymixingsimplecomponents,suchasastiff mineral phase of carbonated hydroxyapatite with a softer organic phase, principally composed of type I collagen and a small amount of non-collagenous proteins, nature constructs a strong and tough nanocomposite [12,13].Brittle mineralplatelets of nanometer di- mensionscan sustainlargestress dueto theirsmallsize[14]and increase the ECM stiffness significantly [15]. On the other hand, the softer organic phase provides flexibility and allows energy dissipation throughout several toughening mechanisms [16–23]. Through its complex hierarchical organization spanning several lengthscales, boneisable toincrease itstoughness bya several- foldincrease[20].Asaresult,boneistoleranttodefectsgivingrise tostress concentrations,such as lacunae andcanaliculi (contain- ing bone cells and their processes), cavities encompassing blood cells,aswell asinternalmicrocracks.Bone’sresistancetofracture originates from the great number of interfaces distributed over thewholehierarchicalarchitecture[19,24,25].Interfacesplayakey rolein dissipatingenergyby creatinga multitudeofdeformation andtoughening mechanisms that act simultaneously at different length scales [20,26]. Learning how nature attains thisattractive combinationofmechanicalproperties froma limitedselection of constituents can provide useful insights for the development of multifunctional bio-inspired materials [27,28]. At the same time, abetter understanding of bone failure mechanisms andmechan- icscan leadto improvementsinbone fractureprevention inage- relateddiseases [29,30]. Because of bone’s structural complexity, understandingandseparatingtheroleofsinglecomponents,their organizationandtheirinteractionacrosslengthscales ischalleng- ingandrequiresstudiesonseveraldifferentlengthscales[11].

Recentadvancesinexperimentaltechniques,suchasmicropillar compressiontomeasuretheuniaxialmechanicalresponseofama- terialatthemicrometerscale[31],allowedto shedlightonbone yieldand failure properties,aswell as onits deformation mech- anismsatthe lamellar level [32–36]. Thesestudies highlighted a greater strength compared to macroscale that was attributed to ascale-dependent flaw distribution [34]. Micropillarcompression alsorevealedapparentductilitywiththeabsenceofdamageupto failure[32].Thisisincontrasttothequasi-brittleresponseseenat themacroscale,inwhichfailure istypicallycausedbygrowthand coalescenceofmicrocracksgeneratedatinterfaces,orinthevicin- ityofpores [37].MCFsbridging andkinking,crackdeflectionand ligamentbridgingwereidentifiedasmaintougheningmechanisms in compression [32,35]. These experiments have been extremely helpfultobetter understandbone hierarchicalstructurebutwere so far limited to compressive loading. Macroscopically, bone ex- hibitsa loadingmode asymmetry andfailsat considerablylower stressesundertension.Thenanocompositenatureoflamellarbone suggeststhata strength asymmetry mightalsobe presentatthe microscale.Since fracture istypically initiatedin tension,charac- terizingboneunderthisloadingmodeisparticularlyimportantfor clinical studies. To investigate this, we developed a microtensile

setup [38] and performeduniaxial tensile experiments on single bonelamellaepreparedbyfocusedionbeam(FIB)milling(Fig.1).

The aim of this study was (a) to characterize the anisotropic tensileyield andfailure propertiesofbone atthe length scaleof asinglelamella,(b)torevealtherespectivedeformationandfail- ure mechanismsunder uniaxial tensileloading,and(c) topostu- late a failure modelable to predict the anisotropic compression- tension strength asymmetry of the ECM.Microscopic ovine bone tensile specimens were fabricated via focused ion beam milling onprimary osteonalbone alongaxialandtransverseorientations.

Thespecimens weresuccessivelytestedinuniaxial tensioninside a scanningelectronmicroscope (SEM).Analyticaltechniquessuch asscanningtransmissionelectronmicroscopy(STEM)andfracture surfaceanalysisby high-resolutionSEM(HR-SEM)wereemployed to reveal nanoscale deformation and failure mechanisms under tension.Thefindingswere comparedtopreviousmicroscalecom- pression data obtainedin similar conditions.Finally, a composite failure model based on physical considerations wasidentified to capturethemicromechanicalstrengthoflamellarbone asafunc- tionoffibrilorientationforbothtensionandcompression.

2. Materials&Methods 2.1. Samplepreparation

An ovine tibia (2 years old) was obtained from a local abat- toirandcutatthediaphysisintoaxialandtransversesamplesus- ing a diamond-coatedband saw (Exact, Germany).Samples were gluedontoSEMstubsusingcyanoacrylateglue(Ergo5011,Switzer- land) and air-dried. Smooth and flat surfaces were obtained by ultramilling (Polycut E, Reichert-Jung, Germany). A 10 nm thick Au film was sputtered (Leica ACE600, Germany) on the samples to reduce chargingduringelectronandionbeam irradiation.Mi- crotensilespecimensofgauge dimensionsof1.5μmx5μmx10 μmwerefabricated attheedges ofthesamplesvia top-downFIB millingonovineprimaryosteonalboneinaxialandtransverseori- entations,followingapreviouslyestablishedprotocol[38].Axenon (Xe) plasma-FIB (Tescan Fera, Czech Republic) operated at 30kV wasemployedfortheroughmilling,whileagallium(Ga)FIB(Tes- canLyra,CzechRepublic)operatedat30kVandsuccessivelyat5 kVwasusedforthefinal preparationstepstominimize FIBdam- age. Prior to FIB milling, a platinum (Pt) cap of 1 μm thickness was deposited on the top of the area of interest, to reduce sur- faceroughness("curtaining")andFIBdamage.Samplecuttingand fabrication,includingspecimenorientation,are illustratedinSup- plementaryFig.S1.Atotalof27tensilespecimenswerefabricated (13axial,14transverse).Fivespecimens(3axialand2transverse) werediscardedfromthestudyastheyincludedosteocytelacunae orvisiblemicrocracks.

2.2. Microtensiletesting

An in situ micromechanical testing platform (Alemnis AG, Switzerland), equipped with a self-aligning single crystal silicon (Si)gripper(SupplementaryFig.S2a,b)[38],wasusedtopullthe specimens in displacement control. Experiments were performed invacuum, inside an SEM(Zeiss DSM962,Germany)operatingat 5 kV to allow for precise positioning and tracking of the defor- mationmechanisms.Tensiletestswereconductedataquasi-static strain rateof ~ 3·104 s1, which is in the same order ofmag- nitudeasthestrainrateappliedinprevious micropillarcompres- sion testson ovine lamellar bone [32]. Foreach orientation (ax- ial andtransverse), fivespecimenswere loaded untilfailure after beingsubjectedtothreepartialloading-unloadingcyclesduringa

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Fig. 1. Hierarchical organization of bone with respect to the microtensile specimen geometry. Bone exhibits a hierarchical structure spanning from the organ level to the molecular level. MCFs and EFM constitute the fibers and matrix of the bone ECM composite. To characterize the tensile properties of bone at the lamellar scale, microtensile specimens featuring gauge dimensions in the order of a few microns are tested under uniaxial conditions.

portionofthelinearelasticresponse.Thiswasperformedtomea- sure the elastic modulus since duringthe unloading segments it is assumedthatthe specimendeforms elastically.The restofthe specimenswereloadedmonotonicallyuntilfailure.Supplementary Video1 showsan exampleof acyclic test(video speed:30x ex- perimentalspeed).Force anddisplacementwere monitoredat20 Hz samplingrate. Gauge displacementwascomputed by correct- ing the totaldisplacement by theinstrumentandsubstrate com- pliance, asexplained in detail elsewhere [38]. Engineering stress was obtained by dividing the measured force by the specimen gaugecross-sectionalarea,whileengineeringstrainwascalculated by dividingthecorrectedgauge displacementbythe initialgauge length. Stress-straincurves were offsetto correctfor theadapta- tionresponse(toeregion)observedduringinitialcontactandself- alignment. The correctedzero pointsofstrain were calculated as the intercept of the linear regression of the elastic part of the stress-straincurveswiththezero-stressaxis[39].Bothengineering valueswereconvertedtotruestress-straindatausingtheassump- tionofnegligiblevolumechange.

2.3. Imagingandmicrostructuralcharacterization

Microtensile specimenswere imagedbeforeandafterthe me- chanicaltestsusingahigh-resolutionSEM(HitachiS-4800,Japan) operated at 1.5 kVand 10 μA to measure their dimensions and accurately identifythefracture surfaces’main characteristics.Two axial and three transverse specimens with representative failure stresses were chosen for furtheranalysis.Specifically, a TEM lift- out technique was employed to prepare thin sections for STEM analysis [35] in two main orientations (as specified in Supple- mentaryFig. S2e).Lateralsectionswere obtainedby thinningthe fractured gauge section of the specimens, while frontal sections were milledinthebaseofthespecimens.BF-STEMimagesofthe thinsectionsweretakeninahigh-resolutionSEM(HitachiS-4800, Japan)using atransmissionelectron detectorwhileoperatingthe microscope atan accelerationvoltageof30kVandbeamcurrent of 10 μA. Fibrilorientation wascharacterized usingthe software ImageJ (NIH, Bethesda, Maryland, USA). The plug-in OrientationJ (BiomedicalImagingGroup,EPFL,Switzerland),basedonstructure tensors,wasusedtoevaluatelocalfibrilorientation[40].Avector field analysiswasperformedover aselected region ofinterestof 6× 3μm2 fromtheBF-STEMimages.Afinitedifferencegradient withaGaussianwindowof125nmsizewasappliedoveragridof 125nm periodicitytogeneratelocalorientationsproperties(Sup- plementaryFig.S3). Fromthisdataset,meanfibrilorientation and standarddeviationwereevaluatedusingMATLAB(TheMathWorks, USA)assuminganormaldistribution.

2.4.Failurecompositemodeling

Strength as a function of MCF orientation was modeled us- ing the improved Hashin’s failure criteria [41] developed by Gu andChen[42].Foraunidirectionalfiber-reinforcedcomposite,the planestressfailurecriteriacanbesummarizedwiththefollowing equations:

Tensilefibermode

σ

11 >0

σ

11

T11 = 1 (1)

Compressivefibermode

σ

11 <0

σ

11

C11 = 1 (2)

Tensilematrixmode

σ

22 >0

−2Pt

S21

σ

22+ 1+

2PtT22 S21

T222

σ

222+

τ

212

S221 =1 (3)

WherePtcanbedescribedby Pt=

1

C22C22

4S223

S21

2 (4)

Compressivematrixmode

σ

22<0

− 1 C22 + C22

4S223

σ

22+

σ

222

4S223+

τ

212

S221 =1 (5)

Where

σ

11,

σ

22 and

τ

21 denotetheresolvednormalandshear stresses.T11 and C11 stand for the uniaxial tensileand compres- sive strengths along the longitudinal fiber axis. Whereas, tensile andcompressive strengths in thetransverse orientation are indi- catedby T22 andC22,respectively. Finally, S21 and S23 represent theshearstrengths orientedparallelandperpendiculartothefib- rildirection,respectively(illustratedinSupplementaryFig.S4).

Toevaluatethemodel,compressivestrength C11 andC22 were setto0.49GPaand0.30GPa,respectively.Thesevaluescorrespond tothe compressive yield stressesmeasured by Schwiedrzik etal.

[32] viamicropillarcompression.The shearstrength betweenthe fibrilandtheextrafibrillarmatrixalongthefibrildirection(S21)in dryconditionswascalculatedbasedontheexistingliterature.The influence of hydrationon compressive strength wasobserved by Schwiedrziketal. [35],in which

σ

hydrated/

σ

dry = 0.4. If thisra- tioiscombined withtheshearstress measured by Guptaandal.

[18]inthehydratedstate(80MPa),itispossibletopredictS21in dryconditions(200MPa).Theshearstrengthperpendiculartothe fibrildirectionS23 wassetto280MPabasedonthecriticalshear strengthfoundfortransversemicropillarcompressionindrycon- ditions[32].Atfirst,thefailure criteriawere evaluatedinMathe-

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Fig. 2. Microtensile anisotropic response of lamellar bone. Representative true stress-strain curves for axial (a) and transverse (b) tension of ovine bone at the length scale of a single lamella.

matica(WolframResearch,Inc.,Version12.0,Champaign,IL)byus- ingtheaveragemeasuredmicromechanicaldataandtheirassumed fibrilorientationbasedonsampletype(axial=0°;transverse90°).

Themodelwaslateroptimizedvialeastsquareoptimizationbyfit- tingspecificstrengths andrespectiveaverageMCFsorientation of threemicrotensilespecimensforwhichthemicrostructurewasin- vestigatedbySTEM.Forthefirstcase, allparameterswere prede- termined.Forthesecond case,T11 andT22 werefitted,while the restoftheparameterswereset.

2.5.Statistics

All datamanipulationsandstatisticalanalysiswere performed using MATLAB. Normality of the distributions was tested by the Kolmogorov-Smirnov normality test. Measurements are reported as mean ± standard deviation. Significant differences between datasets were tested using two-tailed t-tests. The significance thresholdwaschosenwithanerrorprobabilityp≤0.05.

3. ResultsandDiscussion

3.1.Microtensilepropertiesoflamellarbone

Uniaxialtensiletestswereperformedatquasi-staticstrainrates of3·104s1onspecimenshavingthicknessesof5.29±0.42μm (mean± standarddeviation),widthsof1.80 ±0.13μmandgauge section lengths of 10.02 ± 0.25 μm. All tested specimens failed within thegauge section. Representative truestress-strain curves obtained from both monotonic and cyclic tests are displayed in Fig.2.Thefullcollectionofthestress-straincurvescanbefoundin SupplementaryFigureS5.Itcanbeobservedthatspecimensexhib- itedapparent brittle failure. Microtensile testsshowedanisotropy inboth strength andstiffness. Axialspecimens were significantly stiffer(p=1.15105)andstronger(p=8.461011)whencom- paredtotheirtransversecounterparts.Elasticmoduluswas27.7± 3.4GPa inaxial orientation and13.6 ±1.1GPa intransverseori- entation. Strength was 0.35 ± 0.05 GPa at 1.8 ± 0.2% strain for axialspecimens,and0.13±0.02GPaat1.3±0.3%strainfortrans- versespecimens.Asexpected, bothstiffnessandstrength showed aprominentanisotropy.

The apparent elastic moduli measured in this study were similartotheonesreportedbymicropillarcompressionperformed on ovine bone [32] and bovine bone [33] in the same testing conditions. Several studies can be found in the literature using

nanoindentationasawaytocharacterizebothelasticmodulusand hardnessforosteonal boneindryconditions[43–49].Oneshould howevercomparetheelasticmoduliobtainedviananoindentation with the datain this studywith some caution for the following reasons. Most of the studies focused on human Haversian bone.

While ovine andhuman bonesshow comparable mineralto ma- trix ratios (Supplementary Information A: Raman spectroscopy), HaversianboneinhumansexhibitsmorecomplexMCForientation patterns (plywood like organization), whereas primary lamellar ovine bone has a ratheruniaxial MCF orientation [35]. The cited nanoindentation studies are based on the Oliver-Pharr method [50] andoften assume the testedmaterial testedto be isotropic.

Thecomplexstressstate belowtheindentation surface,especially in the case of heterogeneous and anisotropic material such as bone,involvesnon-uniformdeformationsinallprincipalaxes.This explainswhyinmoststudies,the reportedelasticmodulus along axial (longitudinal) orientation was lower than the one reported here. The opposite trend was observed for the elastic modulus reported for transverse orientation. However, when interpreting the nanoindentation results using an anisotropic stiffness tensor [51],the literature data fitwell towhat was found inthis study [32,51]. The measurements reportedin Table 1also fitwell with the model proposed by Reisinger et al. [52,53] for a uniaxial mineralized fibril-array in dry conditions, as well as with the modelbyHamedetal.[54]foralignedfibrilswithacorrectionof a20%increaseinstiffnessinalldirectionsfordrycondition[44].

The measured strength on the microscale was considerably larger than what has been reported at the macroscale [55]. A greaterstrength atlowerlength scaleshighlights theinfluenceof thehierarchicalorganizationofboneandisassociatedwithascale effect. In bone, the absence of microdamage, cement lines, and large pores [56], such asHaversiancanals andosteocyte lacunae, resultsinafactorof2.3higherstrengthofmicroscalespecimens.

A similar scaling ratiohas been reportedfor compression exper- iments [32]. Although the volume testedhere wassmaller (38%) thantheonetestedincompression,webelievethatadirectcom- parison betweenthetensileexperiments performedinthisstudy andearliermeasurements incompressionisjustified.Evenbyas- sumingMCF diametersupto200 nmandafibervolumeratioof nomorethan50%,atleast100structuralunits(MCFs)arepresent in the testedvolume. It would be surprising to observe a speci- mensizeeffectforthisscale.ThenumberofMCFsisalsocompara- blewiththenumberofosteons,structuralunitsatahigherlength scale,foundini.e.astandardmacroscopicsamplemeasuring3mm

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Table 1

Micromechanical properties of cortical bone on the microscale. Compression and tensile properties of primary lamellar bone tested in vacuo; mean ±standard deviation of elastic modulus E, maximum stress σmax, strain at maximum stress ε( σmax) and yield stress σy. Whereas, N is the number of specimens tested in the respec- tive loading mode. These data were collected at quasi-static strain rates of ≈3-5 10 −4s −1in both axial and transverse orientations via in situ microtensile tests and micropillar compression.

Sample Orientation Loading mode E (GPa) σmax(GPa) ε( σmax) (%) σy(GPa) N (-) Axial Compression 31.1 ±6.5 0.75 ±0.06 5.4 ±1.7 0.49 ±0.10 19

Tension 28.9 ±3.4 0.35 ±0.05 1.8 ±0.2 - 10 Transverse Compression 16.5 ±1.5 0.59 ±0.04 12.1 ±2.5 0.30 ±0.02 20 Tension 13.6 ±1.2 0.13 ±0.02 1.3 ±0.3 - 12

Data from Schwiedrzik et al. [32] .

indiameter[32].Infact,osteonsdiameterrangesbetween170um and270μm,whereastheir densitytypicallyvariesbetween15to 25unitspermm2dependingonage[57–60].Ourhypothesisisfur- thersupportedbythereportedabsenceofastrengthsizeeffectin therangebetween1and5μmdiameterreportedforcompression ofbonemicropillars[34].

3.2. Tension-compressionasymmetry

Bone, like other brittle materials, is stronger in compression than in tension. Comparing the microtensile data with previous micropillar compressionexperiments,it canbe observedthat the tension-compression strength asymmetry is also seen atthe mi- croscale andisthereforean inherent tissueproperty. Thisis well showninTable1,wherethemicromechanicalpropertiesofovine bone are summarized for both tension and compression exper- iments for dry testing. At the lamellar scale, bone is strongest when compressedalongits mainaxis,exhibitingstrength of0.75

± 0.06 GPa. Contrarily, it performs poorly when it is tested in tension normal to the main MCF orientation and fails at 0.13 ± 0.02GPa.From Table1itcanbe observedthat theloadingmode hadminimalinfluenceontheelasticresponseofbone.Theelastic modulus fortheaxial orientationshowedno statisticaldifference (p = 0.50) between compression and tension. Transverse elastic modulusshowedasignificant(p=9.210−3)butrelativelysmall differencebetweenthetwoloadingmodes.Thisismostlikelydue to the limitedamount of samplestested in tensioncompared to compression.

When the post-yield behavior at the length scale of sin- gle lamellae is compared between loading modes, there is a significant differencebetweentensionandcompression.Forcom- pression, a significant ductility was found. This is not the case for tensileloading for which apparent brittle failure is observed.

Interestingly, strength anisotropy was much more pronounced in tension. In compression,the ratio between ultimateaxial and transversestrengthis1.3,whereas,intension,thisvalueincreases to2.7.Afactorof2.1isthusseenbetweenthetwoloadingmodes.

Asimilartrendisalsonoticedwhenultimatestrengthisreplaced by yield stress (factor of 2.9). The increased strength anisotropy seen in tension compared to compression hints at a change in failuremechanismcallinguponamorein-depthanalysis.

3.3. Failuremodeanisotropy

Images of the fracture surfaces, obtained by high-resolution SEM, confirm that axial and transverse specimens failed in two different ways. Fig. 3 shows the fracture surfaces for three axial specimens(Fig.3a,b,c)andthreetransversespecimens(Fig.3d,e,f).

Here, different morphologies can be distinguished based on the sampleorientation.Axialsurfacesappearroughandrevealanover- allporousstructure.Poresizerangesbetween40to60nmandis comparabletothediameterofindividualMCFs[61].Asinprimary ovine bone MCFs appear mainly oriented along the longitudinal

Fig. 3. Fracture surfaces of axial and transverse specimens. SEM Top view of the fracture surfaces for axial samples (a,b,c) in which canaliculi are seen (white ar- rows). Contrarily, in transverse samples (d, e, f) the lacuno-canalicular network is seen only occasionally. In all specimens, a thin FIB redeposition layer (50-200 nm thickness) is seen in the back of the specimen (black arrows). Scale bars represent 1 μm.

axisofosteons[35], theobservedsurfacetopography(Fig.3a,b,c) can be rationalizedwitha fibril-matrix shear interface failure. In thiscase,interfacesfailurebetweenMCFandEFMleadstosucces- siveMCFsbeingpulledout,resultingina roughandporousfrac- turesurface. Inaxial specimens, canaliculi were presenton each fracturesurface. Inthetransverseorientation,a differentscenario isobserved.Transverse specimensexhibit globallysmootherfrac- ture surfaces with fewer steps andshow a rich fiber texture in the fracture plane. Furthermore, canaliculi were present in only 42%ofthefracturesurfaces.Inalltransversespecimens,thefrac- tureplane wasfound to be highlyorthogonal to the loading di- rection (<3°). As MCFs are mostly aligned perpendicular to the loadingorientation it isvery likelythat thesurfaces displayedin Fig. 3d,e,f are the product of a fibril–matrix interfacial decohe- sionintension,incontrasttointerfacialshearfailureinthe axial direction. Microtensile specimens reveal therefore a failure mode changewhenloadedindifferentorientations.Incompressionsuch a change is absent, and matrix shear failure is always observed [32].Thehigherstrengthanisotropy dependencyobservedinten- sioncompared to compression mightbe explained by thisdiver- gence.

3.4.Influenceofcanaliculiandweakinterfaces

In axial specimens, cracks are always initiated at canaliculi.

Sincecanaliculiare typicallyorientedradially insideosteons[62], theymainlylieperpendiculartotheloadingdirectioninaxialsam- ples.Thesemicrostructuralfeatures leadtolargestressconcentra- tions in thematerial, but they serve a biological function by ac- commodatingosteocytes processes. In the transverse orientation, canaliculi were seen in only 42% of the fracture surfaces. Inter-

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estingly, when a canaliculi was present on the fracture surface themeasured strength(

σ

max =0.11±0.01GPa)wassignificantly lower(p=1.9210−3)thanintherestofthecases(

σ

max =0.15

±0.02GPa). Nosignificantdifferencewasfoundintermsofstiff- ness(p=0.81).Thedifference instrengthbetweenthesetypolo- giesoftransverse specimensmight beexplained by thefact that thetransversespecimens’orientationrangesbetweencircumferen- tialandradial directions. While MCF arrangementis expectedto be transverselyisotropic, porosity isnot. In circumferential spec- imens,canaliculi arepresentalmost perpendicular to theloading direction.Similarly to axialspecimens, thehighstress concentra- tionsinthevicinityofthecanaliculidominatefailureandcreatea fracturesurfacecontainingacanaliculus.Contrarily,inradialspeci- mens,thecanaliculipredominantlyrunalongtheloadingdirection andfailure seems to be dominated by other effects. Bright-field STEM (BF-STEM) performed on both tested and non-tested sec- tions ofmaterial (Supplementary Fig. S6)revealed no observable differencesintheMCForganization,suggestingtheabsenceofsig- nificantductile deformation before failure occurred. Interestingly, regions with ordered anddisordered MCF motifs were observed.

Thisisin linewithearlierstudies [8,35,63] andshowsa keyde- signfeature for crack deflection at the microscale. The interface betweenadisordered andordered phase actsasa weak layer in thestructurethat servestodeflectacrackawayfromtheoriginal planeoffracture.Thisiscomparabletotheeffectoflamellarinter- faces[23,64,65]atthe samelengthscale,aswell ascement lines [66–68]athigherlengthscales.FromtheSTEMimages,itappears thattheseweakinterfacesaretypicallyorientedwiththelongaxis ofosteons. When loaded in tension, as is the case in the radial specimens,theseinterfacesfail bydelaminationofMCF andEFM.

Ifthishappens, fracture surfaceswill reveal aclear fibertexture, asseeninFig.3e.

3.5.Microscalefracturetoughness

Using the modeling assumption that a canaliculus passing through a specimen acts asa through-crack inside a finite plate [69], it is possible to estimate the magnitude of the conditional fracturetoughnessKIQ(modeI)forallaxialspecimens,aswellfor thetransversespecimensexhibitingcanaliculionthefracturesur- face. Using the solution reported by Tada etal. [70] the mode I stressintensityfactorKI foracrackthrough afinite platecanbe describedas:

KI=

σ

π

a

sec

π

a

2T

1/2

1−0.025

a

T

2

+0.06

a

T

4

(6)

Where

σ

isthestress applied,aisthehalf-widthofthecrack

andT isthehalf-thicknessofthe plate,in ourcasethethickness of the specimen. Considering the canalicular diameter measured onthe fracture surfaces (160 ± 59nm), thecritical stress inten- sityfactoris0.17±0.03MPam1/2 and0.07 ±0.01MPam1/2for axialandtransverse orientations,respectively. Thesevalueslikely areonlyaroughestimate ofmicroscalebone’sfracturetoughness in dry conditions as they neglect the finite radius of the initial flawandthemisorientationofthecanaliculitothesurfacenormal, andmightbecalculatedforplanestressconditions.However,they servetohighlight asignificant scale effectsimilarto earlierfind- ings [35,71]. The fracture toughness at the microscale estimated hereis atleast an order of magnitudesmaller than the one ob- servedatthe macroscale[20,66].This islikelycaused bythe ab- senceofextrinsictougheningmechanismssuchascrackdeflection atcement lines,crack-ligament bridging andconstrained microc- rackingwhensmallvolumesofECMaretested.Thisresultunder- lines the importance of bone’s architecture forits fracture resis- tance.

3.6. Microstructureandstrengthcompositemodeling

Inorder torelate the mechanicalbehavior andfailure mecha- nismstothefundamentalmicrostructure,thinsectionsofmaterial were prepared from severalfailed tensile specimens andimaged using BF-STEM. Lateral sections were manufactured by thinning thewidthofthespecimenfracturedgaugesections,whilefrontal sectionswerefabricatedfromtheunderlyingsubstrate(schematics inSupplementaryFig.S2e).Fig.4illustratesthreeBF-STEMimages takenfromlateralthinsectionsoftwoaxialspecimens(Fig.4a,b) and a transverse specimen (Fig. 4c). Darker areas are associated withhigheraveragemassduetostronger electronscattering.Be- causecollagenmoleculesarestaggeredaxiallyalong fibrils[72],it ispossibletoseethefibrousstructureoflamellarbonewhenMCFs primarily lie in the image plane. Ordered regions are identified through the presence of characteristic gap zones (less dense re- gions)andtheirrespectiveperiodicbandingpatternof67nm(al- ternatingdark-brightcontrast).Ingeneral,STEMobservationssug- gested that, differently from secondary osteons, for which MCFs seem to organize in ply-wood like motifs [5–8], the investigated primaryovineosteonsexhibitanoverallhomogeneousMCForien- tation witha general texture along the osteonmain axis.In the twoaxial specimensseeninFig.4,MCFsareorientedattwo dif- ferent (p< 1 1015) angles of8.7 ± 6.4°(Fig. 4a)and 24.5 ± 17.9°(Fig.4b)withrespectto theloadingdirection. Theirrespec- tivefrontalsectionsalsoexhibitedadifference (p< 110−15)in MCF orientation with angles of 5.6 ± 8.8° and12.7 ± 10.9°, re- spectively. Inthe transverse specimen,fibril orientation was88.2

±11.7°(Fig.4c).FrontalSTEMimagescanbefoundinSupplemen- taryFig.S7.

Interestingly,thespecimenshowninFig.4ahasamorecoher- entlyorientedMCFmicrostructurewithanaverageasmalleroffset from the loading directionthan the sample displayed inFig. 4b, but it failed atlower stress (81% of the maximum). This behav- iorseemscounterintuitiveatfirstglance,asonewouldexpectthe materialtobestrongeralongthemainfibrilorientation.However, bone is different from a common engineering composite, which commonlyfeatures stiff andstrong fibersembeddedintoa much more compliant matrix.Here the difference in strength between fiberandmatrixis lessstriking.Moreover, thehighmineralcon- tentpresentintheEFMallowsrelativelyhighshearstrength(upto 280MPain dryconditions[32]), causingamaximum instrength when theunderlyingMCF organization is testedatan angle

θ

= 0°.

Becauseofitssub-lamellarMCForganization,beingmostlyuni- axial, ovine primary osteonal bone on the microscale might be consideredasaunidirectionalfiberreinforcedcomposite.Theclas- sicfailure composite modelproposed by Hashin’s[41] is a well- established model which considers four distinct failure modes – tensileandcompressivefiberandmatrixmodes– andcanbeused todescribethestrengthasafunctionofMCF orientationinbone.

Theimprovedandre-examinedversionoftheHashin’smodel,pro- posedby GuandChen [42],wasapplied tothe datacollectedin thisstudytodescribebonestrengthasafunctionofMCForienta- tion.

At first, the Hashin’s model was evaluated using the data in Table1andassumingMCF orientationof

θ

=0°and

θ

= 90°for axialandtransversespecimens,respectively(dashedlinesinSup- plementary Fig. S8). Despite this generic assumption, the model showed a characteristic trend with maximum strength for MCF mainorientation

θ

=0°.ThisistruedespitethefacttheMCFmain orientation is slightlydifferent for each specimen. A more accu- ratedescription of thetensile behavior oflamellar bone isgiven in Fig. 5, where the MCF main orientation obtained by STEM is considered for the fit. Instead of using the averaged data from Table 1to evaluate the model,in Fig.5 the modelis fitted with

(7)

Fig. 4. STEM imaging of deformed microtensile specimens. BF-STEM images of three lateral thin sections for axial (a, b) and transverse (c) specimens after fracture. The in-plane fibrils’ organization is visible through the characteristic 67 nm collagen banding pattern. In (a), (b) and (c) scale bars represent 1 μm. A higher magnification image (d) highlights the collagen banding pattern (white arrow) and the presence of mineral crystals (black arrow). Unfortunately, crystal geometry could not be fully resolved because of the limited resolution of low voltage STEM. An amorphous layer accounting for less than 35 nm (produced during FIB milling) and a thin layer of Pt are also visible at the edge of the section (grey arrow). A high magnification image of a crack (e) observed in the axial orientation shows roughness at the level of single fibrils as well as fibril bridging. In (d) and (e) scale bars represent 500 nm.

the individual strengths and respective MFC angles of the three tensilespecimens(illustratedinFig.4a,b,c),vialeast-squareop- timization.Thismightbeamorerepresentativedescriptionofthe materialstrengththantheonedescribedearlierbecauseSTEMcan accessspecificMCForganizationthroughthespecimengaugesec- tion. The material propertiescan, therefore, be related to a spe- cific microstructure rather than an assumed average microstruc- ture.Tosummarizethedehydratedmechanicalpropertiesoflamel- lar bone, both tension and compression are illustrated in Fig. 5. Strengthuncertaintiesforthedisplayedindividualdatapoints(ver- ticalerrorbarsforthetensioncase)werecalculatedbyerrorprop- agationanalysis, withtheassumption ofrandomindependent er- rors[73]usingforceandSEMmeasurementsuncertainties(4μNfor forcemeasurementand100nmforgeometricaldeviations).

Theoptimizedmodelpredictsatensilestrengthof330MPaand 125MPaforspecimenshavingfibrilsalignedparallelandperpen- dicularly totheloaddirection, respectively.Themaximumtensile strengthof407MPaisfoundatanangleof26°,whereasthemax- imumcompressiveyieldstrengthof553MPaisfoundatanangle of21°.Theselimitsdenotethechangebetweenfiberfailuremode andmatrix failuremode. Whilethis resultseemsstriking, asim- ilar behavior wasfirstpredictedby Wagner andWeiner [74]and later observed in the case of lamellar stiffness[52,75], withthe latterbeingthelargestatan anglebetween10°and30°withre-

specttothemainosteonaxis.Thegeneraltrendillustratedbythe modelinFig.5 alsocorrelateswell withtheobservations ofWa- germaieretal.[76],Spieszetal.[77] forwhichthe averageMCF mainorientation overseveralhuman osteonallamellaewasmea- suredwithanoffsetof20-30°withrespecttothebone’slongaxis.

SimilarresultswerealsoobservedbyTurneretal.[78]forcanine osteonalbone.Interestingly,thehightolerance(±30°)infibrilori- entationwithrespecttothenanocompositestrengthremainswell noticeable even when taking into account the weakening effect proposed by GuandChen [42] intoHashin’s model(Supplemen- taryFig.S9). Such tolerancemightsuggest theadvantageofrear- rangingtheMCForganizationinsidealamellafromauniaxialpat- terntoaplywood-likepattern[5–8].Moreprecisely, thevariation offibrilangles acrossthe newlyformed tissuecould bea wayto improvebone’sfracturetoughness,whilestillretainingthemajor- ityofitsoverallstrength[79,80].

The illustrated model is most likely an oversimplified repre- sentation of the behavior of lamellar bone but it gives an es- timate of the strength of dry bone. The model neglects factors such as variation in mineralization, MCF waviness and distribu- tion along the main orientation. While a model based on con- tinuum micromechanics might be used to account for thesead- ditionaleffects [81,82], the simple model considered hereseems wellsuitedtocapturethegeneraltrendoftheanisotropicloading

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Fig. 5. Composite failure model of ovine lamellar bone on the microscale in tension and compression. Compressive (blue) and tensile (red) strength of lamellar bone as a function of fibril orientation. The graph is illustrated with the schematics of the offset angle θ between loading orientation and MCF main orientation. Individual strengths of the tensile specimens displayed in Fig. 4 are indicated with their re- spective MCF main orientation. Compressive yield strengths taken from the litera- ture [32] were also fitted with the composite failure model. The error bars in the tension curve denote the experimental uncertainty of individual measurements and are obtained by error propagation analysis.

mode-dependent strength in bone atthe microscale. Evenwhen themodelwasoptimizedtofitthefivedatapointsshowninFig.5, itstillexhibitsthesamecharacteristictrendwhenbiologicalvaria- tionsareconsidered(i.e.fittingthemodelwiththedatainTable1, illustrated inSupplementary Fig. S9). While failure hasshownto bedominatedbycanaliculiduetostressconcentrations,themodel implicitlytakesintoaccount theireffectandsincetheseflawsare fairly consistent in size and well distributed incortical bone for manyspecies, including humans [83,84], the Hashin’s composite failuremodelpresentedherecan beconsidered tobe wellrepre- sentativeofthetissuebehaviorinanaveragesense.

3.7.Limitationsofthestudy

A well-known limitation in micromechanics is the limited quantity ofsamples dueto thetime consuming preparationpro- cess.Here,bothaxialandtransversesampleswerecollectedfrom the same tibia. Nevertheless, since osteons are created individu- allyandonly intwocasestwo specimenswere fabricatedon the sameosteon,theauthorsbelievethespecimensmaybetreatedas non-related.Primaryovineosteonalbonewaschosen overhuman osteonalboneforitssimplerandratherhomogenousMCF organi- zation,thus makingthedata interpretationmorestraightforward.

Learningabout the basicdeformation andfailure mechanisms in lesscomplexmodel materials isa prerequisite forimproving our understandingofhuman bone.Based onthebehavior ofan indi- vidual(uniaxiallyoriented) lamellarply, we are ableto construct thebehavior ofmore complex laminates containingseveralplies usingmodelingapproaches.IfinhumanstheMCFsarearrangedin plywood-likeorganizationinsidetheosteons,classiclaminatethe- oryormorecomplex finiteelement modelscan beused tobuild aspecific modelabletopredictthebehaviorofhumanbone.This ishoweverbeyondthescopeofthismanuscript.Intermsofmin-

eralto matrixratio,humanandovine bone aresimilar andadi- rectcomparisonbetweenthetwo,foraunidirectionallamellarply, seemsjustified.ThiswasconfirmedbyRamanspectroscopy,which revealed mineral/matrix ratios (v2PO4/Amide III; Supplementary Fig.S10) of0.63± 0.05and0.76± 0.08foraxial andtransverse samples,respectively (Supplementary InformationA). These min- eral/matrixratiosareinthesamerangeaswhatisreportedinthe literature forhumanosteonal bone[85,86] andhuman trabecular bone[87].

Anotherlimitationto beconsidered isthatspecimens arefab- ricated via FIB milling. Fabrication artifacts such asredeposition (Fig.3)andFIBdamage(Fig.4d)mightaffectthemechanicalprop- erties of the specimens. Based on previous Monte Carlo simula- tions forGa+ irradiationon bone[32],aswell asfromFig.3 and 4,itwaspossibletodeducethattheseartifactscombinedonlyac- count forlessthan6% ofthetotalgauge cross-sectionarea.Their effectisthereforelikelytobenegligible.

Under tensileloads, drylamellar bone exhibited mode Ifrac- tureperpendicular tothe loadingdirectionandfailedcatastroph- ically dueto unstable crack growth.While the latter mighthave beenpartiallyencouragedbythesystemcompliance[88],theuse ofoursetupensuredthatfailureoccurredinthegaugesectionfor all specimensevenwhen misalignmentmighthavebeen present.

Thisprovidesanaccuratevalueofthematerialstrengthindrycon- ditions.

The major limitationofthis studyisthe fact that both speci- menfabrication and mechanicaltestinghas beenperformedin a vacuumenvironment.Thedryingprocessclearlyaffectsbothelas- ticandyieldpropertiesofbone[35,89,90].Individualcollagenfib- rils haveshownsignificantshrinking andstiffeningwithdecreas- inghydration[91].Waterisan essentialelementforcollagenvis- coelasticity [92] which in turnis reflected on bone’s mechanical response [93]. In terms of toughness, the presence of water in the extrafibrillarmatrix seems tocontribute to plasticityin bone [94]byactingasalubricantbetweenmineralparticles,thuspro- moting inter-fibrillar sliding [95]. In general, hydration increases thenanocomposite toughness throughthe presenceofdissipative mechanisms[18,96,97].SurfaceroughnessinFig.4d,e,hintsatthe existence ofsuch microscaletougheningmechanisms intheform of fibril pull-out and fibril bridging, although these mechanisms are likelyinhibited bythe dryingprocess. Itis expectedthat un- der hydrated conditiontheywill influencecrack resistance,espe- ciallyintension.Setoetal.[89] testedtheECMintensionatthe mesoscaleunder hydrated conditions andobserved plastic defor- mationwithoutprematurefailureatlowstrains.Basedonprevious results,onecouldmakearoughestimateofthepropertiesofbone at the microscale in tension under hydrated condition. In gen- eral,ithasbeen observedthat hydrationdecreasesYoung’s mod- ulus,decreasesstrength,increasesbone’stoughness andincreases strain to fracture [35,44,49,89,90,98,99]. Onthe microscale, com- parativenanoindentation studies betweendry andhydrated con- ditions revealed that wet samples exhibited a decrease in elas- tic modulus compared to dry conditions between 15% and 30%, aswell asa decrease inhardness ranging from10% to 60%. The largescatterinthereporteddataislikelyassociatedwiththecom- plexorganization oftheMCFsfound inhumanbone andthehet- erogeneous stress state below theindented surface. Previousmi- cropillarcompressionexperimentsatthelamellarscaleinbothdry [32,34]andhydratedconditions[35,36]showedthatplasticdefor- mationinboneispredominantlydominatedbyshearintheEFM, or atthe MCFs interfaces.This was alsoobserved in mesoscopic tensile testscoupled with X-ray scatteringand diffraction analy- sis[18,100].Iftheplasticdeformationispredominantlydominated byshearinbothcompressionandtension,itmightbepossibleto make a betterprediction ofthe effectof dehydrationon themi- crotensilespecimenstestedinthisstudybyusingtheinformation

(9)

from micropillar compression rather than the one from nanoin- dentation. Based on the existing micro compression data on pri- mary ovine bone [35], uniaxial microtensile tests performed un- derquasi-physiologicalconditionsshouldleadtoasignificantlyin- creasedductility,areductionoftheelasticmodulusofatleast20%

and a strength decrease in the orderof 60%, when compared to dryconditions.

Still, in order to investigate bone’s microscale properties and deformationmechanismsunderphysiologicalconditions,itiscru- cial to extend the currenttesting methodologiesto the hydrated state.Asetupallowing uniaxialtensiletestingoflamellarbonein the hydrated condition is currently under developmentto verify thesehypotheses.

4. Conclusions

The tensileproperties of ovine lamellar bone were character- izedatthelengthscaleofasinglelamellaunderuniaxialloading usingamicrotensilesetupinsideanSEM.Microtensiletestingwas combinedwithpost-testSTEMobservationtoanalyzedeformation and failure mechanisms, aswell as to define a composite failure model ableto predictstrength andfailure mode asa functionof themainMCForientation.Invacuummicrotensileexperimentson ovine lamellar bone revealed brittle failure, a highly anisotropic responseandasignificantsizeeffectcomparedtomacroscaledata (factorof2.3higherstrength).Axialspecimensexhibitedstrength of 0.35 ± 0.05 GPa, whereas transverse specimens exhibited strength of 0.13 ± 0.02 GPa. Similarly to what was observed at the macroscale, strength anisotropy was considerably greater for tension than forcompression. This discrepancybetween the two loading modes may be attributed to a change in failure mode fromfibril-matrixinterfacialshearingforaxialspecimenstofibril- matrix debonding for transverse specimens. In compression this change isabsent, withfibril-matrix interfacialshearing beingthe failure mode for both axial and transverse specimens. BF-STEM imagingrevealed that forthesmall volumestestedinthisstudy, the sub-lamellar MCF organization of primary lamellar bone is fairly uniaxial and with an orientation close to the longitudinal axis of the bone. Yet, disordered phaseswere also observed and they seem to have an importantinfluence on the failure mecha- nisms,especiallyfortransversespecimens.Disorderedphasesgive risetoweakinterfacesandmightbeakeydesignfeatureforcrack deflection.Theirinfluence issimilar tocementlines andlamellar interfaces, in which cracks can be deviated from critical orien- tations and dissipate deformation energy. Analysis of the failure mechanisms showed also the influence of the lacuno-canalicular system, especially in axial specimens for which failure is always initiated by canaliculi which run in radial direction creating the higheststressconcentrations.Usinglinearelasticfracturemechan- ics it waspossible to estimate the mode I fracture toughness KI inthecaseofaxialfracture(0.17±0.03MPam1/2)andtransverse fracture (0.07 ± 0.01 MPa m1/2). The noticeable reduction ofthe fracture toughness fromthe macroscaleby atleast one orderof magnitudemightberationalizedby theabsenceofthemajor ex- trinsictougheningmechanismsfoundathigherlengthscales,such as uncracked-ligament bridging [101] or crack-deflections/twists at the cement lines [66–68]. Finally, an improved version of the well-establishedHashin’s compositefailure modelwasapplied to describe lamellarbonestrength asa functionofMCFmainorien- tation.Despiteitslimitations,duetothesimplifiedrepresentation of the microstructure of lamellar bone as a uniaxial composite, the model shows good agreement with the experimental data.

The data suggest that lamellar bone strength on the microscale is remarkably tolerant to variations of fibril orientation of about

±30°.Thepresentedstudyestablishesabaselineforthemicroten- sile properties of bone at the lamellar scale and underlines the

importance of bone’s hierarchical microstructure and the need to study structure-property relationships on all length scales for gainingadeeperunderstandingofitsmacroscopicbehavior.

AuthorContributions

Theinitialplanningofthestudywasdoneby J.S.,J.M.andP.Z.

MicrotensilespecimenswerefabricatedbyD.C.andJ.S.Insituex- periments and SEM/STEM imagingwere performed by D.C. Data analysisandinterpretation wasperformedby D.C. incooperation withJ.S. The manuscript waswritten by D.C. withcontributions fromalltheauthors.

FundingSources

Thisstudywasfunded by theSwissNational ScienceFounda- tion(SNSF)grantno.165510andAmbizionegrantno.174192.

DeclarationofCompetingInterest

Theauthorsdeclarenocompetingfinancialinterests.

Acknowledgment

Thisstudywasfunded by theSwissNational ScienceFounda- tion(SNSF)grantno.165510andAmbizionegrantno.174192.The authorsacknowledgetheScientificCenterforOpticalandElectron Microscopy (ScopeM) atETH Zürich forproviding accessto their facilities.TheauthorswouldliketothankDr.J.Reutelerforhisas- sistanceduringplasma-FIBmillingandSTEMlamellaethinning,L.

Pethö formakingpossiblethefabricationofmicrotensilegrippers, G.BuerkiforhistechnicalassistanceduringFIBmillingandT.Ko- chetkovaforherassistanceduringRamanspectroscopy.

Supplementarymaterials

Supplementary material associated with this article can be found,intheonlineversion,atdoi:10.1016/j.actbio.2020.04.030. References

[1] B. Clarke , Normal bone anatomy and physiology, Clin. J. Am. Soc. Nephrol. 3 (Supplement 3) (2008) S131–S139 .

[2] R. Weinkamer , P. Fratzl , Mechanical adaptation of biological materials - The examples of bone and wood, Mater. Sci. Eng. C. 31 (6) (2011) 1164–1173 . [3] C.H. Turner , Three rules for bone adaptation to mechanical stimuli, Bone 23

(5) (1998) 399–407 .

[4] P. Augat , S. Schorlemmer , The role of cortical bone and its microstructure in bone strength, Age and Ageing 35 (S2) (2006) ii27–ii31 .

[5] S. Weiner , T. Arad , I. Sabanay , W. Traub , Rotated plywood structure of primary lamellar bone in the rat: Orientations of the collagen fibril arrays, Bone 20 (6) (1997) 509–514 .

[6] P. Varga , A. Pacureanu , M. Langer , H. Suhonen , B. Hesse , Q. Grimal , P. Cloetens , K. Raum , F. Peyrin , Investigation of the three-dimensional orientation of min- eralized collagen fibrils in human lamellar bone using synchrotron X-ray phase nano-tomography, Acta Biomater 9 (9) (2013) 8118–8127 .

[7] S. Weiner , W. Traub , H.D. Wagner , Lamellar bone: structure– function rela- tions, J. Struct. Biol. 126 (3) (1999) 241–255 .

[8] N. Reznikov , R. Shahar , S. Weiner , Three-dimensional structure of human lamellar bone: The presence of two different materials and new insights into the hierarchical organization, Bone 59 (2014) 93–104 .

[9] P. Fratzl , H.S. Gupta , E.P. Paschalis , P. Roschger , Structure and mechanical qual- ity of the collagen-mineral nano-composite in bone, J. Mater. Chem. 14 (14) (2004) 2115–2123 .

[10] M.J. Buehler , Molecular nanomechanics of nascent bone: fibrillar toughening by mineralization, Nanotechnology 18 (29) (2007) 295102 .

[11] J.Y. Rho , L. Kuhn-Spearing , P. Zioupos , Mechanical properties and the hierar- chical structure of bone, Med. Eng. Phys. 20 (2) (1998) 92–102 .

[12] U.G.K. Wegst , M.F. Ashby , The mechanical efficiency of natural materials, Phi- los. Mag. 84 (21) (2004) 2167–2186 .

[13] H. Gao , Application of fracture mechanics concepts to hierarchical biome- chanics of bone and bone-like materials, Int. J. Fract. 138 (1–4) (2006) 101–137 .

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