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To cite this version :
Vincent MAZEL, Sandra GUERARD, Benjamin CROQUELOIS, Jean-Benoit KOPP, Jérémie
GIRARDOT, Harona DIARRA, Virginie BUSIGNIES, Pierre TCHORELOFF - Reevaluation of the
diametral compression test for tablets using the flattened disc geometry - International Journal of
Pharmaceutics - Vol. 513, n°1-2, p.669-677 - 2016
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Reevaluation
of
the
diametral
compression
test
for
tablets
using
the
flattened
disc
geometry
V.
Mazel
a,*
,
S.
Guerard
b,
B.
Croquelois
a,
J.B.
Kopp
b,
J.
Girardot
b,
H.
Diarra
c,
V.
Busignies
a,
P.
Tchoreloff
aaUniv.Bordeaux,CNRS,BordeauxINP,ArtsetMétiersParisTech,I2M,UMR5295,F-33000Bordeaux,France b
ArtsetMétiersParisTech,Univ.Bordeaux,BordeauxINP,I2M,UMR5295,F-33000Bordeaux,France
c
CNRS,Univ.Bordeaux,BordeauxINP,ArtsetMétiersParisTech,I2M,UMR5295,F-33000Bordeaux,France
Keywords: Tablet Diametralcompression Tensilestrength Compression Numericalsimulation ABSTRACT
Mechanicalstrengthisanimportantcriticalqualityattributefortablets.Itisclassicallymeasured,inthe pharmaceuticalfield,usingthediametralcompressiontest.Nevertheless,duetosmallcontactarea betweenthetabletandtheplatens,someauthorssuggestedthatduringthetest,thefailurecouldoccurin tensionawayfromthecenterwhichwouldinvalidatethetestandthecalculationofthetensilestrength. Inthisstudy,theflatteneddiscgeometrywasusedasanalternativetoavoidcontactproblems.The diametralcompressiononbothflattenedandstandardgeometrieswasfirststudiedusingfiniteelement method(FEM)simulation.Itwasfoundthat,fortheflattenedgeometry,bothmaximumtensilestrainand stresswerelocatedatthecenter ofthetablet,whichwasnotthecaseforthestandardgeometry. Experimentalobservationsusingdigitalimagecorrelation(DIC)confirmedthenumericalresults.The experimentaltensilestrengthobtainedusingbothgeometrieswerecomparedanditwasfoundthatthe standardgeometryalwaysgavelowertensilestrengththantheflattenedgeometry.Finally,high-speed videocaptureofthetestmadeitpossibletodetectthatforthestandardgeometrythecrackinitiationwas alwaysawayfromthecenterofthetablet.
1.Introduction
Mechanicalstrengthisanimportantcriticalqualityattributefor tablets.As such, especially in thedevelopmentof a Qualityby Designapproach,apreciseandreliablequantificationisrequired. For pharmaceutical tablets, the main technique to study the mechanicalstrengthofthetabletisthediametralcompressiontest (alsoknownasBraziliantest)(EUP,2016;USP,2013).Thistestwas developed duringthe 40’s tostudy themechanical strength of concretecylinders (Carneiro,1943; Fairbairn and Ulm,2002).It measuresthetensilestrengthinanindirectmannerwhendirect tensile tests are difficult to perform due to the mechanical propertiesofthetestedmaterial.Firstlyusedforconcreteorrocks, it was introduced, during the 60’s for the characterization of pharmaceutical tablets (Fell and Newton, 1968, 1970). The cylindricalshape isindeed easytoobtainwhen performingdie compressionandthetestisthuswellsuitedfortablets.
Nevertheless,asmentionedbefore,thediametralcompression test is an indirect test. A cylindrical sample is submitted toa compressive forcealong itsdiameterbydiametralcompression between two flat platens. This promotes the development of tensilestressesatthecenterofthecompact.Thesetensilestresses aresupposedtocausethefailure.Then, bysupposing anelastic behaviorofthecompactandbyusingtheelastictheory,ina2D planestress,itispossibletoprovethatthemaximumtensilestress islocatedatthecenterofthecompactandisgivenby:
s
¼p
2FDh ð1Þ
where
s
isthemaximumtensilestress,Fistheappliedforceand,D andharerespectivelythediameterandthicknessofthecylinder. Thus, considering a failure criteria based on the maximum principalstress,thetensilestrengthiscalculatedbysubstituting, inEq.(1),theforcethatcausedthefailure.Themainproblemofthistestgeometryisthecontactinthe loading area. The contact area between the platens and the cylinderisverysmall,anditpromotesthedevelopmentofhigh stresses.Ifthecontactistoosmall,thefailurecouldbecausedby sheareffectsinthisarea,leadingthustoincorrectfailurepattern.
* Correspondingauthorat:I2M,Univ.Bordeaux,146rueLéoSaignat,F-33000, Bordeaux,France.
Toavoidthisproblem,severalauthorshaverecommendedtheuse ofloadingstripsthatarepositionedbetweentheplatensandthe sample(LiandWong,2013).Thismakesitpossibletoincreasethe contact area avoiding shear or compressive failure. Other techniquestoincreasethecontactareahavebeenproposedlike theuseofcurvedplatens(ISRM,1978)ortheuseofflatteneddiscs insteadofcylinder(Wangetal.,2004).Thislastsolution,willbe furtherdevelopedbelowinthearticle.
Inthepharmaceuticalfield,theproblemofcontactwasstudied sincethetestwasintroduced.Inthearticlewhichisthereference for the use of the diametral compression for tablets, Fell and Newton(1970)studiedtheinfluenceofinsertingsheetsofblotting paperbetweentheplatensandthetablet.Diametralcompression testswithandwithoutblottingpaperswerecarriedoutforfive differentlactose batches (one crystalline, and four spray-dried notedA–D).ForthesamplesB–Dtheyfoundthat,withoutblotting paper,thefailurewasduetocompressionandshearatthecontact withplatens.Forthiscase,theuseofblottingpaperwasmandatory toobtainatensilefailure.Forthecaseofcrystallineandspraydried Asamples,theresultsweredifferent.Forthesetwoproducts,with andwithoutblottingpaper,thefailureoccurredintension,i.e.no failureatthecontactpointwasobserved.Nevertheless,thevalues obtainedinthetwocasesweredifferent.Theythenstated“this raisesthequestionastowhichofthevaluesrepresentthetensile strengthofthetablet”.Thecontactproblemwasalsostudiedmore recentlyby Davieset al. (2007). In their study, they used two contactconfigurations.Thefirstonewasclassicalflatplatensand forthesecondconfiguration,theyattachedsemi-circularsteelrods totheplatens.Asitisprovedinthearticle,thislastconfiguration madeitpossibletohaveasmallercontactwidth.Inallthecases, theyobservedfailureintension,buttheyalsoobservedthatfor smalleracontactwidth,theyobtainedalowertensilestrengthby usingEq.(1)whichisexactlythesametrendobtainedbyFelland Newton(1970).Again,duetothefailurepatternobserved,shearor compressionfailure atthe contactpoint could notbetaken as responsible of the difference in tensile strength obtained for differentcontactwidths.Andthequestionmentionedaboveabout whichoneofthevalueisthecorrectvalueofthetensilestrength hasstill,toourknowledge,norealanswerintheliterature.
Nevertheless,theproblemofcontactisgenerallydiscardedin thepharmaceutical field. Agreat number of studies havebeen publishedaboutthefailureofpharmaceuticalcompactsusingthe diametralcompressiontest,studyingforexampletheeffectsofthe shapeofthecompact(Pittetal.,1988;Podczecketal.,2013,2014; Razavietal.,2015;Shangetal.,2013a,2013b)orontheeffectofthe materialproperties(Procopio etal.,2003).Butin nearlyallthe studies,flatplatensareused.Theregulatorytextsalsoadvisefor theuseofflatplatens(EUP,2016;USP,2013)andthevalueofthe diametralcompressiontest is takenas thevalue of thetensile strength and used, for example, as a material characteristic to calibratenumerical models (Brewin, 2008; Cunningham et al., 2004;Wuetal.,2005).
Anotherinterestingpointisthatthetheoreticaldevelopment thatleadstoEq.(1)isa2Done.Itthussupposesthatthereisno3D effects. Nevertheless, 3D effects were demonstrated by both analyticaldevelopments (Wijk,1978)and numerical simulation usingtheFiniteElementMethod(FEM)(Ehrnford,1981; Liand Wong,2013).Allthesestudiesshowthat,ifthecontactsurface betweenthe cylinderand theplaten is too small, hightensile stressesdevelopontheoutersurfaceofthecompactawayfromthe centralaxis.Thevalueandpositionofthesestressesdependonthe contactarea,onthethicknessofthecompactandalsoonPoisson’s ratio. The quantitative determination of these stresses is thus complicated,butasstatedbyEhrnfordalongtimeago,duetothese stresses,“periphericalfracture initiationmustbe regardedas a possibility” (Ehrnford, 1981). Surprisingly, the presence of the
maximum tensile stress awayfrom the center is generally not considered and studies about 3D effects in the diametral compression test mainly focus on the variation of the tensile stress at the center along with the thickness of the compact (Podczecketal.,2013;Yuetal.,2006).
Afterthisbriefreview,itisclearthatthediametralcompression testisstillnotfullyunderstoodandthattheresultsobtained(i.e. tensilestrength)mustbetakenwithcautioniftheyaretobeused asmaterialconstants.Itisalsoclearthattheproblemcomesfrom thecontactareabetweentheplatenandthecompact.Amongthe solutionstoincreasethiscontact,theflattenedBraziliandiscwas proposedforrocks.Itconsistsinintroducingtwoflatendstothe disc (Wang et al., 2004). This technique hasthe advantageof introducingawell-defined andquantifiedcontactareabetween theplatensandthetablet.Bychoosingthecorrectcontactsurface, itshouldthusbepossibletosuppresstheproblemofshearfailure andalsotheperipheraltensilestressesdueto3Deffects.Inthecase of pharmaceutical tablets, by designing tools with the proper shape,itiseasytoproduceflattenedtablets.
Inthiswork,wewantedtostudy,inthecaseofpharmaceutical tablets,theeffectofusingtheflattenedBraziliandisconthevalue ofthetensilestrengthobtainedbydiametralcompression.Inafirst part,FEMstudieswereperformedtoshowthattheuseofspecially designed punches toobtainflattened compactdidnot have an impactonthestressanddensitydistributionsinsidethecompact. This partwas necessary toprove that theflattened and round tablet had thesame density distributionand that their failure behaviorcouldthusbecompared.Inasecondpart,thestressand strain distributions inside the compact during the diametral compressionwereevaluatednumerically(FEM).FEMsimulations werecomparedtotheresultsalreadypublishedintheliterature. Then, DigitalImage Correlation(DIC) was used tocomparethe experimental strain fields tothe ones obtained numericallyin ordertoprovethatFEMsimulationsgaveagoodrepresentationof theactualbehaviorofthecompact.Afterwards,thediametraltest was performedfor bothnormal andflattened discgeometryto comparethevaluesobtainedforthetensilestrength.Finally,ahigh speedcamerawasusedtolocatethecrackinitiationduringthetest onbothgeometries.
2. Materialandmethod
2.1.Powders
Five different powders were used to produce compacts: anhydrous calcium phosphate (aCP) (AnhydrousEmcompress1, JRSPharma,Rosenberg,Germany),calciumphosphatedihydrate (DCP)(EmcompressPremium1,JRSPharma,Rosenberg,Germany), spray-driedlactosemonohydrate(SDLac) (Flowlac190, Meggle, Wasserburg, Germany), granulated lactose monohydrate (GLac) (Tablettose180,Meggle,Wasserburg,Germany)andspray-dried mannitol(SDMan)(Pearlitol1200SD,Roquette,Lestrem,France). Toperformthecompactionexperiments,theproductsweremixed with1%(w/w)ofmagnesiumstearate(Cooper,Melun,France)to minimizethefrictionsinthedie.Theblendingwasperformedat 50rpm for 5min using a turbula mixer (Type T2C, Willy A Bachofen,Muttenz,Switzerland).
2.2.Compression
Allthecompactswereproducedusingacompactionsimulator Stylcam1(Medelpharm,Bourg-en-Bresse,France).Thistableting press isa single stationpress.It is equippedwithforcesensor (accuracy 10N) and the displacements of the punches are monitored with an accuracy of 0.01mm. Two different sets of flat-facedeuroBpuncheswereused(ACM,Avilly-Saint-Leonard,
France).Theprojectionoftheactivesurfaceofthetwosetscanbe foundinFig.1.Thefirstsetwasroundwithadiameterof11mm andmadeitpossibletoobtainroundtablets(Fig.1a).Thesecond setwasmadeofpunchesespeciallydesignedtoobtainflattened discs(Fig.1b).Allthecompactswereobtainedusingthedirectcam modeataspeedof10compactsperminutes(totalcompression timeofabout100ms)and underfouror fivedifferentpressure levelstoobtainseveraldensities.Toavoidanyeffectduetothe thicknessof the compacts, all thecompacts manufacturedhad similarthicknesses around 3.8mm. The density was calculated usingtheweightanddimensionsofthecompacts.ASmarTest50 semi-automatictablettestingsystem(Sotax,Saint-Louis,France) was usedto weightand measure thetablets. For theflattened geometry,thedistancebetweenthetwoflatedgeswasmeasured withaMitutoyomicrometer(Kawasaki,Japan).
2.3.Mechanicalcharacterization
The diametral compression test was performed using a TA. HDplus texture analyzer (Stable microsystems, Surrey, United Kingdom).Compactswerecompressedbetweentwoflatsurfaces ataconstantspeedof0.35mms1withanacquisitionfrequencyof 500Hz.Foreachdensitylevelofeachproduct,tencompactswere broken.For thehighspeed video experiments,due topractical reasons,thetest was performedon a ZwickRoellZ250 (Zwick Roell,Ulm,Germany)testingmachineatthesamespeed.
2.4.Digitalimagecorrelation
DigitalImageCorrelation(DIC)isanoptical-basednon-contact method used to calculate the 2D or 3D full-field surface displacementresponseofstructurestomechanicalloading.Itis based on pattern matching between two images of the same specimenintwodifferentloadingstages(Suttonetal.,2009).
Prior to the tests, the surface of the specimens has been speckledtopresentarandomintensitypattern.Thispatternwas obtainedby applyingblack ink onthe surface of thecompact. Image acquisitionwas made using a camera FASTCAM-APX RS (Photron,SanDiego,USA)witha60Hzfrequencyinordertohave sufficientresolutionforDICcalculation.
DigitalImage Correlation (VIC-2DVic-Snap 2009, Correlated Solutions Inc., Columbia, SC) was performed using a 70-pixel correlation window size and a 7-pixel step size between two consecutivewindowsinordertominimizecalculation uncertain-ties. Displacement field and engineering strains have been determinedusingDIC.
2.5.FEMsimulation
The FEM modeling was performed using Abaqus1 Standard software6.13(DassaultSystèmes,Vélizy-Villacoublay,France).
For the studies about the density distribution inside the compact after compression, the mechanical behavior of the
powderwasmodeledusingDrucker-Prager-Capmodelas gener-allyperformedintheliterature(Brewin,2008;Cunninghametal., 2004;Wuetal.,2005).Theparametersusedwerecharacteristicof anhydrous calcium phosphate and weretaken froma previous publication (Diarra et al., 2015). For the tooling, the elastic properties of steel wereconsidered (E=200GPa and
n
=0.3). A symmetricalcompressionwasconsidered(bothpunchmovingat thesametime)asitisthecaseforthetabletingmachineusedin thisstudy.Fortheexampleshowninthearticle,themovementof thepuncheswasmonitored toobtaina compactionpressureof about150MPaintheaxialdirection.Usingsymmetryreasons,only aquarterofthewholegeometrywasmodeled.Forthesimulationofthediametralcompression,thecompact was considered as an elastic material. The value of Young’s modulus and Poisson’s ratio for the simulation were chosen dependingon thecompactand will begivenin thetext. Their determination was done as described elsewhere (Mazel et al., 2012).Theplatenswerealsotakenaselasticwithelasticconstants equal tothose ofsteel (E=200GPa and
n
=0.3). Thestresswas appliedbymovingdowntheplaten.Usingthesymmetryofthe system, onlyan eighthofthe compactwas modeled(Podczeck etal.,2013).2.6.High-speedvideo
High-speedvideoacquisitionwasperformedduringdiametral compressiontestusingaFASTCAMSA5(Photron,SanDiego,USA). The frame rate was 372000 images per second. We used for standardtabletsaframesizeof32040pixelsandforflattened tabletaframesizeof25648pixels.Theframewascenteredon thetablet.Toenhancethevisualization,greeninkwasappliedon thesurface.Thiscolorcorrespondstothebestspectralresponseof thecamera.
3.Resultsanddiscussion
3.1.Densitydistributioninsidethecompacts
The first concernwas toverify that themodification of the tooling to obtain flattened tablets did not have important consequences concerning the stress and density distributions inside the tablet. For example, it is known that changing the curvatureofthepunchhasdramaticconsequencesonthedensity distribution inside the tablets (Diarra et al., 2015; Sinka et al., 2004).
Nevertheless,inourcase,themodificationdidnotconcernthe curvatureofthepunches.Theusedpuncheswereflatinbothcases. Theonlymodificationwasthat,inthecaseofthepunchesforthe flattenedgeometry,thecylindricalshapewasslightlymodifiedto introduce twoflatends. Astheseflatendswereparalleltothe directionofcompression,notrealinfluencewasexpectedonthe stressanddensitydistributionsinsidethetablet.
Toconfirmthisfact,numericalsimulationwereperformedfor bothgeometries.Asmentionedabove,theparameterstakenfor thesimulationwerethoseofaCP.Asanexample,asymmetrical compressionuptoapressureof150MPawasmodelled.Theresults canbeseeninFig.2.Wefirstcheckedthattheradialstresswasnot influencedbythepresenceoftheflatpart.Asitcanbeseen in
Fig.2aandb,theradialstressnormaltotheflatpart(
s
yyFig.2a)andtheradialstressintheperpendiculardirection(
s
xxFig.2b)arecomparableand,atthecenter,thedifferenceislessthan1%(i.e.the radialstressisnearlyisotropic).Thetwodensitydistributionsare also completely comparable and only small differences were observedneartheendoftheflatportionofthecrown(Fig.2cand d).Thismeansthatthecompactsofboth geometriesshouldbe similar in terms of mechanical properties and of mechanical
Fig.1.Projectionoftheactivesurfaceofthepunchesforthestandard(a)and flattened(b)geometries.
strength.The tensilestrength of thetwo geometriesshouldbe identical. It should thus be possible to compare the results obtainedduringdiametralcompressionforbothgeometries.
3.2.FEMsimulationofthediametralcompressiontest
The second step of this study was to understand the consequence of flattening a compact on the stress and strain distributionsduringthediametraltestbyusingFEMsimulation.As anexample,wechosetheelasticpropertiesofacompactmadeof SDLacobtainedunderapressureof100MPa,whichcorrespondsto aporositylevel of19%. Theelasticconstantsfor thesimulation weredeterminedasdescribedelsewhere(Mazeletal.,2012).The resultsgaveaYoung’smodulusof4.2GPaandaPoisson’sratioof 0.25. The thickness was set to 3.8mm and the diameter to 11.03mmtomatch experimentalcompactsthat wereproduced andthatwereusedfor thefollowingsection.Theresultsofthe simulationsarepresentedinFig.3.Thedisplacementwassetto obtainanappliedforceof100Nonthecompact.
Asalreadydescribedabove,onlyaneighthofthecompactis represented.InFig.3,thesideofthecompactinfrontofthepicture (directionzpositive)isthesurfaceofthecompactandthesideon theback(direction z negative) is the centralplane. The figure representsthenormalstressandstraininthexdirection(i.e.
s
xxand
e
xx).Tomaketherepresentationasclearaspossibleweonlyrepresentedthetensilevalues(i.e.positive).Thepartofthetablet where
s
xxande
xxarecompressiveappearsinblack.Theresultsobtainedonthestandardgeometry(Fig.3aandb) arecomparable tothose presentedbyLiandWong(2013). The highesttensilestrainsarelocatedslightlyunderthecontactpoint. For the tensile stresses, there is a clear 3D effect as already mentioned in otherpublications (Ehrnford,1981; Liand Wong, 2013).Themaximumtensilestressislocatedonthesurfaceofthe compactandisnotcentered.Theobtainedvalue(i.e.
s
xx=3.7MPa)ismoreoversuperiortotheoneobtainedusingEq.(1)whichwould be in this case equal to 1.5MPa. To illustrate this fact, Fig. 4
representsthesamesituationthanFig.3bbutthecolorscalewas modifiedinordertohave,incolor,thepartofthecompactwhere thetensilestressissuperiortotheoneobtainedusingEq.(1).Itcan beseenthatanimportantpartofthecompactissubmittedtoa highertensilestress.
To conclude onthe standard geometry, neitherthe highest tensilestrainnorthehighesttensilestressislocatedatthecenter of the compact. As concluded by Ehrnford (Ehrnford,1981), a fractureinitiationawayfromthecenterofthecompactmustbe regardedasapossibility.Andinthiscase,theuseofEq.(1)would leadtoanunderestimationofthetensilestrengthofthecompact. ThecaseoftheflatteneddiscispresentedinFig.3candd.The stressandstraindistributionsarecompletelydifferentfromthose obtainedinthestandardgeometry.Bothmaximumstressesand strainsarenowlocatedonthecentralaxisofthecompact.The valuesonthesurfaceareslightlyhigherthanthoseobtainedinthe centralplan.Themaximumtensilestrain(
e
xx=5.69.104)obtainedfortheflattenedgeometryismuchlowerthanforthestandardone
Fig.2. FEMsimulationofthecompression:Radialstressdistributionfortheflattenedgeometryatthetopofcompression:(a)syyand(b)sxx;Distributionoftherelative
densityinsidethecompactattheendofthedecompressionfor(c)standardgeometryand(d)flattenedgeometry.Thankstothesymmetryoftheproblemonlyaquarterofthe geometryisrepresented.
(
e
xx=2.99.103).Inthecase of themaximumtensile stress,thevalue is slightly lower than the one predicted by Eq. (1)
(
s
xx=1.32MPa).Thiswasexpectedasseveralpublicationsalreadyshown that, increasing the contact area on which the load is applied,promotes adecrease ofthetensile stressatthecenter (Hondros, 1959).Thus,toobtaintherightvalueofthetensilestress,
a correctionfactormustbeadded toEq. (1). Inthecase ofthe flattened discwith a contact angle of 30, Wang et al. (2004)
recommendedacorrectionfactorof0.92.Nevertheless,theirstudy wasbasedon2Dcalculations.Wethuspreferredtorecalculatethe correctionfactorsbyusing3DFEMsimulations.Thegeometryused wastheonepresentedinFig.3andweusedloadupto500Nwhich isthehighestvaluethatcanbeobtainedexperimentallyonour device.Wefoundthatthecorrectionfactorwasnotinfluencedby theloadvalue.Onlysmallchangeswerenoticedwhenchanging Young’smodulusandPoisson’sratioasexpectedconsideringthe theoryoflinearelasticity(Podczecketal.,2013;Procopioetal., 2003). No significant variation were found for the different thicknesses usedin this study(between3.6 and 4mm).For all the cases a constant correction factor of 0.87 was thus used. Moreover,theratiobetweenthecompressivestressandthetensile stress at the location of the maximal tensile stress was also checked.Avalueof3.2wasfoundwhichisclosetothevalueof3 thatisfoundtheoreticallyforthestandardgeometryatthecenter (Procopioetal.,2003).Thedifferencebeensmall(lessthan10%),it isthusexpectedthatthecompressivestresswillplaythesamerole inbothgeometriesand,asaconsequence,couldnotcauseachange inthetensilestrengthvalue.
Finally,thesimulationspresentedinFig.3indicatethattheuse ofaflatteneddiscisfavorabletoobtainacrackinitiationatthe centerofthecompactas,atthislocation,bothstressesandstrains are maximum. On the contrary, for the case of the standard geometry,neitherthemaximumtensilestressnorthemaximum
Fig.3.FEMsimulationofthediametralcompressiontestforthestandard(aandb)andtheflattened(candd)geometry.Colorscalerepresentsthestrainexx(aandc)orthe
stresssxx(bandd)(inMPa).
Fig.4. FEMsimulationofthediametralcompressionforthestandardgeometry. Thecolorscalerepresentssxxandhasbeenlimitedtothevaluesthatexceedthe
tensilestrainislocatedatthecenter.Thepossibilityofafracture initiationawayfromthecenterofthecompactmustberegardedas apossibility.
Nevertheless,allthedevelopmentsmadeonthediametraltest were based on the assumption of an elastic behavior of the compactduringthediametralcompressiontest.Inthenextpart, thesimulation results were compared toexperimental ones to studyiftheelasticbehaviorisagoodrepresentationoftheactual behaviorofthecompactduringthetest.
3.3.Comparisonwithexperimentalresults(DIC)
DICwasusedtostudytheeffectivemechanicalbehaviorofthe compact during the test. This technique makes it possible, as mentioned before, to measure the displacement fields at the surfaceofthecompactduringthetest.Thedisplacementcanthen be converted in strain field. The idea was to compare these experimental results to those obtained using FEM simulation consideringalinearelasticbehavior.
Asanexample,thecaseofcompactofSDLacobtainedunderan axialpressureof100MPawasagainconsidered.Thechoiceofthis productwas basedonthefact that,as it willbedemonstrated below,SDLacmakesitpossibletoobtainstrongcompacts.During thediametralcompressiontest,relativelyhighforcescanthusbe applied before failure, which makes it possible to obtained relatively highstrains compared toother productslikeaCP for example.Thisproductisthusfavorabletoobtainreliableresults usingDICtechnique.
The exact compactgeometry was implementedfor theFEM simulation and theappliedforcewas equal tothe oneapplied experimentally. Fig. 5 presents both experimental (DIC) and numerical(FEM)strainfieldsintheX-direction(
e
xx).Tomakethecomparison easier, the whole surface of the compact was representedfortheFEMresults byusingthesymmetriesofthe
problem. Moreover, the scale was also slightly modified to enhancedthecontrast(i.e.someareaswereexcluded).Theresults ofFEMaredirectlycomparabletothosepresentedinFig.3butthe appliedforceisslightlydifferenttomatchtheexperimentalone andtorepresentthecompactjustbeforefailure.
Thefirstcommentisthatfromaqualitativepointofview,the straindistributionsobtainedwithDICwerecomparabletotheone predicted using FEM. These results are also coherent with the existingliterature(Stirlingetal.,2013).Asmentionedabove,for thestandard geometry,themaximumtensilestrainwaslocated awayfromthecenter.Onthecontrary,fortheflattenedgeometry the maximum tensile strain is located at the center. The comparison of thepatternsobtainedby DICand FEM makesit possibletoconcludethatthemechanicalbehaviorofthecompact duringthetestis,atleastqualitatively,correctlyrepresentedbya linearelasticmodel.
Itis alsointerestingtolookattheresultfromaquantitative point of view. As it can be seen on Fig. 5a and c, the strains measuredarebetween104and103.Thisvalueisquitesmalland corresponds to the limit of validity of DIC measurements. Nevertheless by comparing DIC and FEM, it is clear that the quantitative values are in the same order of magnitude. For exampleintheflattenedgeometry, themaximum tensilestrain valueinbothcasesisaround103andforthestandardgeometry thestrainvalueatthecenterisaround7.104.Thevalueofthe elasticmodulithatwereusedforthesimulationarethusinthe goodorderofmagnitude.
These results demonstrate that, for this product, the linear elasticmodelissuitabletodescribethemechanicalbehaviorofthe compactduringthetestandthevalueoftheelasticmoduliused are in the good order of magnitude. As a consequence, the calculatedstrainandstressfieldscalculatedbyFEMcanbeusedto interpretthefailureusingthediametralcompressiontest.
3.4.Failureresults
Forthefiveproductsconsideredinthisstudy,compactswere made under at least four pressure levels in order to obtain compactswithincreasingmechanicalstrength.Bothstandardand flattened compacts were manufactured under these different loads. For each product and density, ten compacts were, afterwards, measured and broken diametrically as described above.For eachfailuretest, thetensile strengthwascalculated. Forthestandardgeometry,Eq.(1)wasusedandfortheflattened geometry,Eq.(1)wasmultipliedby0.87totakeintoaccountthe thickness effect as explained in Section 3.2. To quantify the difference between the values obtained in both geometries, a tensile strength differencewas calculated by using the tensile strengthforthestandardgeometry(
s
s)andthetensilestrengthfortheflattenedgeometry(
s
f).Thefollowingexpressionwasused:Tensile strength difference¼
s
fs
ss
s100 ð2Þ
TheresultsarepresentedinFig.6.Tofacilitatethevisualization oftheresults,productsarepresentedintwogroups(Fig.6aandb). Oneachgraph,theX-axisisthetensilestrengthobtainedwiththe standard geometry and the Y-axis is the one obtained for the flattenedcompacts.Itwasfoundthatforeachproductthepoints alignnicelyonastraightlinewithaninterceptequaltozero(Forall theproductsR2issuperiorto0.99).Theslopeofeachstraightline
canbeseeninFig.6.Thisleadstotwocomments.
Thefirstcommentisthatinallthecases,theslopeofthelineis superiorto1.Thismeansthatthevalueobtainedforthestandard geometry is lower than the one obtained for the flattened geometry. Asalready mentioned in the literature,thestandard geometryunderestimatesthetensilestrength.
The second interesting point is thefact that thepoints are aligned.Itmeansthatforoneproduct,whateverthestrength,the tensile strength difference is constant. The tensile strength differencecanbecalculateddirectlyfromtheslope.Theresults arepresentedinTable1.
The tensile strength difference ranged from 17% to 71% dependingontheproduct.Butitisworthnotingthatforallthe products,thefailurepatternusingthediametraltestindicateda failure in tension. It was not possible to infer the differences betweentheproductsonlybylookingatthefailurepattern.This meansthat,ifitisintendedtoproduceacompactwithatensile strengthof2MPaasrecommendedintheliterature(Sunetal., 2009)andifthistensilestrengthismeasuredusingthestandard geometry,itcouldcorrespond,inthecaseoftheproductsofthis study,toatensilestrengthmeasuredusingtheflattenedgeometry rangingfrom2.34to3.44MPa.Thesevaluescorrespond,inreality, toverydifferentcompactstrengths,andthetestwiththestandard geometryisunabletodiscriminatethem.Thisresultisimportant fordevelopmentstudies.Usingthestandardgeometry,theuseofa
specificationofatensilestrengthof2MPaforthedevelopmentofa newcompactisquestionableas,dependingontheproduct,itcan infactcorrespondtoactualverydifferentmechanicalstrength.
Theunderestimationofthetensilestrengthusingthestandard geometry was already predicted above, considering the FEM results.Asthemaximumtensilestressisnotatthecenter,afailure awayforthecentercouldoccur.Ifitwasthecase,calculatingthe tensile strengthusing Eq.(1) which considersthestress atthe center would lead toan underestimation of the actual tensile strength.Soalltheresultsareconsistentwiththefactthat,forthe standard geometry, thefailure occurs awayfromthecenter. In ordertoconfirmthisfact,high-speedvideowasusedtolocatethe crackinitiationinthecompactduringthetestforbothgeometry.
3.5.High-speedvideoresults
Filmed diametral compression tests with high speed video camerawereperformed.Forpracticalreason,itwasnotpossibleto film experimentwith allthecompactspresented above.Sowe chose, for each product, compacts that corresponded to an apparenttensilestrengthof2MPausingthestandardgeometry. Atleastfourcompactsforeach geometrywerebroken andthe videowasthenanalyzedtodetectthecrackinitiation.ForSDLac andGlac,itwaspossibleforbothgeometrytodetectcorrectlythe crackinitiation.ForaCPandDCP,theresolutionofthecameraat theframe speed usedwas notenough tobeabletolocate the initiationproperly,especiallyinthecaseoftheflattenedgeometry. ForSDMan,wefoundthatinthestandardgeometry,thecracktip velocitywasveryhigh(severalhundredm/s)andthatourset-up (framerate/resolutionbalance)didnotmakeitpossibletolocate properlytheinitiation.
Fig.7presentsrepresentativeexamplesofcrackinitiationand propagation for SDLac and GLac for both geometries. For the standardgeometrythefailureinitiatesawayfromthecenterinthe direction of one of the platen before propagating through the wholesample. On the contrary for theflattened geometry, the failure is locatedatthe centerat thesame distancefromeach platen.
Thevideosconfirmalltheresultspresentedabove.Thecrack initiationisawayfromthecenterforthestandardgeometryas predictedbyFEMsimulation. Onthecontrary,for theflattened
Fig.6.Tensilestrengthfortheflattenedgeometry(sf)asafunctionofthetensilestrengthforthestandardgeometry(ss)forthedifferentproducts.
Table1
Tensilestrengthdifferenceforthedifferentproducts.
Product Tensilestrengthdifference
aCP 17%
DCP 29%
SDMan 34%
GLac 35%
geometry,thefailurestartsatthecenterwerethestressandstrain aremaximum.Wecanthusconcludethattheexplanationofthe underestimation of the tensile strength using the standard geometryiscaused bythefactthatthefailuredoesnotinitiate at the center of the compact. Using the standard geometry to performthediametralcompressionofpharmaceuticaltabletdoes thusnotmakeitpossibletocalculatecorrectlythetensilestrength ofthetablet.
4. Conclusion
FEM analysis made it possible to emphasize that, when performing the diametral test using the standard geometry, neitherthe maximum tensile strain nor the maximum tensile stressislocatedatthecenterofthecompact.Outofcentercrack initiationmustthusbeconsideredasapossibility.Onthecontrary, whentheflattenedgeometryisusedboththemaximumtensile stressandstrainarelocatedatthecenter.Thisgeometryisthus morefavorabletomeasurethetensilestrength.
ByusingDICtechnique,itwaspossibletocomparethestrain fieldsobtainedbysimulation tothose obtainedexperimentally. Theywerefoundcomparablewhichmeansthatthelinearelastic model used in the simulation is suitable to represent the mechanical behavior of the compact during the testsand that thestressfieldscalculatedbyFEMareusabletointerpretthetest. Experimental breaking tests using both geometries indicate that the standard geometry always underestimates the tensile strengthof thecompact.Moreover for one product,thetensile strength difference is not dependent on the strength of the compact.Neverthelessthetensilestrengthdifferenceisdependent ontheproduct. Thismeansthattwo compactswhich havethe sametensilestrengthasmeasuredwiththestandardgeometry, couldhaveinfactverydifferentmechanicalstrengths.
Finally, high speed video experiments made it possible to localizethecrackinitiationduring thetests. Itconfirmedwhat wasforeseeninthesimulations:forthestandardgeometry,the
crack initiation is away from the center whereas centered fractureis obtained for theflattened technology.Thisexplains whythe standard geometryalways underestimatesthe tensile strength.
Aswementionedintheintroduction,in1970,FellandNewton asked the question “which of the values represent the tensile strength of the tablet” (Fell and Newton,1970).All theresults presentedinthepapermakeitpossibletoanswerthatthevalue obtainedusingthediametraltestonthestandardgeometrydoes notcorrespondtothetensilestrengthofthetablet,andshouldthus notbeusedassuch.
AppendixA.Supplementarydata
Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j. ijpharm.2016.09.088.
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