Experimentele karakterisatie en modelleringvan het dynamisch materiaalgedrag van de titaniumlegering Ti6Al4VExperimental Characterisation and Modellingof the Dynamic Behaviour of the Titanium Alloy Ti6Al4VJan PeirsPromotoren: prof. dr. ir. P. Verleysen, prof. dr. ir. J. DegrieckProefschrift ingediend tot het behalen van de graad van Doctor in de IngenieurswetenschappenVakgroep Toegepaste MateriaalwetenschappenVoorzitter: prof. dr. ir. J. DegrieckFaculteit Ingenieurswetenschappen en ArchitectuurAcademiejaar 2011 - 2012ISBN 978-90-8578-493-7NUR 971, 978Wettelijk depot: D/2012/10.500/19Dynamic behaviour of Ti6Al4V iPREFACE - ACKNOWLEDGMENTS Ditwerkisergekomendankzijdebijdragenvantalvanmensen.Eenwoord van dank en appreciatie is dan ook gepast. Allereerstwilikprof.PatriciaVerleysenbedankenvoordeuitstekende begeleiding en aanhoudende motivering. Uw ondersteuning overtreft ver de rol die een promotor geacht wordt te vervullen. Behalve voor het wetenschappelijk advies endeveleverrijkendediscussieswilikueveneensbedankenvoorhetinmij gestelde vertrouwen en de geboden vrijheid in het gevoerde onderzoek. Eenbijzonderwoordvandankvoorprof.JorisDegrieck.Dedooru uitgebouwdeonderzoeksgroepbiedtallmogelijkhedenomophoogstaandniveau onderzoekteverrichten.Deongedwongensfeermoedigdeaantotcreatieve oplossingen voor de gestelde uitdagingen. Bovendienwensikprof.WimVanPaepegemendr.PascalLava(KaHoSint-Lieven)tebedankenvoordehulpbijoptischerekmetingen.Ikbedankookprof. RoumenPetrovenPeterMastommijefficienttelerenwerkenmetoptischeen elektronenmicroscopen.Ookdr.IvesDeBaerewilikvanhartebedankenvoorde technische hulp met de trekbanken en de airbrush techniek. Ik heb het geluk gehad om de eerste stapjes in de Hopkinson wereld en de eerste buitenlandse congressen te kunnen doen onder de begeleiding van dr. Joost Van Slycken. Bedankt Joost voor het geluk en plezier dat ik mocht ervaren in jouw voetsporen. IgreatlyappreciatethecollaborationwithallthecolleaguesfromoftheIUAP researchnetwork.Thenumerousideasandsuggestionshaveextensively contributed to this work. A special thanks to Wim Tirry, Frederik Coghe and Gatan Gilles for their valuable work and the agreeable collaboration. Iwouldalsoliketothankthemembersofmyexaminationjuryforthe investment of their time and wisdom in the evaluation of this PhD. MijngrotewaarderinggaatuitnaarLucVandenBroecke.Bedanktvoorde originele ideen en het toegewijde vakmanschap. Ook Pascal Baele heeft tijdens de korteperiodediewehebbensamengewerkteennietonbelangrijkebijdrage geleverdaanhetexperimentelewerk.TenslottewensikookMartineBottete bedanken. Niet alleen voor het uit handen nemen van administratieve taken maar vooral om te waken over de groepssfeer in onze dienst.

iiWatmemisschiennoghetmeestzalbijblijvenishetgezelschapvan fantastischecollegas.Iedereenindevakgroepheeftwelopdeeenofandere manier zijn steentje bijgedragen. Soms door hun kritische commentaar, soms door hunrelativeringsvermogen,somsdoorhunexpertisemaaraltijddoorhun aanstekelijk enthousiasme. EenwoordvandankgaatookuitnaarmijnthesisstudentenWimClaeysen Stefan Sonck die een belangrijke bijdrage aan het experimeneel werk leverden. Mijn ouders wil ik bedanken voor hun onvoorwaardelijke steun bij alles. Zonder hun aanmoedigingen en geloof in mij zou ik het nooit zover gebracht hebben. TenslottewilikmijrichtentotmijnlievevrouwJame.Bedanktvooraldie kerendatjemeopvrolijktenaeendagvanmislukteexperimentenofvastgelopen simulaties.Bedanktvoorjegeduldwanneerereendeadlinediendegehaaldte worden. Dankzij jou is het allemaal de moeite waard. Jan Peirs Gent, 2012 Dynamic behaviour of Ti6Al4V iiiNEDERLANDSTALIGE SAMENVATTING VanalletitaniumlegeringenwordtdelegeringTi6Al4Vhetmeestgebruiktin de industrie. Het materiaal biedt een uitstekende combinatie van hoge sterkte, laag gewicht,vervormbaarheidandcorrosiebestendigheid.Hetmateriaalwordto.a. gebruiktvoorturbinemotorenenstructurelecomponentenvoorlucht-en ruimtevaarttoepassingen,hoogperformanteautoonderdelen,maritime toepassingen,medischeapparatuur,onderdelenvanchemischeinstallaties, sportuitrusting... In al deze toepassingen kan de vervormingssnelheid hoog oplopen tijdens het productieproces, tijdens normaal gebruik of tijdens ongevallen. Daarom iseendiepgaandbegripvanhetmateriaalgedragbijstootbelastingessentieel. Titanium componenten zijn relatief gezien duurder dan componenten gemaakt uit anderepopulairestructurelematerialen.Hetwordtdanookvooralgebruiktvoor veeleisendeonderdelenwaardeprijsminderbelangrijkis.Voordergelijke toepassingen is een goed begrip van het materiaalgedrag van nog groter belang. Hetonderwerpvanditdoctoraatisdekarakteriseringvanhetdynamisch gedrag van Ti6Al4V. Voor dit onderzoek zijn reksnelheden tussen 100s-1 en 1000s-1 vanbelang.Dezesnelhedenkomentypischvoorbijsnellemechanische bewerkingen, auto- en vliegtuigongevallen. De split Hopkinson bar opstelling biedt eenveelzijdigetechniekomopeengecontroleerdewijzeschokbelastingente genereren en gelijktijdig de rek en spanning in het proefstuk te meten. Zoalsdetitelaldoetvermoeden,ishetdoelvanhetvoorgesteldeonderzoek tweeledig.(1)Optimalisatievanbestaandeexperimenteletechniekenen ontwikkelingvannieuwetechiekenvoordekarakteriserenvandynamisch materiaalgedrag. Daarbij wordt aandacht besteed aan de juiste interpretatie van de experimentaleresultaten.(2)Onderzoekvanheteffectvande vervormingssnelheidophetgedragvanTi6Al4V.Ditomvatzowelhetplastische alshetbreukgedrag.Bovendienwordthetfenomeenvanadiabatische afschuifbanden bestudeert. DezestudymaaktdeeluitvanhetIUAP-VIonderzoeksprogrammavanhet FederaalWetenschapsbeleid.HierinzijnzesBelgischeuniversiteitenen onderzoekinstellingenvertegenwoordigdsamenmetnogdriebuitenlandse partners.Elkepartnerheeftspecifiekeexpertiseophetgebiedvanmaterialen onderzoekmetbetrekkingtothetmodelleren,experimenteleenmicrostructurele materiaalkarakterisering,ductielebreuk,microscopieenindustrile vervormingsprocessen...Verschillenderesultateninditwerkzijnverkregenvia samenwerking met collegas uit het IUAP netwerk. Inhoofdstuk2wordtdewetenschappelijkeentechnologischeachtergrond vanditonderzoekgentroceerdaandehandvaneenliteratuuronderzoek.Eerst wordendebelangrijksteeigenschappenbesprokenvantitaniumenTi6Al4Vinhet bijzonder.Veelaandachtwordtdaarbijbesteedaanhetfenomeenvan adiabatischeafschuifbanden.Daarnawordenmodelleringstechniekenvoorhet simulerenvanhetplastischenbreukgedragbesproken.Eenaantalvande voorgesteldemodellenzullenlaterinditwerkgebruiktwordenvooreindige

ivelementensimulaties.VervolgenswordtdewerkingvandesplitHopkinsonbar opstellinguitgelegd.Tenslottewordenverschillendemicroscopietechniekenen methodes voor lokale rekmeting voorgesteld. In hoofdstuk 3 worden statische en dynamische trekproeven gebruikt om het gedragvanTi6Al4Vtekarakteriseren.Voorafgaandaandevoorstellingvande testresultaten wordt een analyse gemaakt van de onnauwkeurigheden die kunnen optredentijdenstrekpreven.Eenpragmatischecorrectiemethodewordt voorgesteld.Vervolgenswordenderesultatenvantrekproevenbijverschillende vervormingssenlhedenvoorgesteld.Daarbijwordtzoweltitaniumindevormvan dunneplaatalsrondestaafgebruikt.Proevenwordenuitgevoerdintwee verschillendetestrichtingenomhetanisotroopmateriaalgedragteonderzoeken. Alleproevenwordengefilmdmeteenhogesnelheidscamera.Metdeverkregen beeldenwordtdanachterafdelokalerekverdelingopgemetenviadigitalimage correlation.Naastdevervormingssnelheidwordteveneensdeinvloedvande temperatuurophetmateriaalgedragonderzocht.Hiervoorwordteenextrareeks statische (isotherme) trekproeven uitgevoerd bij gecontroleerde temperatuur. Een thermischmodelwordtopgesteldvoorhetbepalenvandebalanstussen warmtegeneratie, conductie en convectie. Inhoofdstuk4wordteendynamischeafschuifproefvoordekarakterisering vanplaatmateriaalvoorgesteld.Hiervoorwordteennieuweproefstukgeometrie ontworpen.Eindigeelementensimulatieswordengebruiktomdegeometriete optimaliseren.Bovendienwordensimulatiesgebruiktomhetverbandtussenhet materiaalgedrag enerzijds en de structurele respons van het proefstuk anderzijds te bestuderen.Eveneenswordtopbasisvandiesimulatieseenvergelijkinggemaakt tussenhetnieuweproefstukeneenmeertraditioneelgebruiktproefstuk.Het geoptimaliseerde proefstuk wordt uiteindelijk gebruikt voor een aantal statische en dynamischeproevenmetTi6AlV.Daarbijwordenopnieuwlokalerekmetingen gedaanomeenbeterinzichttekrijgenindeoorsprongvandeexperimentele resultaten. Inhoofdstuk5wordteendynamischetorsietestontwikkeld.Detorsietestis eigenlijkeenafschuifproefdiegeschiktisvoorniet-plaatmaterialen.Eencompleet nieuwetestbankwordtontworpenendaadwerkelijkgebouwd.Bijzondere aandachtwordtbesteedaanhetontwerpvaneengeschikteproefstukgeometrie voordezeproeven.Naeenuitgebreidediscussieoverdeproeftechniekzelf wordenexperimenteleresultatenvantorsieproevenopTi6Al4Vvoorgesteld.Het hoofdstukwordtafgeslotenmetvieruitbreidingvandetorsieopstelling.Dankzij dezeuitbreidingenishetmogelijkomnaastdegewonedynamische torsieproevenookstatischetorsieproeven,Bauschingerproeven,gecombineerde torsie-druk proeven en proeven bij verhoogde temperatuur uit te voeren. Inhoofdstuk6wordteengecombineerdenumeriek-experimentelemethode uitgewerktomhetmateriaalgedragafteleidenuitdynamischeproeven.De methode is interessant voor elke test waar geen eenduidig verband bestaat tussen hetglobalekrach-verplaatsingenlokalespanning-rekgedrag.Demethode integreerthetbepalenvanhetmateriaalgedragmetdeidentificatievan Dynamic behaviour of Ti6Al4V vmateriaalmodelparametersvooreindigeelementensimulaties.Inditwerkwordt gebruik gemaakt van het Johnson-Cook verstevigingsmodel maar andere modellen zijnooktoepasbaar.Metbehulpvandevoorgesteldemethodekanhet materiaalgedragbepaaldwordennainsnoeringvaneentrekproefstuk.Hoofdstuk 6wordtafgeslotenmeteenvergelijkingtussenhetmateriaalgedragonder trekbelasting en afschuifbelasting. Inhoofdstuk7komthetbreukgedragonderimpactbelastingaanbod.De experimenteletechniekenvandevoorgaandehoofdstukkenlatentoeomhet effectvandespanningstoestandopdebreukeigenschappentebestuderen.Eerst wordenexperimenteleresultatenmetbetrekkingtotbreukvoorgesteld.Daarna wordtmicroscopiegebruiktommicrostructurelebreukeigenschappente bestuderen.Daarbijwordteenkwalitatieveenkwantitatieveanalysegemaaktvan dedimplesophetbreukoppervlakenholtesinhetbeschadigdemateriaal.De bedoelingisomhiermeeinzichtteverkrijgenindeonderliggendebreuk mechanismen.Tenslottewordendewaargenomenbreukkenmerkengebruiktom het breukgedrag te modelleren. De bruikbaarheid van twee verschillende modellen wordtnagegaan:hetJohnson-CookschadeinitiatiecriteriumeneenGurson-type poreus materiaalmodel. De resultaten van de simulatie worden bovendien gebruikt voor verbeterde interpretatie van de microscopische waarnemingen. Inhoofdstuk8wordenadiabatischeafschuifbandenbestudeerdmetbehulp van een speciaal ontwikkelde experimentele techniek: dynamische compressie van hoed-vormige proefstukken. Na een korte introductie van de testmethode worden deresultatenvanproevenmetTi6Al4Vvoorgesteld.Dankzijhetgebruikvan onderbrokenproevenkunnenvijfstadiaindevervormingvanhethoed-vormig proefstukonderscheidenworden.Daarnawordtviaeindigeelementensimulaties eenanalysegemaaktvanhetgedragvandehoed-vormigeproefstukken.De simulatieswordengebruiktvooreenbetereinterpretatievandeexperimentele resultaten.Bijzondereaandachtwordtbesteedaandeinvloedvande proefstukgeometrie.DeverkregenafschuifbandenwordenviaTEM(transmissie elektronenmicroscopie)enaanverwantetechniekenonderzochtzodatinzicht verkregen wordt in de microstructuur van gelokaliseerde rek. Debelangrijkstebevindingenvanditonderzoekzijnsamengevatinhoofdstuk 9.Bovendieniseenlijsttoegevoegdvannieuweideenensuggestiesvoorverder onderzoek.

viEXECUTIVE SUMMARY Ti6Al4Visthemostcommonlyusedtitaniumalloyinindustry.Thematerial offersanexcellentcombinationofhighstrength,lightweight,formabilityand corrosionresistance.Someofthemanyapplicationswherethisalloyisusedfor includeaircraftturbineenginecomponents,aircraftstructuralcomponents, aerospacefasteners,high-performanceautomotiveparts,marineapplications, medicaldevices,partsforchemicalinstallations,sportsequipment...Inthese typicalapplications,theloadingspeedcanbeveryhighduringthemanufacturing process,duringnormaloperationoraccidents.Therefore,aprofound understandingofthematerialsresponsetoimpactloadsisessential.Sincethe priceoftitaniumcomponentsishigherthancomponentsfrommanyother structuralmaterials,itisusedforverydemandingapplications.Forsuch applications understanding of the material behaviour is even more crucial. The topic of this PhD is the characterisation of the impact dynamic behaviour of the titanium alloy Ti6Al4V.For this research highstrain rateswithin the range of 102s-1 to 103s-1 are of interest. These strain rates are typically present during high speedmachiningandformingoperations,vehiclecrashapplicationsandimpact. For testing materials in this range of strain rates, the so-called split Hopkinson bar techniqueisused.SplitHopkinsonbarsetupsofferaversatiletechniqueto generate controlled impact loads and simultaneously measure the high strain rate response of the tested material sample. Asthetitlesuggests,theobjectiveoftheproposedresearchistwofold.(1) Optimisingexistingexperimentaltechniquesanddevelopingnewexperimental techniquesforthecharacterisationofthehighstrainratematerialbehaviour. Thereby, attention is paid to the correct interpretation of the experimental results. (2) Characterising the high strain rate behaviour of Ti6Al4V. This includes both the plasticbehaviourandthefracturebehaviour.Furthermore,thephenomenonof adiabatic shear bands is studied. The present work is part of the IUAP VI research programme and is funded by theBelgianSciencePolicy.ItinvolvessixBelgianuniversitiesandthreeforeign partners.Eachpartnerhasspecificexpertiseinthefieldofmaterialsresearch coveringmodelling,microstructuralmaterialcharacterisation,ductilefracture, microscopy, experimental material characterisation, industrial forming processes... Several results in this work are obtained in collaboration with partners of the IUAP project. In chapter 2, the scientific and technological background of this PhD research is introducedwithaliteraturereview.First,anoverviewofthemostimportant featuresoftheinvestigatedTi6Al4Visgiven.Specialattentionispaidtothe phenomenonofadiabaticshearlocalisation.Thenmodellingtechniquesforthe plasticandfracturebehaviourofmetalsarediscussed.Someofthesemodelswill beusedforfiniteelementsimulationslateronthiswork.Finally,ageneral summaryoftheexperimentaltechniquesforhighstrainratematerial Dynamic behaviour of Ti6Al4V viicharacterisationisgiven.Alsotechniquesforfull-fieldstrainmeasurementsand microstructural material characterisation are presented. Inchapter3,tensiletestsareusedtocharacterisethebehaviourofTi6Al4V. Prior to the presentation of the test results, an analysis is made of the inaccuracies that can occur during tensile tests and a pragmatic correction method is proposed. Next,resultsoftensiletestsatdifferentstrainratesonTi6Al4Varepresented. Thereby,sheetspecimensandroundaxis-symmetricdog-boneshapedspecimens areused.Testsareconductedintwoperpendiculardirections.Duringthetests, high speed camera recordings and digital image correlation is applied to obtain the local strain distribution in the specimen. Finally, the effect of thermal softening is studiedbyanadditionalseriesof(isothermal)tensiletestswithcontrolled temperature. In addition, a thermal numerical model for the heat generation, heat conduction and convection is presented. In chapter 4, the development of a dynamic shear test for characterisation of sheetmaterialispresented.Therefore,anovelspecimengeometryisdesigned. Finiteelementsimulationsareusedtooptimisethespecimengeometry.Furthermore,simulationsareusedtostudytherelationbetweenthematerial behaviour and the specimens structural behaviour. A comparison is made between thenovelspecimengeometryandthesimplesheartest.Next,experimentsare carriedoutonTi6Al4Vsheet.Digitalimagecorrelationandtrackingofalinegrid are two techniques that areused forenhanced interpretation of the experimental results. Inchapter5,adynamictorsiontestisdeveloped.Thetorsiontestisashear testforbulkmaterials.AnewtorsionalsplitHopkinsonbarsetuphasbeen designed and actually built. Special attention is paid to the design of an appropriate specimengeometryforthesetests.Afteracomprehensivediscussionaboutthe testtechniqueitself,experimentalresultsoftorsiontestsonTi6Al4Vare presented.Finally,fourextensionsofthesetupforcomprehensivematerial characterisationarepresented:quasi-statictorsiontests,Bauschingertests, combined torsion-compression tests and elevated temperature tests. Inchapter6,acombinedexperimental-numericalmethodisproposedto extractthematerialbehaviourfromdynamicexperiments.Themethodis interesting for every test technique where no unambiguous relation exists between theglobalforce-displacementandlocalstress-strainbehaviour.Themethod integratestheidentificationofthematerialmodelparametersusedforthefinite element simulations with the extraction of the material behaviour from mechanical tests.Forthetensiletests,evenstress-straindatabeyonddiffuseneckingare retrieved.Acomparisonismadebetweenthematerialbehaviourextractedfrom the tensile, shear and torsion experiments. Inchapter7,thefinalphaseoftheexperimentsisstudied:fracture.The experimentaltechniques,presentedinthepreviouschapters,allowstudyingthe effectsofstresstriaxialityandstrainrateonthefractureproperties.First,the experimentalresultsrelatedtofracturearepresented.Second,opticaland

viiiscanning electron microscopy is used to gather data on the microstructural fracture properties.Thereby,dimplesonthefracturesurfaceandtheoccurrenceofvoids arestudiedbothqualitativelyandquantitatively.Thegoalistogaininsightinthe underlying fracture mechanisms. Finally, the observed fracture properties are used to model the fracture behaviour for finite element simulations. Performance of the phenomenological Johnson-Cook damage initiation criterion and a physically based Gurson-typefailuremodelarecompared.Thesimulationresultsareusedfor enhanced interpretation of the microscopic observations. Inchapter8,theformationofadiabaticshearbandsinTi6Al4Visstudiedby meansofaspecificexperimentaltechnique:dynamiccompressionofhat-shaped specimens.Afterabriefintroductionofthetestmethod,experimentalresultson Ti6Al4Varepresented.Therebyseveralstagesintheformationprocessofshear bandsaredistinguished.Afterwards,anumericalanalysisismadeofthe mechanicalresponseofthehat-shapedspecimen.Thesimulationsareusedfor enhanced interpretation of the experimental results. Special attention is paid to the influence of the specimen geometry. Finally, TEM techniques are used to study the localmicrostructureandcompositionintheshearbandandassuchthedriving mechanism for the ASB formation. ThemostimportantachievementsofthisPhDresearcharesummarisedin chapter9.Moreover,alistofnewideasandsuggestionsforfutureworkis presented as well. Dynamic behaviour of Ti6Al4V ixTABLE OF CONTENTS PREFACE - ACKNOWLEDGMENTSI NEDERLANDSTALIGE SAMENVATTINGIII EXECUTIVE SUMMARYVI TABLE OF CONTENTSIX CHAPTER 1 INTRODUCTION1 1.1. FRAMEWORK OF THE PHD1 1.2. OBJECTIVES OF THIS PHD2 1.3. METHODOLOGY4 1.4. MATERIALS5 1.5. APPLICATIONS6 REFERENCES8 CHAPTER 2MATERIALS AND METHODS: STATE OF THE ART9 2.1. TI6AL4V9 2.1.1. Introduction [1]9 2.1.2. Microstructure of titanium and Ti6Al4V10 2.1.3. Deformation mechanism of titanium and Ti6Al4V12 2.2. ADIABATIC SHEAR BANDS15 2.2.1. Definition of shear bands [16]15 2.2.2. Characteristics of shear bands [16]16 2.2.3. Formation of ASBs18 2.2.3.a. Mechanism18 2.2.3.b. Prediction of occurrence of shear bands19 2.2.4. Dynamic recovery and recrystallization within shear bands21 2.2.4.a. Microstructural restoration21 2.2.4.b. Dynamic restoration22 2.2.4.c. DRX in shear bands26 2.2.5. Unsolved questions regarding shear bands29 2.3. MATERIAL MODELLING TECHNIQUES30 2.3.1. Plastic material behaviour30 2.3.1.a. Introduction30 2.3.1.b. Yield surface30 2.3.1.c. Flow rule31 2.3.1.d. Hardening law32 2.3.2. Damage and fracture33 2.3.2.a. Introduction33 2.3.2.b. Johnson-Cook damage initiation criterion34 2.3.2.c. Porous metal plasticity35

x2.3.3. Microstructural evolution37 2.3.3.a. Introduction37 2.3.3.b. Crystal plasticity models37 2.3.3.c. Phase-field modelling38 2.3.3.d. Cellular automaton39 2.4. FINITE ELEMENT MODELLING (FEM)43 2.5. HIGH STRAIN RATE TESTING: SPLIT HOPKINSON TENSILE BAR SET-UP45 2.5.1. Introduction45 2.5.2. Principle45 2.5.3. Practical realisation48 2.6. FULL-FIELD STRAIN MEASUREMENT49 2.7. MICROSTRUCTURAL CHARACTERISATION52 2.7.1. Introduction52 2.7.2. Optical microscopy (LOM)53 2.7.3. Scanning electron microscopy (SEM)54 2.7.4. Transmission electron microscopy (TEM)54 REFERENCES56 CHAPTER 3 TENSILE TESTS63 3.1. TEST PROGRAM AND SPECIMENS63 3.1.1. Tensile test method63 3.1.2. Sheet material64 3.1.3. Bulk material65 3.2. EXPERIMENTAL SET-UP67 3.2.1. Static experiments67 3.2.1.a. Sheet materials67 3.2.1.b. Bulk materials71 3.2.2. Dynamic experiments72 3.2.2.a. Sheet materials72 3.2.2.b. Bulk materials72 3.3. EXPERIMENTAL RESULTS73 3.3.1. Quasi-static tensile experiments on GL50 specimens73 3.3.2. Static and dynamic tensile experiments on GL5 specimens75 3.3.3. Static and dynamic tensile experiments on round specimens79 3.3.3.a. Influence of the strain rate79 3.3.3.b. Influence of the initial texture80 3.3.3.c. Strain distribution81 3.4. STATIC COMPRESSION EXPERIMENTS ON CT SPECIMENS82 3.5. INFLUENCE OF TEMPERATURE VARIATIONS85 3.5.1. Introduction85 3.5.2. Simulation of heat generation and transfer86 3.5.2.a. Thermal model86 3.5.2.b. Temperature profile in the specimen89 Dynamic behaviour of Ti6Al4V xi3.5.2.c. Temperature evolution in the centre of the specimen91 3.5.2.d. Transition from isothermal to adiabatic process92 3.5.2.e. Heat conduction in a narrow band93 3.5.3. Temperature controlled experiments94 3.5.3.a. Experimental set-up94 3.5.3.b. Results of temperature controlled tensile tests95 3.6. CONCLUSIONS99 3.6.1. Conclusions related to the behaviour of Ti6Al4V99 3.6.2. Conclusions related to tensile testing99 REFERENCES101 CHAPTER 4 IN-PLANE SHEAR TESTS103 4.1. INTRODUCTION TO SHEAR TESTS103 4.2. DESIGN OF THE IN-PLANE SHEAR TEST104 4.2.1. Introduction104 4.2.2. Shear specimen requirements106 4.2.3. Finite element simulations107 4.2.4. Specimen geometry optimisation109 4.2.4.a. Notch shape109 4.2.4.b. Width and length of the shear region111 4.2.4.c. Notch position112 4.2.5. Final design114 4.3. DISCUSSION115 4.3.1. Determination of stress and strain115 4.3.2. Comparison with simple shear test117 4.4. SHEAR EXPERIMENTS ON TI6AL4V119 4.4.1. Test program119 4.4.2. Experimental results120 4.4.3. Effect of strain rate on strain distribution125 4.5. APPLICABILITY OF THE PLANAR SHEAR SPECIMEN TO OTHER MATERIALS126 4.6. CONCLUSIONS127 REFERENCES129 CHAPTER 5 DYNAMIC TORSION TESTS131 5.1. INTRODUCTION131 5.2. PRINCIPLE OF SPLIT HOPKINSON TORSIONAL BAR SET-UP132 5.3. DESIGN OF THE TORSIONAL TEST SETUP134 5.3.1. Specifications of the setup134 5.3.2. Hopkinson bars and supports137 5.3.2.a. Material selection137 5.3.2.b. Bar length138 5.3.2.c. Bar diameter138 5.3.2.d. Bar support139

xii 5.3.3. Drive mechanism139 5.3.4. Clamping mechanism141 5.3.5. Frame143 5.3.6. Pneumatic circuit144 5.3.7. Control and instrumentation145 5.4. MOUNTING OF THE TORSION SPECIMEN147 5.4.1. Requirements147 5.4.2. Specimen with round flanges glued to Hopkinson bar149 5.4.3. Specimens with form-fitting connection150 5.4.4. Practical realisation151 5.4.5. Effect of discontinuity on wave propagation152 5.4.5.a. General FE model152 5.4.5.b. Effects of discontinuity153 5.5. TORSION SPECIMEN GEOMETRY155 5.5.1. Geometry requirements155 5.5.2. FE model of the torsion specimen156 5.5.3. Gauge length Ls157 5.5.4. Diameter di158 5.5.5. Wall-thickness hs159 5.5.6. Radius of the transition zone R1159 5.5.7. Imperfections161 5.5.8. Specimen production and first tests164 5.5.9. Final torsion specimen geometry166 5.6. TEST RESULTS167 5.6.1. Stress-strain curves167 5.6.2. DIC measurements on torsion specimen168 5.7. EXTENSION OF THE HOPKINSON SETUP FOR COMPREHENSIVE MATERIAL CHARACTERISATION170 5.7.1. Overview of the extensions170 5.7.2. Quasi-static experiments170 5.7.2.a. Why quasi-static experiments170 5.7.2.b. Method170 5.7.2.c. Results and discussion172 5.7.3. Bauschinger experiments173 5.7.3.a. Motivation for Bauschinger experiments173 5.7.3.b. Method174 5.7.3.c. Results of Bauschinger tests175 5.7.4. Combined torsion-compression experiments178 5.7.4.a. Motivation for combined torsion-compression experiments 178 5.7.4.b. Method178 5.7.4.c. Results of combined experiments180 5.7.5. Elevated temperature experiments180 Dynamic behaviour of Ti6Al4V xiii 5.7.5.a. Motivation for elevated temperature experiments180 5.7.5.b. Method181 5.7.5.c. Results of elevated temperature experiments182 5.8. CONCLUSIONS183 REFERENCES185 CHAPTER6MATERIALBEHAVIOUREXTRACTIONANDMODELPARAMETER IDENTIFICATION FROM DYNAMIC EXPERIMENTS189 6.1. INTRODUCTION189 6.2. MATERIAL BEHAVIOUR EXTRACTION METHOD192 6.3. APPLICATION ON SHEET MATERIAL194 6.3.1. Extracted model194 6.3.2. Discussion197 6.3.2.a. Evaluation of extracted and modelled material behaviour197 6.3.2.b. Validation of the model and extraction technique200 6.4. APPLICATION ON BULK MATERIAL202 6.4.1. Motivation202 6.4.2. Tensile tests202 6.4.3. Torsion tests205 6.4.4. Comparison tensile torsion206 6.5. CONCLUSIONS206 REFERENCES208 CHAPTER 7 DYNAMIC FRACTURE ASPECTS211 7.1. METHODS211 7.2. EXPERIMENTAL OBSERVATIONS214 7.2.1. Sheet material214 7.2.2. Bulk material217 7.3. FRACTURE ANALYSIS219 7.3.1. Fracture strain219 7.3.2. Fractography222 7.3.2.a. Introduction222 7.3.2.b. Sheet material223 7.3.2.c. Bulk material226 7.3.3. Voids228 7.3.3.a. Introduction228 7.3.3.b. Qualitative analysis229 7.3.3.c. Quantitative analysis232 7.4. SIMULATION OF FRACTURE235 7.4.1. Phenomenological model236 7.4.2. Gurson-Tvergaard-Needleman model240 7.4.2.a. Introduction240 7.4.2.b. Tensile tests on round specimens240

xiv7.4.2.c. Torsion tests241 7.5. CONCLUSIONS243 REFERENCES244 CHAPTER 8 ADIABATIC SHEAR LOCALISATION245 8.1. INTRODUCTION245 8.2. EXPERIMENTAL TECHNIQUE246 8.2.1. The hat-shaped specimen246 8.2.2. Dynamic tests248 8.2.3. Quasi-static tests249 8.2.4. Test programme250 8.3. EXPERIMENTAL RESULTS251 8.3.1. Specimen response251 8.3.2. Deformation process of hat-shaped specimen252 8.3.2.a. Step 1: onset of plastic deformation (Exp8)253 8.3.2.b. Step 2: stable deformation253 8.3.2.c. Step 3: instable deformation (Exp7 and Exp9)254 8.3.2.d. Step 4: fully developed shear band (Exp4, 5, 6, 7, 9)256 8.3.2.e. Step 5: plugging (Exp1, 2 and 3)257 8.3.3. Relation to fracture258 8.4. FE SIMULATIONS260 8.4.1. Introduction260 8.4.2. Finite element model260 8.5. DISCUSSION263 8.5.1. Stress and strain distribution in the specimen263 8.5.2. Stress components265 8.5.3. Influence of the specimen geometry267 8.5.3.a. Width of the shear region268 8.5.3.b. Height of the shear region269 8.5.3.c. Radius of the corners270 8.5.4. Temperature generation in the shear band271 8.5.5. Effect of strain rate and heat conduction272 8.5.6. Effect of non-homogeneous material behaviour272 8.6. FROM GLOBAL TO LOCAL BEHAVIOUR273 8.6.1. Shear stress274 8.6.2. Shear strain276 8.7. TEM-STUDY277 8.7.1. Introduction277 8.7.2. Specimen preparation278 8.7.3. TEM observations279 8.7.3.a. Conventional TEM279 8.7.3.b. Elemental composition284 8.7.3.c. Conical dark field TEM285 Dynamic behaviour of Ti6Al4V xv 8.7.4. Discussion288 8.7.4.a. Grain morphology288 8.7.4.b. Contribution of and phase288 8.7.4.c. Microstructural evolution289 8.7.4.d. Dynamic recrystallization289 8.8. CONCLUSIONS290 8.8.1. Experiments on Ti6Al4V290 8.8.2. Finite element simulations290 8.8.3. TEM study291 REFERENCES293 CHAPTER 9 CONCLUSIONS297 9.1. CONCLUSIONS297 9.2. PERSPECTIVES301 A LIST OF PUBLICATIONS303 A.1. JOURNAL PUBLICATIONS INCLUDED IN THE SCI (A1)303 A.2. JOURNAL PUBLICATIONS NOT-INCLUDED IN THE SCI (A2-A3-A4)303 A.3. CONFERENCE PROCEEDING INCLUDED IN THE CPCI-S (P1)303 A.4. CONFERENCE PROCEEDINGS NOT-INCLUDED IN THE CPCI-S (C1)304 A.5. MISCELLANEOUS305 B INTERNATIONAL CONFERENCES: OVERVIEW OF ACTIVE PARTICIPATION306 C SCIENTIFIC AWARDS306

xvi Chapter 1Dynamic behaviour of Ti6Al4V 1 Chapter 1 INTRODUCTION Thisintroductorychapteroutlinesthecontextofthepresentedwork. Besides its scientific basis, the place in the framework of the IUAP-VI project is shown.Next,thegeneralobjectivesofthestudyareformulatedandthe methodologyfollowedtoachievethemisexplained.Finally,some applications of the research are explained. 1.1. FRAMEWORK OF THE PHD Thepresentresearchcontributestothefiveyearprojectphysicsbased multilevel mechanics of materials thatwas initiatedin 2007. This project is part of the Interuniversity Attraction Poles phase VI research programme and is funded by theBelgianSciencePolicy.ItinvolvessixBelgianuniversitiesandthreeforeign partners:KatholiekeUniversiteitLeuven,UniversiteitAntwerpen,Universit Catholique de Louvain, Universit de Lige, Koninklijke Militaire School, Universiteit Gent, RijksuniversiteitGroningen (NL), Universit Paris 13(FR),Centro de Estudios e Investigaciones Tecnicas (SP). Each partner has a specific expertise in the field of materialsresearchcoveringmodelling,microstructuralmaterialcharacterisation, ductilefracture,microscopy,experimentalmaterialcharacterisation,industrial forming processes... Theprojectsmaintopicistheinteractionbetweenthedeformation mechanismsatvariouslengthscales,includingdamage.Eventsonthevarious length scales, from nano- to macroscale, may also cause important changes of the material and mechanical properties (strength and ductility). Various metal systems arestudied.Themetalsincludedinthestudywereselectedbythework-package leaders in the first year of the project and include AA1050 and 6005A-T6 aluminium alloys,DPFe-MnTWIPsteels,-Ti,Ti5553andTi6Al4Vtitaniumalloys.These materials were chosen because of their interesting plasticity mechanisms and their use in current engineering applications. TheIUAPprojectisdividedinto4workpackageswhichhavetheirowngoals: dislocationdominatedplasticity(WP1),twinningdominatedplasticity(WP2), damage(WP3)andmodellingofmechanicalbehaviour(WP4).Although,the projectcoversawiderangeoftopics,thegeneralobjectiveoftheIUAPprojectis twofold [1]: 1.Understandingandmodellingofthetwo-wayrelationshipbetweenthe structureofmetalsatnano-scaleandmeso-scaleandthemechanical behaviouratthemacro-scale."Structure"isageneraltermincluding dislocationpatterns,microstructure,grainstructure,crystallographic textureanddamage."MechanicalBehaviour"includesflowstress,work hardeningandworksoftening,effectsofstrainpathchanges,ductile fractureandplasticanisotropy.Attentionmustbepaidtothecoupling betweenthelengthscales.Thelatterisbelievedtoinfluenceorbeing Introduction 2 influencedbyalotof phenomena,ofwhichthefollowingaretobetaken intoaccount:dislocation,mechanicaltwinningandcompetitionbetween thesetwo,heterogeneousdistributionsofstressandstrain,sizeeffects and finally also comparing behaviour at low and very high strain rates. 2.Developmentofmodelsforthemechanicalbehaviourofthematerialat macro-scaletobeusedinfiniteelementsimulationsatengineeringscale. Anessentialaspectisthedevelopmentofappropriateschemesforthe identification of the parameters of thesemacro-scale models on the basis of predictions made by multilevel-models. The engineering motivation for looking at these phenomena at different length scales involves the development of higher performance materials, the optimisation of the manufacturing operations, and the improvement of the design and integrity assessment methods for both traditional (transport, energy) and emerging (MeMS, multifunctional active panels) structures. TheroleofthedepartmentofMaterialsScienceandEngineeringofGhent University in this IUAP project mainly focuses on the experimental characterisation andmorespecificdynamicmaterialtesting.Duringthelastyears,thedepartment hasacquaintedalotofexperiencewithexperimentalcharacterisationofthe impact behaviour of materials [2]. Accurate experimental data is not only required fortheidentificationofmaterialmodelparametersbutalsotovalidatethe developedmodels.Dynamictestsyieldadditionalinformationaboutplasticityat themicroscopicscalebecausedeformationmechanismsareoftenstrainrate dependent.GhentUniversityshouldnotonlyprovideexperimentaldatatothe otherpartnersbutalsooptimiseexistingexperimentaltechniquesand development of new techniques.Apart from the experimental work a second task of Ghent University is the development of a new solid-shell element for efficient FE simulationsofthin-walledstructureswithaccuratethroughthicknessstress calculations.InthiswayUGentmakesacontributiontoeachofthe4work-packages. The different IUAP partners decide independently on their research. However, data, materials and other resources are shared to ensure a common working basis. BesidesthegeneralIUAPmeetingswhichareorganisedtwiceayear,meetings betweenthesubgroupsareorganisedregularlytoexchangeknowledge.More information about the practical organisation of the research network can be found in the yearly research reports. 1.2. OBJECTIVES OF THIS PHD The topic of this PhD is the characterisation of the impact dynamic behaviour of the titanium alloy Ti6Al4V.For this research highstrain rateswithin the range of102s-1to103s-1areofinterest.Thesestrainratesaretypicallypresentinhigh speedmachiningandformingoperations,vehiclecrashapplicationsandimpact. For testing materials at this strain rate, the so-called Hopkinson technique is used. Figure 1-1 shows a strain rate classification with corresponding test techniques [3]. Chapter 1Dynamic behaviour of Ti6Al4V 3 Figure 1-1: Overview of strain rates classification Ti6Al4Visthemostcommonlyusedtitaniumalloyinindustry.Thematerial offersanexcellentcombinationofhighstrength,lightweight,formabilityand corrosionresistance.Someofthemanyapplicationswherethisalloyisusedfor includeaircraftturbineenginecomponents,aircraftstructuralcomponents, aerospacefasteners,high-performanceautomotiveparts,marineapplications, medicaldevices,partsforchemicalinstallations,sportsequipment...Inthese typicalapplications,theloadingspeedcanbeveryhighduringthemanufacturing process,duringnormaloperationoraccidentalfailure.Therefore,aprofound understandingofthematerialsresponsetoimpactloadsisessential.Sincethe priceoftitaniumishigherthanothermaterialsitisusedforverydemanding applicationsforwhichunderstandingofthematerialbehaviourisevenmore crucial. Aswillbeseeninthiswork,Ti6Al4Vhassomefeaturesthatcomplicate mechanicaltests.Firstly,Ti6Al4Vhasahighyieldstrengthandconsequently, relativelyhightestforcesarerequiredtodeformthematerial.Secondly,Ti6Al4V doeshavelowstrainhardeningwhichcausesunstableplasticflowandstrain localisationinmanyexperiments.Thirdly,thethermalconductivityofTi6Al4Vis lowincomparisonwithothermetals,promotingnon-uniformtemperature distribution in test specimens. All those aspects ask for a dedicated approach. Asthetitlesuggests,theobjectiveoftheproposedresearchconsistsoftwo main goals: 1.Optimisingexistingexperimentaltechniquesanddevelopingnew experimentaltechniquesforthecharacterisationofthehighstrainrate materialbehaviour.AllusedtechniquesarebasedonthesplitHopkinson bar setup. With this setup a material sample can be subjected to an impact loadinacontrolledandmeasurableway.Differentsetupconfigurations leading to various test conditions are possible. Although the basic principle ofthistestingtechniqueisratherstraightforward,interpretationofthe experimentalresultsislessobvious.Identificationofthematerial behaviourfromadynamictestremainsachallenge.Indeed,the experimentalresultsnotonlyreflectthematerialbehaviourbutalso depend largely on the test setup and the specimens structural behaviour. Introduction 4 Furthermore,thespecimensstructuralbehaviourisinfluencedbythe materialbehaviour.Tounderstandthecomplexinteractionbetweenthe two,finiteelementsimulations(FE)andadvancedmeasurement techniques are indispensable tools.Experimentaltechniquesforstaticmaterialcharacterisationcan usuallynotbecopiedtodynamictestswithoutmodifications.Dynamic testsimposespecificconstraintstotheusedspecimengeometry, boundaryconditionsandinstrumentation.Consequently,cautionis requiredwhenresultsfromstandardisedstaticmaterialtestsare comparedwithresultsfromdynamictests.Ontop,differentmaterials demand for a tailored approach. Newexperimentaltechniquesandapproachesforinterpretationof the experimental results arerequired to continue thefastprogress in the knowledge of the strain rate dependent material behaviour. 2.CharacterisingthehighstrainratebehaviourofTi6Al4Vtitaniumalloy. Thisincludesboththeplasticbehaviourandthefracturebehaviour.For example, titaniumis known to be verysensitive forstrainlocalisation and the formation of adiabatic shear bands (ASBs). Since strain localisation is a precursor to failure, it is very important to comprehend the conditions and mechanisms of this deformation process.The experimental resultswill be usedasinputforthefiniteelementmodelthatisusedforimprovingthe interpretationoftheexperimentalresults.Followingthemultilevel approachoftheIUAPproject,macroscopicexperimentalresultsare combinedwithmicroscopicobservationsofdeformedmicrostructures and damage. Acquiredexperimentaldataandknowledgewerecommunicatedto other IUAP partners who are using it for their multilevel modelling work. 1.3. METHODOLOGY Several test techniques are required to achieve the predefined objectives. The comprehensive material characterisation involves static and dynamic tests, various stressstates,differenttemperatures,macro-andmicroscopicanalysis...The complexinteractionbetweenstrainrate,temperature,loadingconditions, microstructureandthemacroscopicmaterialbehaviourdemandsforaconsistent methodology: 1.A literature review on a selection of useful test and analysis techniques is madeinordertoevaluatetheapplicabilityofthetechniquesfor characterisationofTi6Al4V.Advantagesandshortcomingsofthe techniquesareidentified.Publishedexperimentalresultsaregathered which are used for comparison. 2.Where necessary, the selected experimental techniques are optimised to fitwiththespecificconstraintsimposedbyTi6Al4V.Inthisstep,the availabilityofresourcesistakenintoaccount,suchasmaterials,test setups, manufacturing capabilities and budget... For some techniques only the specimen geometry or instrumentation are adapted while for another testtechniqueacompletenewexperimentalsetupisbuilt.The Chapter 1Dynamic behaviour of Ti6Al4V 5 optimisation of existing techniques and development of new techniques is usually done with the support of finite element simulations. Material data fromliteratureismostlyusedbecauseowntestdataisstillscarceduring this phase of the research. 3.ExperimentsarecarriedoutonTi6Al4Vusingthedevelopedtechniques. Wherepossible,different(redundant)methodsareusedtomeasurethe sameproperties.Inthisway,insightintothemeasurementerrorsis acquired. 4.Therawexperimentaldataiscombinedwithresultsfromfiniteelement simulations to improve the interpretation of the experimental outcome. A combinedexperimental-numericalmethodisdevelopedtoextractthe materialbehaviourfromtheexperimentalresults.Theestablished materialbehaviourisusedforbettermaterialmodelparameter identification. Full-field strain measurement by digital image correlation is usedtovalidatethemodel.Thecombinedexperimental-numerical method is also used in the study of fracture. 5.Specimens are subjected to a microscopic investigation. Light and electron microscopy techniques are used. Microstructural features and damage are characterised.Resultsfromtheseobservationsarealsousedfor identificationofmaterialmodelparameters(e.g.voidnucleationand growthmodels).Resultsfromdifferenttestsarecombinedtoinvestigate thedrivingmechanismsforplasticityanddamage.Thisapproachis reflected in the main and substructure of the work. Thisworkcontributestothefieldsofbothexperimentalmechanicsand materialsscience.Insightinexistingdynamictestingtechniquesisacquiredand wherepossibleimprovementsaremade.Anewmethodforsheartestsonsheet metalsisdeveloped.Forbulkmetals,anewHopkinsontorsionalsetuphasbeen designedandbuiltinthelabofthedepartmentofMaterialsScienceand EngineeringatGhentUniversity.Digitalimagecorrelationisappliedtohighstrain rateexperimentstoimprovetheaccuracyoftheexperimentallyestablished materialbehaviour.Theobservedexperimentalbehaviourismodelledandall experimental results are compared with finite element simulations. A large amount ofdataonthehighstrainratetensileandshearbehaviourofTi6Al4Viscollected. Resultsareputinthelightofplasticityandfailuremechanisms,includingthe formation of adiabatic shear bands. The macroscopic test results are extended with microscopicobservationsbyopticalmicroscopy(LOM),scanningelectron microscopy (SEM) and transmission electron microscopy (TEM). 1.4. MATERIALS TwodifferentproductformsofTi6Al4Vareused:bulkmaterialandsheet material.Eachproductformhasitsownadvantagesfortestingand characterisation of Ti6Al4V. The bulk material comes in the form of hot rolled bars inmill-annealedcondition.Therodshaveadiameterof16mm0.18mm.Thebars areproducedbyTIMETintheUK.Therolledannealedsheetshaveathicknessof 0.6mm0.06mm. The sheets are produced by TIMET in the USA. Both materials are bought via the TIMET Savoie S.A. Service Center located in Ugine, France. Previous Introduction 6 studieshavebeenconductedonthesebarsandsheetsbyrespectivelythe Koninklijke Militaire School and Universit de Lige which are partners in the IUAP project.Althoughtheannealedbulkandsheetmaterialarebothclassifiedas TIMETAL6-4theydonothaveexactlythesamecompositionnormicrostructure. ThetablebelowshowstheirchemicalcompositionasprovidedbytheTIMETtest report [4, 5]: Table 1-1: Typical average chemical composition of used Ti6Al4V (weight %) CFeVAlON Bar0.010.184.146.470.190.005 Sheet0.0090.163.976.260.190.009 Differentbehaviourofthebulkandsheetmaterialisexpectedbecausethe microstructure of Ti6Al4V strongly depends on the production process parameters [6]. More information about Ti6Al4V is found in Chapter 2, 2.1. 1.5. APPLICATIONS The research into the impact behaviour of materials counts numerous practical applicationsincludingfastproductionprocesses,accidentalimpactloadingof componentsincars,aerospacestructuresetc.Manyresultsobtainedinthiswork forTi6Al4Varealsotransmissibletoothermaterials.Theimportanceofthe researchtopicisillustratedbytheseveralindustrialresearchprojectswherethis PhD work was involved in. One fascinating application of titanium is found in aircraft jet engines. The fan blades and the casing of a jet engine are among the numerous titanium parts that areusedinaerospaceapplications(Figure1-2).Oneoftheproblemsthataircraft manufacturersencounterisafanbladebreakingoff,e.g.afterabirdstrike.To avoid possible catastrophic consequences it is necessary that all fragments are kept inside the engine so that they cannot damage other vital components in the wings orfuselage.Thisiscalledacontainedenginefailure.Accuratepredictionofthe forcesexertedbytheloosefanbladeonthecasingandresponseofthecasing requires the knowledge of the materials high strain rate behaviour. This engineering problem is studied in theFABULOUS project (Fan Blade Out). Intheframeworkofthisproject,dynamictensiletestsandtorsiontestsonfan blade material (Ti6Al4V) in two different material orientations and at two different temperatures have been conducted. Hereby, the newly developed dynamic torsion setupisused.Interestingresultsontheanisotropicplasticandfracturebehaviour of the material are found. Chapter 1Dynamic behaviour of Ti6Al4V 7 Figure 1-2: Power source of an Airbus A380: GP7200 engine containing a low pressure compressor with Ti6Al4V blades. Apartfromthisstudyontitaniumforjetengines,alsothedynamicbehaviour ofothermetalshasbeenstudiedtogetherwithindustrialpartners.Forexample, theformingpropertiesathighstrainratesofadvancedsteelsandaluminium alloyshavebeenstudiedintheMAGPULSproject.Theprojectinvolveddynamic tensile tests on several metals to study the effect of the strain rate on the forming limit diagrams (FLDs). Theimpactbehaviourofsawingwireforcuttingsiliconusedforsolarpanels wasstudiedinanotherproject.ThewiresfromBekaertwithadiameterofonly 120m have to be very strong and need to have a sufficient fracture toughness to withstand the impact loads that occur during the cuttingprocess. A technique has beendevelopedformeasuringtheimpactpropertiesofsuchwiresbyHopkinson tensile tests. Test results of seven different types of wire clearly demonstrate that thestrainratedependentbehaviourmakesthedifferencebetweengoodandbad performing wires. Finally, the dynamic fracture toughness of pipeline steels from ArcelorMittal is studied. Fracture toughnessis crucialfor the safety of pipelines transporting oil or gas products. High strain rates can occur during accidental use of the pipeline and duringcrackpropagation.Athoroughunderstandingofthestressstate, temperatureandstrainratedependentfracturepropertiesisrequiredforreliable riskassessment.Forthisproject,quasi-staticanddynamicexperimentswith differentstressstates,temperatures(-60Candroomtemperature)andstrain rates have been carried out on X70 pipeline steel. Introduction 8 REFERENCES [1]B.Verlinden,ProjectP6/24overview:physicsbasedmultilevelmechanicsofmetals. 2007. p.5. [2]J.VanSlycken,AdvancedUseofaSplitHopkinsonBarSetup-ApplicationtoTRIP Steels. vol. PhD thesis, 2008. [3]S.Nemat-Nasser,IntroductiontoHighStrainRateTesting.MaterialsPark:ASM International, 2000. [4]TIMET, Certificate of conformity 80135196. 2002. [5]TIMET, Certificate of conformity H9421--B01. 2007. [6]TIMETAL, Properties and processing of TIMETAL 6-4. Material DATASHEET. Chapter 2Dynamic behaviour of Ti6Al4V 9 Chapter 2 MATERIALS AND METHODS: STATE OF THE ART ThescientificandtechnologicalbackgroundofthisPhDresearchis introduced with a review of the state of the art. First, an overview of the most importantfeaturesoftheinvestigatedTi6Al4Visgiven.Specialattentionis paidtothephenomenonofadiabaticshearlocalisation.Thenmodelling techniquesfortheplasticandfracturebehaviourofmetalsarediscussed. Some of these models will be used for finite element simulations (FE) later on this work. Finally, a general summary of the experimental techniques for high strainratematerialcharacterisationisgiven.Alsotechniquesforfull-field strainmeasurementsandmicrostructuralmaterialcharacterisationare presented. 2.1. TI6AL4V 2.1.1. Introduction [1] Titaniumisarelativelynewmaterial.AlthoughtheelementTihasbeen discoveredmorethantwocenturiesago,difficultiestoproducepuretitanium preventedcommercialuseuntilthedevelopmentoftheKrollprocessinthelate 1930s. Interest in the properties of titanium started after the Second World War in thelate1940sandearly1950s.MilitaryinterestsandmajorU.S.government sponsoredprogramsledtotheinstallationoflargecapacitytitaniumproduction plants,forexampleTIMETin1951.Amajorbreakthroughwastheappearanceof theTi6Al4ValloyintheUSAin1954,combiningexcellentpropertiesandgood producibility. Today, Ti6Al4V is still the most widely used titanium alloy. Somebasiccharacteristicsoftitaniumandothermetallicmaterialsare compared in Table 2-1. Although titanium has the highest strength to density ratio, itisthematerialofchoiceonlyforcertainnicheapplicationareasbecauseofits high price. This price is mainly a result of the high reactivity of titanium with oxygen whichcomplicatestheproductionprocess.Ontheotherhand,thehighreactivity withoxygenleadstotheimmediateformationofastableandadherentoxide surface layer when exposed to air, resulting in the superior corrosion resistance of titanium.Themuchhighermeltingtemperatureoftitaniumascomparedto aluminium,themaincompetitorinlightweightstructuralapplications,gives titaniumadefiniteadvantageaboveapplicationtemperaturesofabout150C. Titaniumisapoorthermalandelectricalconductor.Thethermalconductivityof the alloy Ti6Al4Vis only6.7W/mKwhich iseven significantly lower than the one of pure titanium shown in the Table 2-1. Materials and methods 10 Table 2-1: Some typical indicative properties of titanium and titanium based alloys as compared to other structural metallic materials based on Fe, Ni and Al TiFeNiAl Melting temperature (C)167015381455660 Phase transformation (C) : 882 : 912-- Crystal structurebcc hexfcc bccfccfcc Density (kg/m3)4500790089002700 Corrosion resistanceVery highLowMediumHigh Comparative priceVery highLowHighMedium Thermal conductivity (W/mK)267891238 Youngs modulus E (GPa)11521020072 Yield stress, alloyed (MPa)100010001000500 Highstrength,lowdensityandexcellentcorrosionresistancearethemain propertiesthatmaketitaniumattractiveforavarietyofapplications.Examples includearmorplates,aircraftcomponents,aero-engines,sportsequipment, biomedicaldevicesandcomponentsinchemicalprocessinginstallations.The relatively high cost of titanium has hindered wider use, for example in automotive applications.Tominimisetheinherentcostproblem,successfulapplicationsmust takeadvantageofthespecialfeaturesandcharacteristicsoftitaniumthat differentiateitfromcompetingengineeringmaterials.Thisrequiresamore completeunderstandingoftitaniumalloysascomparedtoother,lessexpensive materials. Thestrainratesensitivemechanicalbehaviourisoneoftheimportant characteristicsoftitanium.Theplasticandfracturebehaviouroftitaniumare significantlyinfluencedbythestrainrate.Highstrainratesaremainlyoccurring duringaccidentaluse(impact,failureofcomponents,crackpropagation...)and during various production processes (punching, deep drawing, incremental forming SPIF,machining...).Thus,knowledgeofthehighstrainratebehaviouris indispensable for both users and manufacturers of titanium components. 2.1.2. Microstructure of titanium and Ti6Al4V Pure titanium exists in two phases, depending on temperature. At 883C, pure titaniumundergoesanallotropicphasetransformationfromhightemperature (body-centredcubic)phasetoalowtemperature(close-packedhexagonal) phase.Theexacttransformationtemperatureisstronglyinfluencedbyinterstitial andsubstitutionalelementssothatthe-phasecanbestableatroom temperature.Commercialtitaniumalloysareclassifiedconventionallyintothree different categories: and near -alloys - alloys alloys The and near alloys typically contain no more than 2% elements other than Ti while the -alloys have usually more than 20% alloying elements. The properties of the individual and phase and the transformation temperature are altered by adding alloying elements. Thus, the and phase can have different properties in Chapter 2Dynamic behaviour of Ti6Al4V 11 different alloys. The -phasecan be strengthened by adding Al. The mechanism is solid solution. The alloying element Al will act as an stabiliser, i.e. it raises the / transitiontemperature.ToomuchAlcanmakethealloybrittle.Precipitationof Ti3Alcanalsocauseastrengtheningeffect.Ontheotherhand,Visastabiliser whichresultsinthereductionofthetransformationtemperatureandVcanmake thephasestronger.Only4%ofVisenoughtostabiliseasmallamountofto roomtemperature.Theeffectofseveralalloyingelementsissummarisedinthe simplified phase diagrams of Figure 2-1. Figure 2-1: Effect of alloying elements on phase diagrams of titanium (schematically) [1] The anisotropic character of the hexagonal crystal structure of the phase has importantconsequencesfortheelasticpropertiesoftitaniumanditsalloys.The modulusofelasticityEofpure-Tisinglecrystalsatroomtemperatureisa functionoftheanglebetweenthec-axisoftheunitcellandthestressaxis.The modulusvariesbetween145GPa(=0)and100GPa(=90).Inpolycrystalline titanium,thevariationsarelesspronouncedanddependontheintensityofthe texture.Themodulusofelasticityof-Tiislowerthantheoneof-Tiandvaries between 70GPa and 90GPa dependent on the concentration of alloying elements. ThealloyTi6Al4Visan-rich-compositionatroomtemperature (approximately 4% ) and is a balance between high strength, toughness and heat treatmentresponse.Transformationofintophaseoccursbetween600Cand 995C [2]. The presence of other elements such as O, N, C ( stabilising) and H, Mo, Fe, Cr ( stabilising) also plays an important role in the metallurgy of Ti6Al4V. They allprovideincreaseinstrengthbutotherwisetheireffectsonmechanical propertiesarenegative[3].TypicallyalltheFepresentinthealloyisconfinedto the -phase [4].Applicationofdifferentthermalandmechanicaltreatmentsresultsinalarge number of different microstructures and properties [5]. This is one of the reasons forthepopularityof+alloys.Twoprincipaltypesoftransformationareof interest for Ti6Al4V [6]. The first of these is the precipitation of from on cooling fromabovethetransusintothe+field.InthiscasetheWidmansttten morphology(plate-likestructure)predominatesatallpracticalcoolingrates.The secondimportanttransformationistheformationofmartensite(diffusionless transformation) that takes place when is rapidly cooled by water quenching. This transformation can be written as where is a supersaturated hcp phase. Themartensitecanbeagedbyheatingtotemperatureswhereappreciable Materials and methods 12 diffusion can occur, in which case the phase can decompose by the precipitation of on the martensite plate boundaries and dislocations. Figure 2-2 shows a cooling diagram of Ti6Al4V. Dependent on the cooling rate, differentmechanismscontrolthephasetransformations[7].Atcoolingrates between410C/sand20C/sthephaseisformedbyamassivetransformation whileatcoolingratesbelow20C/sadiffusionaltransformationtakesplace.In titanium,asecondtypeofmartensiteisobserved:whichisorthorhombic insteadofhexagonal().Martensiteisusuallyformedafterquenchingbutitcan also be formed as a result of external stress which is the case during shock loading [8].Thedeformationinducedmartensitelookslikeneedlesthatcanbeconfused with twinning [4]. Figure 2-2: Schematic continuous cooling diagram for Ti6Al4V showing the cooling rates for martensitic, massive and diffusion controlled phase transformations [7] TheTi6Al4Valloysforengineeringapplicationsareusuallynotusedinthe aboveconditionsbutarehotworkedintheintercritical+regionofthephase diagram in order to break up the structure. This is usually followed by annealing at 700Cwhichproducesastructureofmainlywithfinelydistributedretained. The resulting equiaxed structure is more ductile than the Widmansttten form. The materials used in this PhD have an equiaxed structure. 2.1.3. Deformation mechanism of titanium and Ti6Al4V Themechanicalcharacteristicsoftitaniumalloysareverydiverse.Whilethe yieldstressofcommerciallypure-titaniumisonly170MPa,yieldstressvaluesin excess of 1500MPa are possible for -titanium. The yield stress of the + alloys is intherangefrom800to1250MPa.Differenthardeningmechanismsacton titanium.Solidsolutionstrengtheningbyinterstitialorsubstitutionalatomsis importantforpure-Tialloys.TheveryhighyieldstressesincommercialTialloys are mainly resulting from the precipitation of finely dispersed particles in the and Chapter 2Dynamic behaviour of Ti6Al4V 13 phases.Inaddition,thehighstrengthalloysderivemuchoftheirstrengthfrom boundary strengthening. The and phases act as incoherent phases which results inastrengtheningeffect.So,thesealloyshaveahighdensityof/boundaries whicharebarrierstosliptransmission.Ontheotherhand,these/boundaries aresitesofstrainaccumulationandstrainincompatibilityandthereforeareoften sites for void nucleation during ductile fracture. Thehexagonalstructureof-Tihasalsoconsequencesfortheplastic propertiesoftitanium.Hcpstructuredmetalshaveonlyalimitednumberofslip systems.Inmetals,slipoccurspreferentiallyalongtheclosedpackedplanes. Hexagonalmaterialscanbeclassifiedaccordingtotheprimaryslipsystemthat depends on the c/a ratio of the material. In materials with

3 the primary slip system is prismatic while in materials with

3 the basal slip system is the most important. The -phase of Ti6Al4V has a hcp crystal structure with c/a=1.557. As a consequence,themostcommonslipmodein-titaniumisprismaticglide(1010) andthesecondmostcommonslipsystemusesthebasal(0002)plane.Thereis also slip along the pyramidal (1011) planes but this is less frequent. These three slip systemshaveacommonslipdirection.Allslipsystemsonclosedpacked planes comprise a total of four independent slip systems with an -type Burgers vector in the basal plane (Figure 2-3). Thus, all principal slip directions lie normal to theprismaxis.Deformationparalleltotheprismaxisissimplymoredifficultto activate. Formetalstoundergoplasticdeformationatleastfiveindependentslip systemsarerequired.Deformationbyslipthatleadstoashapechangewithac componentisonlypossiblebyactivatingaslipsystemwithanon-basalburgers vector which has a critical resolved shear stress (CRSS) that is a factor of 3-10 timeshigherthanthatfortypebasalorprismaticslip.Especiallyatlowand roomtemperature,thepyramidaltypeslipsystemsaremoredifficultto activatethanthebasalorprismatictypeslipsystem.Asaconsequencethe crystalsareintrinsicallyanisotropicleadingtointergranular(residual)lattice strains. Figure 2-3: Common slip systems in hcp materials with basal burgers vector [9] Nexttoplasticglide,twinningisseenasanimportantdeformation mechanism in hcp metals. Twinning leads to either extension or compression along thecaxis,whichdependsonthec/aratioofthemetal.Figure2-4explainshowa Materials and methods 14 twincausesadeformationinthec-axis.Twinningmodesareespeciallyimportant for plastic deformation and ductility at low temperatures if the stress axis is parallel to the c-axis. Twinning is the most seen at low temperatures because the CRSS for slip decreases at elevated temperatures.Twinning on the (1012) and (1122) planes result in tensile twinning (elongation along the c axis) while twinning on the (1121) planeresultsincompressivetwinning.Intitanium,themostfrequentlyobserved twinmodeis(1012),whichdisplaysthesmallesttwinningshearof0.174(0)in titanium. The twinned volume has the c axis of the lattice reoriented by almost 85. Consequently,onlyasmallamountoftwinningcanchangethetexturealready significantly.Aftercompressionloading,(1011)twinswerealsoobservedbutonly atrelativelyhighdeformationtemperaturesabove400C[10].Theformationof twinsisaprocesswhichinvolvesnucleationandgrowth.Incontrastwith dislocationplasticity,twinsareunidirectional.Therefore,compression-tension asymmetry has a significant effect on the micromechanical response. Figure 2-4: Principle of the formation of a compression twin Whileitiswidelyacceptedthatcommerciallypuretitaniumwillreadilytwin fromalmosttheonsetofplasticdeformation,Ti6Al4Visconsideredtoshowno twinningundermechanicalloadingconditions.Thisstatementisbasedona number of microstructural observations of deformed Ti6Al4V where no twins were identified.MicroscopicobservationsandEBSDscansdonotshowthetypicaltwin morphology.ItisbelievedthatTi6Al4Vwillnotmechanicallytwinunder conventionalloadingconditionsduetosmallphasedimensions,highsolute content (O and Al) and the possible presence of Ti3Al precipitates [11]. On the other hand,somemodellingandexperimentalstudieshaveindicatedthatinTi6Al4V twinningshouldbetakenintoaccount.Forexample,in1994[12]MeyersM.A. observed twins in Ti6Al4V. Very recently, Prakash [11] showed twinning in Ti6Al4V fordeformationatroomtemperatureandlowstrainrate.InastudyfromPreuss [13], X-ray texture measurements show a dramatic texture change in a compressed Ti6Al4Vsample.Thereorientationofthegrainsissimilartothereorientation accompanying (1012) twinning in zirconium. Since dislocation slip is not capable of causingtheobservedtexturechange,themostlikelyexplanationappearstobe Chapter 2Dynamic behaviour of Ti6Al4V 15 that twin growth has caused entire grains to be reoriented. This might explain why researchershavefounditdifficulttoidentifysignificantlevelsoftwinningin Ti6Al4V.Interestingly,similarobservationsoftwinsthatconsumealmostentire grainshavealsobeenreportedforamagnesiumalloy[14].Atthisstagethe reported observations have to be treated with care since a crystallographic rotation ofawholegrainisdifficulttounderstandfromatransformationmisfitpointof view.Complete grain twinning should be easierwhen theneighbouring grains can deform in a compatible manner which would imply that a strong texture promotes twinning. Clearly more work is needed to confirm that such misfit strain can indeed be accommodated. Also from within the IUAP network observations of twins in Ti6A4V have been made. In the published work of W. Tirry and F. Coghe [15], a low volume fraction of (1012) twinning is identified in sheared Ti6Al4V. 2.2. ADIABATIC SHEAR BANDS Whenstudyingthehighstrainratepropertiesoftitanium,strainlocalisation andtheformationofadiabaticshearbandsareinevitabletopics.Therefore,a literature review about shear bands is welcome. 2.2.1. Definition of shear bands [16] Narrow bands of intense plastic shear strain localisation are called shear bands. Theyaretheresultofunstableplasticflow.Adiabaticshearbandsareatypeof shearbandsthatmainlyoccursindynamicprocesses.Thebandshavewidths between a few and hundreds of microns. Theadjectiveadiabaticreferstotherapidlocalheating,resultingfromthe dynamicdeformation.Insomecases,theremainsofphasetransformations produced owing to the high local temperatures and rapid quenching from the cool surroundings are observed in these shear bands. It should be kept in mind that the termadiabaticshearbandisasimplifiedabbreviationofacomplicated mechanicalandthermodynamicphenomenon.Theabrupttemperaturegradient normal to the band can be important in determining many features of the process, such as the evolution and structure of the shear band, the quenching of the heated material after loading as well as the metallurgical microstructures. Heat conduction mayprovideamechanismforthelimitationofmoreseverelocalisationand therefore the final stage of localisation could be stable. Two categories of shear bands are distinguished according to their appearance: deformedshearbandsandtransformedshearbands.Thefirsttypeonlyshows extremedeformationwhileinthetransformedbandsalsophasetransformations arepresent.BothtypesofshearbandshavebeenobservedinTi6Al4V.The transformed bands contain martensite ( phase) or Ti3Al (2 phase) [17, 18]. Adiabatic shear bands are observed in many applications such as machine chips [19], forging [20], dynamic perforation and ballistic impact loading [17, 21]. In most casestheoccurrenceofadiabaticshearingisundesirable,yetrecentlydeveloped adiabatic cutting and blanking techniques use this phenomenon in their advantage. Materials and methods 16 2.2.2. Characteristics of shear bands [16] Highly localised strain Thewidthoftheshearbandsrangeapproximatelyfrom101to102m.In general,theharderthematerialoftheshearbandis,thenarroweristheshear band.Thelocalshearstrainsaredifficulttomeasurebuttheyareusually estimated in the range between 5 and 50. Shearbandsintitaniumareverynarrow,inmanycases1-10m.Thereisa tendencytowardsanincreaseintheshear-bandwidthwithdisplacement.Inthe hat-shaped experiments of M.A. Meyers [12], the width tends to saturate at 20m. High strain rates Becauseoftheverysmallwidthandlargestrains,thelocalstrainratesinthe shear band are huge and range from 104 to 107s-1. A consequence of the very high strainrateisthatashearbandisnotastaticfeaturebutevolvesduring deformation.Althoughdependentonhowashearbandisdefined,itissaidthat thelifetimeofashearbandisshort,e.g.forTialloysitisaround10s[22]. Thereupon the shear band is destroyed. High temperaturesTheveryhighstrainsandstrainratesconsequentlyresultinveryhigh temperatures.Astrainof=5inahighstrengthsteel(yieldingat900MPa) corresponds already with an adiabatic temperature increase ofmore than 1000C. An indirect proof of the high temperature is found in steels. Adiabatic shear bands maybeclearlyobservedinmanysteelsbecauseoftheappearanceofdistinctive whitebands.Thematerialconstitutingthewhitebandhasbeengenerally identifiedasmartensite.Metallurgically,thisimpliesheating,causingahigh temperaturewithintheband.Thistemperatureisinexcessof1200K,whichleads totransformationofbody-centredcubicferritetothehigh-temperatureface-centred cubic austenite. The austenite is quenched very quickly by the surrounding cooler material to form thin bands of martensite. Other observations have revealed microstructures which can only be formed at almost melting temperatures. Similar white bands have also been observed in Ti6Al4V [23]. Besidestheseindirectindicationsoftheveryhightemperature,many researchersmeasuredthelocaltemperature.Thesmalldimensionsoftheshear band and the very short elapsed time at the high temperature make it very difficult tomeasurethetemperatureaccurately.Thespotsizeofthemeasuringdevice shouldnotbelargerthantheshearbandandlaywithinit.Therefore,absolute values of the temperature have to be handled cautiously. S-C Liao and J Duffy [24, 25] (1992) measured the local temperature rise intorsionalTi6Al4Vspecimenswithanarrayofinfrareddetectors.The width of the observed spot is 17m. The highest temperature measured in the shear band region was in the range of 440-550C. D.A.S.Macdougall(1998)[26]measuredtemperaturesupto200C during torsion tests of Ti6Al4V. The size of the measuring element of the used detector was 50m. Chapter 2Dynamic behaviour of Ti6Al4V 17 Pina[27](1997)measuredamaximaltemperatureof1300Cduringa punching test of Ti6Al4V. Rittel [28] (2008) measured a temperature rise of 200C-250C in Ti6Al4V duringdeformation of ashear-compressionspecimen (SCS).Thesize of the detector elements was 45m. N.Ranc[22](2008)measuredamaximalshearbandtemperatureof 1100C in Ti6Al4V during a dynamic torsion test. The special resolution of thecamerausedinthisstudywas2m.Rancobservedanon-uniform temperature distribution along the shear band. The sameobservation is done by Guduru [29] on shear bands in C300 maraging steel. Macroscopic phenomenon Despitetheirsmallwidth,adiabaticshearbandsareusuallyconsideredasa macroscopicphenomenon.ASBsdonotshowanypreferredcrystallographic orientation.Theorientationofadiabaticshearbandsismainlydeterminedbythe boundaryconditionsimposedbytheloadandthesamplegeometry.Thereare similaritiesbetweentheorientationofshearbandsandslip-lines(orientationsof maximumshearstress).Incontrastslipbands(slip-lines)occuralongactive crystallographic planes and are therefore almost always confined to a single grain. Hardness In many materials, shear bands are harder than thesurrounding material. The transformed shear bands are usually narrower and harder than deformed bands in the same material. AccordingtoMeyersM.A.[12],themicro-hardnessoftheshearbandsin-titanium is not significantly higher than the adjoining matrix. The material adjacent tothebandisworkhardenedbydislocationsanddeformationtwins;insidethe shearband,thestrengthincreasecomesfromareductioningrainsize.Thetwo effectsleadtosimilarhardness.MeasurementsonTi6Al4VbyMurr[17]showed thattheASBaveragemicro-indentationhardnessexceedsthematrixor surrounding microstructure by roughly 16%.Relation to fracture Althoughashearbandisnotafractureitself,severelylocalisedshear deformationcanleadtoprematurefailureinstructures.Thetotalenergy absorption and load carrying capacity of the structure decreases dramatically when thedeformationisstronglylocalised.Thisisclearlyseenbycomparingtheimpact energy needed to make a plate failing by plastic bulging or by plugging. The cracks thatforminadiabaticshearbands,duringtheshearingprocessusuallyhavethe characteristics of a ductile fracture. Strings of voids grow and coalesce which result in a dimpled fracture surface. Materialsthatcontainshearbandsthathavenotyetfailedaresensitiveto successive loadings, particularly if the bands are transformed bands. The extremely fast quenching rate after deformation (106 K/s) are much higher than conventional workshopquenchingrateswhicharemaximumabout102K/sec.Thisquenching canmakethematerialwithintheshearbandharder.Oftenbrittlecracksare Materials and methods 18 observedtoformandgrowwithinoracrosstheshearband.Therefore,problems withthesematerialscomeonsubsequentloadingwhentheshearbandsarecold and brittle. Examples are rolling of explosively welded plates. In general, if fracture isductileitwillhaveoccurredduringtheformationoftheadiabaticshearband whenthebandwashot.Brittlefracturesoccurafterdeformationoftheband. Anyway,inallthedescribedcases,theshearbandcanbetheprecursorsto catastrophic failures. A special feature sometimes observed in adiabatic shear band induced fracture isasolidifiedliquidfilm.Thehightemperaturecanarisefromtheplasticworkor frictionandtransformsthebandmaterialintoliquidwhichisalmostimmediately cooled by the surroundings. Crack growth in a shear band in Ti6Al4V occurs essentially by a process of void coalescence[25,30].Itisalsoknownthatmicro-voidswhicharethebasicsource ofductilefracturegenerallyarenucleatedheterogeneouslyatsiteswhere compatibility of deformation is difficult. For + titanium alloys, it has been shown that the preferred sites for void formation are the / interface [31, 32]. 2.2.3. Formation of ASBs 2.2.3.a. Mechanism ThebasicmechanismproposedbyZenerandHollomonin1944[33]isstill todaygenerallyacceptedastheexplanationfortheformationofadiabaticshear bands. Thewell knownmechanism is based on thedestabilising effect of thermal softeningduetoplasticworkconvertedintoheat.Aprerequisiteforadiabatic shear banding is a sufficient accumulation of localised plastic work in a time which isshorterthanthatrequiredforheatdiffusionawayfromtheplasticzone. Generally,ahighstrainrateisthusnecessaryfortheformationofashearband. However,inmaterialswithlowheatconductionsuchasTi6Al4V,shearbandscan alreadybeformedatrelativelylowstrainrates[34].Thetwomajormaterial parametersarethermalsofteningandstrainhardening.Formationofshearbands willthusbepromotedifthematerialhasalowthermalconductivity,whichisthe case of titanium. Many other parameters affect the shear banding process and have to be taken into account for a thorough understanding of the phenomenon. In addition, a lot of theseparametersevolveduringthedeformationprocesswhichmakesthe modelling ASBs very difficult. Below a non-limitative list:Table 2-2: Parameters affecting the formation of ASBs Material parameters MicrostructureStress stateExternal loading condition Density Specific heat c Thermal conductivity Rate of strain hardening Rate of thermal Grain size and shape Orientation Second phase particles Inclusions Precipitates Texture Porosity Shear stress Shear strain Strain rate Temperature T Hydrostatic pressure p Triaxiality Discontinuities imposed externally Sharpness distribution and energy Chapter 2Dynamic behaviour of Ti6Al4V 19 softening Rate of strain rate hardening Thermal stability of microstructures and transformations Dynamic recovery/ recrystallization Nexttothethermalsoftening,othermechanismshavebeenproposedthat lead to local softening of the material. Many researchers agree that dynamic recrystallization (DRX) takes place duringthedeformationinsideashearbandinmanymaterials[35-37] (see 2.2.4.c). Some researchers believe DRX is not the result of the ASB formationbuttheASBformationandpropagationistheresultofDRX [38]. Nucleation and growth of voids [39, 40] cause softening and subsequent localisation. Voids are suppressed by the hydrostatic pressure which can be an explanation for the effect of hydrostatic pressure on shear bands. The latter mechanism is further investigated by Da Silva and Ramesh [41] who comparedthelocalisationbehaviouroffullydenseandporousTi6Al4V.The behaviourisstronglydependentonthehydrostaticstress.Incompressiontests, the porous Ti6Al4V exhibited higher homogeneous strains than the normal Ti6Al4V. The relativestable deformation of the porous materialisbelieved to be the result of the hardening mechanism afforded by the progressive compaction of pores with increasingcompressivestrain.Ontheotherhand,fordynamictorsionteststhe porousTi6Al4VlocalisesatmuchlowerstrainsthanthedenseTi6Al4V.Herethe voids destabilise the deformation. 2.2.3.b. Prediction of occurrence of shear bands Adistinctionshouldbemadebetweenpredictingtheshearbandformation andtheshearbandpropagation/evolution.Mostpublishedworksdealwithshear bandformation.Shearbandformationisarelativelyslowprocessofthe localisationofdeformation,whichisrelatedtothephenomenonofmaterial instability.Whereastheshearbandpropagationisafastdynamicprocess.Shear bandformationislesscomplicatedtomodelthanshearbandpropagation.Itcan be modelled (to some extent) using a single constitutive law and material instability criterion. ASB propagation has to be considered as a moving boundary problem of a multi-physics constitutive modelling approach [37]. Furthermore a deformed and a transformed shear band will need a different approach. Dependent on the shear band formation mechanism that is regarded to be the mostimportant,differentshearbandnucleationcriteriaexist(thermalsoftening, DRXorvoids).Furthermoredifferentlevelsarepossible:macroscopicmodelslook at the ASBs as a purely thermomechanical problem while microscopic models try to takeintoaccountthemicrostructure,textureandbasicplasticitymechanisms (dislocationsandtwinning).LocalisationcriteriaareforexampleusefulforFE-simulations of applications. Materials and methods 20 Critical strain Averysimplebutcommonlyusedcriterionisbasedonacritical localisation/fracturestrain.Unstabledeformationandtheformationofashear bandstartswhentheequivalentstrainequalsthiscriticalstrain.Thevalueofthe criticalstraincanbeobtainedexperimentallyorcanbecalculatedthroughother shearbandcriteria(seecriticalstress).Forexample,MacDougallandHarding[42] obtained a critical equivalent strain of 23% from dynamic torsion tests on Ti6Al4V. Critical stress Themoststraightforwardcriteriontocalculatethepointofunstable deformationisbasedontheconceptthatunstabledeformationoccursbeyonda stressmaximum.SuchcriterionisanalogoustotheneckingcriterionofConsidre (1885) in tension which expresses the balance between strain hardening and cross-sectionareareduction.Inshear,unstabledeformationcomesfromthermal softening rather than a change in cross-sectional area. If elastic deformation, strain rateendtemperaturehistoryeffectsandphasetransformationsareneglected, then the shear stress can be written as a function of shear strain , shear strain rate and temperature T. ( ) T f , , & = The maximum stress criterion requires d=0: ,, ,0T Td d d dTT | | | | | |= + + = ||| \ \ \ &&&&(2.1) IfstrainratehardeningisneglectedandadiabaticheatingcdT=dis assumed the following criterion is obtained. 11c T | | | | = || \ \ (2.2) In this expression , c and are respectively the density, specific heat capacity andthefractionofplasticworkconvertedintoheat.Fromthisrelation,itisclear thatmaterialswithahighrateofthermalsoftening,lowstrainhardening,low densityandlowspecificheatwillbepronetoadiabaticshearbanding.Because theseareallmaterialparameters,thiscriterionleadstoatypeofclassification, regardingtheirsusceptibilitytoadiabaticshearbanding.Ifaconstitutiveequation ofthematerialisavailable,thenthecriterioncanbesimplifiedtoacharacteristic shear strain i (critical strain for instability). Variantsofthiscriterionarepossible.Softeningduetovoidgrowthcanbe takeninaccount[40]ortheeffectofstrainratehardeningcanbetakeninto account. Critical temperature Because the phenomenon of dynamic recrystallization (DRX) is strongly related to deformation inside shear bands (see further), the formation and propagation of theASBcanbedescribedbytheonsetconditionsaswellasbytheparametersof the DRX inside the ASB. Many factors affect the initiation of DRX in metals. Among Chapter 2Dynamic behaviour of Ti6Al4V 21 themarethematerialscrystallographicstructure,densityofdislocations,initial grainsizeandprecipitates.However,themostimportantfactorsarethe deformationconditions,suchasthestrainrateandtemperature.DRXoccurs duringdeformationwhentemperaturereachessomecriticalvalue(TDRX),whichis usually between 0.4 and 0.5 times the melting temperature. The TDRX is dependent on the strain rate and is lower for higher strain rates. This critical temperature can be used as a shear band initiation and propagation criterion [37]. All previously described criteria predict the formation of adiabatic shear bands whiletheevolutionandpropagationoftheshearbandhasnotbeendealtwith. Predictionoftheshearbandwidth,velocity,grainsize,orientation,spacing between multiple shear bands, temperature distribution inside the shear band are complex. A recent analysis of the dynamic propagation of ASBs is made by Bonnet-Lebouvier, Molinari and Lipinski in [43]. Instability analysis Themaximumshearstresscriterionhasitsrestrictionsforseveralreasons:a numberofassumptionsareimposedandadiabaticshearbandscanonlybedealt withusingcontinuummechanics.Thetemporalandspecialvariationsofstrain, strain rate and temperature can only be described adequately using field equations of a continuum.This is similar to the methods used influid mechanics.The plastic deformationis governed by differentialequations describing the relation between stress,strainandtemperatureinspaceandtime.Thesolutionofthedifferential equationsafterintroductionofinfinitesimalin-homogeneities(perturbations)is studied and leads to an instability criterion. A totally different but general analytical instability analysis is done by Molinary and Clifton [44]. They studied the effect of geometrical defects on the homogeneity ofthestraindistributioninsimpleshear.Thermalsofteningisnottakeninto account.Ifthematerialwilllocalisedoesonlydependontheconstitutive behaviour and the size of the defect. 2.2.4. Dynamic recovery and recrystallization within shear bands As already mentioned before, restoration of the microstructure is taking place duringtheformationofadiabaticshearbandsinmanymaterials.Recoveryand recrystallizationaretworestorationprocessesthatcanoccurstaticallyor dynamically(duringdeformation).Thissectiongivesanoverviewofthese phenomena [45]. 2.2.4.a. Microstructural restoration Recovery Ingeneral,thetermrecoveryreferstomicrostructuralchangesinanon-equilibriummaterialthatpartiallyrestorethepropertiestotheiroriginalvalues before.Thenon-equilibriumanddefectscanbeintroducedbyforexampleplastic deformation,irradiationorquenching.Recoveryismainlyduetochangesinthe dislocation structure of the material. For polycrystalline metals, complete recovery canonlyoccurifthematerialhasbeenlightlydeformed.Formaterialsdeformed Materials and methods 22 intostagesIIorIIIofworkhardening,recrystallizationmayintervenebeforeany significant amount of recovery has taken place.During recovery, the microstructural changes in materials are subtle and occur onasmallscale.Themicrostructure,asobservedbyopticalmicroscopyusually doesnotrevealmuchchangeandforthisreason,recoveryisoftenmeasured indirectlybyabulktechnique,forexamplebyfollowingthechangeinsome physical or mechanical properties. Recrystallization Recrystallizationinvolvestheformationofnewstrain-freegrainsincertain partsofthespecimenandthesubsequentgrowthofthesetoconsumethe deformedorrecoveredmicrostructure.Themicrostructureatanytimeisdivided intorecrystallizedandnon-recrystallizedregionsandthefractionrecrystallized increasesfrom0to1asthetransformationproceeds.Incontrast,recoveryisa homogeneous process without an identifiable beginning or end of the process. Itisconvenienttodividerecrystallizationintotworegimes:nucleationwhich corresponds to the first appearance of new grains in the microstructure and growth duringwhichthenewgrainsreplacethedeformedmaterial.Thetimeforstatic recrystallizationtocompleterangesfromsecondstohours,dependentonthe material,temperature,deformation...ThetemperatureTfortheonsetofthermal recovery or recrystallization in metals is generally expressed by T=0.4Tm -0.5Tm [18]. Recoveryandrecrystallizationarecompetingprocessesasbotharedrivenby thestoredenergyofthedeformedstate.Theprocessofrecoveryoccurspriorto recrystallization.Oncerecrystallizationhasoccurredandthedeformation substructurehasbeenconsumed,thenclearlynofurtherrecoverycanoccur.The extentofrecoverywillthereforedependontheeasewithwhichrecrystallization occurs.Conversely,becauserecoverylowersthedrivingforceforrecrystallization, asignificantamountofpriorrecoverymayinturninfluencethenatureandthe kineticsofrecrystallization.Thedivisionbetweenrecoveryandrecrystallizationis sometimes difficult to define, because recovery mechanisms play an important role in nucleating recrystallization.2.2.4.b. Dynamic restoration Thesofteningprocessesofrecoveryandrecrystallizationmayoccurduring deformationathightemperatures.Then,thesephenomenaarecalleddynamic recoveryanddynamicrecrystallization.Thestaticanddynamicprocesseshave manyfeaturesincommon,althoughthesimultaneousoperationofdeformation and softening mechanisms leads to some important differences. Although dynamic restorationprocessesareofgreatindustrialsignificance,theyarenotwell understoodbecausetheyaredifficulttostudyexperimentallyandtomodel theoretically.Theyareimportantbecausetheylowertheflowstressofthe material,thusenablingittobedeformedmoreeasilyandtheyalsohavean influence on the texture and grain size of the worked material. Chapter 2Dynamic behaviour of Ti6Al4V 23 Dynamic recoveryDynamicrecoveryischaracterisedbyasteady-stateflowstresswhichcanbe seenonthetruestressstraincurves(Figure2-5).Thismeansthatthereisa dynamic equilibrium between the rates ofwork hardening and recovery. Although thedislocationandsubgrainstructuresoftenremainapproximatelyconstant duringsteady-statedeformation,theoriginalgrainboundariesdonotmigrate significantlyandthegrainscontinuetochangeshapeduringdeformation.Thisof coursemeansthatalthoughtheflowstressmayremainconstant,atrue microstructural steady state is not achieved during dynamic recovery. Figure 2-5: Stress-strain curves for AlMg at 400C [45] Dynamic recrystallization Indynamicrecrystallization,asopposedtostaticrecrystallization,the nucleationandgrowthofnewgrainsoccursduringdeformationratherthan afterwards as part of a separate heat treatment. A distinction is made between two differenttypesofdynamicrecrystallization:discontinuousandcontinuous recrystallization. Discontinuous dynamic recrystallization This is the normal dynamic recrystallization. The process has clear nucleation and growth stages and can therefore be classified as a discontinuous process. New grainsoriginateatoldgrainboundaries(Figure2-6).Whenthematerialcontinues todeform,thedislocationdensityofthenewgrainsincreases,thusreducingthe drivingforceforfurthergrowthandtherecrystallizinggrainseventuallyceaseto grow.Insomecases,microstructuralevolutionismorecomplicatedbecausethe onset of dynamic recrystallization may lead to changes in deformation mechanism. Forexample,ifdynamicrecrystallizationresultsinaverysmallgrainsize,then subsequentdeformationmayoccurpreferentiallybythemechanismofgrain boundary sliding. Materials and methods 24 Figure 2-6: Development of microstructure during dynamic recrystallization. (a)-(d) large initial grain size, (e) small initial grain size [45] The general characteristics of dynamic recrystallization can be summarised: As shown in Figure 2-7, the stress-strain curve for a material which undergoesdynamicrecrystallizationgenerallyexhibitsabroad peakthatisdifferenttotheplateau,characteristicofamaterial which undergoes only dynamic recovery. Acriticaldeformation(c)isnecessaryinordertoinitiatedynamic recrystallization. This occurs somewhat before the peak stress. c decreases steadily with decreasing stress. Thesizeofdynamicallyrecrystallizedgrains(Dr)increases monotonically with decreasing stress. Graingrowth does not occur andthegrainsizeremainsconstantduringthedeformation. Formulas andmodels exist to calculate the grain size [46].Thesize predicted by the theory is found to be consistent with the dynamic recrystallized structures in shear bands in Ti6Al4V Theflowstress()andDrarealmostindependentoftheinitial grain size (D0). Dynamicrecrystallizationisusuallyinitiatedatpre-existinggrain boundaries. Chapter 2Dynamic behaviour of Ti6Al4V 25 Figure 2-7: 0.68% C steel deformed in axisymmetric compression, strain rate=10-3 s-1 [45] Figure 2-8: "Universal" plot of normalized grain size as a function of normalised uniaxial normal stress for dynamic recovery and recrystallization ([46]) and titanium datum point. Burgers vector b=0.3e-9m [12]. Continuous dynamic recrystallization At least 2 different types of recrystallization exist in this category: Geometric dynamic recrystallization This type has many similarities with the static recrystallization that is occurring in materials which have undergone very large strains. Rotational recrystallization Strain-inducedformationofnewgrainsduringdeformationbythe progressiverotationofsubgrains.Themechanismsbywhichthis progressive subgrain rotation occurs are not yet entirely clear, but Materials and methods 26 itismostfrequentlyfoundinmaterialsinwhichdislocation motion is inhibited by either lack of slip systems(e.g. magnesium alloys)orbysolutedrag(e.g.aluminium-magnesiumalloys).Itis likelythatitisassociatedwithinhomogeneousplasticityand accelerateddynamicrecoveryinthegrainboundaryregionsand sometimesgrainboundarysliding.Accordingtosome researchers,thisisthetypeofrecrystallizationthatoccurs during the formation of adiabatic shear bands [35]. In contrast to othertypesofrecrystallization,thehightemperatureisnot required.2.2.4.c. DRX in shear bands The very high strains (driving force) and temperatures present in ASBs promote dynamicrecrystallization.Itisnotsurprisinglythatpost-mortemanalysisofshear bands revealed small recrystallized grains. At the one hand, softening is one of the main macroscopic effects of dynamic recrystallization. On the other hand, softening is at the origin for unstable and localised plastic deformation. It is therefore logical toexpectDRXbeingapartoftheformationandpropagationmechanismofshear bandsratherthanonlyaresultofadiabaticshearbanding.However,inliterature thereisnoconsensusontheexactroleofDRXintheshearstrainlocalisation mechanism and how to take it into account for modelling. The problem is complex because also phase transformations can occur in theshear band and interact with thedynamicrecovery/recrystallizationprocess.Thatthestudyofrecrystallization inshearbandsisquiterecentcanbeseenbythefactthatrecrystallizationisnot even mentioned at all in the 350 pages counting review book of Y. Bai and B. Dodd [16] (1992) about adiabatic shear bands. Hereunder, a non-limitative overview can be found of some studies where DRX is taken into account or observed in shear bands: 1981: Rotational recrystallization is a characteristic feature of high strain deformation,aspresentedbyGilSevillanoandP.vanHoutte[47].The mechanism has not been applied on ASBs. 1990:Beatty,L.W.Meyer,M.A.MeyersandNemat-Nasser[48]observe verysmallnano-sizedgrainsinshearbandsofAISI4340highstrength steel, loaded as a hat-shaped specimen. However, no explanation for the formation of these grains is given. 1994:VeryusefulpublicationofM.A.Meyers[12]describingthe evolutionofthemicrostructurewithinshearbandsofTi6Al4Vduring hat-shapedspecimentests.Theexperimentalresultsindicatethat instabilityistheresultofagradualsofteningproducedbyheating, whereaslocalisationisproducedbydynamicrecovery/recrystallization, leadingtoaflowstressdiscontinuitywhichensuresaclearboundary between the shear band and surrounding material. 1997:HinesandVecchio[35]studiedthekineticsofrecrystallization withinASBs.Theyconcludethatclassical(static)recrystallization mechanismsaremuchtooslow.TheyrefertopapersofG.Sevillano Chapter 2Dynamic behaviour of Ti6Al4V 27 aboutrotationalrecrystallizationasapossiblealternative recrystallization mechanism. 1997:NesterenkoandM.A.Meyersproposeamechanismforthe evolutionofthemicrostructureduringshearlocalisationoftantalum. Themicrostructureevolvesin4stages.Forstrainsbetween1and2, subgrains are formed as part of an dynamic recovery process. For strains between2and2.5thesubgrainsbreak-upplusmicrograinsareformed bydynamicrecrystallization.Dynamicrecrystallizationbyarotational mechanism occurs within regions of intense plastic deformation. 1998:Nemat-Nasser[49]performsexperimentsonhatshaped specimensoftantalum.Theshearbandmicrostructureisinvestigated withTEM.Itsconcludedthatdynamicrecoveryandrecrystallizationare taking place, resulting in recrystallized micrograins of 150nm. 2003:M.A.Meyers[36]revealstwodifferentmicrostructuralregionsin adiabaticshearbandsofAISI304Lstainlesssteel:(a)aregionconsisting of100nm-200nmgrainswithwelldefinedgrainboundariesandalow density of dislocations.Thisstructure is produced by rotational dynamic recrystallization.(b)aregionhavingaglassystructurewhichisthefirst observation of amorphisation within a shear band. 2004:D.R.ChichiliandK.T.Ramesh[50]studiesthemicrostructural mechanismsduringshearlocalisationin-titanium(TEM):(a)planar dislocation motion and twinning (b) grouping of dislocations into cells (c) formationofelongatedsubgrainsalongthesheardirection(d) development of equiaxed nanocrystalline grains 50-200nm in diameter. 2006:Kad[51]investigatesthemicrostructureinsidetheshearbandin zirconium.TEMandEBSDareused.Smallequiaxed50nm-200nmgrains areobserved.Themechanismofrotationalrecrystallizationisproposed to explain this ultrafine microstructure (Figure 2-9).2006:XueQandGrayGT[52]studiedthemicrostructureinstainless steelshearbandswithTEM.Theinitiationoftheshearbandis characterisedbyelongatedgrainsanddislocationcells.Developmentof thesubstructureswithinshearbandsiscontrolledbydynamicrecovery andcontinuousdynamicrecrystallization.Thecoreofshearbandsis foundtoconsistoffineequiaxedsubgrainsofsize100nm.Well-developed shear bands are filled with a mixture of equiaxed, rectangular, and elongated subgrains. 2007:Lins[53]alsoobservesverysmallgrainsinshearbandsandcalls the mechanism Progressive subgrain misorientation recrystallization. 2007:criticaltemperatureforDRXisusedascriterionforshearband formation and propagation [37]. 2007:Martinez[54]