Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Extrusion of alumina particulate reinforced metal matrix composites Chen, Wei Chang 1995

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata


ubc_1995-982659.pdf [ 7.55MB ]
JSON: 1.0078443.json
JSON-LD: 1.0078443+ld.json
RDF/XML (Pretty): 1.0078443.xml
RDF/JSON: 1.0078443+rdf.json
Turtle: 1.0078443+rdf-turtle.txt
N-Triples: 1.0078443+rdf-ntriples.txt
Original Record: 1.0078443 +original-record.json
Full Text

Full Text

EXTRUSION OFALUMINA PARTICULATE REINFORCEDMETAL MATRIX COMPOSITESByWEI CHANG CHENB. A. Sc. BeijingUniversity ofIron and SteelTechnology 1983M. Sc. University ofScience andTechnologyBeijing 1986M. A. Sc. UniversityofBritishColumbia 1991ATHESIS SUBMITthD IN PARTIALFULFILLMENTOFTHEREQUIREMENTFORTHEDEGREEOFDOCTOR OFPHILOSOPHYinTHEFACULTY OFGRADUATESTUDIESMETALS AND MATERIALS ENGINEERINGWe acceptthis thesis asconformingto the required standardTHEUNWERSITY OF BRITISHCOLUMBIADecember 1994© WeiChangChen, 1994In presenting this thesis in partial fulfilmentof the requirements for an advanceddegree at the University of British Columbia, Iagree that the Library shall make itfreely available for reference and study. I furtheragree that permission for extensivecopying of this thesis for scholarly purposesmay be granted by the head of mydepartment or by his or her representatives.It is understood that copying orpublication of this thesis for financial gain shallnot be allowed without my writtenpermission.(Signature)Department of fr14TEf1FiL5’ii.The University of British ColumbiaVancouver, CanadaDate Fd.24- 95DE-6 (2188)UABSTRACTAluminaparticulatereinforcedmetalmatrixcomposite is anewkind ofmaterial, whichhas wide potential applications in automobile industry. The study ofits physical nature duringextrusion process is essential to optimize the process which may improve its mechanicalproperties and increase its productivity to finallyreduce its cost and make it more competitiveto othermaterials.Constitutive equations were developed for the alumina particulate reinforced metalmatrix composites (Duralcan materials) based on the hot deformation tests on a ‘Gleeble1500’ machine. Plant trials were conducted for the same materials in both a laboratoryextrusion device at Kingston R & D Center (KRDC), and an industrial extrusion press atUniversal Alloy Corporation, California. Different temperatures and extrusion ratios withdifferentram speeds were adopted during extrusion. Low speed cracking was observed at thefront end of some extrudates, which has not been observed with the unreinforced aluminumalloy (AA6061). Microstructure change with particle fracture and particle distribution wasstudied using an optical microscope and an image analyzerin the deformation zone of a billetand the extrudatesfrom the planttrials.The extrusion processes have been simulated with the aid of a finite element model.The plant trial data were used to validate the model predictions. The model predictions atboth a macroscopic and a microscopic level were correlated with microstructural changes.Extrusion Jimit diagrams for both composites of6061/A1203/lOpand 6061/A1203/20pweredeveloped with low speed cracking boundaries included for the press at UAC. Themechanism of the low speed cracking was proposed based on the FEM and SEM analysis.111Although low-speed cracking was proposed to be associated with void formation in thesurface layer of the extrudates, the voids were not significant to the effect of tensileproperties, because the elastic modulus, the yield stress and the ultimate tensile strengthmeasured from extrudates ofthe plant trials at KRDC did not decline at extrusion ratios from10 to about 30. Minimization of void formation in the composites was discussed andrecommendations have been provided for optimization of the extrusion of the aluminaparticulate reinforced MMCs.Thispage leftblankintentionallyivVTABLE OF CONTENTSABSTRACTTABLEOF CONTENTS vTABLE OFTABLES xiTABLE OFFIGURES xiiiNOMENCLATURE xixACKNOWLEDGEMENTS xxiiDEDICATION xxiiiChapter 1 INTRODUCTION 11.1 Characteristics ofMetalMatrixComposites11.2 Fabrication ofParticulateReinforced MetalMatrixComposites41.3 Processmg and Applications ofParticulateReinforced MMCs1.3.1 Secondary DeformationProcessing 41.3.2 Applications 5Chapter 2 LiTERATUREREVIEW 62.1 ExtrusionProcess62.2 Extrusion RelatedDefects ofParticulateReinforcedMMCs (PRMMCs)82.2.1 ExtrusionRelated Defects 92.2.2 HotWorkabilityofPRMMCs 142.3 DevelopmentofExtrusionLimitDiagrams172.3.1 PeakPressure 182.3.2 Temperature Rise 192.4Finite ElementAnalysisofAnExtrusionProcess212.4.1 Finite ElementAnalysis ofanExtrusionProcess 212.4.2DevelopmentofanExtrusionLimitDiagram UsingFEM 22vi2.4.3 Fracture CriteriaforMonolithic Metals 242.5 Finite ElementAnalysis ofthe PRMMC252.5.1 MultilevelFinite ElementMethod 292.5.2 ParticleFracture Model during Deformation 312.5.3 MicroscopicAnalysis ofPRMMCsunderLargerDeformation 33Chapter 3 SCOPEAND OBJECTIVES 343.1 Scope and Objectives3.2 MethodologyChapter4 EXPERIMENTAL 374.1 Gleeble Tests4.2PlantTrials atUAC,Anaheim404.2.1 ExtrusionProcedure 404.2.2 ExtrusionData 444.3 PilotExtrusion at KRDC, Kingston504.3.1 ExtrusionProcedure 504.3.2 ExtrusionData 524.4Extrusion Surface Defects4.5 Effect ofExtrusionConditions on the Mechanical Properties 584.5.1 Tensile Tests 584.5.2 PropertyChanges afterExtrusion 5864Chapter 5 MODELINGEXTRUSION OF THEPRMMCs5.1 MathematicalModel ofthe ExtrusionProcess645.1.1 Finite ElementModel 645.1.1.1 FlowFormulation 645.1.1.2BoundaryConditions 685.1.2 InputData 705.1.3 FiniteElement Solution 70vu5.2 Sensitivity Analysis ofthe Model725.3 ExtrusionProcess Simulation5.3.1 Processing Conditions 755.3.2 ModelPredictions 765.3.2.1 Deformation Behavior 765.3.2.2TemperatureDistribution 845.3.2.3 Comparison ofPredictionswithMeasured Data 865.4ValidationofModelPredictions895.5 Summary92Chapter 6 MICROMECHANICALANALYSIS OFTHEPRMMCDURINGLARGE 94DEFORMATION6.1 Obstacles and Challenges ofMicromechanical Analysis ofthe PRMMCs6.1.1 ParticlePhenomena 946.1.2 MatrixPhenomena 956.1.3 Modeling Constraints 956.2 MicromechanicalAnalysis during Plane StrainCompression966.2.1 Twin-ParticleModel 986.2.2 Multiple-Particle Model 1046.3 MicromechanicalAnalysis during CylindricalCompression1066.3.1 Single-ParticleModel 1076.3.1.1 MaterialFlow ofa CylindricalSpecimenContaining aParticle 1096.3.1.2EffectofParticle Shape 1156.3.2 Twin-Particle Model 1206.3.2.1 EffectofReduction 1216.3.2.2 EffectofParticle Spacing 1216.4 ModelValidation1266.5 Conclusions126‘InChapter 7 PARTICLEFRACTUREOFTHE PRMMC DURINGEXTRUSION 1287.1 SpecimenPreparationforthe PRMMCs1297.2 MacroscopicExamination ofMetal Flow in the DeformationZone1307.3 Particle Fracture duringExtrusion1347.3.1 QualitativeMicrostructure Analysis 1347.3.1.1 Particle DeformationBehaviorinthe Deformation Zone 1347.3.1.2 MicrostructureAnalysis ofthe Extrudates 140A. Comparison ofMicrostructure inLongitudinal and Transverse Sections 141B. Comparison ofMicrostructurefor606l/A1ZO3/20p and 606l/A12O3/lOp 1437.3.2 Image AnalysisofParticleDistribution inExtrudates 1467.3.2.1 HomogeneityofParticle Distribution 1467.3.2.2 Particle Size 1497.3.2.3 AspectRatio ofParticles 1547.3.2.4Particle Orientation 1567.4 Modeling ParticleFracture during Extrusion1577.4.1 ParticleFractureProbability atHighTemperature 1577.4.2 ParticleFractureModel duringExtrusion 1587.4.3 Application ofthe Model 1607.5 Discussion1627.5.1 Microstructure Comparisonbefore and afterExtrusion 1637.5.1.1 Comparison ofParticleDistributionbefore and afterExtrusion 1637.5.1.2 Particle SizeRefmementafterExtrusion 1687.5.2 Particle Fracture Modes during Extrusion 1687.5.3 Correlationbetween Particle Fracture and BulkDeformation Behavior 1701737.6 SummaryChapter 8 ORIGIN OFLOW SPEED CRACKINGDURINGEXTRUSION OFTHE 177PRMMCsix8.1 Microstructure Examination ofLow-speed Cracks1778.2 Particle Behaviorand MicroscopicDamage1808.2.1 ParticleFracture 1808.2.2 VoidFormation 1838.3 EffectofProcessing ParametersonLow Speed Cracking186EffectofRam Speed 189EffectofBilletTemperature 193EffectofDieTemperature 197EffectofFrictionatDie Interface 198EffectofExtrusionRatio 200EffectofVolumeFraction ofthe Composites 2028.4 Mechanism ofLow Speed Cracking2048.5 APreliminaryCriteriaforLow Speed Cracking206Chapter9 EXTRUSION OFTHEPRMMCs 2109.1 Development ofExtrusionLimitDiagram2119.1.1 Using Empirical Equations 2119.1.2UsingFiniteElementMethod 2159.1.2.1 Application ofthe Finite ElementModel 2159.1.2.2Comparison ofExtrusionLimitDiagrams 2179.2 ExtrusionLimitDiagramwithLow Speed Cracking Boundary2209.2.1 Low Speed Cracking Boundary 2209.2.2EffectofExtrusionRatios 2229.2.3 ExtrusionLimitDiagramwithLow Speed Cracking Boundary 2239.3 Extrusion ofthePRMMCs 2249.3.1 MinimizationofMicrostructuralDamage duringExtrusion 2259.3.2 ImprovementinParticleDistribution and Size Refinement 2299.3.3 Quality and Productivityofthe PRMMCs 231xChapter 10 CONCLUDING REMARKS 23410.1 Summary and Conclusions23410.2FutureWork236REFERENCES 237xTABLE OFTABLESTable 1.1 illustration ofthe principle factorslinked withthe aspectratio 2Table 2.1 Microstructure observed in the particulate reinforced composite before 13and afterextrusionTable 4.1 Material constantsforthe constitutive equationofthe Composites 40Table 4.2 Extrusion programsfor the 7” press atUAC 41Table 4.3 Billettemperaturesimmediatelypriorto extrusionatUAC 43Table 4.4 Planttrial conditions at KRDC 51Table 4.5 Billetdimensions ofeach test atKRDC 53Table 4.6 Measured testdataofthe planttrials atKRDC 53Table 4.7 Extrudate datafrom planttrials atUAC 57Table 4.8 Tensile testresults ofextrudates from the planttrials atKRDC 59Table 5.1 Some dataforsensitivity analysis ofthe FEMmodel 72Table 5.2 Processing Conditions forTwo Simulations 76Table 6.1 Simulationconditionsforplane straindeformation 97Table 6.2 Simulationconditionsforcylindrical compressiontest 107Table 6.3 Particle sizes studied 109Table 6.4 Comparisonofmodel predictions withmeasured data 126Table 7.1 PolishingprocedureforDuralcanmaterials atKRDC 129Table 7.2 Polishingprocedure used atUBC forDuralcanmaterials 130Table 7.3 Extrusionconditions ofthe Trial S92-3 of6061/Al203/20p 131Table 7.4 Listofexaminedextrudates with two differentcross-sections 141Table 7.5 Statistical resultsforvolume fraction distribution ofthe two composites 147Table 7.6 Statisticalresults forthe quantitativemetallography 153Table 7.7 Average number of parts fractured from a single particle in 159606l/A1203/20pTable 7.8 Comparison ofmodel predictions withmeasured data 162Table 8.1 Tensile stressinparticles and matrixatdifferentreductions 182xliTable 8.2 Standardconditions forparametric study 188Table 9.1 Constants in Eq. (9.1) forthe composites 211Table 9.2 Extrusionconditionsforthe specimensexaminedunder an SEM 225xInFigure 2.1Figure 2.2Figure 2.3Figure 2.4Figure 2.5Figure 2.6Figure 2.7Figure 2.8Figure 2.9Figure 3.1Figure 4.1Figure 4.2Figure 4.3Figure 4.4Figure 4.5Figure 4.6Figure 4.7Figure 4.8Figure 4.9Figure 4.10Figure 4.11Figure 4.12Figure 4.13Figure 4.14Figure 4.15Figure 4.16Figure 4.17Figure 4.18TABLE OFFIGURES7101518232627293036384245464647474848495254555658606162Schematic ofa forward extrusionprocessTensile elongation to fracture against strength for A356 alloy and itscomposites with differentvolume fractions of SiCp before and after extrusionatdifferentextrusion temperatures of400°C and 600°CStrain dependence offracturedparticleof6061/SiCp MMCsAschematicextrusionlimit diagramSchematic extrusionlimitdiagramwith low speed crackingFinite elementmodelusedbyAradhya etalMastermeshforgenerating differentmicroscopicmorphologiesThe crackmorphologies generated by the FEMstudyfordifferentoverallfractionofthe angularZr02withtransformation(a) FEMmesh with localrefinement during aplane-strainupsetting; (b) Stressdistribution along theline PQ (Eh=l% calculatedwithABAQUS)’Methodology forthe extrusion ofaluminaparticulatereinforced MMCsSchematic ofthe Gleeble testset-upSchematic ofextrusion setup forDuralcantrialsTypicalload-strokecurvewithvariation ofram speed (S92-3)Die temperature increase during extrusion (S92-3)Effect ofhomogenization on extrusionforce (S92-3 and S92-4)A weak correlation of increasing ram speed with increasing die temperatureduringextrusion (S92-5)Effectofbillettemperature on extrusionforce (S92-5 and S92-6)Effectofbilletlength onextrusionforce during extrusion (S92-3 and J94-12)Effect of volume fraction on extrusion force during extrusion(6061/A1203/1Op: J94-3, and 606l/A12O3/2Op: J94-7)Effectofextrusionratio on extrusionforce (J94-4, J94-lO, J94-15)Schematic drawing ofthe extrusionpress atKRDCTypicalload-stroke curve during extrusionatKRDC (K-7)Variationofram speed atthe press pressurelimit(K-li)Low speed cracking atthe frontend oftwo extrudatesSchematic ofa tensile testspecimenTensile property under differentextrusionratiosElongation ofthe compositesas afunction ofextrusion ratio(a) Tensile property change of6O6l/A12O3/lOpfor different extrusion ratiosxivFigure 4.19Figure 5.1Figure 5.2Figure 5.3Figure 5.4Figure 5.5Figure 5.6Figure 5.7Figure 5.8Figure 5.9Figure 5.10Figure 5.11Figure 5.12Figure 5.13Figure 5.14Figure 5.15Figure 5.16Figure 5.17Figure 5.18Figure 5.19Figure 6.1Figure 6.2Figure 6.3Figure 6.4636568747478787979828384858587878891919798100102with a true volume fraction from 7.0% to 7.4%; (b) Tensile property changeof 606l/A12O3/2Opfor different extrusion ratios with a true volume fractionfrom 19.2% to 19.8%Corresponding elongation values at different extrusion ratios for bothcompositesSchematic ofan extrusionpressInitial finite elementmeshfor the billet and its surrounding toolsSensitivity ofload strokecurve to the numberofelementsin thebilletSensitivity of the maximum temperature to the number of elements in thebilletMaterialflow nearthe end ofupsetting stageEffective straindistributionnearthe end ofupsetting stageVelocity distribution in the billet after a ram displacement of40.7 mm in thelarge extrusion press; length ofarrow is proportional to velocityVelocity distribution in the billet after a ram displacement of 26.7 mm in asmallextrusionpress; length ofarrow isproportionalto velocityMean stress distributionin the billet at a ram displacement of 40.7 mm in thelarge extrusionpress (negativevalues denote compressive stresses)Mean stress distribution in the billet at a ram displacement of 26.7mm in thesmallextrusionpress (negativevaluesdenote compressive stresses)Effective straindistributionofthe billetinthe small pressEffective strainrate distribution ofthe billetinthe smallpressTemperature distributionin the largeextrusionpressTemperature distributionin the small extrusionpressComparison ofpredicted force withmeasured data (largepress)Comparison ofpredictedforce withmeasured data (smallpress)Comparison ofpredictedtemperature withmeasured data (large press)Comparison of FEM force with measured data corrected for extrusion presscompliance according to Eq. (5.26); large pressComparison ofFEM force with measured data corrected for extrusion presscompliance according to Eq. (5.26); smallpressInitialfmite elementmeshesforeachobjectofplane strain deformationInitialfinite elementmesh around two particlesEffective strain distribution at areduction of49%Localized effective strain distribution around two particles at different81reductionxvFigure 6.5Figure 6.6Figure 6.7Figure 6.8Figure 6.9Figure 6.10Figure 6.11Figure 6.12Figure 6.13Figure 6.14Figure 6.15Figure 6.16Figure 6.17Figure 6.18Figure 6.19Figure 6.20Figure 6.21Figure 6.22Figure 6.23Figure 7.1Figure 7.2Figure 7.3Figure 7.4Figure 7.5Figure 7.6Figure 7.7Figure 7.8103105105106108110111112112113114115118119120122123125125131132133134137141142144Effective stressinthe particles atdifferentreductionsLocalized effective strain distribution atareductionof 1%Localized effective stress distribution at areduction of 1%Localized mean stress distributionatareduction of 1%Initialmesh andlocationofaparticle inacylindrical specimenEffective strain distribution in the cylindrical specimen with and without aparticle at a reductionof65%Effective strain distributionaroundthe particle atareduction of65%Effective strain distribution along the center line of the specimen underdifferentreductionsEffective stress distribution in the cylindrical specimen with and without aparticle atareductionof65%Effective stressin the matrix and inthe particle at areductionof65%Mean stress distribution in the cylindrical specimen with and without aparticle at a reductionof65%Mean stress distributionbothin thematrixand in the particle at a reduction of65%Effectofparticle shape on damage factorat a reductionof65%Effectofparticleshape on strain distribution atareduction of65%Effectofparticle shape oneffective stressvariationduringcompressionEffective strain distribution under different reductions with an initial particlespacing of 120 p.mMean stress distribution in the matrix and in the two particles under differentreductionswiththe initialparticle spacing of 120 p.mEffectofparticle spacing on strain distribution atareductionof65%Comparison ofpredictedvaluewithmeasured dataMetal flow ofabilletin acontainerSchematicpositionsforthe pictures takenwithlowmagnificationMetalflowin the deformationzone during extrusionSchematic positionsforthe pictures takenformicro examinationTypicalparticle distributionin the Locations 1 -9Schematic ofexamined extrudate specimenTypical characteristics of particles after extrusion of 6061/A12O3/2Op at anextrusionratio of34Typical characteristics of particles after extrusion of 6O61/A12O3/lOpat anextrusion ratio of34xviFigure 7.9Figure 7.10Figure 7.11Figure 7.12Figure 7.13Figure 7.14Figure 7.15Figure 7.16Figure 7.17Figure 7.18Figure 7.19Figure 7.20Figure 7.21Figure 7.22Figure 7.23Figure 7.24Figure 7.25Figure 7.26Figure 7.27Figure 7.28Figure 7.29Figure 8.1Figure 8.2148148150151152152155155156157161162164165166167167170171171173179179182185185187188190Histogram ofvolumefractionfor6061/Al203/lOpHistogram ofvolumefractionfor6061/AlO3/20pHistogramofthe particle diameterforSample B3 of6061/A1z03/20pHistogram ofthe particle diameterforSample B6 of6061/A12O/lOpHistogram oftheparticle areaforSample B3 of6061/AI3/20pHistogram ofthe particle areafor Sample B6 of6O6l!A12O/lOpHistogram ofthe aspectratio for Sample B3 of606l/Al03/20pHistogram ofthe aspectratio for SpecimenB6 of6061/A12/lOpHistogram of orientation of the particles with respect to extrusion directionforthe Sample B3 of6061/AlO3f20pHistogram of orientation of the particles with respect to extrusion directionforthe Sample B6 of6061/A1203/lOpFractureprobabilityvariationinthe deformationzoneParticle size reduction during extrusionMicrostructure of6061/AlO3/l0pbefore and afterextrusionMicrostructure of6061/A120/20pbefore and afterextrusionVariationofmaximum andminimum aluminaparticle dimensionAspect ratio of alumina particles of6061/A12O3I2Opin back end of a billetand inextrudateOrientation ofaluminaparticles of 6061/A12O3/20pin back end of a billet andinextrudateAschematic diagram forthree particle-fracturemodes duringextrusionEffective strainrate distributioninthe deformationzoneMeanstress distributioninthe deformationzoneShearstress distribution during extrusionVoid formation near a low speed crack tip of J94-14 of 6061/A1203/20pinlongitudinalsectionVoid formation near a low speed crack tip of J94-1lB of 6061/A12O3/lOpinlongitudinal sectionTensile stress in aparticleunderplane straincondition at areductionof 10%Tensile stress distributionin the matrix and aroundparticlesTensile stress distribution in the monolithic material at a reduction of 10%underplane strainconditionTemperature distributionofbillet and die atsteady state extrusionTensile stress (ar) distribution at the die interface zoneEffect of ram speed: (a) Maximum temperature in the die land zone duringFigureFigureFigureFigureFigureFigure8.; (b) Maximum tensile stress inthe die land zone duringextrusionTemperature distribution on both side of the die interface at a ramdisplacementof30mmEffectofram speed on straindistributionthroughradius directionEffectofram speed on stress distribution (az) throughradius directionEffectofram speed oneffective strain ratevariationinextrudateEffect of initial billet temperature:(a) Max. temperature in the die land zoneduringextrusion; (b) Max. tensile stressinthe die land zoneThermal gradient on both sides of the die interface under different billettemperatureEffect of initial die temperature: (a) Maximum temperature in the die landzone during extrusion; (b) Maximum tensile stress in the die land zone duringextrusionThermal gradient on both sides ofthe die interface under different initial dietemperaturesEffect offriction condition at die interface: (a) Maximum temperature in thedie land zone during extrusion; (b) Maximum tensile stress in the die landzone duringextrusionThermal gradient on both sides of the die interface under different frictioncondition at die interfaceEffect of extrusion ratio (a) Maximum temperature in the die land zoneduring extrusion; (b) Maximum tensile stress in the die land zone duringextrusionThermal gradient on both sides of the die interface under different extrusionratiosEffect of volume fraction: (a) Maximum temperature in the die land zoneduring extrusion; (b) Maximum tensile stress in the die land zone duringextrusionThermal gradient on both sides of the die interface under different volumefractionVariationofEvalue during differentconditions butsame extrusionratioVariationofEvalue during extrusion atdifferentextrusionratiosExtrusionlimit diagram at an extrusionratio of28 for6061IAl2O3/20pforthepress atKRDCExtrusion limit diagram at a ram speed of 12.5mm/s for 6061/Al203/20pforthe press atKRDCFigure 8.9Figure 8.10Figure 8.11Figure 8.12Figure 8.13Figure 8.14Figure 8.15FigureFigure8.168.17Figure 8.18Figure 8.19191192192193194195196197199200201202203204208208213213FigureFigure8.208.21Figure 8.22Figure 8.23Figure 8.24Figure 9.1Figure 9.2xviiiFigure 9.3 Extrusionlimitdiagramfor60611A1203/20pat anextrusion ratio of34 for the 214large press atUACFigure 9.4 Extrusionlimit diagram for6061/A1203110pat an extrusionratio of34 forthe 214large press atUACFigure 9.5 Extrusion limit diagram for606l/A1203/20pforthe press at KRDC 216Figure 9.6 The limitdiagramfor6061/A1203/20pfor thepress atUAC 217Figure 9.7 Comparison of the extrusion limit diagram for6061/A1203/20pfor the press 218atKRDCusing differenttechniquesFigure 9.8 Comparison of the extrusion limit diagram for6061/A1203/20pfor the press 219atUAC using differenttechniquesFigure 9.9The extrusion limit diagram for both 6061/A1203/lOpand 6061/A1203/20p219usingthe empiricalequationtechniqueFigure 9.10 Low speed cracking boundary for the extrudate of 6061/A1203120pat an 221extrusionratio of 13Figure 9.11 Low speed cracking boundary for the extrudate of 6061/A1203/20pat an 221extrusion ratio of34Figure 9.12Low speed cracking boundary for the extrudate of 6061/A1203/20pat an222extrusionratio of52Figure 9.13 Effect on extrusion ratios on low speed cracking boundary during extrusion 223of606l/A1203/20pFigure 9.14Extrusion limit diagram of 6061/A1203/20pfor the press at UAC with low-224speed cracking boundariesFigure 9.15 Voids in the surface layer of an extrudate of 606l/A12O3/2Opat an extrusion 227ratio ofabout34 withoutlow speed surface cracking (front end ofJ94-14)Figure 9.16 Voids in the surface layer of an extrudate of6O6l/AI2O3I1Opat an extrusion 228ratio ofabout 28 withlow speed surface cracking (frontend ofK-6)Figure 9.17 SEM image observed in the surface layer of the extrudate at an extrusion 230ratio ofabout34withoutlow speed surface cracking (backend ofJ94-14)NOMENCLATUREA, B, C, E, ExperimentalconstantsF, a, bCross sectionofabillet area,m2C1(t),C2(t) Time-dependentconstantintemperature analysisProductoffracture stress and fracture strainofamaterial, MPac, specificheat, J/kg-K[C] Heatcapacitymatrixd Diffusiondistance,mD Volumeequivalentparticle diameter, jimD1Meanrefinedvolumeequivalentparticle diameter, jimDBInitialbilletdiameter, mInside diameterofacontainer, mExtrudate diameter, mB,E0 Elastic modulus ofasolid phase, GPaOverall stiffness ofapress,kN/mmB Productofmax. tensile stress andmax. effective strain during extrusionF1 Surface tractiononvelocityboundary{f) Residualofthe nodal pointforcevectorh0 Initialwidth ofthe gap between two cracked particles, pmJ Mechanicalequivalentofheatk Thermalconductivity,W/m-° KK,K1,K Penalty constant, and material constants[Ks], [Kc] Stiffensmatrix, andheatcapacitymatrixL0 Initialbilletlength, m1D,L Instantaneouslength ofabilletmeasuredfrom the deadmetal zone, miiDie landlength, mLR Length ofadiscardn Stress exponentxxn Averagenumberofpartsfracturedfrom a singleparticleN, NNumberofbrokenparticles, and numberoftotalparticlesP Extrusionload, NPf Extrusionforce atthe end ofstroke, kNp extrusion pressure, MPaphPressure required formatrixintrusioninto the gap ofcrackedparticles, MPaParticlefractureprobability;1Average particlefractureprobabilityrate overcross sectionin deformation zonePo Fractionofporosityin a solid phase4Heatgenerationrate,WImQHot deformation activation energy, 3Qb, QActivation energiesforsurface and bulkdiffusion{Q)HeatfluxvectorR Extrusion ratioR Gas constant, JImol-°CR1 Radius ofcrosssection in deformation zone duringextrusionS Surface area,m2Sa, Sm Adjusted and measured ram stroke, respectivelyST Totalram stroke, mt Time, sT,{T}Temperature and the matrixofits nodalvalues,0KSummation oftemperature differentiationwithspatialcoordinatesTemperature differentiation with timev,v1,v3 velocity componentVBRam speed, rn/sV Volume,m3x Material constantdepending on internalstructureZ Zener-Hollomanparameter,s1AD/D Meanparticle sizereduction afterextrusionxxiAT Temperature risein extrudedproduct, °KATDInitial temperature differencebetweenthe billetandthechamberor die, °KAt Timeincremental, s{Av},Avj First-ordercorrectionofthe velocity atprevious stepMaterial constant,MPa’; andparticle aspectratio;f3 Time integrationfactor1, iiConstantin particle fracture model,tm3StrainFracture strainofamaterialeN, 60,CJ,Fracture strainofvoid nucleation, growth, andlinkagemax Maximumeffective strainduringextrusionStrainrate, effective strain rate, and volume strainrate,e., e,eCritical strainrate fordislocation accumulationin frontaparticle,HeatgenerationefficiencySemi angle ofextrusion; degreeAngle ofdead metal zone, degreeFunctionalforthe deformationbodypdensity,kg/mda, Flow stress, yield stress, MPa,3m,a1Effective stress, meanstress, and principle stress, MPaFracture stress ofthe compositesaCTz Tensile stress inX-directioninplane straincompression, andinthe extrusiondirection, MPaSub- and Superscripts:s denotesthe steelfortoolsc denotes the compositeforthe billett timexxACKNOWLEDGEMENTSI would like to express my sincere appreciationto Drs. Indira Samarasekera, KeithBrimacombe, Bruce Hawbolt, and ChrisDaviesfortheir supervisionthroughoutthe wholecourse ofthis project. Without their support,my dream ofobtaining a Ph.D. would neverhave come true. Appreciation is extendedto Alcan International Ltd. for providingtestspecimens, technical help and discussions. Thanksto Mr. William (Bill) Dixon ofDuralcan USA, and Dr. David Lloyd, and Mr. ChrisCabryel, of Alcan International Ltd.for their help with the extrusion trials. Thanksare also extended to Dr. Stuart MacEwenforhishelp and discussion offinite elementmodeling ofthe extrusionprocess. Thanks forfinancial support go to the industrial partnersin the Metal Matrix Composite Precompetitive Research Consortium: Mean InternationalLtd., Ontario Hydro Ltd., SherrittGordon Ltd., Pratt and Whitney Canada Inc., IncoLtd. and NSERC, and also to theOntario Center for Materials Research, through whose auspicesthe consortium was setup. Thanks to Ms. MaryMagerforher assistance inusing the SEM.Thanks to ProfessorTara Chandra from University ofWollongong for his interestto this project. A great help from Dr. Warren Poole in this departmentis very muchappreciated. I would also like to thank all my fellow studentsin this department for theirdiscussion and friendship.Finally, I would like to take this opportunity to express my appreciationfrom thebottom of my heart to my mother, and my wife, Xiaoli (Shelly). Without theirlove andemotionalsupport, this Ph. D. projectcouldneverbe finished.DEDICATIONTomymotherxxiliChapter 1 Introduction 1Chapter 1 INTRODUCTION1.1 CharacteristicsofMetalMatrix CompositesMetal Matrix Composite (MMC) research was initiatedin the 1960’s. It is particularlyattractive in applications when the following improvements over monolithic materials arerequired:Easily designedand tailor-madematerial;Improved strength/densityratio;Improved stiffness/densityratio;Improved wearresistance;Improved hightemperaturemechanical properties;Adjustable physical properties (coefficient ofthermal expansion, diffusivity, elasticmodulus).Among the importantMMC systems, the following are ofinterest111:A1203/AlandA1203/Mg;SiC/AlBoron/Aluminium;Carbon/Aluminium.MMC research initially focused on continuous fiber reinforcements which give veryhigh stiffness and strength. Most of the continuous reinforcements are very expensive andhave low workability owing to fiber fracture; they have found applications primarily inaerospace and military. In order to avoid the problems of high cost and low ductility, thereChapter 1 Introduction2has been considerable interest in discontinuousreinforcements such as short fibers, whiskersand particles. The advantagesof discontinuous reinforcements over continuousreinforcementscanbe seeninTable1.1t21.Since particulate reinforced MMCs can be processedby conventional metal workingmethods or techniques to produce all forms ofsemifinished products, they become moreattractive from a cost perspective. Another decisive factor,especially for small industry, isthatpartsmade ofparticulate reinforced MMCsbehave almostisotropically, and are thereforemuch simpler to use in design. Althoughthe strength and elastic modulus of particulatereinforced composites are inferior to those of continuouslyreinforced composites, the lowcost, high workability and isotropic properties render themsuitable for a wider range ofapplications,especiallyin automobileproduction.Table 1.1 fllustrationoftheprinciplefactorslinkedwith theaspectratio(whereV’denotes the advantage and ‘x’ the disadvantage)Advantages Discontinuous ContinuousReinforcement ReinforcementIsotropyxOrientablePropertiesxFormability,DuctilityxFabricationCostsxMaterialCostxRecyclabilityxReinforcementEfficiencyxChapter 1 Introduction31.2FabricationofParticulateReinforcedMetalMatrixCompositesIn discontinuously reinforcedmetal matrix composites,the reinforcements aregenerally ceramic in nature andcan either be added to the matrixas discrete elements orfonned in situ in the matrix.Reactivity with the matrix duringfabrication and service,differences in coefficient ofthermal expansion(CTh) between the matrix andreinforcements,and cost/performance inthe finished product are the critical selectioncriteria used for thereinforcements. Aluminaandsiliconcarbidepowder (greater than 1 micronin size) have beenchosen primarily for the reinforcement,as these materials represent a good compromisebetween density, property improvement, andcost. However, alumina isabout 5-10 timescheaper than silicon carbide powder (SiCp)and 10-100 times cheaper than alumina orsiliconcarbidefilaments131.Moreover, aluminahasa higher stability than silicon carbide inaluminumalloys, such as the 2xxx, 6xxx, and 7xxxseries. Lower manufacturing costprovides apotential forlarge scale productionof a competitively priced product. In fact,the MMC thatisclosest to acommercialbreakthrough isan aluminum matrix composite with discontinuous,particulate ceramic reinforcements (SiCandA1203)141.It is being fabricatedin severaldifferentways:Foundry processes, where particles(or whiskers) are inserted into the moltenmetalbymechanical stirring, and theproductiscastinto aningotofdesiredshape orsize;Powder metallurgy process, where metal powdersand reinforcements are blendedcold, compressedandbonded by diffusion;Squeeze casting, where the molten metalis pressure infiltrated into a preform offibers;Chapter 1 Introduction4Spray deposition technique, where deposition of atomized liquid metalalong withparticulate is employed to fabricateMMC ingots.The attraction ofingot casting is the potential forproducing MMC billetssuitable forutilization on the large scale equipment currently employedfor fabrication of monolithicalloys. This approach will capture economies of scale, and is beingused at AlcanInternational Limited, Canada, Duralcan,USALS],and Hydro Aluminium, Norway’. Meltviscosity limits the volume fraction ofthe reinforcementto approximately 25volume percent.Alcan Aluminium Ltd. has commissioneda 25 million lb/yr facility in Quebec for theproduction of composites for Duralcan in Canada in1990151.The scale-up of the castingprocess to largersizespresents challenges related to: a) the effects ofthe solidificationrate ontheingotcell size, and b) attendantparticle-pushing to the lastregionsto freeze. Acastroutewhich could have more homogeneous particle distribution ina cast product of particulatereinforcedmetalmatrixcompositesis sought. Inaddition, sincematrix-reinforcementreactionis a critical issue in some MMC systems, large ingots which have longersolidification timesresultinincreasedexposure ofthereinforcementto the moltenmetal.1.3 ProcessingandApplicationsofParticulateReinforcedMMCs1.3.1 SecondaryDeformationProcessingMany discontinuously reinforced metal composite products requiresubsequentdeformation processing via rolling, extrusion, or forging to achieve thefinal shape,irrespectiveofhowtheprimary ingotis produced. Dural AluminiumCompositesCorporation(Duralcan), has developed necessary technologies to producea range of ceramic particlereinforced MMCs by the molten metal route. Theirproducts have beenused toproduce castChapter 1 Introduction5shapes, forgings and a wide range ofextruded solid and hollow shapes. Themain thrust oftheir extrusion development has focused on6061 and 2014 alloys, reinforced either withsilicon carbide or aluminaat 10 - 20 volume percentage. Significant improvementsareachieved in the elastic modulus and strength,although ductility is reduced. The elasticmodulus is increased by up to 40%, andthe minimum increase in tensile strength is 20%’.However, defects such as surface tearing are observedduring extrusion, which affect thequality of the final MMC products. To improve thequality of MMC products571,a betterunderstanding ofhow deformation processing influencesthe microstructure and properties inthesematerials is needed.1.3.2ApplicationsMetal matrix composites (MMCs) are now used in, or beingconsidered for use in, avariety of applications in the military, aerospace,automotive, and other commercial areas.Automotive applications include automotive driveshafts, cylinder linings, brake rotors’81;other applications include bicycle frames and components, andtire studs’91.However, theintroduction of the MMCs into actual applicationsis still sparse. No true high volumeapplications exist to date. To promote further use of MMCs, somefundamental changesmust take place. The cost of the compositesmust be reduced, probably by improving themanufacturing processes. A better chemical and physical understandingof the MMCs mustbe developed so thatdesignerscanuse thematerialwithconfidence.Chapter2 LiteratureReview 6Chapter2 LITERATUREREVIEW2.1 ExtrusionProcessExtrusion is a forming technique widely used in the aluminium industry to produceshapes of complex cross section. The extrusion process can be classified into three broadcategories’°’ depending on the directionofextruded materialmovementrelative to the punch.i) Forward extrusion: materialflowsin the same direction as themotion ofthe punch;ii) Backward extrusion: materialflowsin a directionopposite to the motion ofthe punch;iii) Side extrusion: materialflowisperpendicularto the direction ofmotionofthe punch.In the forward aluminium extrusion process, cylindrical billets are preheated to atemperature, between 300°C and5000C,at which point they are transferred to the heatedcontainer of an extrusion press (Figure 2.1). The container is generally heated to atemperature, 30-50°C lower than the billet in order to compensate for cooling during billettransfer. A load is applied to one end of the billet via a ram and dummy block, forcingmaterial through a die of a shape and size calculated to give the dimensions of the finalcooled product. The die is also heated, and sits on top of a number of support components,collectively known as the stack. The die may be classified into shear or flat face die, conical,parabolic and streamlined types, the difference among them being the mathematicalrepresentation of the surface or material path lines. In a shear die, a dead metal zone existsand a shearing band is formed between the dead metal zone and the deformation zone. In aconical die, thematerialpath line is alinear function; in the parabolic die(convex or concave)it is a parabolic function (second order equation); and in the streamlined die a cubic functionhas been used. The conical die, which is relatively easy to design and manufacture, is fairlyChapter2UteratureReview7well known.In this case, material flow is more uniformthan for the shear (or flatface) die.However, the conical die may inducesome rigid body rotationnear the die exitdueto abruptchanges ofmaterialflowatthatpoint. Theparabolicdie(convextype)hasasmoothentry butthe exit is sharp, creatingrigid body rotation and discontinüitiesin the velocity distribution.Dies having both smooth entryand exit are referred toas streamlined dies with the implicitassumption that thematedal path lines coincide with the improved diesurfaces. Streamlineddies have been shown to besuitable for processing “difficultto extrude” metal al1oys101.However, thesheardie typeisstillwidelyused forthe extrusionofaluminium and its alloysinindustry,probablybecauseofitssimpledesignandlowcost.1 - Billet2 - Container3 - Die4 - Extrusion Stem5 - Dummyblock6 - Die holderFigure2.1 SchematicofaforwardextrusionprocessPress sizes range from lab scale- 200ton maximum load, 60mm container I billetdiameter- to industrial-size pressesof up to and greater than 10,000 ton loadcapacity, withbillet diameters of250mm.Extrusion ratios (upset billet area to extrudatearea) ofbetweenChapter2 LiteratureReview 810:1 and 200:1 are typical; associated extrusion speeds, measured at material exit, can rangefrom less than 0.5mlmin. to lOm/min. or greater. The process is stopped short of allthematerial exiting the die; the portion of billet remaining in the container is known as thediscard, the extruded material as the extrudate. The extrudate may either be air cooled, orquenchedwith watersprays.It is also important to note that hydrostatic extrusion is a nearly-ideal friction-freeprocess. Low frictional forces in hydrostatic extrusion permitthe use oflower die anglesandhigh extrusion ratios, both of which lead to higher hydrostatic stress and therefore toconditionswhichsuppressfracture .The uniform deformationnearthe surface, caused bylow friction, reduces the danger of surface cracking and fracture can be suppressed byextruding at high fluid pressure. Therefore, brittle materials were the prime target for theapplication ofthe hydrostatic extrusion1131.Embury et al.[t121have suggested application ofthe hydrostatic extrusion process for MMC processing to increase its fonnability.Unfortunately, thecomplexity oftheproductionprocessleads to ahighercostoftheproduct.2.2 ExtrusionRelatedDefectsofParticulateReinforcedMMCs(PRMMCs)There isaconsiderable interestinthe forming ofmetal matrix composites (MMCs), inparticular, forcontrolling the deformationparameters so asto avoiddefects ormicrostructuraldamage. Of the various forming processes, extrusion has received considerable attention.Not only does the large compressive hydrostatic component of the stress facilitate theimposition of large strain, which homogenizes the particle distribution and heals particlefracture duringthe process,butitalso causes axial alignmentofdiscontinuous reinforcements.DURALCAN®composites havebeenmanufactured byhot, direct (forward) extrusion®OwnedbyAlcanAluminumCorporationChapter2 LiteratureReview9(lubricated and unlubricated) and also by hydrostatic extrusion.Hot direct extrusion withshear-face dies without lubrication is the simplest,the cheapest and the most widely usedmethod. Alternative processes involving conical-entrydies, with or without lubrication, arenot presently being considered, owingto the difficulty of obtaining a high-quality surfacefinish. In an exceptional study, using a conicaldie, Selseth and Lefstad141found that whenextruding the AA6061/SiCp (SiCw) MMCs producedby the powder metallurgy (P/M) route,the necessary extrusion force was about 30% highercompared to a shear-face die. The‘p’and ‘w’ notationsstand forparticle and whiskerreinforcement,respectively.2.2.1 ExtrusionRelatedDefectsAlthough hot extrusion of casting products appearsto homogenize the particledistribution, clustering (defined as the aggregation of particles)and banding are still evidentdue to an insufficient extrusionmtio1.The study by Uoyd’53’also indicatedthat althoughthe tensile elongationof a permanentmould cast compositetestbar (CastA356 -15% SiC) isaround 1%, which is much lower than the unreinforced alloy (Cast A356)as shown in Fig.2.2. Alter extrusion at an extrusion ratio of 70:1 under different temperatures(e.g. at 400°Cand 600°C forA356-lO%SiC and A356-20%SiC), the composite elongationis comparable toor better than the unreinforcedas-cast alloy (Cast A356). However, it is lowerthan the alloyin extruded conditions. During extrusion, surface defects such as surface tearing and crackingappear; some ofthese defects are known to occur during extrusion ofunreinforced materials,while some others are specific features on the MMCs only. These defects will significantlyaffecttheextrudabilityofparticulatereinforced MMCs.Chapter2 LiteratureReview10Elongation to Fractureversus StressA356— SiC0.300.25I::vvA AA A AAI I I I I240 260 280 300320 340 360 380 400Stress (MPa)o *356- 10%SIC (600) C) *356-i0%SiC (400)V P356-20%SiC (600) *356-20%SiC (400)V *356-i5%SiC (600) A Cast P356-i5%SIC• Extruded A356 • Cast *356Figure 2.2 Tensile elongationto fracture againststrengthforA356 alloy anditscompositeswithdifferentvolumefractionsofSiCp beforeandafterextrusionatdifferentextrusiontemperaturesof400°Cand600°C1531Extrudability refers to the maximum attainable speed of the billet without surfacedefects occurring duringextrusion. Based on the early extrusion trials done byHams etal.171,itwas found that (i) two kinds ofdefects occurred during extrusion of6061 and 2014 withaluminareinforced MMCs, and (ii) theirbehaviorwas very differentfromunreinforced alloys.Firstly, considerable surface tearingoccurredatthe frontend ofthe extrusion atlowextrusionspeeds, which persisted over the entire extruded length. However, the intensity of tearingusually reduced with increasing extrusion speed, and on occasion, disappeared completely atintermediate speeds. Secondly, a furtherincrease in speed resulted in the onset ofedge andsurface cracking which differed from the low speed cracking. These cracks were similar inappearance to a type commonlyencountered withconventional aluminium extrusions. It wasChapter2 LiteratureReview11reported that two types of crack mechanisms existfor speed-limiting cracking of Al-Mg-Sialloys. The first type initiated at the die/extrudateinterface, and occurred because the matrixwas not strong enough to withstandfrictional force at the die. The secondtype initiated atsubsurface weaknesses, and was assumedto be due to incipient melting. Obviously,bothtypes oftearing mechanisms are temperaturedependent and are initiated in a regionclose tothe die/extrudate interface. Therefore, the temperaturedistribution resulting from heat lossesand the temperature rise during extrusionneeds to be examined. Althoughboth types ofhighspeed cracking occurred inboth monolithic alloys and the MMCs, low speed tearingwhichshouldbe designated as the third type, appeared only inthe MMCs (Brusethaug etal.61).Thistearing was characterized by deep notches extendingfrom the surface into the material. Aprobable explanation of the mechanism for the thirdtype was given by Hams et a1.7asfollows: In the initial stages of extrusion, the diewas colder than the extrudate. Metaladhering to the die bearing land during this phasewas immediately chilled and its flow stressincreased. This may create conditions which wereenergetically favorable for subcutaneousfracturing, so that the material in contact withthe bearing remained stationary, while thesubsurfacematerial continueditsforwardmotion. Furtherincreaseinpressurebroke the bondbetween the bearing and adhered material; this materialthen moved across the bearingsurface. The entire periphery did not move in unison; differentsegments breaking away atdifferenttimes. New material adhered to thedie bearing land and consequently the extrudatesurface retained this debris. The process was repeated inthe classic stick-slip mode untilconditions were energetically favorable for continuous movementof material across thebearing surface. This low speedtearingintroduces aminimumextrusionspeedforthe MMCs.Chapter2 LiteratureReview 12Obviously, this mechanism needs to be refined, because it does not include the interactionbetweenparticles andmatrixmaterials.Another trial was conducted by Selseth and Lefstad4’in Europe for three differentaluminium composites. They investigated the extrudability of discontinuously reinforcedaluminium alloys. The composites were SiCp, SiCw andA12O3pin an AIMgSi matrix. Thesilicon carbide particle (SiCp) reinforced MMC was fabricated by mixing AIMgSi powder(AA6061) and SiC particlesofsize, while the aluminaparticle(AI2O3p)reinforced MMCwas fabricated bystirring theA1203pofsizeof3Opm into the molten AIMgSi (AA6082). Thevolumefractionsofparticles orwhiskers were all 20%. In the tests, a conventional shear-facedie was used, and the extrusion ratios were 22 and 39. In some ofthe experiments adisc ofunreinforced material was clad in front of the bifiet.. This markedlyreduced the tendencytowards high speed surface tearing, thus increasing the maximumextrusion speed. Theirexperimental results showed that the composite containingthe finest SiC particles (4pm)could be extruded to solid rod at an extrusion speed of250mm/s, while the aluminaparticlereinforced MMC was extruded at a speed of only 83mm/s. Becausethe matrix materials ofAA6061 forSiC particles andAA6082forAl203particlereinforcementwerequite similar, therelatively poorer extrudability for the alumina particlereinforced MMC was related to thedifference ofmicrostructure ofthe MMCs by Selseth andLefstad’41.As described earlier, inAlzO3preinforced MMCs, there were some particleclusters especially at lower volumefraction, such as lOvol% and l5vol%, whichwerenotdiscovered in SiCp reinforced materialsmade by the P/M route. The materialwith the leastclusters,yielded the best surface quality.This could be the reason for its poor extrudabiity.However, the effect of different particleChapter2 LiteratureReview13size forAI2O3p(3Otm) and SiCp( MMCs should also be considered, because it is alsoimportantto the deformation and fracture behavior.Material State Defects MMCsUnreinforcedMatrixAlloyPorosity, voidsAs-cast Cluster, stringersSurface cracksParticlefractureDebondmg atparticle/matrixinterfaceDeformed Nearinterface MatrixFracture(Extruded) Low speed surfacecrackingHighspeedsurface cracking:1) atdie/extrudate interface2) atsubsurface ofbilletRotationandmigrationofparticles*Obviously, the ability of material to withstand high strain rates is vital to theextrudabilityofthecomposite. Higherstrainratesmaycausefractureofthe extruded materialat the extrudate surface and also result in an overheating in the low melting zone at the subsurface ofthe extrudate, givinghotshortness duringextrusion. Allthe defects observed inas-cast and extruded materials are summarized in Table 2.1. Therefore, it is essential to analyzethe process to establishthe optimum operating conditions to produce defect-free products. ItTable2.1 Microstructureobservedin theparticulatereinforcedcompositebeforeandafterextrusion(whereVdenotes the observation ofthe defect.*maynotbe takenas defects.)Chapter2 LiteratureReview14is worth pointing out that the rotation and migrationof particles during extrusion of MMCsproducedby the melt-castingroute will bebeneficial totheparticle distribution.2.2.2 HotWorkabilityofPRMMCsHot workability relates to the ability of a metal or alloyto be deformed underconditions ofhightemperature ((T>0.6TM), where TM is the melting point ofthe material inKelvin), and relatively high strain rates (0.1 to 1 s_i)without forming cracks1”.The twocharacteristics that govern hot workability are strength andductility. Since for a givenmaterial, different strains are attained prior to fracture depending onthe process, workabilityofamaterialis affectedbyboththe material itselfand the externalprocessingconditions, i.e.:Workability=f(material)xf2(process,friction)(2.1)where.,is a function of the basic ductility of the metal andf2that of the external factorswhichmodify the basic ductility. The formulaclearlyimpliesthat the accumulation ofinternaldamage whichleads to fractureis closely related to the deformation and restoration processesoperative duringhotworking.In particulate reinforced metal-matrix composites, the aim has beento combine thebeneficial stiffness ofceramics with the superior ductility and toughness ofmetals. However,this combination produces lower ductility and toughness in composites as compared to thematrix alloy. In order to maximize these properties, it is necessary to understand the localmicromechanical failure modes and their relation to macroscopic toughness. As mentionedabove, these local failure modes are also dependent on the processing details and, for theMMCs, onthematrixtrealmentanditseffectontheinterface. Ingeneral,thefailuremodes inthe particulatereinforcedMMCscanbe due to one ormoreofthefollowing:Particlefracture;Chapter2 LiteratureReview15Debondmg atparticle/matrixinterface;Nearinterfacematrixfracture;Generalfracture mechanismofthe matrix oftheMMCs as the sameas that of theunreinforcedmatrixalloy’’.ThestudybyLloyd’53’showedthat, forthe SiCpreinforcements,fractureoccurs inthelarger size fractionof the particulate population.Fig. 2.3 shows the straindependence offracturedparticles for6061-10and 2Ovol%SiCp atroom temperature.o6061—20%SIC6061— 10% SIC40030o0.0, ; , V I 1 V I I0 1 2 3 4 5 6 7 8 9 1011 121314cxFigure2.3 Straindependenceoffracturedparticleof6061/SiCpMMCs531Itisevidentthattheextentofparticle cracking is lowerinthe lOvol%SiCp composite,which is not surprising consideringthe lower particle content in thiscomposite. The rate ofparticle cracking withstrain is also lower. It is interestingto note that less than5% of theChapter2 LiteratureReview16total particle population has cracked atfracture of the composite. However, it is apparentthatparticle crackingis initiated atlowstrains. In spite ofthis, the voids created do notgrowsufficiently during subsequent straining to affect the final fracture strain; the strain offracturedoes not correspond to the strain for particle cracking. Similar behavior hasalso beenobserved in 606l/A1203composites. This indicates that there is a critical amount of damagedeveloped at large strains. The damage is in the form of voids associated with particleclusters, togetherwiththe occasional cracked particles. The voidshavenotgrown extensivelyin the tensile stress direction. This is generally the case in unreinforced alloys. This alsosuggeststhat the growth strain is negligible in comparisonwith the nucleation strain, and thatvoid nucleation is primarily a result of matrix failure within closely spaced particles.Thereasonfor this behavior is related to the deformation response ofthe particleclustered regionrelative to the rest of the composite. Within clusters, the farfield applied stresses are nolongercontrolling. Actually, higher-stiffness particles constrain the deformationofthe matrixadjacent to them, and this results in a complex triaxial stressbeing developed in the matrixwithin the cluster. Obviously, the triaxial stresses areimportant because a triaxial tensilestressenhancesbothvoidnucleation and voidgrowth.To considerthe effectofthe degree ofthe triaxial tensile stress, aratio ofmean stress toeffective stress,aJ was adopted. Uoydfound that the unreinforced alloys have a significantloss in elongation with increasingtriaxiality, while the composites arerelatively unaffected. This is consistent with the idea thatthe fracture of the composite iscontrolled by the intrinsic triaxiality generated atparticleclusters, and these dominate any imposed far field stressstate. Thao et al have reportedthat as the temperature increases the voidformation due to interface debonding at the ends ofparticles in tensile direction becomes dominant comparingto particle fracture which isChapter2 LiteratureReview17dominantatlow temperature.Lloyd53’also pointed outthat due to the importance ofparticlesize on the deformationand fracture behavior of thecomposite, particle size mustbe limitedto maximize strength,and minimize fracture. It has been indicatedthat using particles ofaround 10 micronswith a tight size distribution, reducesthe propensity for particlefracture,which occurs most readily incoarse particles. However,a small particle size may result inmoreclusters whichare harmfulforthe fmalproperties ofthe MMCs.2.3 DevelopmentofExtrusionLimitDiagramsModeling of extrusion has,at a practical level, been focused on theuse of empiricalequations and analytical solutionsto predict optimum operating conditions1555.Consequently, the determination ofextrudability has been based on extrusionpress-sidemeasurements and property I qualityrequfrements. The extrusion processis governed bythe imposed variables, temperature, strainrate (speed), and strain (reduction ratio)and theirinteraction with the characteristics ofthe material. The significance of eachof theseparameters will be determined by severalfactors, such as surface quality, minimummicrostructural damage if there isany, excessive pressure requirement, etc.. MeadowsandCutler’63 showed that the bounds ofextrudability may be calculated theoretically, anddemonstrate this on a diagramshowing maximum tolerable extrusion pressures andsurfaceincipient melting plotted on the axes ofextrusion speed against temperature for a certainextrusion ratio, as schematically shown in Fig. 2.4.The constant pressure boundary line isdetermined by the extrusion press limit,but is a function ofextrusion ratio, temperature andstrainrate. The incipientmeltingboundaryline is depicted accordingto the temperature at thedie land interface, which isa function of initial extrusion temperature, extrusionratio, ramspeed,frictioncoefficientatinterfaces,etc..Chapter2 LiteratureReview 18Such limit diagrams have been developed to include structural8’591and propertyfeatures’5.Sheppard1reviewed these and other developments, and found that most priorresearchhas been oriented to the prediction ofapeak ormaximumload required ofthe press,and thepredictionoftemperaturerise due to extrusion deformation.SpeedExtrusion TemperatureFigure 2.4 Aschematicextrusionlimitdiagram2.3.1 PeakPressureThe simplestequationforestimationofpeakpressure during extrusionisexpressed as,p=a(a+bInR) (2.2)where a is the flow stress of a material, R is the extrusion ratio, and a and b are constants.The above equation needs to be modified to include friction effects; assuming that stickingfriction condition prevails during extrusion which was widely adopted by researchers inaluminiumextrusionindustry’55,the aboveequationis changedto,p=a[(a+blnR)+4L] (2.3)where L is an instantaneous length ofthe billetmeasured from the dead metal zone and Dcisthe inside diameterofthe container.Chapter2 Literature Review19At high temperature, the flow stress of a material is a function ofstrain rate andtemperature,and may be characterizedby ahyperbolic sineequation,Z=eexp()=Asinh(aa)(2.4)where Z is Zener-Holloman parameter, and A, a,Qand n are material constants. InsertingEq.(2.4) into Eq.(2.3), ageneralequation forpeakpressure duringextrusioncan be derived:(2.5)(xn AADwhere B, C, E, Fare constants for a specific press.The mean strain rate formula adopted inthisstudy is expressed as,_4vDtanq (2.6)— (DaDE)3”2whereDBandDEare diameters ofthe billet and theextrudate,respectively, vB is theram speedand q is the semi angle of the deformation zone outlinedby the shear zone in unlubricatedsheardieextrusion,expressedas1,p=54.1+3.45lnR(2.7)Based on some plant trials, the above four constants for the extrusion presscan beestimated, and the constant pressure boundary line ina limit diagram can be delineated usingEq.(2.5).2.3.2TemperatureRiseA general analytical equation for temperature rise during extrusion wasderived byCastle and Sheppard’651based on a thermal analysis including thebillet, and the sunoundingtools.AT= (O.9PvBt — ATDC2(t))IC1(t)) (2.8)Chapter2 LiteratureReview 20where P is the extrusion force, ATD is the initial temperature difference between the billet andthe container or die,C1(t), andC2(t)are heat flow coefficients and t denotes extrusion time.Sheppardt671claimed that ‘for high conductivity aluminum alloys, thisform oftemperatureincrease may be sufficientlyaccurateforpracticaluse’.In aluminum extrusion practice, it is common for there to be little or no temperaturedifference between the billet and the surroundingtoolstM].However, the generation of heatinternallywillestablish atemperature differential. Therefore, in the calculation oftemperaturerise, the initial temperature difference between the billet and the tools could be ignored. Theaboveequationthenbecomes,AT=0.9PvBt/C1(t) (2.9)=O.9PvBt/(K1t”2+(K2+K4)t213+(K3+K5)t”3+K11t)Alltheconstantsare expressed as below,K— ic(D —D)(kSPSCPS)lI2 (2.9a)112K2 = l(18kSDB(p8C)112 )213 (2.9b)K3=.lD(l8ksD(p$Cps)2)hI3(2.9c)K4=-l(18kSDR(pC8)1/2 )213 (2.9d)K5=.l1(18k8D(p,C,)2)hI3(2.9e)K11= pCCPCRvB1tD/4 (2.9f)whereIDis the deforniation zone depth between the pressure pad and the dead metal zone,lis the die land length,‘pis the angle of dead metal zone, p, k, C, are thermal properties of amaterial, and the subscripts s and c denote the steelfor tools and the composite for the billet,respectively.Chapter2 LiteratureReview212.4 FiniteElementAnalysisofanExtrusionProcess2.4.1 FiniteElementAnalysis ofanExtrusionProcessModeling of an extrusion process for detenninationof punch pressure, stress/straindistributions, material flow pattern, etc., is of extremeimportance to the manufacturingprocess designer for a number of reasons. It providesvaluable information, not only forenhanced design of work tools and process parameters,but is also useful for improvingexisting extrusionmethods oreveninventingnewroutes.Various kinds of extrusion processes have been analyzed for monolithic materialsbythe finite elementmethod at a macroscopicleve114361,usingboth the SolidApproach and theFlow Approach. The Solid Approach treats the solidas an elastic-plastic material duringforming. The significant shortcomingis its complex formulation and the computingcost291.Incontrast, the FlowApproach considers the materialsto behave as a non-Newtonian viscousfluid. Atypical shortcoming ofthis approach isthatitcannotrepresentmany ofthe subtletiesofelastic-plastic constitutive laws; hence it does not provide informationon residual stressesand also does notsolve directly thedisplacements’29331.Forextrusionproblems, depending onthe type ofmodel, the transientand steady-statecomponents of the process can be analyzed. The transient portionis of interest if peakpressure and the deformation behavior at the beginning ofthe extrusion needto be examined.Forthe steady-statesituation, the deformation behaviorofthe head end and the tail end ofthebillet cannot be analyzed; only the deformation behavior in the deformation zone can beinvestigated. TheEulerian descriptionis suitable forthis analysiswith the FlowApproach. Inthe Eulerian description, the mesh is stationary while the material flows through theChapter2 LiteratureReview22deformation zone during deformation.However, for non steady-state (transient) problems,the total Lagrangian or updated Lagrangian descriptionis preferable and is adopted by usingthe SolidApproach or Flow Approach. Ina non steady-state process, such as at the initialstage oftheextrusionprocess, theLagrangian descriptionsuffersfrommajordrawbacks whenthe workpiece endures large or localized deformationand also when the work tools, namelythe punch and the die, have complexshapes orsharpedges. This may be attributed to the factthat, in the Lagrangian description, the fmite elementmesh remains embedded in the materialand moves with it. Lack ofcontrol over the gridmotion often results in excessively distortedelements, thus deteriorating the quality of the finiteelement solutions. Continuing thesimulation beyond certain levels of deformation becomes impossiblein many cases, onaccount ofentangled or non-convexed elements. Therefore, variousremeshing schemes havebeen attempted to overcome theseobstacles391.Another approach is the application of an Arbitrary Lagrangian-Euleriandescription(ALE) to industrial metal forming simulation. In ArbitraryLagrangian-Euleriandescription, the mesh moves at a differentvelocity fromthat ofthe material. The descriptionis a hybrid between the Lagrangian and Eulerian descriptions,i.e., ifthe mesh moves at thesame velocity as material, it is termed Lagrangian, and if the mesh velocityis zero, it isEulerian. However, it is difficult to choose an appropriate mesh velocity; andit appears thatremeshing is required duringlargedeformation.2.4.2DevelopmentofanExtrusionLimitDiagramUsingFEMThe above described semi-empirical equations in Section 2.3 for developmentofextrusion limit diagrams result in mean values for the variable. One recognized69’drawbackof the semi-empirical approach is the problem of analyzingthe close inter-relation of theChapter2 Literature Review23process variables- flow stress, strain rate and temperature. Theintractability of the situationcanleadto alarge numberofexperiments being required.A more attractive, and increasingly accessibleapproach is the use of fmite elementtechniques°41.Grasmo etal.have used a finite elementmodel to simulate theextrusionofan Al-Mg-Si alloy, AA6060. The model considersthe material to behave like a fluidanddoes not include predictions during the billet upsettingphase. However, it is themostpractical and complete model of extrusion developedto date using FEM techniques.Nevertheless, thereislittleliterature using afinite elementtechniqueto developextrusionlimitdiagrams.For the extrusion of particulate reinforced composites, low speed crackingshould beincluded in the limit diagram. However, no workhas been found for the lowspeed cracking.Dixon(91proposed that the low speed cracking boundary is a function of extrusion ratioasschematically shown in Fig. 2.5. The low speed cracking boundary can be determinedby aseries ofplanttrials. Alternatively, a finite elementmodel can also be employed todeterminethisboundaryprovided a suitable criterionisinsertedinto the model.ExtrusionSpeedExtrusion TemperatureFigure 2.5 Schematic extrusionlimitdiagram withlowspeedcracking’5’Chapter2 LiteratureReview 242.4.3Fracture CriteriaforMonolithicMetalsSome fracture criteria for cold and hot working have been established to rationalizethedatawhich are availablefordifferenttestgeometry, i.e., Stress Criterion;Strain Criterion,Plastic-WorkCriterion1491.The Stress Criterion wasbased on the fact that cracking inmetalworking was recognized to be associated withinducedtensile stresses, even in processes suchasforginginwhich the stresses are predominantlycompressive. The importance ofthe tensilestresseswas indirectly confirmed by the large increase in apparent ductility whenmaterials aredeformedunderhydrostaticpressure. The tensilefracture ofconventional alloysis consideredin terms ofthe microvoid coalescence model (MVC) in which the fracture strain expected isthe sum ofthe nucleationstrain, the void growth strain until void coalescence occurs, and thefmallinkage strain,£LLF—eN+8G+eL(2.10)Usuallye, is considered to be small relative to the other terms, therefore the fracture strain isexpressed as:eF—EN-f-CG(2.11)However, in working operations, itis likely that both shear and tensile stresses play apart,since thereisevidence thatlocalizedflow by shearisrequiredto initiate cracks which arethen propagated by tensile stresses. A Strain Criterion has also been suggested by someworkers1501based on the total strain, but difficulties arise since the total strains vary markedlyindifferentprocesses. Therefore,itis reasonable to assume thatany criterion shouldbe basedon some combination of stress and strain rather than on either of these quantities separately.There are indications that the total plastic work to fracture may be an important factor(Plastic-Work Criterion). Cockcroft and Latham proposed that fracture occurs in a ductileChapter2 LiteratureReview25material when, for a given temperature and strain rate,the plastic work done by the highesttensile stressreachesaspecifiedlimit1511.s:”GlI)d= C(2.12)Cockcroft and Latham successfully appliedthe criterion to cold working but did nottest it for hot working. Sellars et al.’491 tested the above equation andconcluded that theequation could be a reasonable criterion for hot working as well as for coldworking, butclaimed thatfurtherdataisrequired to testitmore rigorouslyforhotworking.2.5 FiniteElementAnalysisofthePRMMCsIn modelingmonolithic metalforming, some approximations are alwaysmade, such asconstantvolume ofmaterial, isotropy, coincidence ofthe axis ofprinciple stress and strain, noinfluence of hydrostatic pressure and equivalent response to tensile and compressive loads.For the MMCs, these assumptions are not entirely valid. Therefore, a micro-material modelneeds to be developed to characterize the particle and the material behavioron a microscopicscale due to microstructuralcharacteristics and theirinfluences on properties. However, thereis little published work on the microanalysis ofmechanical working ofthe MMCsat elevatedtemperature. The micromechanical analysis of the particulate reinforced MMCs associatedwiththermal phenomena and simplified loading conditions are discussed to review the currentmethodologyofthe MMCdeformationanalysis.A few studies have been attempted for the micromechanical analysis of materials,includingfiber140421 and particulate reinforcedMMCs143,but most of them are based on aunit cell model with idealized boundary conditions. Aradhya et al.’45’analyzed a simplifiedMMC structure undertensileloading, as showninFig. 2.6.Chapter2 LiteratureReview 26yE1AluminiumSICBjC>_____________________________________I_________________________A01.-rn0IA7/)//,)/,/9///)///m mesh sizeA interparticledistance= particle Lengthb= particle widthFigure 2.6 Finiteelementmodelused byAradhyaetBased on a two-dimensional finite element model, the mechanical properties of 6061AIISiCp composites and the effect of different volume fractions of SiCp on the tensileproperties were investigated. In their analysis, the particle size was assumed to be 4Ojim andunifoimly distributed, and the aspect ratio was taken to be unity. The model predictedthat,below a certain critical volume fraction of SiCp (25%), the matiix material in the compositeyielded at slightly lower stresses compared to the unreinforced material under the tensileloading conditions. This is obviously contrary to the experimental results which indicate thatthe0.2% yield stressofcompositeisinvariably higherthanthe unreinforced matrix alloy.TheapparentdiscrepancybetweentheFEMand the experimentalresultswasexplainedbythefactthatthe properties ofthe unreinforced matrixmaterial were used inthe model to describe thematrixmaterial in the MMCs. The UTS values predicted byFEMwere much lower than theChapter2 LiteratureReview27experimentally observed.The discrepancy between the elasticmodulus prediction by FEMand experimentallymeasuredvalues also existed, and the maximumdifference was about 12%at volume fraction = 0.4. In spite ofthis,the unitcell model with idealized assumptions inaMMC micromechanical analysis,such as, uniform distribution of second phase particlewithregularparticle shape, idealizedboundaryconditions, etc. can give apre1iminwy insightofthemicroscopicbehaviorofthe MMCs, althoughitisfarfromreality.A more flexible discretization for differentvolume fractions of particulatereinforcements was developed by Ramakrishnan etal.1using a master mesh, as shown inFig. 2.7.Figure2.7 Mastermeshforgeneratingdifferentmicroscopicmorpho1ogies’’Chapter2 LiteratureReview28In their finite element analysis, someimportant aspects associated with thetransformation induced plasticity inA1203.-Zr0wereanalyzed. These aspects included: (i) anestimation of the residual stress in the second phase,arising during post fabrication cooling,which affected the critical stress for transfonnation;(ii) the constitutive behavior ofthematerial during the dilatational transformation ofZr02and (iii)the crack deflection due to thetransformation. The study was conducted for angular and spherical shapes ofsecond phaseparticles and also forvarying volume fractions ofthe second phase. Thecrack morphologiesgenerated by the FEM study for different overall fractions ofthe angularZr02are shown inFig. 2.8, based on the assumptionthat the particle/matrixwas perfectly bonded. Because themaster mesh model represents more closely the real situationof the MMCs (with randomlydistributed second phase particle and its random shapes, angular or spherical)than regulararrangementofthe reinforcements withidealized shapes, such as spherical, cylindrical,square,etc. assumed by other unit cell fmite element models described above, the comparisonofanalytical solutions they derived assuming a spherical shape forthe second phase particleswith the results obtained through the simulation showedvery good agreement. However, noexperimentalvalidationwasprovided due to the difficulties foramastermeshmodelto satisfyall the real boundary conditions. Moreover, in their study, since no large deformationwasinvolved, the mesh size and its arrangement were not altered during the simulation. But forlarge deformation ofthe MMCs, the mesh which represents the matrix would distort, whilethe mesh representing the reinforcement would not distort due to its higher stiffness.Therefore, a remeshing technique has to be applied. It is evident that the master meshmodelcannotbe adopted on amicroscopic scaleinthe extrusion process, because a large number ofelements would be required and remeshing would be difficult. However, microscopicChapter2 LiteratureReview29mechanical analysis couldbe conducted based on an idea ofmultilevel finite elementanalysisduiing large deformationwithsomesimplifications.a4wVolumefractionofZr02 = 0.05VOIUIMfractionofZO2 = 0.1— -4111144%cv__VolumefractionofZ,02= 0.2VolumefractionofZ,02= 0.3FIgure 2.8 ThecrackmorphologiesgeneratedbytheFEMstudyfordifferentoverallfractionoftheangularZr02withtransformation23.1 MultilevelFiniteElementMethodMultilevel finite element analysis was first proposed by Kopp et al.1471 in thesimulation ofmetalforming processes to optimize the computation time. At Level 1 (GlobalAnalysis) integral parameters such as the required force and requited work are computedusing a coarse FEM mesh At Level 2 (Local Analysis), an optimized number of elements isused to determine continuum mechanics parameters like stress, strain and temperature;Microscopicphenomena aresimulatedatLevel 3 (Microscopic Analysis), using specialmicro-material elements and thermodynamicmodels. The method has been applied to an upsettingChapter2 LiteratureReview 30:H H1eE.100‘4,(‘4a010 20(1 distance tramingot centerP(b)------ .L._._Ifl______________________________10i225mm(a)Figure2.9 (a)FEMmeshwithlocalrefinementduringaplane-strainupsetting;(b) Stressdistribution alongthe linePQ (e=1% calculatedwithABAQUS)t47’4The results using a multilevel finite element system to calculate the stressconcentrationdueto secondphaseparticlesare showninFig. 2.9(b), based onthe distributionofsecondphaseparticlesalongthe linePQshowninFig. 2.9(a). Figure 2.9(b) showsthat theproblem. The results from Level 1 are sufficient to provide reasonably accuratedata for theestimation of the size of plant needed or the formingschedule of a process. When theformability of a workpiece is concerned, a more detailed analysis(Level 2) is required.Moreover, the results from Level 2 are useful in analysis at Level3. At Level 3, eithermicrostressorthermodynamicevolution, suchas, recrystallization, etc., isofinterest.Using amicroscopicmaterialelement, thestressconcentration around asecond phase particle,suchasa ceramic particle in the MMC5, can also be estimated by locally refining the finite elementmeshas showninFig. 2.9(a).——— a macroscopicstress—b microscopic stressChapter2 LiteratureReview31continuum-mechanics based solution(Level 2: macroscopicstress) yields a normal stress(curve a), while substitutionofthe micro-elements (Level3: microscopic stress) produces astress curve (curve b) in thesame figure with spikes at the positionsof micro-elements.Obviously, the substitution of micro-element(or second phase particles in real materials)changes the local stress in the matrix. For metallurgicalmicroanalysis, FEM results fromLevel 3 areneeded to studymicrostructureevolution duringhotdeformation.2.5.2ParticleFractureModelduringDeformationFinite element analysis at level 2 can reveal the macroscopicdeformation behavior ofthe MMCs during extrusion. However, criteriaquantifying the microstructure(fracture) atlevel 3, based on the deformationbehavior, arerequired. Brechet et al.(75-76]assumed thattheprobability of fracture of a particle,p, is a function of area-equivalent particle diameter, D,and strain, c, atroom temperature asbelow.(2.13)wherefis a constant and the probability is definedas the ratio of the number of crackedparticles to total number of particles. Theirexperimental data had verified the linearrelationship between the fracture (percentage ofparticlescracked) and the imposed level ofstrain by compressinga sample ofAl(A356)-20%SiC. The model did not considerthe shapeof a particle (includingaspect ratio). As observed in the microstructure in extrudatesofalumina particulate-reinforced metalmatrix composites, equiaxed particles crack lesseasily.To take aspectratiointo account,the probability ofaparticlecrackingcanbe expressedas:Pf= 1—exp(—Dae) (2.14)whereais the aspectratio ofaparticleand is aconstant(=l.6x104p.m3).Itisnoted thatEq. (2.14) is consistent withthe experimental data from Brechet eta1761.Actually, if theChapter2 LiteratureReview32exponential term in Eq. (2.14) is less than 1,Eq. (2.14) could be approximately expressedasEq. (2.13). Because the above equationsare valid for room temperature, itis not clearwhether or not the criteria applyto high temperature deformation suchas the hot extrusionprocess. At high temperature, plasticrelaxation around particles iseasier due to possibledislocation climb, and work hardening is not dominant,while the strain rate is more sensitiveto flow stress. Due to the compressivestress state in the hot extrusion process,particlecracking could be the dominantfracture mode.Humphreys andKalu771have investigatedthelow temperature transition ofa second phase particle behavior in a modelmaterial of Al-Sialloy. Atlow temperature,thereis an accumulation ofdislocations atthe particles,whereas athigh temperatures climb is possible withthe consequence that there is no stress build-up.Consequentlytherewill be very little particledamage orinterface decohesion. Theyproposedthat at high temperature the critical strain rate belowwhich stresses will not accumulate isgivenby:cc=Kiexp(—Q /RT)ITd2+K2exp(—QbIRT)/Td3(2.15)where K1 and K2are material constants,QandQbare the activation energies for bulk andsurface diffusion, d is the diffusion distance, and T isthe absolute temperature. They alsopointed out that with appropriate adjustmentsto the constants, the above equation may beused with some confidence to predict the effect ofsecond-phaseparticles on the mechanicalbehaviorofalloysatelevatedtemperature.Basedonthe aboveanalysis, itwould be feasible to neglectthe straineffectbecause ofless work hardening, but add the strain rate and temperatureeffect to account for theprobability ofa particle fracture athigh temperature. Therefore, the strain rate compensatedChapter2 Literature Review33variable, Z= eexp(Q/RT), shouldbe introduced to consider the probabilityof a particlefracture during deformation athigh temperature.Moreover, offractured particlesbyintruding matrixmaterials into thegap oftwo halves has been observed in deformed materialswithsuperimposedhydrostatic pressure.The pressure,Ph’required for the matrixmaterialtointrude into thecracksis expressedast751:2 D ln(DI h)— e(2.16)ph(e)=a [—+—(°)1‘3 3h0 ln(D1h0)whereh0is the initial width ofthe gap ofthe crack and is the flow stress ofthe matrix. Itis evidentthateasier ‘healing’ couldoccurathigh temperatureifthisequation is applicable.2.5.3 MicroscopicAnalysis ofPRMMCsunderLargerDeformationIt is known that a microscopic analysis of the PRMMCduring industrial extrusionprocess is impractical. The multilevel system can be appliedto the analysis of particulatereinforced MMC during large deformationin laboratory tests, although a specific micro-element material model is required on a microscopicscale to induce its anisotropy. At themacroscopic level, the MMCs are assumed to be isotropic andthe continuum plasticity theoryis used. The deformation behavior ofthe MMCs canbe characterized and the fonnability ofthe MMCs can be analyzed by usinga modified Plastic-Work Criterion. At a microscopiclevel, micromechanical analysis ofthe MMCs under large deformationcan be conducted by asingle particle model (micro-element material model)and a multiple particle model to bedescribed in later section. In this study, the behavior ofa particle during a cylindricalcompression and a plane strain test will be analyzed at both the macroscopicand microscopiclevel, to help understand the microstructuralevolution of the PRMMC during largedeformation (including extrusion) athightemperature.Chapter3 Scope andObjectives34Chapter3 SCOPEANDOBJECTIVESParticulate reinforced MMCs are attractive for many applications in the automotiveindustry. However, the demandhasbeenlimited owing to the cost and insufficientknowledgeof the behavior of the MMC materials. Many discontinuously reinforced MMC productsrequire deformation processing via rolling, extrusion, or forging to achieve the final shape.Issues associated withthese processing schedules include equipmentcapabilities, die wear dueto the abrasive nature of the reinforcements and the influence of deformation conditions onmicrostructure and properties. To meet the goal of increased productivity with high qualityand reduced costs, a better understanding is needed ofhow deformationprocessing influencesmicrostructure and propertiesin thesematerials.3.1 Scope and ObjectivesFrom the literature review, it appears that the extrusion process is the widely used andone ofthe most economical secondary processing routes forparticulate reinforced MMCs. Itmay also improve the mechanical properties ofthe material. The scope and objectives of thisstudy are:1) To conduct compression tests using aGleeble®machine to develop constitutiveequationsforthe PRMMCs. The constitutive law willbe adopted in the fmiteelementmodel;2) To better understand the deformationbehavior ofthe aluminaparticulate reinforcedMMCs during extrusion with the aid of a finite element model, DEFORM® , at macroscopiclevel;®GleebleisaregisteredtrademarkofDynamic Systems, Inc., New York, USA.Chapter3 Scope and Objectives353) To conduct extrusion plant trials to examine the microstructural evolution (e.g.,particle fracture and size refinement) and the mechanical property change ofthe MMCs underdifferent extrusion conditions; the plant trial data, such as extrusion force and temperaturemeasurement will be used in validation of the finite element model predictionsand the modelpredictions as well as plant trial data will be applied to the development of an extrusion limitdiagram;4) To establish a correlation between deformation parameters and the low speedsurface cracking by microstructural examination and the finite element analyses at bothmacroscopic and microscopic levels.3.2 MethodologyAn integrated approach has been adopted for this study: Gleeble compression testswere conducted to develop the constitutive law of the alumina reinforced metal matrixcomposites. The constitutive law has been adopted in the finite element analysis of theextrusion process. Extrusion plant trials were conducted and the plant trial data were used invalidation ofthe finite elementmodel predictions. Microstructural evolution for the extrusionbillet and extrudates was examined using an optical microscope and an image analyzer. Acorrelation between deformation variables (e.g., ram speed (strain rate), extrusion ratio andtemperature), and composite failure (including surface cracking) was established basedon anSEM surface crack examination and the FEM analyses. The effect ofextrusion conditionsonthe mechanical property change was investigated byconducting tensile tests ofthe extrudates.Extrusion limit diagrams for the material were finally developed for the purpose of industrialproduction. The overallconception ofthe project is schematicallyshowninFigure 3.1.® DEFORM is aregistered trademarkofScientificForming TechnologyCorporation, Columbus, Ohio.Chapter3 Scope and Objectives36GleebleTestsMicro-IConstitutivemechanical L.awParticle SizeRefinementProductExtrusionLoad strokecurve,AnalYSisAnalysLimitModelDeformationBehaviourLow Speed Cracking,ValidationEffectofExtrusionDevelopmentConditionsiafEFigure 3.1 Methodologyfor the extrusionofaluminaparticulatereinforced MMCs37Chapter4 EXPERIMENTALLaboratory tests and plant trials were conducted to better understand the behavior ofthe alumina particulate reinforced metal matrix composites during processing. Constitutiveequations for three different volume fractions, 10%, 15% and 20%, of the MMCs weredeveloped based on cylindrical compression tests using aGleeble®machine. The constitutiveequations will be used in extrusion process simulation with the aid of a fmite element model.Two plant trials were conducted on a small press in the Kingston Research and DevelopmentCenter (KRDC), and a large industry press at Universal Alloy Corporation (UAC), Anaheim,fortwo differentvolume fractions, 10% and 20%, ofthe composites. The extrusion datasuchas load-stroke and die temperature will be used for validation ofa FEM model prediction anddevelopment ofextrusion limit diagrams. Microstructure evolution of the composites duringextrusion will be examined using microscopes and correlated with the tensile propertiesmeasured from the extrudates ofthe KRDCplanttrials.4.1 GleebleTestsSpecimens of 6061/A1203with three different volume fractions from 10% to 20%were machined from castbilletstocks into cylinders of 10mm diameterby 15mm long. Thespecimens were homogenized at 565°C for 2 hours to improve the as-cast structure,toreduce segregation and precipitates and large dispersoids.Compression testing wasconducted using aGleeble®1500’ thermomechanical simulator. The specimenswereresistance-heated at 5°C/s to test temperatures in the range of400°C to 525°C, held at thattemperature for one minute, and then deformed to a true strain of 1.0 atanominal strain rateof 0.05, 0.1, 1, or l0s-. Graphite shims were inserted between thespecimen and ram toChapter4 Experimental 38prevent excessive barreling (Figure 4.1). The test conditions chosen were based on theextrusionconditionsadopted in industryforthe unreinforced aluminum alloys.The hot working behavior of many conventional alloys has been characterized withan empirical equation derived from creep laws. The equation which is most applicable overthe range of strain rates and temperature encountered of monolithic alloys during hotworkingis the hyperbolic sine constitutiveequation (Equation4•1f8J•Z=eexp(QIRT) =Asinh(xa)(4.1)where Z is the Zener-Hollomon parameter (the temperature compensated strainrate), C isstrain rate,Qis activation energy, R is the universal gasconstant, T is the absolutetemperature, a is the flow stress and A, cz, and n are constants.Itis noted that the equationis strictly valid only over the steady state regime of deformation and as such, itmay not beFigure 4.1 Schematic ofthe Gleebletestset-upChapter4 Experimental 39applicable to the low strain range where transient behavior is observed. However, someworkers have empirically applied the equation over the whole strain range of a test with areasonable fit ofthe dat?9.Typically during analysis for the equation constants, a is set toan arbitrary value and the other parameters are calculated using plots In{sinh(aa)) againstme to determine n, and ln{sinh(a a)) against l/T to determineQ.The method ofunconstrained variables was used in this study to analyze the data for the four parameters inthe constitutive equation. This method, based on a procedure first shown by Sheppard andWright80’, allows all four of the equation constants to vary during iteration to a solution,rather than fixing a, as is common in most other work. For the data analysis, true strain wascalculated from transverse extensometer readings of the variation of specimen diameterduring compression. The flow stress for the analysis was calculated at a strain of 0.5 in thesteady state regime. The nominal strain rate was obtained from the recorded value over astrain range of 0.35 to 0.65, because it varied at the beginning and at the end of thedeformation. The temperature used for the analysis was also the absolute value at a strain of0.5. The values of the four parameters in the hyperbolic sine equation were determinedthrough iteration by minimizing the absolute difference between the measured flow stressand the predicted flow stress. The values of each material constant for the composites arecompared with those for the unreinforced parent alloy in Table 4.1. It is noted that the fourconstants were determined for the best fit of the experimentaldatat8hi.The correlationcoefficient between the predicted and the experimental data for eachvolume fraction is alsolisted in Table 4.1 for reference. It is seen that a good correlation has been obtainedbetweenthe predictedflow stresses and the experimental data.Chapter4 Experimental 40Material Q(kJ/mol-K) A(s’) a(MPa-’) n CorrelationCoefficient6061 197.5 1.97x10’2 0.036 4.11 0.9976061/A1203/lOp 216 9.42x10’4 0.023 5.24 0.98860611A1203115P210 9.77x10’2 0.034 4.00 0.9926061/A1203/20p 220 4.45x10’4 0.024 4.41 0.9874.2 PlantTrialsatUAC, Anaheim4.2.1 ExtrusionProcedureTwo plant trials were held at Universal Alloy Corp., Anaheim, on the Duralcancomposite and its unreinforced material. Two billets each of 6061,6061/A1203/1OPand6061/A1203/20pwere extruded in the first plant trial in September, 1992(designated as‘S92’, hereafter). Only the 6061 and one of the 6061/AlO3/2Opbifiets werehomogenized.The remaining three billets were extruded in the as-cast state. The two 606l/AlO3/lOpbillets were 508 mm (20”) long and all the others were 304 mm (12”) long. Thediameter ofall the billets were 178 mm (7”) in the second plant trial in July, 1994 (designated as ‘J94’,hereafter). 22 billets, 14 of6061/A1203/lOp,and 8 of606l/AlO3I2Op, were extrudedusing4 different dies. They were all prehomogenized at about 570°Cforfourhours. The length ofall 22 billets was 381mm (15”), and the diameter of all thebillets was also 178 mm (7”).Details ofthe extrusionconditionare listedinTable 4.2.Table 4.1 Material constantsforthe constitutiveequationoftheComposites1Chapter4 Experimental41Table 4.2 Extrusionprogramsforthe7” pressatUACTest No. Material BilletDimension DieDiameter Pretreatment_____________(L (mm) xD(mm)) (inch)S92-1 6061 305x178 1.25 HomogenizedS92-2 6061 305x178 1.25 HomogenizedS92-3 606l/A1203/20p 508x178 1.25 HomogenizedS92-4 606iIA12O3I2Op 508x178 1.25 as-castS92-5 606l/A1/lOp 305x178 1.25 as-castS92-6 6061/A1203/l0p 305x178 1.25 as-cast394-1 6061/A1O/iOp 381x178 2 Homogenized394-2 6061/A1203/lOp 381x178 2 Homogenized394-3 6061/A1O3/l0p 381x178 2 Homogenized394-4 606lIAl2O3/iOp 381x178 2 Homogenized394-5 606l/A10/2Op 381x178 2 Homogenized394-6 6061/A123/20p 381x178 2 Homogenized394-7 606l/A10/20p 381x178 2 HomogenizedJ94-8 6061/Al23/lOp 381x178 1.25 Homogenized394-9 606l/A10/lOp 381x178 1.25 Homogenized394-10 606lIAl2O3IlOp 381x178 1.25 HomogenizedJ94-1 1 6061/A10/lOp 381x178 1.25 Homogenized394-1lb 6061/A12O3/iOp 381x178 1.25 Homogenized394-12 606l/A1/2Op 38lxi78 1.25 Homogenized394-13 606l/A1203/20p 381xl78 1.25 Homogenized394-14 606l/A1203/20p 381xl78 1.25 Homogenized194-15 606l/A1O/lOp 381x178 1 Homogenized394-16 606l/AI23/lOp 381x178 1 Homogenized394-17 6O6l/A1O/lOp 381x178 1 Homogenized394-19 606l/A123/2Op 381x178 1 Homogenized394-20 6061/A1O/20p 381x178 1 Homogenized394-ha 6061/A123/lOp 381x178 1.5 Homogenized394-18 606h/Al0/lOp 381x178 1.5 HomogenizedChapter4 Experimental 42A schematic diagram of the press setup at UAC is shown in Fig. 4.2. Billets werepreheated in a gas fired, three-zone, chain belt furnace. Initially the three zone temperatureswere set to 121°C, 321-343°C and 466°C, but the preset temperature of the last zone wasadjusted according to the required extrusion temperature, which is 420°C to 520°C. Billetsresided in the furnace for typically 40 min., although, a billet only progressed when thepreceding one was withdrawn. Contact thermocouples in each fire zone were employed tomeasure billet temperature for furnace control (Fig. 4.2). The final zone temperature wasrecorded in the data spreadsheet as the fmal billet temperature in the furnace. Thesetemperaturemeasurements have the potential to be inaccurate as they were taken directly aftera flame had impinged on the billet surface. Further temperature measurements were takenfrom both the front and the back end of a billet using a hand-held K-type thermocoupleimmediately before the billetenteredthe transfermechanism (Table 4.3).Container, dieProductrunouttablePress hydraulics - - - - — - - — -•Billet_____________________________• I transferImechanismZ2 Z3‘I IlI II II II IBilletloadingDiepreheatingiI boxIl IlThermocouplesThree-zone gas firing furnaceFigure4.2 Schematic ofextrusion setup forDuralcantrialsChapter4 Experimental43Table4.3 BillettemperaturesimmediatelypriortoextrusionatUACTest No. Material PresetTemp. Temp.@front Temp.@back(°C) (°C) (°C)S92-1 6061 427 452 454S92-2 6061 427 424 438S92-3 6061IA12O3I20p 427 429 429S92-4 606l/A1O/20p 427 391 391S92-5 606l/A1203/l0p 427 393 410S92-6 6061/A1/lOp 427 431 443J94-1 60611A12O3/lOp 466 424 426J94-2 6061/A10/l0p 493 399 399J94-3 606l/Al2OlOp 477 459 516J94-4 606l/A103/l0p 493 516 519J94-5 606l/A12!20p 477 452 457J94-6 606l/A1203/20p 477 444 460J94-7 606l/A1/20p 488 458 516J94-8 6061/A1203/l0p 488 463 521J94-9 606l/A1/lOp 488 479 507J94-10 606l/A1203/lOp 488 482 496J94-11 6061/A1/l0p 468 446 457J94-llb 6061IA12O3IlOp 468 434 483J94-12 6061IA1/2Op 468 423 460J94-13 60611M203/20p 491 471 507J94-14 6061/A1/20p 491 461 514394-15 606l/Al2OillOp 491 488 503394-16 6061/A1O3/lOp 491 498 465J94-17 6061/A12/lOp 510 487 529J94-19 606l/A1O3/2Op 510 484 503J94-20 606l/A12O/2Op 477 457474194-ha 6061/A103/l0p 466 451 495J94-18 60611Al21h0p 466 451 457Chapter4 Experimental 44It is seen from Table 4.3 that the temperature distribution is uneven for most of thebillets atthe end ofheating. Ambienttemperature wasrecorded at28oC,rising to 38 to 49°Cnear the press. The total transfer time from furnace to the start of extrusion was 30 to 45seconds. The pressure pad, or ‘dummy block,’ which was transferred along with the billet, waspreheated to around 49 to 92°C (three measurements were made). The die was preheated toa setup temperature ofabout427°Cin adie box, whereas the bolster, upon which the die sits,was placed in the stack at ambient temperature. The die assembly would have lost heatbecause the thermocouple had to be inserted after removal of the assembly from the die box.However, this is of little importance as we have a continuous record of the die temperature.The container temperature was set to heat up to4270C,but temperatures measured at theinletpartofthe containerwithahand-held device indicated avariationof277 to 348°C.The press is a 3000T horizontal press with no extrudate quenching capability.Extrusion speed was manually controlled by a pulley system, and varied significantly for theestablishment of good extrudate surface conditions. A thermocouple was inserted in the dieto a position approximately 1.6 mm away from the die bearing surface, anditseemed to give agood response to billet loading and extrusion. The container has an inside diameter of 184mm. The pressure pad is 89 mm long with a flange at the contact end of 186 mm diameterby12.7 mm, the rest being 178 mm diameter. All the tools were H13 steels, except for the 1.5-inch die used in the secondplanttrial ofJ94-1laand 394-18,which was ceramicmaterial.4.2.2 ExtrusionDataDuring extrusion, the load, ram speed and die and container temperatures wererecorded. A typical load-stroke curve, with the variation ofram speed, is shown in Fig.4.3for the extrusion of Trial S92-3. The peak pressure is reached at the end of the filling-upChapter4 Experimental 45za,0LL0CoI-.wstage, when the billet is about to break through the die aperture. Then the extrusion forcefalls until the pad reaches the dead metal zone, due to the decrease in billet length andconsequent reduction in friction force at the container interface. The reason for the variationin extrusion speed greater than about lmnils are due to operator actions: the process wassurface quality driven withallotherfactors being subservient. Oneoperatorstoodat the pressexit and directed the actions of another operator who was manipulating the speed control.When surface cracking appeared at the front end of the extrudate, the ram speed wasincreased.The increase in die temperature during extrusion is mainly because ofheat conductionfrom the hotter billet (Fig. 4.4). The friction heat at the die interface also heats up thedietemperature. After contacting each other, heatconduction occurs between the billet and thedie, which causes the steep die temperature increase at the beginning. Thedie temperaturetends to level offwhen the steadystateisreached.543101200010000800060004000200000 50100 150 200250Ram Displacement (mm)Figure4.3 Typicalload-stroke curve withvariation ofram speed (S92-3)Chapter4 Experimental4616000_________________F— Homo(S92-3)I.14000—0— Unhomo (S92-4jj12000____10000___80006000400020000III100150200Ram Displacement(mm)1200046010000!8000-2 —0--Load6000- —a— DieTemp.• 4000’20000-310A’2C .—‘‘..,‘jQ0•400j• 370340I II0 50100 150 200 250RamDisplacement(mm)Figure 4.4Die temperatureincreaseduringextrusion (S92-3)I050250Figure4.5 Effectofhomogenizationonextrusionforce (S92-3 and S924)Chapter4 Experimental4764604305DieTemp3700 I Ii—3100 100200 300 400 500RamDisplacement(mm)Figure4.6Aweakcoffelationofincreasingramspeed withincreasing dietemperatureduringextrusion(S92-5)I —a-- 431°C (S92-6)160001—0—393°C (S92-5)12000____Cr.___ ___8000.—40000I II I0 100200 300400 500RamDisplacement(mm)Figure 4.7 Effectofbillettemperature onextrusionforce (S92-5 and S92-6)Chapter4 Experimental4816000120008000—a-- 305 mm (S92-3)400()—a-- 381 mm (394-12)0 50100 150 200 250 300RamDisplacement(mm)Figure 4.8 Effectofbilletlengthon extrusion force duringextrusion (S92-3 and394-12)12000______________—a—20% (194-7)‘-‘ 10000-__ ____—0—10% (J94-3)8000_6000.4000.-200001 I I I I0 50 100 150 200250 300RamDisplacement(mm)Figure4.9Effectofvolume fraction on extrusionforce duringextrusion(606l/A12O3/lOp: 394-3, and 606l/A12O3/2Op: 194-7)Chapter4 Experimental 4915000120009000.600030000300Figure 4.10Effectofextrusionratio onextrusion force (J94-4, 394-10, J94-15)A higher load is required for extrusion of the non-homogenized billets (both6O6l/A1203/l0pbilletsofS92-5 and -6 and6061/A1203/20PofS92-4, Fig. 4.5). This higherload is related to the microstructure of the non-homogenized materials, which containsegregatedelements,precipitatesand large dispersoids.A weak correlation between increasing ram speed and a delayed increase in dietemperature atthethermocouplepositionwas observed, as showninFig. 4.6. This is becausean increase in ram speed leads to a higher strain rate and a higher stress, which results in ahigher rate of heat of deformation. Consequently, a higher billet temperature due tohigherextrusion speed causesanincreaseindie temperature.Ahigher load is also needed forextrusion oflower temperaturebillets, because ofthehigherflow stress at lower temperatures (Fig. 4.7). The extrusion pressure is dependent onlyon the flow stress when the extrusion ratio is constant. The increase in extrusion force0 50 100 150 200250RamDisplacement(mm)Chapter4 Experimental 50associated with an increase in billet length (Fig. 4.8) is due to friction at the containerinterface; the friction force at the container interface is proportional to the billet length.Figure 4.9 shows that the extrusion force increases with volume fraction of reinforcementbecause the composite with a higher volume fraction of the particle has a higher flow stress.However, the similar value of the extrusion force for both volume fractions at steady state isdue to high initial temperatures of the billet at the back ends, (516°C, see Table 4.3), inaddition to temperature rise due to heat of deformation, which results in a similar flow stressfor both volume fractions. The effect of extrusion ratio on extrusion force, shown in Fig.4.10, confirms that a higher extrusion ratio leads to a high extrusion pressure. The influenceofextrusionratio and billetlengthon extrusionforce are also well explained by Eq. (2.2-5).A higher initial bifiet temperature was also tested (e.g., J94-17, J94-19) to try toobserve the incipient melting, but it failed because of low maximum ram speed of the press.•The control device consists of a pulley rig which opens or closes a valve in the hydraulicsystem. This accountsforthe fluctuations ofless than about lmmls: the press does not havevery good speed control, and themaximum speed whichcanbe realized is less than 10mm/s.4.3 PilotExtrusionatKRDC, Kingston4.3.1 ExtrusionProcedureA total of 14 extrusion tests were performed at Kingston Researchand DevelopmentCenter, Kingston, with two volume fractions (6061/A1203/lOpand60611A1203/20p)underdifferent extrusion conditions, as listed in Table 4.4. Themicrostructure of the extrudateswere examined for different extrusion conditions. The extrusion datarecorded were usedChapter4 Experimental 51both in validation of a finite element model and in development ofextrusion limitdiagrams ofthe composites. The testnumberis designatedhereafteras ‘K-’, as showninTable 4.5.Table4.4: Planttrial conditionsatKRDC6061/Al203/lop606l/Al03/2OpV= 0.8-0.9mm/sVl= 0.8-0.9mm/sT1 = 400°C,T2= 500°C T1= 400°C,T2= 500°CR1=lO,R2=28,R3=64 R1=l0,R2=28,R3=64The billets were in the as-cast condition. The billet was typically 76 mm long and 53mm diameter. All the billets were preheated in an electric furnace for about three hours toachieve a uniform temperature. The temperature of an instrumented billet of 6061 aluminumalloy in the furnace was monitored and controlled using a thermocouple. The die and thepressure pad were heated at the same time. However, the container was heated separately bythree heaters around the outer surface ofthe container along its axial length (Fig. 4.11). Theset-up temperature for the container was 500°C, but the air temperature measured in thecontainer was -.410°C. The ambient temperature was recorded at 24°C. Before extrusion,the die was first inserted into the container from the bottom, then the billet was loaded fromthe top within 5-10 seconds; finally, the pressure pad was placed on the top ofthe billetbeforethe stem began to press it. The press is a lOOT vertical machine. A schematic drawing ofthepress set-up is shown in Fig. 4.11. During extrusion, load, ram speed, and ram position wererecorded by a data acquisition system at a rate of 1 Hz. Unfortunately, no thermocoupleswere inserted into either the die or the container to record the temperature variation duringextrusion. Only the billet temperature was measured before it was loaded into the containerby ahand-held device.Chapter4 Experimental52Extrusion speed could not be controlled very well at high speeds (—4mmls).Therefore, a ram speed ofabout 1 mm/s was adopted. Only one extra test was conducted at aram speed ofabout 3.0mm/s with6Ol/Al2O3/lOp.All the extrudates were air cooled. Thesurface finish of most of the extrudates was acceptable, except for K-b, which exhibitedsevere die land lines and K-il which showed slight low speed cracks. More details on thelow speed cracking will be described in Section4.4.Figure 4.11 Schematic drawing ofthe extrusionpress atKRDC4.3.2ExtrusionDataThe dimensions ofthe billets and the extrudates afterextrusion were measured (Table4.5). The containerhad an inside and outside diameter of57mm (2.25”) and 111mm (4.375”)respectively, and its length was 203mm (8”). The pressure pad was 19.05mm (3’74) long witha flange at the contact end of57mm (2.25”) diameter by 3.18mm (1”18), the rest being 53mm(2.09”). The outside diameterofthe die was the same as the inside diameter ofthe container.The die land lengths were 2.48mm, 1.73mm, and 4.15mm for the 1”/4, 3”18, and 5”/8 dies,respectively. All the other data are listedin Table 4.5.Chapter4 Experimental53Table4.5 BilletdimensionsofeachtestatKRDCTrial No. MMC Billet Die Size Extrudate Discard(vol%) Dimension Diameter Thickness(mm) (inch) (mm) (mm)K-i 20% 50.80x87.0 5’78 15.74 3.0K-2 20% 50.80x87.05U1815.75 2.6K-3 10% 50.80x87.0 5’I8 15.75 1.5K-4 10% 50.80x87.0 5”18 15.75 3.0K-5 10% / I I /K-6 10% 50.85x86.40 3”18 9.72 4.0K-7 20% 50.76x88.13 3I8 9.72 11.3K-8 20% 50.82x85.91 1”14 6.42 6.0K-9 10% 50.66x58.61 1”/4 6.40 1.8K-b 10% 50.90x59.02 3”/8 9.72 2.0K-il 20% 50.75x84.42 3”18 9.46 5.0K-i2 20% 50.78x90.89 578 15.875 6.0K-13 10% 50.51x87.37 578 15.75 4.0K-14 10% 50.67x86.90 578 15.75 5.5Table4.6 MeasuredtestdataoftheplanttrialsatKRDCTrial No. MaterialTB(Meaq’d TC(sethn’)Ram Speed Remark(vol%) (°C) (°C) (mmls)K-i 20% 464 500 0.8-0.9 no crackK-2 20% 464 500 0.8-0.9 no crackK-3 10% 464 500 0.8-0.9 no crackK-4 10% 464 500 0.8-0.9 no crackK-5 10% 430 / / /K-6 10% 496 500 0.8-0.9 no crackK-7 20% 467 500 0.8-0.9 no crackK-8 20% 482 500 0.8-0.9 no crackK-9 10% 442 500 0.8-0.9 no crackK-b 10% 418 475 0.8-0.9 dielineK-il 20% 400 475 0.8-0.9 surface crackK-12 20% 435 475 0.8-0.9 no crackK-13 10% 436 475 0.8-0.9 no crackK-14 10% 436 475 2.70no crackwhereTBandTCare billetandcontainertemperature respectively.Chapter4 Experimental 54Figure4.12 shows a typical force-displacementresponse and coffespondmg ram speedfortestK-7. The extrusion datahas the same characteristics as the data from UAC, Anaheim,and the salientfeaturesare provided below:i) The typical load-displacement curve for direct extrusion is shown in Fig. 4.12. Thefirst stage is upsetting of the billet to fill the container, followed by a characteristic “breakthrough pressure”, which leads to a steady state region with decreasing force due todecreasingfriction.Figure 4.12Typicalload-strokecurve during extrusionatKRDC (K-7)ii) the ram speed was controlled atapproximately lmmls, except for those trials inwhich the extrusion force exceeded the presslimit, such as trials K-8, K-b, K-il, K-i2.Whenthe extrusionforceexceeded thepresslimit(lOOT), the ram slowed down automaticallyto keep pushing the billet through the die aperture, until theextrusion force required becamelessthanthe press limit, and thenthe ram speed increasedagain (Fig. 4.13).I1200900600300010.80.6a)a)0.4’0.200 2040 6080RamDisplacement(mm)Chapter4 Experimental 55iii) Other features, similarto those in the plant trials at UAC, were also observed, e.g.,a higher extrusion force was obtained at either a lower extrusion temperature, a higherextrusionratio oralargervolume fractionofthe particle.1200-1.5•______1.2__A ) I0.9600xf___—a-Force0.63o0cF—a--Speed__0.30 I II0 20 40 60 80RamDisplacement(mm)Figure 4.13 Variationofram speedatthe presspressurelimit(K-il)4.4 ExtrusionSurfaceDefectsDuring the above two plant trials, the extrudatesgenerally had a good surface finish.However, low speed cracks were observedat the front end ofsome extrudates from theplanttrials at UAC when the ram speed wasrelatively low. This phenomenondisappeared if theram speed was increased. It occurred morefrequently in the extrudates of6061/A1203/20pthan in606l/A1203/lop.The higherthe extrusion ratio, the more severethe cracking. Figure4.14 shows extrudates of 606l/A1203/2Opwith different extrusionratios of 13, 34, 52progressing from the ruler side;an extrudate of6061/A12O3I1Opwiththe extrusionratio of34is also shown at the right for comparison.It was interesting to note that low speedcrackinghappenedmuchmore frequently in the planttrials at UAC, Anaheim,than in the plant trials atChapter4 Experimental 56KRDC, Kingston. However, there was no low speed cracking in any extrudate when the ramspeed was above 6mm/s at any extrusion ratio at UAC. The length ofeach extrudate coveredwithlow-speed cracks for the plants trials at UAC was measured and is listed in Table 4.7.The mechanism of low speed cracking will be analyzed in Chapter 8 based on finite elementanalysesandmicrostructuralexamination.Figure 4.14 Low speed cracking atthe frontend oftwo extrudatesSome minor defects were also noticed in the composite materials. These were due toagglomerates of alumina particles showing at the surface and were statistically likely,assuming that the agglomerations were unifonnly distributed throughthe casting. Die lineswere evident on all extrudates. These were present in all extrusions and cannot becounteredwith current technology. Some chatter crazing was observed on the lastextrudates of eachdie. This defect was due to build-up ofmaterial on the die surface.Severe die wearing wasevident, as shown by measurement ofextrudate diameterfrom each die (Table4.7). No highChapter4 Experimental 57speed cracking was observed, because the initial bifiettemperature and the ram speed forbothplanttrials werenothighenough.Table4.7 ExtrudatedatafromplanttrialsatUACTest No. Material Nominal Extrudate Coverage oflow speed cracksDie Dia. Dia. atfrontend ofextrudates(mm) (mm) slight(mm) severe(mm)S92-l 6061 31.75 / notavailable notavailableS92-2 6061 31.75 31.98 notavailable notavailableS92-3 606l1A1203120p 31.75 32.00 notavailable notavailableS92-4 606l1A1120p 31.75 32.00 notavailable notavailableS92-5 606l/A12O3/lOp 31.75 32.03 notavailable notavailableS92-6 606l/A10/lOp 31.75 32.03 notavailable notavailableJ94-l 6061/A123/l0p 50.80 50.95 0 0J94-2 606l/A1O/lOp 50.80 51.18 0 0394-3 606l/A1203/lOp 50.80 50.93 0 0394-4 6061/A1O/lOp 50.80 50.95 0 0394-5 606l/A1203/20p 50.80 51.10 102 0J94-6 6061/Al/2Op 50.80 51.13 229 0194-7 6061/Al203/20p 50.80 51.03 38 0J94-8 6061/Al/lOp 31.75 31.75 0 0194-9 6061/Al2OillOp 31.75 31.75 76 0394-10 606l/A103/l0p 31.75 31.78 114 0J94-11 6O6l/A12/lOp 31.75 31.85 3810 3048J94-llb 6O61/A1O3/1Op 31.75 31.95 406 0394-12 606l/A120120p 31.75 31.98 457 356394-13 6061/A13/2Op 31.75 32.00 127 102J94-14 6061/A1O3/20p 31.75 32.13 381 2286J94-15 6061/A1203/lOp 25.40 25.40 51 0394-16 606l/A1/l0p 25.40 25.43 203 0394-17 606l/Al203/l0p 25.40 25.44 127 0J94-19 6061/Al/20p 25.40 25.53 127 0194-20 6061/AlO3/20p 25.40 25.78 2286 4318394-ha 6O6h/A12O/hOp 38.10 38.10 0 0394-18 606l/Al3IlOp 38.10 38.10 0 0Chapter4 Experimental584.5 EffectofExtrusionConditions on TensilePropertiesofExtrudatesPlant trials have been conducted at different extrusion conditions. It is known thatmechanical properties ofthe PRMMCs are improved after extrusion compared to the as-caststate. However, the effect ofextrusion conditions on the mechanical property change is notclear yet.4.5.1 Tensile TestsTo investigate the tensile property change of the composites, four double-shouldertensile specimens were machined from each extrudate ofthe plant trails at KRDC, Kingston,for tensile strength measurement and for elastic modulus evaluation for each condition. Allthe specimens were in T4 heat treatment condition before testing, i.e., 1 hour holding at550°C, followed by quenching and aging at room temperature for 48 hours or more. Aschematic of the tensile test specimen is shown in Fig. 4.15. The tests followed the ASTMstandardprocedure’°21.Figure 4.15 Schematic ofatensile testspecimen4.5.2TensilePropertiesunderDifferentExtrusion ConditionsFrom the tensile tests, 0.2% offset yield strength, ultimate tensile strength (UTS),elastic modulus, and %-elongation, were all recorded for the extrudate obtained from the twodifferent extrusion ratio tests performed at KRDC, Kingston. The mean value of the tensileChapter4 Experimental59data from foursamplestestedforeachconditionis listedinTable 4.8. Unfortunately, onlythestandard deviation for tensile elongation is available. The exact extrusion ratio for each testwas obtained based on the measurement of the extrudate diameter after extrusion. Thevariation of the values is mainly due to the change of die for each test.The tensile propertychange of the 6061/Al2O3IlOpfor different extrusionratios is shown in Fig. 4.16(a). It isevident that the elastic modulus, yield stress, and ultimatetensile strength do not show asignificant increase for extrusion ratios up to approximately 27.However, for ratios above27, the properties increase slightly. The same is true of the extrudates of6O6iIAl2O3/20p(Fig. 4.16(b)). Acorresponding decreasing trend is evidentin the elongation ofthe extrudatesforbothcomposites (Fig. 4.17). Although scattering ofthe data exists,the change in value ofthe elongation seemslargerthan the standard deviations (i’able 4.8).Table4.8 Tensiletestresultsofextrudates from theplanttrialsatKRDCTriai#ExtrusicJE Yield - UTSJE1opgJ(%) (°C) Ratio (GPa) (MPa) (MPa) Stand. Dev.(%)6061/A1203/20pK-i 19.8 484 10.40 99.9 188.0 290.0 8.7/1.0K-2 18.0 484 10.40 97.7 179.0 276.0 10.2/0.4K-12 19.2 435 10.23 99.0 183.0 287.0 8.9/0.7K-7 18.0 467 27.30 97.3 179.0 283.0 10.0/0.4K-il 19.8 400 28.80 100.5 187.0 290.0 7.5/0.760611A12031lopK-13 9.0 436 10.28 81.5 160.0 276.0 15.7/1.0K-14 7.0 436 10.35 76.6 156.0 274.0 20.0/1.3K-3 7.4 484 10.40 79.8 163.0 277.0 17.0/0.3K-4 7.4 484 10.40 80.1 158.0 274.0 16.0/0.6K-6 8.8 496 27.34 79.0 168.0 287.0 15.0/1.0K-b 7.0 418 27.42 80.4 161.0 281.0 17.0/1.2K-5 7.0 430 28.44 84.3 179.0 296.0 12.0/1.7Chapter4 Experimental 603006_. — —— _ — — — — — — — — — —250 —ii----E-Modulus(GPa)--x - YieldStress(MPa)200UTS(MPa)x15010050 I I I10.00 15.00 20.00 25.0030.00ExtrusionRatio(a) 6061/A1203/lOp300— a a — a — — ——S250 .—a----- B-Modulus (OPa)--X - YieldStress(MPa)200 .- UTS (MPa)-z15010050 II I10.00 15.00 20.0025.00 30.00Extrusion Ratio(b) 6061IA12O3I20pFigure4.16 Tensile propertyunderdifferentextrusionratiosChapter4 Experimental612017a14T-10%118\5.I10.00 15.0020.00 25.0030.00Extrusion RatioFigure 4.17 Elongationofthe composites as afunction ofextrusionratioThe tensile properties are dependent on the volumefraction ofthe particle, as seen bycomparing the dataof6061/Al2OillOp and6061/Al2Oil2Op. Itisevidentthatahighervolumefraction results in a higher yield strength, UTS, andelastic modulus, but a lower elongationvalue. Therefore, the true volume fraction in each extrudate testedshould be deteniiined,because under the same nominal volume fraction of 10and 20% the true volume fraction mayvary from specimen to specimen. By dissolution of the matrixof the extrudates, moreaccurate volume fraction for each extrudate tested was obtained, aslisted in Table 4.8 withthe tensile properties. It is seen that for the extrudatesof 6O6lIAlzOil2Op, the true volumefraction varies from 18% to 19.8%, while for the extrudatesof6061/A12O3/lOp,it changesfrom 7.0% to 9.0%. The evaluation of theproperty change at different extrusionratiosshould be conducted at the same true volume fraction(rather than a nominal value, asplottedin Fig. 4.16 and Fig. 4.17). The results ofthe tnaisofK-i, K-12, and K-il with a narrowerrange of volume fraction from 19.2% (K-12) to 19.8%(K-i, K-12) were re-plottedforChapter4 Experimental 626O6lIAl2Oil2Opin Fig. 4.18(a) and 4.19. For the 6061/A12O3/lOp,the trials of 7% volumefraction (K-14, K-b, K-5) to 7.4% (K-3, K-4) were adopted, as shown in Fig. 4.18(b) andFig. 4.19. The effect of extrusion ratio on mechanical properties are shown in Fig. 4.18(a)and (b) for yield strength, UTS, and the elastic modulus, and Fig. 4.19 for the %-elongation.Itis seenthatfor6061/A12O3/2Opthe elastic modulus, the yield strength and the UTS increasevery little with increasing extrusion ratios from 10 to 28 (Fig. 4.18(a)). However, for606l/A1203/lOp,a slightincrease in the elastic modulus, yield strength and UTS are shown inFig. 4.18(b). The elongation of both composite materials decreases with an increase inextrusion ratio, while a more gradual decrease is seen for the 606l/Al2Oil2Op than for the606lIAlzO3/lOp. However, it is worth pointing out that the small variation of the tensilestrengths and the elastic modulus could be within the range of their standard deviation.Unfortunately, the valuesare notavailable atthe moment.3251III — — — — a — — — aa a — — a — — ——275—---UTS (MPa)225Yield (MPa)175EE (GPa)12575.10 1520 2530ExtrusionRatioFigure 4.18(a) Tensile property change of606l/AlO3/2Opfordifferentextrusion ratioswith atrue volume fractionfrom 19.2% to 19.8%Chapter4 Experimental63300. — — —— — — — —— . — — — — — — — —— 0----.-----. UTS (MPa)250aYield (MPa)200xW2XE150E (GPa)100A50 I II10 15 2025 30Extrusion RatioFigure4.18(b) Tensile propertychange of6061/A12O3I1Opfordifferentextrusionratioswithatruevolume fractionfrom7.0% to 7.4%20174—N — — —o — — ———146061/A1203/lOp00116061/A1203/20p8’5 II10 1520 2530Extrusion RatioFigure 4.19 Coffespondingelongationvalues atdifferentextrusionratiosforbothcompositesChapterS Modeling the Extrusion ofthe PRMMCs 64Chapter5 MODELING THEEXTRUSION OF THEPRM[VICsThe literature review suggests thatlittle work has beencarried out on the analysis ofatransient extrusion process at high temperature and none for the extrusion of the PRMMCs.To betterunderstand the extrusion process, one test from each plant trial was simulated withthe aid of a finite element package, DEFORM®’821,by applying the alumina PRMMCs as amonolithic material. The plant trial data were then used to validate the model predictions.The results duringhotextrusion willhelp to understand particle fracture and surface cracking.5.1 MathematicalModelofExtrusionProcess5.1.1 FiniteElementModel5.1.1.1 FlowFormulationDEFORM® is based on a Flow Formulation approach with a penalty functionprocedureusing anupdated Lagrangianprocedure’831.The choice ofthe package was dictatedby two factors: the requirement that it should be capable of modeling large scale hotdeformation (strains of up to four and greater), and the need to predict loads over the wholerange of deformation (i.e. under transient and steady-state conditions). It contains anautomatic re-meshing feature, which facilitates the modeling of transient large deformationprocesses, such as are found forextrusion processes. In this study, the model consists offourobjects to be simulated in the extrusion press: billet, pressure pad, container and die, asschematically shown in Fig. 5.1. The ram and stack were ignored, as was the elasticdeformation of the extrusion presses, for the purposes of this work. Because of the largeplastic deformation associated withthe process, thebilletmaterial was assumed to behave as aChapterS Modeling the Extrusion ofthe PRMMCs65rigid-plastic material, whereas the other three objects weredefined as being rigid incomputation and only the billet was involved in deformation to which the flow formulationapplies.FORCE APPLIEDCONTAINER_________________PRESSUREPADSTACKCOMPONENTSFigure 5.1 Schematic ofanextrusionpressBased on the virtual work-rate principle, the following variational equation wasobtained831.=Ja6cdV+JKe3edV—JF1&vdS=O(5.1)where V is the flow domain of the billet, and F1 is the tractionspecified on the surfaceboundary 5; and are effective stress and effective strain rate,respectively, which aredefinedas:II— IEX11WDAThIChapterS Modeling the Extrusionofthe PRMMCs 66=(aa..)’(5.2)2”’(5.3)Due to incompressibility, the rate ofvolumetric straining should be zero, i.e.:(5.4)To preserve the incompressibilitycondition valid in the deformation analysis, a term of0.5K,where K is a very large constant,_108, or called penalty constant, was introducedinto the virtual work principle functional to guarantee the volume constancy (second term inEq. (5.1)). This is called the Penalty Function procedure, which is widely used in finiteelement deformationanalysisL83l.The mean stress, or the hydrostatic stress, which is definedas the mean of three normal stress components,am,obeys the following equation based onthe penalty functionprocedure831:am=42Ke(5.5)The compatibilitybetween the strain rate, and the velocity,v, is defined as:1 (5.6)C.=(v,+v,)where the comma between the ‘i’ and ‘j’ denotes differentiation with respect to spatialcoordinates.The deviatoric stress, a,is related to stress,a,and themeanstress, am, as follows:a=a—öjjam(5.7)where ö is the Kronecker delta. According to the Levy-Mises theory, the constitutive lawcanbe expressed asfollows:8313_ .. (5.8)a=(—a/E)eChapterS Modeling the Extrusion ofthe PRMMCs67Equation (5.1) can be converted to a series of non-linear algebraic equations by anormalFEM discretizationprocedure, resulting in:acIv(acI) (5.9)av, — av,Linearization of this equation was achieved by Taylor expansion near an assumed solutionpointv =v0(initial guess), resulting in,_____(5.10)+[L=,Av3= 0av13where Av is the first-order correction of the velocityv0. Equation. (5.10) can be written inmatrixform,[K]{zv}={f) (5.11)where [Kj is the stiffness matrix,{Av}is the velocity correction term, and[f)is the residualofthe nodalpointforce vector.Since the PRMMCs are extruded at high temperature, heat transfer occurs throughoutall the objects due to differentinitialtemperatures and internal heat ofdeformationin the billetand frictionheatatthe interface. The governing equationforthe heattransferis:kT,1,+q—pc T=O(5.12)where the first term of the equation is the heat transfer rate, with the comma denotingdifferentiation with respect to spatial coordinates and with the repeated subscript meaningsummation; k denotes thermal conductivity. The second term is the rate ofgeneration ofheatarising from deformation, whichis obtainedfrom the following wellknownformula:—. (5.13)q=iGewhereris the efficiency ofconversion ofdeformationenergy to heat, and is assumed to be inthe range of 0.90 to 0.95, depending on the material being formed. Thusheat transfer andChapterS Modeling the Extrusion ofthe PRMMCs 68deformation heating are coupled in the simulation. However, this heat generation rate termonly applies to the billet, because all the surrounding tools are assumed to be rigid. The thirdterm inEq. (5.12) is the rate ofaccumulation ofinternalenergy. Eq. (5.12) can be discretizedfollowing atraditionalGalerkinfmiteelementmethod and writteninmatrixfonnas11:[C]{T)+[K]{T} = {Q}(5.14)where [C] is the heat capacity matrix,[Ks]the heat conduction matrix,[Q)the heat fluxvector, [T] the vector of the nodal temperature and {T) the vector ofthe nodal temperaturechange withtime. objects were discretized into a series of 4-node iso-parametric elements(Fig.5.2). Due to axisymmetry, an axisymmetrical sliceofthe press setup was analyzed with a 2-Dmodel. The basic variables: velocity and temperature,were linear within each element. The0.2400.046-0.149[343-0.537-0.731-0.926-1.1200.0 12.024.0 36.048.0 60.0Radius (mm)Figure 5.2 Initialfiniteelementmesh forthebilletand its surrounding toolsChapterS Modeling the Extrusion ofthe PRMMCs694-node iso-parametricelementwas used because itmaderemeshingeasiei137’821.Due to limitation ofthe DEFORM®model, heatwas oniy conducted between the billetand the surrounding tools. However, interface heat transfer between varioustools, e.g.,between pressure pad and container, between container and die, was ignored(Fig. 5.2). Thethermal boundarycondition betweenthe billetand the tools is expressedas:= h(TBS—T)at interface boundary (5.15)where k is the thermal conductivity ofthe bifiet, andTB8,and TT8are interface temperature ofthe bifiet and its contacted tool (pressure pad, container, and die), respectively;h is the heattransfer coefficient at the interface. For surfaces ofall objects which are exposed to air, suchas, a part of surface of the billet at the die aperture, the thermal boundary condition isexpressed as:= hair(T&— T.j at surface boundary exposed to air (5.16)Atthe centerline ofthe billet, due to axisymmetry, the heattransferrateis zero.kTB=0 atthe center line ofthe billet (5.17)At the outer surface of the container, because of the induction heater, the surfacetemperature waskeptconstantas measured, i.e.,T =7 at outersurface boundary ofthe container (5.18)For simplicity, the outer surfaces of the pressure pad and the die were assumed to beexposed to the air, as in Eq. (5.16), due to cold ram and die stack.The mechanical boundary conditions of the deformed billet to be satisfied are asfollows: atthecenterline ofthe billet, the velocity in the radial direction is zero;Vr= 0 atthe center line ofthe billet (5.19)Atthe containerand the die interfaces, the velocitynormal to the boundary,v, is zero,while the velocitynormal to the interface at the pressurepad is equal to the ram speed.ChapterS Modeling the Extrusion ofthe PRMMCs70v=0 at the containerand die interface (5.20)v=v0(t) atthe pressure pad interface (5.21)In addition, a friction stress was applied to the interface between the billetand the surroundingtools as stress boundary conditions. The shear factor friction law, t=mk, wasadopted in hotdeformation, wheretis the friction stress, m the shear factor, and k the shear strength of thebillet1831.The free surface at the bottom end ofthe billet and the free surface ofthe extrudatehave no surface traction.5.1.2 InputDataIn common with observations made by others1M’851,sticking friction conditions wereassumed to prevail atthe interfaces between the billet and the container, and the billet and die,i.e., m=1, for the shear factor friction law, t=mk. For the interface between the pressure padand billet, a shear factor of m=0.7 was assumed due to the cold pad’831.The heat transfercoefficient at these interfaces was assumed to be 200kW/m2K,based on the laboratory workon aluminum alloys byH1ady1861.A hyperbolic sine constitutive equation developed using theGleeble® machine was employed in the model to calculate the effective stress in Eq. (5.8).The thermophysical properties of the billet (the PRMMCs) and the tools (H13) used in theheat transfer model were all temperature dependent, except for the density of the material,whichwas assumed to beconstant11181.5.1.3 SolutionProcedureThe convergence of the scheme requires consistency and stability. The consistencyrequirementensures that as the size ofthe elements tends to zero, the approximationequation(5.14) will represent the exact diffeintial equation (5.12) and its boundary conditions(Equations 5.15-5.16), andis satisfied by an approximationofthe type,ChapterS Modeling the Extrusion ofthe PRMMCs 71T+ =T+tt[(l—f3)1+fT+](5.22)The termfis a time integration factor used to average temperature over time, at time t =and t = t + tt, and varies between 0 and 1. For unconditional stability,fshould be greaterthan0•5L841,and in the current model a value of 0.75 was chosen. The total number ofelements in the billet was 1000 at the upsetting stage, and increased to 1250 afterwards. Forthe surrounding tools (e.g., the pressure pad, the container, and the die), the number ofelements in each rigid object was from 200 to 400, since only a heat transfer analysis wasconducted. Because most of the deformation occurred in the die region after the upsettingstage, the elements of the mesh at the die exit zone were refined relative to the size of theelements under the pressure pad, to achieve a more accurate solution.The solution of the velocity and temperature field was obtained alternatively by directiteration followed by a modified Newton-Raphson method. The convergence criteria forvelocity and extrusion force had to be satisfied forfurthertemperature calculation in the same• . . V.time step, viz.: forvelocity e1 (=0.5x10),where I lvii etc. is anerrornorm, defmed asIIvii(vTv)1fl,and v is a vector, and for extrusion force e(=0.lxlO2). After thetemperature of all the objects was calculated, the geometry ofthe bifiet was updated based onnodal velocities. The velocity solution was iterated again at a new step. The simulationproceeded in this maimer until a negative determinant ofJacobian matrix was encountered inone distorted element, which indicated that the mesh had been severely distorted.Therefore,remeshing was conducted over the whole billet. However, the distributionof the new meshdensity was similar to that of the old one prior to remeshing; in this way remeshingerrorsChapterS Modeling the Extrusion ofthe PRMMCs72were minimized due to interpretation. The stroke step, As,(=V At, whereVB is the ramspeed, and At is time step), adoptedforthe simulation was 0.25mm during the upsetting stage,and 0.05mm afterthat. The simulation was terminated when the extrusion reachedthe ‘steadystate’ region.5.2 SensitivityAnalysisoftheModelA sensitivity analysis in mathematical modeling should be conducted ifvalues ofsomeparameters are uncertain. In our study, the parameters, such as friction shear factor, m, heattransfer coefficient, h, at the interface, and heat generation efficiency, r), are reasonably wellknown as described in previous sections. However, the number of elements affects theaccuracy of the results, therefore, a sensitivity analysis was conducted, with 500, 750, 1000,and 1250 elements in the billet. Because the surrounding tools were only involved with heattransfer, the number ofelements in each tool (pressure pad, container and the die) were keptunchanged in the sensitivity analysis. The simulation and boundary conditions used in themodel were the same as described in the above sections. The thermophysical properties forthe surrounding tools (H13) and the billet of6061/AI2O3/20pwere obtained from DuralcanUSA’181as mentioned in Section 5.1.2. The otherinputdataare listedinTable 5.1.Table 5.1 Some dataforsensitivityanalysisoftheFEMmodelBillettemperature,T 425°CContainertemperature, Tr 395°CDie temperature,T 395°CPressure padtemperature, Ti,.. 70°CExtrusion ratio 34.0Billetdimension 4178x305mmChapterS Modeling the Extrusion ofthe PRMMCs73Because the peak extrusion force and the maximum temperature of the billet duringextrusion is crucial to the developmentofextrusion limit diagrams, the effect ofthe numberofelements in the bifiet on these two maximumvalues were studied. The maximum temperaturewas usually reached in the die land zone because ofsevere deformation at the die throat. Thiswill be seen clearly in the section of model predictions (Section The extrusionprocess of the large press at UAC, Anaheim, was simulated with four different number ofelements. Each simulation was stopped when the steady state was reached at a ramdisplacement of 25 mm for the sake of CPU time. The load-stroke curves predicted for thefour different numbers of elements are shown in Fig. 5.3. It is evident that the load isinsensitive to the number ofelements in this range. The effect ofthe number ofelements onthe maximum temperature is shown in Fig. 5.4. It is seen that when the number of elementsincreases, the curves of the temperature converge; although in the range of the number ofelements from 500 to 1250, the differences between them are all quite small and within 5°C.This may result from the fact that although the total nuiñber of elements in the billet aredifferent, the mesh size in the die exit zone for all the cases is fine enough to becomeinsensitive to the peak load and the maximum temperature prediction. However, a smallnumber ofelements in the billet, e.g., 500, may cause other problems, such as an interferenceof billet mesh with the rigid die boundary at the die exit corner. This could affect theprediction ofthe effective strain rate and the stress at that corner. Hence, in industry processsimulation, 1250 elements were used in the billet after the upsetting stage and the meshwasrefined with a higher mesh density in the die exit zone to achieve a higher accuracy of theresults (based on the fact that severe deformation occurred in the die exit zone) whileonly1000 elements in thebilletwere adopted in the upsetting stage.ChapterS Modelingthe Extrusionofthe PRMMCs7412000 -10000-0 12508000-—-—-10007506000500400020000. II I0 510 1520 25Displacement(mm)Figure5.3 Sensitivityofload stroke curve to the numberofelementsin the billet465-455..445125014’ 1000I—-—-7505004351I425 I I I I20 21 22 23 24 25 26Displacement(mm)Figure 5.4 Sensitivityofthemaximum temperatureto the numberofelements in thebilletChapterS Modeling the Extrusion ofthe PRMMCs75This sensitivity analysis was conducted for the large press. However, the resultsshould also be applicable to the smallpress because the extrusionratiosforbothpresseswhichare going to be simulatedin the subsequentsection are similarat approximately 30. Thereforethe elementsize in the billetofthe small presswould be about 10 times smaller whenthe samenumber ofelements was applied, because the deformation zone of the billet in the large presswas about 10 times largerthan thatin the small press.5.3 ExtrusionProcessSimulation5.3.1 ProcessingconditionsThe extrusion process simulation was conducted for one test from each plant trial:S92-3, for the large scale industrial machine, and K-7, for the laboratory press. In the firstcase, a homogenized billet of approximately 178mm diameter by 305mm was heated to429°C in a continuous, gas fired furnace. The billet temperature at the furnace exit wasrecorded using a hand-held probe. The time to transfer the billet from the furnace to thepress was around 40 seconds. The extrusion container was heated to a nominal temperatureof425°C, and the die to 336°C and the pressure pad to 70°C. The die was a flat faced die,with an aperture diameterof32mm. A thermocouple was embedded in the die 1.6mm awayfrom the die bearing, in orderto record the temperature change during extrusion.The billet for the second press was substantially smaller, around 51mm in diameterby 88mm in length, and was heated to 467°C in an electric muffle furnace. Thedeliverytime ofthe billetfrom the furnace to the press was around 10 seconds. Aflat-faced die withan aperture diameter of 10mm was employed. The die and pressure padwere heated in thesame furnace as the billet; however, no continuous die temperature monitoring wasconducted. The container was heated to 475°C by an induction heater placed around theChapterS Modeling the Extrusion ofthe PRMMCs76outside surface of the container. The details of the process conditions ofthe two plant trialssimulated are summarized inTable 5.2 forclarity.Table 5.2 Processing ConditionsforTwo SimulationsParameter S92-3, atUAC K-7, at KRDCTB429°C 467°CT425°C 475°C336°C 467°CTp 70°C 70°CRam Speed —2.6mm/s 0.9mm/sTransferTime 40 sec 10 secExtrusion Ratio 34 28.0BilletDimension Ø178x305mm Ø51x88mmNo. ofElementsin Billet 1250 12505.3.2Model PredictionsEach ofthe extrusion trials was simulated from the start ofextrusion until the steadystate was reached after the peak pressure. The deformation behavior of the billet as well asthe thermal history of each object, was predicted during extrusion. Material flow, stressstate, strain and strain-rate distribution in the deformation zone, and also the temperaturedistribution in all the objects were characterized. The predicted extrusion load and dietemperature were compared with the measured data. DeformationBehaviorAfter the billet was loaded into the container, there was a gapbetween the billet andthe inside surface of the container due to the smallerbilletdiameter than the inside diameterof the container (Fig. 5.2). When the pressure pad pressed the billet, itcommencedupsetting, and the containerwas gradually filled up. Figure 5.5 shows the material flownearChapterS Modeling the Extrusion ofthe PRMMCs 77the end of the upsetting stage. The arrowheads are the nodal velocities starting at nodepositions in the finite element mesh ofthe billet. The length of the arrow is proportional tothe value of velocity. The apparent ‘wavy’ nature of the velocity arrows is due to thepositioning ofthe nodes in the finite element mesh. It is seen that the gap between billet andthe container had almost been filled, only the bottom-right part at the die-container cornerremained to be filled up with the billet material flowing towards the corner. At the samestage, the part of the billet at the die aperture had been pushed into the die throat with acontact with the die bearing land, and apparently the material velocity in the die exitincreased. The effective strain distribution at this stage was still relatively small with thelarge values concentrated at all the corners, such as die-container corner and die exit corner(Fig. 5.6).As the extrusion proceeded, the die-container corner was filled up, and then all thematerial would flow towards the die aperture. A break-through pressure (the peak point inthe load-stroke curve) was necessary for the billet to be pushed through the die land. Afterpassing the peak pressure, the so-called ‘steady-state’ deformation began, although theextrusion force decreased due to the drop in friction force at the container interface. Thevelocity fields at the steady state are shown in Fig. 5.7 and Fig. 5.8 for both large and smallpresses. The velocities ofthe material at the die exit were significantly higher than those inthe container because of the high extrusion ratio. The ‘dead metal zone’ atthe cornerbetween the die and the container was present in both instances (see also Figures 7.1and7.3). Although a tendency of material flow stillappeared in the dead zone, the value ofvelocity at each node in the dead metal zone was close to zero(again, the apparent‘wavy’nature ofthe velocityarrows is due to the positioning ofthe nodes in the finite elementmesh).Chapter5 Modeling theExtrusionofthe PRMMCs78-15.0Velocity 3 (mm/s)-— TV, V V yyyy yV VVVVVVVVVV V \\\VVV450(J-55.01,110.00 6.00 12.00 18.00 24.00 30.00Radius (mm)Figure 5.5 Materialflowneartheendofupsettingstage-15.0 -‘ ? NL._ Eff. Strain—3——BilletAO.50000E41Bx0.000C0.35000-35.0oo.5ooooE.065000Fo.eOOoo0,z0.00 6.00 12.00 18.00 24.00 30.00Radius (mm)Figure5.6 EffectivestraindistributionneartheendofupsettingstageEE010,Figure 5.7 Velocity distributioninthe billetafteraram displacementof40.7 mminthe largeextrusionpress; lengthofarrowisproportionalto velocity,‘,, ,,1?VVVP7pppPppPvVPr?p,ppppPPp,Pp P p PP?PVVPppPpPPPPp P,,ppppppppp,PP PpPr,,PPPPPPPPP,,,rrPP Pp;;‘Pp?p,,rP Pp,,PPpPPPP,,,ppPPPPp,ppPPppppP pp• ppmfrppPFFFftP F FF F F ppFA Fa aFigure 5.8 Velocitydistributionin the billetafteraram displacementof26.7 mm in asmallextrusionpress: lengthofarrow isproportional to velocityVp p FpChapterS Modeling theExtrusionofthe PRMMCs79Velocity 217.8 (mm/s)42504.500-3.750-4000pp‘pP P‘PP,‘PP.pP pPPP p-425010 50.5 753Radius (mm)1000Velocity 81 (mmls)-7200-7.700-82004.700EE0)0,IVFVPPPPP-920012.00 1800 24.00 30.00Radius (mm)ChapterS Modeling the Extrusion ofthe PRMMCs80It is worth pointing out that, in the finite element large deformation analysis, an absolutedead metal zone could not exist, because otherwise the nodal strain-rate in that zone wouldbecome zero, which could result in a numerical difficulty. For this, in our study, a limitstrain-rate was defined which was io times less than the mean effective strain-rate over thedeformation zone. Ifthe calculated nodal strain-rate was less than the limit strain-rate, thenthe limitvalue replaced the corresponding nodalvalue, and the zone was taken as ‘rigid’.The mean stress is representative of the stress state because it is defined as the meanofall the normal stress components: ifthe mean stress is negative, a compressive stress stateis dominant. However, ifthe mean stress is positive, there must exist at least one dominanttensile stress component. Fig. 5.9 and Fig. 5.10 show the mean stress distribution at steady-state during extrusion. It is evident that the stress state in the deformation zone is almost allin compressive exceptin the surface layer near the die land. The absolute value ofthe meanstress in the container decreases from the pressure end to the die exit, which implies that thebillet tends to be in tension in the extrusion direction when approaching the die exit, due toelongation. The positive value in the surface layer apparently is due to two factors: firstly,the material flows faster in the center zone than in the surface layer, which has beenconfirmed by an experimental technique°1;and secondly, friction stress at the die landsurface exists.By comparing Figures 5.9 and 5.10, itis seenthatthe meancompressive stresses aresignificantly higherin the largerpress, as would be expected due to the lowerinitialtemperature ofthebilletand higherram speed. However, acommonfeature forbothpressesis the negativevalue ofthe mean stressinthe deformation zone and positive value in thesurface layeratthe die land area. The significance ofthe negativemean stress is thatitmayChapterS Modelingthe Extrusionofthe PRMMCs 81help minimize themicrostructuraldamages(e.g.,potentialvoid formationdueto decohesionandparticlefracture)duringextrusionofthe MMCs. However, theexistenceofatensilestresscomponentinthe surfacelayerinthe die land areamightcontributeto thesource oflowspeedcracking, whichisaspecificfeature ofextrusionoftheparticulatereinforcedMMCs.Thiswillbe discussedinmoredetailinChapter8.MeanStress(MPa)-2.750B(etA= -335.008=-310.00C=-285.00D=-260.00-3050E= 23500F=-210.00G=-185.00H= -160.001= -135.00J=-110.00-3350K--8000L=-60.000M= -35.000N= -10.0000= 15.000-3.650-3.95040.0 60.0100.0Radius (mm)Figure5.9 Meanstressdistributioninthebilletataram displacementof40.7mmin thelarge extrusionpress (negativevalues denote compressivestresses)Althoughthemean stressesare quite different, the effective strainnearthe dieisintherange ofabout4-5 forboth presses, as expected because oftheirsimilarextrusionratios. Atypical effective strain distributionis shown in Figure 5.11 for thesmall press at a ramdisplacement of 26.7mm.The annular strain pattern in the extrudateis also as would beexpected from a qualitative assessmentofextrusions which shows a recrystallizedring after4.250ChapterS ModelingtheExtrusionofthe PRMMCs 82extrusion’91.Thecorrespondingeffectivestrainrate distributionis shown in Fig. 5.12 forthesmallpress. Itis seenthatthe strainrate distribution isconfined in the die throatzone, and itsform is similar to predictions made by Chen, Oh and Kobayashit1201 for extrusion throughconical dies. The maximum strain rate is reachedat the die exit corner whereextrudate2MeanStress(MPa)Biliet-0.500A=-270.00B=-245.00C.-220.00D= -195.00E=-170.00-0.600F=-145.00G=-120.00H= -95.0001= -70.000J= -45.000K= -20.000-0.70050000I:i:-0800-0.9006.00 12.00 18.00 24.0030.00Radius (mm)Figure 5.10 Meanstress distributioninthebilletafteraram displacementof26.7mminthe smallextrusionpress (negativevalues denote compressivestresses)surfaceformsfromboththe shearzone and a smallvolume ofdead zone at the bottom ofthedieinterface1”71.This feature is in accord with other observations, both experimental187’andFEM172”201 . The maximum strain rate is in the range of values typical of those found inextrusiont63’651,and similar to the maximum strain rate of about 21.5 s4for the small press,estimated using another empirical equation(5,23)1611.However, the mean strain rate-1.0000.00Chapter5 Modeling the Extrusionofthe PRMMCs 83calculatedusinganempiricalequation(5.24)[61)is only2.4s. The low value estimated bythesecond empirical equation results from the assumption that the deformation is homogeneousthroughout the billet. This restriction does not apply to the finite element analysis, whichconsequently predicts a higher mean effective strain rate of 13.7s1,which probably moreaccurately reflects the deformation of the billet. Furthermore, the empirical equation (5.24)cannot take into account the large-scale variations in ram speed observed during the trials,whereas the finite-elementanalysis isideal forthissituation.— 6VBR(5.23)max— DE4Dvtanq(5.24)Em—‘3I2si.BLE)2LII. Strain-0.650 BIetA= 0.900008= 1.7000C= 2.5000D= 3.3000-0.720%....E= 4.1000F= 4.9000-0860____________0.930 --1.000 I0.00 5.0010.00 15.00 20.0025.00Radius (mm)Figure 5.11 Effectivestraindistributionofthebilletinthe smallpressChapter5 Modeling theExtrusionofthePRMMCs 84-8.000Eff. Stn Rt (us)A= 0.0000B= 3.0000C= 6.00000= 9.0000E= 12.000F= 15.000G= 18.000H= 21.000EE-8.5000)ci-8.7506.00 9.00Radius (mm)Figure 5.12 Effectivestrainratedistribution ofthebilletinthe smallpress5.3.2.2TemperatureDistributionBecause the flow stress ofthe composites is very sensitive to temperature,thetemperature drop during transferof the billet from the furnace to the container wasalsoincluded in the simulationbasedon the measurementofthe delivery time (Chapter4). At thebeginning ofthe extrusion, due to thecold pressure pad andlower initial die temperature ofthe largepress, a ‘cbilling’ effectexists atbothends ofthe billet,whichconsequentlyheatsupthe pressure pad and thedie by heat conduction throughthe interface. After the upsettingstage, the bifiettemperatureexhibits the effect of deformationheating toward the die entry,althoughin thelargerbillet, this is morepronounced because ofits lowerinitial temperature(Figures 5.13 and5.14).-9.0000.00 3.0012.00 15.00Chapter5 Modeling the Extrusionofthe PRMMCs 852 Temperature (C)x )-3250 -A= 405.008= 415.00C- 425.000=435.00-3.450 E= 445.00F= 455.00G= 465.00\11= 475.00Cr4.650- A= 400.008= 405.00C- 410.000= 415.00De-3.850A= 330.008=345.00C- 360.000= 375.00E= 390.00F= 405.004.050G= 420.00H= 435.001= 450.00J= 465.00-4.2500.0 25.0 50.0 75.0 100.0 125.0Radius (mm)Figure 5.13 Temperaturedistributioninthelarge extrusionpress8d2Temperature (C)A= 447.008=453.00C- 459.000= 465.00E= 471.00F= 477.00-0.700A= 440.008=446.00C- 452.000=458.00EE= 464.00De.850AA= 360.00:cC- 400.000= 4200E= 440.00F= 460.00-1.000-_______________I ______________________________________—1.150 -—______________________________________________________________________0.0 15.030.0 45.0 60.0Radius (mm)Figure 5.14 Temperaturedistributioninthe smallextrusionpressChapterS Modeling the Extrusion ofthe PRMMCs 86Temperature increases of approximately 70°C and 23°C were predicted for the largepress and the small press, respectively, because ofthe heat ofdeformation. This is again dueto the low initial temperature of the billet and higher ram speed of the large press, whichincreases the flow stress and the strain rate, resulting in a higherrate ofheat generation. Themaximumtemperature ofabout484°C and 479°C forthe large and smallpresses, respectively,is reached at the surface ofthe extrudate in the die land zone. The maximum temperature ofthe dieis about 10°C less than the maximumvaluein the billetdue to the thermalresistance atthe die interface. Because the thermal diffusivity of the die material (H13) is about 7 timesless thanthatofthe 606l/A12O3/20p,a muchlargerthermal gradient exists in the die land thaninthe extrudate. Themorepronounced thermalgradientinthe die land for the large press is aresult ofthe difference in initial die and bifiet temperatures while the large thermal gradientinthe extrudate ofthe large press is due to the larger diameter ofextrudate and the higher ramspeed, whichresultsin amore pronounced adiabaticheateffect. Comparison ofPredictionswith MeasuredDataLoad/ stroke predictions are compared with measured data for displacementbeyondthe peak load in Figures 5.15 and 5.16. The agreement is good during the upsetting stage,and within 10% at the higher loads in both instances. However, the load increase at the endof the upsetting stage is faster in the FEM prediction than in the measured data, especiallyforthe small press,inwhichalarger shiftinthe peakload appears. Thismightbe due to theassumptionofrigidtoolsin the FEMmodel, while inreality there always exists deformationofthe press. The large shiftin the peakloadmightbe partly due to the capacity ofthe smallpress (lOOT) whichwas almostfully loaded in the test, while the 3000Tcapacity ofthe largepressmeantitwas onlyhalfused. Therefore the compliance ofthepress has to be estimated.ChapterS Modeling the ExtrusionofthePRMMCs 8714000___________Measured12000FEM‘10000V8000. 6000:t20000I I I0 10 20 30 40Ramdisplacement (mm)Figure 5.15 Comparisonofpredictedforcewithmeasureddata(largepress)12001000__Measured800‘FEMC)600CL4002000 I I0 10 20 30Ramdislacement(mm)Figure 5.16 Comparisonofpredictedforcewithmeasureddata(smallpress)ChapterS Modeling theExtrusion ofthe PRMMCs88440420U_________0380360•5340320300- I0 10 20 30 40Ramdisplacement (mm)Figure 5.17 Comparisonofpredictedtemperature withmeasureddata(large press)The predicted temperature at the thermocouple position of approximately 1.6 mmaway from the die bearing in the die for the largerpress (Figure 5.17) is within 10°C ofthemeasured temperature over the range of the simulation, although itdoes not follow thevariation closely. The model seems to have overpredicted the temperature after the peakload has been achieved, but the difference is still less than three percent. Actually, thediscrepancy between the predicted and the measured temperature could also be due totheassumption of initial uniform die temperature and the error of the thermocouple positionbecausethethermocouplewas insertedinto theholeinthedie afterthe die wasputinto placebefore extrusion. It is worth pointing out that the reason for fewer predicted points in theupsetting stage in the FEM curve (Fig. 5.17) is that fewer time steps with predicted resultsMeasuredFEMaaaaaaChapter5 Modeling the Extrusion ofthe PRMMCs89were saved to prevent a big size (couldbe up to 300MB) of the output databasefile duringsimulation. However, the loadvalue wassavedautomaticallyforeachstep in themodel.5.4 ValidationofModelPredictionsModel predictions must be evaluated in the lightof the fact that the boundaryconditions in some areas were not precisely defined,and this may affect the results. Thefriction between the billet and containeror die surfaces was assumed to be stickingfrictionbut was notmeasured. Furthermore,the temperature field in the billets extrudedthrough thelarge-scale press was not accurately known,due to the constraints imposed by the conditionsunder which the trial was conducted. In addition, thetemperature at the die inthe smallerpress was not recorded. The predictionof the forces required for extrusionis mostsusceptible to temperature variations. Finally, it mustbe recognized that the simulation is atwo-dimensional simulation, and any results should be treated withcaution, although for theaxisymmetricalcase consideredhere, errorsarelikelyto below.Notwithstanding these limitations, the modeling has resulted ina reasonably accurateprediction of load and temperature rise. Furthermore, predictionsin the upsetting stage aredifficult with a fluid-flow type model°’, but in this workthe agreement between predictionsand measured data was very good. The abilityto predict forces in the upsetting stage has aconcatenation effect in that it influences the subsequent predictionsof, for example,temperature and strain.Load predictions resulting from the finite-element analysis are close to the valuesmeasured from each press, although the prediction for the larger press is considerablycloserto the measured value. The predicted sharp rise in load after upsettingof the billet does notaccurately follow the measurements (the scale of the abscissa in Figs.5.15 and 5.16 distortsChapterS Modeling the Extrusionofthe PRMMCs 90the difference however). This is not an anomaly ofthe model, as mentioned before, butratheris a consequence of defming the die, container, and pressure pad as rigid objects duringthesimulation. In reality, the components are not rigid, but this assumption was needed tocomplete the simulation in a reasonable CPU time. Thus, the model predicts onlytheresponse ofthe material, whereas the instruments on the press read the response ofthe wholesystem.It is known that the difference between the length ofa billet before extrusion and thelength ofthe remained butt end after extrusion is the real displacement the billet experiencedduring extrusion. If the press (assuming the billet is rigid-plastic) were rigid, thentherecorded ram stroke would be exactly the same as the real displacement. Therefore, thedifference (a total elastic deformation of the press) between the real displacement and therecorded ram stroke was used as a simple examination of the contribution of machinecompliance to the load-stroke curve. For the lOOT press, the total elastic deformation,includingthe elasticdeformationofthebifiet, was obtainedto be 5.27mm forthegiventest.The maximum ram stroke was reached when the final ram speed approached zero.Considering the measured extrusion force at the maximum ram stroke for that given test,F1=808kN, an overallelastic deformationconstantforthepress was calculated as:E0= Ff/(ST - (L0- LR)) = l53kN/mm (5.25)Applying this constant to the measured stroke, the adjusted stroke excluding the elasticdeformation, as simulatedbyDEFORM® , canbe obtained as:Sa(t) Sm(t) F(t)1E0(mm) (5.26)where Sa(t) and Sm(t) are the adjusted and measured ram stroke, respectively; F(t) is thçextrusion force, andtdenotesextrusion time.Chapter5Modeling theExtrusionofthe PRMMCs9114000___________Measured12000FEMz10000I‘1.)° 8000I.° 60004000,,:10 10 20 30 40Ramdisplacement(mm)Figure 5.18 ComparisonofFEMforce withmeasureddatacorrected forextrusionpresscomplianceaccording to Eq. (5.26);large press12001000• Measured•iFEMz- 800________0600•04002000L1 I I0 1020 30Ramdisplacement (mm)Figure 5.19ComparisonofFEMforce withmeasureddatacorrectedforextrusionpresscompliance accordingto Eq. (5.26);smallpressChapter5 Modeling the Extrusionofthe PRMMCs 92Another way to calculate the E0 is to measurethe unloading slope of the extrusionforce-stroke curve. The averageE0forthe largerpressismeasured as 2777kN1mm from fourtests. Corrections to the measured data accountingfor the machine compliance align themeasurements with the simulation (Figures 5.18 and5.19). In principle, the reverse ispossible: the simulation could include an elasticcomponent in order to better modelthespecific extrusionpressunderinvestigation, attheexpenseofsimulationtime.Thevariationinthe load prediction, afterthepeakloadhasbeen reached (Figures 5.15and 5.16), is due to a node in the bifiet losing contactwith the die and a consequent drop inthe extrusion force. The software attemptsto compensate for this node unpinning, causingthe observed behavior. The prediction could be improved ina number ofways, although anybenefit derived from eliminating the small variation (less than10%) would itself be canceledout bythe large increases in CPU time required to achieve the followingsolutions. Either themesh at the die throat could be further refmed by increasingthe number of elements, or theArbitraryLagrangian-Eulerian(ALE) methodcouldbeused, thoughthereis no guarantee thata re-meshing would not be required; furthermore, the mesh velocity wouldbe difficult todetermine. In addition, itis unlikely that in either case the proximity ofthe predictionto themeasureddatawould be altered.5.5 SummaryAmodelhas been developed and verified to simulate the extrusion ofPRMMCs. Themodel is a bulkformingmodel with the material assumed to be monolithic with the propertiesof the composites. Both the transient and steady state parts of extrusion were modeled.Adescription ofthe bulk extrusion ofthis MMC has been presented and shownto be valid forthe prediction ofextrusion loads, and consequently deformationin the billet during extrusion.ChapterS Modeling the Extrusion ofthe PRMMCs 93Load predictions resulting from this model agree to within ten percent ofthe measured value,and in the upsetting stage, to ahigher accuracy. Temperature predictions agree to within lessthanthree percent. Slightdiscrepanciesbetween themodel and measurements in the region ofmaximum rate ofchange in load have been accounted for by elastic deformationof the presscomponents. The model is useful for macroscopic analysis, such as the development ofextrusionlimitdiagrams, butcannotcorrectly predictdeformation on the scale ofthe particles.However, the stress, temperature, and straindistributions can be related to the propensity forparticle fracture and/orvoid formation.Chapter6 MicrostructuralAnalysisofthe PRMMCduringLargeDeformation 94Chapter6 MICROMECHANICALANALYSIS OF THEPRMMC DURING LARGEDEFORMATION6.1 Obstaclesand ChallengesofMicromechanicalAnalysis ofthePRMMCsIn recent years, micromechanical analysis of particulate reinforced MMCs has beenconducted1105°81 to better understand the MMC’s response during either thermal ormechanical changes. However, almost all of the finite element analysis on particle behaviorof the MMCs were based on the unit cell model with simplified boundary conditions, asdescribed in the literature review (Chapter 2). The characterization of behavior of theparticulate reinforced MMCs under large deformation conditions has received little attention,probably because ofthe obstacles statedbelow.6.1.1 ParticlePhenomenaIt is the presence of particles that results in the improvement of properties of theMMCs in many aspects. However, the particles have some specific features in real MMCs:(a) the shapes of particles in the MMCs are not regular rectangles or circles as assumed bysome investigators in two-dimensional unit cell models; (b) the size of the particles varieswidely from a few microns to 50p.m or even more for theDuralcan®composites; (c) it isknown that large particles tend to fracture more easily than small particles; (d) moreimportantly, the distributionofthe particles in as-castMMCs fabricated by the molten route isnot uniform but contains clusters and voids due to solidification; and micro-fracture initiatesmore easily within clusters during deformation. Therefore, to account for particle behaviorunder large deformation with the aid of a finite element model, the shape and size of theChapter6 MicrostructuralAnalysisofthe PRMMCduringLargeDeformation 95particles and clustersshould be takeninto account. However,because the average dimensionsof a particle (up the MMCs are significantly (—10k times) smaller than those ofthe workpiece (e.g. 10 mm), ifthe deformationofthe particles in the MMCs were studied, atleast108elements would be necessary for a two dimensional analysis with the element sizeclose to a particle dimension. Obviously, this is impractical from acomputational stand point.Then the question is, how can a micromechanical analysis ofthe MMCs be conducted with atraditionalfiniteelementmodel?6.1.2 MatrixPhenomenaThe MMCs are not simply a mixture of the particles and the matrix. In fact, theinteractions ofa second phase particle with the matrixduring deformationisvery complex. Itis known that additional phenomena will occur, such as (a) precipitation of fine particlesformed by chemical reaction between the particles and matrix alloy; (b) interface bonding andits strength; (c) residual stress due to mismatch ofthe thermal expansion coefficient betweenthe particle and the matrix; (d) strain induced dynamic recovery and particulate stimulatednucleation for recrystallization; (e) fracture of particle and decohesion of the interface,rotation and migration ofthe particle during deformation, etc., The question is, how could afiniteelementmodeltake thosefactors into consideration?6.1.3 ModelingConstraintsTo investigate the micromechanical behavior of the MMCs, a physical constitutiveequation (not like the phenomenological one as developed in Chapter 4) needs to bedeveloped by combining microscopic variables and macroscopic process parameters.Although a few simplified physical constitutive equations have been developed, they areincomplete. Hence, how can a physical constitutive equation be developed whichincludes allChapter6 MicrostructuralAnalysisofthe PRMMCduringLargeDeformation96the factors or at least the most dominant (ifknown)ones influencing the dynamic behavior ofthe MMCs by combining both the macroscopic andmicroscopic process parameters? If itwere developed, could itbe applied to a multiaxial stressstate during processing by validatingonlythroughuniaxialcompressionand/ortensile testing?Itseems impractical to overcomeallthese obstaclesby the available plasticitytheoryand computationtechnology.6.2MicromechanicalAnalysisduringPlaneStrainCompressionUnder the above mentioned circumstances, it istherefore impractical to conductmicromechanicalanalysis ofthe MMCsduring industrialextrusion. Nevertheless,a laboratoryplane strain test was simulated to analyze the behavior ofparticles during hot deformation.To simplify the analysis, a twin-particle model and a multiple-particle modelwere adoptedwith each particle size of40x40 p.m2in the planar cross section. In the twin-particlemodel,two particles were arranged such that the particle movement in the lateraldirectionperpendicularto theloading directioncould be analyzed. In the mode1, the matrixaround theparticle behaves as a monolithic material with the deformation propertiesof the composite,and the particle has its own properties and flows along withthe matrix during deformation.TheDEFORM®, as describedinChapter5, was adoptedforthe micromechanicalanalysis.The initial setup ofthe plane strain test simulation with finite elementmeshes foreachobjectis showninFig. 6.1. Because the particle size is only 40p.m2, the elementsize aroundthe particles is tremendously refined. The detailed finite element mesh aroundthe twoparticles is shown in Fig. 6.2 for the twin-particle model. For a plane strain test simulation,only ahalfofthe setwas analyzed due to its symmetry. The friction shear factor, m, and theheat transfercoefficient, h, at the interface between the specimen and the anvil were assumedChapter6 MicrostructuralAnalysisofthePRMMCduringLargeDeformation 97to be0.7 and 200kW/m2K1861,respectively. The test simulationconditions are listed inTable6.1. Thenominalstrainrate is0.05/s.The totalreductionwas about 50%.Table6.1 SimulationconditionsforplanestraindeformationObjectName (No.) Material SizeTemperature Numberof(mm)(°C) ElementsUpperAnvil (#1) 718 (rigid) 8.64x3.0 445100Specimen (#2) 606l/AI2O3/2Op 25.4x10450 2500(rigid-plastic)BottomAnvil(#3) 718(rigid) 8.64x3.0 445100Particle (#4) A1203(elastic)40x40urn2450 18-3614.0010.60 -720E>-3.80______0.00 3.40 6.80 10.20 13.60 17.00X (mm)Figure 6.1 Initialfiniteelementmeshesforeach objectofplane straindeformationChapter6 MicrostructuralAnalysisofthe PRMMCduringLargeDeformation 986.2.1 TwinParticleModelFor the twin-particle model, one particle was located at the center line of thespecimen, therefore only half of the particle was considered due to symmetry. The otherparticle was initially located 4Otm apart in the lateral direction( see Fig. 6.2). The interfacebetween theparticle and the matrixwas assumedto be perfectly bonded. The elasticmodulusof the particle was 450 GPa; the Poisson ratio was 0.25, and the coefficient of thennalexpansion was 7.7x1041°Cwith the reference temperature of 450°C, based on data in theliteratureforthe samekindofMMC’1.5.1505.1005.050>-5.0004.9500200Figure6.2InitialfiniteelementmesharoundtwoparticlesThe effective strain distribution in the specimen at a reduction ofabout 49% is shownin Fig. 6.3(a) and (b) with and withoutparticles, respectively. From the figure, itis seen thatthe overall effective strain distributions for both cases are quite similar, but deformation0.000 0.0500.100 0.150X (mm)Chapter6 MicrostructuralAnalysisofthe PRMMCduringLargeDeformation99localization occurs around the particles. This is because only two particles are considered inthe micromechanical analysis. The localized effective strain is shown more clearlyin Fig. 6.4as a function of reduction. Fig. 6.4 (a) shows the effective strain distributionaround twoparticles at a reduction of 10%. It is seen that the highest strain is concentrated inthe middleofthe two particles (Contour line ‘C’), and the strain around the two particlesis at about thesame level (contour line ‘B’). As the reduction increases, the particle locatedoutside thecenter line is pushed away by matrix material along the flow direction. The distancebetweenthe two particles becomes about 130J1m (Fig. 6.4(b)). As a result, the effect of clusteringisdecreasing, although the higheststrainis stillconcentratedbetweenthe two particles(Contourline ‘F’). Atareductionofabout49%, two closelydistributedparticles are pushedapartfromaninitial spacing of40tmto more than 300J1m (Fig. 6.4(c)). It is seen thata low strain zone(contour line ‘F’) appears close to the particle. The higheststrain is obtained outside the lowstrain zone both parallel and perpendicular to the loading direction (Contour line ‘H’). Thisindicates that as the reduction increases, the interaction between two particles becomes weak,and each particle plays its own part in the material during deformation. Obviously, themigration of particles in real composites helps break the clusters formed in casting andimproves the homogeneity of particle distribution after secondary processing. Especially, inextrusion processing, due to large deformation, fractured particles can be separated by sheardeformationandhealedbycompressivehydrostaticpressure.The effective stress in the particles at two different reductions of 10% and 49% isshowninFig. 6.5. Itis seenthatthe stresslevel ismuchhigherthanthatoftheeffective stressin the matrix, which is about 6OMPa. This is partly due to the assumption of planestrahideformation, in which the strain in the third directionis constrainedto be zero. Therefore,Chapter6 MicrostructuralAnalysisofthePRMMCduringLargeDeformation 1009.80 -EU. SwainObedS 2cA=0.00000E.00B=0.300006.60- C=0.600000=0.90000EE=12000F=1.5000>-G= 1.80001-1= 2.10003.401= 2.4000C020-3.00-0.00 3.40 6.80 10.20 13.60 17.00X (mm)(a)Twinparticlemodel-0.020EU. StrainObed12cA= 0.00000E*00B= 0.30000-0.340- C=0.600000=0.90000EE= 12000EF=1.5000>-G=18000H= 2.1000-0.660_______1= 2.4000DEC-0.980—1.3000.00 3.40 6.80 1020 13.6017.00X (mm)(b) homogeneousMMCSFigure 6.3 Effectivestraindistribution atareductionof49%Chapter6 MicrostructuralAnalysisofthePRMMCduringLargeDeformation1014900Objedl2A=0.00000E.008=0.30000C=0.600000=0.90000- E= 12000F=1.5000G= 18000H= aiooo1= 2.40004.580 -E4.42042604.100._— I I I0.000 0.160 0320 0.480 0.640 0.800X (mm)(a) atareductionof10%3.620Eff. Slrain3.5460Objed# 2A=0.00000E.e008=0.30000,DCES__________C=0.600000=0.90000E= 12000F= 1.50003.460G= 1.8000H= 2.10001= 2.40003.3803.300—10.000 0.0800.160 02400.320 0.400X (mm)(b) atareductionof30%Chapter6 MjcrostructuralAnalysisofthe PRMMCduringLargeDeformation 1022.850 Eff. StrainObject # 2A= 0.00000E÷008=0.30000C= 0.60000D= 0.90000:::=2.40002.490-2.3702250-0.000 0.1600.320 0.4800.640 0.800X (mm)(c) atareductionof49%Figure6.4Localizedeffectivestraindistributionaroundtwoparticlesatdifferentreductionseven a very small strain in the thirddirection could lead to a largestress because of highelasticmodulus ofthe particle. Itis alsointeresting to see that the value ofthe effectivestressin the particlesincreases as thereductionincreases. Besides the effectofmatrixdefonnation,thiscouldbealso due to thebuild-up ofthermalstress inthe third directionwhentemperaturein the particle changes during deformation.The larger value of the effectivestress in theparticlesatasmallreductionduringlarge defonnationconfirms thatparticles could fractureataearlystageofdeformation,ifthefracturestressoftheparticleisreached.Chapter6 MicrostructuralAnalysisofthePRMMCduringLargeDeformation103Elf. Stress(UPa)4.700objedl 4 (right)A= 40.0008= 80.000C= 120.000= 160.004.620Ex 200.00Ot*d1 5(drhne)A= 40.000-j)8= 80.0004540 .C= 120.00E____0= 160.00E= 200.00>-4.4604.380 -4.300 I0.000 0.080 0.160 0240 0.3200.400X (mm)(a) ata reductionof 10%2.750Elf. Stress(UPa)Obed1 4 (right)A= 40.0008=80.000C= 120.002.6700= 160.00E= 200.00Object15(drne)A= 40.0002.5908=80.000C= 120.000= 160.00E= 200.00>-2.5102.4302.3500.000 0.080 0.160 0.2400.320 0.400X (mm)(b) at areductionof49%Figure6.5 Effectivestressinthe particlesatdifferentreductionsChapter6 MicrostructuralAnalysisofthe PRMMCduringLargeDeformation 1046.2.2 Mulliple-ParticleModelTo consider the effect ofclustering ofparticles ina composite, a four-particle modelwas developed with two more particles added to the twin-particlemodel, as shownin Fig. 6.6.Due to the presence ofmore hard-to-deform elastic particles in this model,remeshing for thematrix around four particles becomes very difficult. Therefore,a total reduction of only 1%was considered. The effective strain distribution in the cluster zone in Fig.6.6 shows that ahigherstrainzone (Contourline ‘B’) appears inthemiddle oftwo particles in both the loadingand the lateral directions in the planar cross section; however,a lower strain zone (Contourline ‘A’) exists in the center of four-particle cluster. This is becauseat the early stage ofdeformation, four particles act as a cluster; therefore, the center ofthe cluster is hardlydeformed. The effective stress distribution in both particles and the matrix isshown in Fig.6.7. Considering the stress distribution in the matrix, it is seen thata low stress zone(Contour lines ‘D’) exists in the center ofthe four-particle cluster. Again, the effectivestressin the particles are more than 4 times higher than that in thematrix, which is similar to thetwin particle model as described above. The mean stress distribution in the matrixshows atensile stress state in the zone between the two particles in the lateral direction (Fig.6.8),whilstthe stress state between the two particles in the loading direction is compressive.Thestress statein each particle is quite similara tensile stress componentexists atthe top and thebottom surface ofeach particle (the locations ofcontour line ‘E’ in each particle) due tothepositivevalue ofthemeanstress, whichcouldbeapotentialsiteforcracking.105Chapter6 MicrostructuralAnalysisofthe PRMMCduringLargeDeformationEff. Strain5200ot4edl 2A=0.0150B=0.0350C= 0.0550D= 0.07505.100E= 0.09605.000>-4.9004.8004.7000.000E>-0.070 0.140 0.2100280X (mm)0.350Figure6.6 Localizedeffective straindistributionatareductionof 1%5.0755.0254.975Eff.Stress(MPa)Objedl 2A= 10.0008=20.000C= 30.0000=40.000E= 50.000F= 60.0004.925Objedl 4 -17A= 80.0008=120.00C- 160.000=200.00E= 240.00F. 280.004.8754.8250.000 0.050 0.1000.150 0200X (mm)0250Figure 6.7 Localizedeffectivestress distributionatareductionof 1%Chapter6 MicrostructuralAnalysisofthe PRMMCduring LargeDeformation 106Mean Stress(MPa)Object# 2A= -130.008=-90.000C=-50.000D= -10.000E= 30.000F= 70.000Object#4-#7A=-70.0008= -50.000C=40.000D= -10.000E= 10.000F= 30.0005.0505.000EE4.g504.9004.8500200Figure6.8 Localizedmeanstress distributionatareductionof 1%0.000 0.050 0.1000.150X (mm)6.3MicromechanicalAnalysisduringCylindricalCompressionAlthough a unit cell model in plane strain condition has beenwidely adopted byresearchers for particle analysis at a microscopic level, obviously the particle model is notrepresentative ofareal three dimensionalparticulate, but instead ofaninfinitebarin the thirddirection (perpendicular to the plane). Therefore, it would be ideal to develop a three-dimensional model. However, the large number of elements needed for 3-D analysis, asmentioned in Section 6.1, would be impractical from the perspective of computation costs.Hence a laboratory axisymmetric cylindrical compression test was simulated by insertingparticles at the center line of the specimen. As a result, the shape of a particle is eitherChapter6 MicrostructuralAnalysisofthePRMMCduringLargeDeformation 107cylindrical or spherical in 3-D due to axisymmetry. The simulation conditions are listed inTable 6.2.Table6.2 Simulation conditionsforcylindricalcompression testObjectName Material SizeTemperature(°C) No. ofElements(No.)UpperAnvil 71820x20mm 449 150(#1) (rigid)Specimen 6061/A12O3/2Op410x15mm 450 2500(#2) (rigid-plastic)BottomAnvil 718420x20mm 449 150(#3) (rigid)Particle AI2O320.440im 450 18-36(#4) (elastic)The initialfinite elementmesh ofaspecimen includingparticlesis shownin Fig. 6.9(a).Again, the element size around the particle was tremendouslyrefined, as shown in Fig.6.9(b)for a single particle and Fig. 6.9(c) for a twin-particle model. The nominal strainrate for thetest is 0.05/s, and the nominalstrainis 1.0. The other boundary conditions are the same as inthe plane strainsimulation.6.3.1 SingleParticleModelA single-particle model refers to a cylindrical specimen under large hot deformationcontaining only one particle at the center line. For the cylindrical compressiontest, only anaxisymmetrical plane was analyzed due to its axisymmetry. The particle had to be in thecenterline because otherwiseitwould become a ring. Two extreme shapes ofa particle wereconsidered,i.e., acylinderand asphereinthreedimensions. Fourdifferentparticlecaseswerestudied. Theparticle sizeforeachsingle-particlemodel adoptedis listedinTable 6.3.Chapter6 MicrostructuralAnalysisofthe PRMMCduringLargeDeformationE16.00(a) initialfiniteelementmeshinaspecimen108—4 I %I j_...4 % V7.6007.4000.000 0.0500.100 0,.15012.809.606.40 -3200.000.00 2.00 4.00 6.00Radius (mm)8.00 10.007.6007.5507.5007.5500.000 0.050 0.1000.150Radius (mm)(b) mesharoundaparticle7.450E4-C)0,:i:7.5007.4007.450Radius (mm)(c) mesharound the twinparticlesFigure 6.9 Initialmeshandlocationofaparticleinacylindrical specimenChapter6 MicrostructuralAnalysisofthe PRMMCduringLargeDeformation 109Table 6.3 Particlesizes studiedCase Comp-1 Comp-2 Comp-3 Comp-4Shape Cylinder Cylinder Sphere CylinderSize($Imxlim)40x40 420x20 42Oct20x80AspectRatio 1.0 1.0 1.0 MaterialFlowofaCylindrical SpecimenContainingaParticleThe effective strain distribution in a cylindrical specimen with and without a particle isshown in Fig. 6.10(a) and (b) for a reduction of 65%. It is evident that the overall straindistributionsfortwo specimens are very similar, but a largerstrain is reached near the particledue to strainlocalization. Details ofthe local straindistribution around the particle are shownin Fig. 6.11 for the 40x40im particle. In the loading direction, it is seen that a low-strainzone appears atboththe top and the bottom ofthe particle; however, ahighstrainzone showsup adjacentto the low strain zone. This is because during compression, matrixmaterial nearthe center line flows towards the particle which is located at thecenter ofthe specimen; andmaterial changes its flow direction when it approaches the particle due to the high elasticmodulus of the particle. A dead metal zone thus forms around the cylindricalsurface.Effective strainvariations along the centerline in the loadingdirectionfordifferent reductionsare shown inFig. 6.12. It is seenthat, as the reductionincreases, the non-uniformity ofstraindistribution becomes more severe. The effective stress distributionfor both cases, with andwithout particles, is shown in Fig. 6.13(a), and (b). Again, theoverall distributions of theeffective stress are quite similar to each other; but stresslocalization occurs around theparticle (Fig. 6:14). Amaximumeffectivestress ofaround 260 MPain the particle isreached,which is almost 4 to 5 limes larger than that of the matrix. The corner of theparticle is aEfi. StrainObject # 2A= 0.200008= 0.530000=0.86000D= 1.1900E= 1.5200F= 1.8500G= 2.1800H= 2.51001= 2.8400J= 3.1700K= 3.5000Chapter6 MicrostructuralAnalysisofthePRMMCduringLargeDeformation 110region of high stress concentration, which implies that the corners are the potential crackinitiation sites. This prediction is consistent with the phenomenon of corner fracture of asharp particle observed in microstructure during extrusion (see Fig. 7.5). Mean stressdistributions in the deformation zone of the matrix for both cases show that compressivestresses prevail during compression, except in the bulge zone, where a tensile hoop stressexists which might lead to surface cracks at the bulge surface under some conditions (Fig.6.15(a) and (b)). The mean stress distributions in both the matrix around the particle and inthe particle are shown in Fig. 6.16, in which a tensile stress component (positive value)appears in the upperand thebottom zonein the particle.6.004.50EE3.000)z1.500.0010.000.00 2.00 4.006.00 8.00Radius (mm)Figure6.10Effectivestraindistributioninthecylindricalspecimenatareductionof65%: (a) monolithicChapter6 MicrostructuralAnalysisofthePRMMCduring LargeDeformationRadius (mm)Eff. StrainObject# 2A= 0.20000B= 0.53000C= 0.86000D= 1.1900E= 1.5200F= 1.8500G= 2.1800H= 2.51001= 2.8400J= 3.1700K= 3.5000Eff. StrainObjed1 2A= 0.20000B= 0.53000C= 0.86000D= 1.1900E= 1.5200F= 1.8500G= 2.1800H= 2.51001= 2.8400J= 3.1700K= 3.50001116.004.50EE3.000)0)1.500.000.0010.00Figure6.10 Effectivestraindistributioninthecylindricalspecimenatareductionof65%: (b) withaparticle2.00 4.00 6.00 8.00Radius (mm)EEC)a,z2.7102.6702.6302.5902.5500.030 0.060 0.090 0.120 0.150Figure 6.11 Effective straindistributionaroundtheparticleatareduction of65%Chapter6 MicrostructuralAnalysisofthePRMMCduring LargeDeformation 11232.52Cl)1.510.504-x24 6810 12Distance fromSurfaceof theBottomAnvil (mm)Figure 6.12 Effectivestraindistributionalong thecenterline ofthe specimenunderdifferentreductions600Eff. Stress(UPa)Objed#2A= 20.0008= 24.000C= 28.000450D= 32.000E= 36.000F= 40.0006(44614= 48.0003001=52.000- J= 56.000K= 60.0001.500.000.0010.00Figure 6.13 Effective stressdistributioninthecylindrical specimenatareductionof65%: (a)monolithicwithoutaparticle2.00 4.006.00- 8.00Radius (mm)Chapter6 MicrostructuralAnalysisofthePRMMCduringLargeDeformation6.004.50E3.000):i:1.500.000.00Radius (mm)En. Stress (UPa)Object 1 2A= 20.0008= 24.000C= 28.0000=32.000E= 36.000F= 40.000G= 44.000H= 48.0001= 52.000J= 56.000K= 60.00010.00113Figure 6.13 Effective stressdistributioninthe cylindricalspecimenatareductionof65%: (b) witha particle2.00 4.00 6.00 8.00EE0)0)2.7102.6702.6302.5902.550aEff. Stress (UPa)ObjectI 2A= 20.0008= 24.000C= 28.0000= 32.000E= 36.000F= 40.000G= 44.000H= 48.0001= 52.000J= 56.000K= 60.000Object1 4A= 20.0008= 60.000C= 100.000=140.00E= 180.00F= 220.00G= 260.00H= 300.001= 340.00J= 380.00K= 420.000.030 0.060 0.090 0.120Radius (mm)0.150Figure 6.14Effectivestressbothinthematrixandintheparticle atareductionof65%Chapter6 MicrostructuralAnalysisofthePRMMCduringLargeDeformation 114Mean Stress (UPa)6.00Objed#2 ‘A=-150.00(B= -133.00C= -116.00D= -99.0004.50E= -82000F= -65.000- NG=-48000\H=-31.000I=-14.0003.00ç J= 3.0000r K=20.000a,:i:1.500.00 I II0.002.00 4.006.00 8.0010.00Radius (mm)(a) monolithic withoutaparticleMean Stress(UPs)6.00Objed#2A= -150.00C= -116.000..-99.0004.50E=-82.000F.. -65.000EG=-48.000EH=-31.000I I.. -14.000b i-IJ=3.0000B= -133.00rK= 20.0001.500.00I II I0.00 2.004.00 6.00 8.0010.00Radius (mm)(b) withaparticleFigure6.15 Meanstressdistributioninthecylindricalspecimenwith andwithoutaparticleat areductionof65%Chapter6 MicrostructuralAnalysisofthe PRMMCduring LargeDeformation115Mean Stress(MPa)Object#22.710 A= -150.008= -133.00C=-116.OO0= -99.000E= -82.000)F=-65.0002.670 -‘ / /G=-48.000//3= 3.0000C) k=20.0002.630-s(Object#4A=-150.00Y-N:8= -127.00C= -104.002.590- F= -35.000G= -12.000H= 11.0001= 34.000.1= 57.000K= 80.0002.550 -0.000 0.030 0.060 0.090 0.120 0.150Radius (mm)Figure6.16 Meanstress distributionbothin the matrixandintheparticleat areductionof65% EffectofParticleShapeDifferentparticle shapes were analyzed during the compressiontest, as listed in Table6.3. A damage factor was modified based on theplastic workfracture criterion proposed byLathem andCockcroft1511, and was used to compare the effectofparticle shape on the stressandstrainstate atareductionof65% duringcompression(Fig. 6.17)(a)-(d)).Df=f(-)d(6.1)where a1 is the maximum principal tensile stress, is the effective stress, andd is theeffectivestrainincrement. As describedinthe literature review, incold forming operations, itwas found that failure ofa monolithic material at some point occurs when the damage factorreaches a critical value. This criterion, together with finite element modeling, has been usedChapter6 MicrostructuralAnalysisofthe PRMMCduringLargeDeformation 116extensively to predict the occurrence of damage during cold forming’49”°91.Sellars etal.49tested the above equation and concluded that the equation could be a reasonable criterion forhot working as well as forcold working, but furtherdata is required to testit more rigorouslyfor hot working. By comparing the above fracture criterion to both the Stress Criterion andthe Strain Criterion described in the literature review, Syu and Ghosh11121 confirmedthat theproposed fracture criterion is the best for the development of forging limit diagrams forparticulate reinforced MMCs in laboratory upsetting tests. Figure 6.17 shows that themaximum value of the damage factor near the particle with the an aspect ratio of 4 is abouttwice as large as that near the spherical particle; a greater value of the damage factor ispredicted forthe largercylindrical particle than for the smaller particle. These results indicatethat a spherical particle gives rise to the least damage potential in the surrounding matrixmaterial, and non-regular particles, such as the particle with an aspect ratio of 4, have thelargest effect. For the equiaxed particles, larger particles have a more severe effect on thematrixdamage than the small ones, especially atthe corners (Fig. 6.17).Figure 6.18(a) shows the effect ofparticle shape on the effective strain variation alongthe center line nearthe particle at a reduction of65%. It is shown again that severe localizedstrain occurs around all the particles, with the particle of the largest aspect ratio having thehighest strain and the spherical particle, the smallest The effective strain along thehorizontalmid-plane is shown in Fig. 6.18(b). It is evident that the strain near the sphericalparticle isquite uniform compared to the case with no-particle. However, a significant straindrop waspredictedin the radial direction nearthe interface and4Ox4Ojim.Chapter6 MicrostructuratAnalysisofthe PRMMCduring LargeDeformation1172.750DamageObed$ 2A= O.00000E.008= O.38000E-01C=0.76000E-010=0.114002.710E=0.15200F= 0.19000G=022800H= 0266001=0.304003=0.342002.670K= 0.38000Z2630.2.590 -2.5500.000 0.0300.060 0.090 0.1200.150Radius (mm)(a) ‘3i40x4() (cylinder)DamgeObed# 22.710A= 0.00000E+008= 0.38000E.01C= 0.76000E-010=0.11400E= 0.15200F=0.190002.670G=022800H=026600=0.304003=0.34200K= 0.380000)2.630 -2.5902.550 -0.000 0.030 0.060 0.090 0.120 0.150Radius (mm)(b) 420x20(cylinder)Chapter6 MicrostructuralAnalysisofthe PRMMCduring LargeDeformation 1182.750DamageObjecll2A= 0.00000E+008=0.38000E01C=0.76000E-01D= 0.114002.710E=0.15200F=0.19000G=022800H=0266001=0304002.670- .3= 0.34200K= 0.38000E.2’2.630-0)2.5902.5500.000 0.030 0.060 0.090 0.1200.150Radius (mm)(c)cI2O (sphere)2.710DamageObied1 2A= 0.00000E+008=0.38000E-010=0.11400E= 0.15200F=0.19000H= 0266002.630 -1= 0.304002.670-C=0.76000E-010).3=0.342002.590K= 0.380002.550 I0.000 0.0300.060 0.090 0.1200.150Radius (mm)(d)c120x80 (cylinder)Figure 6.17 Effectofparticleshape ondamagefactoratareductionof65%Chapter6 MicrostructuralAnalysisofthe PRMMCduringLargeDeformation2.7 2.75 2.8 2.85 2.9Distancefromsurface ofthe bottom anvil (mm)(a) along thecenterline ofthe specimen (40x40 etc are the particlesizeinmicrons)(b) along themid-planeinradial direction(40x40etcare the particlesizeinmicrons)Figure 6.18 Effectofparticle shapeon straindistribution atareductionof65%119- --. No Particle— Cylinder40x40Cylinder 20x20a Sphere 20Cylinder20x803.75 . -3.252.752.251.751.250.752.252.6 2.65.C’,V.C.)C’,a)>2.95 31.851.451.050.650.25/17O O—- o—a-__ a-’4’No ParticleICylinder40x40‘ICylinder20x20Io Sphere20ICylinder20x80— II0 0.20.4 0.60.8Distancefromcenter lineto thebulge surface(mm)1Chapter6 MicrostructuralAnalysisofthe PRMMCduring LargeDeformation 120450 +400 + + + + + ++ °Cylinder40x40350 ACylinder20x20300A25000 ASphere 20200 + Cylinder20x80150• 10050 I20 30 40 5060 70Reduction (%)Figure 6.19 Effectofparticleshape on effective stressvariationduringcompression(40x40, 20x20, 20, and 20x80 are all the particlesizes analyzedinmicrons)The effective stress in the particle is not so sensitive to thereduction for all the fourparticle shapes, as shown in Fig. 6.19; however, the particle shapeitself affects the stressvalue quite significantly, from about 125MPa for the sphericalparticle (‘Sphere201.Lm’),to425MPa for the highest aspect ratio particle (‘Cylinder 20x80p.m’in Fig. 6.19). The valuesfor the cylindrical particles with an aspect ratio ofunity are quite close. Therefore, it isconcluded that the particle fracture is sensitive to theshape of particles, especially for thosewithalargeraspectratio, while the size ofequiaxedparticlesislessimportant.6.3.2MultipleParticleModelThe characterization of single particlebehavior during cylindrical compressionmightonly apply to the situation in which particles areseparated by a large distance relative totheirChapter6 MicrostructuralAnalysisofthe PRMMCduring LargeDeformation 121size. However, for the particulate reinforced MMCs fabricated by a cast route, particleaggregations, or clusters, are always present. Therefore, a multiple particle model is needed,in which twin cylindrical particles with a particle size of40x40 located at the center line ofthe compression specimen were studied. EffectofReductionParticle spacing changes during compression, as predicted in plane strain compressionin Section 6.2. For a starting particle spacing of 120 jim in the center line, the effective straindistribution is relatively uniform at a reduction of33%, and its characteristics are quite similarto thatofa single particle model (Fig. 6.20(a)). However, at a reduction of65%, deformationaround the particle becomes more severe. A localized strain zone extends in the radialdirection as a resultofmaterial flow (Fig. 6.20(b)). The maximum value around the particle islarger for the twin-particle case than that for the single particle, which indicates that moresevere deformation occurs for the multi-particle situation. The mean stress distribution ineach particle at a reduction of 33% (Fig. 6.21(a)), also shows similarity to the single particlemodel (Fig. 6.11) due to the large spacing, although the values of stress are different. Themean stress distribution around the particle under this reduction is relatively uniform at a levelof -12 MPa to -44 MPa. At a reduction of 65% (Fig. 6.21(b)), the value of the mean stresschanges from -44 MPa to -300 MPa; also a large mean stress gradient appears in the gapbetween the two particles, whichimplies acomplextn-axial stress state. Effect ofParticleSpacingThree different initial particle spacings of20,40, and 120pm were studied. The effectof particle spacing on strain values along the center line of the specimen are shownin Fig.6.22(a). It is seenthatthe strainreaches a maximum at apoint abouthalfa particle sizeaboveElf. StrainObject 41 2A= 0.20000B= 0.53000C= 0.86000D= 1.1900E= 1.5200F= 1.8500G= 2.1800H 2.51001= 2.8400J= 3.1700K= 3.5000Chapter6 MicrostructuralAnalysisofthe PRMMCduringLargeDeformation 122the particle, and the maximum values for each spacing are not much different, with thesmallestspacing being the largest. The minimumstrain value is located at the right top oftheparticle, with the smallest value for the largest spacing (120 jim). In the zone between twoparticles, obviously, the larger the spacing, the larger the strain. This is because for largespacing the matrix deformation is increased. Figure 6.22(b) shows the strain distributionalong the radial direction in the mid-plane between the two particles. It is seen that a smallerparticle spacing (20.un) leads to less deformationinthe gap.5.2005.1505.100E0)0)5.0505.000Figure 6.20 Effective straindistributionatdifferentreductionswith a startingparticlespacing of 120 jim: (a)33%4.9500.000 0.030 0.0600.090 0.120 0.150Radius (mm)Chapter6 MicrostructuralAnalysisofthe PRMMCduring LargeDeformationFigure 6.21 Meanstress distributionin the matrix and inthe two particles1232.7102.6702-C0)2.630Elf. SkanObje#2A= 0.20000B= 0.53000C= 0.86000D. 1.1900E= 1.5200F 1.8500G= 2.1800H= 2.5100I 2.8400.1= 3.1700K= 3.50000.030 0.060 0.090 0.120 0.1502.5902.550Radius (mm)Figure 6.20 Effective straindistributionatdifferentreductionswithastarting particlespacing of 120 pm: (b) 65%Mean Stress(MPa)ObjeI 2A= -300.00B= -268.00C= -236.000= -204.00E= -172.00F= -140.00G= -108.00H= -76.0001= -44.000.J=-12.000K= 20.000Obel 4# 5A= -120.00B= -102.00C= -84.0000= -66.000E= -48.000F= -30.000G= -12.000H= 6.00001= 24.000J= 42.000K= 60.0005.1505.10020)5.0505.0004.9500.030 0.060 0.090Radius (mm)0.120 0.150underdifferentreductions withtheinitial particle spacingof 120pm: (a) 33%Chapter6 MicrostructuralAnalysisofthe PRMMCduringLargeDeformationRadius (mm)Figure 6.21 Mean stress distributioninthe matrix andinthe twoparticlesunderdifferentreductions withtheinitialparticlespacingof 120 pm: (b) 65%Distance fromsurfaceofthe bottomanvil (mm)124EE0)0)D2.7102.6702.630 -2.5902.550Mean Stress (UPa)Objed#2Am-300.008=-268.00Cm-236.000=-204.00E. -172.00Fm -140.00Gm-108.00H.-76.0001 -44.000.3. -12.000K= 20.000Obed1 4#5Am -120.00B.-102.ooC. 84.0000.-6&000E= -48.oooF= -30.000G=-12.000H= 6.00001= 24.000.3= 42.000K. 60.0000.000 0.030 0.060I I- - I0.090 0.120 0.150V0V‘.4-3.532.521.51No Particlex 40 Microns20Micronso120 Micronsc]X<0I II I I2.6 2.65 2.7 2.752.8 2.85 2.9 2.95 3(a) along the centerline ofthespecimenIChapter6 MicrostructuralAnalysisofthe PRMMCduring LargeDeformation(b) along themid-plane betweentwoparticlesinradialdirectionFigure 6.22 Effectofparticle spacing onstraindistributionatareductionof65%12510864200 2 3 4 5 6Displacement(mm)9 MicronsI—x—40 Microns—D —l20MicronsI I0 0.2 0.4 0.6 0.8Distancefromcenterline to thebulgesurface (mm)1MeaswedIzIFEMzzzFigure 6.23 Comparisonofpredicted value withmeasureddataChapter6 MicrostructuralAnalysisofthe PRMMCduring LargeDeformation 1266.4 ModelValidationFor validation ofthe model predictions, the final geometry of the simulated cylindricaltest specimen was measured. Table 6.4 shows the final maximum diameter measured andpredicted during compression, whichsuggestsbarreling.Table 6.4 Comparisonofmodelpredictions withmeasureddataItis seenthatthepredictions are invery good agreement with the measured data. This can befurthervalidated by comparison ofthe load-displacement curve for the monolithic model withthe measured data (Fig. 6.23).6.5 ConclusionsBased on the above micromechanical analysis, some conclusions can be drawn onparticle behaviorin MMCs duringlarge hot deformation.1) Large deformation leads to more severe localized deformation around the particle,and also to particle rotation and migration. The particle migration during large deformationhelps breakclusters and heal the fractured particles;2) The stress value in a particle is not very sensitive to strain during hot deformation.Therefore, particle fracture may occur at a very small strain, ifthe stress in a particle is largeenough;3) The shape of a particle has a large effect on fracture of both theparticle and itssurrounding matrix underlarge deformation, and particles with sharp corners and largeaspectratios have the greatestpropensityto fracture;Chapter6 MicrostructuralAnalysis ofthe PRMMCduring Large.Deformation1274) Particle fracture is not very sensitive to the size ofequiaxed particles;however, it isknown that the probability ofparticle fracture is a function of the probabilityof finding a flawin the particle and the probability ofactivating a flaw. Apparently,largerparticles may have ahigh frequency of flaws. Because this effect has notbeen considered in this work, it is stilltrue thatlarge particlesmayhave higherprobabilityto fracture during largedeformation.5) Small particle spacing results in a complex stress state in the cluster zone.However, as the particle spacing increases, the interaction between particlesdecreases. Thetensile stress generatedin the interparticle zonein the flow directionmay causevoid formationduring deformation or promote void growth if the voids are present whilethe hydrostaticpressure may help stop void formation and growth.6) Localized particle deformation does not affect the macroscopic performance of thematerial. Therefore, a phenomenological constitutive law of the MMCs characterizes themacroscopic behaviorofthe material.128Chapter7 PARTICLEFRACTUREOFTHEPRMMCDURING EXTRUSIONCommercial exploitation of MMCs is dependent on the reproducibility of propertiesand achieving high productivity at minimum cost. Thus, controlling the fracture of particlesduring extrusion of the PRMMCs is of interest. Particle fracture is a potential defect ifassociated with void formation: notably the modulus of the resultant extrudate could bedeleteriously affected. However, if void formation is suppressed, then benefits in terms ofmechanical properties may result from the increased homogeneity ofparticle distribution, andfrom a decrease in particle size.The fracture of particles during cold deformation has been extensively investigatedover the past few yearst7778’8951 but the systematic examination of fracture duringhotdeformation has received little attention. Furthermore, deformation to high strain atlowtemperature has been limited by the low failure strain of the MMCs. Therefore, therearefeatures of low temperature deformation which are expected to relate todeformation underconditions characteristic of extrusion. Particle fracture occursowing to the inability of thematerial to accommodate local stresses. Fracture at low temperatureis related to strain,particle size, particle aspectratio175’761(see also Section8.2 for the micromechanical analysis)and volume fraction1”.The superimposed hydrostaticpressure during deformation extendsthe ductility, and effectively inhibits voidfoniation”90911.Under such circumstances matrixmaterialmay also flowinto thevoidsbetween fracturedparticlesunderlarge deformation.To elucidate the nature of particle fracture during thehot extrusion process, themicrostructure of the composite in the deformation zone and of the extrudatesofChapter 7ParticleFracture ofthe PRMMCduringExtrusion1296O611A12O3/lOpand6061/A12O3/20pwas examined, i.e., particle distribution,size refinement,and orientation and migration ofparticleswere characterized.7.1 SpecimenPreparationforthePRMMCsA specimen of area about lOxlO was cut using eithera hack saw, or a TiVcutting wheel blade. The specimen was mounted and polished in an automaticpolishingmachine. The detailed polishing procedure adopted at KRDC, Kingston, is listed inTable 7.1.Table7.1 PolishingprocedureforDuralcanmaterialsatKRDCStep Paper/Cloth GritSize Time Lubricant Load Remark(jim) (mm.) (N)1 SiC paper Grit 120 until water 100 flatflat2 Petrodisk 15 10 Struer’s blue 80- flatwithlessDiamond plate lubricant 100 scratches3 Perforated 15 10-15 Struer’s blue 100 moreshinnycloth lubricant4 Perforated 3 10 Struer’s blue 100 less scratchescloth lubricant5 PanW 3 5 Struer’s red 100 veryfew scratchespolishingcloth lubricant6 OP Chem. fmal 0.05 1-2 ColloidalSi02 100 cleanboundarypolishingclothsuspensionaround particlesAnother polishing procedure modified from Newell11001 was adopted for the automaticpolishingmachine at UBC, as listed at Table 7.2. A very clean background resulted followingpolishing for both procedures, which was necessary for microstructural analysis, especiallyChapter 7ParticleFracture ofthe PRMMCduring Extrusion 130image analysis. The last step was quite effective to clean the boundaries between the matrixand the particles.Table7.2 PolishingprocedureusedatUBC forDuralcanmaterialsStep Paper/Cloth Grit Size Time Lubricant Pressure Remark(pm) (miii.) (psi)1 SiC Paper 180 3 Water 30 overall flat2 SiC Paper 320 3 Water 30 flat3 SiC Paper 500 3 Water 30 flatwithlessscratches4 SiC Paper 1000 3 Water 30 less scratches5 Texture Paper 6 tm 10 Diamond 30 few scratchessuspension6 Texture Paper 3 .tm 5 DP- 30 veryfewsuspension scratches7 OPChem. final 0.05urn1-2 Colloidal 30 clean boundarypolishingcloth Si02 aroundparticlessuspension7.2 MacroscopicExaminationofMetal FlowintheDeformationZoneMacro-examination of metal products can reveal the grain size and shape as well asfabricating orcasting defects. An end-of-extrusion billet of6061/A1203/20pfrom the trial ofS92-3, 184 mm in diameter, was sectioned by a hacksaw along the extrusiondirection. Theextrusionconditions are listedin Table 7.3 forconvenience.Mixed-acid etchants are excellent for revealing grain size, shape, and contrast.Theetchantusedforthe composite was amixed solution of lOmi HC1 (concentrated), 3Oml HNO3(concentrated), 2OmlH20,and 5g FeCl3961.The solution was mixed justbefore use. TheChapter 7 Particle Fracture of the PRMMC during Extrusion 131Billet Temperature (°C) 429Billet Diameter (mm) 178Extrudate Diameter (mm) 32Extrusion Ratio 33.6Figure 7.1 Metal flow of a billet in a containerA dead metal zone existed at the corner between the die and the container,and a shear zoneshowed up between the dead metal zone and the deformation zone. The accumulationof themetal at the corner of the pressure pad and the container was probably due to the stickingfriction at the container interface. Some porosity was also observed at the etched surface.longitudinal section of the billet was first ground on SiC paper (Grit 60 - 600), and then wasimmersed at room temperature into the solution for a few seconds, rinsed in cold water, andrepeated until the desired effect was obtained, as shown in Fig. 7.1.Table 7.3 Extrusion conditions of the Trial S92-3 of 6061/A1203/20p.--------;c;_____•_•Chapter 7 Particle Fracture of the PRMMC during Extrusion 132More detailed metal flow of the billet was examined by an optical microscope with amagnification of 50X. The zones examined in the billet are schematically shown in Fig. 7.2.Pressure Pad End4Deformahon Zone2’. 58Sheai Zonei3 ‘.6 9_______________________- - --. Dead ZoneIIDie ExitFigure 7.2 Schematic positions for the pictures taken with low magnificationThe metal flow at each location is shown in Fig. 7.3. At Location 1, the matrixmaterial has accumulated due to sticking friction at the interface between the billet and thecontainer. A localized material flow pattern near the gap between the pressure pad and thecontainer is revealed in Fig. 7.3 (Location 1).At Location 2, in the shear zone, the metal flow along the shear boundary is clearlyshown. However, in the dead metal zone there is little metal flow (Location 3). At Location4, only a small tendency of metal flow in the downward direction can be seen. Metal flowlines are clearer in Location 5, in the deformation zone; here the flow lines approach thehorizontal direction near the die interface (Location 6). At the center line of the deformationzone, due to axisymmetry, metal flows close to the extrusion direction, and the tendencyincreases from under the pressure pad (Location 7) to the die entry (Location 9). AtLocations 4 and 7, under the pressure pad, a hard-to-deform zone exists.Chapter 7ParticleFracture ofthe PRMMCduringExtrusionEii133Figure7.3 Metal flow in the deformationzone during extrusionChapter 7Particle Fracture ofthe PRMMCduring Extrusion 134The metal flow pattern shown here is consistent with experimental observation byotherresearchers1211,and also, qualitatively, with the velocity vector distribution of the FEMmodelprediction in Chapter5.7.3 Particle FractureduringExtrusionA microscopic study of particle fracture and particle distribution was conducted bothqualitatively, using an optical microscope, and quantitatively using an image analyzer. Thedynamic behavior, such as recoveiy and recrystallization, which occurs in the hot extrusionprocess, is beyond the scope ofthis project.7.3.1 QualitativeMicrostructureAnalysis7.3.1.1 ParticleDeformation Behaviorin the Deformation ZoneThe other half of the butt-end was divided into several small sections on a cuttingmachine with aTi-V wheel blade, and 9 samples from the longitudinal section, with an area ofabout lOxlO2, were polished at UBC for micro-examination. The location of the 9samplesinthe billets inside the containerare schematically showninFig. 7.4.Pressure Pad EndDie ExitFigure7.4 Schematic positionsforthe picturestakenformicro examination7__4__1Sh&irZoneDeformationZone8 5 2DeadZone - 9 6 3—Chapter 7Particle Fracture ofthe PRMMCduringExtrusion135The particle distribution and particle fracture behavior for each sample,located indifferent zones, was investigated under an optical microscope. At Location 1,the upper rightcorner ofthe billetwhere there is contact with the pressure pad and the container,a “particle-free” zone (with a small number ofparticles) was formed (see Figs.7.1 and 7.3). This is theresult of accumulation of the matrix material near the gap between the pressurepad and thecontainer: during extrusion, as the pressure pad pushes the bifiet forward, the matrix materialadheres to the container, while the particlesin the subcutaneous layerofthe billetwere pushedforward. As a result, matrix material accumulated at the corner. Very few particles weretrapped in this ‘particle-free’ zone. Beside this large ‘particle-free’ zone, more particles werefound but still with lower local volume fraction compared to other locations, as shown inLocation 1, Fig. 7.5(a).Roughly a 1-mm thickparticle-free layer at the billet surface was observed at Location2 (r =R0). The formation ofthis layer was again a result of adhesion with the container. Atthe intersection of the shear boundary and the container interface (See Fig. 7.1), part of thislayer began to flow into the shear zone along the shear boundary to form a particle-free bandduring extrusion. it is this particle-free band that outlined the dead metal zone in themacroetched butt-end (Fig. 7.1). In the adjacent zone, severe particle fracture was evidentdue to large shear deformation (Location 2, Fig. 7.5 (a)). Most of the particles wereorientated along the shear direction. All the large particles that did not crack were found tohave a regular shape with an aspect ratio close to unity, which implies that equiaxedparticlesare harder to fracture even with a larger diameter(Location 2, Fig. 7.5 (a)). Thisresultconfinns the predictions of the effect of particle shape on particle fracture in themicromechanical analysis in Chapter 6. With a —1 mm thick particle-free layer being alsoChapter 7ParticleFracture ofthe PRMMCduringExtrusion 136present at the billet surface in the dead metal zone (Location 3), a conclusion can be drawnthat during hot extrusion of particle reinforced MMCs, a particle-free layer is formed at theinterfaceofthe billet and containerbecause ofadhesion, and part ofthe matrixmaterial in thislayerflows into the shear zone to form a particle-free band in the shear direction. In the deadmetal zone, all the particles were distributed with no preferred orientation and had a similarspatial disthbution to those in the as-cast composites. Fractured particles were occasionallyobserved but not separated as in the shear deformation zone, i.e., the particles were justcracked (Location 3, Fig. 7.5(a)).Mid-way between the container interface and the center line of the billet(r Ro/2)under the pressure pad (Location 4), it was observed that fewer particles were fractured dueto formation of the ‘hard-to-deform’ zone, and particle clusters also remained (Location 4,Fig. 7.5(b)). Fewerclusters, but more fractured particles, were observed in the region belowthe ‘hard-to-deform’ region, as deformation increased. Particles were orientated towards thedirection ofmetal flow (No. 5, Fig. 7.5(b)). At Location 6, which included both a part ofthedeformation zone and a part ofthe dead metal zone, a ‘particle-free’ band was also observedin the shearzone withmore particles presentthan in the up stream band. Due to the low localvolume fraction of the particles in this band, no extensive particle fracture was observed.However, in the adjacent zone, more fractured particles were found due to the large sheardeformation, as seen in Location 6, Fig. 7.5 (b). Moreover, particles in the shear zone tendedto alignin the sheardirection.At the top surface zone around the center line (r= 0) ofthe billet (Location 7),someparticle clusters remained, as observed at Location 4, with similar particle distribution to theas-castproducts. However, fracturedparticles in clusters were observed occasionallybecauseChapter 7ParticleFractureofthe PRMMCduringExtrusion137Figure 7.5 (a) Typicalparticle distributionin the Locations 1,2 and 3(‘P.C.’=particlecluster ‘P.F.Z.’=particle-free zone; ‘P.P.B.’—particle-free band;‘S.D.’=sheardirection)Chapter 7ParticleFractureofthe PRMMCduringExtrusion138Figure 7.5 (b) Typicalparticle distribution atthe Locations4,5 and 6(‘P.C.’particle c1uster ‘P.F.Z.’=particle-free zone; ‘P.F.B.’—particle-free band; ‘S.D.’=sheardirection)Chapter 7ParticleFractureofthePRMMCduringExtrusioniF1139N,Figure 7.5 (c) TypicalparticledistributionattheLocations7,8 and9(‘P.C.’=particlecluster; ‘PEZ.’—particle-freezone; ‘P.F.B.’=paiiicle-freeband;4B.D.’=extrusiondirection)Chapter 7ParticleFractureofthe PRMMCduringExtrusion 140of local tn-axial stresses (Location 7, Fig. 7.5 (c)). The most obvious characteristicsatLocation 8 were the alignment of the particles and the formation ofparticle-free bands alongthe extrusion direction. This is due to axisymmetnic material flow which forces particlestoalignin the extrusion direction and also elongates the particle-free zones in the cast materialto form the ‘particle-free’ bands (Location 8, Fig. 7.6(c)). It was interesting to note thatalthough some cracks in the deformation zone align along the flow direction due to shearstress, other cracks perpendicular to the flow direction were observed, especially for thoseparticles with a large aspect ratio. This is a result of load transfer from the matrix to theparticle along the flow direction, which generates tensile stresses in the particle (See Chapter8). If the tensile stress exceeds the fracture stress of the particle, it cracks perpendicular tothe flow direction. Near the center line at the die entry, alignment of particles and particle-free bands along the extrusion direction were even more obvious. However, at positions offthe center line, particles were aligned not in the extrusion direction, but in the flow direction.Nearthe die throat, more smallparticleswere found which implies severe particle fracture dueto sheardeformation (Location 9, Fig. 7;5(c)).It is worth pointing out that all the features described above in the deformation zoneare a summary of an overall examination of the sample at each location. However, they allcouldnotbe shown in one typical pictureforeach location, as in Fig. samples ofeach extrudate were cut from both the front end(named “F’) and thebackend (named “B”). Caution was takenwhen eachpiece was sectioned along theextrusiondirection using a Ti-V wheel blade, as shown in Fig. 7.6. All the specimens were polishedatUBC following the procedure listed in Table 7.2. The particle distribution in boththeChapter 7Particle Fracture ofthe PRMMCduring Extrusion 141transverse section (perpendicular to the extrusion direction) and the longitudinal section(parallel to the extrusion direction) was examined by an optical microscope. The samplesexamined are listed inTable 7.4.ExtrudateSample Transverse LongitudinalSample Cross 6061 60611A1203120P 60611M203110PName Section Alloy (W6A20) (W6A1O)TrialNo. S92-2 592-3 S92-6FrontEnd Transversal F2-T F3-T F6-TFrontEnd Longitudinal F2-L F3-L F6-LBackEnd Transversal B2-T B3-T B6-TBackEnd Longitudinal B2-L B3-L B6-LA. ComparisonofMicrostructureinLongitudinal andTransverseSectionsBased on the optical microscopic examination of transverse and longitudinalsectionsof the extrudates of606l/AlO3/20p,some typical characteristics of the particledistributionin the transverse sectionofthe specimenare summarized:(1) particles were randomly oriented, i.e., with no preferred orientation;(ii) particle size was nonuniform;Figure 7.6 Schematic ofexaminedextrudate specimenTable7.4 Listofexaminedextrudates with twodifferentcross-sectionsChapter 7ParticleFracture ofthe PRMMCduringExtrusion142(b) LongitudinalFigure 7.7 Typicalcharacteristics ofparticles afterextrusion of606l/AI2O3I2Opat anextrusion ratio of34(a) TransverseChapter 7ParticleFracture ofthe PRMMCduring Extrusion143(iii) manysmallparticles wereobserved;(iv) particles were quite uniformly distributed. The particle distribution in the transversesection with some ofthe above features is shown in Fig. 7.7(a).In the longitudinal section, some salientfeatures are summarized as:(i) mostofthe particles with alargeaspectratio were alignedin the extrusion direction;(ii) fracturedparticleswere found in clusters;(iii) equiaxed particles (i.e., aspectratio ofthe particle is close to unity) were harderto crack;(iv) for the situations where a single particle positioned between two large particles,themiddle particle had ahightendency to fracture;(v) more extensive particle fracture was observed in the longitudinal section; howeverfractured particles seemed to have healed with intrusion of the matrix material into theresulting gap under high hydrostatic pressure, or because fractured pieces were shifted bylocalmetal flow during sheardeformation;(vi) most ofthe cracks (the gap between two fractured parts) were in the extrusion direction.This was due to the fact that particles were fractured in the shear deformation zone andfinally rotated into the extrusion direction, if these cracked parts had not been shiftedsufficiently far apart. A typical particle distribution with some of the above features isshowninFig. 7.7(b).B. ComparisonofMicrostructurefor6061/A1203/20pand6061/A1203110pFor the extrudates of6061/Al203/lOp,similar characteristics of particle fracture tothe 60611A1203/20pwere also recognized (Fig. 7.8), such as:(i) particles were also randomly oriented in transverse section, but aligned in the extrusiondirectioninthe longitudinal section;Chapter 7Particle Fracture ofthe PRMMCduring Extrusion 144(b) LongitudinalFigure 7.8 Typical characteristics ofparticles afterextrusionof606lIAlzO3IlOpatanextrusion ratio of34(a) TransverseChapter 7ParticleFractureofthe PRMMCduringExtrusion 145(ii) multiple fracture was observed from large particles with a high aspect ratio and those inclusters.The salient features of the microstructure of the extrudates of 6061/AlO3/10pcompared to6061/Al203/1OPare:(i) particle size was much smaller than that in the 606l/A1O3/20p, and the size distributionwasmore uniform;(ii) large particle-free zones in the transverse section and particle-free bands were morefrequently observed in the longitudinal section due to the small volume fraction and nonuniform distribution of particles in the cast billet. The ratio of the length to the width ofthe bands in the longitudinal section was measured under the microscope and found tolie in the range of20 to 27, whichiscomparable to the extrusion ratio of34. This impliesthat the formation of the particle-free bands are most probably due to elongation of theparticle-free zone in the as-castbillet;(iii) more clusters remained afterextrusion;(iv) although the aspect ratio change is not as obvious, most of the small particles have anaspectratio close to one.For the extrudates ofthe aluminum alloy, 6061, many precipitates were present, mostof which were MgSi. It was found that the size of the precipitates was around onemicronand they were quite uniformly distributed throughout each section. In the longitudinalsection, the precipitates were aligned in the extrusion direction. These precipitateswere alsopresent in the composite extrudates, though not visible at themagnification shown in Fig. 7.7and 7.8.Chapter 7ParticleFracture ofthe PRMMCduringExtrusion1467.3.2 ImageAnalysisofParticleDistributioninExtrudatesAn image analyzer was used to quantify the particle size and orientation. Theparticlesize was measured in terms of particle area and maximumand minimum diameter. Theparticle area was defined as the cross sectional area ofa particle on the polishedsurface, whilethe maximum and minimum diameter were defmed as the longest and the shortest dimensionof a particle on the polished surface, respectively. In addition, particle aspect ratio andorientation were also measured. The particle aspect ratio was defmed as the ratio of themaximum diameter to the minimum diameter, and the orientation ofa particle was determinedby the angle from the direction ofits longest axis withrespectto aspecified direction,e.g., theextrusiondirection in the longitudinal section. Thus, ifthe angle was zero degree, the particlewasconsidered as aligned in the extrusion direction. Atotal ofmore than 2000 particles weremeasuredforarelative errorin the measurements ofless than±5% with95% confldence971. HomogeneityofParticleDistributionThe homogeneity of particle distribution is difficult to characterize quantitatively.However, the variation oflocal volume fraction in the composites could be a measure of theuniformity ofparticle distribution. Aparticle-free zone results in a zero local volume fraction,while afieldfull ofclustersmightapproach 100% local volume fraction in extreme conditions.Apparently, a uniform distribution ofparticles would lead to a small range of variation in thelocal volume fraction.The local volume fraction from position to position was measured using a Letiz ImageAnalyzer. A total of500 fields were examined. The local volume fraction varied from 5% to29% for the extrudates of6061/Al203110p. The frequency of local volume fractions in therange of 1% to 30% is shown in the histogram in Fig. 7.9 for the extrudate ofChapter 7ParticleFracture ofthe PRMMCduringExtrusion1476061/A12O3/lOpfor both the transverse and the longitudinal sections. The mean volumefraction for the transverse section and longitudinal section were calculated to be 12.48% and14.52%, respectively. The corresponding standard deviations were 2.34% and 3.52%, andthe relative coefficients were 0.1875 and 0.2424, respectively, which is defined as the ratio ofthe standard deviation to the mean value. Obviously, the distribution of the particles in the606l/A1203/lOpcomposite is non-uniform, and the non-uniformity in the longitudinal sectionis even more than in the transverse section based on the standard deviation and relativecoefficientvalues. This is due to the bandformationin the longitudinal section.The histogram of the volume fraction for the extrudate of 606l/A1O3/20p in Fig.7.10 shows that the variation of local volume fraction varied from 13% to about 35%. Themeanvalues ofthe volume fraction in the transverse and longitudinal sections are 24.52% and24.45%, respectively, while the corresponding standard deviations are 3.74% and 4.05%, withthe relative coefficients being 0.1525 and 0.1656, respectively. The values of relativecoefficients indicate that, firstly, the particle distribution for the6061/A1203/20Pis moreuniform than in the 606l/A1O3/l0p(Table 7.5); secondly, the particle distribution in thetransverse section is more uniform than in the longitudinal section for both volume fractions.However, all the measuredvaluesofthe volume fractions were largerthan the nominalvalues,as the designationindicates.Table7.5 Statisticalresultsforvolume fractiondistributionofthe two composites6061/A1203/lOp 6061/A1203120PSection Mean Standard Relative Mean StandardRelativeValue Deviation Value DeviationCoeff. Coeff.(%) (%) (%) (%)Transverse 12.48 2.34 0.188 24.52 3.74 0.152Longitudinal 14.52 3.52 0.242 24.45 4.05 0.166Chapter 7ParticleFracture ofthe PRMMCduringExtrusion1489O8070•B6-T600B6-L50II -:1357911131517192123252729Volume Fraction (%)Figure7.9 Histogramofvolume fractionfor6061/Al203/lOp6050B3-T40 L0B3-L30Iin111,11 13 15 17 19 21 23 25 27 29 31 33 35 37 39Volume Fraction (%)Figure 7.10Histogramofvolumefractionfor606l/A1O3/2OpChapter 7Particle Fracture ofthe PRMMCduring Extrusion 1497.3.2.2Particle SizeTo evaluatethe particle sizevariation in the composites afterextrusion, the dimensionsof a particle in terms of its area, maximum and minimum diameter (dimension) weremeasured. The details ofthe measurements with statistical analysis are listedinTable 7.6.A. ParticleDiameterThe histograms ofthe maximum diameter and minimum diameterfor B3 (Back end ofthe extrudate S92-3: 6061/AI2O3I2Op) and B6 (Back end of the extrudate S92-6:606l/A12O3/lOp) are shown in Figs. 7.11 and 7.12. From Fig. 7.11, it is seen that thevariation ofthe maximum diameter in a total count ofabout 2000 particles in B3 is from 50.0.Lm to 3.3p.m, while the minimum diametervaries from 1.67pm to 44pm. However, the meanvalues ofboth the maximum and minimum diameter are largerin the longitudinal section thanin the transverse section, as seen in Table 7.6. For 60611A1203/lOp(B6), in Fig. 7.12, it isseen that the range ofthe variation ofthe maximum diameteris from about to andthe minimum diameterfrom 1.3Jm to 15pm, which is almosthalfofthe values ofthe particlesin 6061IAI2O3I2Op(B3 and F3). Similar to the 20% composite, the mean values ofboth themaximum and minimum diameter ofthe particles are larger in the longitudinal section than inthe transverse sectionforthe 10% composite, as seeninTable 7.6.B. ParticleAreaThe variation of particle area may reflect the particle size distribution in thecomposites more directly. Figure 7.13 shows the particle area distribution for the samecountofparticles in the extrudate of606l/A1203120Patthe backend. It is seen that there is a largevariations in the particle area, from —l6jim2to 480 urn2.Again, the mean value of theparticle area in the longitudinal sectionare largerthan those in the transverse section, which isChapter 7ParticleFractureofthe PRMMCduringExtrusion150200180160•B3-T140E B3-L120_______D100880iiIl_1.67 6.68 11.69 16.721.71 26.72 31.73 36.74 41.75 46.76Maximum Particle Diameter(Micron Meter)(a) Max. Diameter400350________300250Ln.L20001501000:9I -1.67 6.68 11.69 16.7 21.7126.72 31.73 36.74 41.75 46.76Minimum Particle Diameter(Micron Meter)(b) Miii. DiameterFigure 7.11 Histogram oftheparticle diameterforSampleB3 of606l/A120il20pChapter 7ParticleFracture ofthePRMMCduringExtrusion151350300250D1B&L2008150mai1Ii1.33 3.99 6.65 9.31 12 14.6 17.3 20 22.625.3 27.9Maximum Diameter(Micron Meter)(a) Max. Diameter600500ii•B6-TILi2001 C,I [I1.33 3.99 6.65 9.31 11.97 14.6317.29 19.95 22.61Minimum Diameter(Micron Meter)(b) Min DiameterFigure7.12 Histogram ofthe particle diameterforSample B6of6061/AI2O3IIOpChapter 7ParticleFracture ofthe PRMMCduringExtrusion 152350300250•B3-T200I11111LDB3-LliiiI116 49 81 114 146179 211 243 276 308 341 373406 438 471Part1ceArea (SquareMicron Meter)Figure 7.13 Histogramofthe particle areafor Sample B3 of606l/A12O3/2Op450400I350I•B6-T300 [IB6LC2508200150100i9Ihhl1r-thI ‘ti -i -i —i i8.6 26 43 60 7895 112 129 147 16.4 181198 216 233 250ParticleArea (SquareMicron Meter)Figure 7.14Histogram ofthe particleareaforSample B6 of6061/A1203/lOpChapter 7ParticleFractureofthe PRMMCduringExtrusion 153Table7.6StatisticalresultsforthequantitativemetaflographyMMC No. of Particle Area Max.Diameter Min.Diameter Aspect RatioParticles (.tm2) (pm)(pm)Mean Std. Mean Std. Mean Std. Mean Std.Value Dev. I Value Dev. / Value Dev. / Value DevJRel. Rel. Re!. Re!.Coeff Coeff Coeff CoeffLocation 4 2259 179.79 140.21 21.61 9.94 12.12 5.99 2.01 0.59inFig.7.4 / I I /(S92-3) 0.780 0.460 0.494 0.294Location 7 2256 161.63 132.43 20.83 9.73 11.23 5.73 2.12 0.66inFig.7.4 / / / I(S92-3) 0.819 0.467 0.510 0.311B3-T 2282 134.09 122.52 17.97 9.47 10.07 5.24 2.00 0.56I / / /0.914 0.527 0.520 0.280B3-L 2508 174.07 143.27 19.57 11.23 11.43 6.73 1.99 0.55I / I /0.823 0.574 0.589 0.276F3-T 3269 136.90 124.37 18.62 9.60 10.14 5.20 2.07 0.62I / I /0.908 0.516 0.513 0.300F3-L 2020 161.59 140.19 20.17 10.65 11.50 6.44 1.99 0.57I / / /0.868 0.528 0.560 0.286B6-T 2137 34.37 24.67 8.75 3.72 5.55 2.19 1.77 0.47I / I I0.718 0.425 0.395 0.266B6-L 2245 44.16 33.34 10.17 4.27 6.16 2.45 1.87 0.54I I / /0.755 0.420 0.398 0.289F6-T 1965 31.20 22.04 8.64 3.66 5.13 2.06 1.92 0.57I I / I0.706 0.424 0.401 0.297F6-L 3004 38.54 35.54 8.99 4.56 5.71 2.72 1.750.47I I / /0.922 0.507 0.476 0.269Note: ‘Rel. Coeff.’ in the table is arelative coefficientwhichis defined as the ratio ofstandarderrorto themeanvalue.Chapter 7Particle Fracture ofthe PRMMCduringExtrusion154due to the re-orientation of particles along the extrusion direction. Thevariation of theparticle area for the 6061/AlO3/lOp is from 8.6p.m2to around 20Oim2(Fig. 7.14).Themean value of the particle area is about 4 times less than that ofthe 6061fAlO3I20p (Table7.6). This is principally due to different initial range ofparticle sizesadopted in the fabricationofthe composites. Aspect RatioofParticlesThe aspect ratio of a particle is defmed as the ratio of its maximum dimension to itsminimum dimension. The distributions of aspect ratio in the two sampleswith differentvolume fractions are shown in Figs. 7.15 and 7.16. It is seen that the variation ofthe aspectratio is from 1.2 to 4.5 for both materials. The mean aspect ratio in extrudates for the6061/A1203/20pis around 1.99 to 2.07, while the aspect ratio for the 6061/Al203/lOpisaround 1.75 to 1.92 (Table 7.6), which confirms the observation that more particles have anaspect ratio close to unity in6061/A1203/1OP.The relative coefficients (Table 7.6) of theparticle size (e.g., area, diameters) are generally smaller for 6O6l/Al203/lOpthan for6061/A1203/20p,which also confirms that the particle size is more uniform in extrudates of606l/AlO3/l0pthan in 606l/A1203/20p,becausethe particle size is smaller.Chapter 7ParticleFracture ofthe PRMMCduringExtrusion155350300250•B3-T200B3-L8150I I I I I I I I II1Ih:0.15 0.6 1.05 1.5 1.95 2.4 2.85 3,3 3.75 4.2AspectRatioFigure 7.15 Histogramofthe aspectratio forSample B3 of6061/AlO3/20p• 400•B6-T300[]B6-L÷... 250_________8150100I I I I I-H-Ii0.2 0.5 0.8 1.11.4 1.7 2 2.32.6 2.9 3.2 3.53.8 4.14.4Aspect RatioFigure7.16Histogram ofthe aspectratio forSpecimenB6 of6061/AlO3/10pChapter 7ParticleFractureofthe PRMMCduringExtrusion1567.3.2.4 PartideOrientationOrientation ofthe particles with respect to extrusion direction was also analyzed withthe LeitzImage Analyzer. Theextrusion directionwassetto be 0° or 180°. The entire rangefrom 0° to1800was divided into 12 groups, with the group width being150.The frequencyof the particle orientation with respect to its maximum dimension in the different groups forthe extrudates is shown in Figs. 7.17 and 7.18. It is obvious that particles in the transversesection have no preferred orientation, because the frequencies (counts) of the orientation foreachclass are similar. However, higher frequenciesofthe particle orientationin 0 to300and165 to1800were measured in the longitudinal section, which means the particles in thelongitudinal section are aligned in the extrusion direction. Thesemeasurements are consistentwith the microscope observations (Figs. 7.7 and 7.8).600500400-4-C300(-)2001000Figure7.17 Histogramoforientationofthe particles withrespecttoextrusiondirectionforthe Sample B3 of606l/Al203/20p15 3045 6075 90105 120135 150165 180Orientaionw.r.t.ExtrusionDirectionChapter 7Particle Fractureofthe PRMMCduringExtrusion157450400350300250820015010050015 30 45 6075 90 105 120135 150 165 180Orientation w.r.t. ExtrusionDirectionFigure 7.18 Histogramoforientationoftheparticleswithrespecttoextrusiondirectionforthe SampleB6 of606l/AlO3IlOp7.4ParticleFractureModelduringExtrusion7.4.1 ParticleFractureProbabifityatHigh TemperatureParticle fracture has been observed during the extrusionprocess; and this results inparticle size refinement. There are twofactors whichare known to determine particle fractureand its influence on material properties inservice: local stress(related to imposed strain atlow temperature), and hydrostatic pressure,which is obviously of importanceduringextrusion. Atlow temperature theprobability offracture is correlated tostrin’1,(see alsoEq. 7.1), whereas, at high temperatureit is expedient to correlate fractureto the ZenerHollomanparameterand its timeeffect, asit is the Zener-Hollomanparameterthat determinesthe flow stressofthe matrixmaterialduring hotextrusion..Pr=1—exp(D3ae)(7.1)Chapter 7ParticleFractureofthe PRMMCduringExtrusion 158If the particle fracture process is stochastic, then the fracture probability can bederived to predict the particle size refinement during =1_exp(J(_31D3aZ)dt) (7.2)where f3 is a constant with the unit being [1/jim3],and detennined by quantitativemicrostructure analysis; D is the volume equivalent particle diameter, [jim]; (X is the meanparticle aspect ratio; and Z=eexp(Q/RT), [us]. It is noted that dt considers theaccumulation effectofparticle fracture in the extrusion process. The term—31D3aZreflectsthe flow stress level, which controls the particle fracture process, and also represents thefracture rate during extrusion[b03j•In the subsequent section, this fracture probability will beapplied to the hotextrusionprocess to calculate the particle size refinement.7.4.2ParticleFractureModelduringExtrusionIt was observed thatparticles undergo multiple fracture. Hence, the assumption that aparticle fractures into two approximately equal halves75’761,may require re-evaluation for amodel ofparticle fracture under extrusion conditions. In the case underevaluation, it wouldseem that this assumption denies the evidence of a large increase in small particles. Toestimate the average number of parts formed from a single particle fracture event, a totalnumber ofaround 50 counts ofa single particle fracture event was made for both transverseand longitudinal section ofan extrudate. The number ofparts fractured from a single particleevent(including afracture eventin a cluster) was recorded. Therefore, the average number ofparts, n, formedfroma singleparticle fracture event, is simply;(7.3)n=NChapter 7ParticleFractureofthe PRMMCduringExtrusion159where Nis the number ofcounts, 50 in this case as mentioned above and N1is the number ofparts counted from each fracture event. It was found that a large singleparticle oftenfractures into two parts with one part twice the area ofthe other one. However,a particle ina cluster often is crushed into 3 or more parts with equivalent size. With respectto differentextrusion ratios, more fractured particles were observed ata high extrusion ratio. Theaverage number ofparts from a single fracture event for different sections of an extrudateatdifferent extrusion ratios is listed in Table 7.7. It is seen that more parts areformed from asingle particle fracture event in an extrudate at a higher extrusion ratiothan at a lowerextrusionratio. This also implies thatthe highertheextrusionratio, the larger the particle sizereduction.Table7.7 Averagenumberofpartsfracturedfromasingleparticlein6061/A1203/20pExtrusionratio Longitudinal Transverse BothinofanExtrudate (‘L’) (‘T’) ‘L’and’T’64.00 (K-8) 2.78 2.44 2.6328.80 (K-li) 2.52 2.18 2.3710.23 (K-12) 2.42 2.22 2.24The particle fracture probability,Ppis a function oftemperature and strain rate, and isalso associated with the deformation time. To determine the final fracture probability ofparticles at the die exit during extrusion, an integration over the deformation zone isnecessary, i.e.,=J(—i1DocZ)dt=Jtaf(r,z)dt(7.4)Chapter 7ParticleFractureofthe PRMMCduringExtrusion 160where af provides the fracture rate, which varies both in the radial direction, r, and in theextrusion direction, z, over the deformation zone of the billet. To simplify the numericalcalculation, an average fracture rate over a cross section of the billet in the deformation zoneduring extrusion was determined first, i.e., the fracture rate was integrated over a crosssectional area at a certain depth,z, in the deformation zone, and was divided by the crosssectional area to obtain an average as described below.—(75)p=f2af(r,z)rdr/Rwhere R1is the radius of the deformation, which is outlined by the shear zone boundary. Itvaries from the initial radius ofthe billet(R0)at the back end ofthe deformation zone, to theradius of the extrudate (RE) at the die exit. If one assumes that a particle with a volumeequivalent diameter, D, is fractured into n equally sized particles during extrusion, the volumeequivalent diameter of each fractured piece is DITh.Because the number of brokenparticles, N is equal toPf*N, where is the total number of particles in thedeformationzone, the meanrefined particle diametercan be derived as:— (D/)3113— 1D(7.6)—(1+(,-1)p)”3Then, the particle size reductionat thatstage is defmedas:%=-x1OO%(7.7)7.4.3ApplicationoftheModelFrom an image analysis ofthe extrudate from Trial S92-3 atUAC, Anaheim, the meanparticle diameter,Dime, in the extrudate wasfound to be 12.41pm; while the meansizeoftheparticle, at the back-end of the bifiet was 13.07p.m. The mean value of the maximumChapter 7ParticleFractureofthe PRMMCduring Extrusion161diameter of the particles, was 18.77tm and 21.22tm for theextrudate,D1,and the billet,respectively. UsingEq. (7.6), the overall fracture probability wasestimated as 12.20%,and consequently the constantfiin the fracture model (Eq. 7.2) is3.07x1021[1/pm3].Boththe mean particle size (diameter) and the mean value ofthe maximum diameterare predictedusing the DEFORM results for temperature and strain rate in the deformationzone (Table7.8). It is evident that there is good agreement between the mean particle diameter and themeanvalue ofthe maximum particle dimension.The probability variation at each time step through the deformation zone wasestimated using Eq. (7.2). Figure 7.19 shows that a maximum fracture probability is reachednear the exit of the die aperture. This indicates that the most severe particle fracture occursnearthe die throatby severe shear deformation due to choke of metal flow into the dieaperture, which is consistent with the microstructural examination in the deformation zone.The corresponding meanparticle size reduction is showninFig. 7.20.100‘0.12800.10.08 .60-0.06€I3.440-I 0.04200.020- I I Ii—-•0315 330 345360 375 390 405Depthinto Deformation Zone (mm)Figure7.19 Fracture probabilityvariation inthe deformation zoneS.a0a*IIIIIIIShearB’dary- -- ProbabilityaIaIDie ThroatIIChapter 7ParticleFractureofthe PRMMCduringExtrusion 162100- 13.38OShearB’daryl- 13.1MeanDia.-12.9E 60ES.—40Ct125i20 --12.3Die Throat0- II 12.1315 330 345 360375 390 405Depthinto DeformationZone (mm)Figure 7.20 Particle sizereductionduringextrusionTable7.8 Comparison ofmodelpredictionswithmeasureddataMeanParticleDiameterReductionD(im) D1mLm)Red (%)pfMeasured 13.07 12.41 5.02 12.20Model 13.07 12.39 5.19 11.02AverageMaximumParticle DimensionReductionDoinax(i.Lm)D113m) Red (%)Measured 21.22 18.77 11.5532.48Model 21.22 17.64 1687 33.367.5 DiscussionThe particle distribution has been examined during theextrusion process. However,some questions remain. What is the influence of theextrusion process on particleChapter?ParticleFracture ofthe PRMMCduringExtrusion163distribution? How is a particle fractured during deformation, andwhat is the correlationbetween extrusiondeformation behaviorand the particlefracture?7.5.1 MicrostructureComparisonbeforeandafterExtrusion7.5.1.1 ComparisonofParticleDistributionbeforeandafterExtrusionPorosity and voids have been considered to be the mostdetrimental defects in castproducts61.In cast PRMMC products, other defects, such as surface defects(cracks),agglomeration and clustering may also be present. In the microstructure study conductedbyKalu and McNelley’541,it was found thatAl203particles were clustered in theas-cast lOvol%material provided by Duralcan. Similar features were found in6061/A2OillOp,shown in Fig.7.21(a). The distribution of the particles was more uniform in a higher volume fraction,e.g.,6O61IA12O3I2Opcomposite, as shown in Fig. 7.22(a). The non-uniformity is a result ofentrapment of the particles in the interdendritic regions during solidification. These arepotential sites for crack formation in service because a complex tn-axial stress state is easilyestablished in clusters (see Fig. 6.8 inChapter6).The microstructures of a transverse section of the lOvol% and 2Ovol% compositesafterextrusion at a ratio of34 at UAC, are shown in Fig. 7.21(b) and Fig. 22(b), respectively.It is quite obvious that the homogeneity of particle distribution is improved after extrusion,especially for 606i1Al2O3/iOp,although some clusters still remain in the transverse section,while extrusion bands are evident in the longitudinal section. The number of small particlesincreases as a result of particle fracture during extrusion. This is more obvious withquantitativeparticle size analysis using the image analyzer. Evidently, heavierextrusion ratiosimprove the homogeneity of particle distribution. However, a larger extrusion ratio at arelatively low temperature mayintroducevoidsin the surface layerofextrudates due to tensileChapter 7Particle Fracture ofthe PRMMCduringExtrusion 164(b) AfterextrusionFigure 7.21 Microstructure of606l/A1203/lOpbefore and afterextrusion(a) Before extrusionChapter 7Particle Fracture ofthe PRMMCduringExtrusion 165(b) AfterextrusionFigure7.22 Microstructureof6061IAI2O3I2Opbefore andafterextrusion(a) BeforeextrusionChapter 7ParticleFracture ofthe PRMMCduringExtrusion 1660.25_________0.2•back___Qextrud.o0.15_______o.iJ]I V0.0:I I‘iii0-5 5-10 10- 15- 20- 25- 30- 35-40- 45- >5015 20 25 30 35 40 45 50Sizeclass (microns)(a) Maximumaluminaparticledimensionof6061/A1203/20pinbackendofabilletandinextrudate0.45________0.40.35•back0.3Llextrud.[ -1Il_ri_-0-5 5- 10- 15- 20-25- 30- 35- 40- 45- >5010 15 20 2530 35 40 45 50Size class (microns)(b) Minimum aluminaparticledimensionin606l/A12O3/20pin backendofabilletandinextrudateFigure7.23Variationofmaximumand minimumaluminaparticle dimensionChapter 7ParticleFractureofthe PRMMCduringExtrusion167>0a)za).>0I)za)a)>..IbackOextrud.i]I11IIII[_____________AspectratioclassFigure7.24 Aspectratio ofaluminaparticlesof6061/A1203/20pin backend ofabilletandinextrudate0. 15-3030-45 45-60 60-75Angle toextrusiondirection(degrees)75-90Figure7.25 Orientationofaluminaparticlesof60611A1203/20pinbackendofabillet andinextrudateChapter 7Particle Fracture ofthe PRMMCduring Extrusion 168stress, which may cause deteriorationofthe mechanical properties ofthe MMCs, based on thestudies on the materials atlowtemperature192951221• RefinementafterExtrusionTo quantify the change in particle size during processing, the particle size distributionat two locations was analyzed, atthe backend ofthe billet (Locations 4 and 7 in Fig. 7.4), andfrom the longitudinal section of the extrudate. The statistical results shown in Table 7.6reveal that the variables characterizing particle size, such as particle area, maximum andminimum dimension, and even aspect ratio, are greater at Locations 4 and 7. The smallerrelative coefficients of particle size at Locations 4 and 7 indicate that the particle sizedistribution is more uniform in the material before extrusion; in other words, some particlesfracture into smallerpieces during extrusion. This can also be seen through the distribution ofthe maximum and minimumparticle dimensions (Figure 7.23(a)-(b)). The increase in numberofsmall particles is quantified. The decrease in mean aspect ratio ofparticles is accompaniedby a rise in the class ofparticles with an aspect ratio close to one, as shown in Figure 7.24.The orientationdistribution ofparticlesis distinctin Figure tendency for the particle size distribution to skew towards lower size classes is inaccord with observations of material deformed at low temperatureunder hydrostaticpressure76’(Fig. 7.23(a) and (b)). Such observations are indicative of the comminutionofparticles98’(Comminutionmode in Fig. 7.26(a)). It is also noted that in the transversesectionofthe extrudate there appear to be substantially more smallparticles than in the longitudinalsection: this is, in part, an effect of particle re-orientation. It wasobserved that fracturedpieces healed due to the low flow stress of the matrix material and high hydrostaticpressureChapter 7Particle Fracture ofthe PRMMCduringExtrusion169encountered during extrusion, which results in matrix material being forcedinto cracks175’901.This feature is the major difference between low strain/low temperature andlarge strain/hightemperature behavior. However, at high temperature, under tensile stress, thePRMMCs tendto form voids behind the particles’1011.This will be discussed in more detailin subsequentchapters.Particle re-orientation during extrusion may also have an effect on the propensity ofparticles to fracture. It was interesting to note that most of the cracks in the particles(fracture gap) were parallel to the flow direction, and particles seem to be most affected whenthey lie parallelto the extrusion directionin the longitudinal section ofthe extrudate. This maybe caused by the shear stress acting on the particles under high hydrostatic pressure (Shearmode inFig. 7.26(b))’991.The skewing of the aspect ratio data (Fig. 7.24) suggests that particles with a largeaspect ratio are more likely to fracture during extrusion. From the microstructureexamination, some cracks were observed perpendicular to the flow direction for thoseparticles with a large initial aspect ratio. The fracture may result from tensile load transferbetween the matrix and the particle due to its large initial aspect ratio. A tensile mode ofparticle fracture was therefore proposed during extrusion (Fig. 7.26(c)). This is also afracture atlow temperature inthe loadingdirection761,and is retained athightemperatures.Based on the above analysis, three basic modes are proposed for particle fractureduring extrusion, i.e., the comminution mode, the shear mode and the tensile mode (Fig.7.26). Particle fracture during extrusion is a very complex phenomenon. Not only does asingle mode function, but particle fracture may be affected by a combination of two or eventhree modes at the same time, especially for particles in a cluster. However, fromChapter 7ParticleFractureofthe PRMMCduringExtrusion 170microstructural examination, the shearmode may be more applicable in the shear deformationzone, where most of the deformation occurs; the tensile mode may be more effective at theposition where elongation is very severe, such as near the die exit zone; and the comminutionmode may occur anywhere in the deformation zone for a single particle, but most probably inclusters where large compressive tn-axialstresses are present.w‘I,(a) Comminutionmode (b) Shearmode (c) Tensile modeFigure7.26 Aschematic diagramforthree particle-fracture modes duringextrusion7.5.3 CorrelationbetweenParticleFractureandBulkDeformationBehaviorTo understand the particle fracture during extrusion, thedeformation behavior of thecomposite billetwasanalyzedwiththe aid ofDEFORM® asdescribed in Chapter 5. A typicaleffective strainrate distributionnearthe dieexit area atasteady state is shown in Fig.7.27.U UChapter 7ParticleFractureofthe PRMMCduringExtrusion1711X )Etf.StnRl(1/s)-7.750 -BilletA. 0.00008= 3.0000C- 60000-8.0500— 8.0000E. 12.000F. 15.000Gm 18.000lb 21.000-8.350-8.950-9250 I I I0.00 6.00 12.0018.00 24.00 30.00Radius (mm)Figure7.27 Effective strainrate distributioninthe deformationzone2 Mean Stress(MPa)-0.500BilletA— -270.008=-245.00C.-220.000=-19500E=-170.00-0.600F.-146.00G.-120.001= -70.000J-45.000_K. -20.000-0.700 -E 1= 5.0000.800 -lbE0,—1.000 — I I I0.00 6.00 12.00 18.00 24.00 30.00Radius (mm)Figure7.28 Mean stressdistributioninthe deformation zoneChapter 7ParticleFracture ofthe PRMMCduring Extrusion172It is seen that the highest strain rate is reached at the die throat, where metal flowwaschoked. Therefore, mostsevere particle fracturecould occur in thischoked zone. This is alsoconsistent with the particle fracture probability prediction in Section 7.4.3. The mean stress(hydrostatic stress) corresponding to the strain rate state is shown in Fig. 7.28. It is evidentthat over most ofthe bifiet, the stress state is in compression (negative value),and a very highhydrostatic pressure exists in the deformation zone. Comminution ofa particle orparticles ina cluster could result under such a large hydrostatic pressure which may also healthefractured particle under the large deformation during extrusion (Comminution mode).However, nearthe die exitzone, tensile stresses appear, especially at the die-bearing interface,which is due to high elongation ofthe billet and the friction stress at the die interface. Thesetensile stresses could lead to particle fracture (Tensile mode), or voids behind particles. FEMmodel predictions confirm the existence of a large shear zone during extrusion, as shown inFig. 7.29. In this shear zone, velocity gradients appear from the dead metal zone to thedeformation zone. As a particle flows along the shear direction, the shear deformation forcesthe particle to rotate into the flow direction (which finally leads to an alignment of theparticles along the extrusion direction). However, if the stress in the particle from both theshear and the hydrostatic pressure is large enough, the particle could fracture (Shear mode);healing could consequently occur if the matrix material intrudes into the gap of the crackunder high hydrostatic pressure or the fractured pieces were shifted apart because of thevelocity gradient under large deformation”t.Evidence of particle fracture and healing arepresented in this chapter.Chapter 7ParticleFractureofthePRMMCduringExtrusion 1732RZ Stress(MPa)-ooo/BilletIA. -20.000B. -12.000C-4.0000I0. 4.0000-0.500 .iz.oooF. 20.000(G. 28.000IH. 36.000-0.600-0.700 --0.900 -—1.000 —— II II I0.00 6.0012.00 18.0024.00 30.00Radius (mm)Figure 7.29 Shearstress distributionduringextrusion7.6SummaryMacro- andmicro-exmiination of a billet during extrusion sheds light onthe metalflowpatternand particle fracture. It was found thatthe particles fractured in the severesheardeformation zone atthe die throat, butmostfracturedparts healedinthe extrudatesdue to thehigh temperature and large hydrostatic pressure,which has also been confirmed by DuralcanUSALIOSI.Some majorfindings are summarizedbelow.Chapter 7ParticleFractureofthe PRMMCduringExtrusion174(i) Due to adhesion friction between the billet and the container in hot extrusion,aparticle-freelayer was formed at the interface, and the particle -free matrix material flows intothe shear deformation zone to form a particle-free band in the extrudates inthe extrusiondirection. In this zone, very few particles reside, and therefore therewas less fracture of theparticles;(ii) More obvious particle alignment along the flow direction was observed in thesevere deformation zone than in the dead metal or hard-to-deform zone under the pressurepad. The formation ofthe particle-free bands along the extrusion direction was obviously dueto the elongation of the particle-free zone in the as-cast material during extrusion. Thefrequency ofparticle fracture depended on deformation conditions. In the deformation zone,more fractured particles were observed than in the dead metal zone, but most severe particlefracture occurred in the shear deformation zone at the die throat. The fractured parts werehealed due to the low flow stress of the matrix material at high temperature and the largehydrostatic pressure. However, clusters in the hard-to-deform zone under the pressure pad,or even in the dead metal zone, showed evidence ofparticle fracture due to the comminutioneffects. In the dead metal zone, some particles were cracked, but not separated, due to smalldeformation;(iii) Mostofthe singleparticles thatfracturedhad alarge aspect ratio orsharp corners.Equiaxed particles were much harder to fracture; all the large particles which remainedunfractured in different zones had an aspectratio close to unity;(iv) Many cracks in particles were in the flow direction due to shear deformation, butsome cracks perpendicular to the flow direction were also observed, especially inparticlesChapter 7ParticleFractureofthe PRMMCduringExtrusion175with a large aspect ratio. This was probably due to the tensile stressin the particle in the flowdirection.The size and distribution of the particles in the extrudates havealso been examinedusing both an optical microscope and an image analyzer.Comparing the transverse sectionwiththe longitudinal section, some important featuresare:(i) Orientation of the cracks in the transverse section was randomlydistributed.However, many ofthe cracks in the particles in the longitudinalsection were either parallel orperpendicular to the extrusion direction. Most of the particles with anaspect ratio greaterthanone were aligned in the extrusion direction;(ii) Particles with a different aspect ratio were observed in both the transverse andthelongitudinal sections. Largerparticlesespecially with sharp corners or large aspect ratios, andthose in clusters, fractured more easily. More small particles were found in the transversesections than in the longitudinal section, partly because of re-orientation of particles duringextrusion;While comparing the extrudate of6O6l/AlO3/lOp to that of6O6lIAl2O3/20p,it wasfound that:(i) Particles were much smaller in 606l/AlO3/l0p than in 6061IA12O3I2Op.However, the particle distribution was less homogeneous in 606l/Al203/lOp than in606l/A1203/20p,i.e., more clusters and more particle-free bands remained in the extrudatesof6061/A1203/lOp;(ii) The mean aspect ratio of particles in 6061/A1203/lOpwas less than that in6061/A1203/20p.Chapter 7ParticleFractureofthe PRMMCduringExtrusion176Quantitative metallography and statistical analysis wereconducted using an imageanalyzer. The particle dimensions, such as minimum and maximum dimension,area, aspectratio, and particle orientation were quantified at different positions in thedeformation zone.The mostsalientpoints are:(i) Particle alignment along the extrusion direction wasconfirmed. Particle fractureduring extrusion leads to more smaller particles. The averageaspect ratio of the particlesafter extrusion is around 1.74 to 2.07 with more uniform size distribution in606l/AlO3/l0pthan in 6061/AlO3/20p. The mean size of the particles in the longitudinal section is largerthan in the transverse section due partly to re-orientation of particles during extrusion.However, the particle distribution is more uniform in the transverse section than in thelongitudinal section;(ii) The four-fold difference in size of particle area in the extrudates between6061/AlO3/l0p and 606l/AlO3/20p is mainly due to a difference in initial particle size ofthe composites. The change in particle size, size distribution, homogeneity, and orientation,and healing ofthe ‘damage’ which accompanies a fracture event, may all have benefits for thein-service mechanical properties ofextruded components. However, the influence ofparticlefracture on mechanical properties, the correlation between the particle size and thedeformationparameters, and the mechanism ofthe low speedcracking, need to be clarified.Chapter8 Origin ofLow SpeedCracking duringExtrusionofthePRMMCs 177Chapter 8 ORIGIN OFLOWSPEED CRACKINGDURINGEXTRUSION OF THEPRMMCsThe particle fracture analysis presented in the previous chapter revealed theimprovement in homogeneity of particle distribution and particle size refinement afterextrusion. This could be beneficial with respect to mechanical properties of the composites.However, low speedcracking was observed in the plant trails at UAC, which is specific to thecomposite material. It is essential to explore the mechanism ofthe low speed cracking duringextrusion.8.1 MicrostructureExaminationofLow-speed CracksAs observed in the plant trial atUAC, low speed cracking occurred at the front end ofextrudates in most of the trials. Although some explanation for the low speed cracking wasproposed by researchers, as described in Chapter 2, it was incomplete because the interactionbetween the particles and the matrix were not considered. To study the mechanism of lowspeed cracldng, extrudates with severe low speed cracks were cut and polished to examineboth longitudinal and transverse sections. The samples were cut from the front end of theextrudates ofJ94-14 and J94-20 of6O61IA12O3I2Opwithvery severe low speed cracking, andJ94-1lB of6O61IAl2O3I1Opwith slight cracking. The polishing procedure of Table 7.2 wasfollowedby using an automaticpolishingmachine atUBC. The samples were examinedunderan SEM, because it is harder to investigate void formation by using an optical microscope,due to its low depth of field. Before examination, a very thin film of Au-Pd was sputtercoated on the surface ofthe polished specimens for about 4 minutes for6O61IAl2O3I2Op,andChapter8 Origin ofLow Speed Cracking during Extrusionofthe PRMMCs178about 3 minutesfor606l/A12O3/lOpsamples. As a result,good contrastbetween the particlesand the matrix was obtained with little electronic charging of theA1203particles. UndertheSEM, it was found that the low speed cracks penetrated into the surface layer, and thatextensive voids existed around the low speed crack tips in all three samples,as shown in Fig.8.1 forJ94-14. It is seen that most of the voids were associated with particles andlocated atthe two ends ofparticles in the extrusion direction (orientation of particles with large aspectratio in the picture). The same phenomenon was also observed around the crack tips of 394-1lB for6061/A1203/lOp,as shown in Fig. 8.2. This is due to the tensile stress state in thematrix between particles in the flow direction, as predicted by the micromechanical analysis inChapter6.Itis interesting to note thatmore severe low speed cracking was observed in 394-14 of6O61IA12O3/20pthan in 394-1lB of 606l/A12O3/lOp,although the initial billet temperature ofJ94-14 was higher at 461°C than 434°C used for J94-11B, as listed in Table 4.3. This is dueto the fact that the lowervolume fractionresultsin higher ductility ofthe composite, while thefracture behavior is controlled by exhaustion of matrix ductility due to the constraints onmatrix plastic flow by the elastic reinforcing particles’1.A high volume fraction of secondphase particles results in more severe constraints of the matrix flow around the particlesduring extrusion, although the6061IA12O3/lOpcomposite has a less uniform distribution thanthe 606l/A12O3/2Op composite, as described in Chapter 7. Crushed particles were alsoobserved at the surface which form the minor defects observed in the extrudate surface.Cracked particles in clusters remained without evidence of healing, although interfacedecohesionseems to be dominantin the surface layer.Chapter8 Origin ofLow SpeedCrackingduringExtrusionofthePRMMCs179Figure 8.1 Void formation neara low speed cracktip of394-14 of6061/A120il20pinlongitudinalsectionFigure 8.2 Void formation near a low speedcracktip ofJ94-1lB of6061/A1203/lOpin longitudinal sectionChapter 8 Origin ofLow Speed Crackingduring ExtrusionofthePRMMCs 1808.2 Particle BehaviorandMicroscopic DamageThe above microstructure indicates that the low speed cracking is associated withparticle behavior and its consequent microscopic damage, such as particle fracture and voidformation. Therefore, particle behavior and its constraints to the plastic flow of the matrixmaterialbecomesimportant.Micromechanical analysis of particle behavior under both the plane strain and thecylindrical compression has been conducted in Chapter 6. All the particle models (Single-,Twin- and Multiple-particle Model) predict a localized deformation behavior around theparticle, although the overall deformation behavior of a specimen with and without a particleare quite similar to each other. it is the localized deformation that intrinsically leads todynamic microstructural evolution (such as particle fracture, void formation, etc.) duringextrusion.8.2.1 ParticleFractureAt a microscopic level, the predicted localized matrix flow in the vicinity of largealumina particles, especially at both the sharp ends of angular particles and in the vicinity ofparticle clusters, was confirmed for aluminaparticulate reinforced metal matrix composites byFerry and Munroe in the form ofshearbands in the matrix around the particles, based on theirmicrostructural study in Al/A1O3composites”111.They also found that large particles andthose with a high aspect ratio had the greatest propensity to fractureduring deformation.Some particles fractured into very fine (1-2 tIm) pieces and redistributed along the shearbandduring deformation. These observations are also consistent with the single-particlemodelprediction of different shapes of a particle during cylindrical compression and withtheprediction of particle migration in the plane strain simulation. The interaction between theChapter8 Origin ofLow Speed Cracking during Extrusionofthe PRMMCs181particles and the matrix is mutual: the particles in a cluster and those with an irregularmorphology force the matrix to deform in a highly constrained manner (localizeddeformation), and the highly deformed matrix material inversely affects the particle behavior,e.g., the rotation and migration ofthe particle, and consequently the stressstate inthe particle.Therefore, matrix flow and particle behavior are very much temperaturedependent. If thetemperature is low, the matrix work-hardens more easily and the stress in the particle willbehigher, which in turn leads to particle fracture. Because the flow stress of the matrix at lowtemperature is high, the cracked parts are harder to heal by intrusion of matrix material intothe gap. In contrast, at high temperature, due to the low flow stress, there is little workhardening and the matrix flows more easily around the particle. Consequently, the stress inthe particle is low and the particle is harder to fracture. Even if a particle fractures, thecracked parts heal easily by matrix intrusion into the crack under hydrostatic pressure, or thetwo cracked parts are separated away by shear deformation, as observed in extrusionprocessing. A tensile stress was predicted in a particle with an aspect ratio of 2 under planestrain conditions at a reduction of 10%, as shown in Fig. 8.3. This is consistent with theproposal ofthe ‘Tensile mode’ ofparticle fracture during extrusion, i.e., ifa particle moves inthe matrix flow direction, a tensile stress is generated in the particle. The larger the aspectratio, the higher the tensile stress, and consequently, the higher the propensity to fracture.This is also predicted by study of particles with different aspect ratios under a plane straincondition, whichhave some similardeformationcharacteristicsto the extrusionprocess(Table8.1). The table shows that generally a particle with a large aspect ratio has a higher internaltensile stress in the flow (x) direction. However, as the reduction increases, the tensile stressChapter8 Origin ofLow Speed Cracking during Extrusionofthe PRMMCs182decreases. This is because the interparticle spacing increases,and subsequently, theinteraction between the twoparticles becomes weaker.Table8.1 TensilestressinpartidesandmatrixatdifferentreductionsAspect ObjectNo. Reduction:10% Reduction: 30% Reduction:—50%Ratio (Material) MiMax. Miii. Max. Miii.Max.(MPa) (MPa) (MPa) (MPa)(MPa) (MPa)#2(Matrix) -50 42-51 30 -64 38A.R.=1 #4(Particle offC.L.)-8 83 -28 89 -4572#5(Particle @ C.L.) -489 -18 69 -34 50#2(Matrix) -131 125 -60 54-57 34A.R.=2 #4(Particle offC.L.) 9 158-12 84 -26 55#5ParticIe @ C.L.) 56 170 8 92-24 544.600X Stress(UPa)Objed#4(dght)A. 10.0008= 25.000C= 40.0004.570D= 55.000E= 70.000F. 85.000_______________F______________(IH. 115.00G= 100.00I. 130.00EE>EL4=145.004.540-______K. 160.00__________Objed#5(drline)E____4.510A. 10.0008=25.000C. 40.000D. 55.000E= 70.0004.480F. 85.000G= 100.00H. 115.001= 130.004= 145.00K= 160.004.4500.000 0.030 0.060 0.090 0.120 0.150X (mm)Figure 8.3 Tensile stressin aparticle underplane strainconditionatareductionof 10%Chapter 8 Origin ofLow Speed Cracking during Extrusionofthe PRMMCs1838.2.2VoidFormationVoids have been observed with an SEM in the surface layer of some extrudates withsevere low speed surface cracking, as described in Section 8.1. It was found that voids weremore frequently present at the ends oftwo closely spaced particles which were aligned in theextrusion direction. The void formation could be explained by the local stress state owingtothe presence ofthe particles. Figure 8.4 shows the tensile stress(ar) distribution around theparticles at a reduction of 10% under the plane strain condition. A high tensile stress zone isgenerated between two particles in the x-direction. A smaller spacing ( between thetwo particles with a large aspect ratio leads to a higher value of the tensile stress in theinterparticle zone (see contourline value of ‘J’ of 104 MPa in Fig. 8.4(b) and compared to thecontourline ‘G’ of28MPainFig. 8.4(a) for a particle spacing of40pm). Ahigh tensile stressvalue is also predicted for the multiple-particle model at a reduction of 1% (see contour line‘E’ of 6OMPa in Fig. 8.4(c)). This implies that in the matrix material within closely spacedparticles, such as within a cluster, it is easier to initiate voids. The predictions are consistentwith the results obtained by Poole eta!.1113-114JIt is interesting to note that the tensile stresscomponent in the x-direction in the center zone of the monolithic material with no particlespresent is less than 6MPa, although all the other simulationconditions are the same, as showninFig. 8.5.X (mm)‘I0.100X (mm)X S1m1 (UPa)ObdI 2A= -20.0008=-12.000Cs4.00000= 4.0000Es 12.000F= 20.000G= 28.000H= 36.000Chapter8 OriginofLow Speed Cracking during ExtrusionofthePRMMCs 1844.6504.600E 4.550>-4.5004.450(00.000 0.050 0.1000.150 0200(a) Twin-particlemodel withaunityaspectratioatareduction of 10%E>-4.6504.6004.5504.5004.450X Qrese(UPa)Objed1 2A= -130.008=-104.00C= -78.0000= -52.000Es -26000F= 0.0000G. 26.00014= 52.0001= 78.000.1= 104.00K= 130.000.000 0.050 0.150 0200(b) Twin-particle model with anaspectratio of2 atareductionof 10%Chapter8 Origin ofLow Speed Cracking during Extrusionofthe PRMMCs 185X Streu(UPa)5.060Cbed#2A-40008..15.000C. 10.000______0-35.000E. 60.0005.000EE 4.960>-____4.9004.850Ii %0.0000.050 0.1000.150 0.200X (mm)(c) Multiple-particle modelwithaunitaspectratioatareductionof 1%Figure 8.4Tensile stress distributioninthe matrixand aroundparticles10.020- xOX Stress(UPa)Objed1 2A- -30.0008=-24.000C.-18.000_. -0260 -E 0=-12.000E E=4.0000F= O.00000E+00>-G= 6.0000H. 12.000-0.540 - 1= 18.000J. 24.000K= 30.000—1.100—I I0.00 2.805.608.40 11.2014.00X (mm)Figure 8.5 Tensile stressdistributionin the monolithicmaterialatareductionof 10% underplane strain conditionChapter8 Origin ofLow Speed Cracking duringExtrusion ofthePRMMCs 186Therefore, even though the monolithic stress state is compressive, a local tensile stresscomponentaround particles may exist. Itis the local tensile stressbehind a particle in the flowdirection which leads to void formation, as observed in the extrudates. The hydrostaticpressure helps to stop void formation and growth during extrusion which explain why theelastic modulus ofthe extrudates doesnot decline as the extrusion ratio increases.8.3 EffectofProcessingParameterson Low Speed CrackingFrom the microscopic analysis in the above section, it is known that low speedcracking is related to the presence of a tensile stress both in the particle and in the matrix,which might lead to particle fracture and void formation, respectively. However, themicroscopic behavior must be related to the macroscopic extrusion parameters, such asextrusion temperature, speed and the material itself. The temperature is, however, affected bymany factors such as ram speed, initial billet and die temperature and die material, etc.. Anefforthas beenmade to explore the origin oflow speed cracking during extrusion with the aidofthe finite elementmodel, DEFORM’.The temperature distribution ofboth the billet of 6061IA12O3I2Opand the die nearthedie exit zone, during extrusion at steady state, is shown in Fig. 8.6.The simulation conditionsare listed in Table 8.2. It is evident that the billettemperature is increased to about 460°Cfrom the initialvalue of425°C due to the heat ofdeformationforan extrusion ratio of34; andthe die interface also heats up due to heat conduction.Obviously, the thermal diffusivity ofthe die material is also very importantto the temperaturedistributionin boththe extrudate andthe die interface. Figure 8.7 shows the tensilestress builds up at the die land area in theextrudate during extrusion. All the other zonesin the billet are in a compressive stress,whichTenipefature(C)aaA 426.00B 426.00C. 432.000-438.00E 444.00F. 450.00G= 456.00H. 462.00I- 468.00DieA. 378.598. 389.56C. 400.520- 411.49E. 445F. 433.42G. 444.38H. 455.351. 466.31Chapter8 OriginofLow SpeedCracking duringExtrusionofthePRMMCs187may help prevent void growth or crack formation. Apparently, both the temperatureandtensile stress in this die land zone are crucial to the low speed cracking. As described inthelast section, the fracture behavior of the composite is controlled by exhaustion of matrixductility due to the constraints on matrix plastic flow by the elastic reinforcing partic1e”’.Therefore, the lower the billet temperature in the die land zone, the lower the matrix ductility.On the other hand, the larger the tensile stress generated in the surface layer in the die landzone, the higher the propensity.for void formation due to local tensile stress near the ends ofparticles in the extrusion direction, especially for those closely distributed particles (e.g.,particlecluster), based on the micromechanicalanalysisconductedinChapter6.4.0004.3004.600I4.90042004.5000.0 30.060.0 90.0120.0Radius (mm)150.0Figure 8.6 Temperature distributionofbilletand die atsteadystateextrusionChapter8 Origin ofLow Speed Cracking during ExtrusionofthePRMMCs 188Table8.2Standardconditions forparametricstudyRam speed: 1mm/sInitial billettemperature: 425°CFriction shearfactoratthecontainerand dieinterface: m=1 (sticking)Friction shearfactoratpressure padinterface: m=0.7Initial die temperature: 395°CBilletdiameter 178mm (7”)Containinside diameter: 184(7.25”)Extrusionratio: 342-2.750ZSkees(MPa)A— -420.02\B-359.45\C=-296.89\D=-238.32-3.050E-177.75F— -117.18\G.-56.616H 3.95171= 64.519-3.3504959250- -0.0 30.0 60.0 90.0120.0 150.0Radius (mm)Figure 8.7 Tensile stress(as) distribution atthe die interface zoneTo determine the effectofextrusionvariables on the temperature and thetensile stressin the dieland zone, a systematic study ofthe extrusion of6061/A1203/20pwas conducted forChapter 8 Origin ofLow Speed Cracking during Extrusionofthe PRMMCs189all the process parameters, such as ram speed, initial billettemperature, initial die temperature,frictional condition at the die interface, extrusion ratio and the billet materials. The standardsimulationconditions are listed inTable 8.2.EffectofRam SpeedFigure 8.8(a) and (b) show the effect of ram speed on the variation of the maximumbillet temperature and the maximum tensile stress in the extrudate in the die landzone duringextrusion. Figure 8.8(a) shows that the temperature increases much faster at the speed of6mm/s than at 1mm/s. This is because a higher speed results in a higher heat generation rate,and also the higher speed reduces the time of heat transfer from the extrudate to the die,which generates a steeper thermal gradient near the die interface, as shown in Fig. 8.9.Tensile stress, az, (where Z denotes the extrusion direction) in the die land zone decreasesduring extrusion, because ofthe temperature rise (Fig. 8.8(b)). Ahigher ram speed results ina sharper decrease in the stress value because of the higher heat generation rate. Apparently,the tensile stress value is quite sensitive to the extrusiontemperature.Figure 8.9 shows that the temperature distribution through the whole radius of theextrudate is higherforthe ram speed of6mm/s, and also that the thermal gradientis greater atthe interface, due to the shorter heat transfer time. On the other side ofthe die interface, thethermal gradient is even greater because of the lower thermal diffusivity (the thermaldiffusivity ofH13 is about 7 times lower than that ofthe composite material). Again, becauseof the shorter heat transfer time, the thermal gradient is greater for the ram speed of 6mm/sand the inside temperature ofthe die is even lower than thatofthe ram speed of 1mm/s.Chapter8 Origin ofLow SpeedCracking duringExtrusionofthe PRMMCs190520— — —500— — — —/U/‘‘ 480/4601.0mm/s///1Z6.5440-42020 2224 26 28 3032RamDisplacement(mm)(a) Maximumtemperaturein the die land zone duringextrusion85I1.Omnilsl‘6.5mmIsj75C’,C,,‘1)556520 2224 26 2830 32RamDisplacement(mm)(b) Maximumtensile stressin thedie land zone duringextrusionFigure 8.8 Effectofram speedChapter8 Origin ofLow Speed Cracking during ExtrusionofthePRMMCsU01)1910 5 10 1520 25 30Distance from the Centerofextrudate(mm)525500475450425400Figure 8.9 Temperaturedistributiononbothside ofthe die interfaceataramdisplacementof30mmFigure 8.10 shows the effective strain distribution through the whole radius of theextrudate atthe die exit. Itis seen thatthestraindistributionis not sensitive to the ramspeed,because the strain is more dependent on extrusion ratio. The distributionofstress componentin the extrusion direction (az) along the radius of extrudate, indicates that the stressiscompressive near the center and gradually becomes tensile near the surface of theextrudate(Fig. 8.11). Obviously, in a surface layer ofmore than aquarter ofthe radiusofthe extrudatethere exists a tensile stress in the extrusion direction. Theexistence ofthe tensile stress statein the surface layer may promote void formation ifthe temperature ofthe billet atthe surfacein the die land zone islow; thismayfmally lead tolow speedcracking, aswasobserved.Chapter8 OriginofLow Speed Cracking during Extrusionofthe PRMMCs1924.36____1OmmJs2.8 -2.42 I I I0 4 812 16Distance from the CenterLine (mm)Figure 8.10Effectoframspeedonstrain distributionthroughradiusdirection60 -I40- I——— 1.0mm/si6.5mm/si________—20-000U0-0020-.0oI.—z•000-600481216Distance fromthe CenterLine (mm)Figure 8.11 Effectofram speedonstressdistribution(az) throughradius directionChapter8 Origin ofLow Speed CrackingduringExtrusionofthe PRMMCs1938— —— 1.0mm/s66.5mm/s4,20 4 8 1216Distance from the CenterLine (mm)Figure 8.12 Effectoframspeedoneffective strainratevariationinextrudateA big difference in effectivestrainrate is expected because ofthe different ram speeds(Fig. 8.12) but near the exit of the die land, the strain rate is concentrated only within thesurface layer.EffectofBillet TemperatureWith all the other conditions kept the same, the effect of initial billet temperature onthe tensile stress in the extrusion direction and the temperature rise was studied (Fig. 8.13(a)and (b)). Thus the higher the initial temperature, the higher the extrusion temperature.However, the temperature rise is lower for the higher initial billet temperature (—20°C) thanfor the lower initial temperature(—40°C); because ofthe lower flow stress and thelow heatgeneration obtained for the higher billet temperature. Correspondingly, the maximumtensilestressin the extrusion direction (CT) is lower, as shownin Fig. 8.13(b). A 75°Cincrease in0IChapter8 Origin ofLow Speed Cracking during Extrusionofthe PRMMCs194520500L)0E4604404205°C500a e — a—— a•••—aa•• —aaSI I I,I I I I I85756555453520 22 24 26 28 30 32RamDisplacement(mm)(a) Max. temperature in the die land zone duringextrusion. - — —— 425 °Caa500°C..aba:20 22 24 26 2830 32RamDisplacement(mm)Figure 8.13 Effectofinitialbillettemperature: (b)Max. tensile stressinthe die land zoneChapter8 OriginofLow Speed Cracking duringExtrusionofthe PRMMCs 195550- -- 425 °C525500°C475into Billetinto DieS 0 0S S450-Die Interfaca425 I00 5 10 15 20 25 30Distancefrom the Centerofextrudate (mm)Figure 8.14Thermalgradientonbothsidesofthe die interfaceunderdifferentbillettemperaturebillet temperature results in a drop ofmaximum tensile stress of 3OMPa. It is obviousthatthe effectofbillet temperature on the maximum tensile stress is quite significant.It is knownthat a higher tensile stress may increase the propensity ofvoid formationat high temperaturein particulate reinforced MMCs1011.Therefore, temperature control is important toeliminatelow speed cracking during extrusion. On the otherhand, ata lowerinitialbillet temperatures,the tensilestressintheextrusion direction in thesurface layerofthe extrudate decreases morerapidly because ofthehigherheatgeneration ratedue to the high flow stress (Fig. 8.13(b)).Because the ram speeds are the samefor both cases, the thermal gradientin theextrudate is about the same (Fig.8.14). However, on the die side, the thermalgradient islargerforthe lowerinitialbifiettemperature of425°C, becausethe temperatureriseishigher.- -- 500°C-395°CI500°G470°C22 24 26 28RamDisplacement(mm)(b) Maximum tensilestress inthe die landzone during exirusionFigure 8.15 Effectofinitial die temperatureC-)0IIChapter 8 Origin ofLowSpeed Cracking during ExtrusionofthePRMMCs19653048065605550454035.I I I I20 22 24 26 28 30 32RamDisplacement(mm)(a) Maximumtemperature in the die land zone duringextrusion-- 500°C-395°C500°C-470°C...I I I I I20 3032Chapter8 Origin ofLow Speed Cracking duringErtrusionofthe PRMMCs 197550- -- 500°C-395°C530 500°C-470°C—‘ 510: _ _ _ . _ — _ = =— = — —— ——into Billet490intoDieU470Die Interfac450- I II0 5 10 15 20 2530Distance from the Centerofextrudate (mm)Figure 8.16Thermalgradienton bothsidesofthe die interfaceunderdifferentinitialdie temperaturesEffectofDie TemperatureFrom the above analysis, it can be seen that the tensile stress is very sensitive to thetemperature of the extrudate in the die land zone. Because the die temperature is not verywell controlled in the plant thai at UAC, the sensitivity ofdie temperature was also analyzed(Fig. 8.15). Die temperatures of 395°C and 470°C were used with the same initial billettemperature of 500°C. From Fig. 8.15(a), it is seen that, because of the lower initial dietemperature of395 °C, the maximum defonnation temperature oftheextrudate is about 15°Clower than that ofthe die temperature of470°C, and the extrusion temperature is even belowits initial temperature of 500°C at the end of the upsetting stage (at a ram displacementofChapter8 Origin ofLow Speed Cracking during Extrusion ofthe PRMMCs 198about 21mm) due to the cold die ‘chilling’ effect. As a result, the tensile stress of theextrudate in the surface layer within the die land zone is higher (Fig. 8.15(b)). Thetemperature distribution in the cross section of the extrudate is more uniform than that onthe die side because ofthe higher thermal diffusivity. The lower initial die temperature resultsin a steeperthermal gradient onthe die side(Fig. 8.15).EffectofFrictionatDieInterfaceWithsticking frictionconfmed to the containerinterface, the sensitivity oftwo extremefriction conditions was studied with the friction shear factor being set at 0 and unity,respectively. It is worth pointing out that in DEFORM®, when considering the stickingfriction condition, the relative velocity between two objects in contact is not restricted; incontrast, a shear stress with an equivalent value ofshear strength ofthe deformed material, isapplied at theboundary1831.Therefore, although asticking friction conditionwas specified, thenodes of the deforming finite element object (billet) in contact with the stationary object(tools) are still movable. Figure 8.17 shows the sensitivity of the friction condition at thedieinterface.Without friction heating at the die interface, the maximum temperatureof theextrudate during extrusion is lower than, but very close to, the value of theextrudatetemperature withfriction. This is because the die land length is only about2 to 3mm; and thusthe contribution of friction heating is very small. The small effect offriction on thetemperature rise can also be seen from the thermal gradient on bothsides of the die interface,as shown in Fig. 8.18. However, the difference in tensilestress related to the two differentfriction conditions is quite obvious (Fig. 8.17(b)). It is interesting tonote that even with nofrictioncondition applied atthe die interface, the tensile stress stillexists. This indicates thatChapter8 Origin ofLowSpeed Cracking duringExtrusionofthe PRMMCs199470 -460___I.• — — — — —U -0 —‘450/_____/Im=1440____430-420 ‘ II I20 22 2426 28 30 32RamDisplacement(mm)(a) Maximum temperature m the die land zone duringextrusion9080—70zm=1r5O5040 I I20 22 24 2628 30 32RamDisplacement(mm)(b) Maximumtensile stressin thedie land zone duringextrusionFigure 8.17 EffectoffrictionconditionatdieinterfaceChapter8 Origin ofLow Speed Crackingduring Extrusionofthe PRMMCs 200475463c-)0‘— 451427415Figure 8.18 Thermalgradientonboth sidesofthe die interfaceunderdifferentfrictioncondition atdie interfacethe tensile stress build-up in the die land zone is not only due to friction, but also duetomatérial flow itself, because metal flows faster at the inside layerofthe extrudate than at theoutside layer and also there is no back pressure applied onto the frontend of the extrudate.Therefore, it is this velocity difference that causes thetensile stress at the die exit. Severefrictionconditionssimplymake the situationworse.EffectofExtrusionRatioAtemperature riseofthe billetundersmallerextrusionratiosis expectedto belower ifall other conditions are kept the same.At an extrusion ratio of 13, the extrudate temperaturerise is only about 15°C comparedto 45°C for anextrusion ratio of34. About 30°C differencehasbeenpredictedforthe extrusionratio of 13and 34(Fig. 8.19(a)). Becauseoftherelatively0 510 1520 2530Distancefrom theCenterofExtrudate (mm)Chapter8 OriginofLowSpeedCracking during ExtrusionofthePRMMCs 201470— R=13R=34,— 450 -C-)o— — — ——0’E/430/410I II2025303540RamDisplacement(mm)(a) Maximumtemperatureinthe die land zoneduringextnision8520 253035 40RamDisplacement(mm)(b) Maximumtensilestressin the die landzone duringextrusionFigure 8.19 EffectofextrusionratioChapter8 Origin ofLow SpeedCracking during Extrusionofthe PRMMCs 202525500U0— 4752450425400-10 0 10 20 3040Distance from the CenterofExtrudate (mm)Figure 8.20Thermalgradientonbothsidesofthe die interfaceunderdifferentextrusionratioshigher heat generation rate for the higher extrusion ratio, a greaterthermal gradient ispredicted for both sides ofthe billet and the die, as shown in Fig.8.20. The tensile stress ishigher initially for the higherextrusion ratio, but decrease rapidly because of therapidtemperature increase (Fig. 8.19(b)).EffectofVolume FractionoftheCompositesThe sensitivity analysis conducted abovewas for the 606l/A12O3/2Op. The effectof10% and 20% volume fraction of the PRMMCswas also conducted for a similar sensitivityanalysis (Fig. 8.21). As expected, ahigh volume fraction ofparticles results in a highertemperature rise due to the higherflow stress (Fig. 8.21(a)). The tensilestress is alsogreater- -R=13R=34into Billet4—into Die• — — _ a aa a aa a aa aa —Die•—— —Chapter8 OriginofLow Speed Cracking during Extrusionofthe PRMMCs 203470460 -—I — — — —/ I—f — — —c_) / —I.450-—— 10%volI”20%vol4401/Il/I430j420 II I20 22 24 2628 30 32RamDisplacement(mm)(a) Maximumtemperature in the die land zoneduringextrusion80246283032RamDisplacement(mm)(b) Maximum tensilestressin thedie land zoneduringextrusionFigure 8.21 EffectofvolumefractionChapter8 Origin ofLow Speed Crackingduring ExtrusionofthePRMMCs204470460‘—‘ 450I430420Figure 8.22Thermalgradientonbothsidesofthe die interfaceunderdifferentvolume fractionfor the larger volume fraction material. This means that the decrease in flow stress due totemperature rise cannot compensate for the effectof a larger volume fraction of thereinforcement. The difference in thermal diffusivity of differentcomposite materials can beseen from the thermal gradient in the extrudate, although it is quite small. Thehigherthermal diffusitivity of 6061/A1ZO3/lOp resultsin a slightly flatter temperature distributionthrough the radius ofthe extrudate (Fig. 8.22).8.4MechanismofLowSpeedCrackingBased on the analyses described in theabove sections, itis believed that the lowspeedcracking is induced by both the low ductility ofthe composite and microstructuraldamage0 5 1015 2025 30Distancefrom theCenterofextmdate (mm)Chapter8 Origin ofLow Speed CrackingduringExtrusionofthe PRMMCs 205(such as voids including decohesion and unhealed cracks) during extrusionas follows: 1) atthe beginning ofextrusion, the die temperature is lower than thatof the billet, so a ‘chilling’effect occurs at the front end ofthe billet when it is in contact withthe ‘cold’ die. The lowertemperature results in lower ductility of the composites; and 2)the extrudate surface isgenerated from two distinct regions ofthe composite: the deformationzone ofintense shear,decorating the dead metal zone, which is the major contribution and the smallerdeformationvolume near the die throat, moving along the die facet1171.With the presenceof particleswhich constrain the surrounding matrix deformation, especiallyat low temperature, severedefonnation near the die throat may lead to matrix failure at the particle interface (voidformation) and particle fracture in particle clusters in the composite during extrusion. Thetensile stress generated in the die land zone may not only leave the cracked particle unhealed,but also promote the void growth. When the fraction ofthe voids reaches a certain value, thevoids may link each other to result in a tearing at the extrudate surface within the die landlength, due to low ductility at low temperatures.At high extrusion speed, because the heat generation rate of deformation is greater,and also because the thermal diffusivity ofthe die material (H13 and the ceramic die) is about7 to 10 times lower than that ofthe composites, the temperature at the die interface increasesvery rapidly (See Fig. 8.8). However, at low speed, the heat generation rate is lower and theheat has time to diffuse through the die, due to the relatively longer extrusion time (Fig. 8.9).Therefore, if either the initial bifiet temperature or initial die temperature is low, the matrixwithin the particles is constrained much more than at higher temperature, because the flowstress is muchhigher at lowertemperature (see also Figs. 8.13 and 8.15). Voids are easier toform and grow under tensile stress (see also Figs. 8.4 and 8.5). Therefore, low speed cracksChapter8 Origin ofLow Speed Crackingduring ExtrusionofthePRMMCs 206appear. Apparently, all the extrusionconditions that may result in lower billet temperatureand higher tensile stress inthe surface layer ofthe extrudate in the die land zonemay lead tolow speed cracking during extrusion,such as lower initial billet and die temperature, low ramspeed, higher extrusion ratio, higherfriction condition at the die interface, and also highvolume fraction of the particle reinforcement. Thisis consistent with the plant trialobservations at UAC and at KRDC, Kingston. At UAC, more severelow-speed cracking inthe 606l/Al2Oil2Op composite at higher extrusionratio (1” and 1.25” die) has been found;and the low-speed cracking disappeared when the ramspeed was increased. However, onlyone extrudate with low-speed crackingwas found in the trials at KRDC, in which the ramspeed was considerably lower than the setvalue of 0.9mm/s. This occurred when the presslimit was exceeded due to low initial billet temperatureof 400°C. At a ram speed of—0.9mm/s. low speed cracking always appeared inthe plant trials at UAC. However, no lowspeed cracking wasobserved in theplanttrials atKRDC. This is becausethe die and the billetwere heated atthe sametime in afurnaceatKRDC, and the temperature ofthe containerwaseven higher than that ofthe billet. The ‘stick and slip’ observed,is due to the fact that whenvoids link to form a crack, the tensile stress generatedis released. This process repeats itselfas long as the temperature of the billet remains low and alsothe tensile stress is sufficientlyhighto promote voidformationinthe extrusionprocess.8.5 APreliminaryCriteriaforLowSpeedCrackingIt is clear now that the onset oflow speed cracking is controlledby both the fracturestress and fracture strain (ductility) ofthe material. Therefore,a preliminary fracture criterionisproposed forthe low speed cracking during extrusionbased on the idea ofthe plastic-workcriterion5t1:Chapter8 OriginofLow Speed Crackingduring Extrusionofthe PRMMCs207E—a2cGF6F =CF(8.1)where(Yzis the maximumprinciple stress, andis the maximumtensile strain obtainedduring extrusion,which is defined as thestrain induced undera tensile stress, while GFEFisthe product of thefracture stress andtensile fracturestrain of the material.The low speedcracking is inducedby local failuresof the composite,related to the localtensile stress andstrain. However,because it is difficult toknow the localtensile stress andstrain, themonolithic tensilestress and strainare used in thecriterion. Since the fracturestrain of amaterial is also dependenton the process itself,a tensile strainis used, although it ishard todetermineitsvalueinanextrusionprocess.Apparently,iftheproduct ofthe maximumtensilestress and the maximumtensile strainin the composites exceedsa critical value,which is theproduct ofthe fracturestress and strain,low speed crackingwould occur. Thereason to usea product insteadof a single stress(Stress Criterion)or strain (StrainCriterion) is becausethe onset oflow-speedcracking is inducedby the combinationofthose two factors,i.e., themicrodamage wouldbe inducedfor a certain strain(fracture strain)within particles,and thetensile stress wouldpromote the voidgrowth to linkvoids to form thelow speed cracksfor acertainstressvalue(fracture stress).According to Eq.(8.1), the effect of avariation ofthe product(E) of the maximumtensile stress and themaximum extrusionstrain in theextrudate (rather thanthe difficulttoobtain tensile strain)during extrusionunder differentconditions, but forthe same extrusionratio of 34, was shownin Fig. 8.23. J94-12has the highestvalue of B, becauseit has thelowest temperatureof423°C. Thehigher startingvalueofEofJ94-13, with higherinitialChapter8 OriginofLow SpeedCracking duringExtrusionofthePRMMCs208450194-12420 -..— J94-13194-143904-360330300 I I II24 28 32 3640RamDisplacement(mm)Figure 8.23 VariationofEvalue duringdifferentconditions butsameextrusionratio530480194-6394-14J94-20430380330280 - = - * --.230 I II I24 28 3236 40RamDisplacement(mm)Figure 8.24VariationofEvalue duringextrusionatdifferentextrusionratiosChapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 209billet temperature of 47 1°C, must be related to the lower initial die temperature.Although thestarting values of E for both J94-12 and J94-13 are higher, they decrease morerapidly thanthose in 394-14. This implies that the low speed cracking would disappearin the extrudateearlier than noted in J94-14. This is consistent with the low speed cracking rangesat the frontend of each extrudate, with J94-14 having the longest low speed cracking lengthand J94-13the shortest (Table 4.7).The variation of E during extrusion for different extrusion ratios, is shown inFig. 8.24.Apparently, the highest extrusion ratio of J94-20 has the highest E value withthe longest lowspeed cracking range in its extrudate. 394-6, with the smallest extrusion ratio, has the lowestE value and the shortest cracking range (Table 4.7). Although theE value variationcorresponds qualitatively with the low speed cracking, the determination of theCf value isdifficult, because it is dependent on temperature, strain rate, and the process itself.However,in the plant trials at UAC, the large variation of ram speed would result in bothstrain rate andtemperature fluctuations in the deformation zone. One way to determine the product of aeis to conduct a series of tests (e.g., collar tests) in the laboratory at different temperatures andstrain-rates to measure the fracture stress and strain. However, it would stillbe difficult tospecify the fracture stress and strain at the crack position; and moreover, the applicability ofthe laboratory test results to the industrial process would need to be verified.210Chapter 9 EXTRUSION OF THE PRIVIMCsIt is conceivable that the unique properties of particulate reinforced MMCs will ensuretheir place in automobiles and other applications by the year 2000 or before11151. Asmentioned in the literature review, MMCs can be applied in the manufacture of theautomobiles in several areas, such as drive shafts, brake rotors, engine blocks and cylinderliners, connecting rods and pistons, tire studs, etc. Although, of the mentioned parts, only thedrive shafts and the connecting rods are produced through extrusion processing, the.manufacturing technologies, involving control of consistent material quality and high-tolerance tube extrusion techniques, etc., are critical to the successful implementation of driveshafts in high-volume automotive applications. Quality aspects of the MMCs of concern tothe customer for application in the auto industry include specific stiffness, fatigue life, wearresistance, tailorable properties (e.g., thermal expansion)181.However, different parts havedifferent quality requirements. Taking the drive shafts for example, the high specific modulusof MMCs is a veiy cost-effective improvement. Although the elastic modulus reductionoccurs during low temperature defonnation because of damage by particle fracture, especiallyfor metal matrix composites with a high volume fraction (e.g., 20%)[995.h161,it has beenconfirmed that the hot extrusion process does not reduce the elastic modulus and tensilestrength. Instead, it may increase the tensile properties due to an increase in the homogeneityof the particle distribution and particle size refinement. Fatigue life of the composites couldalso be affected by thennomechanical processing (e.g. hot extrusion). Improvements in thefatigue strength of MMCs, compared to parent alloys are reported, but a lower specificfatigue strength for 606lIAlO3I20p compared to 6061 is also seen, which could dependChapter 9 Extrusion ofthe PRMMCs 211critically on both the method of testing and the quality of the composites’81.Therefore,acceptable process windows for reliably producing higher quality and high-volume productionof the MMCs are yet to be defmed.9.1 Development of Extrusion Limit Diagram9.1.1 Using Empirical EquationsThe empirical equations used for the development of extrusion limit diagrams havebeen described in Section 2.3 in the literature review. For convenience, two main equationsare listed below in Eq. (9.1) and (9.2). The extrusion pressure can be estimated using Eq.(9.1), which is related to the press parameters (e.g., R, L,Dc) and the extruded materialproperties (e.g., (X, n, A). From the plant trial data at KRDC, and at UAC, the four constantsin Equation (9.1) have been estimated for both the extrusion presses (Table 9.1).p=!{B+CinR+Elfl..+FQ.)(....L)}(9.1)an AADTable 9.1 Constants in Eq. (9.1) for the compositesB C E F CorrelationCoeff.Small Press at KRDC 36.07 17 16.8 147 -43.9526 40.6549 0.9882for 606l/A12O3/20pLarge Press atUAC 291.0946 214.6415 -205.3810 218.3884 0.9804for 6061/A1203/20pLarge Press atUAC 443.0187 260.1046 -211.9300 205.3414 0.9381for 6061/A12031l0pA good correlation was obtained between the measured peak load and the predictionby the above equation. Hence the pressure limit line in a limit diagram can be delineated, atleast tentatively, using Eq.(9. 1), based on the press limit15551.Chapter9 Extrusionofthe PRMMCs212With respect to the bifiet temperaturerise during extrusion, the followingequation(see also Eq. 2.9) is used,based on an assumption that there islittle or no temperaturedifference between the billet andthe surrounding tools’631.This assumptionis valid for theplant trial at KRDC, becauseboth the die and the billet wereheated at the same time inthesame furnace. However, the die temperaturein the plant trial at UACwas significantly lowerthan that of the billet. For simplicity,in the calculation of temperaturerise, the initialtemperature difference betweenthe bifiet and the tools was ignored,while the internalgenerationofheatestablishesatemperaturedifferential,AT= 0.9PvBtI C1(t)= O.9PvBtI(K1t”2+(K2+K4)?’3+(K3÷K5)t”3+K11t) (9.2)Based on Eqs. (9.1) and (9.2) for peakpressure and temperature rise,extrusion limitdiagrams can be developed for theDuralcan®composite materials extruded inthe small pressat KRDC and the large pressat UAC. Figure 9.1 shows a limit diagramat a constantextrusion ratio of28 for6061/A1203/20pfor the press at KRDC. Dueto the low capacity ofthe press (—l000kN), the operatingwindowforextrusionprocessingis small.Figure 9.2 shows a limit diagram forthe same material at a constant ramspeed of12.5mmJs (maximum speed forthe press at KRDC). A ram speed of35mm/s for Duralcan®material processed at an extrusionratio of 25 and 14mm/s for SiCp reinforcedcomposites(matrix alloy: A357)at an extrusion ratio of 36 has been reported in industrialextrusionpractice’9’’. A limit diagram for 606l/A12O3!2Opfor the large press at UACunder anextrusionratio of34is showninFig. 9.3.Itis seenthat, due to the large capacityofthe press(3000 tons), the process window is much largerthan that at KRDC. This indicatesthat thepressure limitfor the large press at UACis not a problem for extrusion of the compositesathightemperature.Chapter9 Extrusion ofthe PRMMCs2136050ExtrusionRatio:28F. 14030j42010PressureLimitIncipientMelting0 i420 440 460 480500 520 540ExtrusionTemperature(°C)Figure 9.1 Extrusionlimitdiagramatanextrusionratio of28 for6061/A1203/20pforthe press atKRDC86 RamSpee& 12.5mm/s350 375 400425 450475 500 525550 575ExtrusionTemperature(°C)Figure9.2Extrusionlimitdiagramataramspeedof 12.5mm/sfor6061/A1203/20pforthe pressatKRDCChapter9 Extrusionofthe PRMMCs 2141251000- 0‘g75PressreLimitIncipient Melting04Cl)5025I I II250 300 350 400450 500 550ExtrusionTemperature (°C)Figure9.3 Extrusionlimitdiagramfor 6061/Al203/20patanextrusionratioof34forthelarge press atUAC400300200ressure LimitIncipient Meltingl000 II200 250 300 350 400 450 500 550ExtrusionTemperature (°C)Figure9.4ExtrusionlimitdIagramfor60611A1203/lOpatanextrusionratioof34forthe largepress atUACChapter9 Extrusionofthe PRMMCs 215An extrusion limitdiagram for606l/A12O3I1Opwas also developed for the large pressat UAC using the empirical equations (Fig. 9.4). It is evidentthat the process window of6061/A1203/lOpis evenlargerthanthat for606l/A1203/20pdueto itslowerflow stress.9.1.2UsingFiniteElementMethod9.1.2.1Application oftheFiniteElementModelExtrusion limit diagrams are usually developed using the aboveempirical equations,based on extrusion plant trials. The assumptions and simplification of heat transfer analysisfor derivation of the empirical equation for temperature rise during extrusionmay lead toinaccuracy ofthe processing window. Moreover, to have an accurate load prediction,a smallnumberofplant trials are necessary to determine the coefficients in Eq.(9.1). Obviously, thisapproachisnotcosteffective.As computation technology advances, extrusion limitdiagramscan also be developedusing the fmite element technique. Based on the fmite element predictions,a relationshipbetweentemperaturerise andbillettemperature andextrusionspeedmaybe obtained,AT=fI(T,vB) (9.3)Similarly, arelationship betweenpeakpressure and thetwovariablescanalsobeestablished:P=f2(T,vB) (9.4)With the aid of DEFORM, extrusion of the composite material was simulated atdifferent ram speeds and different initial billet temperatures. The ram speed varied from 1 to50 mm/sforthe press at KRDC and 1 to 75mm/s forthe press at UAC; while the initial billettemperature changed from 400°C to 550°C for the press at KRDC (because of its low loadcapacity) and 300°C to 570°C for the press atUAC. The initial die temperature was assumedto be 30°C less than that ofthe billet, while the containertemperature was thesame as that ofChapter9 ExtrusionofthePRMMCs 216the die. The temperature ofthe pressure pad was 70°C. The interface friction was assumedto be sticking between the billet and the die, and between the billet and the container, while africtionshearfactorofm=0.7 was assigned to the interface between the billetand the pressurepad, due to its lowertemperature. The heat transfercoefficientat the interfaces was assumedto be 2O0kW/m°C18.All the other boundary conditionswere the same as described inChapter 5. The incipient melting point of 582°C forthe 6061/A1203/20pcomposite materialwasused155571,and was taken as the limiting boundaryfor the incipient melting line in theextrusionlimitdiagram.An extrusion limitdiagram for6061/A1203120pforthe small press at KRDC was thusdeveloped, as shown in Fig. 9.5. Correspondingly, the extrusion limit diagram for60611A1203/20Pforthe press atUAC is shown in Fig. 9.6. Again, the processing window forthepressatUAC ismuchlargerthanthatforthepress atKRDC.160120I80400375 425475 525575ExtrusionTemperature (°C)FIgure9.5Extrusionlimitdiagramfor6061/A1203/20pforthe pressatKRDCChapter9 Extrusionofthe PRMMCs217125100j7550Pressure LimitIncipient Melting250 I250 300 350 400 450 500 550ExtrusionTemperature(°C)Figure9.6 Thelimitdiagramfor6061/A1203/2Opforthepress atUAC9.1.2.2ComparisonofExtrusionLimitDiagramsThe extrusion limit diagrams for606l/A12O3/2Opfor the press at KRDC and UAC byboth the empirical-equation technique and the finite element method are shown in FIgs. 9.7and 9.8. The pressure limit lines in the diagram from both techniques are quite close,especiallyin the limitdiagram forthe press at KRDC. This is expected because the empiricalpressure equation (9.1) was determined using the plant trial data. The discrepancy betweenthe pressure limitlines obtained bythe two techniques in the diagramforthe press atUAC isdue to the lowboundary temperature ofabout 250-300°C, because this temperatureisbeyondthe valid extrusion temperature range of 390°C - 485°C used to determine the empiricalequation (9.1). This might result in inaccuracy of the pressure prediction by the empiricalequation (9.1). The difference between the two incipientmelting lines is more obvious. Thisis mainly due to simplification ofheat transfer analysis for the temperature rise estimation inChapter9 Extrusionofthe PRMMCs218the empirical equation (9.2), because the FEM model consideredcoupled thermal andmechanical phenomena for both the billet itself and the suffounding tools duringextrusion tosteady state. The model predictions have been validated by comparison withthe measureddatainChapter5.Limit diagrams for both the 6061/A12031l0pand the 6061/Al2O’2Opusing theempirical equations are shown in Fig. 9.9. It is seen that the processingwindow for the6061/A1203120pis totally within the window of6061/A1203/lOp. This is due to the lowerflow stress of6061!A1203/lOp. It thus can be concluded that the safe processing conditionsfor6061/A1203/20pare alsosafeforthe processingof6061/A1203/lOp.160140 ExtrusionRatio: 28._120----FEM100 EmpiricalEquation80604020PressureLimit -frfIncipientMelting0 -- r -i375 395 415 435 455 475495 515 535 555 575ExtrusionTemperature(°C)Figure9.7 Comparisonoftheextrusionlimitdiagramof6061/A1203/2OpforthepressatKRDCusing differenttechniquesChapter9 Extrusionofthe PRMMCs2191251;_____FEM.-- —-- Empncal75’IIncipient Melting50:II25.:‘PreureLimft0I250 300 350400.450500 550ExtrusionTemperature(°C)Figure9.8 Comparisonoftheextrusionlimitdiagramof6061/A12O3I2Opforthe pressatUACusing differenttechniques200_____20%15OI::PressureL\tMe200 250300 350400 450500550ExtrusionTemperrature(°C)Figure9.9 Theextrusionlimitdiagramforboth6061/A1203/lOpand6061/A120y’2OpusingtheempiricalequationtechniqueChapter9 Extrusionofthe PRMMCs2209.2 ExtrusionLimitDiagramwithLowSpeedCrackingBoundaryAs observed in the plant trial at UAC, low speedcracking occurs at the front ofextrudates in most ofthe trials. It is veiy important todelineate the boundaries oflowspeedcracking in the extrusion limitdiagram for safe processing. Although apreliminary fracturecriterion for the low speed cracking has been proposedin Chapter 8, it is still difficulttopredict the low speed cracking by includinga low speed criterion in the finite elementmodel.Fortunately, substantial data on low speed crackingduring the planttrial at differentextrusionconditions has been generated, and the boundariesoflow speed cracking can be delineated byprocessing the data.9.2.1 LowSpeed CrackingBoundaryDuring extrusion in the planttrial at UAC, the ramspeed varied from less than 1mm/sto about 6mm/s, and the coverage of low-speed crackson the surface of the extrudateschanged from a few centimeters to more than6 meters under different extrusion speeds andtemperatures (Table4.7). Because the billettemperaturechanges duringextrusion, due to theheat of deformation, to track the billet temperaturechange, DEFORM was applied to thecases exhibiting long coverage oflow-speedcracks through the extrudates (e.g., J94-6, J94-12, J94-13, J94-14, J94-20). The varying extrusiontemperature and ram speed were tracedfrom the front end of the extrudates exhibiting low speedcracks, toward the back end, untilthey disappeared. Then the data points traced fromthe recorded ram displacement weredivided into two groups, the one associated with lowspeed cracking (termed as ‘Fail’), andthe otherwithoutlow speed cracks (termedas ‘Safe’). Thusthe lowspeedcracking boundaryof the extrudates of 6061/Al203/20punderthe same extrusion ratio can be delineated, asshowninFigs. 9.10 to 9.12forthreedifferentextrusionratios.Chapter9 Extrusionofthe PRMMCs2218R=13—‘6a 394-5-sa0•: Safe‘. 394-6-sx 394-7-f(/2oJ94-7-s2 :&.— BoundaryFail :e.*.*..t0 I I445 450 455 460 465 470 475ExtrusionTemperature (°C)Figure9.10Lowspeed cracking boundaryfortheextrudateof606lIAl2O3I20patanextrusionratio of 138x S91-3-fR=346o S91-3-s0 A 194-12-fSafe394-12-s4X 394-13-fo 394-13-sFail+ 394-14-fa 394-14-sAAZ4aBoundary0- I420 450 480510 540ExtrusionTemperature (°C)Figure9.11 Lowspeed cracking boundaryfortheextrudateof606l/A12OJ2Opatanextrusionratio of34Chapter9 Extrusionofthe PRMMCs2228R=52z 394-19-f- * 394-19-sSafe A 394-20-f4 394-20-sFailBoundaryA420 440 460 480500 520 540560ExtrusionTemperature (°C)Figure9.12Low speed crackingboundaryfortheextrudateof6061/A1203/20patanextrusionratio of52In the legend of Figs. 9.10 to 9.12, the symbol ‘-f and ‘-s’ denote ‘fail’ and ‘safe’,respectively foreach extrudate. Due to less databeing available for the 6061/A1203/lOp,thelow speedboundarycouldnotbe delineated.9.2.2EffectofExtrusionRatiosThe effect of extrusion ratio on the low speed cracking boundary is shown in Fig.9.13. It is noted that to understand the effectofthe extrusion ratio, the ram speed should beconverted into extrusion exitspeed, whichis multipliedby the extrusion ratio. It is seen thatas the extrusion ratio, R, increases, the low speed cracking boundary shifts toward highextrusion speed and higher temperature. This is consistent with the observation ofthe planttrial results, that is, more frequentlow speed cracking occurred when the extrusion ratio wasincreased. The trend ofthe low speed cracking boundaries indicates that at a low extrusionChapter9 ExtrusionofthePRtfMCs223ratio, temperature has a larger effect than the ram speed, and vice versaat a high extrusionratio. This is because atlow extrusion ratio, the temperature rise ofthebillet due to the heatofdeformation is low, and atahighextrusionratio,because ofhigherexitspeed, the adiabaticeffectbecomesmore significant..350___________ri R=13-fail300m R=13-safe250R=34-failSafe200* R=34-safe .AaIncreasing RA150R=52-fail100R=52-safe500Fail0cLowSpeed Cracldng Boundary420 450 480 510 540ExtrusionTemperature (°C)Figure9.13 Effectonextrusionratios onlowspeedcrackingboundaryduringextrusionof6061/A1O3/20p9.2.3ExtrusionLimitDiagramwithLowSpeedCrackingBoundaryThe boundaries of low-speed cracking at different extrusion ratios are incorporatedwith the extrusion limit diagram developed using the FEM technique, as shown in Fig. 9.10.However,becauseofthe limitedrangeforthe lowspeed cracking, only apartofthe extrusionlimit diagram is presented to clarify the low speed cracking boundaries. The high speedboundary refers to the incipient melting line obtained from Fig. 9.6.It is evident that anincrease ineither temperature or extrusion speed is beneficial to preventing occurrenceoftheChapter9 Extrusion ofthe PRMMCs224low-speed cracking. The boundary line shiftstowards the high speed cracking line(highspeed boundary) as the extrusion ratio increasesto reduce the size of processingwindow.However, becauseno lowspeedcrackingwas observedataram speed of-6mm/sintheplanttrials at UAC, 6mm/s is the minimumram speed forthe 7-inchpress at UAC forextrusion ofthePRMMCs atthe extrusionratio of52.600500— HighSpeedR=13High Speed Boundary, 400R=34c300— R=52 Increasing R Fail_____________Safe100\Fail_________________LowSpeed Boundary0II420 450 480 510 540 570ExtrusionTemperature (°C)Figure9.14Extrusionlimitdiagramof606l/A1203/20pforthepressatUACwithlow-speedcrackingboundaries9.3 ExtrusionofthePRMMCsParticle fracture, with its size refinement and particle redistribution during extrusion,hasbeenexamined inChapter7. The originoflow speed cracking observedin the planttrialshas been explored with the aid ofbothmacroscopic and microscopic finite elementmodels inChapter 8. It is therefore essential to minimize the potential microscopic damage, such asunhealed fractured particles and interface decohesion, which might lead to macroscopic lowChapter 9 Extrusionofthe PRMMCs 225speed cracking on the extrudate surface, and also to improve the quality of the PRMMCs byoptimizing the extrusionprocessingconditions formaximum productivity.9.3.1 MinimizationofMicrostructuralDamageduringExtrusionThe extrudates from two plant trials at KRDC and UAC were cut and polished. Thespecimen from the planttrial at KRDC was cut from the front end of the extrudate, K-6, andpolished at KRDC following the procedure listed in Table 7.1; the specimens from the planttrial at UAC were also cut from the front end of the extrudates, 394-14, 394-20, with severelow speed cracks visible on the surface, and J94-l1B, with slight low speed cracks, andpolished atUBC following the procedure in Table 7.2. The extrusion conditions for the fourspecimens are listed in Table 9.2. The polishing samples were examined under an SEM formicrostructurecomparison. Itseemed thatsomevoidswerepresentinthe surface layerfor allextrudates. The voids in the specimen from UAC were recognized as the origin of the lowspeed cracks, as showninFig. 9.15 from J94-14; whilevoidsinK-6 specimenwere associatedwithclusters, as showninFig. 9.16forboththe longitudinal andtransverse sections.Table9.2Extrusionconditionsforthespecimens examinedunderan SEMTrial# Material Temp. Extrusion BilletDin. Remark(°C) Ratio(mm)394-14 20% 461 (Front) 34 178 Severecracking394-20 20% 457 (Front) 52 178 SeverecrackingJ94-11B 10% 434 (Front) 34 178 SlightcrackingK-6 10% 496(Front) 28 51 No crackingIn the longitudinal section, again, most of the voids were formed at two ends ofaligned particles in the extrusion direction, although some were also associated with particlefracture. The voids in the transverse section were randomly located around a particle or in aChapter9 Extrusionofthe PRMMCs226cluster. The voids observed in the surface layerof the front-end extrudates could be duetothe following reasons:i) some voids could have been in the as-cast materials,not removed by extrusion,especially those in clusters. Any processing route in whichthe ceramic particles are not fullyseparated is susceptible to voids. In the cast materials,the voids are located between theparticles (e.g., in clusters). Therefore , there is more likelihoodof seeing voids in the as-cast6O6l/A12O3/lOp because of the smaller particle size andits tendency towards particleclustering. This kind ofvoid could be removedby either improving the particle distributionduring the meltfabricationorbreaking the clustersduring extrusion.ii) Voids form when a fractured particle was not healedby intruding the matrixmaterial into the cracked gap. Most of these voidswould be avoided by high hydrostaticpressure duringextrusion athightemperature.iii) Voids may also form by interface decohesion. Decohesion isencouraged by weakinterfaces, such as obtained by spinel formation, MgA12O4,atthe particleinterfacet1231.Thegenerationoftensile stress in the surface layer ofthe extrudatein the die land area would leadto void formation, if either the tensile stress is higher or the interface wasweak enough.Therefore, the tensile stress should be minimizedby controlling all the possible extrusionparameters studied in Chapter 8, e.g., higher initial temperatureof billet and die, high ramspeed,lowfrictionatthe die interface. Eliminationofspinelformation attheparticle interfacebyincreasing the magnesium contentin the matrix alloy has beenstudied231,and new matrixalloys could also be sought with a better ductility1’221and free of spinelformationU23lduringprimary processing. In addition, a better die design, suchas stream linedie2Awasrecommended to minimizethe fracturebehaviorduring extrusionof MMCs. However, itisChapter9 Extrusionofthe PRMMCs(b)LongitudinalFigure9.15 Voidsinthesurfacelayerofanextrudate of6061/Al2Oil2Opatan extrusionratio ofabout34 withlow speed cracking (frontendofJ94-14)227(a) Transverse‘IChapter9 Extrusionofthe PRMMCs228(b) LongitudinalFigure9.16 Voidsin the surfacelayerofanextrudate of6061/A1203110patanextrusionratio ofabout28withlow speedcracking (frontend ofK-6)(a) TransverseChapter9 Extrusionofthe PRMMCs 229unclear whether the use of a stream line die may sacrifice the improvement ofparticledistribution obtained by the flat face die extrusion, or increase the tendencyof low speedcracking due to die interface friction. The adoption ofa hydrostatic extrusionprocess11112’761is certainly helpful to suppress void formation, although the production cost couldbecome aconcern.It is interesting to note that no obvious voids were present in the surfacelayer of theextrudatescutfrom the back end without visible low speed cracks on the surface, as shown inFig. 9.17 forJ94-14. This is mainly due to differentextrusion temperatures and different ramspeeds for the extrudates from the plant trials at UAC. Taking J94-14 for an example: at thefront end, the extrusion temperature is about 460°C at a ram speed of about 1mm/s.However, at the back end, the extrusion temperature is about 55-60°C higher than that at thefrontendbecause ofheatofdeformationataraisedram speed ofabout6mm/s.Because microstructural damage, such as particle fracture and/or void formation, mayaffect the elastic modulus ofthecomposites995”1,the variation ofvalues of the extrudatesobtained under different extrusion conditions provide information on the effect ofmicrostructural damage. The correlation betweenYoung’s modulus, E, of a hardened cementpaste and theporosityP0wasdescribedas follows:E=E0exp(—xP) (9.5)where E0is the modulus of the solid phase without any pores and x is a material constantdependent on the internalstructureElO4i.This may also be applicable to the compositematerials during extrusion, where E is the elastic modulus of the composites after extrusionandE0is astandardelasticmodulus whichisafunctionofmatrixalloy, reinforcementmaterialand volume fraction of the reinforcement for a specific MMC. Hence the change in elasticChapter9 Extrusion ofthe PRMMCs 230modulus of the composites for different extrusion conditions should reflect the existence ofsignificantvoidsin the extrudates asaresultofparticle cracks, interface debonding, etc.For the extrudates from KRDC, the elastic modulus as well as yield strength and theUTS for two different extrusion ratios (10 and 28) were tested, with little difference beingfound (See Fig. 4.18). This indicates that the void formation is not significant based on Eq.(9.5), although the elongationwas sacrificed probably due to the presence ofvoids and/or theslight increase in the tensile strength. Obviously, the high hydrostatic pressure in thedeformation zone helped suppress the void formation and growth during hot extrusion.However, it should be pointed out that at a higher temperature itseems likely that the lowestmelting point phases could melt, leading to void formation. The low melting point phasesmustbe associated with particles which were found at the dendrite extremities in the as-caststate.Figure 9.17 SEMimageinthe surfacelayerofthe extrudateinlongitudinal sectionatan extrusionratio ofabout34withoutlow speed surfacecracking (backend of394-14)Chapter9 Extrusionofthe PRMMCs2319.3.2ImprovementinPartideDistributionandSizeRefinementIt is well known that at room temperature the elastic modulus deterioratesas strainincreases, due to particlefracture7576’94.This is because the fractured particleswere nothealed at room temperature. However, in the hot extrusion process, thestress state in thedeformation zone is tn-axial compressive, except in the surface layer of theextrudate in thedie land area where the stress component in the extrusion directionis tensile. Thecompressive stress state results in two beneficial effects: firstly, void formationand growth islargely suppressed; secondly, most of the fractured particles werehealed due to both severeshear and compressive deformation, because there is no oxidation infreshly formedsurfaces11-12,75-76].Reduction in particle size is known to be associated with an increase inthe yieldstrength of composite materials. This decrease in size, in conjunction withthe increasedhomogeneity ofthe particle distribution and reduction in aspect ratio, is expectedto improvethe fracture toughness. The healing offractured particles will allow the materialto attain itsmaximum potential elastic modulus. However, it could be balanced by the void formation ifthe secondary processing, e.g., extrusion, was not well controlled. A slight increasein theelastic modulus of the composites with an increase of the extrusion ratio (fromthe tensiletests) indicates that a large extrusion ratio should be beneficial to the improvementofmechanicalproperties,ifand onlyifthevoidscanbe minimized.9.3.3 QualityandProductivityofthePRMMCsBased on the above analysis, for a betterquality control, a high extrusion temperaturewith a high absolute reduction would be suggested for the processing ofthe PRMMCsbecause ofthe followingreasons:Chapter9 Extrusionofthe PRMMCs 232i) the increase in temperature improves the matrix flowdue to lower flow stress, which, inturn, results in a series of beneficial effects: a)a lower tensile stress in the surface layer ofthe extrudate in the die land zone, which also leads to a lowerlocal tensile stress at theendsof a particle, which could become a source of interface decohesion;b) a lower particlefracture probability based on the particle fracture model; c) easier to heal the gap betweenfracture particles due to matrix flow; d) more importantly, an increase inthe ductility ofthecomposite materials, which is the one of the controlling factor for fracture behavior ofparticulatereinforcedMMCs11221;ii) a higher absolute reduction is likely to result in a larger movement of particles in thedeformation zone during extrusion which helps break clusters to improve the particledistribution; the clusters are always the source of potential damage,as presented in themicromecharncal analysisofthe PRMMCs inChapter6 andChapter 8.Ahigherextrusion speed is also recommended forextrusion ofthe PRMMCs. This ismainlydue to:i) ahigherextrusionspeed will eliminatethe low speed cracking,as describedinChapter 8;ii)italso helps the break-up of the particle clusters in the shear deformationzone; the clusteracts as a harder zone during deformation whose effect decreases as the strain rateincreases11;iii) more importantly, the higher extrusion speed will result ina larger productivity of thecomposites, which reduces the production cost, and consequently makes the product morecompetitive.Certainly, the high productivity is constrained by the high speed defects (such as voidformation due to low melting phases, and high speed cracks on the surface). For this reason,Chapter 9 Extrusion ofthe PRMMCs233the composites should be processed withinthe high speed boundary of the extrusion limitdiagram developed.Chapter10 ConcludingRemarks 234Chapter 10 CONCLUDINGREMARKS10.1 SummaryandConclusionsTo convince customers to useDuralcan®materials, high quality product must beproduced with a competitive price. A complete physical and chemical understanding of theproduct is essential for better quality and higher productivity. Hence, two extrusion planttrials were conducted on theDuralcan®materials; and the extrusion processes in two differentpresses have been simulated with the aid of a finite element model, DEFORM®. The planttrial data were used to validate the model predictions. Particle fracture and size refmementwere observed in microstructural examination of the composites during extrusion. The finiteelement model predictions at both macroscopic and microscopic level were correlated withmicrostructure changes. Extrusion limit diagrams for both the 6O61IA12O3IlOpand the60611A12O3/20p were developed by both an empirical technique and the finite elementtechnique, and modified with the low speed cracking boundary which is specific to thePRMMCs. The mechanism of low speed cracking was studied with the aid of the finiteelement model and the SEM analysis. The major findings from this study are summarized asfollows:1) Particles fractured during extrusion with accumulation of smaller particles inextrudates. Three particle fracture modes were proposed, i.e., comminution mode, shearmode, and tensile mode. Most of the fractured particles were healed under large hydrostaticpressure and sheardeformation athigh temperature.Chapter 10 ConcludingRemarks2352) Particles are aligned in the extrusion direction with formation ofextrusion bands,especially in the606lIAl2O3I10p. Voids were observedin the surface layer of the extrudateswithlow speed cracks, and alsointhose extrudates withsevere particle clusters, especially the606l/A12O3/lOp.Thecauses forvoidformationcouldbe three-fold:i) retainedfrom the as-castmaterial,especiallyforthose inclusters;ii)unhealedparticlefractureinthe surfacelayeratrelativelylow temperature;iii) weak particle interface under high local tensilestress at the ends of the particles,especiallyforthoseinclustersin the surfacelayeroftheextrudate.These voids can be avoided by controlling the processing parametersin both theprimary and secondly processing routes. The hydrostatic pressure generatedduring flat-facedie extrusion may help suppress void formation and growth. This is why the elasticmodulusand other tensile strengths (e.g., yield stress, and the ultimate tensile strength)do not declineunder an extrusion ratio ofabout 30, although the elongation is sacrificed.The improvementinhomogenizationofparticledistributionand the particle sizerefinement afterextrusion allowthe maximum potential increase of tensile properties and also the fracture toughness,if thevoidformationcanbe suppressed bygeneration ofa high hydrostatic pressure andlow tensilestressinthe surfacelayeras obtainedinhighertemperatureextrusion.3) The safe processing window for the extrusion of the Duralcan materials wassqueezed towards the high temperature side by the low speed cracking boundary. The lowspeed cracking, observed at the front end of extrudates, is believed to be induced by lowductility of the materials and void formation and growth at relative low temperature undertensile stressin the dieland zone. Both the low speed cracking and the voidformationcanbesuppressed by increasing the initial billet and die temperature and the extrusion speed withinChapter10 ConcludingRemarks236the limit of the high speed cracking boundary (incipient meltingline) with better quality andlargerproductivity ofthe PRMMCs.10.2FutureWorkTo betterunderstand thephysical and chemicalnatureofthe composites, the followingworkissuggested based onthe abovestudy.1) Because the origin of the low speed cracking is associatedwith void formation, aquantitative analysis ofthe fractionofvoidsformed underdifferenttemperature and strainrateis beneficial for a more accurate control of the processingparameters, such as temperatureand extrusion speed, to improve quality (to minimizevoids and obtain more homogenizedparticle distribution atafinerand amoreuniformparticlesize level) and productivity;2) A fracture criterion for low speed cracking or potentialmicrostructural damageduring extrusion needs to be developed and verified. The fracture criterioncan then beincorporated into the finite elementmodel to cost-effectively develop extrusion limitdiagramsfordifferentmaterials.3) An effective technique is required at the fabrication stage to improveboth theparticle distribution and the bonding strength between the particles and thematrix to preventpotential interface decohesion. New choices ofmatrix alloys with higherductility but free ofspinel formation are needed. Abetter design of the die to haveimproved quality and higherproductivity of the extruded products should also be studied.New processing technologieswhichproduce defectfreeproducts withlowerproductioncosts shouldbe explored.References 237REFERENCES[1] Chawla, K.K.: ‘Composite Materials, Science and Engineering’, Material Research andEngineering (MRE), Springer-Verlag, 1987.[2] Caron, S.; Masounave, J.: A Literature Review on Fabrication Techniques of ParticulateReinforced Metal Composites, Proc. of mt. Conf on Particulate Reinforced MetalComposites, Ed. by J. Masounave & F.G. Hamel, Montreal, Quebec, Canada, 17-29, Sept.,1990,pp.79-86.[3] Hoover, W.R.: Commercialization of DURALCAN Aluminum Composites, PrivateCommunication, Dural Aluminum Composites Corporation, San Diego, CA, USA, 1992,pp.211-217.[4] Selseth, J.E. and Lefstad, M.: Extrusion ofAluminium Matrix Composites, 5th ScandinavianSymposiumonMaterials Science, Copenhagan, May 22-25, 1989,pp.1-8.[5] Jeffrey, P.W.; Holcomb, S.: Extrusion of Particulate-Reinforced Aluminium MatrixComposite, Proc. ofmt. Conf on Particulate Reinforced Metal Composites, Ed. by J.Masounave & F.G. Hamel, Montreal, Quebec, Canada, 17-29, Sept., 1990,pp.181-186.[6] Brusethaug, S.; Reiso, 0.; Ruch W.: Extrusion of Particulate-Reinforced Aluminium Billetsmade by D.C. Casting, Proc. ofmt. Conf on Particulate Reinforced Metal Composites.Ed. by J. Masounave & F.G. Hamel, Montreal, Quebec, Canada, 17-29, Sept., 1990,pp.173-179.[7] Hams, R.W.; Morris, P.L.; Jeffrey, P.W.: Extrusion ofAluminium Metal Matrix Composites,Proc. ofmt. Symp. AdvancedStructuralmaterial, 1988,pp.53-60.[8] Allison, J.E. and. Cole, G.S.: Metal Matrix Composites in the Automotive Industry:Opportunities andChallenges,JOM, January 1993, Vol. 45,pp.19-24.[9] Dixon William: Extrusion of Particulate-Reinforced Aluminium-Based Metal MatrixComposites, 5thInternationalAluminum Extrusion Technology Seminar, Vol. 1, Chicago,illinois, USA, 19-22 May 1992,pp.429-436, TheAluminium Association.[10] Ghosh, S.: Finite Element Simulation of Some Extrusion Process Using the ArbitraryLagrangian-EulerianDescription, J. Mater. Shaping Technology, (1990), 8:53-64.[11] Embury J.D. and Zok, F.: Forming of Metal-Matrix Composites under SuperimposedHydrostatic Pressure, MMCs workshop at the University of B.C., Vancouver, B.C.,Canada, May 19-20, 1994.[12] Embury J.D.; Tao S.; Newell J. and Zok, F.: Damage Accumulation in Metal-MatrixComposites and ItsRole inHydrostaticExtrusion, Private Communication, 1991.[13] Inoue, N. and Nishihara, M. (Eds): ‘Hydrostatic Extrusion, Theory and Application’,ElsevierApplied Science Publishers, 1985.References238[14] Coffier, J.R.; Gunasekera, J.S.;Sargand, S.M.: Streamlined Diesand Profiles Extrusion,ANTEC’87,pp.203-206.[15] Gelin, J.C. and Predeleanu, M.:Finite StrainElasto-PlasticityIncludingDamage-Applicationto Metal Forming Problems, Numiform89, Thompson et a!. (Eds.),1989, Balkema,Rotterdam, pp. 151.[16] Ghosh, S.: A New Finite ElementDescription for Simulation of MetalForming Processes,Numiform 89, Thompsonetat. (Eds.),1989, Balkema, Rotterdam,pp.159.[17] Hussin, A.A.M.; Hartley, P.;Sturgess, C.E.N.; Rowe, G.W.: Elastic-PlasticFinite ElementModeling of A Cold-ExtrusionProcess Using a Microcomputer-BasedSystem, J. ofMechanical Working Technology,16 (1988), 7-19.[18] Wang, A.C.: Computer Modelingof Extrusion Elastic-Plastic Process,Computer Eng.,1988, Proc., PublishedbyASME, NewYork, USA,pp.211-216.[19] Russel, P.N.: Problems and Progress in ExtrusionStudies, Num. Method in md. FormingProcesses,Pattman/Wood/Alexander/Zienkiewicz(eds), 1982,pp.75.[20] Roll, K.; Neitzert,T.: OntheApplicationofDifferentNumericalMethods toCalculateColdForming Processes, Num.Method in md. FormingProcesses,Pattman/Wood/Alexander/Zienkiewicz(eds), 1982,pp.97.[21] Wertheimer, T.B.: Thermal Mechanically Coupled Analysis inMetal Forming Processes,Num. Method in md. Forming Processes, Pattman IWood /Alexander/Zienkiewicz (eds),1982,pp.425.[22] Abo-Elkhier, M., Orvas, G.A.; Dokainish, M.A.: A ConsistentEulerian Formulation forLarge Deformation Analysis With Reference to Metal-Extrusion Process,mt. J. NonLinearMechanics, Vol. 23, No. 1,pp.37-52, 1988.[23] Crochet, M.J.; Delvaux, V.; Marchal, J.M.: Numerical PredictionofViscoelastic ExtrudateSwell,Numiform89, Thompson eta!. (Eds.), 1989, Balkema, Rotterdam,pp.17.[24] Yamada, Y.; Wifi, A.S. and Hirakawa, T.:Analysis of Large Deformation and Stress inMetal Forming Processes by Finite Element Method, International Symposiumon MetalFormingPlasticity, Germany, 1978,pp.158-189.[25] Rusia, D.K.; Gunasekera, J.S.: AModifiedViscoplastic Formulationfor Large DeformationUsing Bulk Modules, Numiform 89, Thompson et a!. (eds), Fort Collins, Colorado, June26-30, 1989.[26] Argyris, J.H.; Doltsinis, 3. St; Luginsland, 3., Shenze Hong: NumericalSimulation ofForward Extrusion by the Finite Element Method, Numiform 89, Thompson et at. (Eds.),1989, Balkema,Rotterdam,pp.529.[27] Srinivasan, R.; Gunasekera, J.S.; Gegel, H.L. and Doraivelu, S.M.: Extrusion ThroughControlled strainRate Dies,J. Mater. Shaping Technol., Vol. 8 1990,pp.133-141.References239[28] Chen, H.L.; Lehnhoff, T.F.; Doraivelu, S.M.: A Stress RatioParameter for Studying theWorkability of Metals-Extrusion, J. Mater. Shaping Technol., Vol.8, No. 4, 1990,pp.209-218.[29] Liu, T.S., Chung, N.L.: ExtrusionAnalysis and WorkabilityPrediction UsingFinite ElementMethod, Computers & Structures, Vol. 36, No. 2,pp.369-377, 1990.[30] Shimazaki, Y.: A Penalty Function Method forNon-isothennal Axisymmetric FlowProblems,Numiform89, Thompsonetat. (Eds.), 1989, Balkema,Rotterdam,pp.593.[31] Menges, G.; Masberg, U.; Gesenhues,B.; Berry, C.: Numerical Simulation of Three-Dimensional Non-Newtonian Flow in Thermoplastics Extrusion Dieswith Finite ElementMethods, Numerical Analysis of Forming Process, Edited by J.F.T.Pittman, O.C.Zienkiewicz, R.D. Wood, and J.M. Alexander, 1984, John Wileyand Sons Ltd.pp.307-350.[32] Zienkiewicz, O.C.; Godbolt, P.N.: Flow of Plastic and Visco-Plastic Solidswith SpecialReference to Extrusion and Forming Processes, mt. J for NumericalMethods inEngineering,Vol. 8,pp.3-16, 1974.[33] Zienkiewicz, O.C.; Jam, P.C.; Onate, E.: Flow of Solids during Forming and Extrusion:SomeAspectsofNumerical Solutions,mt. J. Solids Structures, 1978, Vol. 14,pp.15-38.[34] Zienkiewicz, O.C. and Huang, G.C.: Adaptive Modeffing of Transient Coupled MetalForming Processes,Numform 89, Thompsonetat. (Eds).,1989, Balkema, Rotterdam.[35] Wang, K.C.; Carey, G.F.: Modelling Extrusion Using Adaptive Grid Refinement, Numiform89, Thompson etat. (Eds).,1989, Balkema,Rotterdam,pp.229.[36] Gelten, C.J.M.; Konter, A.W.A: Application ofMesh-Rezoning in the Updated LagrangianMethod To Metal Forming Analysis, Num. Method in md. Forming Processes,Pattman/WoodlAlexander/Zienkiewicz (eds), 1982,pp.511.[37] Wu, W.T.; Oh, S.L; Altan, T.; Miller, R.A.: Automated Mesh Generation for FormingSimulation-I, Private Communication, Scientific Forming Technology Corporation,Columbus,Ohio, 1992.[38] Park, J.J. and Kobayashi, S.: Three-Dimensional Finite Element Analysis of BlockCompression,mt. J. ofMech. Sci., Vol. 26, No. 3,pp.165-176.[39] Cheng J.-H.: Automatic Adaptive Remeshing for Finite Element Simulation of FormingProcesses,mt. .1. ofNumericalMethods in Engineering, Vol. 26, No. 1, Jan, 1988,pp.1-18.[40] Wu, J.F.; Shephard, M.S.; Dvorak, G.J. and Bahei-El-Din, Y.A.: A Material Model for theFinite Element Analysis of Metal Matrix Composite, Composite Science and Technology,Elsevier SciencePublishersLtd.,England, 1989.References240[41] Bohm, H.J. and Rammerstorfer F.G.:Micromechanical investigation ofthe processing andloading of Fiber-reinforced metal matrix composites,Materials Science and Engineering,A135, (1991),pp. 185-188.[42] Levy, A.; Papazian,J.M.: Elastoplastic Finite Element Analysisof the Effects of ThennalTreatment on Discontinuously Reinforced SiC/AlComposites, Metal & Ceramic MatrixComposites:Processing,Modeling &MechanicalBehavior,1990,pp.319-326.[43]. Zhang H.Y.; Daehn, G.S. and WagonerR.H.: The Temperature-CyclingDeformation ofParticle Reinforced Metal Matrix Composites-- A Finite Element Study,ScriptaMetallurgicaetMaterialia, Vol. 24,pp.2151-2155, 1990.[44] Zahl, D.B. and McMeeking, R.M.: TheInfluence of Residual Stress onthe Yielding ofMetalMatrixComposite,ActaMetal!. Mater., Vol.39, No. 6,pp.1117-1122, 1991.[45] Aradhya, K.S.S. and Surappa, M.K.: EstimationofMechanical Properties of6061Al-SiCpComposites Using Finite Element Method, Scripta METALLURGICA,Vol. 25,pp.817-822, 1991.[46] Ramakrishnan, N.; Okada, H.; Atluri, S.N.: Computer Simulationof TransformationInduced Plasticity Using Finite Element Method,Acta Metal!. Mater., Vol.39, No. 6,pp.1297-1308.[47] Kopp Reiner: Multi-Level Simulation of Metal-FormingProcesses, 2nd InternationalConference on TechnologyofPlasticity, Stuttgart, 24-28 Aug., 1987.[48] Kopp Reiner and Cho, Myong-Lae: Influence of Boundary Conditions onResults of theFinite Element Simulation, 2nd International Conference on Technologyof Plasticity,Stuttgart, 24-28 Aug., 1987,pp.165.[49] Sellars, C.M.; McG. Tegart, W.J.: Hot Workability,International Metallurgical Review,Review 158, Vol. 17, 1972,pp.1-24.[50] Datsko, J. and Yang, C.T.: Coffelation of Bendability of Materials with Their TensileProperties, J. ofEngineeringforIndustiy, Vol. 82, Nov. 1960,pp.309-314.[51] Lathem, D.J. and Cockcroft, M.G.: Ductility and the Workabilityof Metals, J. Inst. Met.,1968,pp.33.[52] Manoharan M.; and Kamat, S.V.: On the Fracture Toughnessof Particulate ReinforcedMetal Matrix Composites, Scripta Metallurgica et Materialia, Vol. 25,pp.2121-2125,1991.[53] Lloyd, D.J.: Particulate Reinforced Composites Producedby Molten Metal Mixing, HighPeiformance Compositesforthe 1990s, Ed. by S.K. Das, C.P. Ballardand F. Marikar, TheMinerals, Metals and Materials Society, 1991,pp.33-45.[54] Kalu, P.N., McNelley, T.R.: Microstructural Refinement by ThermomechanicalTreatmentof a Cast and Extruded 6061 Al-Al203Composite, Scripta Metallurgica et Materialia,Vol. 25, No. 4., April 1991,pp.853-858.References241[55] Clode, M.P. and Sheppard, T.: Extrusion Limit Diagrams Containing StructuralandTopological Information for AA6063 Aluminum Alloy, Material Scienceand Technology,April 1993, Vol. 9, pp. 313-318.[56] Sheppard,T.: TheExtrusionofAluminumAlloys: AThermomechanical Process,AluminumAlloys ‘90. Proceedings of the 2nd mt. ConL of AluminumAlloys--Their Physical andMechanical Properties, Oct. 9-13, 1990, Beijing, China.Ed. C.Q. Chen, and E.A. Starke,Jr.,pp.744-754, InternationalAcademicPublishers.[57] Raybound, D. and Sheppard,T.: AxisymmetricalExtrusion: The EffectofTemperature Riseand Strain Rate on the Activation Energyand Material Constants of Some AluminumAlloys and Their Relation to Recrystallization,Substructure, and Subsequent MechanicalProperties,JournalofInstituteofMetals, Vol. 101,1973,pp.65-72.[58] Sheppard, T. and Raybound, D.: ANew Approach to the ConstructionofExtrusion-Limit-Diagrams, Giving Structural Infonnationwith Application toSuperpure Aluminum and Al-Zn-Mg Alloys,JournalofInstitute ofMetals, Vol. 101, 1973,pp.72-78.[59] Oddvin Reiso: The Effect of Billet Preheating Practice on ExtrudabilityofAIMgSi Alloys,4thmt. AluminumExtrusion TechnologySeminar, Chicago, Di, 1988.[60] Zasadzinski, J.; Libura,W.; Richart, 3. and Misiolek, W.Z.: Modeling ofTemperature-SpeedParametersinAluminumExtrusion,LightMetalAge, August, 1992,pp. 60-64.[61] Richardson,G. 3.; Hawkins, D. N. and Sellars, C. M.: ‘WorkedExamples in Metalworking’,The InstituteofMetals, London, 1985,pp.144-161.[62] Sheppard, T.: Extrusion of AA2024 Alloys, Materials Science and Technology, Vol.9,May, 1993,pp.430-440.[63] Meadows, B. I. and Culler, M. J.: A Theoretical Derivation of Stress/StrainRate/Temperature Relationships in the Extrusion of Al-Mg-Si Type Alloys, Journal ofInstituteofMetals, Vol. 97, 1969,pp.321-326.[64] McQueen, H.J. and Ceffiers, O.C.: Application of Hot Workability Studies to ExtrusionProcessing, I. ExtrusionControl Parameters and Constitutive Equations, Materials Forum,Vol. 17, 1993, pp. 1-13.[65] Castle, A.F. and Sheppard, T.: Hot-Working Theory Applied to Extrusion of SomeAluminumAlloys,Metals Technology, Vol. 3, October 1976,pp.454-475,.[66] Brusethaug, S. and Reiso, 0.: Extrusion of SiCp Reinforced Al-Alloys, 12th RisoInternational Symposium on Materials Science, 1991, Roskilde, Denmark, Riso NationalLaboratory.[67] Sheppard, T.: Press Quenching of Aluminum Alloys, Materials Science and TechnologyVol. 4, July 1988,pp.635-643.[68] Geitser, I. S.: MasterThesis,TheUniversityofBritishColumbia, 1992.References242[69] Sheppard, T.; Raybound, D.: OnLoad and Temperature Rise duringthe Extrusion ofSuperpure Al. Al-Zn, andAl-Zn-Mg Alloys,J. Inst. Metals, 1973, Vol. 101,PP.33-44.[70] Grasmo, K.; Hoithe, K.; Støren,S.; Valberg, H.; Flatval, R.; Hanssen, L.; Lefstad,M.;Lohne, 0.;Web, T.; ørsund,R.; Herberg,J.: Modelling ofTwo-DimensionalExtrusion, in‘5th International Aluminum ExtrusionTechnology Seminar’, Chicago,ilL, May, 1992,pp.367-376,Washington,TheAluminumAssociation.[71] Reinikainen, T.; Andersson, K.; Kivivuori,S.; Kothonen, A.S.: Finite-ElementAnalysis ofCopper ExtrusionProcesses,J. Mater. Proc.Tech., Vol. 34, 1992,pp.101-108.[72] Alto, A.; Galantucci, L.M.; Tricarico,L: AParametric FEM Analysis ofExtrusionUsing aPersonalComputer, J. Mater. Proc. Tech., Vol. 31,1992,pp.335-345.[73] Devadas, C.; Celliers, O.C.: Metal Flow duringthe Extrusion Process, in ‘5th InternationalAluminum Extrusion Technology Seminar’,Chicago, ifi., May, 1992,pp.359-368,Washington,The AluminumAssociation.[74] Davies, C.HJ.; Chen, W.C.; Samarasekera,I.V.; Hawbolt, E.B. and Brimacombe,J.K.:Extrusion ofMetal Matrix Composites, -Modelingand Experimental, Proceeding of123rdTMSAnnualMeeting, SanFrancisco, Feb. 27-Mar.3, 1994.[75] Brechet, Y.; Newell, J.; Tao, S. and Embury, J.D.: A Noteon Particle Comminution atLarge Plastic Strains in Al-SiC Composites, Scripta MetallurgicaetMaterialia, Vol. 28,No. 1, 1992,pp.47-51.[76] Brechet, Y.; Embury, J.D.; Tao, S. and Luo, L.: DamageInitiation in Metal MatrixComposites,ActaMetall. mater., Vol. 39, No. 8,pp.1781-1786, 1991.[77] Humphreys, F.J.; Kalu, P.N.: Dislocation-Particle Interactionsduring High TemperatureDeformation ofTwo-Phase AluminumAlloys,ActaMetall. Mater.,Vol. 35, No. 12, 1987,pp.2815-2859.[78] Jonas, J.J.; Sellars, C.M.; Tagart, W.J. McG.: Strength and Structure underHot WorkingConditions,MetallurgicalReview, Vol. 14, 1969, Review No.130, 1-24.[79] Rao, K.P.; Hawbolt, E.B.: Development of Constitutive Relationships Using CompressionTesting of a Medium Carbon Steel, J. Engrg. Mats.& Tech. (Trans. ASME), Vol. 114,Jan., 1992, 116-123.[80] Sheppard, T. and Wright, D.S.: Determination ofFlow Stress: Part 1 Constitutive EquationforAluminiumAlloysatElevatedTemperature,Metals Tech., Vol. 6, 1979,pp.215-223.[81] Davies, C.H.J.; Chen, W.C.; Geltser, I.S.; Samarasekera, I.V.; Hawbolt,E.B. andBrimacombe, J.K.: Hot defomiation of 6061/Aluminacomposite materials, Proceedingsofthe 32nd CIMMetallurgist Conf., Quebec, Canada,Aug. 22-24, 1993.[82] Oh, S. I.; Wu, W.T.; Tang, J.P.; Vedhanayagam A.: Capabilitiesand applications ofFEMcodes DEFORM: the perspective ofthe developer, J. Mater. Proc. Tech., 1991, Vol. 27,25-42.References243[831 Kobayash, S.; Oh, SI.; Altan T:‘Metal Formingand the Finite ElementMethod’, 1st Ed.,pp.111-130, 1989, O.U.P.,Oxford, U.K..[84] Zienkiewicz,O.Z.; Taylor, R.L.:‘The Finite ElementMethod, BasicFormulation andLinearProblems’,Vol. 1,4thedition,McGraw-HillBookCompanyEurope, 1993.[85] Sheppard, T.:Extrusion of AA2024Alloy, Mater.Sci. Technol., Vol.9, May 1993,pp.430-440.[86] Hlady,C.O.: Master Thesisof Applied Science,The Universityof British Columbia,Vancouver, B.C., Canada,1994.[87] Chevalier,L.; Dahan, N.: Metal-FormingProcess Analysisby the ViscoplasticityMethod:Application to Stationaryand Non-StationaryProcesses, J. Mater.Proc. Tech., 1992,Vol.31, 199-208.[88] McShane H.B.;Sheppard, T.; Raghunathan,N.; Subramaniyan:On Property ProcessRelationships WhenExtruding AA2024Alloy, in ‘Intl.Conf on AluminumAlloy 2’,Beijing, China, 1990,(ed. C.Q. Chen, E.A.Starke),pp.325-336, InternationalAcademicPublishers.[89] Hunt, W.H.;Jr., Brockenbrough,J. and Magnusen, P.E.:An Al-Si-Mg CompositeModelSystem: MicrostructuralEffects on Deformationand Damage Evolution,Scripta Metal!.Mater., Vol. 25, No. 1,1991, pp. 15-20.[90] Liu, D.S.; Manoharan,M. and Lewandowski,J.J.: Effects of Microstructureon theBehavior of an AluminumAlloy and an AluminumMatrix CompositeTested under LowLevels ofSuperimposedHydrostaticPressure,Met. Trans. A, 20A,2409-2417 (1989).[91] Lewandowski,J.J.; Liu,D.S. and Liu,C.: Observation on the EffectsofParticulate SizeandSuperposed PressureonDeformation ofMetal MatrixComposites,Scripta Metall. Mater.,Vol. 25, No. 1, 1991,pp.21-26.[92] Lloyd, D.J.:Aspects ofFracturein Particulate ReinforcedMetal Matrix Composites,ActaMetall. Mater, Vol.39, No. 1, 1991,pp.59-71.[93] Mummery, P.M.;Derby, B. and Scruby,C.B.: Acoustic Emissionfrom Particulate-Reinforced MetalMatrixComposites,Acta metal!.mater., Vol. 41, No.5,pp.1431-1445,1993.[94] Mochida,T.; Taya, M.; and Obata, M.: Effectof Damaged Particleson the Stiffness of aParticle/Metal MatrixComposite, JSME InternationalJournal, Series I, Vol. 34,No. 2,1991.[95] Mochida,T.; Taya M. and Lloyd, D. J.: Fracture ofParticles in a Particle/MetalMatrixComposite under PlasticStraining and Its Effecton the Young’s Modulusof theComposites,MaterialsTransactions,JIM, Vol. 32, No. 10, 1991,pp.931-942.[96] MetalHandbook, Metallographyand Microstructure, 9thEdition, Metals Park,Ohio, ASM,Vol. 9, 1985,pp.352.References 244[97] Pickering, F.B.: ‘The Basis of Quantitative Metallography’, Institute of MetallurgicalTechnicians,Monography No. 1, July 1975, pp. 5.[98] Davies, C.H.J.; Chen, W.C.; Hawbolt, E.B.; Samarasekera, I.V. and Brimacombe, J.K.:Particle Fracture During Extrusion of 6061/ Alumina Composites, Scripta Metallurgica etMaterialia, Vol. 32, 1995.[99] Ehrstrom, J.C.; Kool, W.H.: Migration of Particles during Extrusion of Metal MatrixComposites, J. ofMaterialsScience Letters, Vol. 7, No. 6, 1988,pp.578-580.[100] Newell, J.: MasterThesis, McMasterUniversity, Hamilton, Ontario, Canada, 1992.[101] Thao, D.; Tuler, F.R. and Lloyd, J.D.: Fracture at Elevated Temperature in a ParticleReinforcedComposite,ActaMetall. Mater., Vol. 42, No. 7,pp.2525-2533, 1994.[102] Metal Handbook, MechanicalTest, 9thEdition, MetalsPark, Ohio, ASM, Vol. 1, 1985.[103] Yokobori, T.; Yokobori, A.T. Jr. and Awaji, H.: Stochastic Approach to StatisticalAspects ofFailure,ProbabilisticMethods in theMechanicsofSolidsandStructures, ed. S.Eggwertz, and N.C. Lind,IUTAM Symposium Stockholm/Sweden 1984,pp.199-212.[104] Mihashi, H.: Stochastic Approach to Study the Fracture and Fatigue of Concrete,Probabilistic Methods in the Mechanics ofSolids and Structures, ed. S. Eggwertz, andN.C. Lind, IUTAM Symposium Stockholm/Sweden, 1984,pp.307-317.[105] Dixon, W.: Particle Fracture during Drawing and Extrusion, Private Communication,DuralcanUSA, SanDiego, C.A.,USA, May 1992.[106] Xu, X.Q. and Watt, D.F.: Basic Role of a Hard Particle in a Metal Matrix Subjected toTensile Loading, Private Communication, Department of Mechanical Engineering,University ofWindsor,Windsor, Ontario, Canada, N9B 3P4.[107] Davis, L.C. and Allison, J.E.: Residual Stresses and Their Effects on Deformation inParticle Reinforced Metal Matrix Composites, Metallurgical Transactions A, Vol. 24A,November, 1993,pp.2487-2496.[108] Finot, M.; Shen, Y.-L; Needleman, A: and Suresh, S.: Micromechanical ModelingofReinforcement Fracture in Particle-Reinforced Metal-Matrix Composites, MetallurgicalandMaterials Trans. A, Vol. 25A, Nov. 1994,pp.2403-2420.[109] Kobayashi, S. and Lee, C. H.: Deformation Mechanics and Workability in UpsettingSolidCircularCylinders,Proc. NAMRC, Vol. 1,p.185.[110] Oh. S.I. and Kobayashi, S.: Workability of Aluminum Alloy 7075-T6in Upsetting andRolling, Trans. ASME, J. ofEngr.formd., 1976,p.1.[111] Ferry M. and Munroe P.R.: The Effect of Matrix Temper on ParticulateIntegrity in anAl/A12O3Metal MatrixComposite, ScriptaMetallurgica etMaterialia, Vol. 31, No. 2,pp.143-148, 1994.[112] Syu, D.-G. C and GhoshA.K.: Forging Limits for anAluminumMatrixComposite:PartII.Analysis,Metal. andMaterials TransA, Vol. 25A, September, 1994,pp.2039-2047.References245[113] Poole, W.J.; Embury, J.D.; MacEwen, S. and Kocks, U.F.: Large StrainDeformation of aCopper-Tungsten Composite System, I. Strain Distributions, PhilosophicalMagazine A.,1994, Vol. 69, No. 4,pp.645-665.[114] Poole, W.J.; Embury, J.D.; MacEwen, S. and Kocks, U.F.: Large StrainDeformation of aCopper-Tungsten Composite System, II. Applications, PhilosophicalMagazine A., 1994,Vol. 69, No. 4,pp.667-687.[115] Hunt, W. H., Jr.: Redefming the Limits of Aluminum-Based Materials,JOM, January1993,p.18.[116] Derby, B.: Fracture and Damage in Metal Matrix Composites, Los Alamos National LabWorkshop, USA, Oct. 28-30, 1992.[117] Sheppard T. and Clode M.P.: The Origin ofSurface Defects during Extrusion ofAA6063Alloy, 4th International Aluminum Extrusion Technology Seminar, Vol. 2, Chicago,illinois, USA, 11-14 April 1988,pp.329-341.[118] Data Brochure on DURALCAN Composites for Wrought Products, Mechanical andPhysical Property Data, Duralcan USA, Division of Alcan Aluminum Corporation, SanDiego, California92121, 1991.[119] Blecic, S.; Libura,W. and Zasadzinski, J.: Extrusion TechnologyofAIMgSi Alloys, in ‘5thInternational Aluminum Extrusion Technology Seminar’, Vol. H, The AluminumAssociation, Washington, 1992, 485-494.[120] Chen, C.C., Oh, S.I. and Kobayashi, S.: Ductile Fracture in Axisymmetric Extrusion andDrawing, Part 1: Deformation Mechanics ofExtrusion and Drawing, Trans. ASME, J., Vol. 101,pp.23-35, 1979.[121] Laue, K. and Stenger, H.: ‘Extrusion: Processing, Machinery Tooling’, Translators fromthe German Version, A.F. Castle, Gernot Lang, Metal Park, Ohio, American Society forMetals, c1981.[122] Lloyd, J.D.: Factors Influencing the Tensile Ductility of Melt Processed ParticleReinforced Aluminium Alloys, Private Communication, Kingston Research andDevelopmentCenter, AlcanInternationalLimited, 1994.[123] Lloyd, J.D.; Jin, I. and Weatherly, G.C. Controlling the Interface Reaction in AluminaReinforcedAluminumComposites, ScriptaMetallurgica etMaterialia , Vol. 31, No. 4,pp.393-396, 1994.[124] Ghosh, A. K: Solid-State Processing, Chapter 2, ‘Fundamentals of Metal MatrixComposites’, Ed. by Subra Suresh, Andreas Mortensen, and Alan Needleman,Butterworth-Heinemann, 1993,pp.23-41.


Citation Scheme:


Usage Statistics

Country Views Downloads
United States 7 0
Germany 4 14
India 3 2
Belgium 3 0
Nigeria 3 0
Iran 2 0
Russia 1 0
Netherlands 1 0
South Africa 1 10
Japan 1 0
City Views Downloads
Unknown 8 15
Ashburn 4 0
Leuven 3 0
Erlangen 2 0
Aachen 2 0
Arvada 1 0
Wilmington 1 0
Redmond 1 0
Chandigarh 1 0
Johannesburg 1 0
New Delhi 1 1
Tokyo 1 0

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}
Download Stats



Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            async >
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:


Related Items