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

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EXTRUSION OF ALUMINA PARTICULATE REINFORCEDMETAL MATRIX COMPOSITESByWEI CHANG CHENB. A. Sc. Beijing University of Iron and Steel Technology 1983M. Sc. University of Science and Technology Beijing 1986M. A. Sc. University of British Columbia 1991A THESIS SUBMITthD IN PARTIAL FULFILLMENTOF THE REQUIREMENT FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESMETALS AND MATERIALS ENGINEERINGWe accept this thesis as conformingto the required standardTHE UNWERSITY OF BRITISH COLUMBIADecember 1994© Wei Chang Chen, 1994In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may 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 shall not be allowed without my writtenpermission.(Signature)Department of fr14TEf1FiL 5’ii.The University of British ColumbiaVancouver, CanadaDate Fd. 24 - 95DE-6 (2188)UABSTRACTAlumina particulate reinforced metal matrix composite is a new kind ofmaterial, whichhas wide potential applications in automobile industry. The study of its physical nature duringextrusion process is essential to optimize the process which may improve its mechanicalproperties and increase its productivity to finally reduce its cost and make it more competitiveto other materials.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 withdifferent ram 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 analyzer in the deformation zone of a billetand the extrudates from the plant trials.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 of 6061/A123/lOp and 6061/A123/20p weredeveloped 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 of the 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.This page left blank intentionallyivVTABLE OF CONTENTSABSTRACTTABLE OF CONTENTS vTABLE OF TABLES xiTABLE OF FIGURES xiiiNOMENCLATURE xixACKNOWLEDGEMENTS xxiiDEDICATION xxiiiChapter 1 INTRODUCTION 11.1 Characteristics of Metal Matrix Composites 11.2 Fabrication of Particulate Reinforced Metal Matrix Composites41.3 Processmg and Applications of Particulate Reinforced MMCs1.3.1 Secondary Deformation Processing 41.3.2 Applications 5Chapter 2 LiTERATURE REVIEW 62.1 Extrusion Process 62.2 Extrusion Related Defects of Particulate Reinforced MMCs (PRMMCs) 82.2.1 Extrusion Related Defects 92.2.2 Hot Workability of PRMMCs 142.3 Development of Extrusion Limit Diagrams 172.3.1 Peak Pressure 182.3.2 Temperature Rise 192.4 Finite Element Analysis of An Extrusion Process 212.4.1 Finite Element Analysis of an Extrusion Process 212.4.2 Development of an Extrusion Limit Diagram Using FEM 22vi2.4.3 Fracture Criteria for Monolithic Metals 242.5 Finite Element Analysis of the PRMMC 252.5.1 Multilevel Finite Element Method 292.5.2 Particle Fracture Model during Deformation 312.5.3 Microscopic Analysis of PRMMCs under Larger Deformation 33Chapter 3 SCOPE AND OBJECTIVES 343.1 Scope and Objectives3.2 MethodologyChapter 4 EXPERIMENTAL 374.1 Gleeble Tests4.2 Plant Trials at UAC, Anaheim 404.2.1 Extrusion Procedure 404.2.2 Extrusion Data 444.3 Pilot Extrusion at KRDC, Kingston 504.3.1 Extrusion Procedure 504.3.2 Extrusion Data 524.4 Extrusion Surface Defects4.5 Effect of Extrusion Conditions on the Mechanical Properties 584.5.1 Tensile Tests 584.5.2 Property Changes after Extrusion 5864Chapter 5 MODELING EXTRUSION OF THE PRMMCs5.1 Mathematical Model of the Extrusion Process 645.1.1 Finite Element Model 645.1.1.1 Flow Formulation 645.1.1.2 Boundary Conditions 685.1.2 Input Data 705.1.3 Finite Element Solution 70vu5.2 Sensitivity Analysis of the Model 725.3 Extrusion Process Simulation5.3.1 Processing Conditions 755.3.2 Model Predictions 765.3.2.1 Deformation Behavior 765.3.2.2 Temperature Distribution 845.3.2.3 Comparison of Predictions with Measured Data 865.4 Validation of Model Predictions 895.5 Summary 92Chapter 6 MICROMECHANICAL ANALYSIS OF THE PRMMC DURING LARGE 94DEFORMATION6.1 Obstacles and Challenges of Micromechanical Analysis of the PRMMCs6.1.1 Particle Phenomena 946.1.2 Matrix Phenomena 956.1.3 Modeling Constraints 956.2 Micromechanical Analysis during Plane Strain Compression 966.2.1 Twin-Particle Model 986.2.2 Multiple-Particle Model 1046.3 Micromechanical Analysis during Cylindrical Compression 1066.3.1 Single-Particle Model 1076.3.1.1 Material Flow of a Cylindrical Specimen Containing a Particle 1096.3.1.2 Effect of Particle Shape 1156.3.2 Twin-Particle Model 1206.3.2.1 Effect of Reduction 1216.3.2.2 Effect of Particle Spacing 1216.4 Model Validation 1266.5 Conclusions 126‘InChapter 7 PARTICLE FRACTURE OF THE PRMMC DURING EXTRUSION 1287.1 Specimen Preparation for the PRMMCs 1297.2 Macroscopic Examination of Metal Flow in the Deformation Zone 1307.3 Particle Fracture during Extrusion 1347.3.1 Qualitative Microstructure Analysis 1347.3.1.1 Particle Deformation Behavior in the Deformation Zone 1347.3.1.2 Microstructure Analysis of the Extrudates 140A. Comparison of Microstructure in Longitudinal and Transverse Sections 141B. Comparison of Microstructure for 606 l/A1ZO3/20p and 606l/A12O3/lOp 1437.3.2 Image Analysis of Particle Distribution in Extrudates 1467.3.2.1 Homogeneity of Particle Distribution 1467.3.2.2 Particle Size 1497.3.2.3 Aspect Ratio of Particles 1547.3.2.4 Particle Orientation 1567.4 Modeling Particle Fracture during Extrusion 1577.4.1 Particle Fracture Probability at High Temperature 1577.4.2 Particle Fracture Model during Extrusion 1587.4.3 Application of the Model 1607.5 Discussion 1627.5.1 Microstructure Comparison before and after Extrusion 1637.5.1.1 Comparison of Particle Distribution before and after Extrusion 1637.5.1.2 Particle Size Refmement after Extrusion 1687.5.2 Particle Fracture Modes during Extrusion 1687.5.3 Correlation between Particle Fracture and Bulk Deformation Behavior 1701737.6 SummaryChapter 8 ORIGIN OF LOW SPEED CRACKING DURING EXTRUSION OF THE 177PRMMCsix8.1 Microstructure Examination of Low-speed Cracks 1778.2 Particle Behavior and Microscopic Damage 1808.2.1 Particle Fracture 1808.2.2 Void Formation 1838.3 Effect of Processing Parameters on Low Speed Cracking 186Effect of Ram Speed 189Effect of Billet Temperature 193Effect of Die Temperature 197Effect of Friction at Die Interface 198Effect of Extrusion Ratio 200Effect of Volume Fraction of the Composites 2028.4 Mechanism of Low Speed Cracking 2048.5 A Preliminary Criteria for Low Speed Cracking 206Chapter 9 EXTRUSION OF THE PRMMCs 2109.1 Development of Extrusion Limit Diagram 2119.1.1 Using Empirical Equations 2119.1.2 Using Finite Element Method 2159.1.2.1 Application of the Finite Element Model 2159.1.2.2 Comparison of Extrusion Limit Diagrams 2179.2 Extrusion Limit Diagram with Low Speed Cracking Boundary 2209.2.1 Low Speed Cracking Boundary 2209.2.2 Effect of Extrusion Ratios 2229.2.3 Extrusion Limit Diagram with Low Speed Cracking Boundary 2239.3 Extrusion of the PRMMCs 2249.3.1 Minimization of Microstructural Damage during Extrusion 2259.3.2 Improvement in Particle Distribution and Size Refinement 2299.3.3 Quality and Productivity of the PRMMCs 231xChapter 10 CONCLUDING REMARKS 23410.1 Summary and Conclusions 23410.2 Future Work 236REFERENCES 237xTABLE OF TABLESTable 1.1 illustration of the principle factors linked with the aspect ratio 2Table 2.1 Microstructure observed in the particulate reinforced composite before 13and after extrusionTable 4.1 Material constants for the constitutive equation of the Composites 40Table 4.2 Extrusion programs for the 7” press at UAC 41Table 4.3 Billet temperatures immediately prior to extrusion at UAC 43Table 4.4 Plant trial conditions at KRDC 51Table 4.5 Billet dimensions of each test at KRDC 53Table 4.6 Measured test data of the plant trials at KRDC 53Table 4.7 Extrudate data from plant trials at UAC 57Table 4.8 Tensile test results of extrudates from the plant trials at KRDC 59Table 5.1 Some data for sensitivity analysis of the FEM model 72Table 5.2 Processing Conditions for Two Simulations 76Table 6.1 Simulation conditions for plane strain deformation 97Table 6.2 Simulation conditions for cylindrical compression test 107Table 6.3 Particle sizes studied 109Table 6.4 Comparison of model predictions with measured data 126Table 7.1 Polishing procedure for Duralcan materials at KRDC 129Table 7.2 Polishing procedure used at UBC for Duralcan materials 130Table 7.3 Extrusion conditions of the Trial S92-3 of 6061/Al2/20p 131Table 7.4 List of examined extrudates with two different cross-sections 141Table 7.5 Statistical results for volume fraction distribution of the two composites 147Table 7.6 Statistical results for the quantitative metallography 153Table 7.7 Average number of parts fractured from a single particle in 159606l/A123/20pTable 7.8 Comparison of model predictions with measured data 162Table 8.1 Tensile stress in particles and matrix at different reductions 182xliTable 8.2 Standard conditions for parametric study 188Table 9.1 Constants in Eq. (9.1) for the composites 211Table 9.2 Extrusion conditions for the specimens examined under 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 OF FIGURES7101518232627293036384245464647474848495254555658606162Schematic of a forward extrusion processTensile elongation to fracture against strength for A356 alloy and itscomposites with different volume fractions of SiCp before and after extrusionat different extrusion temperatures of 400°C and 600°CStrain dependence of fractured particle of 606 1/SiCp MMCsA schematic extrusion limit diagramSchematic extrusion limit diagram with low speed crackingFinite element model used by Aradhya et alMaster mesh for generating different microscopic morphologiesThe crack morphologies generated by the FEM study for differentoverall fraction of the angular Zr02with transformation(a) FEM mesh with local refinement during a plane-strain upsetting; (b) Stressdistribution along the line PQ (Eh=l% calculated with ABAQUS)’Methodology for the extrusion of alumina particulate reinforced MMCsSchematic of the Gleeble test set-upSchematic of extrusion setup for Duralcan trialsTypical load-stroke curve with variation of ram speed (S92-3)Die temperature increase during extrusion (S92-3)Effect of homogenization on extrusion force (S92-3 and S92-4)A weak correlation of increasing ram speed with increasing die temperatureduring extrusion (S92-5)Effect of billet temperature on extrusion force (S92-5 and S92-6)Effect of billet length on extrusion force during extrusion (S92-3 and J94-12)Effect of volume fraction on extrusion force during extrusion(606 1/A1203/1Op: J94-3, and 606 l/A12O3/2Op: J94-7)Effect of extrusion ratio on extrusion force (J94-4, J94-lO, J94-15)Schematic drawing of the extrusion press at KRDCTypical load-stroke curve during extrusion at KRDC (K-7)Variation of ram speed at the press pressure limit (K-li)Low speed cracking at the front end of two extrudatesSchematic of a tensile test specimenTensile property under different extrusion ratiosElongation of the composites as a function of extrusion ratio(a) Tensile property change of 6O6l/A123/lOp for 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/A12O3/2Op for different extrusion ratios with a true volume fractionfrom 19.2% to 19.8%Corresponding elongation values at different extrusion ratios for bothcompositesSchematic of an extrusion pressInitial finite element mesh for the billet and its surrounding toolsSensitivity of load stroke curve to the number of elements in the billetSensitivity of the maximum temperature to the number of elements in thebilletMaterial flow near the end of upsetting stageEffective strain distribution near the end of upsetting stageVelocity distribution in the billet after a ram displacement of 40.7 mm in thelarge extrusion press; length of arrow is proportional to velocityVelocity distribution in the billet after a ram displacement of 26.7 mm in asmall extrusion press; length of arrow is proportional to velocityMean stress distribution in the billet at a ram displacement of 40.7 mm in thelarge extrusion press (negative values denote compressive stresses)Mean stress distribution in the billet at a ram displacement of 26.7mm in thesmall extrusion press (negative values denote compressive stresses)Effective strain distribution of the billet in the small pressEffective strain rate distribution of the billet in the small pressTemperature distribution in the large extrusion pressTemperature distribution in the small extrusion pressComparison of predicted force with measured data (large press)Comparison of predicted force with measured data (small press)Comparison of predicted temperature with measured data (large press)Comparison of FEM force with measured data corrected for extrusion presscompliance according to Eq. (5.26); large pressComparison of FEM force with measured data corrected for extrusion presscompliance according to Eq. (5.26); small pressInitial fmite element meshes for each object of plane strain deformationInitial finite element mesh around two particlesEffective strain distribution at a reduction of 49%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 stress in the particles at different reductionsLocalized effective strain distribution at a reduction of 1%Localized effective stress distribution at a reduction of 1%Localized mean stress distribution at a reduction of 1%Initial mesh and location of a particle in a cylindrical specimenEffective strain distribution in the cylindrical specimen with and without aparticle at a reduction of 65%Effective strain distribution around the particle at a reduction of 65%Effective strain distribution along the center line of the specimen underdifferent reductionsEffective stress distribution in the cylindrical specimen with and without aparticle at a reduction of 65%Effective stress in the matrix and in the particle at a reduction of 65%Mean stress distribution in the cylindrical specimen with and without aparticle at a reduction of 65%Mean stress distribution both in the matrix and in the particle at a reduction of65%Effect of particle shape on damage factor at a reduction of 65%Effect of particle shape on strain distribution at a reduction of 65%Effect of particle shape on effective stress variation during compressionEffective strain distribution under different reductions with an initial particlespacing of 120 p.mMean stress distribution in the matrix and in the two particles under differentreductions with the initial particle spacing of 120 p.mEffect of particle spacing on strain distribution at a reduction of 65%Comparison of predicted value with measured dataMetal flow of a billet in a containerSchematic positions for the pictures taken with low magnificationMetal flow in the deformation zone during extrusionSchematic positions for the pictures taken for micro examinationTypical particle distribution in the Locations 1 -9Schematic of examined extrudate specimenTypical characteristics of particles after extrusion of 6061/A12O3/2Op at anextrusion ratio of 34Typical characteristics of particles after extrusion of 6O61/A123/lOp at anextrusion ratio of 34xviFigure 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 of volume fraction for 6061/Al203/lOpHistogram of volume fraction for 606 1/AlO3/20pHistogram of the particle diameter for Sample B3 of 6061/A1z0/20pHistogram of the particle diameter for Sample B6 of 6061/A1O/lOpHistogram of the particle area for Sample B3 of 6061/AI23/20pHistogram of the particle area for Sample B6 of 6O6l!A1/lOpHistogram of the aspect ratio for Sample B3 of 606l/Al23/20pHistogram of the aspect ratio for Specimen B6 of 6061/A1/lOpHistogram of orientation of the particles with respect to extrusion directionfor the Sample B3 of 6061/AlOf20pHistogram of orientation of the particles with respect to extrusion directionfor the Sample B6 of 6061/A1203/lOpFracture probability variation in the deformation zoneParticle size reduction during extrusionMicrostructure of 6061/AlO3/l0p before and after extrusionMicrostructure of 6061/A12/20p before and after extrusionVariation of maximum and minimum alumina particle dimensionAspect ratio of alumina particles of 6061/A12O3I2Op in back end of a billetand in extrudateOrientation of alumina particles of 6061/A12O3/20p in back end of a billet andin extrudateA schematic diagram for three particle-fracture modes during extrusionEffective strain rate distribution in the deformation zoneMean stress distribution in the deformation zoneShear stress distribution during extrusionVoid formation near a low speed crack tip of J94-14 of 6061/A123/20p inlongitudinal sectionVoid formation near a low speed crack tip of J94-1 lB of 6061/A12O3/lOp inlongitudinal sectionTensile stress in a particle under plane strain condition at a reduction of 10%Tensile stress distribution in the matrix and around particlesTensile stress distribution in the monolithic material at a reduction of 10%under plane strain conditionTemperature distribution of billet and die at steady state extrusionTensile stress (ar) distribution at the die interface zoneEffect of ram speed: (a) Maximum temperature in the die land zone duringFigureFigureFigureFigureFigureFigure8.38.48.58.68.78.8xviiextrusion; (b) Maximum tensile stress in the die land zone during extrusionTemperature distribution on both side of the die interface at a ramdisplacement of 30mmEffect of ram speed on strain distribution through radius directionEffect of ram speed on stress distribution (az) through radius directionEffect of ram speed on effective strain rate variation in extrudateEffect of initial billet temperature:(a) Max. temperature in the die land zoneduring extrusion; (b) Max. tensile stress in the 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 of the die interface under different initial dietemperaturesEffect of friction condition at die interface: (a) Maximum temperature in thedie land zone during extrusion; (b) Maximum tensile stress in the die landzone during extrusionThermal 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 volumefractionVariation of E value during different conditions but same extrusion ratioVariation of E value during extrusion at different extrusion ratiosExtrusion limit diagram at an extrusion ratio of 28 for 6061IAl2O3/20pfor thepress at KRDCExtrusion limit diagram at a ram speed of 12.5mm/s for 6061/Al23/20p forthe press at KRDCFigure 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 Extrusion limit diagram for 60611A123/20p at an extrusion ratio of 34 for the 214large press at UACFigure 9.4 Extrusion limit diagram for 6061/A123110pat an extrusion ratio of 34 for the 214large press at UACFigure 9.5 Extrusion limit diagram for 606l/A123/20p for the press at KRDC 216Figure 9.6 The limit diagram for 6061/A123/20pfor the press at UAC 217Figure 9.7 Comparison of the extrusion limit diagram for 6061/A123/20p for the press 218at KRDC using different techniquesFigure 9.8 Comparison of the extrusion limit diagram for 6061/A123/20p for the press 219at UAC using different techniquesFigure 9.9 The extrusion limit diagram for both 6061/A123/lOp and 6061/A123/20p 219using the empirical equation techniqueFigure 9.10 Low speed cracking boundary for the extrudate of 6061/A123120p at an 221extrusion ratio of 13Figure 9.11 Low speed cracking boundary for the extrudate of 6061/A123/20p at an 221extrusion ratio of 34Figure 9.12 Low speed cracking boundary for the extrudate of 6061/A123/20p at an 222extrusion ratio of 52Figure 9.13 Effect on extrusion ratios on low speed cracking boundary during extrusion 223of 606l/A123/20pFigure 9.14 Extrusion limit diagram of 6061/A123/20p for the press at UAC with low- 224speed cracking boundariesFigure 9.15 Voids in the surface layer of an extrudate of 606l/A12O3/2Op at an extrusion 227ratio of about 34 without low speed surface cracking (front end of J94-14)Figure 9.16 Voids in the surface layer of an extrudate of 6O6l/AI23I1Op at an extrusion 228ratio of about 28 with low speed surface cracking (front end of K-6)Figure 9.17 SEM image observed in the surface layer of the extrudate at an extrusion 230ratio of about 34 without low speed surface cracking (back end of J94-14)NOMENCLATUREA, B, C, E, Experimental constantsF, a, bCross section of a billet area, m2C1(t),C2(t) Time-dependent constant in temperature analysisProduct of fracture stress and fracture strain of a material, MPac, specific heat, J/kg-K[C] Heat capacity matrixd Diffusion distance, mD Volume equivalent particle diameter, jimD1 Mean refined volume equivalent particle diameter, jimDB Initial billet diameter, mInside diameter of a container, mExtrudate diameter, mB, E0 Elastic modulus of a solid phase, GPaOverall stiffness of a press, kN/mmB Product of max. tensile stress and max. effective strain during extrusionF1 Surface traction on velocity boundary{f) Residual of the nodal point force vectorh0 Initial width of the gap between two cracked particles, pmJ Mechanical equivalent of heatk Thermal conductivity, W/m-° KK, K1, K Penalty constant, and material constants[Ks], [Kc] Stiffens matrix, and heat capacity matrixL0 Initial billet length, m1D, L Instantaneous length of a billet measured from the dead metal zone, mii Die land length, mLR Length of a discardn Stress exponentxxn Average number of parts fractured from a single particleN, N Number of broken particles, and number of total particlesP Extrusion load, NPf Extrusion force at the end of stroke, kNp extrusion pressure, MPaph Pressure required for matrix intrusion into the gap of cracked particles, MPaParticle fracture probability;1 Average particle fracture probability rate over cross section in deformation zonePo Fraction of porosity in a solid phase4 Heat generation rate, WImQ Hot deformation activation energy, 3Qb, Q Activation energies for surface and bulk diffusion{ Q) Heat flux vectorR Extrusion ratioR Gas constant, JImol-°CR1 Radius of cross section in deformation zone during extrusionS Surface area, m2Sa, Sm Adjusted and measured ram stroke, respectivelyST Total ram stroke, mt Time, sT, { T } Temperature and the matrix of its nodal values, 0 KSummation of temperature differentiation with spatial coordinatesTemperature differentiation with timev, v1, v3 velocity componentVB Ram speed, rn/sV Volume, m3x Material constant depending on internal structureZ Zener-Holloman parameter, s1AD/D Mean particle size reduction after extrusionxxiAT Temperature rise in extruded product, °KATD Initial temperature difference between the billet and the chamber or die, °KAt Time incremental, s{ Av }, Avj First-order correction of the velocity at previous stepMaterial constant, MPa’; and particle aspect ratio;f3 Time integration factor1, ii Constant in particle fracture model, tm3StrainFracture strain of a materialeN, 60, CJ, Fracture strain of void nucleation, growth, and linkagemax Maximum effective strain during extrusionStrain rate, effective strain rate, and volume strain rate,e., e, eCritical strain rate for dislocation accumulation in front a particle,Heat generation efficiencySemi angle of extrusion; degreeAngle of dead metal zone, degreeFunctional for the deformation bodyp density, kg/mda, Flow stress, yield stress, MPa, 3m, a1 Effective stress, mean stress, and principle stress, MPaFracture stress of the compositesa CTz Tensile stress in X-direction in plane strain compression, and in the extrusiondirection, MPaSub- and Superscripts:s denotes the steel for toolsc denotes the composite for the billett timexxACKNOWLEDGEMENTSI would like to express my sincere appreciation to Drs. Indira Samarasekera, KeithBrimacombe, Bruce Hawbolt, and Chris Davies for their supervision throughout the wholecourse of this project. Without their support, my dream of obtaining a Ph.D. would neverhave come true. Appreciation is extended to Alcan International Ltd. for providing testspecimens, technical help and discussions. Thanks to Mr. William (Bill) Dixon ofDuralcan USA, and Dr. David Lloyd, and Mr. Chris Cabryel, of Alcan International Ltd.for their help with the extrusion trials. Thanks are also extended to Dr. Stuart MacEwenfor his help and discussion of finite element modeling of the extrusion process. Thanks forfinancial support go to the industrial partners in the Metal Matrix Composite Precompetitive Research Consortium: Mean International Ltd., Ontario Hydro Ltd., SherrittGordon Ltd., Pratt and Whitney Canada Inc., Inco Ltd. and NSERC, and also to theOntario Center for Materials Research, through whose auspices the consortium was setup. Thanks to Ms. Mary Mager for her assistance in using the SEM.Thanks to Professor Tara Chandra from University of Wollongong for his interestto this project. A great help from Dr. Warren Poole in this department is very muchappreciated. I would also like to thank all my fellow students in this department for theirdiscussion and friendship.Finally, I would like to take this opportunity to express my appreciation from thebottom of my heart to my mother, and my wife, Xiaoli (Shelly). Without their love andemotional support, this Ph. D. project could never be finished.DEDICATIONTo my motherxxiliChapter 1 Introduction 1Chapter 1 INTRODUCTION1.1 Characteristics of Metal Matrix CompositesMetal Matrix Composite (MMC) research was initiated in the 1960’s. It is particularlyattractive in applications when the following improvements over monolithic materials arerequired:Easily designed and tailor-made material;Improved strength/density ratio;Improved stiffness/density ratio;Improved wear resistance;Improved high temperature mechanical properties;Adjustable physical properties (coefficient of thermal expansion, diffusivity, elasticmodulus).Among the important MMC systems, the following are of interest111: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 Introduction 2has been considerable interest in discontinuous reinforcements such as short fibers, whiskersand particles. The advantages of discontinuous reinforcements over continuousreinforcements can be seen in Table 1.1t21.Since particulate reinforced MMCs can be processed by conventional metal workingmethods or techniques to produce all forms of semifinished products, they become moreattractive from a cost perspective. Another decisive factor, especially for small industry, isthat parts made of particulate reinforced MMCs behave almost isotropically, and are thereforemuch simpler to use in design. Although the strength and elastic modulus of particulatereinforced composites are inferior to those of continuously reinforced composites, the lowcost, high workability and isotropic properties render them suitable for a wider range ofapplications, especially in automobile production.Table 1.1 fllustration of the principle factors linked with the aspect ratio(where V’ denotes the advantage and ‘x’ the disadvantage)Advantages Discontinuous ContinuousReinforcement ReinforcementIsotropy xOrientable Properties xFormability, Ductility xFabrication Costs xMaterial Cost xRecyclability xReinforcement Efficiency xChapter 1 Introduction 31.2 Fabrication of Particulate Reinforced Metal Matrix CompositesIn discontinuously reinforced metal matrix composites, the reinforcements aregenerally ceramic in nature and can either be added to the matrix as discrete elements orfonned in situ in the matrix. Reactivity with the matrix during fabrication and service,differences in coefficient of thermal expansion (CTh) between the matrix and reinforcements,and cost/performance in the finished product are the critical selection criteria used for thereinforcements. Alumina and silicon carbide powder (greater than 1 micron in size) have beenchosen primarily for the reinforcement, as these materials represent a good compromisebetween density, property improvement, and cost. However, alumina is about 5-10 timescheaper than silicon carbide powder (SiCp) and 10-100 times cheaper than alumina or siliconcarbide filaments131. Moreover, alumina has a higher stability than silicon carbide in aluminumalloys, such as the 2xxx, 6xxx, and 7xxx series. Lower manufacturing cost provides apotential for large scale production of a competitively priced product. In fact, the MMC thatis closest to a commercial breakthrough is an aluminum matrix composite with discontinuous,particulate ceramic reinforcements (SiC and A1203)14. It is being fabricated in severaldifferent ways:Foundry processes, where particles (or whiskers) are inserted into the molten metalby mechanical stirring, and the product is cast into an ingot of desired shape or size;Powder metallurgy process, where metal powders and reinforcements are blendedcold, compressed and bonded by diffusion;Squeeze casting, where the molten metal is pressure infiltrated into a preform offibers;Chapter 1 Introduction 4Spray deposition technique, where deposition of atomized liquid metal along withparticulate is employed to fabricate MMC ingots.The attraction of ingot casting is the potential for producing MMC billets suitable forutilization on the large scale equipment currently employed for fabrication of monolithicalloys. This approach will capture economies of scale, and is being used at AlcanInternational Limited, Canada, Duralcan, USALS], and Hydro Aluminium, Norway’. Meltviscosity limits the volume fraction of the reinforcement to approximately 25 volume percent.Alcan Aluminium Ltd. has commissioned a 25 million lb/yr facility in Quebec for theproduction of composites for Duralcan in Canada in 1990151. The scale-up of the castingprocess to larger sizes presents challenges related to: a) the effects of the solidification rate onthe ingot cell size, and b) attendant particle-pushing to the last regions to freeze. A cast routewhich could have more homogeneous particle distribution in a cast product of particulatereinforced metal matrix composites is sought. In addition, since matrix-reinforcement reactionis a critical issue in some MMC systems, large ingots which have longer solidification timesresult in increased exposure of the reinforcement to the molten metal.1.3 Processing and Applications of Particulate Reinforced MMCs1.3.1 Secondary Deformation ProcessingMany discontinuously reinforced metal composite products require subsequentdeformation processing via rolling, extrusion, or forging to achieve the final shape,irrespective of how the primary ingot is produced. Dural Aluminium Composites Corporation(Duralcan), has developed necessary technologies to produce a range of ceramic particlereinforced MMCs by the molten metal route. Their products have been used to produce castChapter 1 Introduction 5shapes, forgings and a wide range of extruded solid and hollow shapes. The main thrust oftheir extrusion development has focused on 6061 and 2014 alloys, reinforced either withsilicon carbide or alumina at 10 - 20 volume percentage. Significant improvements areachieved in the elastic modulus and strength, although ductility is reduced. The elasticmodulus is increased by up to 40%, and the minimum increase in tensile strength is 20%’.However, defects such as surface tearing are observed during extrusion, which affect thequality of the final MMC products. To improve the quality of MMC products571,a betterunderstanding of how deformation processing influences the microstructure and properties inthese materials is needed.1.3.2 ApplicationsMetal matrix composites (MMCs) are now used in, or being considered for use in, avariety of applications in the military, aerospace, automotive, and other commercial areas.Automotive applications include automotive drive shafts, cylinder linings, brake rotors’81;other applications include bicycle frames and components, and tire studs’91. However, theintroduction of the MMCs into actual applications is still sparse. No true high volumeapplications exist to date. To promote further use of MMCs, some fundamental changesmust take place. The cost of the composites must be reduced, probably by improving themanufacturing processes. A better chemical and physical understanding of the MMCs mustbe developed so that designers can use the material with confidence.Chapter 2 Literature Review 6Chapter 2 LITERATURE REVIEW2.1 Extrusion ProcessExtrusion 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 direction of extruded material movement relative to the punch.i) Forward extrusion: material flows in the same direction as the motion of the punch;ii) Backward extrusion: material flows in a direction opposite to the motion of the punch;iii) Side extrusion: material flow is perpendicular to the direction of motion of the punch.In the forward aluminium extrusion process, cylindrical billets are preheated to atemperature, between 300°C and 5000C, 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, the material path line is a linear 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 fairlyChapter 2 Uterature Review 7well known. In this case, material flow is more uniform than for the shear (or flat face) die.However, the conical die may induce some rigid body rotation near the die exit due to abruptchanges ofmaterial flow at that point. The parabolic die (convex type) has a smooth entry butthe exit is sharp, creating rigid body rotation and discontinüities in the velocity distribution.Dies having both smooth entry and exit are referred to as streamlined dies with the implicitassumption that the matedal path lines coincide with the improved die surfaces. Streamlineddies have been shown to be suitable for processing “difficult to extrude” metal al1oys101.However, the shear die type is still widely used for the extrusion of aluminium and its alloys inindustry, probably because of its simple design and low cost.1 - Billet2 - Container3 - Die4 - Extrusion Stem5 - Dummy block6 - Die holderFigure 2.1 Schematic of a forward extrusion processPress sizes range from lab scale- 200 ton maximum load, 60mm container I billetdiameter- to industrial-size presses of up to and greater than 10,000 ton load capacity, withbillet diameters of 250mm. Extrusion ratios (upset billet area to extrudate area) of betweenChapter 2 Literature Review 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 all thematerial 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, orquenched with water sprays.It is also important to note that hydrostatic extrusion is a nearly-ideal friction-freeprocess. Low frictional forces in hydrostatic extrusion permit the use of lower die angles andhigh extrusion ratios, both of which lead to higher hydrostatic stress and therefore toconditions which suppress fracture . The uniform deformation near the 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 of the hydrostatic extrusion1131. Embury et al. [t121 have suggested application ofthe hydrostatic extrusion process for MMC processing to increase its fonnability.Unfortunately, the complexity of the production process leads to a higher cost of the product.2.2 Extrusion Related Defects of Particulate Reinforced MMCs (PRMMCs)There is a considerable interest in the forming of metal matrix composites (MMCs), inparticular, for controlling the deformation parameters so as to avoid defects or microstructuraldamage. 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 during the process, but it also causes axial alignment of discontinuous reinforcements.DURALCAN® composites have been manufactured by hot, direct (forward) extrusion® Owned by Alcan Aluminum CorporationChapter 2 Literature Review 9(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-entry dies, with or without lubrication, arenot presently being considered, owing to the difficulty of obtaining a high-quality surfacefinish. In an exceptional study, using a conical die, Selseth and Lefstad141 found that whenextruding the AA6061/SiCp (SiCw) MMCs produced by the powder metallurgy (P/M) route,the necessary extrusion force was about 30% higher compared to a shear-face die. The ‘p’and ‘w’ notations stand for particle and whisker reinforcement, respectively.2.2.1 Extrusion Related DefectsAlthough hot extrusion of casting products appears to homogenize the particledistribution, clustering (defined as the aggregation of particles) and banding are still evidentdue to an insufficient extrusion mtio1. The study by Uoyd’53’ also indicated that althoughthe tensile elongation of a permanent mould cast composite test bar (Cast A356 -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 for A356-lO%SiC and A356-20%SiC), the composite elongation is comparable toor better than the unreinforced as-cast alloy (Cast A356). However, it is lower than the alloyin extruded conditions. During extrusion, surface defects such as surface tearing and crackingappear; some of these defects are known to occur during extrusion of unreinforced materials,while some others are specific features on the MMCs only. These defects will significantlyaffect the extrudability of particulate reinforced MMCs.Chapter 2 Literature Review 10Elongation to Fracture versus StressA356— SiC0.300.25I::vvA AA A AAI I I I I240 260 280 300 320 340 360 380 400Stress (MPa)o *356 - 10%SIC (600) C) *356 - i0%SiC (400)V P356 - 20%SiC (600) *356 - 20%SiC (400)V *356-i 5%SiC (600) A Cast P356-i 5%SIC• Extruded A356 • Cast *356Figure 2.2 Tensile elongation to fracture against strength for A356 alloy and itscomposites with different volume fractions of SiCp before and after extrusionat different extrusion temperatures of 400°C and 600°C1531Extrudability refers to the maximum attainable speed of the billet without surfacedefects occurring during extrusion. Based on the early extrusion trials done by Hams et al.171,it was found that (i) two kinds of defects occurred during extrusion of 6061 and 2014 withalumina reinforced MMCs, and (ii) their behavior was very different from unreinforced alloys.Firstly, considerable surface tearing occurred at the front end of the extrusion at low extrusionspeeds, 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 further increase in speed resulted in the onset of edge andsurface cracking which differed from the low speed cracking. These cracks were similar inappearance to a type commonly encountered with conventional aluminium extrusions. It wasChapter 2 Literature Review 11reported that two types of crack mechanisms exist for speed-limiting cracking of Al-Mg-Sialloys. The first type initiated at the die/extrudate interface, and occurred because the matrixwas not strong enough to withstand frictional force at the die. The second type initiated atsubsurface weaknesses, and was assumed to be due to incipient melting. Obviously, bothtypes of tearing mechanisms are temperature dependent and are initiated in a region close tothe die/extrudate interface. Therefore, the temperature distribution resulting from heat lossesand the temperature rise during extrusion needs to be examined. Although both types of highspeed cracking occurred in both monolithic alloys and the MMCs, low speed tearing whichshould be designated as the third type, appeared only in the MMCs (Brusethaug et al.61). Thistearing was characterized by deep notches extending from the surface into the material. Aprobable explanation of the mechanism for the third type was given by Hams et a1.7 asfollows: In the initial stages of extrusion, the die was colder than the extrudate. Metaladhering to the die bearing land during this phase was immediately chilled and its flow stressincreased. This may create conditions which were energetically favorable for subcutaneousfracturing, so that the material in contact with the bearing remained stationary, while thesubsurface material continued its forward motion. Further increase in pressure broke the bondbetween the bearing and adhered material; this material then moved across the bearingsurface. The entire periphery did not move in unison; different segments breaking away atdifferent times. New material adhered to the die bearing land and consequently the extrudatesurface retained this debris. The process was repeated in the classic stick-slip mode untilconditions were energetically favorable for continuous movement of material across thebearing surface. This low speed tearing introduces a minimum extrusion speed for the MMCs.Chapter 2 Literature Review 12Obviously, this mechanism needs to be refined, because it does not include the interactionbetween particles and matrix materials.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 and A12O3pin an AIMgSi matrix. Thesilicon carbide particle (SiCp) reinforced MMC was fabricated by mixing AIMgSi powder(AA6061) and SiC particles of size 4j.tm, while the alumina particle (AI2O3p)reinforced MMCwas fabricated by stirring theA1203pofsize of 3Opm into the molten AIMgSi (AA6082). Thevolume fractions of particles or whiskers were all 20%. In the tests, a conventional shear-facedie was used, and the extrusion ratios were 22 and 39. In some of the experiments a disc ofunreinforced material was clad in front of the bifiet.. This markedly reduced the tendencytowards high speed surface tearing, thus increasing the maximum extrusion speed. Theirexperimental results showed that the composite containing the finest SiC particles (4pm)could be extruded to solid rod at an extrusion speed of 250mm/s, while the alumina particlereinforced MMC was extruded at a speed of only 83mm/s. Because the matrix materials ofAA6061 for SiC particles and AA6082 forAl203particle reinforcement were quite similar, therelatively poorer extrudability for the alumina particle reinforced MMC was related to thedifference of microstructure of the MMCs by Selseth and Lefstad’41. As described earlier, inAlzO3p reinforced MMCs, there were some particle clusters especially at lower volumefraction, such as lOvol% and l5vol%, which were not discovered in SiCp reinforced materialsmade by the P/M route. The material with the least clusters, yielded the best surface quality.This could be the reason for its poor extrudabiity. However, the effect of different particleChapter 2 Literature Review 13size forAI2O3p(3Otm) and SiCp (4j.tm) MMCs should also be considered, because it is alsoimportant to the deformation and fracture behavior.Material State Defects MMCs UnreinforcedMatrix AlloyPorosity, voidsAs-cast Cluster, stringersSurface cracksParticle fractureDebondmg at particle/matrix interfaceDeformed Near interface Matrix Fracture(Extruded) Low speed surface crackingHigh speed surface cracking:1) at die/extrudate interface2) at subsurface of billetRotation and migration of particles*Obviously, the ability of material to withstand high strain rates is vital to theextrudability of the composite. Higher strain rates may cause fracture of the extruded materialat the extrudate surface and also result in an overheating in the low melting zone at the subsurface of the extrudate, giving hot shortness during extrusion. All the defects observed in as-cast and extruded materials are summarized in Table 2.1. Therefore, it is essential to analyzethe process to establish the optimum operating conditions to produce defect-free products. ItTable 2.1 Microstructure observed in the particulate reinforced compositebefore and after extrusion(where V denotes the observation of the defect. * may not be taken as defects.)Chapter 2 Literature Review 14is worth pointing out that the rotation and migration of particles during extrusion of MMCsproduced by the melt-casting route will be beneficial to the particle distribution.2.2.2 Hot Workability of PRMMCsHot workability relates to the ability of a metal or alloy to be deformed underconditions of high temperature ((T> 0.6TM), where TM is the melting point of the material inKelvin), and relatively high strain rates (0.1 to 1 s_i ) without forming cracks1”. The twocharacteristics that govern hot workability are strength and ductility. Since for a givenmaterial, different strains are attained prior to fracture depending on the process, workabilityof a material is affected by both the material itself and the external processing conditions, i.e.:Workability = f (material) x f2 (process, friction) (2.1)where.,is a function of the basic ductility of the metal and f2 that of the external factorswhich modify the basic ductility. The formula clearly implies that the accumulation of internaldamage which leads to fracture is closely related to the deformation and restoration processesoperative during hot working.In particulate reinforced metal-matrix composites, the aim has been to combine thebeneficial stiffness of ceramics with the superior ductility and toughness of metals. 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, on the matrix trealment and its effect on the interface. In general, the failure modes inthe particulate reinforced MMCs can be due to one or more of the following:Particle fracture;Chapter 2 Literature Review 15Debondmg at particle/matrix interface;Near interface matrix fracture;General fracture mechanism of the matrix of the MMCs as the same as that of theunreinforced matrix alloy’’.The study by Lloyd’53’showed that, for the SiCp reinforcements, fracture occurs in thelarger size fraction of the particulate population. Fig. 2.3 shows the strain dependence offractured particles for 6061-10 and 2Ovol%SiCp at room temperature.o 6061—20%SIC6061— 10% SIC40030o0.0 , ; , V I 1 V I I0 1 2 3 4 5 6 7 8 9 1011 121314cxFigure 2.3 Strain dependence of fractured particle of 6061/SiCp MMCs531It is evident that the extent of particle cracking is lower in the lOvol%SiCp composite,which is not surprising considering the lower particle content in this composite. The rate ofparticle cracking with strain is also lower. It is interesting to note that less than 5% of theChapter 2 Literature Review 16total particle population has cracked at fracture of the composite. However, it is apparentthat particle cracking is initiated at low strains. In spite of this, the voids created do not growsufficiently during subsequent straining to affect the final fracture strain; the strain of fracturedoes not correspond to the strain for particle cracking. Similar behavior has also 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, together with the occasional cracked particles. The voids have not grown extensivelyin the tensile stress direction. This is generally the case in unreinforced alloys. This alsosuggests that the growth strain is negligible in comparison with the nucleation strain, and thatvoid nucleation is primarily a result of matrix failure within closely spaced particles. Thereason for this behavior is related to the deformation response of the particle clustered regionrelative to the rest of the composite. Within clusters, the far field applied stresses are nolonger controlling. Actually, higher-stiffness particles constrain the deformation of the matrixadjacent to them, and this results in a complex triaxial stress being developed in the matrixwithin the cluster. Obviously, the triaxial stresses are important because a triaxial tensilestress enhances both void nucleation and void growth. To consider the effect of the degree ofthe triaxial tensile stress, a ratio of mean stress to effective stress, aJ was adopted. Uoydfound that the unreinforced alloys have a significant loss in elongation with increasingtriaxiality, while the composites are relatively unaffected. This is consistent with the idea thatthe fracture of the composite is controlled by the intrinsic triaxiality generated at particleclusters, and these dominate any imposed far field stress state. Thao et al have reportedthat as the temperature increases the void formation due to interface debonding at the ends ofparticles in tensile direction becomes dominant comparing to particle fracture which isChapter 2 Literature Review 17dominant at low temperature. Lloyd53’also pointed out that due to the importance of particlesize on the deformation and fracture behavior of the composite, particle size must be limitedto maximize strength, and minimize fracture. It has been indicated that using particles ofaround 10 microns with a tight size distribution, reduces the propensity for particle fracture,which occurs most readily in coarse particles. However, a small particle size may result inmore clusters which are harmful for the fmal properties of the MMCs.2.3 Development of Extrusion Limit DiagramsModeling of extrusion has, at a practical level, been focused on the use of empiricalequations and analytical solutions to predict optimum operating conditions1555.Consequently, the determination of extrudability has been based on extrusion press-sidemeasurements and property I quality requfrements. The extrusion process is governed bythe imposed variables, temperature, strain rate (speed), and strain (reduction ratio) and theirinteraction with the characteristics of the material. The significance of each of theseparameters will be determined by several factors, such as surface quality, minimummicrostructural damage if there is any, excessive pressure requirement, etc.. Meadows andCutler’63 showed that the bounds of extrudability may be calculated theoretically, anddemonstrate this on a diagram showing maximum tolerable extrusion pressures and surfaceincipient melting plotted on the axes of extrusion 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 of extrusion ratio, temperature andstrain rate. The incipient melting boundary line is depicted according to the temperature at thedie land interface, which is a function of initial extrusion temperature, extrusion ratio, ramspeed, friction coefficient at interfaces, etc..Chapter 2 Literature Review 18Such limit diagrams have been developed to include structural8’591 and propertyfeatures’5. Sheppard1reviewed these and other developments, and found that most priorresearch has been oriented to the prediction of a peak or maximum load required of the press,and the prediction of temperature rise due to extrusion deformation.SpeedExtrusion TemperatureFigure 2.4 A schematic extrusion limit diagram2.3.1 Peak PressureThe simplest equation for estimation of peak pressure during extrusion is expressed 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 inaluminium extrusion industry’55,the above equation is changed to,p = a[(a+blnR)+4L] (2.3)where L is an instantaneous length of the billet measured from the dead metal zone and Dc isthe inside diameter of the container.Chapter 2 Literature Review 19At high temperature, the flow stress of a material is a function of strain rate andtemperature, and may be characterized by a hyperbolic sine equation,Z = e exp() = Asinh(aa) (2.4)where Z is Zener-Holloman parameter, and A, a, Q and n are material constants. InsertingEq.(2.4) into Eq.(2.3), a general equation for peak pressure during extrusion can be derived:(2.5)(xn A ADwhere B, C, E, F are constants for a specific press. The mean strain rate formula adopted inthis study is expressed as,_4vDtanq (2.6)— (DaDE)3”2where DB and DE are diameters of the billet and the extrudate, respectively, vB is the ram speedand q is the semi angle of the deformation zone outlined by the shear zone in unlubricatedshear die extrusion, expressed as1,p=54.1+3.45lnR (2.7)Based on some plant trials, the above four constants for the extrusion press can beestimated, and the constant pressure boundary line in a limit diagram can be delineated usingEq.(2.5).2.3.2 Temperature RiseA general analytical equation for temperature rise during extrusion was derived byCastle and Sheppard’651 based on a thermal analysis including the billet, and the sunoundingtools.AT = (O.9PvBt — ATDC2(t)) I C1 (t)) (2.8)Chapter 2 Literature Review 20where P is the extrusion force, ATD is the initial temperature difference between the billet andthe container or die, C1(t), and C2(t) are heat flow coefficients and t denotes extrusion time.Sheppardt671 claimed that ‘for high conductivity aluminum alloys, this form of temperatureincrease may be sufficiently accurate forpractical use’.In aluminum extrusion practice, it is common for there to be little or no temperaturedifference between the billet and the surrounding toolstM]. However, the generation of heatinternally will establish a temperature differential. Therefore, in the calculation of temperaturerise, the initial temperature difference between the billet and the tools could be ignored. Theabove equation then becomes,AT =0.9PvBt / C1 (t) (2.9)=O.9PvBt/ (K1t”2+(K2+K4)t213 +(K3+K5)t”3+K11t)All the constants are expressed as below,K— ic(D —D)(kSPSCPS)lI2 (2.9a)1 12K2 = l (18kSDB(p8C)112)213 (2.9b)K3 =.lD(l8ksD(p$Cps)2)hI3 (2.9c)K4 =-l (1 8kSDR (pC8)1/2 )213 (2.9d)K5=.l(18kD(p,C,)2)hI3 (2.9e)K11 = pCCPCRvB1tD /4 (2.9f)where ID is the deforniation zone depth between the pressure pad and the dead metal zone, lis the die land length, ‘p is the angle of dead metal zone, p, k, C, are thermal properties of amaterial, and the subscripts s and c denote the steel for tools and the composite for the billet,respectively.Chapter 2 Literature Review 212.4 Finite Element Analysis of an Extrusion Process2.4.1 Finite Element Analysis of an Extrusion ProcessModeling of an extrusion process for detennination of punch pressure, stress/straindistributions, material flow pattern, etc., is of extreme importance to the manufacturingprocess designer for a number of reasons. It provides valuable information, not only forenhanced design of work tools and process parameters, but is also useful for improvingexisting extrusion methods or even inventing new routes.Various kinds of extrusion processes have been analyzed for monolithic materials bythe finite element method at a macroscopic leve11436,using both the Solid Approach and theFlow Approach. The Solid Approach treats the solid as an elastic-plastic material duringforming. The significant shortcoming is its complex formulation and the computing cost291.In contrast, the Flow Approach considers the materials to behave as a non-Newtonian viscousfluid. A typical shortcoming of this approach is that it cannot represent many of the subtletiesof elastic-plastic constitutive laws; hence it does not provide information on residual stressesand also does not solve directly the displacements’29331.For extrusion problems, depending on the type of model, the transient and steady-statecomponents of the process can be analyzed. The transient portion is of interest if peakpressure and the deformation behavior at the beginning of the extrusion need to be examined.For the steady-state situation, the deformation behavior of the head end and the tail end of thebillet cannot be analyzed; only the deformation behavior in the deformation zone can beinvestigated. The Eulerian description is suitable for this analysis with the Flow Approach. Inthe Eulerian description, the mesh is stationary while the material flows through theChapter 2 Literature Review 22deformation zone during deformation. However, for non steady-state (transient) problems,the total Lagrangian or updated Lagrangian description is preferable and is adopted by usingthe Solid Approach or Flow Approach. In a non steady-state process, such as at the initialstage of the extrusion process, the Lagrangian description suffers from major drawbacks whenthe workpiece endures large or localized deformation and also when the work tools, namelythe punch and the die, have complex shapes or sharp edges. This may be attributed to the factthat, in the Lagrangian description, the fmite element mesh remains embedded in the materialand moves with it. Lack of control over the grid motion often results in excessively distortedelements, thus deteriorating the quality of the finite element solutions. Continuing thesimulation beyond certain levels of deformation becomes impossible in many cases, onaccount of entangled or non-convexed elements. Therefore, various remeshing schemes havebeen attempted to overcome these obstacles391.Another approach is the application of an Arbitrary Lagrangian-Eulerian description(ALE) to industrial metal forming simulation. In Arbitrary Lagrangian-Euleriandescription, the mesh moves at a different velocity from that of the material. The descriptionis a hybrid between the Lagrangian and Eulerian descriptions, i.e., if the mesh moves at thesame velocity as material, it is termed Lagrangian, and if the mesh velocity is zero, it isEulerian. However, it is difficult to choose an appropriate mesh velocity; and it appears thatremeshing is required during large deformation.2.4.2 Development of an Extrusion Limit Diagram Using FEMThe above described semi-empirical equations in Section 2.3 for development ofextrusion limit diagrams result in mean values for the variable. One recognized69’drawbackof the semi-empirical approach is the problem of analyzing the close inter-relation of theChapter 2 Literature Review 23process variables- flow stress, strain rate and temperature. The intractability of the situationcan lead to a large number of experiments being required.A more attractive, and increasingly accessible approach is the use of fmite elementtechniques°41.Grasmo et al. have used a finite element model to simulate the extrusionof an Al-Mg-Si alloy, AA6060. The model considers the material to behave like a fluid anddoes not include predictions during the billet upsetting phase. However, it is the mostpractical and complete model of extrusion developed to date using FEM techniques.Nevertheless, there is little literature using a finite element technique to develop extrusion limitdiagrams.For the extrusion of particulate reinforced composites, low speed cracking should beincluded in the limit diagram. However, no work has been found for the low speed cracking.Dixon (91 proposed that the low speed cracking boundary is a function of extrusion ratio asschematically shown in Fig. 2.5. The low speed cracking boundary can be determined by aseries of plant trials. Alternatively, a finite element model can also be employed to determinethis boundary provided a suitable criterion is inserted into the model.ExtrusionSpeedExtrusion TemperatureFigure 2.5 Schematic extrusion limit diagram with low speed cracking’5’Chapter 2 Literature Review 242.4.3 Fracture Criteria for Monolithic MetalsSome fracture criteria for cold and hot working have been established to rationalizethe data which are available for different test geometry, i.e., Stress Criterion; Strain Criterion,Plastic-Work Criterion1491. The Stress Criterion was based on the fact that cracking in metalworking was recognized to be associated with induced tensile stresses, even in processes suchas forging in which the stresses are predominantly compressive. The importance of the tensilestresses was indirectly confirmed by the large increase in apparent ductility when materials aredeformed under hydrostatic pressure. The tensile fracture of conventional alloys is consideredin terms of the microvoid coalescence model (MVC) in which the fracture strain expected isthe sum of the nucleation strain, the void growth strain until void coalescence occurs, and thefmal linkage strain, £LLF—eN+8G+ L (2.10)Usually e, 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, it is likely that both shear and tensile stresses play apart, since there is evidence that localized flow by shear is required to initiate cracks which arethen propagated by tensile stresses. A Strain Criterion has also been suggested by someworkers1501 based on the total strain, but difficulties arise since the total strains vary markedlyin different processes. Therefore, it is reasonable to assume that any criterion should be 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 ductileChapter 2 Literature Review 25material when, for a given temperature and strain rate, the plastic work done by the highesttensile stress reaches a specified limit1511.s:”Gl I)d = C (2.12)Cockcroft and Latham successfully applied the criterion to cold working but did nottest it for hot working. Sellars et al.’491 tested the above equation and concluded that theequation could be a reasonable criterion for hot working as well as for cold working, butclaimed that further data is required to test it more rigorously for hot working.2.5 Finite Element Analysis of the PRMMCsIn modeling monolithic metal forming, some approximations are always made, such asconstant volume of material, isotropy, coincidence of the axis of principle 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 behavior on a microscopicscale due to microstructural characteristics and their influences on properties. However, thereis little published work on the microanalysis of mechanical working of the MMCs at elevatedtemperature. The micromechanical analysis of the particulate reinforced MMCs associatedwith thermal phenomena and simplified loading conditions are discussed to review the currentmethodology of the MMC deformation analysis.A few studies have been attempted for the micromechanical analysis of materials,including fiber140421 and particulate reinforced MMCs143,but most of them are based on aunit cell model with idealized boundary conditions. Aradhya et al.’45’ analyzed a simplifiedMMC structure under tensile loading, as shown in Fig. 2.6.Chapter 2 Literature Review 26yE1 Aluminium SICBjC>_____________________________________I_________________________A01.-rn0 I A7/)// ,)/,/9///)///m mesh sizeA interparticle distance= particle Lengthb = particle widthFigure 2.6 Finite element model used by Aradhya etBased 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 predicted that,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 thatthe 0.2% yield stress of composite is invariably higher than the unreinforced matrix alloy. Theapparent discrepancy between the FEM and the experimental results was explained by the factthat the properties of the unreinforced matrix material were used in the model to describe thematrix material in the MMCs. The UTS values predicted by FEM were much lower than theChapter 2 Literature Review 27experimentally observed. The discrepancy between the elastic modulus prediction by FEMand experimentally measured values also existed, and the maximum difference was about 12%at volume fraction = 0.4. In spite of this, the unit cell model with idealized assumptions in aMMC micromechanical analysis, such as, uniform distribution of second phase particle withregular particle shape, idealized boundary conditions, etc. can give a pre1iminwy insight of themicroscopic behavior of the MMCs, although it is far from reality.A more flexible discretization for different volume fractions of particulatereinforcements was developed by Ramakrishnan et al.1 using a master mesh, as shown inFig. 2.7.Figure 2.7 Master mesh for generating different microscopic morpho1ogies’’Chapter 2 Literature Review 28In their finite element analysis, some important aspects associated with thetransformation induced plasticity inA1203.-Zr0 were analyzed. 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 of thematerial during the dilatational transformation of Zr02 and (iii) the crack deflection due to thetransformation. The study was conducted for angular and spherical shapes of second phaseparticles and also for varying volume fractions of the second phase. The crack morphologiesgenerated by the FEM study for different overall fractions of the angular Zr02 are shown inFig. 2.8, based on the assumption that the particle/matrix was perfectly bonded. Because themaster mesh model represents more closely the real situation of the MMCs (with randomlydistributed second phase particle and its random shapes, angular or spherical) than regulararrangement of the reinforcements with idealized shapes, such as spherical, cylindrical, square,etc. assumed by other unit cell fmite element models described above, the comparison ofanalytical solutions they derived assuming a spherical shape for the second phase particleswith the results obtained through the simulation showed very good agreement. However, noexperimental validation was provided due to the difficulties for a master mesh model to satisfyall the real boundary conditions. Moreover, in their study, since no large deformation wasinvolved, the mesh size and its arrangement were not altered during the simulation. But forlarge deformation of the 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 mesh modelcannot be adopted on a microscopic scale in the extrusion process, because a large number ofelements would be required and remeshing would be difficult. However, microscopicChapter 2 Literature Review 29mechanical analysis could be conducted based on an idea of multilevel finite element analysisduiing large deformation with some simplifications.a 4wVolume fraction of Zr02 = 0.05 VOIUIM fraction of ZO2 = 0.1— -4111144%cv__Volume fraction of Z,02 = 0.2 Volume fraction of Z,02 = 0.3FIgure 2.8 The crack morphologies generated by the FEM study for differentoverall fraction of the angular Zr02with transformation23.1 Multilevel Finite Element MethodMultilevel finite element analysis was first proposed by Kopp et al.1471 in thesimulation of metal forming 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;Microscopic phenomena are simulated at Level 3 (Microscopic Analysis), using special micro-material elements and thermodynamic models. The method has been applied to an upsettingChapter 2 Literature Review 30:H H1eE.100‘4,(‘4a0 10 20(1 distance tram ingot center P(b)------ .L._._Ifl______________________________10i2 25mm(a)Figure 2.9 (a) FEM mesh with local refinement during a plane-strain upsetting;(b) Stress distribution along the line PQ (e=1% calculated with ABAQUS)t47’The results using a multilevel finite element system to calculate the stressconcentration due to second phase particles are shown in Fig. 2.9(b), based on the distributionof second phase particles along the line PQ shown in Fig. 2.9(a). Figure 2.9(b) shows that theproblem. The results from Level 1 are sufficient to provide reasonably accurate data for theestimation of the size of plant needed or the forming schedule 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 Level 3. At Level 3, eithermicrostress or thermodynamic evolution, such as, recrystallization, etc., is of interest. Using amicroscopic material element, the stress concentration around a second phase particle, such asa ceramic particle in the MMC5, can also be estimated by locally refining the finite elementmesh as shown in Fig. 2.9(a).——— a macroscopic stress—b microscopic stressChapter 2 Literature Review 31continuum-mechanics based solution ( Level 2: macroscopic stress) yields a normal stress(curve a), while substitution of the micro-elements (Level 3: microscopic stress) produces astress curve (curve b) in the same figure with spikes at the positions of micro-elements.Obviously, the substitution of micro-element (or second phase particles in real materials)changes the local stress in the matrix. For metallurgical microanalysis, FEM results fromLevel 3 are needed to study microstructure evolution during hot deformation.2.5.2 Particle Fracture Model during DeformationFinite element analysis at level 2 can reveal the macroscopic deformation behavior ofthe MMCs during extrusion. However, criteria quantifying the microstructure (fracture) atlevel 3, based on the deformation behavior, are required. Brechet et al. (75-76] assumed that theprobability of fracture of a particle, p, is a function of area-equivalent particle diameter, D,and strain, c, at room temperature as below.(2.13)where f is a constant and the probability is defined as the ratio of the number of crackedparticles to total number of particles. Their experimental data had verified the linearrelationship between the fracture (percentage of particles cracked) and the imposed level ofstrain by compressing a sample of Al(A356)-20%SiC. The model did not consider the shapeof a particle (including aspect ratio). As observed in the microstructure in extrudates ofalumina particulate-reinforced metal matrix composites, equiaxed particles crack less easily.To take aspect ratio into account, the probability of a particle cracking can be expressed as:Pf = 1—exp(—Dae) (2.14)where a is the aspect ratio of a particle and is a constant (= l.6x104p.m3). It is noted thatEq. (2.14) is consistent with the experimental data from Brechet et a1761. Actually, if theChapter 2 Literature Review 32exponential term in Eq. (2.14) is less than 1, Eq. (2.14) could be approximately expressed asEq. (2.13). Because the above equations are valid for room temperature, it is not clearwhether or not the criteria apply to high temperature deformation such as the hot extrusionprocess. At high temperature, plastic relaxation around particles is easier due to possibledislocation climb, and work hardening is not dominant, while the strain rate is more sensitiveto flow stress. Due to the compressive stress state in the hot extrusion process, particlecracking could be the dominant fracture mode. Humphreys and Kalu771 have investigated thelow temperature transition of a second phase particle behavior in a model material of Al-Sialloy. At low temperature, there is an accumulation of dislocations at the particles, whereas athigh temperatures climb is possible with the consequence that there is no stress build-up.Consequently there will be very little particle damage or interface decohesion. They proposedthat at high temperature the critical strain rate below which stresses will not accumulate isgiven by:cc = Ki exp(—Q / RT)ITd2+K2exp(—Qb IRT)/ Td3(2.15)where K1 and K2 are material constants, Q and Qb are the activation energies for bulk andsurface diffusion, d is the diffusion distance, and T is the absolute temperature. They alsopointed out that with appropriate adjustments to the constants, the above equation may beused with some confidence to predict the effect of second-phase particles on the mechanicalbehavior of alloys at elevated temperature.Based on the above analysis, it would be feasible to neglect the strain effect because ofless work hardening, but add the strain rate and temperature effect to account for theprobability of a particle fracture at high temperature. Therefore, the strain rate compensatedChapter 2 Literature Review 33variable, Z = eexp(Q / RT), should be introduced to consider the probability of a particlefracture during deformation at high temperature. Moreover, of fractured particles byintruding matrix materials into the gap of two halves has been observed in deformed materialswith superimposed hydrostatic pressure. The pressure, Ph’ required for the matrix material tointrude into the cracks is expressed ast751:2 D ln(D I h ) — e (2.16)ph(e)=a [—+—( ° )1‘ 3 3h0 ln(D1h0)where h0 is the initial width of the gap of the crack and is the flow stress of the matrix. Itis evident that easier ‘healing’ could occur at high temperature if this equation is applicable.2.5.3 Microscopic Analysis of PRMMCs under Larger DeformationIt is known that a microscopic analysis of the PRMMC during industrial extrusionprocess is impractical. The multilevel system can be applied to the analysis of particulatereinforced MMC during large deformation in laboratory tests, although a specific micro-element material model is required on a microscopic scale to induce its anisotropy. At themacroscopic level, the MMCs are assumed to be isotropic and the continuum plasticity theoryis used. The deformation behavior of the MMCs can be characterized and the fonnability ofthe MMCs can be analyzed by using a modified Plastic-Work Criterion. At a microscopiclevel, micromechanical analysis of the MMCs under large deformation can 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 of a particle during a cylindricalcompression and a plane strain test will be analyzed at both the macroscopic and microscopiclevel, to help understand the microstructural evolution of the PRMMC during largedeformation (including extrusion) at high temperature.Chapter 3 Scope and Objectives 34Chapter 3 SCOPE AND OBJECTIVESParticulate reinforced MMCs are attractive for many applications in the automotiveindustry. However, the demand has been limited owing to the cost and insufficient knowledgeof 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 with these processing schedules include equipment capabilities, 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 of how deformation processing influencesmicrostructure and properties in these materials.3.1 Scope and ObjectivesFrom the literature review, it appears that the extrusion process is the widely used andone of the most economical secondary processing routes for particulate reinforced MMCs. Itmay also improve the mechanical properties of the material. The scope and objectives of thisstudy are:1) To conduct compression tests using a Gleeble® machine to develop constitutiveequations for the PRMMCs. The constitutive law will be adopted in the fmite element model;2) To better understand the deformation behavior of the alumina particulate reinforcedMMCs during extrusion with the aid of a finite element model, DEFORM® , at macroscopiclevel;® Gleeble is a registered trade mark of Dynamic Systems, Inc., New York, USA.Chapter 3 Scope and Objectives 353) To conduct extrusion plant trials to examine the microstructural evolution (e.g.,particle fracture and size refinement) and the mechanical property change of the MMCs underdifferent extrusion conditions; the plant trial data, such as extrusion force and temperaturemeasurement will be used in validation of the finite element model predictions and 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 of the finite element model 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 based on anSEM surface crack examination and the FEM analyses. The effect of extrusion conditions onthe mechanical property change was investigated by conducting tensile tests of the extrudates.Extrusion limit diagrams for the material were finally developed for the purpose of industrialproduction. The overall conception of the project is schematically shown in Figure 3.1.® DEFORM is a registered trade mark of Scientific Forming Technology Corporation, Columbus, Ohio.Chapter 3 Scope and Objectives 36Gleeble TestsMicro- I Constitutivemechanical L.awParticle SizeRefinementProductExtrusionLoad stroke curve,AnalYSisAnalysLimitModelDeformationBehaviourLow Speed Cracking, Validation Effect ofExtrusionDevelopmentConditionsiafEFigure 3.1 Methodology for the extrusion of alumina particulate reinforced MMCs37Chapter 4 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 a Gleeble® 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,for two different volume fractions, 10% and 20%, of the composites. The extrusion data suchas load-stroke and die temperature will be used for validation of a FEM model prediction anddevelopment of extrusion limit diagrams. Microstructure evolution of the composites duringextrusion will be examined using microscopes and correlated with the tensile propertiesmeasured from the extrudates of the KRDC plant trials.4.1 Gleeble TestsSpecimens of 6061/A123with three different volume fractions from 10% to 20%were machined from cast billet stocks into cylinders of 10mm diameter by 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 a Gleeble® 1500’ thermomechanical simulator. The specimens wereresistance-heated at 5°C/s to test temperatures in the range of 400°C to 525°C, held at thattemperature for one minute, and then deformed to a true strain of 1.0 at a nominal strain rateof 0.05, 0.1, 1, or l0s-. Graphite shims were inserted between the specimen and ram toChapter 4 Experimental 38prevent excessive barreling (Figure 4.1). The test conditions chosen were based on theextrusion conditions adopted in industry for the 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 hotworking is the hyperbolic sine constitutive equation (Equation4•1f8J•Z = eexp(Q I RT) = Asinh(xa) (4.1)where Z is the Zener-Hollomon parameter (the temperature compensated strain rate), C isstrain rate, Q is activation energy, R is the universal gas constant, T is the absolutetemperature, a is the flow stress and A, cz, and n are constants. It is noted that the equationis strictly valid only over the steady state regime of deformation and as such, it may not beFigure 4.1 Schematic of the Gleeble test set-upChapter 4 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 of the 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( a a)) againstme to determine n, and ln{sinh(a a)) against l/T to determine Q. 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 experimental datat8hi. The correlationcoefficient between the predicted and the experimental data for each volume fraction is alsolisted in Table 4.1 for reference. It is seen that a good correlation has been obtained betweenthe predicted flow stresses and the experimental data.Chapter 4 Experimental 40Material Q(kJ/mol-K) A(s’) a(MPa-’) n CorrelationCoefficient6061 197.5 1.97x10’2 0.036 4.11 0.9976061/A123/lOp 216 9.42x10’ 0.023 5.24 0.98860611A1203115P 210 9.77x10’2 0.034 4.00 0.9926061/A123/20p 220 4.45x10’ 0.024 4.41 0.9874.2 Plant Trials at UAC, Anaheim4.2.1 Extrusion ProcedureTwo plant trials were held at Universal Alloy Corp., Anaheim, on the Duralcancomposite and its unreinforced material. Two billets each of 6061, 6061/A1203/1OP and6061/A123/20p were extruded in the first plant trial in September, 1992 ( designated as‘S92’, hereafter). Only the 6061 and one of the 6061/AlO3/2Op bifiets were homogenized.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. The diameter ofall the billets were 178 mm (7”) in the second plant trial in July, 1994 (designated as ‘J94’,hereafter). 22 billets, 14 of 6061/A123/lOp, and 8 of 606l/AlO3I2Op, were extruded using4 different dies. They were all prehomogenized at about 570°C for four hours. The length ofall 22 billets was 381mm (15”), and the diameter of all the billets was also 178 mm (7”).Details of the extrusion condition are listed in Table 4.2.Table 4.1 Material constants for the constitutive equation of the Composites1Chapter 4 Experimental 41Table 4.2 Extrusion programs for the 7” press at UACTest No. Material Billet Dimension Die Diameter Pretreatment_____________(L (mm) x D(mm)) (inch)S92-1 6061 305x178 1.25 HomogenizedS92-2 6061 305x178 1.25 HomogenizedS92-3 606l/A123/20p 508x178 1.25 HomogenizedS92-4 606iIA12O3I2Op 508x178 1.25 as-castS92-5 606l/A1/lOp 305x178 1.25 as-castS92-6 6061/A123/l0p 305x178 1.25 as-cast394-1 6061/A1O/iOp 381x178 2 Homogenized394-2 6061/A123/lOp 381x178 2 Homogenized394-3 6061/A1O3/l0p 381x178 2 Homogenized394-4 606lIAl2O3/iOp 381x178 2 Homogenized394-5 606l/A1/2Op 381x178 2 Homogenized394-6 6061/A13/20p 381x178 2 Homogenized394-7 606l/A1/20p 381x178 2 HomogenizedJ94-8 6061/Al3/lOp 381x178 1.25 Homogenized394-9 606l/A12/lOp 381x178 1.25 Homogenized394-10 606lIAl2O3IlOp 381x178 1.25 HomogenizedJ94-1 1 6061/A1/lOp 381x178 1.25 Homogenized394-1 lb 6061/A123/iOp 381x178 1.25 Homogenized394-12 606l/A1/2Op 38lxi 78 1.25 Homogenized394-13 606l/A123/20p 381xl 78 1.25 Homogenized394-14 606l/A123/20p 381xl 78 1.25 Homogenized194-15 606l/A1O/lOp 381x178 1 Homogenized394-16 606l/AI23/lOp 381x178 1 Homogenized394-17 6O6l/A1/lOp 381x178 1 Homogenized394-19 606l/A123/2Op 381x178 1 Homogenized394-20 6061/A1O/20p 381x178 1 Homogenized394-ha 6061/A13/lOp 381x178 1.5 Homogenized394-18 606h/Al2/lOp 381x 178 1.5 HomogenizedChapter 4 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 12 1°C, 32 1-343°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. Thesetemperature measurements 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 billet entered the transfer mechanism (Table 4.3).Container, dieProduct runout tablePress hydraulics - - - - — - - — -• Billet_____________________________• I transferI mechanismZ2 Z3‘I IlI II II II IBilletloadingDie preheatingiI boxIl IlThermocouplesThree-zone gas firing furnaceFigure 4.2 Schematic of extrusion setup for Duralcan trialsChapter 4 Experimental 43Table 4.3 Billet temperatures immediately prior to extrusion at UACTest No. Material Preset Temp. 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/A13/l0p 427 393 410S92-6 6061/A12/lOp 427 431 443J94-1 60611A13/lOp 466 424 426J94-2 6061/A12/l0p 493 399 399J94-3 606l/AlOlOp 477 459 516J94-4 606l/A123/l0p 493 516 519J94-5 606l/A1!20p 477 452 457J94-6 606l/A123/20p 477 444 460J94-7 606l/A1/20p 488 458 516J94-8 6061/A13/l0p 488 463 521J94-9 606l/A12/lOp 488 479 507J94-10 606l/A13/lOp 488 482 496J94-11 6061/A12/l0p 468 446 457J94-llb 6061IA1O3IlOp 468 434 483J94-12 6061IA12/2Op 468 423 460J94-13 60611M3/20p 491 471 507J94-14 6061/A1/20p 491 461 514394-15 606l/AlOil Op 491 488 503394-16 6061/A123/lOp 491 498 465J94-17 6061/A1/lOp 510 487 529J94-19 606l/A1O3/2Op 510 484 503J94-20 606l/A1/2Op 477 457 474194-ha 6061/A123/l0p 466 451 495J94-18 60611Al1h0p 466 451 457Chapter 4 Experimental 44It is seen from Table 4.3 that the temperature distribution is uneven for most of thebillets at the end of heating. Ambient temperature was recorded at 28oC, 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 of about 427°C in a die 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 to 4270C, but temperatures measured at theinlet part of the container with a hand-held device indicated a variation of 277 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, and it seemed 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 diameter by12.7 mm, the rest being 178 mm diameter. All the tools were H13 steels, except for the 1.5-inch die used in the second plant trial of J94-1 la and 394-18, which was ceramic material.4.2.2 Extrusion DataDuring extrusion, the load, ram speed and die and container temperatures wererecorded. A typical load-stroke curve, with the variation of ram speed, is shown in Fig. 4.3for the extrusion of Trial S92-3. The peak pressure is reached at the end of the filling-upChapter 4 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 with all other factors being subservient. One operator stood at 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 of heat conductionfrom the hotter billet (Fig. 4.4). The friction heat at the die interface also heats up the dietemperature. After contacting each other, heat conduction occurs between the billet and thedie, which causes the steep die temperature increase at the beginning. The die temperaturetends to level off when the steady state is reached.543101200010000800060004000200000 50 100 150 200 250Ram Displacement (mm)Figure 4.3 Typical load-stroke curve with variation of ram speed (S92-3)Chapter 4 Experimental 4616000_________________F—Homo (S92-3) I.14000 —0— Unhomo (S92-4jj1200010000_80006000400020000 I I I100 150 200Ram Displacement (mm)12000 46010000! 8000-2 —0--Load6000- —a— Die Temp.• 4000’20000 -310A’2C .—‘‘..,‘j Q0•400j• 370340I I I0 50 100 150 200 250Ram Displacement (mm)Figure 4.4 Die temperature increase during extrusion (S92-3)I0 50250Figure 4.5 Effect of homogenization on extrusion force (S92-3 and S924)Chapter 4 Experimental 476 460430 5Die Temp 3700 I I i—3100 100 200 300 400 500Ram Displacement (mm)Figure 4.6 A weak coffelation of increasing ram speed with increasing dietemperature during extrusion (S92-5)I —a-- 431°C (S92-6)16000 1—0— 393°C (S92-5)12000____Cr.___ ___8000.—40000 I I I I0 100 200 300 400 500Ram Displacement (mm)Figure 4.7 Effect of billet temperature on extrusion force (S92-5 and S92-6)Chapter 4 Experimental 4816000120008000—a-- 305 mm (S92-3)400()—a-- 381 mm (394-12)0 50 100 150 200 250 300Ram Displacement (mm)Figure 4.8 Effect of billet length on extrusion force during extrusion (S92-3 and 394-12)12000______________—a— 20% (194-7)‘-‘ 10000-__ ____—0—10% (J94-3)80006000.4000.-200001 I I I I0 50 100 150 200 250 300Ram Displacement (mm)Figure 4.9 Effect of volume fraction on extrusion force during extrusion(606 l/A12O3/lOp: 394-3, and 606 l/A12O3/2Op: 194-7)Chapter 4 Experimental 4915000120009000.600030000300Figure 4.10 Effect of extrusion ratio on extrusion force (J94-4, 394-10, J94-15)A higher load is required for extrusion of the non-homogenized billets (both6O6l/A1203/l0pbillets of S92-5 and -6 and 6061/A1203/20P of S92-4, Fig. 4.5). This higherload is related to the microstructure of the non-homogenized materials, which containsegregated elements, precipitates and large dispersoids.A weak correlation between increasing ram speed and a delayed increase in dietemperature at the thermocouple position was observed, as shown in Fig. 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 to higherextrusion speed causes an increase in die temperature.A higher load is also needed for extrusion of lower temperature billets, because of thehigher flow 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 50 100 150 200 250Ram Displacement (mm)Chapter 4 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, (5 16°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 influenceof extrusion ratio and billet length on extrusion force 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 accounts for the fluctuations of less than about lmmls: the press does not havevery good speed control, and the maximum speed which can be realized is less than 10mm/s.4.3 Pilot Extrusion at KRDC, Kingston4.3.1 Extrusion ProcedureA total of 14 extrusion tests were performed at Kingston Research and DevelopmentCenter, Kingston, with two volume fractions (6061/A123/lOp and 60611A123/20p) underdifferent extrusion conditions, as listed in Table 4.4. The microstructure of the extrudateswere examined for different extrusion conditions. The extrusion data recorded were usedChapter 4 Experimental 51both in validation of a finite element model and in development of extrusion limit diagrams ofthe composites. The test number is designated hereafter as ‘K-’, as shown in Table 4.5.Table 4.4: Plant trial conditions at KRDC6061/Al203/ lop 606 l/Al03/2OpV = 0.8-0.9 mm/s Vl = 0.8-0.9 mm/sT1 = 400°C, T2 = 500°C T1 = 400°C, T2 = 500°CR1 = lO,R2=28,364 R1 = l0,R2=28,R364The 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 of the 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 of the billet beforethe stem began to press it. The press is a lOOT vertical machine. A schematic drawing of thepress 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 a hand-held device.Chapter 4 Experimental 52Extrusion speed could not be controlled very well at high speeds (—4mmls).Therefore, a ram speed of about 1 mm/s was adopted. Only one extra test was conducted at aram speed of about 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 Section 4.4.Figure 4.11 Schematic drawing of the extrusion press at KRDC4.3.2 Extrusion DataThe dimensions of the billets and the extrudates after extrusion were measured (Table4.5). The container had an inside and outside diameter of 57mm (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 of 57mm (2.25”) diameter by 3.18mm (1”18), the rest being 53mm(2.09”). The outside diameter of the die was the same as the inside diameter of the 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 listed in Table 4.5.Chapter 4 Experimental 53Table 4.5 Billet dimensions of each test at KRDCTrial 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% 50.80x87.0 5U18 15.75 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 5.5Table 4.6 Measured test data of the plant trials at KRDCTrial No. Material TB(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 die lineK-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 2.70 no crackwhere TB and TC are billet and container temperature respectively.Chapter 4 Experimental 54Figure 4.12 shows a typical force-displacement response and coffespondmg ram speedfor test K-7. The extrusion data has the same characteristics as the data from UAC, Anaheim,and the salient features are 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 todecreasing friction.Figure 4.12 Typical load-stroke curve during extrusion at KRDC (K-7)ii) the ram speed was controlled at approximately lmmls, except for those trials inwhich the extrusion force exceeded the press limit, such as trials K-8, K-b, K-il, K-i2.When the extrusion force exceeded the press limit (lOOT), the ram slowed down automaticallyto keep pushing the billet through the die aperture, until the extrusion force required becameless than the press limit, and then the ram speed increased again (Fig. 4.13).I1200900600300010.80.6a)a)0.4’0.200 20 40 60 80Ram Displacement (mm)Chapter 4 Experimental 55iii) Other features, similar to 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 higherextrusion ratio or a larger volume fraction of the particle.1200 - 1.5•______1.2__A ) I 0.9600xf__—a-Force 0.63o0 cF —a--Speed__0.30 I I I0 20 40 60 80Ram Displacement (mm)Figure 4.13 Variation of ram speed at the press pressure limit (K-il)4.4 Extrusion Surface DefectsDuring the above two plant trials, the extrudates generally had a good surface finish.However, low speed cracks were observed at the front end of some extrudates from the planttrials at UAC when the ram speed was relatively low. This phenomenon disappeared if theram speed was increased. It occurred more frequently in the extrudates of 6061/A123/20pthan in 606l/A123/lop. The higher the extrusion ratio, the more severe the cracking. Figure4.14 shows extrudates of 606l/A123/2Op with different extrusion ratios of 13, 34, 52progressing from the ruler side; an extrudate of 6061/A12O3I1Opwith the extrusion ratio of 34is also shown at the right for comparison. It was interesting to note that low speed crackinghappened much more frequently in the plant trials at UAC, Anaheim, than in the plant trials atChapter 4 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 of each extrudate coveredwith low-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 elementanalyses and microstructural examination.Figure 4.14 Low speed cracking at the front end of two 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 through the casting. Die lineswere evident on all extrudates. These were present in all extrusions and cannot be counteredwith current technology. Some chatter crazing was observed on the last extrudates of eachdie. This defect was due to build-up of material on the die surface. Severe die wearing wasevident, as shown by measurement of extrudate diameter from each die (Table 4.7). No highChapter 4 Experimental 57speed cracking was observed, because the initial bifiet temperature and the ram speed for bothplant trials were not high enough.Table 4.7 Extrudate data from plant trials at UACTest No. Material Nominal Extrudate Coverage of low speed cracksDie Dia. Dia. at front end of extrudates(mm) (mm) slight(mm) severe(mm)S92-l 6061 31.75 / not available not availableS92-2 6061 31.75 31.98 not available not availableS92-3 606l1A123120p 31.75 32.00 not available not availableS92-4 606l1A1120p 31.75 32.00 not available not availableS92-5 606l/A1O3/lOp 31.75 32.03 not available not availableS92-6 606l/A12/lOp 31.75 32.03 not available not availableJ94-l 6061/A13/l0p 50.80 50.95 0 0J94-2 606l/A12O/lOp 50.80 51.18 0 0394-3 606l/A13/lOp 50.80 50.93 0 0394-4 6061/A12/lOp 50.80 50.95 0 0394-5 606l/A13/20p 50.80 51.10 102 0J94-6 6061/Al/2Op 50.80 51.13 229 0194-7 6061/Al3/20p 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/A13/l0p 31.75 31.78 114 0J94-11 6O6l/A12/lOp 31.75 31.85 3810 3048J94-llb 6O61/A13/1Op 31.75 31.95 406 0394-12 606l/A12120p 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/A123/lOp 25.40 25.40 51 0394-16 606l/A1/l0p 25.40 25.43 203 0394-17 606l/Al23/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/A1/hOp 38.10 38.10 0 0394-18 606l/Al23IlOp 38.10 38.10 0 0Chapter 4 Experimental 584.5 Effect of Extrusion Conditions on Tensile Properties of ExtrudatesPlant trials have been conducted at different extrusion conditions. It is known thatmechanical properties of the PRMMCs are improved after extrusion compared to the as-caststate. However, the effect of extrusion 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 of the 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 ASTMstandard procedure’°21.Figure 4.15 Schematic of a tensile test specimen4.5.2 Tensile Properties under Different Extrusion 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 tensileChapter 4 Experimental 59data from four samples tested for each condition is listed in Table 4.8. Unfortunately, only thestandard 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/Al2O3IlOp for different extrusion ratios is shown in Fig. 4.16(a). It isevident that the elastic modulus, yield stress, and ultimate tensile 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 of 6O6iIAl23/20p(Fig. 4.16(b)). A corresponding decreasing trend is evident in the elongation of the extrudatesfor both composites (Fig. 4.17). Although scattering of the data exists, the change in value ofthe elongation seems larger than the standard deviations (i’able 4.8).Table 4.8 Tensile test results of extrudates from the plant trials at KRDCTriai# ExtrusicJE Yield - UTS J E1opgJ(%) (°C) Ratio (GPa) (MPa) (MPa) Stand. Dev.(%)6061/A123/20pK-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 7.5/0.760611A123lopK-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 12.0/1.7Chapter 4 Experimental 603006_. — — — _ — — — — — — — — — —250 —ii----E-Modulus(GPa)-- x - Yield Stress (MPa)200 UTS(MPa)x15010050 I I I10.00 15.00 20.00 25.00 30.00Extrusion Ratio(a) 6061/A123/lOp300— a a — a — — — — S250 .—a----- B-Modulus (OPa)-- X - Yield Stress (MPa)200 .- UTS (MPa)-z15010050 I I I10.00 15.00 20.00 25.00 30.00Extrusion Ratio(b) 6061IA12O3I20pFigure 4.16 Tensile property under different extrusion ratiosChapter 4 Experimental 612017a14 T-10%118\5. I10.00 15.00 20.00 25.00 30.00Extrusion RatioFigure 4.17 Elongation of the composites as a function of extrusion ratioThe tensile properties are dependent on the volume fraction of the particle, as seen bycomparing the data of 6061/Al2OillOp and 6061/Al2Oil2Op. It is evident that a higher volumefraction results in a higher yield strength, UTS, and elastic modulus, but a lower elongationvalue. Therefore, the true volume fraction in each extrudate tested should be deteniiined,because under the same nominal volume fraction of 10 and 20% the true volume fraction mayvary from specimen to specimen. By dissolution of the matrix of the extrudates, moreaccurate volume fraction for each extrudate tested was obtained, as listed in Table 4.8 withthe tensile properties. It is seen that for the extrudates of 6O6lIAlzOil2Op, the true volumefraction varies from 18% to 19.8%, while for the extrudates of 6061/A12O3/lOp, it changesfrom 7.0% to 9.0%. The evaluation of the property change at different extrusion ratiosshould be conducted at the same true volume fraction (rather than a nominal value, as plottedin Fig. 4.16 and Fig. 4.17). The results of the tnais of K-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-plotted forChapter 4 Experimental 626O6lIAl2Oil2Op in 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.It is seen that for 6061/A12O3/2Op the elastic modulus, the yield strength and the UTS increasevery little with increasing extrusion ratios from 10 to 28 (Fig. 4.18(a)). However, for606l/A123/lOp, a slight increase 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 values are not available at the moment.3251III — — — — a — — — a a a — — a — — — —275 —---UTS (MPa)225 Yield (MPa)175EE (GPa)12575.10 15 20 25 30Extrusion RatioFigure 4.18(a) Tensile property change of 606l/AlO3/2Op for different extrusion ratioswith a true volume fraction from 19.2% to 19.8%Chapter 4 Experimental 63300. — — —— — — — — — . — — — — — — — — — 0----.-----. UTS (MPa)250a Yield (MPa)200xW2 XE 150 E (GPa)100A50 I I I10 15 20 25 30Extrusion RatioFigure 4.18(b) Tensile property change of 6061/A12O3I1Opfor different extrusion ratioswith a true volume fraction from 7.0% to 7.4%2017 4 —N — — —o — — — — —14 6061/A1203/lOp0011 6061 /A1203/20p8’5 I I10 15 20 25 30Extrusion RatioFigure 4.19 Coffesponding elongation values at different extrusion ratios for both compositesChapterS Modeling the Extrusion of the PRMMCs 64Chapter 5 MODELING THE EXTRUSION OF THE PRM[VICsThe literature review suggests that little work has been carried out on the analysis of atransient extrusion process at high temperature and none for the extrusion of the PRMMCs.To better understand 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 during hot extrusion will help to understand particle fracture and surface cracking.5.1 Mathematical Model of Extrusion Process5.1.1 Finite Element Model5.1.1.1 Flow FormulationDEFORM® is based on a Flow Formulation approach with a penalty functionprocedure using an updated Lagrangian procedure’831.The choice of the 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 for extrusion processes. In this study, the model consists of fourobjects 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 with the process, the billet material was assumed to behave as aChapterS Modeling the Extrusion of the PRMMCs 65rigid-plastic material, whereas the other three objects were defined as being rigid incomputation and only the billet was involved in deformation to which the flow formulationapplies.FORCE APPLIEDCONTAINER_________________PRESSUREPADSTACKCOMPONENTSFigure 5.1 Schematic of an extrusion pressBased on the virtual work-rate principle, the following variational equation wasobtained831.=Ja6cdV+JKe3e dV—JF1&vS=O(5.1)where V is the flow domain of the billet, and F1 is the traction specified on the surfaceboundary 5; and are effective stress and effective strain rate, respectively, which aredefined as:II— IEX11WDATh IChapterS Modeling the Extrusion of the PRMMCs 66= (aa..)’(5.2)2”’(5.3)Due to incompressibility, the rate of volumetric straining should be zero, i.e.:(5.4)To preserve the incompressibility condition 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 deformation analysisL83l. 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 function procedure831:am=42Ke(5.5)The compatibility between 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 the mean stress, am, as follows:a=a—öjjam (5.7)where ö is the Kronecker delta. According to the Levy-Mises theory, the constitutive lawcan be expressed as follows:8313_ . . (5.8)a =(—a/E)eChapterS Modeling the Extrusion of the PRMMCs 67Equation (5.1) can be converted to a series of non-linear algebraic equations by anormal FEM discretization procedure, resulting in:acIv(acI) (5.9)av, — av,Linearization of this equation was achieved by Taylor expansion near an assumed solutionpoint v = v0 (initial guess), resulting in,_____(5.10)+ [ L=, Av3 = 0av13where Av is the first-order correction of the velocity v0. Equation. (5.10) can be written inmatrix form,[K]{zv}={f) (5.11)where [Kj is the stiffness matrix, { Av } is the velocity correction term, and [f) is the residualof the nodal point force vector.Since the PRMMCs are extruded at high temperature, heat transfer occurs throughoutall the objects due to different initial temperatures and internal heat of deformation in the billetand friction heat at the interface. The governing equation for the heat transfer is: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 of generation of heatarising from deformation, which is obtained from the following well known formula:—. (5.13)q=iGewhere r is the efficiency of conversion of deformation energy to heat, and is assumed to be inthe range of 0.90 to 0.95, depending on the material being formed. Thus heat transfer andChapterS Modeling the Extrusion of the 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 in Eq. (5.12) is the rate of accumulation of internal energy. Eq. (5.12) can be discretizedfollowing a traditional Galerkin fmite element method and written in matrix fonn as11:[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 of the nodal temperaturechange with time.5.1.1.2 Boundary ConditionsFour objects were discretized into a series of 4-node iso-parametric elements (Fig.5.2). Due to axisymmetry, an axisymmetrical slice of the 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 12.0 24.0 36.0 48.0 60.0Radius (mm)Figure 5.2 Initial finite element mesh for the billet and its surrounding toolsChapterS Modeling the Extrusion of the PRMMCs 694-node iso-parametric element was used because it made remeshing easiei137’821.Due to limitation of the DEFORM® model, heat was oniy conducted between the billetand the surrounding tools. However, interface heat transfer between various tools, e.g.,between pressure pad and container, between container and die, was ignored (Fig. 5.2). Thethermal boundary condition between the billet and the tools is expressed as:= h(TBS — T) at interface boundary (5.15)where k is the thermal conductivity of the bifiet, and TB8, and TT8 are interface temperature ofthe bifiet and its contacted tool (pressure pad, container, and die), respectively; h is the heattransfer coefficient at the interface. For surfaces of all 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)At the center line of the billet, due to axisymmetry, the heat transfer rate is zero.kTB =0 at the center line of the billet (5.17)At the outer surface of the container, because of the induction heater, the surfacetemperature was kept constant as measured, i.e.,T = 7 at outer surface boundary of the 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: at the center line of the billet, the velocity in the radial direction is zero;Vr = 0 at the center line of the billet (5.19)At the container and the die interfaces, the velocity normal to the boundary, v, is zero,while the velocity normal to the interface at the pressure pad is equal to the ram speed.ChapterS Modeling the Extrusion of the PRMMCs 70v =0 at the container and die interface (5.20)v =v0(t) at the pressure pad interface (5.21)In addition, a friction stress was applied to the interface between the billet and the surroundingtools as stress boundary conditions. The shear factor friction law, t=mk, was adopted in hotdeformation, where t is the friction stress, m the shear factor, and k the shear strength of thebillet1831. The free surface at the bottom end of the billet and the free surface of the extrudatehave no surface traction.5.1.2 Input DataIn common with observations made by others1M’851,sticking friction conditions wereassumed to prevail at the 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/mK, based on the laboratory workon aluminum alloys by H1ady1861. 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,which was assumed to be constant11181.5.1.3 Solution ProcedureThe convergence of the scheme requires consistency and stability. The consistencyrequirement ensures that as the size of the elements tends to zero, the approximation equation(5.14) will represent the exact diffeintial equation (5.12) and its boundary conditions(Equations 5.15-5.16), and is satisfied by an approximation of the type,ChapterS Modeling the Extrusion of the PRMMCs 71T+ = T + tt[(l — f3) 1 + fT+] (5.22)The term f is 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, f should be greaterthan 0•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 for further temperature calculation in the same• . . V .time step, viz.: for velocity e1 (=0.5x10 ), where I lvii etc. is an error norm, defmed asII vii(vTv)1fl, and v is a vector, and for extrusion force e (=0. lxlO2). After thetemperature of all the objects was calculated, the geometry of the 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 of Jacobian 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 distribution of the new meshdensity was similar to that of the old one prior to remeshing; in this way remeshing errorsChapterS Modeling the Extrusion of the PRMMCs 72were minimized due to interpretation. The stroke step, As, (= V At, where VB is the ramspeed, and At is time step), adopted for the simulation was 0.25mm during the upsetting stage,and 0.05mm after that. The simulation was terminated when the extrusion reached the ‘steadystate’ region.5.2 Sensitivity Analysis of the ModelA sensitivity analysis in mathematical modeling should be conducted if values of someparameters 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 of elements 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 of 6061/AI2O3/20p were obtained from DuralcanUSA’181 as mentioned in Section 5.1.2. The other input data are listed in Table 5.1.Table 5.1 Some data for sensitivity analysis of the FEM modelBillet temperature, T 425°CContainer temperature, Tr 395°CDie temperature, T 395°CPressure pad temperature, Ti,.. 70°CExtrusion ratio 34.0Billet dimension 4178x305mmChapterS Modeling the Extrusion of the PRMMCs 73Because the peak extrusion force and the maximum temperature of the billet duringextrusion is crucial to the development of extrusion limit diagrams, the effect of the number ofelements in the bifiet on these two maximum values were studied. The maximum temperaturewas usually reached in the die land zone because of severe deformation at the die throat. Thiswill be seen clearly in the section of model predictions (Section 5.3.2.2). 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 of elements in this range. The effect of the number of elements 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 of elements 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 of the 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 mesh wasrefined 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) while only1000 elements in the billet were adopted in the upsetting stage.ChapterS Modeling the Extrusion of the PRMMCs 7412000 -10000-0 12508000- —-—-10007506000 500400020000. I I I0 5 10 15 20 25Displacement (mm)Figure 5.3 Sensitivity of load stroke curve to the number of elements in the billet465-455..445125014’ 1000I —-—-750500435 1I425 I I I I20 21 22 23 24 25 26Displacement (mm)Figure 5.4 Sensitivity of the maximum temperature to the number of elements in the billetChapterS Modeling the Extrusion of the PRMMCs 75This sensitivity analysis was conducted for the large press. However, the resultsshould also be applicable to the small press because the extrusion ratios for both presses whichare going to be simulated in the subsequent section are similar at approximately 30. Thereforethe element size in the billet of the small press would be about 10 times smaller when the samenumber of elements was applied, because the deformation zone of the billet in the large presswas about 10 times larger than that in the small press.5.3 Extrusion Process Simulation5.3.1 Processing conditionsThe 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 temperatureof 425°C, and the die to 336°C and the pressure pad to 70°C. The die was a flat faced die,with an aperture diameter of 32mm. A thermocouple was embedded in the die 1.6mm awayfrom the die bearing, in order to 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. The deliverytime of the billet from the furnace to the press was around 10 seconds. A flat-faced die withan aperture diameter of 10mm was employed. The die and pressure pad were 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 of the PRMMCs 76outside surface of the container. The details of the process conditions of the two plant trialssimulated are summarized in Table 5.2 for clarity.Table 5.2 Processing Conditions for Two SimulationsParameter S92-3, at UAC K-7, at KRDCTB 429°C 467°CT 425°C 475°C336°C 467°CTp 70°C 70°CRam Speed —2.6mm/s 0.9mm/sTransfer Time 40 sec 10 secExtrusion Ratio 34 28.0Billet Dimension Ø178x305mm Ø51x88mmNo. of Elements in Billet 1250 12505.3.2 Model PredictionsEach of the extrusion trials was simulated from the start of extrusion 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.5.3.2.1 Deformation BehaviorAfter the billet was loaded into the container, there was a gap between the billet andthe inside surface of the container due to the smaller billet diameter than the inside diameterof the container (Fig. 5.2). When the pressure pad pressed the billet, it commencedupsetting, and the container was gradually filled up. Figure 5.5 shows the material flow nearChapterS Modeling the Extrusion of the PRMMCs 77the end of the upsetting stage. The arrowheads are the nodal velocities starting at nodepositions in the finite element mesh of the billet. The length of the arrow is proportional tothe value of velocity. The apparent ‘wavy’ nature of the velocity arrows is due to thepositioning of the 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 of the material at the die exit were significantly higher than those inthe container because of the high extrusion ratio. The ‘dead metal zone’ at the cornerbetween the die and the container was present in both instances (see also Figures 7.1 and7.3). Although a tendency of material flow still appeared in the dead zone, the value ofvelocity at each node in the dead metal zone was close to zero(again, the apparent ‘wavy’nature of the velocity arrows is due to the positioning of the nodes in the finite element mesh).Chapter 5 Modeling the Extrusion of the PRMMCs 78-15.0 Velocity 3 (mm/s)-— TV, V V yyyy yV VVVVVVVV VV V \\\V VV450 ( J-55.0 1, 110.00 6.00 12.00 18.00 24.00 30.00Radius (mm)Figure 5.5 Material flow near the end of upsetting stage-15.0 -‘ ? NL._ Eff. Strain—3——BilletA O.50000E41Bx 0.000C 0.35000-35.0 oo.5ooooE. 065000F o.eOOoo0,z0.00 6.00 12.00 18.00 24.00 30.00Radius (mm)Figure 5.6 Effective strain distribution near the end of upsetting stageEE010,Figure 5.7 Velocity distribution in the billet after a ram displacementof 40.7 mm in the large extrusion press; length of arrow is proportional to velocity, ‘ , , , ,1?VVVP7ppp P p pPvVPr?p,ppppPPp, Pp P p PP?PVVPppPpPPPPp P,,ppppppppp, PP PpPr,, PPPPPPPPP,,,rrP PP p;;‘Pp?p,,rP Pp,,PPpPPPP,,,ppPPPPp, p pPPppppP p p• ppmfrppPFFFftP F FF F F p pFA Fa aFigure 5.8 Velocity distribution in the billet after a ram displacementof 26.7 mm in a small extrusion press: length of arrow is proportional to velocityVp p FpChapterS Modeling the Extrusion of the PRMMCs 79Velocity 217.8 (mm/s)42504.500-3.750-4000pp‘pP P‘PP,‘PP.pP pP PP 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 of the PRMMCs 80It 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. If the calculated nodal strain-rate was less than the limit strain-rate, thenthe limit value replaced the corresponding nodal value, and the zone was taken as ‘rigid’.The mean stress is representative of the stress state because it is defined as the meanof all the normal stress components: if the mean stress is negative, a compressive stress stateis dominant. However, if the 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 except in the surface layer near the die land. The absolute value of the 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, it is seen that the mean compressive stresses aresignificantly higher in the larger press, as would be expected due to the lower initialtemperature of the billet and higher ram speed. However, a common feature for both pressesis the negative value of the mean stress in the deformation zone and positive value in thesurface layer at the die land area. The significance of the negative mean stress is that it mayChapterS Modeling the Extrusion ofthe PRMMCs 81help minimize the microstructural damages (e.g., potential void formation due to decohesionand particle fracture) during extrusion of the MMCs. However, the existence of a tensilestress component in the surface layer in the die land area might contribute to the source of lowspeed cracking, which is a specific feature of extrusion of the particulate reinforced MMCs.This will be discussed in more detail in Chapter 8.Mean Stress (MPa)-2.750 B(etA= -335.008= -310.00C= -285.00D= -260.00-3050 E= 23500F=-210.00G= -185.00H= -160.001= -135.00J= -110.00-3350 K- -8000L=-60.000M= -35.000N= -10.0000= 15.000-3.650-3.95040.0 60.0 100.0Radius (mm)Figure 5.9 Mean stress distribution in the billet at a ram displacement of 40.7 mmin the large extrusion press (negative values denote compressive stresses)Although the mean stresses are quite different, the effective strain near the die is in therange of about 4- 5 for both presses, as expected because of their similar extrusion ratios. Atypical effective strain distribution is shown in Figure 5.11 for the small press at a ramdisplacement of 26.7mm. The annular strain pattern in the extrudate is also as would beexpected from a qualitative assessment of extrusions which shows a recrystallized ring after4.250ChapterS Modeling the Extrusion of the PRMMCs 82extrusion’91.The corresponding effective strain rate distribution is shown in Fig. 5.12 for thesmall press. It is seen that the strain rate distribution is confined in the die throat zone, and itsform is similar to predictions made by Chen, Oh and Kobayashit1201 for extrusion throughconical dies. The maximum strain rate is reached at the die exit corner where extrudate2 Mean Stress (MPa)Biliet-0.500A= -270.00B= -245.00C. -220.00D= -195.00E= -170.00-0.600 F=-145.00G=-120.00H= -95.0001= -70.000J= -45.000K= -20.000-0.700 50000I:i: -0800-0.9006.00 12.00 18.00 24.00 30.00Radius (mm)Figure 5.10 Mean stress distribution in the billet after a ram displacement of 26.7mmin the small extrusion press (negative values denote compressive stresses)surface forms from both the shear zone and a small volume of dead zone at the bottom of thedie interface1”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 s4 for the small press,estimated using another empirical equation (5,23)1611. However, the mean strain rate-1.0000.00Chapter 5 Modeling the Extrusion of the PRMMCs 83calculated using an empirical equation (5.24) [61) is only 2.4s. The low value estimated by thesecond 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 13.7s, 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-element analysis is ideal for this situation.— 6VBR (5.23)max— DE4Dvtanq (5.24)Em—‘3I2si.BLE)2 LII. 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 5.00 10.00 15.00 20.00 25.00Radius (mm)Figure 5.11 Effective strain distribution of the billet in the small pressChapter 5 Modeling the Extrusion of the PRMMCs 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 Effective strain rate distribution of the billet in the small press5.3.2.2 Temperature DistributionBecause the flow stress of the composites is very sensitive to temperature, thetemperature drop during transfer of the billet from the furnace to the container was alsoincluded in the simulation based on the measurement of the delivery time (Chapter 4). At thebeginning of the extrusion, due to the cold pressure pad and lower initial die temperature ofthe large press, a ‘cbilling’ effect exists at both ends of the billet, which consequently heats upthe pressure pad and the die by heat conduction through the interface. After the upsettingstage, the bifiet temperature exhibits the effect of deformation heating toward the die entry,although in the larger billet, this is more pronounced because of its lower initial temperature(Figures 5.13 and 5.14).-9.0000.00 3.00 12.00 15.00Chapter 5 Modeling the Extrusion of the 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-3.850 A= 330.008=345.00C- 360.000= 375.00E= 390.00F= 405.004.050 G= 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 Temperature distribution in the large extrusion press8d2 Temperature (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 15.0 30.0 45.0 60.0Radius (mm)Figure 5.14 Temperature distribution in the small extrusion pressChapterS Modeling the Extrusion of the PRMMCs 86Temperature increases of approximately 70°C and 23°C were predicted for the largepress and the small press, respectively, because of the heat of deformation. 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 higher rate of heat generation. Themaximum temperature of about 484°C and 479°C for the large and small presses, respectively,is reached at the surface of the extrudate in the die land zone. The maximum temperature ofthe die is about 10°C less than the maximum value in the billet due to the thermal resistance atthe die interface. Because the thermal diffusivity of the die material (H13) is about 7 timesless than that of the 606l/A12O3/20p, a much larger thermal gradient exists in the die land thanin the extrudate. The more pronounced thermal gradient in the die land for the large press is aresult of the difference in initial die and bifiet temperatures while the large thermal gradient inthe extrudate of the large press is due to the larger diameter of extrudate and the higher ramspeed, which results in a more pronounced adiabatic heat effect.5.3.2.3 Comparison of Predictions with Measured DataLoad / stroke predictions are compared with measured data for displacement beyondthe 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, especiallyfor the small press, in which a larger shift in the peak load appears. This might be due to theassumption of rigid tools in the FEM model, while in reality there always exists deformationof the press. The large shift in the peak load might be partly due to the capacity of the smallpress (lOOT) which was almost fully loaded in the test, while the 3000T capacity of the largepress meant it was only half used. Therefore the compliance of the press has to be estimated.ChapterS Modeling the Extrusion ofthe PRMMCs 8714000___________Measured12000FEM‘10000V8000. 6000:t20000 I I I0 10 20 30 40Ram displacement (mm)Figure 5.15 Comparison of predicted force with measured data (large press)12001000__Measured800‘FEMC)600CL4002000 I I0 10 20 30Ram dislacement (mm)Figure 5.16 Comparison of predicted force with measured data (small press)ChapterS Modeling the Extrusion ofthe PRMMCs 88440420U_________0380360•5 340320300- I0 10 20 30 40Ram displacement (mm)Figure 5.17 Comparison of predicted temperature with measured data (large press)The predicted temperature at the thermocouple position of approximately 1.6 mmaway from the die bearing in the die for the larger press (Figure 5.17) is within 10°C of themeasured temperature over the range of the simulation, although it does 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 to theassumption of initial uniform die temperature and the error of the thermocouple positionbecause the thermocouple was inserted into the hole in the die after the die was put into 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 resultsMeasuredFEMaaa aaaChapter 5 Modeling the Extrusion of the PRMMCs 89were saved to prevent a big size (could be up to 300MB) of the output database file duringsimulation. However, the load value was saved automatically for each step in the model.5.4 Validation of Model PredictionsModel predictions must be evaluated in the light of the fact that the boundaryconditions in some areas were not precisely defined, and this may affect the results. Thefriction between the billet and container or die surfaces was assumed to be sticking frictionbut was not measured. Furthermore, the temperature field in the billets extruded through thelarge-scale press was not accurately known, due to the constraints imposed by the conditionsunder which the trial was conducted. In addition, the temperature at the die in the smallerpress was not recorded. The prediction of the forces required for extrusion is mostsusceptible to temperature variations. Finally, it must be recognized that the simulation is atwo-dimensional simulation, and any results should be treated with caution, although for theaxisymmetrical case considered here, errors are likely to be low.Notwithstanding these limitations, the modeling has resulted in a reasonably accurateprediction of load and temperature rise. Furthermore, predictions in the upsetting stage aredifficult with a fluid-flow type model°’, but in this work the agreement between predictionsand measured data was very good. The ability to predict forces in the upsetting stage has aconcatenation effect in that it influences the subsequent predictions of, 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 considerably closerto the measured value. The predicted sharp rise in load after upsetting of the billet does notaccurately follow the measurements (the scale of the abscissa in Figs. 5.15 and 5.16 distortsChapterS Modeling the Extrusion of the PRMMCs 90the difference however). This is not an anomaly of the model, as mentioned before, but ratheris a consequence of defming the die, container, and pressure pad as rigid objects during thesimulation. In reality, the components are not rigid, but this assumption was needed tocomplete the simulation in a reasonable CPU time. Thus, the model predicts only theresponse of the material, whereas the instruments on the press read the response of the wholesystem.It is known that the difference between the length of a billet before extrusion and thelength of the remained butt end after extrusion is the real displacement the billet experiencedduring extrusion. If the press (assuming the billet is rigid-plastic) were rigid, then therecorded 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,including the elastic deformation of the bifiet, was obtained to be 5.27mm for the given test.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 overall elastic deformation constant for the press 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 simulated by DEFORM® , can be 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, and t denotes extrusion time.Chapter 5 Modeling the Extrusion ofthe PRMMCs 9114000___________Measured12000FEMz 10000 I‘1.)° 8000I.° 60004000,,:10 10 20 30 40Ram displacement (mm)Figure 5.18 Comparison of FEM force with measured data corrected for extrusion presscompliance according to Eq. (5.26); large press12001000 • Measured• iFEMz- 800_0600•04002000L1 I I0 10 20 30Ram displacement (mm)Figure 5.19 Comparison of FEM force with measured data corrected for extrusion presscompliance according to Eq. (5.26); small pressChapter 5 Modeling the Extrusion of the PRMMCs 92Another way to calculate the E0 is to measure the unloading slope of the extrusionforce-stroke curve. The average E0 for the larger press is measured as 2777kN1mm from fourtests. Corrections to the measured data accounting for the machine compliance align themeasurements with the simulation (Figures 5.18 and 5.19). In principle, the reverse ispossible: the simulation could include an elastic component in order to better model thespecific extrusion press under investigation, at the expense of simulation time.The variation in the load prediction, after the peak load has been reached (Figures 5.15and 5.16), is due to a node in the bifiet losing contact with the die and a consequent drop inthe extrusion force. The software attempts to compensate for this node unpinning, causingthe observed behavior. The prediction could be improved in a number of ways, although anybenefit derived from eliminating the small variation (less than 10%) would itself be canceledout by the large increases in CPU time required to achieve the following solutions. Either themesh at the die throat could be further refmed by increasing the number of elements, or theArbitrary Lagrangian-Eulerian (ALE) method could be used, though there is no guarantee thata re-meshing would not be required; furthermore, the mesh velocity would be difficult todetermine. In addition, it is unlikely that in either case the proximity of the prediction to themeasured data would be altered.5.5 SummaryA model has been developed and verified to simulate the extrusion of PRMMCs. Themodel is a bulk forming model with the material assumed to be monolithic with the propertiesof the composites. Both the transient and steady state parts of extrusion were modeled. Adescription of the bulk extrusion of this MMC has been presented and shown to be valid forthe prediction of extrusion loads, and consequently deformation in the billet during extrusion.ChapterS Modeling the Extrusion of the PRMMCs 93Load predictions resulting from this model agree to within ten percent of the measured value,and in the upsetting stage, to a higher accuracy. Temperature predictions agree to within lessthan three percent. Slight discrepancies between the model and measurements in the region ofmaximum rate of change in load have been accounted for by elastic deformation of the presscomponents. The model is useful for macroscopic analysis, such as the development ofextrusion limit diagrams, but cannot correctly predict deformation on the scale of the particles.However, the stress, temperature, and strain distributions can be related to the propensity forparticle fracture and/or void formation.Chapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation 94Chapter 6 MICROMECHANICAL ANALYSIS OF THEPRMMC DURING LARGE DEFORMATION6.1 Obstacles and Challenges ofMicromechanical Analysis of the PRMMCsIn 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 of the obstacles stated below.6.1.1 Particle PhenomenaIt 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 the Duralcan® composites; (c) it isknown that large particles tend to fracture more easily than small particles; (d) moreimportantly, the distribution of the particles in as-cast MMCs 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 theChapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation 95particles and clusters should be taken into account. However, because the average dimensionsof a particle (up to 501.tm) in the MMCs are significantly (—10k times) smaller than those ofthe workpiece (e.g. 10 mm), if the deformation of the particles in the MMCs were studied, atleast 108 elements would be necessary for a two dimensional analysis with the element sizeclose to a particle dimension. Obviously, this is impractical from a computational stand point.Then the question is, how can a micromechanical analysis of the MMCs be conducted with atraditional finite element model?6.1.2 Matrix PhenomenaThe MMCs are not simply a mixture of the particles and the matrix. In fact, theinteractions of a second phase particle with the matrix during deformation is very 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 of the 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 of the particle during deformation, etc., The question is, how could afinite element model take those factors into consideration?6.1.3 Modeling ConstraintsTo 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 which includes allChapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation 96the factors or at least the most dominant (if known) ones influencing the dynamic behavior ofthe MMCs by combining both the macroscopic and microscopic process parameters? If itwere developed, could it be applied to a multiaxial stress state during processing by validatingonly through uniaxial compression and/or tensile testing? It seems impractical to overcome allthese obstacles by the available plasticity theory and computation technology.6.2 Micromechanical Analysis during Plane Strain CompressionUnder the above mentioned circumstances, it is therefore impractical to conductmicromechanical analysis of the MMCs during industrial extrusion. Nevertheless, a laboratoryplane strain test was simulated to analyze the behavior of particles during hot deformation.To simplify the analysis, a twin-particle model and a multiple-particle model were adoptedwith each particle size of 40x40 p.m2 in the planar cross section. In the twin-particle model,two particles were arranged such that the particle movement in the lateral directionperpendicular to the loading direction could be analyzed. In the mode1, the matrix around theparticle behaves as a monolithic material with the deformation properties of the composite,and the particle has its own properties and flows along with the matrix during deformation.The DEFORM®, as described in Chapter 5, was adopted for the micromechanical analysis.The initial setup of the plane strain test simulation with finite element meshes for eachobject is shown in Fig. 6.1. Because the particle size is only 40p.m2 , the element size aroundthe particles is tremendously refined. The detailed finite element mesh around the twoparticles is shown in Fig. 6.2 for the twin-particle model. For a plane strain test simulation,only a half of the set was analyzed due to its symmetry. The friction shear factor, m, and theheat transfer coefficient, h, at the interface between the specimen and the anvil were assumedChapter 6 MicrostructuralAnalysis ofthe PRMMC during Large Deformation 97to be 0.7 and 200 kW/m2K1861,respectively. The test simulation conditions are listed in Table6.1. The nominal strain rate is 0.05/s. The total reduction was about 50%.Table 6.1 Simulation conditions for plane strain deformationObject Name (No.) Material Size Temperature Number of(mm) (°C) ElementsUpper Anvil (#1) 718 (rigid) 8.64x3.0 445 100Specimen (#2) 606l/AI2O3/2Op 25.4x10 450 2500(rigid-plastic)Bottom Anvil(#3) 718(rigid) 8.64x3.0 445 100Particle (#4) A1203(elastic) 40x40 urn2 450 18-3614.0010.60 -720E>-3.80______0.00 3.40 6.80 10.20 13.60 17.00X (mm)Figure 6.1 Initial finite element meshes for each object of plane strain deformationChapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation 986.2.1 Twin Particle ModelFor 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 the particle and the matrix was assumed to be perfectly bonded. The elastic modulusof the particle was 450 GPa; the Poisson ratio was 0.25, and the coefficient of thennalexpansion was 7.7x1041°C with the reference temperature of 450°C, based on data in theliterature for the same kind ofMMC’1.5.1505.1005.050>-5.0004.9500200Figure 6.2 Initial finite element mesh around two particlesThe effective strain distribution in the specimen at a reduction of about 49% is shownin Fig. 6.3(a) and (b) with and without particles, respectively. From the figure, it is seen thatthe overall effective strain distributions for both cases are quite similar, but deformation0.000 0.050 0.100 0.150X (mm)Chapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation 99localization occurs around the particles. This is because only two particles are considered inthe micromechanical analysis. The localized effective strain is shown more clearly in Fig. 6.4as a function of reduction. Fig. 6.4 (a) shows the effective strain distribution around twoparticles at a reduction of 10%. It is seen that the highest strain is concentrated in the middleof the two particles (Contour line ‘C’), and the strain around the two particles is at about thesame level (contour line ‘B’). As the reduction increases, the particle located outside thecenter line is pushed away by matrix material along the flow direction. The distance betweenthe two particles becomes about 130J1m (Fig. 6.4(b)). As a result, the effect of clustering isdecreasing, although the highest strain is still concentrated between the two particles (Contourline ‘F’). At a reduction of about 49%, two closely distributed particles are pushed apart froman initial spacing of 40tm to more than 300J1m (Fig. 6.4(c)). It is seen that a low strain zone(contour line ‘F’) appears close to the particle. The highest strain 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 sheardeformation and healed by compressive hydrostatic pressure.The effective stress in the particles at two different reductions of 10% and 49% isshown in Fig. 6.5. It is seen that the stress level is much higher than that of the effective stressin the matrix, which is about 6OMPa. This is partly due to the assumption of plane strahideformation, in which the strain in the third direction is constrained to be zero. Therefore,Chapter 6 MicrostructuralAnalysis ofthe PRMMC during Large Deformation 1009.80 -EU. SwainObedS 2c A=0.00000E.00B= 0.300006.60 - C=0.600000=0.90000E E=12000F=1.5000>- G= 1.80001-1= 2.10003.40 1= 2.4000C020-3.00-0.00 3.40 6.80 10.20 13.60 17.00X (mm)(a) Twin particle model-0.020EU. StrainObed 12c A= 0.00000E*00B= 0.30000-0.340 - C= 0.600000=0.90000E E= 12000E F=1.5000>- G=18000H= 2.1000-0.660_______1= 2.4000DEC-0.980—1.3000.00 3.40 6.80 1020 13.60 17.00X (mm)(b) homogeneous MMCSFigure 6.3 Effective strain distribution at a reduction of 49%Chapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation 1014900Objedl2A= 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) at a reduction of 10%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 0.080 0.160 0240 0.320 0.400X (mm)(b) at a reduction of 30%Chapter 6 MjcrostructuralAnalysis of the PRMMCduring Large Deformation 1022.850 Eff. StrainObject # 2A= 0.00000E÷008= 0.30000C= 0.60000D= 0.90000::: =2.40002.490-2.3702250-0.000 0.160 0.320 0.480 0.640 0.800X (mm)(c) at a reduction of 49%Figure 6.4 Localized effective strain distribution around two particlesat different reductionseven a very small strain in the third direction could lead to a large stress because of highelastic modulus of the particle. It is also interesting to see that the value of the effective stressin the particles increases as the reduction increases. Besides the effect of matrix defonnation,this could be also due to the build-up of thermal stress in the third direction when temperaturein the particle changes during deformation. The larger value of the effective stress in theparticles at a small reduction during large defonnation confirms that particles could fracture ata early stage of deformation, if the fracture stress of the particle is reached.Chapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation 103Elf. Stress (UPa)4.700 objedl 4 (right)A= 40.0008= 80.000C= 120.000= 160.004.620 Ex 200.00Ot*d 1 5 (dr hne)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 0.320 0.400X (mm)(a) at a reduction of 10%2.750 Elf. Stress (UPa)Obed 1 4 (right)A= 40.0008=80.000C= 120.002.670 0= 160.00E= 200.00Object 15 (dr ne)A= 40.0002.590 8=80.000C= 120.000= 160.00E= 200.00>-2.5102.4302.3500.000 0.080 0.160 0.240 0.320 0.400X (mm)(b) at a reduction of 49%Figure 6.5 Effective stress in the particles at different reductionsChapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation 1046.2.2 Mulliple-Particle ModelTo consider the effect of clustering of particles in a composite, a four-particle modelwas developed with two more particles added to the twin-particle model, as shown in Fig. 6.6.Due to the presence of more 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 ahigher strain zone (Contour line ‘B’) appears in the middle of two 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 because at the early stage ofdeformation, four particles act as a cluster; therefore, the center of the cluster is hardlydeformed. The effective stress distribution in both particles and the matrix is shown in Fig.6.7. Considering the stress distribution in the matrix, it is seen that a low stress zone(Contour lines ‘D’) exists in the center of the four-particle cluster. Again, the effective stressin the particles are more than 4 times higher than that in the matrix, which is similar to thetwin particle model as described above. The mean stress distribution in the matrix shows atensile stress state in the zone between the two particles in the lateral direction (Fig. 6.8),whilst the stress state between the two particles in the loading direction is compressive. Thestress state in each particle is quite similar a tensile stress component exists at the top and thebottom surface of each particle (the locations of contour line ‘E’ in each particle) due to thepositive value of the mean stress, which could be a potential site for cracking.105Chapter 6 Microstructural Analysis of the PRMMC during Large DeformationEff. Strain5200 ot4edl 2A= 0.0150B= 0.0350C= 0.0550D= 0.07505.100 E= 0.09605.000>-4.9004.8004.7000.000E>-0.070 0.140 0.210 0280X (mm)0.350Figure 6.6 Localized effective strain distribution at a reduction of 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 0.100 0.150 0200X (mm)0250Figure 6.7 Localized effective stress distribution at a reduction of 1%Chapter 6 MicrostructuralAnalysis ofthe PRMMC during Large Deformation 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.g504.9004.8500200Figure 6.8 Localized mean stress distribution at a reduction of 1%0.000 0.050 0.100 0.150X (mm)6.3 Micromechanical Analysis during Cylindrical CompressionAlthough a unit cell model in plane strain condition has been widely adopted byresearchers for particle analysis at a microscopic level, obviously the particle model is notrepresentative of a real three dimensional particulate, but instead of an infinite bar in 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 eitherChapter 6 Microstructural Analysis of the PRMMC during Large Deformation 107cylindrical or spherical in 3-D due to axisymmetry. The simulation conditions are listed inTable 6.2.Table 6.2 Simulation conditions for cylindrical compression testObject Name Material Size Temperature(°C) No. of Elements(No.)Upper Anvil 718 20x20mm 449 150(#1) (rigid)Specimen 6061/A12O3/2Op 410x15mm 450 2500(#2) (rigid-plastic)Bottom Anvil 718 420x20mm 449 150(#3) (rigid)Particle AI2O3 20.440im 450 18-36(#4) (elastic)The initial finite element mesh of a specimen including particles is shown in Fig. 6.9(a).Again, the element size around the particle was tremendously refined, as shown in Fig. 6.9(b)for a single particle and Fig. 6.9(c) for a twin-particle model. The nominal strain rate for thetest is 0.05/s, and the nominal strain is 1.0. The other boundary conditions are the same as inthe plane strain simulation.6.3.1 Single Particle ModelA single-particle model refers to a cylindrical specimen under large hot deformationcontaining only one particle at the center line. For the cylindrical compression test, only anaxisymmetrical plane was analyzed due to its axisymmetry. The particle had to be in thecenter line because otherwise it would become a ring. Two extreme shapes of a particle wereconsidered, i.e., a cylinder and a sphere in three dimensions. Four different particle cases werestudied. The particle size for each single-particle model adopted is listed in Table 6.3.Chapter 6 MicrostructuralAnalysis of the PRMMCduring Large DeformationE16.00(a) initial finite element mesh in a specimen108—4 I %I j_...4 % V7.6007.4000.000 0.050 0.100 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 0.100 0.150Radius (mm)(b) mesh around a particle7.450E4-C)0,:i:7.5007.4007.450Radius (mm)(c) mesh around the twin particlesFigure 6.9 Initial mesh and location of a particle in a cylindrical specimenChapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation 109Table 6.3 Particle sizes studiedCase Comp-1 Comp-2 Comp-3 Comp-4Shape Cylinder Cylinder Sphere CylinderSize($Imxlim) 40x40 420x20 42O ct20x80Aspect Ratio 1.0 1.0 1.0 4.06.3.1.1 Material Flow of a Cylindrical Specimen Containing a ParticleThe 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 straindistributions for two specimens are very similar, but a larger strain is reached near the particledue to strain localization. Details of the local strain distribution around the particle are shownin Fig. 6.11 for the 40x40im particle. In the loading direction, it is seen that a low-strainzone appears at both the top and the bottom of the particle; however, a high strain zone showsup adjacent to the low strain zone. This is because during compression, matrix material nearthe center line flows towards the particle which is located at the center of the 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 cylindrical surface.Effective strain variations along the center line in the loading direction for different reductionsare shown in Fig. 6.12. It is seen that, as the reduction increases, the non-uniformity of straindistribution becomes more severe. The effective stress distribution for both cases, with andwithout particles, is shown in Fig. 6.13(a), and (b). Again, the overall distributions of theeffective stress are quite similar to each other; but stress localization occurs around theparticle (Fig. 6:14). A maximum effective stress of around 260 MPa in the particle is reached,which is almost 4 to 5 limes larger than that of the matrix. The corner of the particle is aEfi. StrainObject # 2A= 0.200008= 0.530000=0.86000D= 1.1900E= 1.5200F= 1.8500G= 2.1800H= 2.51001= 2.8400J= 3.1700K= 3.5000Chapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation 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 upper and the bottom zone in the particle.6.004.50EE3.000)z1.500.0010.000.00 2.00 4.00 6.00 8.00Radius (mm)Figure 6.10 Effective strain distribution in the cylindrical specimenat a reduction of 65%: (a) monolithicChapter 6 MicrostructuralAnalysis of the PRMMC during Large DeformationRadius (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. StrainObjed 1 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)1.500.000.00 10.00Figure 6.10 Effective strain distribution in the cylindrical specimenat a reduction of 65%: (b) with a particle2.00 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 strain distribution around the particle at a reduction of 65%Chapter 6 Microstructural Analysis of the PRMMC during Large Deformation 11232.52Cl)1.510.504-x2 4 6 8 10 12Distance from Surface of the Bottom Anvil (mm)Figure 6.12 Effective strain distribution along the center line of the specimenunder different reductions600Eff. Stress (UPa)Objed#2A= 20.0008= 24.000C= 28.000450D= 32.000E= 36.000F= 40.0006 ( 446 14= 48.0003001=52.000- J= 56.000K= 60.0001.500.000.00 10.00Figure 6.13 Effective stress distribution in the cylindrical specimenat a reduction of 65%: (a) monolithic without a particle2.00 4.00 6.00- 8.00Radius (mm)Chapter 6 MicrostructuralAnalysis of the PRMMCduring Large Deformation6.004.50E3.000):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 stress distribution in the cylindrical specimenat a reduction of 65%: (b) with a particle2.00 4.00 6.00 8.00EE0)0)2.7102.6702.6302.5902.550aEff. Stress (UPa)Object I 2A= 20.0008= 24.000C= 28.0000= 32.000E= 36.000F= 40.000G= 44.000H= 48.0001= 52.000J= 56.000K= 60.000Object 1 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 6.14 Effective stress both in the matrix and in the particle at a reduction of 65%Chapter 6 MicrostructuralAnalysis ofthe PRMMCduring Large Deformation 114Mean Stress (UPa)6.00 Objed#2 ‘A=-150.00( B= -133.00C= -116.00D= -99.0004.50 E= -82000F= -65.000- N G=-48000\ H=-31.000I=-14.0003.00 ç J= 3.0000r K= 20.000a,:i:1.500.00 I I I0.00 2.00 4.00 6.00 8.0010.00Radius (mm)(a) monolithic without a particleMean Stress (UPs)6.00 Objed#2A= -150.00C= -116.000.. -99.0004.50 E=-82.000F.. -65.000E G=-48.000E H=-31.000I I.. -14.000b i- I J=3.0000B= -133.00rK= 20.0001.500.00 I I I I0.00 2.00 4.00 6.00 8.00 10.00Radius (mm)(b) with a particleFigure 6.15 Mean stress distribution in the cylindrical specimenwith and without a particle at a reduction of 65%Chapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation 115Mean 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)Figure 6.16 Mean stress distribution both in the matrix and in the particleat a reduction of 65%6.3.1.2 Effect of Particle ShapeDifferent particle shapes were analyzed during the compression test, as listed in Table6.3. A damage factor was modified based on the plastic workfracture criterion proposed byLathem and Cockcroft1511 , and was used to compare the effect of particle shape on the stressand strain state at a reduction of 65% during compression (Fig. 6.17)(a)-(d)).Df=f(-)d(6.1)where a1 is the maximum principal tensile stress, is the effective stress, and d is theeffective strain increment. As described in the literature review, in cold forming operations, itwas found that failure of a monolithic material at some point occurs when the damage factorreaches a critical value. This criterion, together with finite element modeling, has been usedChapter 6 Microstructural Analysis of the PRMMC during Large Deformation 116extensively to predict the occurrence of damage during cold forming’49”°91. Sellars et al.49tested the above equation and concluded that the equation could be a reasonable criterion forhot working as well as for cold working, but further data is required to test it 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 confirmed that 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 for the larger cylindrical 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 thematrix damage than the small ones, especially at the corners (Fig. 6.17).Figure 6.18(a) shows the effect of particle shape on the effective strain variation alongthe center line near the particle at a reduction of 65%. 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 the horizontalmid-plane is shown in Fig. 6.18(b). It is evident that the strain near the spherical particle isquite uniform compared to the case with no-particle. However, a significant strain drop waspredicted in the radial direction near the interface of particles of 2Ox8Oj.im and 4Ox4Ojim.Chapter 6 Microstructurat Analysis of the PRMMC during Large Deformation 1172.750 DamageObed$ 2A= O.00000E.008= O.38000E-01C= 0.76000E-010=0.114002.710 E= 0.15200F= 0.19000G=022800H= 0266001=0.304003=0.342002.670 K= 0.38000Z2630.2.590 -2.5500.000 0.030 0.060 0.090 0.120 0.150Radius (mm)(a) ‘3i40x4() (cylinder)DamgeObed # 22.710 A= 0.00000E+008= 0.38000E.01C= 0.76000E-010=0.11400E= 0.15200F= 0.190002.670 G=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)Chapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation 1182.750 DamageObjecll2A= 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 0.120 0.150Radius (mm)(c) cI2O (sphere)2.710 DamageObied 1 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 0.030 0.060 0.090 0.120 0.150Radius (mm)(d) c120x80 (cylinder)Figure 6.17 Effect of particle shape on damage factor at a reduction of 65%Chapter 6 Microstructural Analysis of the PRMMC during Large Deformation2.7 2.75 2.8 2.85 2.9Distance from surface of the bottom anvil (mm)(a) along the center line of the specimen (40x40 etc are the particle size in microns)(b) along the mid-plane in radial direction (40x40 etc are the particle size in microns)Figure 6.18 Effect of particle shape on strain distribution at a reduction of 65%119- --. No Particle— Cylinder 40x40Cylinder 20x20a Sphere 20Cylinder 20x803.75 . -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 ParticleI Cylinder 40x40‘I Cylinder 20x20I o Sphere 20I Cylinder 20x80— I I0 0.2 0.4 0.6 0.8Distance from center line to the bulge surface (mm)1Chapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation 120450 +400 + + + + + ++ ° Cylinder 40x40350 A Cylinder 20x20300 A250 00 A Sphere 20200 + Cylinder 20x80150• 10050 I20 30 40 50 60 70Reduction (%)Figure 6.19 Effect of particle shape on effective stress variation during compression(40x40, 20x20, 20, and 20x80 are all the particle sizes analyzed in microns)The effective stress in the particle is not so sensitive to the reduction for all the fourparticle shapes, as shown in Fig. 6.19; however, the particle shape itself affects the stressvalue quite significantly, from about 125MPa for the spherical particle (‘Sphere 201.Lm’), to425MPa for the highest aspect ratio particle (‘Cylinder 20x80p.m’ in Fig. 6.19). The valuesfor the cylindrical particles with an aspect ratio of unity are quite close. Therefore, it isconcluded that the particle fracture is sensitive to the shape of particles, especially for thosewith a larger aspect ratio, while the size of equiaxed particles is less important.6.3.2 Multiple Particle ModelThe characterization of single particle behavior during cylindrical compression mightonly apply to the situation in which particles are separated by a large distance relative to theirChapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation 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 of 40x40 located at the center line ofthe compression specimen were studied.6.3.2.1 Effect of ReductionParticle 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 of 33%, and its characteristics are quite similarto that of a single particle model (Fig. 6.20(a)). However, at a reduction of 65%, deformationaround the particle becomes more severe. A localized strain zone extends in the radialdirection as a result of material 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. 6.2 1(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, which implies a complex tn-axial stress state.6.3.2.2 Effect of Particle SpacingThree different initial particle spacings of 20, 40, and 120pm were studied. The effectof particle spacing on strain values along the center line of the specimen are shown in Fig.6.22(a). It is seen that the strain reaches a maximum at a point about half a particle size aboveElf. StrainObject 41 2A= 0.20000B= 0.53000C= 0.86000D= 1.1900E= 1.5200F= 1.8500G= 2.1800H 2.51001= 2.8400J= 3.1700K= 3.5000Chapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation 122the particle, and the maximum values for each spacing are not much different, with thesmallest spacing being the largest. The minimum strain value is located at the right top of theparticle, 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 deformation in the gap.5.2005.1505.100E0)0)5.0505.000Figure 6.20 Effective strain distribution at different reductionswith a starting particle spacing of 120 jim: (a) 33%4.9500.000 0.030 0.060 0.090 0.120 0.150Radius (mm)Chapter 6 Microstructural Analysis of the PRMMC during Large DeformationFigure 6.21 Mean stress distribution in the matrix and in the 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 strain distribution at different reductionswith a starting particle spacing of 120 pm: (b) 65%Mean Stress (MPa)Obje I 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 0.150under different reductions with the initial particle spacing of 120 pm: (a) 33%Chapter 6 Microstructural Analysis of the PRMMC during Large DeformationRadius (mm)Figure 6.21 Mean stress distribution in the matrix and in the two particlesunder different reductions with the initial particle spacing of 120 pm: (b) 65%Distance from surface of the bottom anvil (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 I I I I2.6 2.65 2.7 2.75 2.8 2.85 2.9 2.95 3(a) along the center line of the specimenIChapter 6 Microstructural Analysis of the PRMMC during Large Deformation(b) along the mid-plane between two particles in radial directionFigure 6.22 Effect of particle spacing on strain distribution at a reduction of 65%12510864200 2 3 4 5 6Displacement (mm)9 102.221.81.61.41.2No Particle.20 MicronsI —x— 40 Microns—D —l20MicronsI I0 0.2 0.4 0.6 0.8Distance from center line to the bulge surface (mm)1Measwed Iz IFEMzzzFigure 6.23 Comparison of predicted value with measured dataChapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation 1266.4 Model ValidationFor validation of the model predictions, the final geometry of the simulated cylindricaltest specimen was measured. Table 6.4 shows the final maximum diameter measured andpredicted during compression, which suggests barreling.Table 6.4 Comparison of model predictions with measured dataIt is seen that the predictions are in very good agreement with the measured data. This can befurther validated by comparison of the 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 behavior in MMCs during large 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 break clusters 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, if the stress in a particle is largeenough;3) The shape of a particle has a large effect on fracture of both the particle and itssurrounding matrix under large deformation, and particles with sharp corners and large aspectratios have the greatest propensity to fracture;Chapter 6 Microstructural Analysis of the PRMMC during Large. Deformation 1274) Particle fracture is not very sensitive to the size of equiaxed particles; however, it isknown that the probability of particle fracture is a function of the probability of finding a flawin the particle and the probability of activating a flaw. Apparently, larger particles may have ahigh frequency of flaws. Because this effect has not been considered in this work, it is stilltrue that large particles may have higher probability to fracture during large deformation.5) Small particle spacing results in a complex stress state in the cluster zone.However, as the particle spacing increases, the interaction between particles decreases. Thetensile stress generated in the interparticle zone in the flow direction may cause void formationduring deformation or promote void growth if the voids are present while the 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 behavior of the material.128Chapter 7 PARTICLE FRACTURE OF THE PRMMCDURING 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 of particle 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 during hotdeformation has received little attention. Furthermore, deformation to high strain at lowtemperature has been limited by the low failure strain of the MMCs. Therefore, there arefeatures of low temperature deformation which are expected to relate to deformation underconditions characteristic of extrusion. Particle fracture occurs owing to the inability of thematerial to accommodate local stresses. Fracture at low temperature is related to strain,particle size, particle aspect ratio175’761 (see also Section 8.2 for the micromechanical analysis)and volume fraction1”. The superimposed hydrostatic pressure during deformation extendsthe ductility, and effectively inhibits void foniation”90911. Under such circumstances matrixmaterial may also flow into the voids between fractured particles under large deformation.To elucidate the nature of particle fracture during the hot extrusion process, themicrostructure of the composite in the deformation zone and of the extrudates ofChapter 7 Particle Fracture of the PRMMC during Extrusion 1296O611A123/lOpand 6061/A12O3/20pwas examined, i.e., particle distribution, size refinement,and orientation and migration of particles were characterized.7.1 Specimen Preparation for the PRMMCsA specimen of area about lOxlO was cut using either a hack saw, or a TiVcutting wheel blade. The specimen was mounted and polished in an automatic polishingmachine. The detailed polishing procedure adopted at KRDC, Kingston, is listed in Table 7.1.Table 7.1 Polishing procedure for Duralcan materials at KRDCStep Paper/Cloth Grit Size Time Lubricant Load Remark(jim) (mm.) (N)1 SiC paper Grit 120 until water 100 flatflat2 Petrodisk 15 10 Struer’s blue 80- flat with lessDiamond plate lubricant 100 scratches3 Perforated 15 10-15 Struer’s blue 100 more shinnycloth lubricant4 Perforated 3 10 Struer’s blue 100 less scratchescloth lubricant5 Pan W 3 5 Struer’s red 100 very few scratchespolishing cloth lubricant6 OP Chem. fmal 0.05 1-2 Colloidal Si02 100 clean boundarypolishing cloth suspension around particlesAnother polishing procedure modified from Newell11001 was adopted for the automaticpolishing machine at UBC, as listed at Table 7.2. A very clean background resulted followingpolishing for both procedures, which was necessary for microstructural analysis, especiallyChapter 7 Particle Fracture of the PRMMC during Extrusion 130image analysis. The last step was quite effective to clean the boundaries between the matrixand the particles.Table 7.2 Polishing procedure used at UBC for Duralcan materialsStep 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 flat with lessscratches4 SiC Paper 1000 3 Water 30 less scratches5 Texture Paper 6 tm 10 Diamond 30 few scratchessuspension6 Texture Paper 3 .tm 5 DP- 30 very fewsuspension scratches7 OP Chem. final 0.05 urn 1-2 Colloidal 30 clean boundarypolishing cloth Si02 around particlessuspension7.2 Macroscopic Examination ofMetal Flow in the Deformation ZoneMacro-examination of metal products can reveal the grain size and shape as well asfabricating or casting defects. An end-of-extrusion billet of 6061/A1203/20p from the trial ofS92-3, 184 mm in diameter, was sectioned by a hacksaw along the extrusion direction. Theextrusion conditions are listed in Table 7.3 for convenience.Mixed-acid etchants are excellent for revealing grain size, shape, and contrast. Theetchant used for the composite was a mixed solution of lOmi HC1 (concentrated), 3Oml HNO3(concentrated), 2Oml H20, and 5g FeCl3961. The solution was mixed just before 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 accumulation of 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/A12/20p.--------;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’. 5 8Sheai Zonei3 ‘.6 9_______________________- - --. Dead ZoneI IDie 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 7 Particle Fracture of the PRMMC during ExtrusionEii133Figure 7.3 Metal flow in the deformation zone during extrusionChapter 7 Particle Fracture of the PRMMC during Extrusion 134The metal flow pattern shown here is consistent with experimental observation byother researchers1211,and also, qualitatively, with the velocity vector distribution of the FEMmodel prediction in Chapter 5.7.3 Particle Fracture during ExtrusionA 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 of this project.7.3.1 Qualitative Microstructure Analysis7.3.1.1 Particle Deformation Behavior in the Deformation ZoneThe other half of the butt-end was divided into several small sections on a cuttingmachine with a Ti-V wheel blade, and 9 samples from the longitudinal section, with an area ofabout lOxlO 2 , were polished at UBC for micro-examination. The location of the 9samples in the billets inside the container are schematically shown in Fig. 7.4.Pressure Pad EndDie ExitFigure 7.4 Schematic positions for the pictures taken for micro examination7__4__1Sh&ir ZoneDeformation Zone8 5 2Dead Zone - 9 6 3—Chapter 7 Particle Fracture of the PRMMC during Extrusion 135The particle distribution and particle fracture behavior for each sample, located indifferent zones, was investigated under an optical microscope. At Location 1, the upper rightcorner of the billet where there is contact with the pressure pad and the container, a “particle-free” zone (with a small number of particles) was formed (see Figs. 7.1 and 7.3). This is theresult of accumulation of the matrix material near the gap between the pressure pad and thecontainer: during extrusion, as the pressure pad pushes the bifiet forward, the matrix materialadheres to the container, while the particles in the subcutaneous layer of the billet were 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 thick particle-free layer at the billet surface was observed at Location2 (r = R0). The formation of this 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 equiaxed particlesare harder to fracture even with a larger diameter(Location 2, Fig. 7.5 (a)). This resultconfinns 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 7 Particle Fracture of the PRMMC during Extrusion 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 theinterface of the billet and container because of adhesion, and part of the matrix material in thislayer flows 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)). Fewer clusters, but more fractured particles, were observed in the region belowthe ‘hard-to-deform’ region, as deformation increased. Particles were orientated towards thedirection of metal flow (No. 5, Fig. 7.5(b)). At Location 6, which included both a part of thedeformation zone and a part of the dead metal zone, a ‘particle-free’ band was also observedin the shear zone with more particles present than 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 align in the shear direction.At the top surface zone around the center line (r = 0) of the billet (Location 7), someparticle clusters remained, as observed at Location 4, with similar particle distribution to theas-cast products. However, fractured particles in clusters were observed occasionally becauseChapter 7 Particle Fracture of the PRMMC during Extrusion 137Figure 7.5 (a) Typical particle distribution in the Locations 1, 2 and 3(‘P.C.’= particle cluster ‘P.F.Z.’=particle-free zone; ‘P.P.B.’—particle-free band; ‘S.D.’=shear direction)Chapter 7 Particle Fracture of the PRMMC during Extrusion 138Figure 7.5 (b) Typical particle distribution at the Locations 4,5 and 6(‘P.C.’ particle c1uster ‘P.F.Z.’=particle-free zone; ‘P.F.B.’—particle-free band; ‘S.D.’=shear direction)Chapter 7 Particle Fracture ofthe PRMMCduring ExtrusioniF1139N,Figure 7.5 (c) Typical particle distribution at the Locations 7,8 and 9(‘P.C.’= particle cluster; ‘PEZ.’—particle-free zone; ‘P.F.B.’=paiiicle-free band;4B.D.’= extrusion direction)Chapter 7 Particle Fracture of the PRMMC during Extrusion 140of local tn-axial stresses (Location 7, Fig. 7.5 (c)). The most obvious characteristics atLocation 8 were the alignment of the particles and the formation of particle-free bands alongthe extrusion direction. This is due to axisymmetnic material flow which forces particles toalign in 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.Near the die throat, more small particles were found which implies severe particle fracture dueto shear deformation (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 allcould not be shown in one typical picture for each location, as in Fig. 7.5.7.3.1.2 Microstructure Analysis of the ExtrudatesTwo samples of each extrudate were cut from both the front end (named “F’) and theback end (named “B”). Caution was taken when each piece was sectioned along the extrusiondirection using a Ti-V wheel blade, as shown in Fig. 7.6. All the specimens were polished atUBC following the procedure listed in Table 7.2. The particle distribution in both theChapter 7 Particle Fracture of the PRMMC during 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 in Table 7.4.Extrudate Sample Transverse LongitudinalSample Cross 6061 606 11A1203120P 60611M203110PName Section Alloy (W6A20) (W6A1O)Trial No. S92-2 592-3 S92-6Front End Transversal F2-T F3-T F6-TFront End Longitudinal F2-L F3-L F6-LBack End Transversal B2-T B3-T B6-TBack End Longitudinal B2-L B3-L B6-LA. Comparison of Microstructure in Longitudinal and Transverse SectionsBased on the optical microscopic examination of transverse and longitudinal sectionsof the extrudates of 606l/AlO3/20p, some typical characteristics of the particle distributionin the transverse section of the specimen are summarized:(1) particles were randomly oriented, i.e., with no preferred orientation;(ii) particle size was non uniform;Figure 7.6 Schematic of examined extrudate specimenTable 7.4 List of examined extrudates with two different cross-sectionsChapter 7 Particle Fracture of the PRMMC during Extrusion 142(b) LongitudinalFigure 7.7 Typical characteristics of particles after extrusion of 606l/AI2O3I2Opat an extrusion ratio of 34(a) TransverseChapter 7 Particle Fracture of the PRMMC during Extrusion 143(iii) many small particles were observed;(iv) particles were quite uniformly distributed. The particle distribution in the transversesection with some of the above features is shown in Fig. 7.7(a).In the longitudinal section, some salient features are summarized as:(i) most of the particles with a large aspect ratio were aligned in the extrusion direction;(ii) fractured particles were found in clusters;(iii) equiaxed particles (i.e., aspect ratio of the particle is close to unity) were harder to crack;(iv) for the situations where a single particle positioned between two large particles, themiddle particle had a high tendency 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 bylocal metal flow during shear deformation;(vi) most of the 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 isshown in Fig. 7.7(b).B. Comparison ofMicrostructure for 6061/A123/20pand 6061/A123110pFor the extrudates of 6061/Al23/lOp, similar characteristics of particle fracture tothe 60611A123/20pwere also recognized (Fig. 7.8), such as:(i) particles were also randomly oriented in transverse section, but aligned in the extrusiondirection in the longitudinal section;Chapter 7 Particle Fracture of the PRMMC during Extrusion 144(b) LongitudinalFigure 7.8 Typical characteristics of particles after extrusion of 606 lIAlzO3IlOpat an extrusion ratio of 34(a) TransverseChapter 7 Particle Fracture of the PRMMC during Extrusion 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 606 1/AlO3/10pcompared to 6061/Al203/1OP are:(i) particle size was much smaller than that in the 606l/A1O3/20p, and the size distributionwas more 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 of 20 to 27, which is comparable to the extrusion ratio of 34. This impliesthat the formation of the particle-free bands are most probably due to elongation of theparticle-free zone in the as-cast billet;(iii) more clusters remained after extrusion;(iv) although the aspect ratio change is not as obvious, most of the small particles have anaspect ratio close to one.For the extrudates of the aluminum alloy, 6061, many precipitates were present, mostof which were MgSi. It was found that the size of the precipitates was around one micronand they were quite uniformly distributed throughout each section. In the longitudinalsection, the precipitates were aligned in the extrusion direction. These precipitates were alsopresent in the composite extrudates, though not visible at the magnification shown in Fig. 7.7and 7.8.Chapter 7 Particle Fracture of the PRMMC during Extrusion 1467.3.2 Image Analysis of Particle Distribution in ExtrudatesAn image analyzer was used to quantify the particle size and orientation. The particlesize was measured in terms of particle area and maximum and minimum diameter. Theparticle area was defined as the cross sectional area of a particle on the polished surface, 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 of a particle was determinedby the angle from the direction of its longest axis with respect to a specified direction, e.g., theextrusion direction in the longitudinal section. Thus, if the angle was zero degree, the particlewas considered as aligned in the extrusion direction. A total of more than 2000 particles weremeasured for a relative error in the measurements of less than ±5% with 95% confldence971.7.3.2.1 Homogeneity of Particle DistributionThe homogeneity of particle distribution is difficult to characterize quantitatively.However, the variation of local volume fraction in the composites could be a measure of theuniformity of particle distribution. A particle-free zone results in a zero local volume fraction,while a field full of clusters might approach 100% local volume fraction in extreme conditions.Apparently, a uniform distribution of particles 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 of 500 fields were examined. The local volume fraction varied from 5% to29% for the extrudates of 6061/Al23110p. 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 7 Particle Fracture of the PRMMC during Extrusion 1476061/A12O3/lOp for 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/lOp composite is non-uniform, and the non-uniformity in the longitudinal sectionis even more than in the transverse section based on the standard deviation and relativecoefficient values. This is due to the band formation in the longitudinal section.The histogram of the volume fraction for the extrudate of 606 l/A1O3/20p in Fig.7.10 shows that the variation of local volume fraction varied from 13% to about 35%. Themean values of the 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 the 6061/A1203/20P is 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 measured values of the volume fractions were larger than the nominal values,as the designation indicates.Table 7.5 Statistical results for volume fraction distribution of the two composites6061/A123lOp 6061/A1203120PSection Mean Standard Relative Mean Standard RelativeValue 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 7 Particle Fracture of the PRMMC during Extrusion 1489O8070•B6-T60 0B6-L50I I -:1357911131517192123252729Volume Fraction (%)Figure 7.9 Histogram of volume fraction for 6061/Al23/lOp6050 B3-T40 L0 B3-L30 Ii n11,11 13 15 17 19 21 23 25 27 29 31 33 35 37 39Volume Fraction (%)Figure 7.10 Histogram of volume fraction for 606l/A1O3/2OpChapter 7 Particle Fracture of the PRMMC during Extrusion 1497.3.2.2 Particle SizeTo evaluate the particle size variation in the composites after extrusion, the dimensionsof a particle in terms of its area, maximum and minimum diameter (dimension) weremeasured. The details of the measurements with statistical analysis are listed in Table 7.6.A. Particle DiameterThe histograms of the maximum diameter and minimum diameter for B3 (Back end ofthe extrudate S92-3: 6061/AI2OI2Op) 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 of the maximum diameter in a total count of about 2000 particles in B3 is from 50.0.Lm to 3.3p.m, while the minimum diameter varies from 1.67pm to 44pm. However, the meanvalues of both the maximum and minimum diameter are larger in the longitudinal section thanin the transverse section, as seen in Table 7.6. For 60611A123/lOp (B6), in Fig. 7.12, it isseen that the range of the variation of the maximum diameter is from about 3.tm to 28j.tm andthe minimum diameter from 1.3Jm to 15pm, which is almost half of the values of the particlesin 6061IAI2O3I2Op (B3 and F3). Similar to the 20% composite, the mean values of both themaximum and minimum diameter of the particles are larger in the longitudinal section than inthe transverse section for the 10% composite, as seen in Table 7.6.B. Particle AreaThe variation of particle area may reflect the particle size distribution in thecomposites more directly. Figure 7.13 shows the particle area distribution for the same countof particles in the extrudate of 606 l/A1203120P at the back end. It is seen that there is a largevariations in the particle area, from —l6jim2 to 480 urn2. Again, the mean value of theparticle area in the longitudinal section are larger than those in the transverse section, which isChapter 7 Particle Fracture of the PRMMC during Extrusion 150200180160 • B3-T140 E B3-L120_______D 100880 iiIl_1.67 6.68 11.69 16.7 21.71 26.72 31.73 36.74 41.75 46.76Maximum Particle Diameter (Micron Meter)(a) Max. Diameter400350___ __300250 Ln.L20001501000 : 9 I -1.67 6.68 11.69 16.7 21.71 26.72 31.73 36.74 41.75 46.76Minimum Particle Diameter (Micron Meter)(b) Miii. DiameterFigure 7.11 Histogram of the particle diameter for Sample B3 of 606l/A120il20pChapter 7 Particle Fracture of the PRMMC during Extrusion 151350300250D1B&L2008150ma i1Ii1.33 3.99 6.65 9.31 12 14.6 17.3 20 22.6 25.3 27.9Maximum Diameter (Micron Meter)(a) Max. Diameter600500 ii •B6-TILi2001 C ,I [I1.33 3.99 6.65 9.31 11.97 14.63 17.29 19.95 22.61Minimum Diameter (Micron Meter)(b) Min DiameterFigure 7.12 Histogram of the particle diameter for Sample B6 of 6061/AI2O3IIOpChapter 7 Particle Fracture of the PRMMC during Extrusion 152350300250 •B3-T200 I11111L DB3-LliiiI 116 49 81 114 146 179 211 243 276 308 341 373 406 438 471Part1ce Area (Square Micron Meter)Figure 7.13 Histogram of the particle area for Sample B3 of 606l/A12O3/2Op450400 I350 I•B6-T300 [IB6LC2508200150100 i9Ihhl1r-thI ‘ti -i -i —i i8.6 26 43 60 78 95 112 129 147 16.4 181 198 216 233 250Particle Area (Square Micron Meter)Figure 7.14 Histogram of the particle area for Sample B6 of 6061/A123/lOpChapter 7 Particle Fracture of the PRMMC during Extrusion 153Table 7.6 Statistical results for the quantitative metaflographyMMC 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 1.75 0.47I I / /0.922 0.507 0.476 0.269Note: ‘Rel. Coeff.’ in the table is a relative coefficient which is defined as the ratio of standarderror to the mean value.Chapter 7 Particle Fracture of the PRMMC during Extrusion 154due to the re-orientation of particles along the extrusion direction. The variation of theparticle area for the 6061/AlO3/lOp is from 8.6p.m2 to around 20Oim (Fig. 7.14). Themean value of the particle area is about 4 times less than that of the 6061fAlO3I20p (Table7.6). This is principally due to different initial range of particle sizes adopted in the fabricationof the composites.7.3.2.3 Aspect Ratio of ParticlesThe 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 samples with differentvolume fractions are shown in Figs. 7.15 and 7.16. It is seen that the variation of the aspectratio is from 1.2 to 4.5 for both materials. The mean aspect ratio in extrudates for the6061/A123/20p is around 1.99 to 2.07, while the aspect ratio for the 6061/Al23/lOp isaround 1.75 to 1.92 (Table 7.6), which confirms the observation that more particles have anaspect ratio close to unity in 6061/A1203/1OP. The relative coefficients (Table 7.6) of theparticle size (e.g., area, diameters) are generally smaller for 6O6l/Al203/lOp than for6061/A123/20p, which also confirms that the particle size is more uniform in extrudates of606 l/AlO3/l0p than in 606l/A123/20p, because the particle size is smaller.Chapter 7 Particle Fracture of the PRMMC during Extrusion 155350300250 • 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 4.2Aspect RatioFigure 7.15 Histogram of the aspect ratio for Sample B3 of 6061/AlO3/20p• 400•B6-T300[]B6-L÷... 250_________8150100I I I I I -H -Ii0.2 0.5 0.8 1.1 1.4 1.7 2 2.3 2.6 2.9 3.2 3.5 3.8 4.1 4.4Aspect RatioFigure 7.16 Histogram of the aspect ratio for Specimen B6 of 6061/AlO3/10pChapter 7 Particle Fracture of the PRMMC during Extrusion 1567.3.2.4 Partide OrientationOrientation of the particles with respect to extrusion direction was also analyzed withthe Leitz Image Analyzer. The extrusion direction was set to be 0° or 180°. The entire rangefrom 0° to 1800 was divided into 12 groups, with the group width being 150. 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 foreach class are similar. However, higher frequencies of the particle orientation in 0 to 300 and165 to 1800 were measured in the longitudinal section, which means the particles in thelongitudinal section are aligned in the extrusion direction. These measurements are consistentwith the microscope observations (Figs. 7.7 and 7.8).600500400-4-C300(-)2001000Figure 7.17 Histogram of orientation of the particles with respect to extrusion directionfor the Sample B3 of 606l/Al23/20p15 30 45 60 75 90 105 120 135 150 165 180Orientaion w.r.t. Extrusion DirectionChapter 7 Particle Fracture of the PRMMC during Extrusion 1574504003503002508 20015010050015 30 45 60 75 90 105 120 135 150 165 180Orientation w.r.t. Extrusion DirectionFigure 7.18 Histogram of orientation of the particles with respect to extrusion directionfor the Sample B6 of 606l/AlO3IlOp7.4 Particle Fracture Model during Extrusion7.4.1 Particle Fracture Probabifity at High TemperatureParticle fracture has been observed during the extrusion process; and this results inparticle size refinement. There are two factors which are known to determine particle fractureand its influence on material properties in service: local stress ( related to imposed strain atlow temperature), and hydrostatic pressure, which is obviously of importance duringextrusion. At low temperature the probability of fracture is correlated to str in’1,(see alsoEq. 7.1), whereas, at high temperature it is expedient to correlate fracture to the ZenerHolloman parameter and its time effect, as it is the Zener-Holloman parameter that determinesthe flow stress of the matrix material during hot extrusion..Pr =1—exp(D3a ) (7.1)Chapter 7 Particle Fracture of the PRMMC during Extrusion 158If the particle fracture process is stochastic, then the fracture probability can bederived to predict the particle size refinement during hot extrusion.pf = 1_exp(J(_3D3aZ)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 effect of particle 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 hot extrusion process to calculate the particle size refinement.7.4.2 Particle Fracture Model during ExtrusionIt was observed that particles undergo multiple fracture. Hence, the assumption that aparticle fractures into two approximately equal halves75’61,may require re-evaluation for amodel of particle fracture under extrusion conditions. In the case under evaluation, 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 of around 50 counts of a single particle fracture event was made for both transverseand longitudinal section of an extrudate. The number of parts fractured from a single particleevent (including a fracture event in a cluster) was recorded. Therefore, the average number ofparts, n, formed from a single particle fracture event, is simply;(7.3)n =NChapter 7 Particle Fracture of the PRMMC during Extrusion 159where N is the number of counts, 50 in this case as mentioned above and N1 is the number ofparts counted from each fracture event. It was found that a large single particle oftenfractures into two parts with one part twice the area of the other one. However, a particle ina cluster often is crushed into 3 or more parts with equivalent size. With respect to differentextrusion ratios, more fractured particles were observed at a high extrusion ratio. Theaverage number of parts from a single fracture event for different sections of an extrudate atdifferent extrusion ratios is listed in Table 7.7. It is seen that more parts are formed from asingle particle fracture event in an extrudate at a higher extrusion ratio than at a lowerextrusion ratio. This also implies that the higher the extrusion ratio, the larger the particle sizereduction.Table 7.7 Average number of parts fractured from a single particle in 6061/A123/20pExtrusion ratio Longitudinal Transverse Both inofanExtrudate (‘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, Pp is a function of temperature 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 7 Particle Fracture of the PRMMC during Extrusion 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=f 2af(r,z)rdr/Rwhere R1 is the radius of the deformation, which is outlined by the shear zone boundary. Itvaries from the initial radius of the billet (R0) at the back end of the 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 DI Th. Because the number of brokenparticles, N is equal to Pf * N, where is the total number of particles in thedeformation zone, the mean refined particle diameter can be derived as:— (D/)3 113 — 1 D(7.6)— (1+(,-1)p)”3Then, the particle size reduction at that stage is defmed as:%=-x1OO%(7.7)7.4.3 Application of the ModelFrom an image analysis of the extrudate from Trial S92-3 at UAC, Anaheim, the meanparticle diameter, Dime, in the extrudate was found to be 12.41pm; while the mean size of theparticle, at the back-end of the bifiet was 13.07p.m. The mean value of the maximumChapter 7 Particle Fracture of the PRMMC during Extrusion 161diameter of the particles, was 18.77tm and 21.22tm for the extrudate,D1 and the billet,respectively. Using Eq. (7.6), the overall fracture probability was estimated as 12.20%,and consequently the constant fi in the fracture model (Eq. 7.2) is 3.07x1021[1/pm]. Boththe mean particle size (diameter) and the mean value of the maximum diameter are predictedusing the DEFORM results for temperature and strain rate in the deformation zone (Table7.8). It is evident that there is good agreement between the mean particle diameter and themean value of the 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 occursnear the die throat by 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 mean particle size reduction is shown in Fig. 7.20.100 ‘0.1280 0.10.08 .60-0.06€I3.440-I 0.04200.020- I I I i—- •0315 330 345 360 375 390 405Depth into Deformation Zone (mm)Figure 7.19 Fracture probability variation in the deformation zoneS.a0a*IIIIIIIShear B’dary- -- ProbabilityaIaIDie Throat IIChapter 7 Particle Fracture of the PRMMC during Extrusion 162100 - 13.38OShearB’daryl- 13.1MeanDia.-12.9E 60ES.—40Ct125 i20 --12.3Die Throat0- I I 12.1315 330 345 360 375 390 405Depth into Deformation Zone (mm)Figure 7.20 Particle size reduction during extrusionTable 7.8 Comparison of model predictions with measured dataMean Particle Diameter ReductionD(im) D1mLm) Red (%) pfMeasured 13.07 12.41 5.02 12.20Model 13.07 12.39 5.19 11.02Average Maximum Particle Dimension ReductionDoinax(i.Lm) D113m) Red (%)Measured 21.22 18.77 11.55 32.48Model 21.22 17.64 1687 33.367.5 DiscussionThe particle distribution has been examined during the extrusion process. However,some questions remain. What is the influence of the extrusion process on particleChapter? Particle Fracture of the PRMMC during Extrusion 163distribution? How is a particle fractured during deformation, and what is the correlationbetween extrusion deformation behavior and the particle fracture?7.5.1 Microstructure Comparison before and after Extrusion7.5.1.1 Comparison of Particle Distribution before and after ExtrusionPorosity and voids have been considered to be the most detrimental 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 conducted byKalu and McNelley’541,it was found that Al203particles were clustered in the as-cast lOvol%material provided by Duralcan. Similar features were found in 6061/A2OillOp, shown in Fig.7.2 1(a). The distribution of the particles was more uniform in a higher volume fraction, e.g.,6O61IA123I2Op composite, 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 in Chapter 6).The microstructures of a transverse section of the lOvol% and 2Ovol% compositesafter extrusion at a ratio of 34 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 withquantitative particle size analysis using the image analyzer. Evidently, heavier extrusion ratiosimprove the homogeneity of particle distribution. However, a larger extrusion ratio at arelatively low temperature may introduce voids in the surface layer of extrudates due to tensileChapter 7 Particle Fracture of the PRMMC during Extrusion 164(b) After extrusionFigure 7.21 Microstructure of 606l/A123/lOp before and after extrusion(a) Before extrusionChapter 7 Particle Fracture of the PRMMC during Extrusion 165(b) After extrusionFigure 7.22 Microstructure of 6061IAI2O3I2Op before and after extrusion(a) Before extrusionChapter 7 Particle Fracture of the PRMMC during Extrusion 1660.25_________0.2 • back___Q extrud.o 0.15_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 50Size class (microns)(a) Maximum alumina particle dimension of6061/A123/20pin back end of a billet and in extrudate0.45__0.40.35 • back0.3 Llextrud.0.250.20.15o.i ri0.0 [ - 1Il_ri-0-5 5- 10- 15- 20- 25- 30- 35- 40- 45- >5010 15 20 25 30 35 40 45 50Size class (microns)(b) Minimum alumina particle dimension in 606l/A12O3/20pin back end of a billet and in extrudateFigure 7.23 Variation ofmaximum and minimum alumina particle dimensionChapter 7 Particle Fracture of the PRMMC during Extrusion 167>0a)za).>0I)za)a)>..I backO extrud.i]I11IIII[_____________Aspect ratio classFigure 7.24 Aspect ratio of alumina particles of 6061/A123/20pin back end of a billet and in extrudate0.140.120.10.080.060.040.0200.40.350.30.250.20.150.10.050backextrud.1-i0-15 15-30 30-45 45-60 60-75Angle to extrusion direction (degrees)75-90Figure 7.25 Orientation of alumina particles of 60611A123/20pin back end of a billet and in extrudateChapter 7 Particle Fracture of the PRMMC during Extrusion 168stress, which may cause deterioration of the mechanical properties of the MMCs, based on thestudies on the materials at low temperature19295 1221•7.5.1.2 Particle Size Refinement after ExtrusionTo quantify the change in particle size during processing, the particle size distributionat two locations was analyzed, at the back end of the 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 smaller pieces during extrusion. This can also be seen through the distribution ofthe maximum and minimum particle dimensions (Figure 7.23(a)-(b)). The increase in numberof small particles is quantified. The decrease in mean aspect ratio of particles is accompaniedby a rise in the class of particles with an aspect ratio close to one, as shown in Figure 7.24.The orientation distribution of particles is distinct in Figure 7.25.7.5.2 Particle Fracture Modes during ExtrusionThe tendency for the particle size distribution to skew towards lower size classes is inaccord with observations of material deformed at low temperature under hydrostaticpressure76’(Fig. 7.23(a) and (b)). Such observations are indicative of the comminution ofparticles98’(Comminution mode in Fig. 7.26(a)). It is also noted that in the transverse sectionof the extrudate there appear to be substantially more small particles than in the longitudinalsection: this is, in part, an effect of particle re-orientation. It was observed that fracturedpieces healed due to the low flow stress of the matrix material and high hydrostatic pressureChapter 7 Particle Fracture of the PRMMC during Extrusion 169encountered during extrusion, which results in matrix material being forced into cracks175’901.This feature is the major difference between low strain/low temperature and large strain/hightemperature behavior. However, at high temperature, under tensile stress, the PRMMCs tendto form voids behind the particles’1011. This will be discussed in more detail in 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 parallel to the extrusion direction in the longitudinal section of the extrudate. This maybe caused by the shear stress acting on the particles under high hydrostatic pressure (Shearmode in Fig. 7.26(b))’991The 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 at low temperature in the loading direction761,and is retained at high temperatures.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 7 Particle Fracture of the PRMMC during Extrusion 170microstructural examination, the shear mode 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-axial stresses are present.w ‘I,(a) Comminution mode (b) Shear mode (c) Tensile modeFigure 7.26 A schematic diagram for three particle-fracture modes during extrusion7.5.3 Correlation between Particle Fracture and Bulk Deformation BehaviorTo understand the particle fracture during extrusion, the deformation behavior of thecomposite billet was analyzed with the aid of DEFORM® as described in Chapter 5. A typicaleffective strain rate distribution near the die exit area at a steady state is shown in Fig. 7.27.U UChapter 7 Particle Fracture of the PRMMC during Extrusion 1711X ) Etf.StnRl(1/s)-7.750 -BilletA. 0.00008= 3.0000C- 60000-8.050 0— 8.0000E. 12.000F. 15.000Gm 18.000lb 21.000-8.350-8.950-9250 I I I0.00 6.00 12.00 18.00 24.00 30.00Radius (mm)Figure 7.27 Effective strain rate distribution in the deformation zone2 Mean Stress (MPa)-0.500 BilletA— -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)Figure 7.28 Mean stress distribution in the deformation zoneChapter 7 Particle Fracture of the PRMMC during Extrusion 172It is seen that the highest strain rate is reached at the die throat, where metal flow waschoked. Therefore, most severe particle fracture could occur in this choked 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 of the bifiet, the stress state is in compression (negative value), and a very highhydrostatic pressure exists in the deformation zone. Comminution of a particle or particles ina cluster could result under such a large hydrostatic pressure which may also heal thefractured particle under the large deformation during extrusion (Comminution mode).However, near the die exit zone, tensile stresses appear, especially at the die-bearing interface,which is due to high elongation of the 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 7 Particle Fracture of the PRMMC during Extrusion 1732 RZ Stress (MPa)-ooo / BilletI A. -20.000B. -12.000C-4.0000I 0. 4.0000-0.500 . iz.oooF. 20.000( G. 28.000I H. 36.000-0.600-0.700 --0.900 -—1.000 —— I I I I I0.00 6.00 12.00 18.00 24.00 30.00Radius (mm)Figure 7.29 Shear stress distribution during extrusion7.6 SummaryMacro- and micro-exmiination of a billet during extrusion sheds light on the metalflow pattern and particle fracture. It was found that the particles fractured in the severe sheardeformation zone at the die throat, but most fractured parts healed in the extrudates due to thehigh temperature and large hydrostatic pressure, which has also been confirmed by DuralcanUSALIOSI. Some major findings are summarized below.Chapter 7 Particle Fracture of the PRMMC during Extrusion 174(i) Due to adhesion friction between the billet and the container in hot extrusion, aparticle-free layer 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 in the extrusiondirection. In this zone, very few particles reside, and therefore there was 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 of the 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 of particle 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 of particle fracture due to the comminutioneffects. In the dead metal zone, some particles were cracked, but not separated, due to smalldeformation;(iii) Most of the single particles that fractured had a large aspect ratio or sharp corners.Equiaxed particles were much harder to fracture; all the large particles which remainedunfractured in different zones had an aspect ratio 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 in particlesChapter 7 Particle Fracture of the PRMMC during Extrusion 175with a large aspect ratio. This was probably due to the tensile stress in the particle in the flowdirection.The size and distribution of the particles in the extrudates have also been examinedusing both an optical microscope and an image analyzer. Comparing the transverse sectionwith the longitudinal section, some important features are:(i) Orientation of the cracks in the transverse section was randomly distributed.However, many of the cracks in the particles in the longitudinal section were either parallel orperpendicular to the extrusion direction. Most of the particles with an aspect ratio greaterthan one were aligned in the extrusion direction;(ii) Particles with a different aspect ratio were observed in both the transverse and thelongitudinal sections. Larger particles especially 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 of 6O6l/AlO3/lOp to that of 6O6lIAl23/20p, it wasfound that:(i) Particles were much smaller in 606l/AlO3/l0p than in 6061IA12O3I2Op.However, the particle distribution was less homogeneous in 606l/Al23/lOp than in606l/A123/20p, i.e., more clusters and more particle-free bands remained in the extrudatesof 6061/A123/lOp;(ii) The mean aspect ratio of particles in 6061/A123/lOp was less than that in6061/A123/20p.Chapter 7 Particle Fracture of the PRMMC during Extrusion 176Quantitative metallography and statistical analysis were conducted using an imageanalyzer. The particle dimensions, such as minimum and maximum dimension, area, aspectratio, and particle orientation were quantified at different positions in the deformation zone.The most salient points are:(i) Particle alignment along the extrusion direction was confirmed. Particle fractureduring extrusion leads to more smaller particles. The average aspect ratio of the particlesafter extrusion is around 1.74 to 2.07 with more uniform size distribution in 606l/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 of the ‘damage’ which accompanies a fracture event, may all have benefits for thein-service mechanical properties of extruded components. However, the influence of particlefracture on mechanical properties, the correlation between the particle size and thedeformation parameters, and the mechanism of the low speed cracking, need to be clarified.Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 177Chapter 8 ORIGIN OF LOW SPEED CRACKINGDURING EXTRUSION OF THE PRMMCsThe 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 speed cracking was observed in the plant trails at UAC, which is specific to thecomposite material. It is essential to explore the mechanism of the low speed cracking duringextrusion.8.1 Microstructure Examination of Low-speed CracksAs observed in the plant trial at UAC, 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 of J94-14 and J94-20 of 6O61IA123I2Opwith very severe low speed cracking, andJ94-1 lB of 6O61IAl23I1Op with slight cracking. The polishing procedure of Table 7.2 wasfollowed by using an automatic polishing machine at UBC. The samples were examined underan 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 of the polished specimens for about 4 minutes for 6O61IAl23I2Op, andChapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 178about 3 minutes for 606l/A12O3/lOpsamples. As a result, good contrast between the particlesand the matrix was obtained with little electronic charging of the A1203particles. Under theSEM, 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 for J94-14. It is seen that most of the voids were associated with particles and located atthe two ends of particles in the extrusion direction (orientation of particles with large aspectratio in the picture). The same phenomenon was also observed around the crack tips of 394-1 lB for 6061/A123/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 inChapter 6.It is interesting to note that more severe low speed cracking was observed in 394-14 of6O61IA123/20p than in 394-1 lB 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 lower volume fraction results in higher ductility of the 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 the 6061IA12O3/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 interfacedecohesion seems to be dominant in the surface layer.Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 179Figure 8.1 Void formation near a low speed crack tip of394-14 of 6061/A120il20p in longitudinal sectionFigure 8.2 Void formation near a low speed crack tip ofJ94-1 lB of 6061/A123/lOp in longitudinal sectionChapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 1808.2 Particle Behavior and Microscopic 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 matrixmaterial becomes important.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 Particle FractureAt 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 alumina particulate reinforced metal matrix composites byFerry and Munroe in the form of shear bands in the matrix around the particles, based on theirmicrostructural study in Al/A1O3 composites”111. They also found that large particles andthose with a high aspect ratio had the greatest propensity to fracture during deformation.Some particles fractured into very fine (1-2 tIm) pieces and redistributed along the shear bandduring deformation. These observations are also consistent with the single-particle modelprediction of different shapes of a particle during cylindrical compression and with theprediction of particle migration in the plane strain simulation. The interaction between theChapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 181particles 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 of the particle, and consequently the stress state in the particle.Therefore, matrix flow and particle behavior are very much temperature dependent. If thetemperature is low, the matrix work-hardens more easily and the stress in the particle will behigher, 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 of the ‘Tensile mode’ of particle fracture during extrusion, i.e., if a 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, which have some similar deformation characteristics to the extrusion process (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 stressChapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 182decreases. This is because the interparticle spacing increases, and subsequently, theinteraction between the two particles becomes weaker.Table 8.1 Tensile stress in partides and matrix at different reductionsAspect Object No. Reduction: 10% Reduction: 30% Reduction: —50%Ratio (Material) Mi Max. Miii. Max. Miii. Max.(MPa) (MPa) (MPa) (MPa) (MPa) (MPa)#2(Matrix) -50 42 -51 30 -64 38A.R.=1 #4(Particle off C.L.) -8 83 -28 89 -45 72#5(Particle @ C.L.) -4 89 -18 69 -34 50#2(Matrix) -131 125 -60 54 -57 34A.R.=2 #4(Particle off C.L.) 9 158 -12 84 -26 55#5ParticIe @ C.L.) 56 170 8 92 -24 544.600 X Stress (UPa)Objed #4 (dght)A. 10.0008= 25.000C= 40.0004.570 D= 55.000E= 70.000F. 85.000_______________F______________ (IH. 115.00G= 100.00I. 130.00EE>E L 4=145.004.540-_K. 160.00Objed #5 (dr line)E4.510 A. 10.0008=25.000C. 40.000D. 55.000E= 70.0004.480 F.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 stress in a particle under plane strain condition at a reduction of 10%Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 1838.2.2 Void FormationVoids 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 of two closely spaced particles which were aligned in theextrusion direction. The void formation could be explained by the local stress state owing tothe presence of the 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 (20j.tm) between thetwo particles with a large aspect ratio leads to a higher value of the tensile stress in theinterparticle zone (see contour line value of ‘J’ of 104 MPa in Fig. 8.4(b) and compared to thecontour line ‘G’ of 28MPa in Fig. 8.4(a) for a particle spacing of 40pm). A high 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 et a!.11 13-1 14J It 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 simulation conditions are the same, as shownin Fig. 8.5.X (mm)‘I0.100X (mm)X S1m1 (UPa)ObdI 2A= -20.0008= -12.000Cs 4.00000= 4.0000Es 12.000F= 20.000G= 28.000H= 36.000Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 1844.6504.600E 4.550>-4.5004.450(00.000 0.050 0.100 0.150 0200(a) Twin-particle model with a unity aspect ratio at a reduction of 10%E>-4.6504.6004.5504.5004.450X Qrese (UPa)Objed 1 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 an aspect ratio of 2 at a reduction of 10%Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 185X Streu (UPa)5.060 Cbed#2A -40008. .15.000C. 10.000______0-35.000E. 60.0005.000EE 4.960>-____4.9004.850 I i %0.000 0.050 0.100 0.150 0.200X (mm)(c) Multiple-particle model with a unit aspect ratio at a reduction of 1%Figure 8.4 Tensile stress distribution in the matrix and around particles10.020 - xOX Stress (UPa)Objed 1 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 2.80 5.60 8.40 11.2014.00X (mm)Figure 8.5 Tensile stress distribution in the monolithic materialat a reduction of 10% under plane strain conditionChapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 186Therefore, even though the monolithic stress state is compressive, a local tensile stresscomponent around particles may exist. It is the local tensile stress behind 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 of the extrudates does not decline as the extrusion ratio increases.8.3 Effect of Processing Parameters on 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.. Aneffort has been made to explore the origin of low speed cracking during extrusion with the aidof the finite element model, DEFORM’.The temperature distribution of both the billet of 6061IA12O3I2Op and the die near thedie 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 billet temperature is increased to about 460°Cfrom the initial value of 425°C due to the heat of deformation for an extrusion ratio of 34; andthe die interface also heats up due to heat conduction. Obviously, the thermal diffusivity ofthe die material is also very important to the temperature distribution in both the extrudate andthe die interface. Figure 8.7 shows the tensile stress builds up at the die land area in theextrudate during extrusion. All the other zones in 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. 466.31Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 187may help prevent void growth or crack formation. Apparently, both the temperature andtensile stress in this die land zone are crucial to the low speed cracking. As described in thelast 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.,particle cluster), based on the micromechanical analysis conducted in Chapter 6.4.0004.3004.600I4.90042004.5000.0 30.0 60.0 90.0 120.0Radius (mm)150.0Figure 8.6 Temperature distribution of billet and die at steady state extrusionChapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 188Table 8.2 Standard conditions for parametric studyRam speed: 1mm/sInitial billet temperature: 425°CFriction shear factor at the container and die interface: m=1 (sticking)Friction shear factor at pressure pad interface: m=0.7Initial die temperature: 395°CBillet diameter 178mm (7”)Contain inside diameter: 184(7.25”)Extrusion ratio: 342-2.750ZSkees(MPa)A— -420.02\ B -359.45\ C= -296.89\ D=-238.32-3.050 E -177.75F— -1 17.18\ G. -56.616H 3.95171= 64.519-3.3504959250 - -0.0 30.0 60.0 90.0 120.0 150.0Radius (mm)Figure 8.7 Tensile stress (as) distribution at the die interface zoneTo determine the effect of extrusion variables on the temperature and the tensile stressin the die land zone, a systematic study of the extrusion of 6061/A123/20pwas conducted forChapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 189all the process parameters, such as ram speed, initial billet temperature, initial die temperature,frictional condition at the die interface, extrusion ratio and the billet materials. The standardsimulation conditions are listed in Table 8.2.Effect ofRam 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 land zone 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 of the temperature rise (Fig. 8.8(b)). A higher 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 extrusion temperature.Figure 8.9 shows that the temperature distribution through the whole radius of theextrudate is higher for the ram speed of 6mm/s, and also that the thermal gradient is greater atthe interface, due to the shorter heat transfer time. On the other side of the die interface, thethermal gradient is even greater because of the lower thermal diffusivity (the thermaldiffusivity of H13 is about 7 times lower than that of the composite material). Again, becauseof the shorter heat transfer time, the thermal gradient is greater for the ram speed of 6mm/sand the inside temperature of the die is even lower than that of the ram speed of 1mm/s.Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 190520— — —500— — — —/U/‘‘ 480/4601.0 mm/s///1Z6.5440-42020 22 24 26 28 30 32Ram Displacement (mm)(a) Maximum temperature in the die land zone during extrusion85I 1.Omnilsl‘6.5mmIsj75C’,C,,‘1)556520 22 24 26 28 30 32Ram Displacement (mm)(b) Maximum tensile stress in the die land zone during extrusionFigure 8.8 Effect of ram speedChapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCsU01)1910 5 10 15 20 25 30Distance from the Center of extrudate (mm)525500475450425400Figure 8.9 Temperature distribution on both side of the die interfaceat a ram displacement of 30mmFigure 8.10 shows the effective strain distribution through the whole radius of theextrudate at the die exit. It is seen that the strain distribution is not sensitive to the ram speed,because the strain is more dependent on extrusion ratio. The distribution of stress componentin the extrusion direction (az) along the radius of extrudate, indicates that the stress iscompressive near the center and gradually becomes tensile near the surface of the extrudate(Fig. 8.11). Obviously, in a surface layer of more than a quarter of the radius of the extrudatethere exists a tensile stress in the extrusion direction. The existence of the tensile stress statein the surface layer may promote void formation if the temperature of the billet at the surfacein the die land zone is low; this may fmally lead to low speed cracking, as was observed.Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 1924.36____1OmmJs2.8 -2.42 I I I0 4 8 12 16Distance from the Center Line (mm)Figure 8.10 Effect of ram speed on strain distribution through radius direction60 -I40- I— — — 1.0mm/si6.5mm/si_____—20 -000U0- 0020-. 0o I.—z •000-600 4 8 12 16Distance from the Center Line (mm)Figure 8.11 Effect of ram speed on stress distribution (az) through radius directionChapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 1938— —— 1.0mm/s6 6.5mm/s4,20 4 8 12 16Distance from the Center Line (mm)Figure 8.12 Effect of ram speed on effective strain rate variation in extrudateA big difference in effective strain rate is expected because of the different ram speeds(Fig. 8.12) but near the exit of the die land, the strain rate is concentrated only within thesurface layer.Effect ofBillet 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 of the lower flow stress and the low heatgeneration obtained for the higher billet temperature. Correspondingly, the maximum tensilestress in the extrusion direction (CT) is lower, as shown in Fig. 8.13(b). A 75°C increase in0IChapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 194520500L)0E4604404205°C500a e — a —— a • •• —aa• • —aaSI I I,I I I I I85756555453520 22 24 26 28 30 32Ram Displacement (mm)(a) Max. temperature in the die land zone during extrusion. - — — — 425 °Ca a 500°C..ab a:20 22 24 26 28 30 32Ram Displacement (mm)Figure 8.13 Effect of initial billet temperature: (b) Max. tensile stress in the die land zoneChapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 195550- -- 425 °C525 500°C475into Billetinto DieS 0 0 S S450-Die Interfaca425 I00 5 10 15 20 25 30Distance from the Center of extrudate (mm)Figure 8.14 Thermal gradient on both sides of the die interfaceunder different billet temperaturebillet temperature results in a drop of maximum tensile stress of 3OMPa. It is obvious thatthe effect of billet temperature on the maximum tensile stress is quite significant. It is knownthat a higher tensile stress may increase the propensity ofvoid formation at high temperaturein particulate reinforced MMCs1011. Therefore, temperature control is important to eliminatelow speed cracking during extrusion. On the other hand, at a lower initial billet temperatures,the tensile stress in the extrusion direction in the surface layer of the extrudate decreases morerapidly because of the higher heat generation rate due to the high flow stress (Fig. 8.13(b)).Because the ram speeds are the same for both cases, the thermal gradient in theextrudate is about the same (Fig. 8.14). However, on the die side, the thermal gradient islarger for the lower initial bifiet temperature of 425°C, because the temperature rise is higher.- -- 500°C-395°CI500°G470°C22 24 26 28Ram Displacement (mm)(b) Maximum tensile stress in the die land zone during exirusionFigure 8.15 Effect of initial die temperatureC-)0IIChapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 19653048065605550454035.I I I I20 22 24 26 28 30 32Ram Displacement (mm)(a) Maximum temperature in the die land zone during extrusion-- 500°C-395°C500°C-470°C...I I I I I20 30 32Chapter 8 Origin ofLow Speed Cracking during Ertrusion of the PRMMCs 197550- -- 500°C-395°C530 500°C-470°C—‘ 5 10 : _ _ _ . _ — _ = = — = — — — ——into Billet490 intoDieU470Die Interfac450- I I I0 5 10 15 20 25 30Distance from the Center of extrudate (mm)Figure 8.16 Thermal gradient on both sides of the die interfaceunder different initial die temperaturesEffect ofDie 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 of die 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 of 395 °C, the maximum defonnation temperature of the extrudate is about 15°Clower than that of the die temperature of 470 °C, and the extrusion temperature is even belowits initial temperature of 500°C at the end of the upsetting stage (at a ram displacement ofChapter 8 Origin ofLow Speed Cracking during Extrusion of the 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 of the higher thermal diffusivity. The lower initial die temperature resultsin a steeper thermal gradient on the die side(Fig. 8.15).Effect of Friction at Die InterfaceWith sticking friction confmed to the container interface, the sensitivity of two 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 of shear strength of the deformed material, isapplied at the boundary1831. Therefore, although a sticking friction condition was 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 the dieinterface.Without friction heating at the die interface, the maximum temperature of theextrudate during extrusion is lower than, but very close to, the value of the extrudatetemperature with friction. This is because the die land length is only about 2 to 3mm; and thusthe contribution of friction heating is very small. The small effect of friction on thetemperature rise can also be seen from the thermal gradient on both sides of the die interface,as shown in Fig. 8.18. However, the difference in tensile stress related to the two differentfriction conditions is quite obvious (Fig. 8.17(b)). It is interesting to note that even with nofriction condition applied at the die interface, the tensile stress still exists. This indicates thatChapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 199470 -460___I.• — — — — —U -0 —‘450 /_____/Im=1440_430-420 ‘ I I I20 22 24 26 28 30 32Ram Displacement (mm)(a) Maximum temperature m the die land zone during extrusion9080—70zm=1r5O5040 I I20 22 24 26 28 30 32Ram Displacement (mm)(b) Maximum tensile stress in the die land zone during extrusionFigure 8.17 Effect of friction condition at die interfaceChapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 200475463c-)0‘— 451427415Figure 8.18 Thermal gradient on both sides of the die interfaceunder different friction condition at die interfacethe tensile stress build-up in the die land zone is not only due to friction, but also due tomatérial flow itself, because metal flows faster at the inside layer of the extrudate than at theoutside layer and also there is no back pressure applied onto the front end of the extrudate.Therefore, it is this velocity difference that causes the tensile stress at the die exit. Severefriction conditions simply make the situation worse.Effect ofExtrusion RatioA temperature rise of the billet under smaller extrusion ratios is expected to be lower ifall other conditions are kept the same. At an extrusion ratio of 13, the extrudate temperaturerise is only about 15°C compared to 45°C for an extrusion ratio of 34. About 30°C differencehas been predicted for the extrusion ratio of 13 and 34(Fig. 8.19(a)). Because of the relatively0 5 10 15 20 25 30Distance from the Center of Extrudate (mm)Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 201470— R=13R=34,— 450 -C-)o — — — ——0’E /430 /410 I I I20 25 30 35 40Ram Displacement (mm)(a) Maximum temperature in the die land zone during extnision8520 25 30 35 40Ram Displacement (mm)(b) Maximum tensile stress in the die land zone during extrusionFigure 8.19 Effect of extrusion ratioChapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 202525500U0— 4752450425400-10 0 10 20 30 40Distance from the Center of Extrudate (mm)Figure 8.20 Thermal gradient on both sides of the die interfaceunder different extrusion ratioshigher heat generation rate for the higher extrusion ratio, a greater thermal gradient ispredicted for both sides of the billet and the die, as shown in Fig. 8.20. The tensile stress ishigher initially for the higher extrusion ratio, but decrease rapidly because of the rapidtemperature increase (Fig. 8.19(b)).Effect of Volume Fraction of the CompositesThe sensitivity analysis conducted above was for the 606l/A12O3/2Op. The effect of10% and 20% volume fraction of the PRMMCs was also conducted for a similar sensitivityanalysis (Fig. 8.21). As expected, a high volume fraction of particles results in a highertemperature rise due to the higher flow stress (Fig. 8.21(a)). The tensile stress is also greater- - R=13R=34into Billet4—into Die• — — _ a a a a a a a aa a a —Die • — — —Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 203470460 -—I — — — —/ I—f — — —c_) / —I.450-—— 10%volI” 20%vol440 1/Il/I430 j420 I I I20 22 24 26 28 30 32Ram Displacement (mm)(a) Maximum temperature in the die land zone during extrusion802462830 32Ram Displacement (mm)(b) Maximum tensile stress in the die land zone during extrusionFigure 8.21 Effect of volume fractionChapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 204470460‘—‘ 450I430420Figure 8.22 Thermal gradient on both sides of the die interfaceunder different volume fractionfor the larger volume fraction material. This means that the decrease in flow stress due totemperature rise cannot compensate for the effect of a larger volume fraction of thereinforcement. The difference in thermal diffusivity of different composite materials can beseen from the thermal gradient in the extrudate, although it is quite small. The higherthermal diffusitivity of 6061/A1ZO3/lOp results in a slightly flatter temperature distributionthrough the radius of the extrudate (Fig. 8.22).8.4 Mechanism of Low Speed CrackingBased on the analyses described in the above sections, it is believed that the low speedcracking is induced by both the low ductility of the composite and microstructural damage0 5 10 15 20 25 30Distance from the Center of extmdate (mm)Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 205(such as voids including decohesion and unhealed cracks) during extrusion as follows: 1) atthe beginning of extrusion, the die temperature is lower than that of the billet, so a ‘chilling’effect occurs at the front end of the billet when it is in contact with the ‘cold’ die. The lowertemperature results in lower ductility of the composites; and 2) the extrudate surface isgenerated from two distinct regions of the composite: the deformation zone of intense shear,decorating the dead metal zone, which is the major contribution and the smaller deformationvolume near the die throat, moving along the die facet1171. With the presence of particleswhich constrain the surrounding matrix deformation, especially at 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 of the 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 of the die material (H13 and the ceramic die) is about7 to 10 times lower than that of the 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 much higher at lower temperature (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 cracksChapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 206appear. Apparently, all the extrusion conditions that may result in lower billet temperatureand higher tensile stress in the surface layer of the extrudate in the die land zone may lead tolow speed cracking during extrusion, such as lower initial billet and die temperature, low ramspeed, higher extrusion ratio, higher friction condition at the die interface, and also highvolume fraction of the particle reinforcement. This is consistent with the plant trialobservations at UAC and at KRDC, Kingston. At UAC, more severe low-speed cracking inthe 606l/Al2Oil2Op composite at higher extrusion ratio (1” and 1.25” die) has been found;and the low-speed cracking disappeared when the ram speed was increased. However, onlyone extrudate with low-speed cracking was found in the trials at KRDC, in which the ramspeed was considerably lower than the set value of 0.9mm/s. This occurred when the presslimit was exceeded due to low initial billet temperature of 400°C. At a ram speed of—0.9mm/s. low speed cracking always appeared in the plant trials at UAC. However, no lowspeed cracking was observed in the plant trials at KRDC. This is because the die and the billetwere heated at the same time in a furnace at KRDC, and the temperature of the container waseven higher than that of the billet. The ‘stick and slip’ observed, is due to the fact that whenvoids link to form a crack, the tensile stress generated is released. This process repeats itselfas long as the temperature of the billet remains low and also the tensile stress is sufficientlyhigh to promote void formation in the extrusion process.8.5 A Preliminary Criteria for Low Speed CrackingIt is clear now that the onset of low speed cracking is controlled by both the fracturestress and fracture strain (ductility) of the material. Therefore, a preliminary fracture criterionis proposed for the low speed cracking during extrusion based on the idea of the plastic-workcriterion5t1:Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 207E—a2cGF6F =CF (8.1)where (Yz is the maximum principle stress, and is the maximum tensile strain obtainedduring extrusion, which is defined as the strain induced under a tensile stress, while GFEF isthe product of the fracture stress and tensile fracture strain of the material. The low speedcracking is induced by local failures of the composite, related to the local tensile stress andstrain. However, because it is difficult to know the local tensile stress and strain, themonolithic tensile stress and strain are used in the criterion. Since the fracture strain of amaterial is also dependent on the process itself, a tensile strain is used, although it is hard todetermine its value in an extrusion process. Apparently, if the product of the maximum tensilestress and the maximum tensile strain in the composites exceeds a critical value, which is theproduct of the fracture stress and strain, low speed cracking would occur. The reason to usea product instead of a single stress (Stress Criterion) or strain (Strain Criterion) is becausethe onset of low-speed cracking is induced by the combination of those two factors, i.e., themicrodamage would be induced for a certain strain (fracture strain) within particles, and thetensile stress would promote the void growth to link voids to form the low speed cracks for acertain stress value (fracture stress).According to Eq. (8.1), the effect of a variation of the product (E) of the maximumtensile stress and the maximum extrusion strain in the extrudate (rather than the difficult toobtain tensile strain) during extrusion under different conditions, but for the same extrusionratio of 34, was shown in Fig. 8.23. J94-12 has the highest value of B, because it has thelowest temperature of 423°C. The higher starting value of E of J94-13, with higher initialChapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs 208450194-12420 -..— J94-13194-143904-360330300 I I I I24 28 32 36 40Ram Displacement (mm)Figure 8.23 Variation ofE value during different conditions but same extrusion ratio530480 194-6394-14J94-20430380330280 - = - * - -.230 I I I I24 28 32 36 40Ram Displacement (mm)Figure 8.24 Variation of E value during extrusion at different extrusion ratiosChapter 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 more rapidly thanthose in 394-14. This implies that the low speed cracking would disappear in the extrudateearlier than noted in J94-14. This is consistent with the low speed cracking ranges at the frontend of each extrudate, with J94-14 having the longest low speed cracking length and J94-13the shortest (Table 4.7).The variation of E during extrusion for different extrusion ratios, is shown in Fig. 8.24.Apparently, the highest extrusion ratio of J94-20 has the highest E value with the 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 the E value variationcorresponds qualitatively with the low speed cracking, the determination of the Cf 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 both strain 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 still be 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 of the 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 A ADTable 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/A123/20pLarge Press atUAC 443.0187 260.1046 -211.9300 205.3414 0.9381for 6061/A1231l0pA 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.Chapter 9 Extrusion of the PRMMCs 212With respect to the bifiet temperature rise during extrusion, the following equation(see also Eq. 2.9) is used, based on an assumption that there is little or no temperaturedifference between the billet and the surrounding tools’631. This assumption is valid for theplant trial at KRDC, because both the die and the billet were heated at the same time in thesame furnace. However, the die temperature in the plant trial at UAC was significantly lowerthan that of the billet. For simplicity, in the calculation of temperature rise, the initialtemperature difference between the bifiet and the tools was ignored, while the internalgeneration of heat establishes a temperature differential,AT = 0.9PvBt I C1 (t) = O.9PvBt I (K1t”2+(K2 +K4)?’3+ (K3 ÷K5)t”3+K11t) (9.2)Based on Eqs. (9.1) and (9.2) for peak pressure and temperature rise, extrusion limitdiagrams can be developed for the Duralcan® composite materials extruded in the small pressat KRDC and the large press at UAC. Figure 9.1 shows a limit diagram at a constantextrusion ratio of 28 for 6061/A123/20p for the press at KRDC. Due to the low capacity ofthe press (—l000kN), the operating window for extrusion processing is small.Figure 9.2 shows a limit diagram for the same material at a constant ram speed of12.5mmJs (maximum speed for the press at KRDC). A ram speed of 35mm/s for Duralcan®material processed at an extrusion ratio of 25 and 14mm/s for SiCp reinforced composites(matrix alloy: A357) at an extrusion ratio of 36 has been reported in industrial extrusionpractice’9’’. A limit diagram for 606l/A12O3!2Op for the large press at UAC under anextrusion ratio of 34 is shown in Fig. 9.3. It is seen that, due to the large capacity of the press(3000 tons), the process window is much larger than that at KRDC. This indicates that thepressure limit for the large press at UAC is not a problem for extrusion of the composites athigh temperature.Chapter 9 Extrusion ofthe PRMMCs 2136050Extrusion Ratio: 28 F. 14030j42010 Pressure Limit Incipient Melting0 i420 440 460 480 500 520 540Extrusion Temperature (°C)Figure 9.1 Extrusion limit diagram at an extrusion ratio of 28 for6061/A123/20p for the press at KRDC86 Ram Spee& 12.5mm/s350 375 400 425 450 475 500 525 550 575Extrusion Temperature (°C)Figure 9.2 Extrusion limit diagram at a ram speed of 12.5mm/s for6061/A13/20pfor the press at KRDCChapter 9 Extrusion of the PRMMCs 2141251000- 0‘g 75 Pressre LimitIncipient Melting04Cl) 5025I I I I250 300 350 400 450 500 550Extrusion Temperature (°C)Figure 9.3 Extrusion limit diagram for 6061/Al23/20p at an extrusion ratioof 34 for the large press at UAC400300200 ressure Limit Incipient Meltingl000 I I200 250 300 350 400 450 500 550Extrusion Temperature (°C)Figure 9.4 Extrusion limit dIagram for 60611A123/lOpat an extrusion ratioof 34 for the large press at UACChapter 9 Extrusion of the PRMMCs 215An extrusion limit diagram for 606l/A12O3I1Opwas also developed for the large pressat UAC using the empirical equations (Fig. 9.4). It is evident that the process window of6061/A123/lOpis even larger than that for 606 l/A123/20p due to its lower flow stress.9.1.2 Using Finite Element Method9.1.2.1 Application of the Finite Element ModelExtrusion limit diagrams are usually developed using the above empirical equations,based on extrusion plant trials. The assumptions and simplification of heat transfer analysisfor derivation of the empirical equation for temperature rise during extrusion may lead toinaccuracy of the processing window. Moreover, to have an accurate load prediction, a smallnumber of plant trials are necessary to determine the coefficients in Eq. (9.1). Obviously, thisapproach is not cost effective.As computation technology advances, extrusion limit diagrams can also be developedusing the fmite element technique. Based on the fmite element predictions, a relationshipbetween temperature rise and billet temperature and extrusion speed may be obtained,AT=fI(T,vB) (9.3)Similarly, a relationship between peak pressure and the two variables can also be established: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/s for the press at KRDC and 1 to 75mm/s for the 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 at UAC. The initial die temperature was assumedto be 30°C less than that of the billet, while the container temperature was the same as that ofChapter 9 Extrusion of the PRMMCs 216the die. The temperature of the 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 afriction shear factor of m=0.7 was assigned to the interface between the billet and the pressurepad, due to its lower temperature. The heat transfer coefficient at the interfaces was assumedto be 2O0kW/m°C18. All the other boundary conditions were the same as described inChapter 5. The incipient melting point of 582°C for the 6061/A123/20p composite materialwas used155571, and was taken as the limiting boundary for the incipient melting line in theextrusion limit diagram.An extrusion limit diagram for 6061/A12320p for the small press at KRDC was thusdeveloped, as shown in Fig. 9.5. Correspondingly, the extrusion limit diagram for606 11A1203/20P for the press at UAC is shown in Fig. 9.6. Again, the processing window forthe press at UAC is much larger than that for the press at KRDC.160120I80400375 425 475 525 575Extrusion Temperature (°C)FIgure 9.5 Extrusion limit diagram for 6061/A123/20pfor the press at KRDCChapter 9 Extrusion of the PRMMCs 217125100j7550 Pressure Limit Incipient Melting250 I250 300 350 400 450 500 550Extrusion Temperature (°C)Figure 9.6 The limit diagram for 6061/A123/2Op for the press at UAC9.1.2.2 Comparison ofExtrusion Limit DiagramsThe extrusion limit diagrams for 606l/A12O3/2Op for 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,especially in the limit diagram for the press at KRDC. This is expected because the empiricalpressure equation (9.1) was determined using the plant trial data. The discrepancy betweenthe pressure limit lines obtained by the two techniques in the diagram for the press at UAC isdue to the low boundary temperature of about 250-300°C, because this temperature is beyondthe 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 incipient melting lines is more obvious. Thisis mainly due to simplification of heat transfer analysis for the temperature rise estimation inChapter 9 Extrusion of the PRMMCs 218the empirical equation (9.2), because the FEM model considered coupled thermal andmechanical phenomena for both the billet itself and the suffounding tools during extrusion tosteady state. The model predictions have been validated by comparison with the measureddata in Chapter 5.Limit diagrams for both the 6061/A1231l0p and the 6061/Al2O’2Op using theempirical equations are shown in Fig. 9.9. It is seen that the processing window for the6061/A123120p is totally within the window of 6061/A123/lOp. This is due to the lowerflow stress of 6061!A123/lOp. It thus can be concluded that the safe processing conditionsfor 6061/A123/20p are also safe for the processing of 6061/A123/lOp.160140 Extrusion Ratio: 28._120 ----FEM100 Empirical Equation80604020 Pressure Limit - frf Incipient Melting0 - - r - i375 395 415 435 455 475 495 515 535 555 575Extrusion Temperature (°C)Figure 9.7 Comparison of the extrusion limit diagram of 6061/A123/2Opforthe press at KRDC using different techniquesChapter 9 Extrusion of the PRMMCs 219125 1;_____FEM.-- —-- Empncal75’I Incipient Melting50 : II25.:‘PreureLimft0 I250 300 350 400 .450 500 550Extrusion Temperature (°C)Figure 9.8 Comparison of the extrusion limit diagram of 6061/A12O3I2Opforthe press at UAC using different techniques200___20%15OI:: PressureL \tMe200 250 300 350 400 450 500 550Extrusion Temperrature (°C)Figure 9.9 The extrusion limit diagram for both 6061/A123/lOpand6061/A120y’2Op using the empirical equation techniqueChapter 9 Extrusion of the PRMMCs 2209.2 Extrusion Limit Diagram with Low Speed Cracking BoundaryAs observed in the plant trial at UAC, low speed cracking occurs at the front ofextrudates in most of the trials. It is veiy important to delineate the boundaries of low speedcracking in the extrusion limit diagram for safe processing. Although a preliminary fracturecriterion for the low speed cracking has been proposed in Chapter 8, it is still difficult topredict the low speed cracking by including a low speed criterion in the finite element model.Fortunately, substantial data on low speed cracking during the plant trial at different extrusionconditions has been generated, and the boundaries of low speed cracking can be delineated byprocessing the data.9.2.1 Low Speed Cracking BoundaryDuring extrusion in the plant trial at UAC, the ram speed varied from less than 1mm/sto about 6mm/s, and the coverage of low-speed cracks on the surface of the extrudateschanged from a few centimeters to more than 6 meters under different extrusion speeds andtemperatures (Table 4.7). Because the billet temperature changes during extrusion, due to theheat of deformation, to track the billet temperature change, DEFORM was applied to thecases exhibiting long coverage of low-speed cracks through the extrudates (e.g., J94-6, J94-12, J94-13, J94-14, J94-20). The varying extrusion temperature and ram speed were tracedfrom the front end of the extrudates exhibiting low speed cracks, toward the back end, untilthey disappeared. Then the data points traced from the recorded ram displacement weredivided into two groups, the one associated with low speed cracking (termed as ‘Fail’), andthe other without low speed cracks (termed as ‘Safe’). Thus the low speed cracking boundaryof the extrudates of 6061/Al23/20p under the same extrusion ratio can be delineated, asshown in Figs. 9.10 to 9.12 for three different extrusion ratios.Chapter 9 Extrusion ofthe PRMMCs 2218R=13—‘6 a 394-5-sa 0•: J944.fo Safe‘. 394-6-sx 394-7-f(/2oJ94-7-s2 :&. —BoundaryFail :e.*.*. . t0 I I445 450 455 460 465 470 475Extrusion Temperature (°C)Figure 9.10 Low speed cracking boundary for the extrudate of606lIAl2O3I20pat an extrusion ratio of 138x S91-3-fR=346o S91-3-s0 A 194-12-fSafe 394-12-s4 X 394-13-fo 394-13-sFail + 394-14-fa 394-14-sA AZ4 a Boundary0- I420 450 480 510 540Extrusion Temperature (°C)Figure 9.11 Low speed cracking boundary for the extrudate of606l/A12OJ2Op at an extrusion ratio of 34Chapter 9 Extrusion of the PRMMCs 2228R=52z 394-19-f- * 394-19-sSafe A 394-20-f4 394-20-sFailBoundaryA420 440 460 480 500 520 540 560Extrusion Temperature (°C)Figure 9.12 Low speed cracking boundary for the extrudate of6061/A123/20pat an extrusion ratio of 52In the legend of Figs. 9.10 to 9.12, the symbol ‘-f and ‘-s’ denote ‘fail’ and ‘safe’,respectively for each extrudate. Due to less data being available for the 6061/A123/lOp, thelow speed boundary could not be delineated.9.2.2 Effect of Extrusion RatiosThe effect of extrusion ratio on the low speed cracking boundary is shown in Fig.9.13. It is noted that to understand the effect of the extrusion ratio, the ram speed should beconverted into extrusion exit speed, which is multiplied by 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 of the planttrial results, that is, more frequent low speed cracking occurred when the extrusion ratio wasincreased. The trend of the low speed cracking boundaries indicates that at a low extrusionChapter 9 Extrusion of the PRtfMCs 223ratio, temperature has a larger effect than the ram speed, and vice versa at a high extrusionratio. This is because at low extrusion ratio, the temperature rise of the billet due to the heatof deformation is low, and at a high extrusion ratio, because of higher exit speed, the adiabaticeffect becomes more significant..350___________ri R=13-fail300m R=13-safe250 R=34-fail Safe200 * R=34-safe . Aa Increasing R A150R=52-fail100R=52-safe500Fail 0c Low Speed Cracldng Boundary420 450 480 510 540Extrusion Temperature (°C)Figure 9.13 Effect on extrusion ratios on low speed cracking boundaryduring extrusion of 6061/A1O3/20p9.2.3 Extrusion Limit Diagram with Low Speed Cracking BoundaryThe 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, because of the limited range for the low speed cracking, only a part of the 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 in either temperature or extrusion speed is beneficial to preventing occurrence of theChapter 9 Extrusion of the PRMMCs 224low-speed cracking. The boundary line shifts towards the high speed cracking line (highspeed boundary) as the extrusion ratio increases to reduce the size of processing window.However, because no low speed cracking was observed at a ram speed of -6mm/s in the planttrials at UAC, 6mm/s is the minimum ram speed for the 7-inch press at UAC for extrusion ofthe PRMMCs at the extrusion ratio of 52.600500 —High SpeedR=13 High Speed Boundary, 400R=34c 300 —R=52 Increasing R Fail_____________Safe100 \Fail_________________Low Speed Boundary0 I I420 450 480 510 540 570Extrusion Temperature (°C)Figure 9.14 Extrusion limit diagram of 606l/A123/20p for the press at UACwith low-speed cracking boundaries9.3 Extrusion of the PRMMCsParticle fracture, with its size refinement and particle redistribution during extrusion,has been examined in Chapter 7. The origin of low speed cracking observed in the plant trialshas been explored with the aid of both macroscopic and microscopic finite element models 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 Extrusion of the PRMMCs 225speed cracking on the extrudate surface, and also to improve the quality of the PRMMCs byoptimizing the extrusion processing conditions for maximum productivity.9.3.1 Minimization ofMicrostructural Damage during ExtrusionThe extrudates from two plant trials at KRDC and UAC were cut and polished. Thespecimen from the plant trial 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-l 1B, with slight low speed cracks, andpolished at UBC 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 formicrostructure comparison. It seemed that some voids were present in the surface layer for allextrudates. The voids in the specimen from UAC were recognized as the origin of the lowspeed cracks, as shown in Fig. 9.15 from J94-14; while voids in K-6 specimen were associatedwith clusters, as shown in Fig. 9.16 for both the longitudinal and transverse sections.Table 9.2 Extrusion conditions for the specimens examined under an SEMTrial # Material Temp. Extrusion Billet Din. Remark(°C) Ratio(mm)394- 14 20% 461 (Front) 34 178 Severe cracking394-20 20% 457 (Front) 52 178 Severe crackingJ94-11B 10% 434 (Front) 34 178 Slight crackingK-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 aChapter 9 Extrusion of the PRMMCs 226cluster. The voids observed in the surface layer of the front-end extrudates could be due tothe 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 which the 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 likelihood of seeing voids in the as-cast6O6l/A123/lOp because of the smaller particle size and its tendency towards particleclustering. This kind of void could be removed by either improving the particle distributionduring the melt fabrication or breaking the clusters during extrusion.ii) Voids form when a fractured particle was not healed by intruding the matrixmaterial into the cracked gap. Most of these voids would be avoided by high hydrostaticpressure during extrusion at high temperature.iii) Voids may also form by interface decohesion. Decohesion is encouraged by weakinterfaces, such as obtained by spinel formation, MgA12O4at the particle interfacet1231. Thegeneration of tensile stress in the surface layer of the extrudate in the die land area would leadto void formation, if either the tensile stress is higher or the interface was weak enough.Therefore, the tensile stress should be minimized by controlling all the possible extrusionparameters studied in Chapter 8, e.g., higher initial temperature of billet and die, high ramspeed, low friction at the die interface. Elimination of spinel formation at the particle interfaceby increasing the magnesium content in the matrix alloy has been studied231,and new matrixalloys could also be sought with a better ductility1’221 and free of spinel formationU23 duringprimary processing. In addition, a better die design, such as stream line die2A wasrecommended to minimize the fracture behavior during extrusion of MMCs. However, it isChapter 9 Extrusion ofthe PRMMCs(b) LongitudinalFigure 9.15 Voids in the surface layer of an extrudate of 6061/Al2Oil2Opat an extrusion ratio of about 34 with low speed cracking (front end of J94-14)227(a) Transverse‘IChapter 9 Extrusion of the PRMMCs 228(b) LongitudinalFigure 9.16 Voids in the surface layer of an extrudate of 6061/A123110pat an extrusion ratio of about 28 with low speed cracking (front end of K-6)(a) TransverseChapter 9 Extrusion of the PRMMCs 229unclear whether the use of a stream line die may sacrifice the improvement of particledistribution obtained by the flat face die extrusion, or increase the tendency of low speedcracking due to die interface friction. The adoption of a hydrostatic extrusion process11112’76is certainly helpful to suppress void formation, although the production cost could become aconcern.It is interesting to note that no obvious voids were present in the surface layer of theextrudates cut from the back end without visible low speed cracks on the surface, as shown inFig. 9.17 for J94-14. This is mainly due to different extrusion 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 thefront end because of heat of deformation at a raised ram speed of about 6mm/s.Because microstructural damage, such as particle fracture and/or void formation, mayaffect the elastic modulus of the composites995”1,the variation of values of the extrudatesobtained under different extrusion conditions provide information on the effect ofmicrostructural damage. The correlation between Young’s modulus, E, of a hardened cementpaste and the porosity P0 was described as follows:E = E0 exp(—xP) (9.5)where E0 is the modulus of the solid phase without any pores and x is a material constantdependent on the internal structureElO4i. This may also be applicable to the compositematerials during extrusion, where E is the elastic modulus of the composites after extrusionand E0 is a standard elastic modulus which is a function ofmatrix alloy, reinforcement materialand volume fraction of the reinforcement for a specific MMC. Hence the change in elasticChapter 9 Extrusion of the PRMMCs 230modulus of the composites for different extrusion conditions should reflect the existence ofsignificant voids in the extrudates as a result of particle 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 elongation was sacrificed probably due to the presence of voids 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 it seems likely that the lowestmelting point phases could melt, leading to void formation. The low melting point phasesmust be associated with particles which were found at the dendrite extremities in the as-caststate.Figure 9.17 SEM image in the surface layer of the extrudate in longitudinal sectionat an extrusion ratio of about 34 without low speed surface cracking (back end of 394-14)Chapter 9 Extrusion of the PRMMCs 2319.3.2 Improvement in Partide Distribution and Size RefinementIt is well known that at room temperature the elastic modulus deteriorates as strainincreases, due to particle fracture7576’94.This is because the fractured particles were nothealed at room temperature. However, in the hot extrusion process, the stress state in thedeformation zone is tn-axial compressive, except in the surface layer of the extrudate in thedie land area where the stress component in the extrusion direction is tensile. Thecompressive stress state results in two beneficial effects: firstly, void formation and growth islargely suppressed; secondly, most of the fractured particles were healed due to both severeshear and compressive deformation, because there is no oxidation in freshly formedsurfaces11-12,75-76].Reduction in particle size is known to be associated with an increase in the yieldstrength of composite materials. This decrease in size, in conjunction with the increasedhomogeneity of the particle distribution and reduction in aspect ratio, is expected to improvethe fracture toughness. The healing of fractured particles will allow the material to 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 increase in theelastic modulus of the composites with an increase of the extrusion ratio (from the tensiletests) indicates that a large extrusion ratio should be beneficial to the improvement ofmechanical properties, if and only if the voids can be minimized.9.3.3 Quality and Productivity of the PRMMCsBased on the above analysis, for a better quality control, a high extrusion temperaturewith a high absolute reduction would be suggested for the processing of the PRMMCsbecause of the following reasons:Chapter 9 Extrusion of the PRMMCs 232i) the increase in temperature improves the matrix flow due 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 lower local tensile stress at the endsof 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 in the ductility of thecomposite materials, which is the one of the controlling factor for fracture behavior ofparticulate reinforced MMCs11221;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 analysis of the PRMMCs in Chapter 6 and Chapter 8.A higher extrusion speed is also recommended for extrusion of the PRMMCs. This ismainly due to:i) a higher extrusion speed will eliminate the low speed cracking, as described in Chapter 8;ii) it also helps the break-up of the particle clusters in the shear deformation zone; the clusteracts as a harder zone during deformation whose effect decreases as the strain rateincreases11;iii) more importantly, the higher extrusion speed will result in a 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 of the PRMMCs 233the composites should be processed within the high speed boundary of the extrusion limitdiagram developed.Chapter 10 Concluding Remarks 234Chapter 10 CONCLUDING REMARKS10.1 Summary and ConclusionsTo convince customers to use Duralcan® 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 the Duralcan® 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 6O61IA123IlOp and 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 shear deformation at high temperature.Chapter 10 Concluding Remarks 2352) Particles are aligned in the extrusion direction with formation of extrusion bands,especially in the 606lIAl2O3I10p. Voids were observed in the surface layer of the extrudateswith low speed cracks, and also in those extrudates with severe particle clusters, especially the606l/A12O3/lOp. The causes for void formation could be three-fold:i) retained from the as-cast material, especially for those in clusters;ii) unhealed particle fracture in the surface layer at relatively low temperature;iii) weak particle interface under high local tensile stress at the ends of the particles,especially for those in clusters in the surface layer of the extrudate.These voids can be avoided by controlling the processing parameters in both theprimary and secondly processing routes. The hydrostatic pressure generated during flat-facedie extrusion may help suppress void formation and growth. This is why the elastic modulusand other tensile strengths (e.g., yield stress, and the ultimate tensile strength) do not declineunder an extrusion ratio of about 30, although the elongation is sacrificed. The improvementin homogenization of particle distribution and the particle size refinement after extrusion allowthe maximum potential increase of tensile properties and also the fracture toughness, if thevoid formation can be suppressed by generation of a high hydrostatic pressure and low tensilestress in the surface layer as obtained in higher temperature extrusion.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 stress in the die land zone. Both the low speed cracking and the void formation can besuppressed by increasing the initial billet and die temperature and the extrusion speed withinChapter 10 Concluding Remarks 236the limit of the high speed cracking boundary (incipient melting line) with better quality andlarger productivity of the PRMMCs.10.2 Future WorkTo better understand the physical and chemical nature of the composites, the followingwork is suggested based on the above study.1) Because the origin of the low speed cracking is associated with void formation, aquantitative analysis of the fraction of voids formed under different temperature and strain rateis beneficial for a more accurate control of the processing parameters, such as temperatureand extrusion speed, to improve quality (to minimize voids and obtain more homogenizedparticle distribution at a finer and a more uniform particle size level) and productivity;2) A fracture criterion for low speed cracking or potential microstructural damageduring extrusion needs to be developed and verified. The fracture criterion can then beincorporated into the finite element model to cost-effectively develop extrusion limit diagramsfor different materials.3) An effective technique is required at the fabrication stage to improve both theparticle distribution and the bonding strength between the particles and the matrix to preventpotential interface decohesion. New choices of matrix alloys with higher ductility but free ofspinel formation are needed. A better design of the die to have improved quality and higherproductivity of the extruded products should also be studied. New processing technologieswhich produce defect free products with lower production costs should be 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. 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