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Microstructural evolution during hot deformation of the 6061 aluminium alloy based Al₂O₃ metal matrix… Geltser, Ilia Samsonovich 1993

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Microstructural EvolutionDuring Hot Deformation of the 6061 Aluminium Alloy BasedAl203 Metal Matrix CompositesByIlia Samsonovich GeltserM.Sc. (Physics of Metals), Moscow Institute of Steel and Alloys, 1990A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESMETALS AND MATERIALS ENGINEERINGWe accept these thesis as conforming to the requested standardTHE UNIVERSITY OF BRITISH COLUMBIAFebruary, 1993© Ilia S. Geltser, 1993In presenting this thesis in partial fulfillment of the requirements for anadvanced degree at the University of British Columbia, I agree that the Libraryshall make it freely available for reference and study. I further agree thatpermission for extensive copying of this thesis for scholarly purposes may begranted by the head of my department or by his representatives. It is understoodthat copying or publication of this thesis for financial gain shall not be allowedwithout my written permission.Metals and Materials EngineeringThe University of British Columbia2075 Wesbrook MallVancouver, CanadaV6T 1Z1Date:^12^tie„e iqqsAbstractThe development of conventional direct casting techniques to produce aluminiumalloy based metal matrix composites and the successful fabrication of these compositesby extrusion and forging processing has contributed to their successfulcommercialization. The Center for Metallurgical Process Engineering recently initiated acollaborative research study with the Ontario Center for Materials Research to develop amathematical model describing microstructural evolution of 6061-alumina metal matrixcomposite during extrusion processing. The research described in this thesis was directedat quantifying the microstructural changes associated with hot axisymmetric testing of a6061 aluminium alloy reinforced with 10, 15 and 20% alumina particulate.Cylindrical specimens 10 mm diameter x 15 mm height were compressed in thetemperature range of 573-823 K (300-550 °C), at a strain rate of 0.01-10 /s. Theresulting true stress-true strain data corrected for deformation heating were used byanother researcher to develop the constitutive equations for hot deformation. True localstrains at different points within the heterogeneously deformed specimen weredetermined by metallographic measurements of the aspect ratio of the deformed grains.To reveal the aluminum grain boundaries, existing etching techniques weremodified. Grain and subgrain size evolution was investigated by optical metallography.Recovery behavior of the 6061 and the composites was very similar whilerecrystallization behavor differed markedly. Only up to 5% fraction recrystallized wasobserved in the 6061 material deformed at temperatures above 723 K and annealed at thedeformation temperature, while grain growth was more apparent. Deformation at 723-773 K and annealing at 798 K produced up to 8% fraction recrystallized. Five regionsiiiiiwith different microstructural behaviour were identified for the composites:i) below 673 K recovery is sluggish and deformation flow lines persist during annealing;ii) at temperatures above 673 K at strain rates less than 0.5 /s, recovery is intensive, theoptically visible subgrains form and the original grain boundaries persist duringdeformation;^at strain rates from 0.1 to 1 /s static recrystallization occurs;iv) at strain rates from 1 to 5 /s in the composites there is a region of metadynamicrecrystallization; v) at strain rates above 5 /s dynamic recrystallization occurs.The mixed static/metadynamic recrystallization kinetics (static or dynamicnucleation and static growth of recrystallized grains) in the composites in the temperaturerange 723-788 K for strain rates of 0.5-5 Is and strains of 0.4-1.2, could be describedusing the Avrami equation with n=1.4 and the time for 50% recrystallisation as:t50%^• exp 293000  ) ERTwith x-2 and T1=5.3.In the region exibiting dynamic recovery, the temperature-strain rate dependenceof the resulting subgrain size was determined to bedsub=-0.686+0.044.In(Z),in good agreement with literature data.After deformation to a strain of 1, the average angle between the maximumcluster or particle dimension and the matrix flow direction was measured as 21 and 30degrees respectively. No particle fracture, particle debonding or de-clustering wasobserved.-17ivTable of ContentsAbstract ^ iiiTable of Contents^ i vTable of Figures ixTable of Tables^ xiiList of Symbols x i vAcknowledgment^ xvi1. Introduction  11.1. Discontinuously Reinforced Aluminum Based Metal Matrix Composites(MMCs)^ 11.2. MMC Consortium and Present Research^ 22. Current Industrial Processing of MMCs by ALCAN. 42.1. Influence of the Homogenisation Treatment on Microstructure^ 42.1.1. Residual Strains and Quenched-in Dislocations^ 42.1.2. Precipitation of Second Phases.^ 72.2 Effect of Temperature on Microstructure  112.2.1. Structure and Properties of the Matrix/Reinforcement Interface^ Crystallographic Relationships^ Chemical Reactions Between Matrix and Reinforcement^ Strength of the Interface Bonding^ 122.2.2. Interactions Between Particles and Dislocations^ Theories of Strengthening^ Activation Energies of High-Temperature Relaxation^ Strain Localization and Dislocation Climb^ 192.3. Effect of Thermomechanical Processing on Microstructure 212.3.1. Static Recovery in Aluminum Alloys^ 21V2.3.2. Dynamic Recovery in Aluminum Alloys^ Steady State, Equilibrium Subgrain Size and Misorientation ^ 222.3.3. Static Recrystallization^ Nucleation of Recrystallized Grains^ Heterogeneity of Deformation and Nucleation SiteDistribution^ Nucleation Efficiency at Large Particles^ 302. Nucleation Rate for Avrami Theory 312.3.3.2. Growth Rate^ 322. Driving Force for Static Recrystallisation in MMCs^ 322. Variations of the Growth Rate Near Large Particles^ 322. Variations in the Growth Rate Caused by Recovery^ 342. Influence of Small Particles and their Coarsening^ 372.3.3.3. Applications to the Grain Size and Texture Control in Al-alloys^ 372.3.4. Metadynamic Recrystallization^ 392.3.5. Dynamic Recrystallization (DRX) 392.4. Extrusion Processing^ 422.4.1. Temperature Evolution 432.4.2. Strain Distribution^ 432.4.3. Microstructural Effects 442.4.3.3. Macrodamage^ 442.4.3.2. Particle Alignment and Macrosegregation^ 452.4.3.1. Microstructural Damage^ 453. Experimental^ 483.1. Mechanical testing^ 483.1.1. The Gleeble 1500 Thermomechanical Simulator^ 48vi3.1.2. Working Range of Strains, Strain Rates and Temperature^ 483.1.2.1. Temperature Histories of the Tested Specimens 503.1.3. Temperature, Stress and Strain Control^ 513.2. Sample Preparation^ 534. Results and Discussion 544.1. Preliminary Metallography^ 544.1.1. Mechanical Sectioning, Grinding and Polishing^ 544.1.2. Chemical Etching^ 564.1.3. Electrochemical Etching and Polishing^ 574.1.3.1. Barker's Reagent^ 584.1.3.2. Optimum Temperature-Voltage-Current Conditions^ 604.1.3.3. Optimum Etching Time and Passivation Efficiency^ 624.1.4. Specimen Preparation for SEM^ 644.1.5. Quantitative Metallographic Observations^ 654.2. Microstucture of the As-cast and As-homogenized Materials^ 664.2.1. The 6061 Al Alloy^ 674.2.1.1. Grain size and shape^ 674.2.1.2. Matrix Composition. Precipitate Composition, Size andDistribution^ 684.2.2. The 6061/Al203 composites^ 694.2.2.1. Grain size and shape 704.2.2.2. Reinforcement Size and Distribution^ 734.2.2.3. SEM/EDX Analysis of the Matrix / Reinforcement Interface ^ 744.2.2.4. Precipitate Composition, Size and Distribution^ 754.3. Microstructure of Thermomechanically Processed 6061 Al-Alloy^ 764.3.1. Strain Inhomogeneity in Hot Compressed Cylindrical Specimens^ 764.3.1.1. Comparison With the Finite Element Simulations^ 78vii4.3.2. Effect of Temperature on Mg2Si Precipitation and Coarsening^ 824.3.3. Recovery, Grain Growth and Recrystallization in the 6061 Alloy^ 864.3.3.1. Precipitate Pinning of Dislocations and Grain Boundaries inthe 6061 alloy^ 864.3.3.2. Metallography of Recovery, Grain Growth andRecrystallization in the 6061^ 884.4. Microstructure of Thermomechanically Processed 6061-AluminaComposites^ 974.4.1. Effect of the Hot Deformation on the Reinforcement Distribution^ 974.4.2. The Mg2Si Precipitation and Coarsening in MMCs^ 994.4.3. Temperature-Strain Rate Processing Maps for the MMCs^ 1024.4.3.1. Domain of no Subgrain Formation^ 1044.4.3.2. Domain of the Dynamic Recovery via Subgrain Formation ^ 1044. Temperature - Strain Rate Dependence of DynamicRecovery^ 1074.4.3.3. Domain of the Dynamic Recrystallization (DRX)^ 1104. Critical Strain for Recrystallization^ 1154. Influence of Matrix Precipitation and Recovery^ 1154.4.4. Mechanical Behaviour of the MMCs^ 1174.4.4.1. Mechanical Response to DRX 1174.4.4.2. Mechanical Response to Precipitation^  1184.4.5. Static and Metadynamic Recrystallization in the MMCs^ 1224.4.5.1. Quantification of recrystallization   1234.4.5.1. Grain size after recrystallization. ^  127Conclusions^  129Future Research Requirements^  133Literature Cited^  135viiiAppendix A. A Conceptual Model for Dynamic Recovery / Static Recovery andRecrystallization^ 141A.1. Driving Forces 142A.1.1. Precipitation Model^ 143A.2.The recovery processes   144A.2.1. Subgrain Evolution^  146A.3. Nucleation and Recrystallization  148A.3.1. Nucleation rate^  148A.3.2. Fraction recrystallized  148A.3.3. Softening due to recrystallization•^  148A.4. Example Calculations^  149A.S. Summary^ 149Appendix B - Programs for the Leitz Image Analyzer^  150B.1.Measurements of the Interparticle Spacing  150B.2.Particle Size and Orientation Distribution^  152B.3. Distance to the Closest Neighbor Measurements 154I XTable of FiguresFigure 1-1. Properties of the 6061/Al203 composites compared to those of the6061 alloy^ 2Figure 1-2. The MMC consortium research assignments.^ 3Figure 2-1. Temperature dependence of the flow stress for 6061 alloy reinforcedwith different size SiC particulate, after Humphreys (1991)^ 18Figure 2-2. Fractional residual strain hardening curves for isothermal annealing ofCu and Al (Furu et al., 1990).^ 22Figure 2-3. Equivalent true stress-true strain curves for A1-1Mn-1Mg alloy(Castro-Fernandez and Sellars,1988).^ 23Figure 2-4. Time dependence of the recrystallized volume fraction in thedeformation zone model (Furu et al., 1990).^ 34Figure 2-5. Recovery and recrystallization reactions in CP Al modeled by Furu etal. (1990).^ 36Figure 2-6. Maps showing the grain size resulting after cold rolling and annealingof various aluminum alloys as functions of rolling deformation and secondphase dispersion level (Nes, 1989) ^ 38Figure 3-1. Schematic diagram of the Thermomechanical Simulator^ 49Figure 3-2. Temperature histories of the compression specimen in several sets oftests.^ 52Figure 3-3. Strain rate behavior of three compression tests of 6061/Al203/20p atT=798 K at a nominal strain rate of 1/s.^ 53Figure 4-1. Grinding and polishing of homogenized 6061/Al203/20p composite. ^ 55Figure 4-2. Cast and homogenized 6061 alloy after chemical etching in H2SO4-HF-H20^ 57Figure 4-3. Electropolishing of the 6061 alloy and the 6061/Al20 3/15p inBarker's reagent.^ 59xFigure 4-4. Electropolishing in the reagent N 2 at 5 V, 253 K.^ 60Figure 4-5. Homogenized 6061 alloy after electropolishing in Reagent N2.Polarized light.^ 61Figure 4-6. Time dependence of current during electropolishing of the 6061 alloy^ 63Figure 4-7. Homogenized 6061 alloy after electropolishing for 7 time segments of10 s with 1 min. intervals^ 63Figure 4-8. SEM observations of alumina reinforcement and subgrain boundariesin the MMCs.^ 64Figure 4-9. Particle area, size and aspect ratio distribution the 6061/Al203/15p. ^ 66Figure 4-10. As-cast (a) and as-homogenized (b) 6061 Al alloy.^ 67Figure 4-10. Precipitates in the 6061 alloy exposed by chemical etching (H2SO 4-HF'-H20, 30 s at room temperature)^ 69Figure 4-12. The homogenized MMC's microstructures.^ 72Figure 4-13. The reaction product at the matrix/particle interface in6061/Al203/20p ^ 74Figure 4-14. Strain distribution in a hot compressed 6061 cylidrical specimen.^ 76Figure 4-15. The grain size and aspect ratio distribution in 6061 cylidrical sampledeformed to the nominal strain 1 ^ 77Figure 4-16. Correction coefficients for calculation of true local strains e z fromnominal strain ez at several points in the sample.^ 78Figure 4-17. Vertical section of the compressed specimen 79Figure 4-18. Grain aspect ratios at a nominal strain 1 derived from FEMsimulations.^ 79Figure 4-19. Distribution of normal stress azz and mean normal stress azzin in acompressed cylindrical specimen (Kopp et al., 1988)^  81Figure 4-20. Distribution of FEM calculated equivalent strain, strain rate E andtemperature at a nominal strain of 47% (Kopp et al., 1988). ^ 81xiFigure 4-21. Precipitation of Mg2Si in the 6061 alloy during annealing.^ 85Figure 4-22. A pinning pressure evolution during annealing.^ 87Figure 4-23. Recovery and grain growth in 6061 alloy deformed to a strain of 1^ 92Figure 4-24. Grain growth and recrystallisation in 6061 alloy heated up afterdeformation at a strain rate 15 /s.^ 95Figure 4-25. Particle distribution in deformed MMCs. As-polished ^ 98Figure 4-26. Particle alignment along the flow direction during deformation.^ 99Figure 4-27. Precipitation of Mg2Si in 6061/Al203 composites during annealing ^ 101Figure 4-28. Microstructural evolution map for 6061/Al203/p composites. Up-heating^  103Figure 4-29. Flow lines after deformation of the 6061/Al203/20p at 573 K^ 105Figure 4-30. Recovery in the composites via subgrain formation^ 107Figure 4-31. Correlations between subgrain size, temperature compensated strainrate and temperature.^  109Figure 4-32. Dynamic recrystallisation in composites. ^  113Figure 4-33. Strain dependence of recrystallisation in the 6061/Al203/15pdeformed at 773 K and air cooled.^  114Figure 4-35. Mechanical behaviour of the 6061 alloy and the MMCs ^ 119Figure 4-36. Mechanical responce to precipitation. Up-heating vs down-quenching tests.^  121Figure 4-37. Avrami plot for mixed metadynamic/static recrystallization kineticsin 6061/Al203/10p ^ 124Figure 4-38. Derivation of parameters for describing recrystallization in6061/Al203/1 0p ^  125Figure A-1. Interaction of dislocations during subGB formation or dissolution. ^ 146Figure B-1. Vertical section of the compression specimen^ 150xiiTable of Tables Table 2-1. Properties of matrix and reinforcements.^ 5Table 2-2. Experimental and calculated dislocation densities in 6061/Al203/pcomposites (after Dutta et al, 1991).^ 7Table 2-3. Compositions of the 6061 alloy used by different researchers^ 8Table 2-4. Peak temperatures (K) of DSC exotherms.^ 9Table 2-5. Hardness peaks in 6061 and composites, after Dutta et al. (1991)^ 10Table 2-6. Kinetics of precipitation in 6061 and composites, after Dutta et al.(1991) and Dionne et al. (1991).^  10Table 2-7. Summary of activation energies and work hardening rates for hotdeformation of Al alloys and composites.^  15Table 2-8. Static recrystallisation in Al alloys. 26Table 2-9. Activation energies of static recrystallization (Wells 1991).^ 27Table 2-10. Tensile Properties of 6061/Al203/p, after Nakagava and Gungor. ^ 47Table 3-1. The Compositions of the 6061 alloy used by DURALCAN^ 49Table 3-2. The test matrix for the 6061 alloy and the composites. 50Table 4-1. Particle volume fraction, particle area, maximum dimension and aspectratio in the 6061/Al203/15p^ 66Table 4-2. WDX composition measurements in FeSiA15 precipitate free matrixregions of the 6061 alloy compared with manufacturer's specifications forthe 6061 alloy.^ 69Table 4-3. EDX measurements of composition of several precipitates^ 69Table 4-4. Grain size and aspect ratio in homogenized materials. 72Table 4-5. Particle and cluster size, shape and standard deviation in homogenizedcomposites^ 72Table 4-6. Composition of FeSiA15 precipitate free matrix regions in the as-homogenized 6061/Al203/20p composite and 6061 alloy.^ 75Table 4-7. Matrix compositions of as-homogenized and annealed 6061 alloyobtained by WDX analysis.^ 82Table 4-8. The precipitate size evolution in base alloy during annealing.^ 83Table 4-9. Kinetics of Mg2Si precipitaion calculated from measurements ofMondolfo (1976) at 573 K.^ 86Table 4-10. Grain Size and Shape Evolution in 6061 on Static Annealing^ 93Table 4-11. Sizes and Aspect Ratios for Original and Recrystallized Grains^ 95Table 4-12. The precipitate size evolution in 6061 alloy and MMCs duringannealing.^  100Table 4-13. Matrix compositions of as-homogenized and annealed MMCs and6061 alloy^  100Table 4-14. Dependence of the subgrain size from the temperature compensatedstrain rate in aluminium alloys (after Wells, 1991). ^  110Table 4-15. Parameters of the recrystallization kinetics in the 6061/Al203/p andin aluminum alloys.^  126x i VList of SymbolsPdisl - dislocation density^ m-2f - volume fraction of the reinforcementC - thermal expansion coefficient^ m/(m•K)b - burgers vector^ mdpart - particle (reinforcement) diameter^ m'Fe - critical temperature of the GP zone dissolution^ KG°800K - Gibb's free energy at 800 K^ JQo - addition to the activation energy of diffusion under pressure^JVvac - vacancy volume^ m3P0 - hydrostatic pressure Paa - true stress^ PaE - true strainG - shear modulus^ PaR - universal gas constant, also extrusion ratioD - diffusion coefficient^ m2/sQdef - activation energy for deformation^ J/molQdif - activation energy for volume diffusion J/molQrec - activation energy for recrystallisation^ J/mold - grain diameter^ mdrub - subgrain diameter mF - grain growth rate^ m/st50% - time for 50% volume fraction recrystallized^ sTHD - temperature of hot deformation^ KTa - annealing temperature^ Kdo - initial grain size (before deformation)^ ms-1Z - temperature compensated strain raten - work hardening rate (stress sensitivity of strain rate)Go - tensile threshold stress for the start of deformationto - shear threshold stress for the start of deformationCm - strain to the steady stageec - critical strain for the start of lattice rotations near particlesv - nucleation frequencyN - nucleation rateNo - number of nucleation sitesv - dislocation energy per unit lengthn* - Avrami exponent0 - misorientation angleco- width of deformation zone around particleA, - interparticle distanceX - volume fraction recrystallisedXext - extended volume recrystallizedXVPaPs-1nuclei/sJ/mIllmS - recrystallized fraction of interfacial area per unit volumeSext - extended recrystallized interfacial areaFR - driving force for recrystallisation^ Pay - shear strain, also grain boundary energyP - instantaneous stored energy^ JPr - non recoverable stored energy JPz - Zener pinning force^ Palc - passivation coefficientIinit - current at the start of the polishing cycle^ AIstat - current in the established polishing regime AV - voltage^ VAcknowledgmentThanks to my supervisor Dr. Bruce Hawbolt it became possible for me to come toCanada and to become a UBC student. Thanks to his patience, insights andencouragement this work is accomplished in its present form. Thanks to hisunderstanding and support, an opportunity to significantly widen my qualifications andunderstand the North American way of doing things was realised for me.Active interest, significant factual input and comments of Dr. Chris Davies werevery helpful and are gratefully acknowledged. The accuracy of Binh Chau in planningand conducting compression tests proved invaluable. Suggestions of Mary Mager andDr. Desmond Tromans on various stages of this work are appreciated. Thanks also go tofellow students who helped me to integrate into the new environment.I acknowlwdge the encouragement and attention given to me by my wife, AnnaLevitan. I am grateful to the governments of Canada and the USA and their citizens forgiving refuge to me and my relatives and, thus, making it possible for me to concentrateon my studies.xvi1. Introduction1.1. Discontinuously Reinforced Aluminum Based Metal MatrixComposites (MMCs)"Lighter, stiffer than steel, more wear resistant - in short, a breakthrough inmaterials technology", that is how the makers of Duralcan Metal Matrix Compositesdescribe their recent developments as shown in Figure 1-1 (Canadian Welder, 1991).The 6061 reinforced with 20% powder alumina is 10 times more wear resistantthan the matrix alloy and has 30% lower thermal expansion coefficient. Compared tosteel, the composite has 35% higher specific stiffness, allowing for 17% higher driveshaftspeeds in automobiles. It is expected that following the general trend in aluminumreplacing steel in automotive applications, aluminum based MMCs will find applicationsin brake rotors and other moving parts. The confidence of Duralcan in marketability oftheir product is so high that they built a $3-million plant in Quebec to manufacture up to12,000 tons of the composites per year.Alumina powder has been chosen as a reinforcement for its cost advantages (5-10times cheaper than SiC powder, 10-100 times cheaper than SiC or Al203 whiskers) andalso for its higher stability than SiC in Al-alloy melts.As of February 1990, the material was available in foundry ingots and extrusionbillets. Billets were offered for $2.00 to $3.50 per lb. Extrusions and tubing were soldfor $3.00-$7.00 per lb. Thus, hot deformation accounted for about 50% of the costs.That is one reason why Duralcan is so interested in optimizing hot deformationconditions and attaining controlled structure and properties of the product.1EgYield Strength II Ultimate Strength [a Elongation^E Elastic Modulus2Figure 1-1. Properties of the 6061/Al203 composites compared to those of the 6061 alloy.MMCs have a higher elastic modulus than aluminum because of the stiffness ofthe alumina being higher. Wear resistance of composites is higher because of the higherhardness of the alumina. The strength of composites is determined by several physicalprocesses responsible for deformation, relaxation of internal or external stresses andmicrostructural damage. Because of the strength of the alumina being higher than that ofthe matrix, the reinforcement particles can be considered as non-deformable. At ambienttemperatures the reinforcement restricts dislocation glide and cross-slip (this increases0.2% proof stress) and results in higher work-hardening (this increases ultimate strength).At high temperatures, flow localisation near particles reduces the yield strength, but withthe work hardening being higher than in unreinforced material, the 0.2% proof stress andthe ultimate strength is not affected.1.2. MMC Consortium and Present ResearchSponsored by ALCAN, INCO, Sherritt Gordon, Ontario Hydro and NSERC amajor University/Industry research initiative was created. The distribution of tasksModelling of Hot DeformationProf. E.B. Hawbolt, Prof. I.V. Samarasekera,Prof. K.J. BrimacombeMechanicalbehaviourduring hotdeformation(constitutiveequations)Microstructural^Stress-strain andevolution^microstructuralduring hot responce ofdeformation^plain strain vsaxisymmetrictestingDr. Chris Davie- Mr. Ilia Geltser^Mr. Saul MartinezFinite element model ofhot deformationMr. Weichang ChenU of TFatigue(Windsor UniversitWear [McMaster UniversityMixing, SolidificationFracture, InterfacesQueen's UniversityElectrochemical route,Infiltration,Interface reactions. j( Western OntarioNon-destructive evaluationModelling of internal stresses/UBC3among the participants, as well as the emphasis of the present research in the UBCcontribution is shown in Figure 1-2. The UBC's component of the research is to developa database and a Finite Element Model for the microstructural evolution in 6061/aluminacomposites during extrusion processing.One research goal of the present thesis is to systematically investigate and, wherepossible, to quantify, reinforcement redistribution and grain and subgrain evolution undervarious temperature, strain and strain rate conditions during hot compression testing. Thesecond goal is to quantify static recrystallisation behaviour in the composites after hotdeformation under various conditions. The third goal is, by comparison of the compositeand of the unreinforced matrix alloy, to improve the theoretical understanding of theeffects of alumina reinforcement on microstructural evolution and mechanical responseduring hot deformation.This research has been conducted in close collaboration with the constitutiveequation research of Dr. C. Davies (1992) for inclusion into the final hot deformationmodel.Figure 1-2. The MMC consortium research assignments.2. Current Industrial Processing of MMCs by ALCAN.ALCAN's (DURALCAN) industrial process (Lloyd, 1991b), includes melting ofthe aluminum alloy, addition of alumina particles, mixing and direct chill casting.The ingot is then heat treated at 838 K for approximately 2 hours to homogenize thedistribution of Mg and Si and to transform a-FeSiA1 precipitates into 13-FeSiAl.Upon homogenization samples are air cooled, heated to deformation temperature,deformed, cooled, reheated for solutionizing for 2 hours at 803 K, rapidly cooled toprevent precipitation of Mg2Si, and, finally, aged (Klimovicz and Vecchino, 1990).This review summarizes the homogenisation and deformation stages. However,the effects of homogenisation before deformation and solution treatment afterdeformation on the subsequent precipitation are very similar; therefore, most of theconsiderations of section 2.1 are valid for solution treatment. Consideration of thedeformation effects also includes static transformations that take place after deformation.2.1. Influence of the Homogenisation Treatment on Microstructure2.1.1. Residual Strains and Quenched -in DislocationsOn rapid cooling during chill casting, the difference in the thermal expansioncoefficients (CTE) of aluminum and alumina (Table 2-1) causes non-uniformcompressive internal stresses in the reinforcement and tensile stresses in the matrix. Inthe latter, the stresses manage, in part, to relax via generation of an array of prismaticdislocation loops, as documented experimentally by Vogelsgang et al. (1986).Dislocation generation occurs primarily at large, non spherical particles. The non-relaxedinternal stresses are called "back stresses" (Taya et al., 1991a).45Table 2-1. Properties of matrix and reinforcements (Lloyd, 1992).Material Modulus E, GPa Poisson ratio CTE, 10-6/K6061 68.3 0.3 23.2SiC 427.0 0.17 4.3Al203 403.0 0.23 7.0Miller and Humphreys (1991) argued that on "rapid cooling", when no diffusionalrelaxation occurs, most of the misfit strain is retained as a residual stress. Measurementsof these internal strains after water quenching showed them to be similar to thosegenerated by an approximately 200 K temperature drop. On slower cooling, diffusionalrelaxation operates up to some temperature and, if this temperature is less than 473 K,then no dislocations should be generated and only residual stresses should be produced.According to Lloyd (1992), for reinforcement with small particle aspect ratios,the residual stresses are hydrostatic and, thus, do not influence the yield stress of thecomposite but should influence microstructural development, deformation and fracture.No more specific data is available. Assuming no stresses in the material before coolingand no dislocation generation on quenching from 803 K to 298 K, Lloyd (1992)calculated the tensile stresses in the 6061/Al203/20p matrix as 144 MPa. Using the sameassumptions, Shouxin et al. (1991) calculated by FEM the average residual stresses in thematrix of an Al/SiC composite. For the yield stress of the material equal to 130 MPa andcooling from 623 K, the predicted residual stress of 70 MPa corresponded well to the X-ray measurements. More specifically, for the 6061/SiC/30p 2 after hot rolling and T6 3 ,Ledbetter and Austin (1991) measured a 206 MPa hydrostatic tensile stress in the matrix(75% of its yield strength).2 6061/SiC/30p designates a 6061 alloy reinforced with 30% vol. of SiC particles; w, f and p stand forwhiskers,fibers or particulates.3 T6 is a generic term for solutionizing and ageing to a peak hardness; for the 6061 alloy that is solutiontreatment at 803 K for 2 hours followed by quenching and ageing at 448 K for 8 hours.6Dislocation structures cause an increase in the yield stress after quenching. Also,in principle, quenched-in dislocations influence the microstructure formation on heatingfor hot deformation or recrystallization annealing both directly and indirectly by:-providing nucleation sites for precipitates,-accelerating diffusion,-forming stable dislocation substructures which influence microstructureand strength in the early stages of the hot deformation (up to c=0.3),-providing additional driving force for static recrystallisation.For the purpose of the present review the question, whether these dislocationsstructures can affect microstructure formation during subsequent treatment, is important.Vogelsgang et al. (1986) indicate that the "CTE mismatch" dislocations disappear inaluminum on heating to 650 K. Therefore, their effect can be significant duringsubsequent aging at 443-473 K, but is unlikely to be noticed at extrusion temperatures(723-823 K). According to Humphreys (1988), it is unlikely that a higher dislocationdensity around particles can cause an earlier start of dislocation movement in regionsbetween particles, resulting in a lower yield stress and a higher rate of work hardening.Miller and Humphreys (1991) referred to measured typical dislocation densitiesof 10 12 m-2 for both typical aluminum alloys and slow cooled particle reinforcedcomposites. Dutta et al. (1991) have measured dislocation densities in 6061/Al203/pcomposites (samples 2x1x0.4 cm, solutionized at 813 K and ice-water quenched) asshown in Table 2-2. In a smaller sample 0.76'0.38 cm (where higher cooling rates can beachieved) of 6061/Al203/15p quenched after 4 hours at 583 K into ice-water,Levandovski et al. (1990) measured pdis1=1.2.10 14 m-2 .Taking into account the CTE misfit only, the dislocation density can be calculatedas:Pcaiculated=(12•f•C•T) / b•d^ (2.1)7where f is the volume fraction of the reinforcement, C is the difference in thermalexpansion coefficients of the matrix and the particles, T is the temperature drop, b is theburgers vector and d is the particle diameter. From the formula (2.1) Lloyd (1992)calculated the incremental strengthening due to the higher dislocation densities. Acalculated increase in the flow stress of 20 MPa for 6061/Al203/20p was in goodagreement with the measured proportionality limit, but was about 4 times less than the0.2% offset yield stress.Table 2-2. Experimental and calculated dislocation densities in 6061/Al203/p composites(after Dutta et al, 1991).Material 6061 6061/Al203/10p 6061/Al203/15p Calculated,6061/Al203/20pPdisl, m-2 (3.1+-3.6)1010 (4.5+-2).1012 (7.3+4.8)1012 7.5.10122.1.2. Precipitation of Second Phases.The dislocation density discussed in the previous section acts as a driving forcefor microstructural changes. The stored energy associated with dislocations is dissipatedby recovery and recrystallisation processes. Mobility of subgrain boundaries created byrecovery is controlled, in part, by the distribution and size of second phase particles.There are basically two types of precipitates observed in the 6061 alloy of thecompositions shown in Table 2-3: Mg2Si and Fe-Si-Al modified by Cr. The precipitatesize and volume fraction vary with the composition and heat treatment. Aftersolidification Mg2Si and FeSiA15 form; FeSiAl5 precipitates have 2-5 tm size anddecorate dendrite cell boundaries. They are also often associated with alumina particles,because of both solute and particle rejection by the solidifying Al matrix. The Mg2Siprecipitates produce hardening during ageing. According to the Metal Handbook (1973),at 793 K 0.77 wt.% Mg and 0.45 wt.% Si can theoretically be in solid solution in8aluminum. As solubility increases with temperature, in an alloy containing 1.13 wt.% Mgand 0.57 wt.% Si, higher hardness is achieved by ageing after solutionizing at 823 K ascompared to solutionizing at 793 K (Salvo et al., 1991).Table 2-3. Compositions of the 6061 alloy used by different researchers.Mg Mn Fe Si Cu Others Reference0.84 0.65 0.18 0.21Zn Appendino, 19911.25 0.80 0.25 Appendino, 19911.01 0.03 0.29 0.44 0.22 0.23Cr, 0.01Zn Badini, 19901 0.47 0.75 0.39 0.15Cr Mabuchi et al., 19910.8-1 0.15 0.7 0.4- 0.15 0.04-0.35Cr, Metal^Handbook,max max 0.8 -0.4 0.25Zn max, 0.15Ti max 1982Because the Mg2Si-Al-Mg eutectic lies at 831 K, this requires some care to betaken during annealing of the as-cast materials. Dionne and Lo (1991) observed in an Al-0.7Mg-0.25Si-0.3Cu-0.12Fe-0.1Cr alloy that, unlike the Mg2Si, the Fe-Si-Al precipitatesdo not dissolve during solution treatment at 803 K for 2 hours. They do not dissolveduring homogenization at 838 K, either, only change their form from a into p.The following transformations occur on cooling, as described by Dutta andBourell (1990). Si clusters form on quenched-in vacancy loops and are precursors of GPzones. Thus, GP1, GP2 and then do not require new nuclei formation.Dutta et al. (1991) showed that growth of Si clusters is accelerated by reinforcement.The Si-clusters (2-3 nm in diameter) formed in composites almost immediately onquenching and did not grow substantially during holding at ambient temperature. Thesame authors suggested that Mg diffusion is accelerated by a higher dislocation density.The apparent diffusivity of Mg, which controls the GP zones formation and growth, wasfound to increase linearly with dislocation density. Resistivity measurements indicatedthat transformation of the GP2 zones into 13 1 -Mg2Si increases matrix strain and thus maybe affected by the pre-existing strains.9After water quenching and immediate heating at a heating rate of 10 K/min, peaktemperatures of differential scanning calorimetry (DSC) exotherms were measured byDutta et al. (1991), as given in Table 2-4. These authors also noticed that preageing atroom temperature changed the heat effects of the precipitation reactions but did not shifttheir temperature intervals. The different interpretation of the DSC exotherms byAppendino et al. (Table 2-4) may result from a slightly different composition of the 6061(Table 2-3) and from a higher heating rate.Table 2-4. Peak temperatures (K) of DSC exotherms.Reference Appendino et al., (1991) Dutta et al., (1991)Heating rate 20 K/min 10 K/minMaterialPreagate6061 6061 6061/Al203/10p6061/Al203/15pSi-clusters 355 355 form on quenchingGP1, GP2 formation 373GP1, GP2 dissolution 48313' formation 523 572 564 55913 formation from p' 573-603 770 765 757ri dissolution 813 805 790A critical role of the "CTE mismatch" dislocations and residual stresses on Sicluster formation, precipitate nucleation and growth during heating for deformation isbest illustrated by the accelerated ageing of composites. As shown in Table 2-5 (afterDutta et al., 1991), the 6061/Al203/p exhibited higher peak microhardness and agedfaster. The strengthening effect of the "CTE mismatch" dislocations was more noticeablein the beginning of ageing.Salvo et al. (1991) believe that reinforcement accelerates ageing of the 6061 onlyabove some critical temperature Tc , which is the dissolution temperature of the GP-zones, and was found to be 463 K for 6061/Al20 3/10p and 6061/SiC/10p . Below Tc the10vacancy concentration in the composite matrix is not as high as in the pure alloy due toannihilation of vacancies on quenched-in dislocations. Hence, vacancy loops, which areprimary places for Si-clusters and GP zone formation, are not as abundant. At T>T cprecipitates nucleate on dislocations, which are more abundant in composites. Reportedparameters of the ageing kinetics and sizes of second phase precipitates are presented inTable 2-6 (Dutta et al., 1991 and Dionne and Lo, 1991)Table 2-5. Hardness peaks in 6061 and composites, after Dutta et al. (1991).6061 6061/Al203/10p 6061/Al203/15pHardness (peak), MPa 825 950 960Ageing time to peak hardnessat 473K, min.65 40 25Table 2-6. Kinetics of precipitation in 6061 and composites, after Dutta et al. (1991) andDionne et al. (1991).Type of precipitates T, K t, s precipitatesize, nmIncrease^inmicrohard-ness, MPaMaterialSi-clusters 473 50 1-2 30 6061GP1 zones 473 100 2-4 6061GP2 zones 473 2000 diam.^5,length^20,rods6061I3'-Mg2Si^semicohe-rent, II to <100> Al473 4000 diam.^10,length (150-200), rods6061[3'-Mg2Si, semicohe-rent, II to <100> Al473 300 diam. 20 6061/Al203/15Dcorresponds^to60000s^ageing^ofpure 606113'-Mg2Si 10x100, rods 6061, peak aged at443-473 Kj3-Mg2Si 100,equiaxed6061, peak aged at443-473 K112.2 Effect of Temperature on MicrostructureThis part of the review summarizes the literature on the effect of temperature onmechanical response of aluminum alloys and composites to hot deformation.2.2.1. Structure and Properties of the Matrix/Reinforcement Interface2.2.1.1. Crystallographic Relationships Aluminum oxide layers growing on aluminum alloys are usually amorphous.However, 50-500 nm thick aluminum layers deposited on alumina substrate were foundto exhibit a weak <111> texture (Alpas et al., 1990). Although anisotropy of the Al/Al203interface energy is expected to play a significant role in nucleation of solidification andrecrystallization, the Al203 reinforcement particles do not nucleate solidification, but arepushed or entrapped by the solidification front in materials with low or high volumefractions of reinforcement, respectively. No quantitative measurements of the anisotropyof the interfacial bonding or related phenomena were found in the literature. Chemical Reactions Between Matrix and ReinforcementThe equilibrium segregation of alloying elements to the 6061/Al203 boundaryoccurs below the solutionizing temperature of 803 K when the alloying element contentin the matrix is within the solubility limit. For 0, N, C, H atoms the segregationcoefficient( [solute ] boundary  ) may be 10-1000, which may result in a depletion of the[solute ]volumesolute atoms in the adjacent 0.01-1 gm region of the matrix (Bockstein et al., 1988). ForMg, Si, Fe atoms this segregation coefficient should be less than 10, producing a muchsmaller effect in the matrix.Solid state chemical reactions between matrix and reinforcement are thermo-dynamically possible. At high temperatures Mg reduces Al203 according to the reaction:y-Al203 + 3Mg = 3MgO + 2A1,12G°800K = -89 .5 kJimol 02 ,^ (2.2)Formation of magnesia, which has a different specific volume per oxygen atom,may cause fracturing of the alumina or some stresses in it. A Mg content lower than 1%results in stability of MgAl204 (Vasudevan, 1990).Chemical reactions between liquid metal and reinforcement are more pronounced,and the amount of Mg depletion in the matrix may be quite significant. Yang and Scott(1991) found that the reaction with Al203 fiber reinforcement (30% volume) consumed0.2% Mg from the matrix. As a result, no formation of Mg 2Si was noticed on cooling. Itshould be noted that one of the advantages of the alumina reinforcement is that chemicalinteraction with the molten matrix is not as intense as for a SiC reinforcement. Strength of the Interface BondingIt is generally agreed that Al-alumina bonding in cast materials is associated withthe formation of MgAl2O4 and CuAl204 spinel layers at the interface (Kamat et al., 1989).Qualitative judgment on the strength of matrix/particle bonding is often done on the basisof particle pullout during tensile tests. Alpas et al. (1990) investigated strength andfracture of very thin layers (5 nm thick) and very pure Al/Al203 laminates. Tensile testswere performed at 297, 577 and 683 K at strain rates 10 -2-104 /s. Tear energy decreasedfrom 12 to 5.8 10/m2 with an increase in interlamellar spacing from 50 to 500 nm.2.2.2. Interactions Between Particles and DislocationsStrength of the composite is determined by several physical processes responsiblefor deformation, relaxation of internal or external stresses and microstructural defects(dislocations, dislocation piles, point defects, stacking faults, etc.). These include:- dislocation glide, cross-slip and climb,- detachment of dislocations from particle after climb,- dissolution and regeneration of dislocations on the particle surface,- vacancy and atom diffusion,13- dynamic precipitation 4 . Theories of Strengthening"Rule of mixtures" models are often used to evaluate the strength increment of thematrix due to the presence of fibers. The theory does not consider the dislocationbehavior and has not been successfully applied to particulate reinforced MMCs.Taya (1991) described the following dislocation models (Orowan model, foresthardening model, elastic peg model and Tanaka and Mori's model), which consider workhardening and no recovery, that were used to describe strengthening in particulatereinforced MMC during room temperature deformation.The Orowan model considers particles inside of the shear stressed single crystaland supposes that strengthening occurs due to an increase in the length of expandingdislocation loops around particles. Humphreys et al. (1990) emphasizes that Orowanloops can form at low strains (<1%) and then relax to more stable configurations, whichresult in the local rotation of the matrix in the narrow deformation zone near the particle.The forest hardening model considers spherical non-deformable particlesembedded in a single crystal. The misfit between the spherical shape and the ellipsoidalshape that the particle should attain, be it the same strength as the matrix, is eliminatedby generation of dislocation loops along the secondary slip planes.The elastic peg model again considers dislocation loops around particles. InTanaka and Mori's model their effect is represented as a "transformation strain", which isdefined inside the particle. The calculated work hardening depends on the particle shape.One of the most successful, the Eshelby model, is described in detail by Taya(1991).The major disadvantages of the model in application to MMCs are its inability to4 This term was used by Sheppard et al. (1986) for the effect of sinking of solute atoms on climbingdislocations.14predict local variation of stress near the particle/matrix interface (which is important forrelaxation processes) and its limitation to a low volume fraction of particles. Activation Energies of High-Temperature RelaxationMost relaxation processes are diffusionally controlled and have activationenergies approximating the energy of self-diffusion of aluminum (140 kjimol)•However, different diffusivities of solute atoms can modify this simple assumption.For example, in Al-2Mg alloy the activation energy of self diffusion of Al at 773 Kequals 156 1d/moi and the activation energy of interdiffusion equals 135/kj‘ mol.Therefore, Mg diffuses more rapidly at high temperatures and is believed to control thedislocation movement (Sheppard et al., 1986b).Apart from some limitations discussed in the Appendix A, the best indicator forthe deformation mechanism is the activation energy derived in the constitutive equations.The general form of a constitutive equation is:dad Ale)^+( 67) S^TSSe E,TdE 8 e e,Tde 8) e,È^(2.3)All three terms can be obtained from appropriate tests (Dieter, 1986). Forcharacterizing hot working conditions the following equation is often used:= A • (sinh 005) n • exP(42def/RT) (2.4)where A, a, n are constants. For the case of au<1, a simplified Dorn equation is givenby Taya and Arsenault (1989):i = A • ( (X ) n • D o - exp( -Qdef/RT)The following equation was used by Mishra and Pandey (1990) for explaining thesuperplastic behavior (at strain rates 10 -5 - 1 /s) of several MMCs:i=_A ( GDb ) ( CT - 00 ) n ( 1) ) Pl kT )^G j . l d) (2.6)(2.5)15where ao is the temperature dependent threshold stress, d is the grain size, D is thevolume diffusion coefficient, p is a parameter (p=2 when volume diffusion is the limitingstage for creep and p=3 is for boundary diffusion), n is usually equal to two.Sometimes the same experimental data can be described by different constitutiveequations, the implied mechanisms depending on the equation used. For example, experi-ments on 6061/SiC/w fitted equation (2.5) (Nieh, 1986) and equation (2.6) (Mishra andPandey, 1990) with different values of n and Q_def. A summary of the reported data isshown in Table 2-7. With an increase in the strain rate, n was found to change from 8 to 2.Table 2-7. Summary of activation energies and work hardening rates for hot deformationof Al alloys and composites.Material Processing TestconditionsEquation Parameters Reference2124/Si3N4/w2124PM+HIP+Ext (R=44,T=773)Tension•c =4•10-5-1 /s,(2.5) n=14 (573 K)n=10 (673 K)n=7 (798 K)Q= 140 ki/moin=10 (573K)n=8.5 (673K)n=3 (798K)Q= 140 /modTsunemichiet al., 19906061/SiC/10pCast^+extrudedCompressioni =0.001-1 /s,T=473-573 KT=573-773 K(2.5) n=11Q= 158 kJ/ff,,iQ= 229 Id/m„iChandraand^Dake,19902124/SiC/w torsiony=100-(2.5) n=8.1 (450K)Q=227 kl/m01(422-477K)n=21(561 K)Q=413 16/moi(547-575K)Nardone ,19876061/Al203/18w,diam. 3PM+HIP(T=873)+Extrusioni—9 -1—0- 4 -1 /s(2.5) Q,, = 150 ki/moi(750-860K)Stanford-anBeale andClyne,19896061/SiC/17w = 4.10-9 -8.10-6 AT = 505, 561,616 K(2.6)a0=-153.4113 , 550n=8Q=140 kr/moiMishra(1990)T16Table 2_7 (continued)2124/SiC/20p6061/SiC/30p6061/SiC/20wdiam. 0.5m,length 51.imPM+extrusion+T4PM^+extrusiondouble^sheartest,^i =4.10-7-8-10-4 /sST 30 min.before testing atT=573-723K.tension^test^atconstant^a,i =10-9-10-5 /s,ST 30 min.before testing atT=505-644K.(2.5)(2.5)Q=400 kjimoln=9.5n=5Q=390 /d/moin=20.5Nieh et al.,19886061/SiC/20p6061TorsionT=473-773 K,£ =0.1-10 /s(2.4) Q=252U/moi, n=2.4Q=188U/mol, n=5,9Pickens etal., 19876061/Al203/15pExtruded,ST,Torsion,T=473-773 Ki =0.1-4 /s(2.4) Q=233^Id/inni,n=2.71992Sarakis andMcQueen,PM64/SiC/10-20p(2.6) Q=313 kjimol , n=2 Mishra '19902219/Al203/15p2219Cast + Ext(R=20)Compression,i =0.001-1 /s,T=663-783Kto e=0.8(2.5) Q=70kjimoln=7Q=70 kjimol , n=5our compi-lation fromresults ofTuler (1990)6061/SiC/30p3.6+-0.4 p.mPM + Ext +ST(723K 4h)constant^stressdouble sheari =3.10-9-0.01/s, T=618-678KT=30 MPaT=12 MPa(2.5)^withthethresholdstress T0=8MPa Q=270 U/moi, n=7Q=4941/moi, n=22Park et al.,1990A1-2.3%Li-4%Mg-0.1%Zr-0.1%FeTorsion^testi =0.03-29 /sT=573-773K(2.4) Q=168 kl/moin=2.15, lnA=24.5,a=0.033Parson andSheppard ,1985the^same+0.8%CuQ=153n=2.28,^lnA=24a=0.025Parson andSheppard,(1985)6061/Al203/0-10p6061/Al203/15p6061/Al203/20pCast+ExtrudedCompression£ =0.05-10 /sT=723-823 K(2.4)Q=170 1c1/moi,Q=181 la,/moiQ=200 Id/moi,Davies etal., 1992PM - Powder Metallurgy route, HIP - Hot Isostatic Pressing, ST - Solution Treatment, R - extrusion ratio,HR - Hot Rolling, w - whiskers, p - particles, f - fibers17Nieh and co-workers (1988), in their very well documented study, did notobserve any threshold stress for 2124/SiC/p and 6061/SiC/w composites (see Table 2-7for details). This was related to the magnitude of the Orowan stress calculated from themicroscopically observed interparticle spacing which was found to be lower than theapplied stresses used in the experiment. It was also found that the 2124/SiC/w samplesdid not exhibit a well defined steady state creep stage in tension, while 6061/SiC/w did.The minimum creep rate for the 2124/SiC/p was found at strains of 10-20% and followedthe equation (2.5) with n=9.5 and n=5 for reinforced and unreinforced materials,respectively. The steady state strain rate in 6061/SiC/w obeyed the same law with n=20.5and n=3 for reinforced and unreinforced 6061 alloys, respectively.In the very detailed work of Park and coworkers (1990) for a 6061/SiC/30pcomposite a threshold shear stress, to, was found and measured to be 8 MPa at 648 K.Comparison of this value with predictions from the Orowan dislocation bowing,dislocation climbing and detachment of the climbed dislocation from the particle insideof the grain gave approximately the same results. The same authors also observed adecreasing (lief with increasing stress, increasing n near the threshold stress andincreasing Q_def with increasing temperature. Nardonne (1987) has also found a highactivation energy and high n with the same temperature behavior. Tsunemishi (1990)reported an activation energy close to that of self-diffusion, which increased abruptlywith temperature.The activation energy, Qdef, is used for calculation of Zener-Hollomonparameter, Z, which is the temperature compensated strain rate, and for description ofdynamic recovery. Unfortunately, to date there is no agreement as to its value.McQueen et al. (1984) found Qd er=164 kJ/mol for the A1-5Mg-0.8Mn alloy and alsoreferred to values of 150 Id/m01 for pure Al and Al with less than 0.8% Si, Mn, Mg andto 153-156 kJ/mol for Al-(2-3)Mg alloys. For the 6061/SiC/10p Chandra et al. (1990)Id/moi in theobtained Qdet=300 kJ/moi in the 573-773 K temperature interval and 1586.5—6 -.-5.5—5-'g04.5_4 -3.5—--.-- 6061 ahoy—...— 6061/SiC/p, size 20 micron.—.--6061/SiC/p, size 3 micron---.— 6061/SiC/p, size 1 micron3 —2.5—218473-573 K interval. Davies et al. (1992) found Q_d ef=170-200 U/mol over the tempera-ture interval 723-823 K and strain rate interval 0.05-10 /s. A summary of literature forunreinforced A1-0.5-1%Mg alloys of various purity by McQueen and Conjrod (1986)shows variations in the measured activation energy from 135 to 170 kJ/ moi•It seems plausible to suggest that values above the Qdif=140-150 Id/moi occur whenprecipitate coarsening or dissolution are responsible for the dislocation or boundarymobility or when alloying elements in solid solution increase Qdif of aluminum. Thus,measured Qdef values would strongly depend on the thermomechanical history of thematerial and the shape, size and distribution of GP zones and second phases.The data in Table 2-7 indicates that there is an interdependence between strain,temperature and strain rate intervals and the observed Qd ef. Usually Qdef, which isproportional to the slope of the logarithm of flow stress vs reciprocal temperature curve,increases with an increase in strain rate or temperature (Figure 2-1), but does not dependon strain. This observation indicates a change in the relaxation mechanism but does notresolve the nature of the change.0.001^0.0015^0.002^0.0025^0.003^0.0035reciprocal temperature, 1/KFigure 2-1. Temperature dependence of the flow stress for 6061 alloy reinforced withdifferent size SiC particulate, after Humphreys (1991).19The deformation test configuration determines the stress state in the material.That slightly influences Qdif and Qdef via change in the vacancy energy (and decrease invacancy concentration) which is obtained in a compressive hydrostatic pressure(Stanford-Beale and Clyne, 1989) as:Qo Vvac.130^ (2.7)where Q0 is the increase in vacancy energy, vac is the vacancy volume and Po is thehydrostatic pressure. At pressures of 500 MPa this increase can be about 5 kj/mol•The influence of boundary effects are introduced in the concept of matrix/particle sliding. For an explanation of the 313 Id/m0i activation energy of creep in6061/SiC/p composite, Nieh et al. (1988) introduced the activation energy of creep inSiC, which was found to be 300 Id/moi. The process of dislocation climb along theinterface has to be controlled by aluminum diffusion along Al203/A1 or along theAl/MgAl204 interface. The closest estimate of its activation energy is 420 k-T/moi - theactivation energy for Al diffusion along Al203 grain boundaries (Kaur, 1989).In summary, when authors did not deliberately set Qdef=Qdif, they obtainedvalues 2-2.5 higher. For the following calculations Qdef=160 kJ/moi was chosen. Strain Localization and Dislocation ClimbTemperature inhomogeneity may occur due to flow localisation near particles anddue to localized flow softening of the relatively soft intercluster matrix regions.Flow softening usually occurs when the parameter v is greater than 5 (Dieter, 1985):(2.8)= d In a/de , yn = dln a/where 4-^ /d e -For MMCs n is larger than in unreinforced alloys (Table 2-7). Work hardening,in the beginning of deformation is higher in MMCs than in conventional aluminumalloys. As a result, MMCs are very susceptible to flow localization and flow softeningand parameters in constitutive equations become averaged over the different regions.20Humphreys (1988) extended the ideas of the flow localisation and diffusionalrelaxation for interaction of dislocations and particles inside grains. He said that there is acritical strain rate below which dislocation climb does not allow dislocations toaccumulate around particles. Initially, he proposed that the climb of Orowan loops iscontrolled by pipe diffusion and the critical strain rate is inversely proportional to thefifth power of the particle diameter. He compared his findings with the theory of Ashby(1972) where the climb is controlled by surface diffusion and the critical strain rate isinversely proportional to the fourth power. The most recent equation proposed byHumphreys and Kalu (1987) involves an inverse dependency on the second and thirdpower of particle size. The critical strain rate is given by:exp(—Q,k) exp(—Qbk)Ott+   Kb^T • dp..2 t^T dPart (2.9)where dpart is a particle size (diffusion distance) and Kv , Kb depend on atomic volume,shear modulus, thickness of the boundary and on pre-exponential terms for volume orboundary diffusion. The first term in equation (2.9) is responsible for volume diffusionand dominates at high temperatures and long diffusion distances. The second term is forboundary diffusion. This equation can be used as a definition of the critical temperature,below which dislocations would accumulate at the particles at a given strain rate.Experimental observations of hard Si particles in pure Al (Humphreys and Kalu,1987) demonstrated a four times increase in the work hardening rate associated with a twoorders of magnitude change in strain rate near its critical value or with a one hundreddegree temperature change near the critical temperature. In these intervals, importantindirect evidence of dislocation accumulation near the particle was the ten times increasein the subgrain misorientation near the particle, with no change in the misorientation inthe bulk. Lattice rotations near particles were also observed optically. In summary, theobserved higher n values in MMCs (as compared to matrix alloys) over a range of strainrates (Table 2-7) are due to flow localisation at critical strain rates near reinforcement.212.3. Effect of Thermomechanical Processing on MicrostructureDynamic and static recovery and recrystallization are softening processesassociated with hot working of aluminum and aluminum based MMCs.2.3.1. Static Recovery in Aluminum AlloysStatic recovery includes dislocation and vacancy annihilation and dislocationrearrangement processes which lead to subgrain formation and an overall decrease indislocation density. Both processes result in a decrease of the yield strength andmicrohardness. In typical aluminum alloys static recovery is very rapid so that theprobability of static recrystallization is substantially lower than in iron or copper alloys(Figure 2-2). In a 5083 Al alloy McQueen et al., (1984) found that static recovery wasresponsible for softening; no recrystallisation occurred during holding at the deformationtemperature (573-773 K) after deformations up to a total strain of 3.2. No staticrecrystallization occurred in commercial purity (CP) P/M AVSiC/20p extruded and heldat 723 K, although subgrain boundaries sharpened and subgrain interiors markedlyreduced their dislocation densities (Shahani and Clyne, 1991). A 30 s delay in quenchingafter rolling caused a 22-35% increase in the subgrain size and microcell formationinside subgrains in 5052 Al alloy, as shown by Sheppard et al. (1986).The dislocation arrangements, starting with cell formation, can lead to stabledislocation structures, which will strongly affect the microstructure formation insubsequent processing. Vogelsang et al. (1986) demonstrated that subgrain structuresformed in a 6061/SiC composite during previous processing remain on heating to 800 K.2.3.2. Dynamic Recovery in Aluminum AlloysDue to the high stacking fault energy of Al and most of its alloys, dynamicrecovery is the major softening mechanism during deformation regardless of theconcurrent occurrence of dynamic recrystallisation (McQueen et al., 1984).2210 10'TIME (h110 11021 0125•C^t 100•C^72•C^SO•C^Tr(10_JCDU.) 10UJ-100^10'^101'^100.8 -0.6COPPER (99.95)LO NA R01-110).-3.7COOK ANORiENAROS (181Figure 2-2. Fractional residual strain hardening curves for isothermal annealing of Cuand Al (Furu et al., 1990). a. cold deformed high purity copper, b. CP aluminum; (arrowsindicate onset of recrystallization). Steady State, Equilibrium Subgrain Size and MisorientationDynamic recovery competes with deformation mechanisms responsible fordislocation generation. Comparison of an A1-1.1Mg-1.Mn-0.5Fe-0.14Si alloy in the wellannealed (at 873 K) condition with the same alloy as deformed showed that the initialinternal dislocation structure affected the work hardening up to strains from 0.1 to 0.33,depending on the deformation temperature (Figure 2-3). This implies that the substruc-ture of the hot-rolled material effectively contributed a residual strain of about 0.15.23as received^ recrystollisedFigure 2-3. Equivalent true stress-true strain curves for A1-1Mn-1Mg-0.5Fe-0.14Si alloyobtained from plain strain compression with constant strain rate 5 Is (Castro-Fernandezand Sellars, 1988).The presence of Mg, which is the major alloying element in the 6061, is believedto increase the dislocation density during deformation between 298 and 523 K, mainly bydynamic strain ageing (McQueen, 1984). Above 523 K for alloys with up to 5% Mg,strain ageing disappears, leading to a well-recovered, recrystallization resistant structure.Although the content of precipitate forming elements in the 6061 alloy isrelatively low, the shape of the stress-strain curve (corresponding to dynamic recovery),can depend on the homogenisation or solution treatment before deformation. For severalAl-Li-Cu-Mg alloys it was shown by Niikura et al., (1985) that an increase in thesolution treatment temperature from 673 to 823 K caused a "peak stress behavior".Depending on the solution treatment, the peak stress corresponded to a true strain, C m , inthe 0.05-0.1 interval and was 20% higher than the steady state stress obtained after24em=0.3. Guttierres and Fuentes (1990) found that for CP Al the steady state flow occursat em=2.0 - 10-3 •Z0.2, where Z=s •exp( 158000/RT), For e =5 Is and T=573-773 K,em=0.4-2.0 (Sellars, 1990) .In summary, during hot deformation after strains of approximately 0.3, a stablesubgrain size forms. It slowly changes with an increase in strain due to the original grainboundaries (GB) becoming closer, and noticeably changes with an increase in strain rateor temperature. Sheppard (1986a) has reported three ways for subgrains to change theirsize: complete unraveling of subboundaries, migration of subboundaries and formation ofnew subboundaries by cross-slip and climb of weakly pinned dislocations. Subgrainmisorientation changes in parallel with subgrain size, rising to its steady state value.Sheppard et al. (1979) reported for Al-5Mg extruded at 573 K, subgrain misorientationangles from 0.2 to 3 degrees.Equation (2.10) describing the steady state subgrain size, d sub, in terms of Zener-Hollomon parameter, Z, is thought to be valid for most aluminum alloys irrespective ofthe mode of deformation (Zaidi and Wert, 1989).1d s bu = a + b In Z (2.10)According to Sheppard et al. (1986), the subgrain size in the 5052 alloy (A1-2Mg-0.3Fe-0.26Mn-0.17Si) decreased from 9 to 6.4 gm and stabilized early in the roll gapduring hot rolling (773 K): stabilization occurred after the first 10 mm of contact, whilethe total contact length was equal to 35 mm The authors say that "it illustrates that theuse of a mean strain and an average temperature rise is unlikely to result in thecalculation of a temperature compensated strain rate ... parameter Z consistent with thefinal substructure. ...the temperature compensated strain rate at the point of stabilizationcan be shown to be Z=1.52.10 11 /s, while the average for the total pass is Z=8.10 10 /s."Sheppard and Tutcher (1980) extruded Al-5Mg alloy at 573 K, R=40:1. Theyshowed that the subgrain size (average 2.5 gm) changed insignificantly with an increase25in strain. In the beginning of deformation subgrains formed preferentially near grainboundaries (center of the billet, far from the die) or within deformation bands (near thedie mouth). In the last case subgrains tended to be elongated (aspect ratio 3) and to havea small (0.1-0.250) misorientation angle across the deformation band.For MMCs, which exhibit inhomogeneity of strain rate vs distance from aparticle, only average values for d sub are given in the literature. Shahani and Clyne(1991) found 2 gm subgrains in CP A1/Al203/10p (12 pm) extruded at 723 K, R=1: Static RecrystallizationExtensive research has been published documenting the recrystallization of coldworked aluminum alloys. Dynamic recovery and/or dynamic recrystallization at hightemperatures are so rapid that there is little chance for static recrystallization to occur.Table 2-8 summarizes the literature data on recrystallization after hot deformation andshows that the unreinforced alloys with a composition close to 6061 half-recrystallize infrom ten minutes to two hours after deformation at a strain rate of 1 /s, for a strain of 1 ata temperature of approximately 673 K.As can be further observed from Table 2-8, large particles are able to acceleraterecrystallization, decreasing recrystallization times to minutes and seconds. In MMCsparticles are large and numerous enough to promote extremely fast recrystallizationfollowing deformation or on cooling. Together with the intensity of static recovery inaluminium alloys, this could explain why no signs of static recrystallization wereobserved by Badini (1990) in hot extruded 6061/SiC/15w after annealing at 793 K for 2hours, by Mabuchi (1991) in hot extruded 6061/Si3N4/20w after 30 min. annealing at798-823 K, and by Shahani (1990) in hot rolled or hot extruded 6061/Al203/10p.On the contrary, Sun and Greenfield (1988) noticed static recrystallization in hotdeformed 2124/SiC/p as evidenced by a sharper and stronger <100> texture component(vs the observed deformation <111> component for unreinforced alloy).26Table 2-8. Static recrystallisation in Al alloys.Composition Deformation Recrystallisation Particles t50%, Reference5Mg-0.16Fe-0.13Mn-0.05Si-0.12CrRolling: e=0.52,i =2.39 /sT=573 KT73 KT=773 KQuenching afterdeformation andthen reheating todeformationtemperature31.un, 2 vol.%Al t 5(FeMn),Si ;<0.5^gmMg7All^andMnA16600 s1200 s7200 sRaghunathan et al.,19861.1Mg-lMn-0.48Fe-0.14Si-0.024CuAnnealed at 873 K,6 days0.33, £ =5 /s,T=753 KRolled / quenchedc=0.33, i =5 /s,T=753 KHolding^afterdeformationT=753 KT=753 K5 vol.%, 1.5 gmparticles5 vol.%, 0.1 i..unprecipitatestock=1 s8 s7200 sCastro-FernandezandSellars,19891.1Mn-0.2Si-0.18Fe-0.12Cu-Rolling, X0.52,T=623 K, i =4 /sReheating^forannealingT=828 K"large",(FeMn)A16 andAl, 6(FeMn)1Si; 10-200 sRojas andPuchi,19891Mg-0.16Cu-0AFe-0.12Si -0 .05Mn-0.013TiPlain straincompression,T=673 K, i =1 Is0.330.67 (nominal)Holding^afterdeformation^atdeformationtemperatureNot described1800 s180 sSellars^etal., 1985CP Al Torsion testing,water quenchingi =0.86 /s, c=3T=598 KT=683 KReheating^forannealing^atdeformationtemperatureNone46800 s4680 sGutierrezet al., 19902Mg-0.26Mn-0.17Si-0.3FeRolling, T=673K,reduction 50%,i =0.62 /sHolding^afterdeformation2iim, (FeMn)A16All (FeMn)1Si;0.1 gm Mg2A13<900 s Zaidi^andSheppard,1983The first approach to quantitative description of static recrystallization usesphenomenological equations. Only limited energy can be stored in the material afterdeformation. Thus, there should exist some finite strain at which no additionaldeformation can accelerate recrystallisation. Raghunathan et al. (1986) described this forthe 5056 alloy as:t50%-1 / (0.0286+1.8.Eaverage 2)^ (2.11)In experiments on CP aluminum, Guttierres et al. (1990) represented the time to 50%recrystallization (t50%), the recrystallized grain size, d, and the grain growth rate, F, interms of the annealing temperature, T a, and the temperature of hot deformation, THD, as:27Rt 50% = 1.5. 10-4- c-13 • Z -Ck75 • exp(  2 000 )RTaz = g . exp (158000 )RTHDd =1.5. 10 -4 • £415 • Z""'exp(3°"T  )r = 0.64 • t"' • es • VA4 • exp( 6R3"^ )T (2.12)(2.13)(2.14)(2.15)A more generalized relationship includes the power law function of initial grainsize. In a plain strain compressed A1-1Mg-0.16Cu-0.4Fe-0.11Si alloy, the recrystallizedgrain size increased with an increase in the initial grain size prior to rolling (Sellars et al.1986). The t50% was described by equation (2.16), where the activation energy for graingrowth is 58 la/moi• Literature data on values of Qrec are presented in Table 2-9.t50% =10. d1035. E-2.7z -1.1 . exp(  230000  )RTa (2.16)Table 2-9. Activation energies of static recrystallization (Wells 1991).Alloy Qrec, U/mol ReferenceA1-1%Mg 230 Sellars et al., 1985AA 1100 220 Gutierres et al., 1990AA 5056 212 Zaidi & Sheppard., 1986AA 5083 183 Zaidi & Sheppard., 1986The second approach to quantifying static recrystallization kinetics uses theJMAK theory of phase transformations and is classically based on the assumptions ofrandom and homogeneous nucleation and homogeneous isotropic growth (Cahn, 1956):X = 1 — exp (-0.693 (X50% ) n )^(2.17)Two limiting cases of three dimensional nucleation are often assumed:- early site saturation,- constant nucleation rate,28when above equation holds, with n equal to three or four for each case, respectively. Thesame author modified classical JMAK theory to account for heterogeneous grainboundary, grain edge or grain corner nucleation; the resulting kinetics follow the sameequation but n varies from 1 to 3.The theory does not account for oriented nucleation in cases when there is somecrystallographic relationship between the original and the transformed phases.The assumption of isotropic growth can be violated for two reasons. Firstly, the grainboundary mobility depends on the misorientation angle, on the GB orientation in space,and on the interaction of the mobile GB with a diffusion sources (Diffusion InducedGrain Boundary Migration). Secondly, an alignment of the second phase precipitates andreinforcement particles in the extrusion, rolling or forging direction retains grain growthin the perpendicular direction. Nucleation of Recrystallized Grains2. Heterogeneity of Deformation and Nucleation Site DistributionIn practice, inhomogeneity of the nucleation site distribution can control the size,shape and texture of recrystallized grains. This is because at strains c>1, nucleation ofrecrystallization in Al during annealing has been shown by Nes and Hutchinson (1989) tobe associated only with:- transition bands (separate parts of old grains which were split during deforma-tion so that individual new parts have rotated towards different orientations),- shear bands,- grain boundary regions,- deformation zones around large non-deformable particles.The sharp orientation gradients (5-10 degrees/gm) are typical for theseheterogeneities. Thus, a minimum amount of recovery and subgrain coalescence isneeded to create a mobile high-angle boundary. In addition to direct TEM or optical29observations, some indirect evidence of the relative activity of the nucleation sites ofdifferent types is given by the recrystallization texture. The cube oriented grains( 112} <111> and sometimes the Goss {011 }<100> texture nucleates in aluminum attransition bands, where subgrain misorientation is higher than in other metals (such as Feor Cu at the same homologous temperatures (Nes, 1990)). Shear bands are the result offlow instability during deformation. This instability is sensitive to external variables(strain rate and temperature) and to the initial grain size. Nes et al. (1989) point out thatshear bands form more frequently in higher strength alloys at lower temperatures (whichdoes not hold for hot deformed, relatively low strength 6061 alloy); grains, nucleatedfrom shear bands often have (001}<110> texture.Two mechanisms for the frequently observed nucleation in the vicinity of priorgrain boundaries include grain boundary (GB) bulging (this mechanism preserves thedeformation texture) and subgrain coalescence. In practice the most explicit evidence ofGB nucleation is the dependence of the recrystallized grain size and the time to 50%recrystallization (t50%) on the initial grain size. Rojas and Puchi (1989) conductedrecrystallization experiments (deformations at 723 K, strain rate 3.5 /s) on A1-1Mg alloywith different initial grain sizes (d 0). They concluded that the t50% increased propor-tionally to d023 and the Avrami exponent n *=0.41: X(t) = 1 — exp{-11.8 . d,;(193 • t°.41 }.Others have reported n * values from 1.14 to 3 (Wells, 1991).When large particles are present, their effect on both the nucleation andthe growth of recrystallized grains is much more substantial than that of GBs.Experiments by Humpreys and Kalu (1987) showed that at high strains several slipsystems produce lattice rotations near particles. This results in: a) a spread of theorientation of the nuclei and b) a weakened texture. However, there is contradictoryevidence reported by Jensen et al. (1989) on cold rolled and annealed Al/SiC/2f,which demonstrated preferential (100 }<013> development.30Furu et al. (1990) showed for unreinforced Al that nucleation at the above namednucleation sites does saturate during static recrystallization. The assumption of surfacesite saturation at the particles implies that the number of nuclei formed near each particleis much larger than one and the particle volume has to be included in the transformedvolume in such a way that X(0)=f. Furu et al. (1990) found this to result in an unrealistictransformation kinetics.In summary, nucleation near large particles can be expected to be the dominatingnucleation mechanism in ceramic reinforced aluminum composites. Nucleation Efficiency at Large ParticlesKalu and Humpreys (1988), based on experimental data for AI-0.8Si, proposed acritical strain rate, ic , for lattice rotations to occur at particles of diameter, dpi (m):E = exp(140"), 0.011 RT.^TcPp., (2.18)where 140000 J is the activation energy for diffusion. Sellars (1990) fit the sameexperimental points with the same equation (2.18) but with different parameters. He alsorearranged (2.18) to give the minimum particle size (in gm), at which rotations willoccur and particle stimulated nucleation (PSN) will be possible (Sellars, 1990):370000d=part^(T Z)A(2.19)The formula is also the definition of the critical temperature or strain rate atwhich PSN starts. This formula may also be understood as that given the same strain rateand temperature, a particle which is larger than the critical size should nucleateproportionally more grains. Unfortunately, there is no direct measurements of thisnucleation efficiency. The formula considers only the steady state regime. However, italso implies that in the beginning of deformation, at a larger particle the critical strainwill be reached earlier during deformation and repetitive nucleation may occur.31Castro-Fernandez et al. (1988) have reported experimental evidence that nucleiform near coarse particles at relatively low strains of e<0.33 through subgraincoalescence. This was observed in TEM by Castro-Fernandez and Sellars on A1-1.1Mg-lMn-0.48Fe-0.14Si and by Zaidi and Sheppard (1983) on A1-2Mg-0.26Mn-0.17Fe-0.17Si. The latter authors totally ruled out nucleation by bulging of the original GBs. Nucleation Rate for Avrami TheoryIn Avrami theory, regardless of the type of active nucleation sites, the nucleationrate can be expressed via the number of potential nucleation sites No, each having anucleation frequency v. As the sites are used up during recrystallization the number ofremaining potential sites decreases following:N=No•exp(-vt) (2.20)If v is very large then the recrystallization reaction is site saturated and theaverage grain size is given by d=(N0) -1/3 ; if v is very small, then the nucleation rate, 1ST,is constant and equal to vNo . In this case the average recrystallized grain size is:d=(F/vN0) 1/4, where growth rate r is assumed constant.Following Nes and Wert (1984), particle reinforced Al composites can beapproximated as: i) all reinforcing particles having the same size, which is larger than thecritical size at all reasonable T and Z, ii) one nuclei per particle forms which grows aftersome critical degree of work hardening is reached, iii) local softening at one particle doesnot affect nucleation on the neighboring particles (nucleation is random in time),iv) nucleation is homogeneous to the extent that the particle distribution is.Thus, PSN being a dominating nucleation mechanism simplifies the complexity of thenucleation situation for description by the JMAK equation.322.3.3.2. Growth Rate2.33.2.1. Driving Force for Static Recrystallisation in MMCsIt is likely that in cold deformed 6061/Al203 recrystallization nuclei form nearlarge particles on heating for annealing, while in hot deformed material the nuclei existbefore the end of deformation. The growth rate of the nuclei depends on the mobility ofthe interface (which is left aside in the present review) and the thermodynamic drivingforce (the decrease in energy upon recrystallization). Sellars (1990) described therecrystallisation driving force for a typical Al/Al203/p composite as:FR = G•b2•p/2 = 5.103 Pa^ (2.21)where G is the shear modulus, 2.6.10 10 Pa, b is the Burger's vector 2.8.10 -10 m, p is thedislocation density 10 13 nr2 (section 2.1.1). In this case, the dislocation density is thatnear the particle after rapid quenching from 773 to 273 K. The "CTE mismatch "dislocations form during cooling and add to the recrystallisation driving force upon fastheating. If static recrystallization occurs immediately following hot deformation, thedislocation density near particles depends on the prior balance of the degree of recoveryand the supply of dislocations from the bulk of the specimen.Nes (1984) estimated the driving force from a mean subgrain size, d sub (typically1-10 g.tm in Al alloys) and a misorientation angle, 8 (typically 1-3 degrees) as:FR = p•4) = (K.8/b•dsul) (G.b2/2) = 1.5.104 Pa^(2.22)where k is a constant of the order unity and (t• is the dislocation energy per unit length. Variations of the Growth Rate Near Large ParticlesFuru et al. (1990) assumed that a deformation zone of width co ( approximatelyequal to the particle size) surrounds each coarse particle so that the deformation zonesfrom neighboring particles do not overlap. The co can be assumed as w<1-3 iirn, whichcorresponds to the distance to which "CTE mismatch dislocations" can be punched out onX(t) = 1— exp[--4 r N(fr dtji33(2.25)33cooling. The dislocation density, p, is assumed to decrease hyperbolically with thedistance, r, from the particle of radius dpart/2, as shown in equation (2.23). The growthrate can then be described by equation (2.24).P = ( ^ Po(r d2 k + (1 — k)^d p„, r<dpart/2+o)^(2.23)Fm[k2+2- (1-k)Fmt/co] -1/2^t<t*^(2.24)r(o=Fm^t>t*where t*.( 1+k)a)/2rm is the time required to consume the deformation zone of width co,k is the constant to be determined experimentally, po is the dislocation density near theparticle and To = rak is the initial growth rate at the particle interface.If one new grain forms in each deformation zone, the volume of particles can beconsidered as a part of the transforming matrix, which gives the following kinetics:where N is the number of nucleation sites per unit volume. Furu et al. (1990) integratedequation (2.25) for co=dpart, as shown in Figure 2-4. The Avrami exponent was observedto be nearly constant, to decrease with an increase in the volume fraction of particles andto vary by less than 15% when k varies from 0.06 to 0.4. A value of k=0.1 was assumedbased on experimental observations of Humpreys (1977) that the subgrain size in thedeformation zone is an order of magnitude smaller than in the surrounding matrix.Integration of growth and nucleation rates over the recrystallization time givesX(t). If the F(t) and N(t) functions are chosen to be simple enough, they can be backcalculated from X(t) and/or S(t) (where S is the interfacial area per unit volume).Vandermeer and Rath (1989) assumed power law functions. Then they fittedexperimental Xext and S ext (extended volume fraction recrystallized and extended34interface area per unit volume) to power laws (which is the JMAK case, becauseXext=in { 14140} )• Then the Laplace transformants of Xext and Sext were used to backcalculate parameters in the IST(t) and F(t) power laws. This experimental work was doneon Fe single crystals.Figure 2-4. Time dependence of the recrystallized volume fraction in the deformationzone model (Furu et al., 1990). a) Volume fraction vs time; b) Corresponding Avramiplots. Variations in the Growth Rate Caused by RecoveryThe effects of recovery were accounted for by Furu et al. (1990) by assuming thesubgrain growth as the dominant recovery mechanism for the non-heat treatablealuminum alloys:35r = ro^(-)1 bT i (2.26)where t1(T) is the temperature dependent relaxation time parameter.The driving pressure acting on the recrystallization front was calculated as:^FR=1"idsub(t)^ (2.27)where y(t) is the instantaneous subGB energy and d sub(t) is the mean subgrain size.The growth rate and the subgrain size evolve as:r(t)=M•FR(t).^ (2.28)^d, 1, (t)=d am 0 + C • t (2.29)Combination of the last three equations produced the recrystallization kinetics:2^1-b^3-1{ 4 Ir^1.1 ^1 -I- --tX(t) = 1 - exp^ —) —1]3^[(I – b)-1- 2 j [(^Ti (2.30)where ; = (N • 1-03 ) -X - is a relaxation time for the recrystallization reaction.In the limiting case t 1/T2>>1 there is no time for recovery to occur, and theequation (2.30) simplifies to the usual Avrami solution for constant r and site saturation(n=3). When the relaxation time relationship is reversed, the solution becomes:Ti[ t)3•(1-b)X^—4= 1^exp {– 7r]3(1– b) • r 23 (2.31)With an increase in the t 1tr2 ratio, n changes from 3 to 3(1-b). This alsocorrelates with slowing of the growth rate to zero. For grain edge nucleation aftersaturation (2D growth) n changes from 2 to 2(1-b).In the modeling of recrystallization, static recovery in aluminum alloys issometimes neglected. For example, for 1-10 s interpass intervals during rolling Sellars(1990) simply added the pass strains to predict the total deformation for the start ofrecrystallization.36RECRYST.fq 12n=3(1-b).2/ri. 0.03Figure 2-5. Recovery and recrystallization reactions in CP Al modeled according toequations (2.29) and (2.31) by Furu et al. (1990).To check the theory, Furu et al. (1990) replotted Figure 2-2, which describesannealing at 598 K of the cold rolled (e=3) CP aluminum. The X(t) was obtained frommetallographic measurements, and FR - from microhardness tests. The new plot inFigure 2-5 explains the n value and recrystallization kinetics.An alternative approach to account for recovery effects by Borelius et al. (1952)and Kuhlmann et al. (1949), as presented by Vandermeer and Rath (1989), is supposedlybased on the climb and annihilation mechanisms:dPdt = (P Pr ). K..exp{ Q P(13 Pr ) }RT^RT(2.32)where P is the instantaneous stored energy, Pr is the stored energy unrecoverable afterlong annealing, Ko, Q and 13 are temperature dependent parameters.As the same authors note, the analytical solution of (2.32) is impossible and asophisticated "exponential integrals" technique is required. Great simplifications could beachieved if (3 was assumed to be zero or the degree of strain hardening (P-P r) was small,but experiments do not allow this simplification (Figure 2-2).3723.3.2.4. Influence of Small Particles and their CoarseningSmall particles exert drag pressure on dislocations, subgrain and grainboundaries. This Zener drag pressure on the grain boundary can be written in the form:PZ = a "Y fir, (2.33)where f is the volume fraction of dispersoids, r is the mean dispersoid radius, 7 is theboundary energy (0.3 N/m for subgrain boundary and 1 N/m for GB in Al) and a is 3/4following the original work of Zener. Parameters f and r are functions of time andtemperature. Grain boundary energy depends on the segregation of solute atoms, but maybe considered constant, because Mg, Si, Fe have a segregation factor of less than 10, andsegregation occurs very fast (1 s at 473 K).Very small precipitates can exert significant drag pressure on movingsubboundaries, comparable in magnitude with the recrystallization driving force given byequations (2.21) and (2.22). In this case, precipitate coarsening during longrecrystallization times might become a controlling factor for recrystallization. This effectwas observed by Castro-Fernandez and Sellars (1989) in the A1-1Mg-lMn alloy2.3.3.3. Applications to the Grain Size and Texture Control in Al-alloys Grain growth is limited by Zener drag pressure and by the stored deformationenergy, which for cold deformation is proportional to strain. According to Ridley (1990),deformation maps of the type shown on the Figure 2-6 are used to predict the grain size.For the materials shown, the grain size - nucleation site relationship agreed with the sitesaturation assumption (discussed in section For the 7075 alloy the constantnucleation rate assumption was more valid (Nes and Wert, 1984). The Rockwell route forproduction of the superplastic 7475 aerospace alloy includes solutionizing, overaging,warm rolling (85%) and rapid heating to 673 K to recrystallize to <10 gm grains.Addition of 15 vol.% of 8 p.m SiC particles increase the nucleation site density andreduced grain size to 6 lam .38Figure 2-6. Maps showing the grain size resulting after cold rolling and annealing ofvarious aluminum alloys as functions of rolling deformation and second phase dispersionlevel (Nes, 1989).Nes and Hutchinson (1989) reported that due to the orientation relationships forvarious nucleation mechanisms, the texture of the recrystallized Al alloys includesseveral components:T=Nparticles [random texture, diffuse rolling texture]+nGoss [in transition bands: {011}<100>]+ nGB [diffuse rolling texture] + ncube [from {112}<111> transition bands: {100}<100>] +nsubGB [in shear bands: {001)<110>, diffuse rolling texture]According to Nes and Hutchinson (1989), in production of the 3004 Al alloybeverage cans, the purpose is to increase the cube texture component. This was achieved39by decreasing the fraction of random and diffuse rolling textures via decreasing thenumber of large particles (nucleation sites) and increasing the number of pinning smallparticles.2.3.4. Metadynamic RecrystallizationCastro-Fernandez and Sellars (1989) reported for an A1-1.1Mg-lMn-0.024Cu-0.48Fe-0.14Si alloy that dynamically recrystallized (DRX) grains never grew beyond1011m, because of the substructure development in them. They called this situation a"limited dynamic recrystallization" and underlined that its occurrence can not be detectedby any change in the mechanical behaviour during continuous deformation. Unlikeprevious authors, McQueen et al. (1984) suggested that what they call "discontinuousdynamic recrystallization" can be revealed from the existence of the peak stress beforesoftening on the hot deformation curve, whereas dynamic recovery should result in asteady state flow curve. Grains dynamically recrystallized in the beginning ofdeformation and then deformed further should possess on quenching a well definedsubstructure as opposed to substructure-free statically recrystallized grains.2.3.5. Dynamic Recrystallization (DRX)Recrystallisation during hot working (dynamic recrystallization) was confidentlydistinguished from that after hot working of aluminum alloys only in the beginning of the1980-s (Zaidi and Wert, 1989) and no aluminum alloy was reported to recrystallizecompletely during deformation. Dynamic recrystallization can be positively identified bythe presence of fine equiaxed grains having a well-defined substructure inside the grains.During deformation, an additional driving force is acting on the subgrains, whichis larger than the "static" driving force associated with the dislocation density:Fm.t•b/s=106 Pa^ (2.34)40where t is the shear flow stress (about 50 MPa at 773 K) and S is the spacing betweendislocations in a subgrain boundary, typically —14 nm As a consequence of this force,subgrains should be able to "collect" more dislocations from the grain interiors andacquire higher misorientations. Combined with a stress concentration near large particles,this explains why grains nucleate easier during deformation than during annealing.In observations by McQueen et al. (1984), Sheppard et al. (1980) for the 5083alloy, Radhakrishna et al. (1991) on 2124/SiC/20p composite and Castro-Fernandez andSellars (1988) for the A1-1.1Mg-lMn-0.5Fe-0.14Si alloy, DRX was observed only in thepresence of particles and only above 673 K. Factors promoting DRX also included largealloying content, high strain rates and large strains. It was believed, for example, that thestacking fault energy in Al is reduced from 200 to 50 J/m2 by 1 at.%. Mg, which allowsthe dislocations to separate into partials, makes recovery process less likely and increasesthe driving force for recrystallization. Therefore, the Al-Mg alloys could be expected torecrystallize dynamically. In fact, DRX was not observed unless Mg concentrationsreached 4.5% (Sheppard et al., 1986).The DRX should not be dependent on strain, once the critical strain has beenachieved, only on Z and T. However, only for the high strains of 9 (723 K, 0.7 /s), whensections of the original grains decreased to the subgrain size, did Usui and Inaba (1986)obtain DRX in pure Al and Al-3Mg.Rollett et al. (1992) analyzed recrystallization in terms of the incubation strain forthe onset of dynamic recrystallization and the strain required for its completion. Formodeling of DRX by the Monte-Carlo method, they assumed that the total energy of thecrystal is the sum of the grain boundary energies and the dislocation energies. The first iscalculated over all pairs of points participating in the model, while the second representsstored energy and has one component dependent on the mutual orientation of the pointand its neighbors and another dependent on the point itself. The new step represents therandom reorientation of each point and may either create a new nucleus or move an41existent boundary and/or decrease the amount of stored energy. The total number ofnuclei and new dislocations added on each step are fixed. Modeling showed that therecrystallized grain size asymptotically decreased with an increase in a strain rate and anincrease in the nucleation rate. Initial grain size mattered only at low strains.Small grains (<10 gm) formed by DRX can produce a superplastic mechanicalbehaviour of the material via the mechanism of grain boundary sliding. Macroscopically,superplasticity correlates with a high strain rate sensitivity of stress, which helps to avoidnecking (Stanford-Beale, 1989). This type of superplasticity was reported by Tsunemichiet al., (1988) for 2124/SiC/w, PM64/SiC/p and 7075 composites. However, nosuperplasticity was observed in 6061/SiC/w, processed in a manner similar to the2124/SiC/w superplastic composite.The last authors observed superplasticity in 6061/Si3N4/w composite (initialwhisker length 15 gm, diam. 1 gm). The composite was sintered (873 K, 200 MPa invacuum) from 44 gm alloy powder, hot pressed in air (873 K, 390 MPa), extruded(773 K, R=44), solution treated (773 K for 16 hours) and aged (463 K for 16 hours). Insubsequent tensile tests at 798 K, the composite exhibited 250% deformation at a strainrate of 0.2 /s. This superplastic strain rate was approximately the same for a 7064-basedcomposite and 1-2 orders of magnitude lower in the unreinforced 7064 alloy. Mabuchi etal. (1991) found superplastic behaviour in tension in 20% whisker or particle reinforcedPM 6061 at temperatures of 798-818 K and strain rate of 10 /s.In summary, there is no apparent reason for the 6061/SiC composite not toexhibit superplastic behavior, except for having a lower alloying content, which isassociated with lower dynamic precipitation and higher recovery rates. Smallerreinforcing particles and tensile test conditions favor superplasticity.422.4. Extrusion ProcessingThe extrusion of aluminum alloys is usually accomplished without billetlubrication. The billet shears within itself near the container wall to create its owninternal conical die surface. According to the Metal Handbook (1982), and to Gunasekera(1989), typical extrusion rates for 6061 alloy are 0.1-0.8 m/ s . Extrusion of the wroughtMMCs by DURALCAN differs from that of the hard aluminum alloys by a 20%increased pressure and increased abrasive wear of the steel dies.The extrusion is followed by solutionizing above 803 K and ageing at 443-463 K.In theory, before ageing material can be given additional cold deformation to create morenucleation sites for Mg2Si precipitates. Nucleation site density can also be increased byrapid cooling after extrusion. This should preserve the hot deformation substructure andproduce additional density of "quenched-in" dislocations.For the description of the microstructure of the extruded product, the followingparameters of the extrusion process are important:- extrusion ratio,- initial temperature,- die temperature,- ram speed,- ram pressure,- die angle,- friction at the die and the container wall.The microstructural modeling starts from the average strain rate being calculatedfrom the ram speed (local conditions may vary significantly):6. v. Db - lnR. tanaD3 - D3b e (2.35)43where v is the ram speed, Db is the diameter of the billet, D e is the diameter of theextruded rod, R is the extrusion ratio (ratio of crossection areas of the billet and theextruded rod) and a is the semi-the angle.From the temperature and strain rate history the microstructure can be forecast.For example, Tuler and Klimovicz (1990) used compression testing to derive strain rate-temperature processing maps for forging of 2124/Al203/p and 2219/Al203/p indicatingunstable regions and regions of maximum forming efficiency.2.4.1. Temperature EvolutionHains et al. (1988) indicate that 95% of the mechanical energy of extrusion isconverted to heat. Approximately 20-30% of this energy is consumed in a shear zonenear the container wall and more than 50% in the boundary layer with the dead metal(10% of the billet thickness). Assuming the flow stress to be approximately 30 MPa,the friction force to be 30 MPa, the die angle a= 45 0 and the extrusion ratio 1nR=4,the extrusion pressure can be estimated as 00=270 MPa (Dieter, 1982). Assuming thatall work is adiabatically converted into heat, the maximum temperature elevation inextruded Al bar can be estimated as 100 K. Stanford-Beale and Clyne (1989) measuredtemperature evolution during extrusion of MMCs with a boron nitride lubricatedthermocouple inserted into a hole in a billet. The initial temperature was about 20 Kabove the solidus, the die temperature was 200 K lower and all billets were solid duringextrusion with R=10, i =0.1-1 /s. This indicated that the heat loss to the die was higherthan the heat generated from deformation.2.4.2. Strain DistributionDuring extrusion surface layers undergo higher deformation than the billet center.In an Al-7Mg alloy Sheppard (1986a) has shown that extrusion resulted in a surfacerecrystallized layer whose depth decreased linearly with increasing ln(Z). The grain sizefollowed the same trend. The interior of the billet had a dynamically recovered structure .44The only experimental observation of strain evolution in the MMCs during theactual extrusion process was reported by Stanford-Beale and Clyne (1989). A squarenetwork of gold wires was inserted between two halves of a longitudinally cut billetbefore extrusion. Coordinates of the wires were measured after the process by X-rayradiography. This allowed the calculation of maximum strain rates in the billet (0.15-2 /sfor ram speeds 0.2-1.6 mm/s). Although the applied strain rates were lower than thosenormally used because of the relatively coarse wire (60 gm), they were still 5-10 timeshigher than the average strain rates predicted by equation (2.35). It was found that alower die angle and higher temperatures decrease both the maximum value of strain rateand the strain rate variations across the billet. High ram speeds and high peak strain rateswere found to cause lower strain rates in the center of the billet. This wide variation oflocal strain rates precluded Stanford-Beale from establishing any correlation between theapplied extrusion pressure and the material properties.2.4.3. Microstructure! EffectsIt is generally accepted that compressive hot working (rolling, forging, extrusion,pressing) eliminates interparticle voids and micropores, breaks particle clusters andhomogenizes the distribution of solute elements across the matrix (Dutta et al., 1990). MacrodamageAccording to Haim et al. (1988), hot unlubricated extrusion of SiC and Al203reinforced Al alloys produces three common kinds of defects. Surface tearing due to thefriction between the metal and the die occurs primarily at the front end of extrusions andcan spread through the whole length at low extrusion speed. This defect is typical forMMCs but not for unreinforced alloys. High extrusion speed correlated with theappearance of the second kind of defects, edge and surface cracks, both thought to becaused by incipient melting. The delay in quenching after extrusion could cause surfacegrain growth, a third type of macrodamage that is connected with the previous one.45Available pressure and need for defect free product lead to restrictions on theacceptable extrusion ratio, ram speed and billet temperature parameters, presented byParson and Sheppard (1985) in the form of extrusion limit diagrams. Particle Alignment and MacrosegregationRelatively rapid solidification during DC casting of the 6061/Al203 compositesresults in relatively uniform reinforcement distribution. Still, it can be further improvedby subsequent extrusion processing. In order to achieve a decrease in the particle size andto disperse particle clusters, the conclusions of Stanford-Beale for preserving Al203fibers in the 6061 matrix from fracture during extrusion, should be reversed. Namely,high matrix stresses must be achieved by decreasing the extrusion temperature andincreasing peak strains with the help of high-angle dies and high ram speeds.McNelley and Kalu (1991) showed that hot extrusion of a 6061/Al203/p brokeparticle clusters and, thus, decreased the effective particle size. According to Sun andGreenfield (1988), hot extrusion with 98% reduction in area decreased the mean size ofSiC particles from 8 to 2 gm and introduced some particle alignment. This was mostnoticeable in the outer regions of the extruded bar. Lagace and Lloyd (1990) found verylittle particle alignment, in terms of oriented aspect ratio, in extruded 6061/SiC/p.Particle migration into the dead metal zone was reported by Ehrstrom and Kool(1988) for SiCp reinforced Al alloys hot extruded at 723-753 K. It was explained bygradients in flow stress, which were caused by the non-uniform strain rate. Incompressive load conditions particles tended to move to the area of lower stresses. Micro structural DamageMicrostructural damage during hot deformation usually takes the form of eitherdislocation and vacancy generation, formation of microvoids in the matrix, decohesion ofthe matrix-particle interface or particle fracture.46Lloyd (1991a) demonstrated that regions of tensile strain localization (associatedwith the fracture region during tensile tests) correlated with the percent of fracturedparticles. He also showed that "particles most susceptible to fracture are ... in the largersize range of the <particle> population". Park (1990) reported that extrusion of a6061/SiC/30p composite resulted in a decrease in the particle size from 5.1 to 3.6 gm.In other research Lloyd (1991b) investigated the strain to fracture of prestrainedand solution treated 6061/Al203 samples. He found that prestrains almost up to fracturecause microstructural damage that can not be recovered during solution treatment, and,therefore, the strain to fracture after solution treatment is substantially decreased.Although stress conditions in tensile tests differ from those in extrusion processing, theconclusion that "solution treatment recovers the tensile ductility, but does not fullyrecover the yield stress", might be applicable to recovery of the dislocation and vacancytypes of damage during solutionizing after extrusion.Levandovski et al., (1991) showed that subjecting the cast and extrudedunreinforced 6061 alloy to hydrostatic pressures up to 300 MPa did not affect thesubsequent tensile properties at atmospheric pressure. Investigation of a cast, extruded,solution treated (783 K for 4 hours) 6061/Al203/15p composite demonstrated thatpreliminary pressurization at 300 MPa produced an increase of 50-60 MPa in the flowstress measured in a tensile experiment at atmospheric pressure. It was accompanied byan increase in the elongation of the composite from 15 to 120%. This is suggestive of therecovery of microvoids, but was not proposed by the authors. Instead they explained theeffect by the "pressure induced generation of dislocations". It can also be suggested thatvoid nucleation in the matrix can occur even in the relatively soft stress conditions of theextrusion process by the mechanism associated with shear banding or with stressconcentration at the head of dislocation pile ups at particles.Void nucleation between closely spaced particles in clusters is also important(Lloyd, 1991a). On one hand, fewer dislocations can gather in the pile up due to the short47slipping distance (<1 gm). On the other hand, relaxation is inhibited due to suppressionof secondary slipping systems in the thin metal layer due to rigid particles on both sides.Voids may grow during annealing. Imposed hydrostatic pressure (105 MPa, for 2 hoursat 793K) can eliminate shrinkage porosity (Lloyd et al., 1988), suppress microvoidgeneration and abruptly increase ductility (Lloyd, 1991b).Nakagava and Gungor (1990) showed that hot extrusion (R=1.9, T=700 K) of a6061/Al203/p composite (volume fraction of the reinforcement unknown) resulted in anincrease in the tensile properties (Table 2-10). Hot Isostatic Pressing (HIP) for 2 hours at700 K, 103 MPa after extrusion increased the tensile strength properties, although not assignificantly as for an as-cast material. Microstructural defects (porosity) were not,therefore, completely eliminated during extrusion, probably because of the very lowextrusion ratio. Alternatively, these same defects could be introduced by extrusion due tolarge shear deformation and tensile stresses in the subsurface regions. Larger hydrostaticstress during HIP eliminated voids and pores. Limited particle fracture and extensiveparticle/matrix decohesion during fracturing indicated that extrusion does not improvethe interface bond strength.Table 2-10. Tensile Properties of 6061/Al203/p, after Nakagava and Gungor.Condition ay, MPa ass, MPa Elongation, % Modulus, GPaAs cast 75 110-116 2.5-4.5 46-62As cast + T6 227-237 228-238 0.2-0.4 66-72Extrudedlongitudinal 81 139-13 9.8-11.8 96-126transverse 84 118-148 7.7-9.7 63-101Extruded + T6longitudinal 305-311 325-327 1.4-1.6 76-118transverse 324-326 329-331 0.3-0.9 123-137As cast, HIP, T6 344-354 303-365 0.3-0.8 81-108Extruded, HIP, T6longitudinal 328-340 361-372 0.6-2.3 84-98transverse 347-369 370 0.9-1.9 92-1583. Experimental3.1. Mechanical testing3.1.1. The Gleeble 1500 Thermomechanical SimulatorHot compression tests were performed to characterize the microstructural andmechanical behavior of the 6061 alloy and the 6061/Al203/p MMCs at different strains,temperatures and strain rates. The composition of the 6061 alloy used as a matrixmaterial is shown in Table 3-1. The "Gleeble 1500" servohydraulic testing machine isschematically shown in Figure 3-1. Cylindrical specimens 10 mm in diameter by 15 mmheight were machined from cast materials at the ALCAN Labs in Kingston, Ontario.After machining, all samples were homogenized for 2 hours at 838 K and water quenched.Graphite foil (0 5 mm thick) was used at the sample/ram interface as a lubricant todecrease friction and associated bulging of the sample. Force, specimen longitudinal andtransverse displacements at the half-height (mid-plane), mid-plane surface temperatureand ram displacement were recorded using the computer data acquisition system.3.1.2. Working Range of Strains, Strain Rates and TemperatureThe test matrix for the 6061 alloy and for the MMCs is presented in Table 3-2.These tests were intended to establish the microstructure evolution maps for an averagediametral true strain of 1, as measured in situ by the crosswise LVDT gage. Some of thesamples were held after deformation at the deformation temperature for times of 1, 3, 10or 30 minutes to characterize microstructural changes that occur.Additional tests were performed on the 6061/Al203/15p at a fixed temperature of798 K and a strain rate 5 /s to strains of 0.3, 0.4, 0.5 and 1, followed by helium or air48ThermocouplesGraphite foilto decrease frictiontr•Movingstainless steelanvilStationarystainless steelanvil(Load cell) ( AuxilaryLoad cell )Crosswise strainmeasurement (LVDT)Length strainmeasurements (LVDT)49cooling, with a zero or 600 s delay time after deformation. These tests were intended todetermine the critical strain for the onset of dynamic or static (in tests with measurabledelay time) recrystallisation.One other set of tests was performed on both the 6061 alloy and the6061/Al203/15p to investigate the influence of second phase precipitates on therecrystallization. This set included either resolutionizing in the Gleeble (1 hour at 803 K)before deformation, or heating to 798 K for annealing after deformation. Thetemperature histories of the samples are shown in Figure 3-2.Table 3-1. Compositions of the 6061 alloy used by DURALCAN.Mg Mn Fe Si Cu Cr Zn Ti Reference0.8-1.20.15max0.7max0.4-0.80.15-0.40.04-0.350.25max0.15maxAlcan Specifications,1992Figure 3 - 1. Schematic diagram of the Thermomechanical Simulator.50Table 3-2. The test matrix for the 6061 alloy and the composites.Material Temperature, K Strain rate, Is0.01 0.02 0.05 0.1 0.2 0.5 1 2 5 106061 573 X X X X X X623 X X X X X X673 X X X X723 X X X X X X X X773 X X X X X X798 X X X X823 X X X X X X X0.01 0.02 0.05 0.1 0.2 0.5 1 2 5 106061/A1,01/10p 573 X X X X X X X623 X X X X673 X X X X723 X X X X X X X X773 X X X X X X798 X X X X X823 X X X X X X X X0.01 0.02 0.05 0.1 0.2 0.5 1 2 5 106061/A1,0,1/15p 573 X X X X X X X623 X X X X673 X X X X723 X X X X X X X X773 X X X X X X798 X X X X X823 X X X X X X X X0.01 0.02 0.05 0.1 0.2 0.5 1 2 5 106061/A1,0.1/20p 573 X X X X X X X623 X X X X673 X X X X X723 X X X X X X X X773 X X X X X X798 X X X X X X X X823 X X848 X X3.1.2.1. Temperature Histories of the Tested Specimens All samples were resistance heated to the testing temperature with an averageheating rate of 5 K/s. The contact at the lubricative graphite foil and the specimen oftenwas a source of arcing, which sometimes resulted in melting of the specimen. Followingthe thermomechanical treatment, three cooling regimes were used: air cooling, heliumquenching and water quenching.To air cool the specimen after deformation, the heating current was shut off andthe specimen was left to cool by conductive heat flow into the rams and heat loss to the51adjacent air. The cooling rate achieved typically decreased from 5 K/s at 773 K to 2 K/sat 573 K. In He-quenching the gas impinged on the specimen surface, starting about 0.1 safter the end of deformation and producing a surface cooling rate of approximately50 K/s at 773K. Measurements with an additional thermocouple inserted into a holedrilled to the center of the He quenched specimen showed that the temperature at thecenter was about 40 K higher than on the surface which was equivalent to approximatelya 1 s delay in cooling. In water-quenching, the specimens were pushed manually into acontainer of water. The time delay was measured to be approximately 0.6 s for thesurface of the specimens and surface cooling rates approached 1000 K/s at 773 K.3.1.3. Temperature, Stress and Strain ControlStroke rate control (constant travel rate of the deforming ram) was chosen insteadof strain rate control as giving more reproducible results, especially at high strain rateswhen the machine was not able to provide rapid enough strain rate changes to assure asmooth a-c response. Both the longitudinal strain and the mid-plane diameter wererecorded during testing; the diametral (crosswise) strain was used for the calculation ofthe true stress and true strain for correlation with microstructural observations.The constant stroke rate resulted in a strain rate variation during tests, particularlynoticeable at high strain rates 1-10 /s, but not exceeding 40% of the nominal value, asshown in Figure 3-3. Examination of the stress-strain data by Davies and Hawbolt (1991)showed that a temperature increase from 573 to 623 K caused the flow stress to decreaseby 35%, while an order of magnitude change in the nominal strain rate (from 1 to 10 /s)caused flow stress to increase by 10%. Hence, even at 40% variations of the strain rateduring the constant stroke test, the associated stress variations are within 2% of itsaverage value.The temperature was controlled by a chromel-alumel thermocouple spot weldedto the mid-plane of the cylindrical samples, which provided an instantaneous temperature52Presolutionizing with Air CoolingPost-Deformation Annealing, Air CoolingFigure 3-2. Temperature histories of the compression specimen in several sets of tests.feedback control. The machine provided compensation for adiabatic heating at strainrates up to 1 /s, but could not respond fast enough during short test times (less than 0.1 s)53at strain rates of 10/s. At strain rates above 10 /s, the deformation heating caused thesurface temperature to increase by up to 40 K at the testing temperature 623 K, and by upto 8 K at 773 K. This required correction of the stress-strain data for deformationheating.3.2. Sample PreparationFollowing a very detailed description of all steps in Al/SiC/p sample preparationreported by Lagace and Lloyd (1991), the 6061 and the MMC samples were sectioned,mounted in cold setting resin, ground on SiC paper (grits 320, 600) and polished withdiamond pastes. The polished samples were chemically etched with H2SO4+HF+H20 orelectropolished in a HC104/Ethanol based solution. Some specimens were Au-Pd coatedand observed on the SEM. Quantitative measurements of the microstructure were doneon the Leitz Image Analyzer, which includes a Leitz microscope and a DEC-11 computer.The optimized experimental procedures are presented in detail in the following section.Figure 3-3. Strain rate behavior of three compression tests of 6061/Al203/20p at T=798 Kat a nominal strain rate of 1/s.4. Results and Discussion4.1. Preliminary MetallographyThe metallographic procedures for the unreinforced 6061 alloy are wellestablished (Vander Voort, 1984) and worked well in the present experiments withoutany modifications. However, considerable time was spent in establishing appropriatemetallographic procedures for quantifying the microstructural changes associated withthe thermomechanical processing of the MMCs. For this reason, the details are includedin this section.4.1.1. Mechanical Sectioning, Grinding and PolishingAt the sectioning step, the increased wear resistance of the composites comparedto the unreinforced 6061 alloy displayed itself in a 10-30 times shorter blade life. Duringgrinding, the harder SiC particles abraded the matrix and also fractured the softeralumina particles leaving some fractured segments embedded in the matrix, producing avery "gritty" surface in the initial stages of polishing (Figure 4-1 a). Further polishingwith the alumina powder caused particles to be pulled out of the matrix rather than to bepolished. This lead to the formation of "groves" and dimples around particles.Fine polishing with hard diamond paste was found to give the best result. Six andone micron water based diamond suspensions supplied by Buehler were used. A Struerswater-oil lubricant (A2 red) decreased the polishing time by a factor of two and helped toavoid the particle pull-out that occurred after long polishing times. Extensive polishing(more than one hour) caused rounding of the edges of the sample and dimple formation,especially in the softer 6061/Al203/10p composites. Six and four minutes of polishing5455with 6 and 1 j.tm powders respectively was required for the 6061 alloy. Fifteen and tenminutes polishing times were required for composites to remove the broken Al203 pieces(Figure 4-1 b).b)c) d)Figure 4-1. Grinding and polishing of homogenized 6061/Al203/20p composite.a) x200. After grinding on 600 paper for 2 min.; b) x200. After 12 min. polishing with5 pm diamond paste; c) x200. After 5 min. fine polishing with 1 pm diamond paste;d) x1000. The same sample as c.56The appearance of the polished composites is shown in Figure 4-1 c. The matrixis almost clear from fractured segments of Al203 particles; however, they tend to beretained within the particle clusters. It can also be seen at higher magnifications(Figure 4-1 d) that the near-particle regions are darker than the rest of the matrix, whichis suggestive of some excessive deformation around particles. This localized damagereduces the Al203/A1 contrast, making it more difficult to quantitatively measure particlesize and aspect ratio.4.1.2. Chemical EtchingFollowing recommendations in the Metal Handbook (1985) and Vander Voort(1984), the following chemical etchant compositions were tried:1. Poulton reagent (30 ml HNO3 + 5 ml H2O + 60 ml HC1 + 5 ml HF);2. Reagent for hot worked and heat treated 6061 alloy (10 ml H2SO4 + 5 ml HF +85 ml H2O);3. Graff-Sergent reagent (15.5 ml HNO3 + 84 ml H2O + 3 g Cr03 + 0.5 ml HF).On cast and homogenized 6061 alloys (T4: 848 K, 2h and natural aging at roomtemperature) it was found that all of these reagents etch the second phases (which oftenprecipitate at grain boundaries) but not the grain boundaries of the 6061 matrix(Figure 4-2). The grain boundaries decorated by Fe-Si-Al precipitates appear to lookdiscontinuous and can not be used for quantitative observations.Chemical etching of composites did not give satisfactory results. The regionsaround the particles are preferentially etched, which can be explained by alloyingelement segregation or by enhanced localized strain in the matrix near hard particlesduring grinding and polishing. The preferential deep etching of the matrix near non-etched particles made it difficult to focus on grain boundaries during metallographicobservations.Figure 4-2. x1000. Cast and homogenized 6061 alloy after chemical etching in H2SO4-HF-H20 for 30 s at 298 K.4.1.3. Electrochemical Etching and PolishingThe lack of success in using chemical reagents to reveal the grain boundaries inthe MMCs required that electrochemical reagents be tested. Two reagents were used:1. Barker's reagent (5 ml HBF4 + 200 ml H20; recommended t=60 s,j=0.2 km2);2. Reagent N2 (55 ml 60% water solution of HC104 + 700 ml ethanol + 135 mlH20 + 10 ml 10% water solution of Al(C104)3 + 100 ml butoxyethanol, added justbefore polishing).In most cases, a stainless steel cathode in the form of the 200 ml beaker was used.However, some experiments were done with Baker's reagent in a plastic beaker of thesame size and shape, but with a vertical or horizontal aluminium cathode.Electromagnetic stirring was applied; the stirring speed depended on the viscosity of thesolution. In all experiments the same amount of reagents was used (100 ml) to maintain58the reproducibility of the electrical resistance of the solution. A 500 ml paper beaker forliquid nitrogen surrounded the stainless steel beaker to keep the reagents cool.To establish the electrochemical etching response of the 6061 alloy and theMMCs, samples were etched in solutions of each composition at voltages in 1-30 Vinterval. Measured current densities in the beginning of etching, jinitio, were used to cor-relate the etching response with the position on the voltage-current polarization curves. Barker's ReagentThis reagent was widely recommended for Al-alloys in the literature (see MetalHandbook, 1985) and was tested in the present work. As explained by Vander Voort(1984), during electropolishing, a passivating thin film is forming on each grain. Thethickness and orientation of this film depend on the orientation of the underlying grainand determine the film's transparency for visible light and rotation angle of the lightpolarization plane (when used in polarized light observations).Figure 4-3 a was obtained by etching at low voltages (5V), at current densities of0.1 A/cm2, which is below the 0.2 A/cm2 value recommended by Metal Handbook (1985).This regime did not allow the development of any passivating film and, therefore, did notproduce any contrast in polarized light. Application of the same procedure to thecomposite revealed only few grain boundaries. Preferential etching of the matrix aroundthe reinforcement caused additional obstacles for quantitative metallography.Electropolishing of the 6061 in the Barker's reagent on the horizontal part of thepolarization curve (obtained at 10-35 V) revealed in the normal light only second phaseprecipitates arranged along grain boundaries, but not the boundaries themselves (Figure4-3 b). Additional contrast between the grains in polarized light made the grainboundaries appear more continuous. Electropolishing of the homogenized6061/Al203/20p in the Barker's reagent revealed most of the grain boundaries(Figure 4-3 c), but the contrast was not sufficient to permit quantitative metallography.ti• i.".••• \b)••59Figure 4-3. x200. Electropolishing of the 6061 alloy and the 6061/Al203/15p in Baker'sreagent at T=293 K (vertical Al cathode, intensive stirring). a) As-cast 6061electropolished for 20 s, at 1 V, iAnitial'a 1 A/cm2; b) As-cast 6061 electropolishedfor 4 times 5 s, at 30 V, jin itial=0.9 A/cm2; c) Homogenized 6061/Al203/15pelectropolished for 50 s, at 30 V. Polarized light.a) b)I„604.1.3.2. Optimum Temperature-Voltage-Current Conditions The reagent N2 is based on recommendations of the Metal Handbook (1985).Recommended etching at low voltages in the beginning of the polarization curverevealed grain boundaries as shown in Figure 4-4 a, although it can be seen at highermagnifications that they are not continuous. The grain interiors are etched as well.Application of the same procedure to the composites revealed few grain boundaries andproduced preferential etching of the matrix near reinforcing particles, making it difficultto simultaneously focus on the matrix and on the particulate, as shown in Figure 4-4 b.Longer etching times in the interval V=4-12 volts caused heavy etching of grain interiors.Figure 4-4. x200. Electropolishing in the reagent N 2 at 5 V, 253 K. a) As cast 6061 alloypolished for 12 s, b) As cast 6061/Al203/20p polished for 5 s.61It was suggested that the etching of the matrix could be decreased by formingpassive film at higher electropolishing voltages and by increasing the A1+ 3 activity in thesolution. For this later purpose Al(C104)3 was added before polishing. The bestmicrostructural detail of the 6061 alloy was obtained by electropolishing at high voltages20-28 V (increasing with decreasing temperature) in the range 223-263 K. ConditionsT=243-248 K and V=23 V was found to produce the best results. An example of the6061 alloy in the polarized light is given in Figure 4-5. All other micrographs in thiswork are made in the normal light.Figure 4-5. x200. Homogenized 6061 alloy after electropolishing in Reagent N2, with astainless steel beaker cathode, t=6 times 5 s with 4 min. intervals, at 24 V, T=249 K.Polarized light.624.1.3.3. Optimum Etching Time and Passivation EfficiencyTo summarize the electrochemical behaviour, a typical example of the current vstime curve is shown in Figure 4-6. At T=253 K, V=22 V, the minimum on the curveoccurs at 10 s for the 6061, at 7 s for the 6061/Al203/10p, at 5 s for 6061/Al203/15p andat 4 s for 6061/Al203/20p. During polishing of the 6061 alloy, the sample first loses itsbrightness, corresponding to light etching of grains, usually stronger in the center of thespecimen for lower stirring speeds and voltages. At this stage continuous grainboundaries are visible in normal light. On exceeding the minimum on the curve, thespecimen becomes bright again and, after 30 s, bright, differently colored grains can bevisually observed in normal light (Figure 4-7). During electropolishing of the MMCs, thesample first loses its brightness due to the etching of grains. Only few grain boundariesare visible at this stage. On exceeding the minimum on the current-time curve the wholesample becomes heavily etched (after 15 s) with no distinguishable GBs.Two values of current, Iinit and 'm in , shown in Figure 4-6 were used to define thepassivating efficiency parameter, K = 'Wit / 'min, for the 6061 and for the MMCs. Largevalues of K are consistent with good contrast between grains and well defined grainboundaries, while low K values correspond to etching of the grain interiors withoutrevealing grain boundaries. It was found that K changes with temperature and atT=248 K varies from 4 for the easy-to-etch 6061 alloy to 1.4 for the hard-to-etch6061/Al203/20p. It is thought that alumina reinforcement polarizes the matrix, whichprevents the passive layer formation. The maximum values of K are believed to bedesirable when optimizing the composition of the etching solution, the electropolishingvoltage and temperature.The following rule of thumb was derived: electrochemically etch for a short time(slightly less than for attaining minimum current Im in), pause for 1 -3 minutes keeping thesample in the solution and repeat the etching. In this work the etching cycle was repeated5 times for each specimen.63250init200Current, 150milliamper100I stat50min00^20^40^60^80Time, sFigure 4-6. Time dependence of current during electropolishing of the 6061 alloy atT=263 K, U=14 V, sample area 0.3 cm2 .Figure 4-7. x200. Homogenized 6061 alloy after electropolishing for 7 time segments of10 s with 1 min. intervals, at 22 V, T=256 K.644.1.4. Specimen Preparation for SEMBecause alumina is non-conductive, it tends to charge electrically in the electronbeam. This decreases the contrast between the reinforcement and the matrix and alsoproduces artifacts such as a dark band around particles (Figure 4-8 a). To avoid this, aAu-Pd coating approximately 10 nm thick was sputtered in vacuum onto the polishedsurface. For the 6061 alloy no coating was used, but the non-conductive cold setting resinwas painted with a conductive carbon paint. The SEM was successful in observations ofthe individual grain and subgrain boundaries (Figure 4-8 b) in tilted specimens but wasnot as effective as optical metallography for observation of large numbers of grains orsubgrains to obtain statistically significant grain size and shape measurements.aFigure 4-8. SEM observations of Al203 reinforcement and subgrain boundaries in theMMCs. a) Charging of alumina particles under the electron beam in the uncoatedhomogenized polished 6061/Al203/20p. The flat surface of the largest particle coincideswith the polished surface; b) Subgrain boundaries in the deformed and electropolished6061/Al203/20p.654.1.5. Quantitative Metallographic ObservationsTo quantify the suitability of the Leitz Image Analyser to characterize themicrostructural detail, to establish the reproducibility of measurements and to examinepossible sources of errors, the following parameters were measured on the 15 vol.%particulate MMCs and compared with those provided by the more sophisticatedequipment employed at the ALCAN Research Labs:1. The area fraction of the particle reinforcement,2. The aspect ratio of the particle,3. The particle area, gm2 ,4. The maximum and minimum particle dimensions, gm.The results are shown in Figure 4-9 and compared with ALCAN's data inTable 4-1. It can be seen from the Table that our results correspond within 10% to thosemeasured by ALCAN Research Labs. The lower deviation of our results is thought to bedue to the high magnification of x500 used for measurements and due to wideclassification intervals (Figure 4-9). In our measurements, the typical variation indiscrimination parameters (in the "Detection" mode), all of which visually seem to givethe best contrast between particles, grains and grain boundaries, may cause up to 15%variation in measurements of the particle volume fraction.In addition, the angle between maximum particle dimension, distances betweenparticles at a certain angles to the flow stress direction and distance to the closestneighbor were measured using procedures and software described in Appendix B.The same software was used for characterizing the particulate reinforcement, thereinforcement clusters and the matrix grains at magnifications of x500, x50 and x50respectively. When incomplete grain boundaries were observed in deformed and/orpartially recrystallized samples, measurements of grain parameters via manualcompleting of missing grain contours was used, although this method was open to errorsand the subjectivity of the operator.66Figure 4-9. Particle area, size and aspect ratio distribution for the 6061/Al203/15pmeasured by quantitative image analyzer.Table 4-1. Particle volume fraction, particle area, maximum dimension and aspect ratioin the 6061/Al203/15p.Reference Parameter Particlevol.%Particlearea,Particle max.dimension,Particleaspect ratiowm2 PmAlcan^data, Mean 17.48 110 16.65 2.011992 Stand. deviation 1.05 100 8.38 0.75Counts 25 3438 3438 3438Our Mean 18.73 109 16.2 1.96measurements Stand. deviation 2.21 70 7.36 0.69Counts 19 514 514 5144.2. Microstucture of the As-cast and As-homogenized MaterialsBoth the 6061 alloy and composites were received as 0.2 m diameter direct castbillets. The microstructural investigations started with the 6061 alloy, which has beenextensively researched and characterized. Quantitative measurements of grain size andsecond phase precipitate size and distribution were made using the Image Analyzer. The67same measurements were made for the MMCs, but additional structural effects such asinhomogeneity of reinforcement particle distribution and matrix-reinforcement chemicalinteraction were also examined.4.2.1. The 6061 Al Alloy4.2.1.1. Grain size and shapeMicrostructures of the as-cast and as-homogenized (for 2 hours at 798 K) 6061alloy are shown in Figures 4-10. The as-cast alloy has large equiaxed grains thought to beoriginal equiaxed dendrites. After homogenization, the grain size remains approximatelythe same with an average grain diameter of 120 pm, while the grain aspect ratiodecreases slightly from 1.6 to 1.34. The driving force for that process is thought to be adecrease in GB area.a)^ b)Figure 4-10. x100. As-cast (a) and as-homogenized (b) 6061 Al alloy. 2 M D.68I $nThe results of WDX measurements of the composition of the 6061 alloy arecompared with the manufacturer's specifications in Table 4-2. Only matrix regions freeof large precipitates were analyzed; only Mg and Si were included in the WDX analysisand the Al content was calculated as a balance to 100%. Also, Mg contents may not bedetermined properly in small amounts, due to its Ka line being adjacent to the strongerAlKa line. The Fe content in the matrix was not measured in this work due to very highcurrent densities required for observations of the FeLa at the 20 kV excitation voltageused in the measurements.For this composition range of the 6061 alloy Mondolfo (1976) lists the possiblesecond phases as Mg2Si, Fe2SiA18(a) and FeSiA15((3). Ideally the Mg:Si wt.% ratioshould be 1.73 as this produces maximum strengthening on ageing. However, excess ofeither element decreases hot shortness and, thus, is tolerable.The solubility of Fe in Al does not exceed 0.04%. Therefore, almost all Fe in thealloy (0.7 wt.% max) should form FeSiAl compounds. The a-FeSiAl precipitates fromliquid at 902 K and is present in as-cast material in the form of elongated 0.5 pm thickparticles located at the original dendrite boundaries (Figure 4-2, Figure 4-11 a).The homogenisation at 838 K transforms a-FeSiAl into 13-FeSiAl of similar size andshape. However, the total amount of phase decreases as some Si goes into solid solution.The large P-FeSiAl precipitates were not included in the analyzed matrix regions. Thus,total Si content in the 6061 and the MMCs is somewhat larger than given in Table 4-2.The 13-FeSiAl phase is stable up to 884 K and does not coarsen during homogenization(Figure 4-11 b). The Energy Dispersion Analysis (EDX) measurements shown in Table4-3 demonstrate that the composition of the precipitates is more complex than simpleFeSiAl5. The exaggerated aluminum content in the precipitates is thought to be a resultof the diameter and depth of the exited zone approaching 2 pm, which is 5 times largerthan the precipitate size.69Table 4-2. WDX composition measurements in FeSiA1 5 precipitate free matrix regions ofthe 6061 alloy compared with manufacturer's specifications for the 6061 alloy.Mg Si Fe Cu Cr Zn Mn TiAlc an Specifica-tions, 19920.8-1.2 0.4-0.8 0.7max0.15-0.40.04-0.350.25max0.15max0.15maxAs-cast 0.90+-0.05 0.43+-0.05As-homogenized 0.92+-0.04 0.45+-0.04Table 4-3. EDX measurements of composition of several precipitates.Precipitate Precipitate Content (at.%)type Al Si Mg Fe Cr Mn Cuunknown 92.8 6.2 1unknown 85 14.5 0.5Mg2Si 88 4.5 7.5unknown 82 15 3FeSiA15(13) 87 7.5 4.5 0.15 0.22 0.75Coarse Mg2Si precipitates with the rod morphology crystallographically relatedto matrix are present in grain interiors in the slow cooled as-cast material, as shown inFigure 4-11 a. Apparently, they formed after solidification on cooling with moderatecooling rates. No optically visible Mg2Si was observed in small samples after air coolingat 5 K/s or after water quenching. The Mg2Si free zones surrounding each a-FeSiAlparticle in Figure 4-11 a indicate incomplete homogenisation in the as-cast material.The Mg2Si phase dissolves during homogenization at 838 K for 2 hours as shown inFigure 4-11 b and then re precipitates again during heating for deformation.4.2.2. The 6061/Al203 compositesThe homogenized 6061-alumina composites are shown in the as-polishedcondition in Figure 4-12 a,c,e and in the etched condition in Figure 4-12 b,d,f. Themicrostructural features visible in these Figures and discussed in detail in subsequentsections are particles, particle clusters, grains and pores. In termetallic phases which arenot visible in the etched samples are also discussed.70bFigure 4-11. x1000. Precipitates in the 6061 alloy exposed by chemical etching(H2SO4+HF+H20, 30 s at room temperature). a) As cast slow cooled 6061 alloy showingthe a-FeSiAl particles visible on grain boundaries; b) Homogenized and water quenched6061 with the O-FeSiAl phase decorating the grain boundaries. Grain size and shapeThe matrix grain size and aspect ratio in the homogenized composites are shownin Table 4-4, as measured from micrographs of the etched samples similar toFigure 4-12 b, d, f. After homogenization, the original equiaxed interdendritic structureis only evidenced by an interdendritic particulate distribution. From the Figures it canbe observed that grain growth during homogenisation is restricted by particle clusterpinning. In the more clustered 10% composite larger grains can grow (Figure 4-12 b) inthe intercluster regions devoid of reinforcement, while smaller grains remain in theA. Ato. r-w- • 01' ;era -lir 4c71cluster regions. The grain size in the MMCs may be exaggerated compared to the 6061alloy, because not all grain boundaries may be visible in cluster regions.72Figure 4-12. x100. The homogenized MMC's microstructures: The 6061/Al203/10p aspolished (a) and etched (b); the 6061/Al203/15p as polished (c) and etched (d);6061/Al203/20p as polished (e) and etched (f).Table 4-4. Grain size and aspect ratio in homogenized materials.Material 6061 6061/Al203/10p 6061/Al203/15p 6061/Al203/20pAverage^graindiameter, .1,m120 150 130 100Grain aspect ratio 1.34 1.73 1.47 1.42Table 4-5. Particle and cluster size, shape and standard deviation in homogenizedcomposites.Material 6061/Al203/10p 6061/Al203/15p 6061/Al203/20pParticle area, square .i.m 56+-72% 109+-64% 220+-76%Maximum dimension, 1,tm 12+-45% 16+-46% 24+-49%Particles analyzed 102 514 45Cluster area, square lam 660+-87% 1080+-75% 480+-68%Particle^as^a^fraction^ofclusters55-75% 55-75% 85-90%Number^of^particles^percluster7-8 6 2734.2,2.2. Reinforcement Size and DistributionReinforcement particle size was measured using the Leitz Image Analyser atmagnification x500 and the software described in detail in Appendix B. The results arepresented in Table 4-5. The composites under investigation exhibit different particlesizes, the largest particles being in the 6061/Al203/20p.Defining a cluster as a "set of particles such that for each particle there is amember of the set within 1/20 of the particle diameter (approximately lgm)", the clustersizes were measured at magnification x50. The results are presented in Table 4-5. Thestandard deviation of the cluster size is large, compared to its mean value. The6061/Al203/10p is most clustered, as demonstrated by the highest number of particlesper cluster. In the 6061/Al203/20p the relatively small average cluster size reflects thatmost particles are separated from their neighbors. Another characteristic of clustering isthe ratio of the volume fraction of particles (measured at a magnification x500) to thevolume fraction of clusters (measured at a magnification x50), also shown in Table 4-5.This ratio is higher for the 6061/Al203/20p reflecting that very little matrix isencompassed by particles in clusters. Multiplication of the cluster area by the fractionof particles in the cluster and division by the average particle area gives the averagenumber of particles per cluster.The largest clusters are seen in the 10 and 15% composites shown in Figures 4-12a-d and can be seen to have pores inside. The mechanism for cluster and pore formationis believed to be by the microsegregation of particles pushed by the solidification frontinto interdendritic regions. Pores in the Mg-Si 6061 alloy are usually associated with ahigher concentration of solute atoms and with the presence of low melting Mg2Si and Al-Fe-Si phases (Lagace, 1990) and are believe to result from shrinkage in the regions thatwere the last to solidify (Dutta et al, 1990a). Pores in clusters may also result from anincomplete wetting and flocculation of particles. Clustering and shrinkage pores are thetwo main defects of the as-cast MMC microstructures, which have to be eliminated or atleast minimized by subsequent thermomechanical processing.744,2,2.3. SEM/EDX Analysis of the Matrix / Reinforcement InterfaceIn the light microscope it is apparent that the particle surface is not smooth, but isvery irregular (Figure 4-13 a). Figure 4-13 b shows the SEM image of the exposedparticle surface at higher magnification. An interface reaction product (pyramidal0.5-1 tm high crystals) previously described as a spinel is apparent. The spinel formswhen Mg from the molten alloy reduces alumina. Formation of this product consumes acertain amount of Mg and Si from the solid solution, as shown by the WDXmeasurements presented in Table 4-6. An EDX analysis revealed a composition ofapproximately 12:88 Mg:Al atomic percent ratio in the spinel. More accurate WDXmeasurements gave Mg:Al at.% ratio of 22:73 as given in Table 4-6. Both EDX andWDX measurement did not measure oxygen content. The measured Al content is highera bFigure 4-13. The reaction product at the matrix/particle interface in 6061/Al20 3/20p. a)X1000. Homogenized and mechanically polished; b) x6000. Homogenized, electrolyticallypolished and Au-Pd coated.75than that of the ideal spinel composition, MgAl2O4. This is thought to be due to theelectron beam excitation zone (2-3 gm) being larger than the spinel thickness 0.5-1 gm.Correcting for the presence of 5-10 at.% silica, the Mg content in the spinel should beapproximately 13 at.%. For uniformly spaced 10 gm particulate reinforcement, thedecrease in Mg content in the matrix can be estimated to be between 0.4 and 0.8 wt.%.The experimentally observed value is only about 0.25 wt.% (Table 4-6). This suggeststhat, because of clustering, not all particles are covered with a spinel. This is in goodagreement with Boyd (1992) who measured by TEM of ion-beam thinned6061/Al203/20p an approximately 0.5 gm thick spinel layer only on "some" particles.Table 4-6. Composition of FeSiA15 precipitate free matrix regions in the as-homogenized6061/Al203/20p composite and 6061 alloy.Mg Si Al6061 (matrix), wt.% 0.92+-0.04 0.45+-0.04 bal6061/Al203/20p (matrix), wt.% 0.67+-0.04 0.41+-0.05 balParticle/matrix^reaction^product,normalized at.%22 5 734.2.2.4. Precipitate Composition, Size and DistributionThe Mg2Si and (Fe,Cr,Mn)-Si-Al precipitates would be expected to predominatein the MMCs. From the Table 4-6 it can be inferred that 0.13 wt.% Mg in excess of thatneeded for the formation of Mg2Si is present in the 6061 alloy and 0.04 wt.% in the6061/Al203/20p. For condition of no excess Mg the following solid solubilities of Mg2Siin Al (in wt.%) can be calculated from Mondolfo (1976): 1.33% at 798 K, 1.12% at 773K, 0.77 at 723 K, 0.55 at 673 K and 0.34 at 573 K. Comparison of these limits withTable 4-6 suggests that the Mg2Si dissolution temperature should decrease in the MMCsas compared to the matrix alloy from approximately 803 K to approximately 773 K.Therefore, the resolution of the optical technique in measuring the precipitate size andthe volume fraction limits the measurements to coarse Mg 2Si particles. Such coarseningrequires long annealing and, therefore, is considered in subsequent sections on annealing.764.3. Microstructure of Thermomechanically Processed 6061 Al-Alloy4.3.1. Strain Inhomogeneity in Hot Compressed Cylindrical SpecimensThe homogenized 6061 sample was deformed at 723 K, strain 1, strain rate 1 Isand rapidly cooled to preserve the as-deformed grain size and shape. The micrograph ofone quarter of the vertical section of the sample is shown in Figure 4-14. A very non-uniform distribution of grain size and aspect ratio can be observed from the Figure,evidence of the non-uniformity of deformation over the sample. The grain size andaspect ratio were quantitatively measured with the image analyzer using softwarepresented in detail in Appendix B. Figure 4-15 shows measured grain area, graindimension and grain aspect ratio; each frame is 760 gm x 760 p,m, giving at least 70grains for analysis.Figure 4-14. x20: Grain distribution in a 6061 cylindrical specimen hot compressed at723 K, strain 1, strain rate 1 /s.It can be seen from Figure 4-15 that the relative standard deviations of theindividual measurements are quite high. Part of the deviation is due to the randomness ofthe sectioning of the grains. For example, for a perfect sphere sectioned at a randomheight, the average area of the section should be 2 313.1- and the relative standard deviation77from the average can be calculated as y4-5- , which is 45%. The remaining 9% of thedeviation is true experimental error. When grain size is so large that sufficient statisticscan not be collected in small frames on the specimen, or when the quality of the sampledoes not allow reliable observation of a sufficient number of grains in each frame, thegrain parameters have to be measured over a significant area on the sample. Whenparameters are averaged over the whole area of the sample, the inhomogeneity of grainsize and shape contributes to a larger standard deviation. For the sample shown in Figure4-14, the deviation of the average grain area was measured as approximately 69%. Thedeviation exceeded 100% for some other samples, which sometimes meant the existenceof two or more different grain distributions (original and recrystallized grains, forexample). Also, it should be noted that the deviation of the average from its mean valueis proportional to the deviation from the average divided by the square route of thenumber of observations. In each frame at least 70 grain size/dimension/aspect ratiomeasurements have been made, which lowers the deviation in the estimate of the meanvalues to 5-10%, thus allowing support of some qualitative conclusions.5490 3400 474036/58 138/39 203/40 Grain area,2.44 3.61 5.00 sq. micronsMax. dimension/Min. dimension,microns5470 4480141/56 153/46 Aspect ratio2.80 3.454450 6970 7980 6700 7590 8300165/47 194/56 148/74 144/69 147/72 145/793.50 3.55 2.08 2.17 2.08 2.04Figure 4-15. The grain area, grain dimensions and grain aspect ratio distribution in 6061cylindrical sample deformed to the nominal strain 1. The average relative standarddeviation for grain area is 54%, for max. grain dimension 80%, for min. grain dimension30% and for grain aspect ratio 20%. The arrow shows the orientation of the maximumgrain dimension.78The aspect ratio (a.r.) parameter can be directly related to the shear component ofstrain (assuming no recrystallization occurs during or after deformation):a.r.= e(erez)^(4.1)where ez<0 is the strain component in the compression (vertical) direction, er>0 is thestrain component in the radial direction. The true local strains e z at a nominal strain ez=1can be determined for several points in the compression specimen from the measuredaspect ratios shown in Figure 4-15 using the equation e z=-2Er (volume remainsunchanged). This allows the derivation of the correction coefficients (the deviation fromthe nominal strain of 1) shown in Figure 4-16. Multiplication of the nominal strain bythese coefficients produces a true local strain in each point. It is recognized that the straindistribution and correction coefficients will change with change in nominal strain; thesignificance of the variation is discussed later in section 4-16. Correction coefficients for calculation of true local strains e z from nominalstrain Ez at several points in the sample.43,1.1, Comparison With the Finite Element Simulations The aspect ratio measurements were compared with FEM simulations (DEFORMpackage), contributed to this work by W. Chen. The simulation was done assuming a vonMises material (homogeneous, isotropic, independent of hydrostatic pressure) based onthe constitutive equation (equation 2-4) used by Dr. C. Davies, which relates the averageuniaxial true stress and average uniaxial strain rate at steady state flow stress conditions.As a result of the simulation, strain rate components in the r, z, rz and 0 directions79Figure 4- 17. Vertical section of the compressed specimen. 1.81 19.52.44 4-18. Grain aspect ratios at a nominal strain 1 derived from FEM simulations.Experimental values are given in denominator.(Figure 4-17) were produced. The last component is neglected, because it describesdeformation in a horizontal section. The strain rates were integrated over time to producestrains in points A, B and C when a total nominal strain of 1 is reached. Then, theprinciple values of the strain (in the vertical section) were calculated and the aspect ratioswere found according to equation (4.1), as shown in Figure 4-18.There is only qualitative agreement between the experimental observations ofgrain aspect ratio (Figures 4-15) and the FEM simulations (Figure 4-18). At points A andC the discrepancy may be due to the fact that the experimental frame was 760 in size(vs approximately 500 gm for a FEM element) and that the frame could not bepositioned at the edge of the sample.In general, the FEM analysis predicted more non-uniform strain distribution thanwas actually observed. This might be explained if the stress sensitivity of the strain rate80in equation (2.4), n, used in the constitutive equations at this particular test temperatureand nominal strain rate was too large. A high n value could be obtained if n is both strainrate and temperature dependent and has a maximum in the investigated interval.However, the n, a, Qdef and A parameters for constitutive equation (2.4) were obtainedby the "best fit" for the whole strain rate and temperature interval under investigation.Measurements of the aspect ratio distribution in samples deformed at varioustemperatures and strain are needed to elucidate this. Also, the constitutive equation usedin the FEM analysis was derived for the steady state flow conditions and did notcorrectly describe the initial stages of deformation up to a strain of 0.3.The apparent variability of strain rate in the test sample makes it unclear whichvalue of stress, strain and strain rate should be used to derive the constitutive equationparameters (Table 2-7). An iterative FEM simulation could be used to derive aconstitutive equation which satisfies the experimental observations. A constitutiveequation would be assumed and the flow stress for the whole sample is calculated atseveral T, E and compared with experimental results. The equation is then modified toimprove the "fit" until the agreement is obtained between the FEM predictions andexperimental observations. However, this was not attempted in this research study.The inhomogeneity of stress, strain and strain rate in compression testing was alsoexamined by Kopp et al. (1988). Their FEM simulations of steel samples (Figures 4-19,4-20) indicate that the strain rate, strain and stress can deviate in the compressed sampleby 90% from their nominal values. That result is consistent with the FEM simulationsobtained by W. Chen in this work.Although a more uniform strain distribution can be produced in tensile tests, theupper strain limit is only about 20% in MMCs at high temperatures. Tension undersuperimposed hydrostatic pressure would be ideal, but such tests require expensiveequipment. For the microstructural investigation per se the strain inhomogeneity over thesample can be an advantage, because the spectrum of strains can be achieved in onesingle test. Further, all microstructural evaluations are performed in the regions whereFigure 4-19. Distribution of normal stress a ^mean normal stress azzm in acompressed cylindrical specimen along a line AB at a nominal strain (Kopp et al., 1988).Evt-I^I^temperature °CFigure 4-20. Distribution of FEM calculated equivalent strain c, equivalent strain rate E.and temperature at a nominal strain of 47% (Kopp et al., 1988).82the local strain approximately equals the nominal strain for the sample, except whenotherwise indicated.4.3.2. Effect of Temperature on Mg2Si Precipitation and CoarseningFollowing the homogenization treatment at 838 K for 2 hours and waterquenching, the 6061 alloy samples were heated to several hot deformation temperatures,deformed and held at the deformation temperature (annealed). Sufficiently longannealing times (>180 s) produced coarse Mg2Si precipitates which were opticallyexamined to determine the equilibrium precipitate size and volume fraction, chemicalcomposition of precipitate free matrix regions and precipitate coarsening kinetics.SEM measurements produced very low contrast, but were used infrequently to measurethe size of the submicron precipitates. Literature data were used to make reasonableassumptions about the earlier stages of precipitation and to speculate about how smallprecipitates may affect the mechanical response and microstructural evolution.The matrix composition of the FeSiAl5 precipitate free matrix regions in the 6061alloy was compared with the composition of FeSiAl5 and Mg2Si precipitate free matrixregions using WDX analysis. During annealing and Mg2Si precipitation the solutecontent in the precipitate free matrix regions can be seen to decrease, as shown in Table4-7. The average size of a precipitate free matrix region is equal to the average inter-precipitate distance of about 5-10 gm (Figure 4-21).Table 4-7. Matrix compositions (wt.%) of as-homogenized and annealed 6061 alloyobtained by WDX analysis.Mg Si AlHomogenized and quenched 6061, 0.92+-0.04 0.45+-0.04 balFeSiAl s precipitate free matrixHomogenized and quenched 6061 annealed at573 K for 30 min.FeSiAl 5 and Mg2Si free matrix 0.78+-0.04 0.30+-0.04 balall matrix 0.88+-0.05 0.51+-0.04 bal83During electropolishing, an etch pit forms around each precipitate; the pit isoptically visible before the precipitate itself. However, once the precipitate reaches about0.2 gm, it also becomes optically visible, as shown in Figures 4-21. The kinetics ofprecipitation measured by quantitative image analysis is characterized in Table 4-8. Theaccuracy of the numbers is limited due to the Mg2Si precipitate size being near theresolution limit of the optical technique. Comparison with the SEM measurementssuggests that for precipitates 0.2-0.5 gm in size, optical measurements give 20-30%larger size. It is shown in the Table that air cooling from 773 K is equivalent to 8 sisothermal delay before He-quenching. This estimate is discussed in detail later in sectionon recrystallization.Table 4-8. The precipitate size evolution in base alloy during annealing. Where adeviation is indicated, at least 400 counts has been made at a magnification x1600.TimeTemperate eUp-heating,60 sannealingand HeliumquenchingDown-quenching*,0 s annealingand aircooling (8 s)Up-heating,60 sannealingand aircooling (8 s)Up-heating,600 sannealingand aircooling (8 s)Up-heating,1800 sannealingand aircooling (8 s)798K <0.2 lam773 K <0.21..tm 0.2-0.3 um 1.3 2.1+-11.78+-0.6723 K no pptes no pptes less^than0.51+-0.3 pm0.5-0.8 1.25+-0.551.36+-0.52673 K no pptes no pptes 0.8-1Cooling from the solutionizing temperature 803 K to deformation temperature at a rate 5K/sAccording to Mondolfo (1976), the dissolution temperature for Mg2Si in the 6061is 803 K, which corresponds to a total of 1.37 wt.% Mg+Si available for precipitateformation. That is in excellent agreement with the experimental value (Table 4-7). Someadditional silicon in the stable P-FeSiA15 precipitates (which content was not measured)is not available for the Mg2Si formation. The experimental observation of some Mg2Si84precipitates in the 6061 annealed for 1800 s at 798 K and no Mg2Si after annealing at823 K, agrees with the composition measurements.No data is available for the kinetics of nucleation and growth at hot deformationtemperatures. The author believes that the optical observations presented in Table 4-8correspond to the end of the diffusion controlled growth stage (which is notexperimentally proved) and to the beginning of the coarsening stage (which is reflectedby no change in Mg2Si volume fraction in the 6061 during 3 to 30 min. holding at773 K). What follows is an attempt to assess the precipitation kinetics at the beginning ofthe diffusion controlled growth stage at deformation temperatures 623-798 K.Mondolfo (1976) suggests the "nose" of the C-curve for an alloy with 1.8%Mg2Si is approximately 623 K (although no observations has been reported fortemperatures higher than 603 K). According to the same author, one hour at 573 Kproduced 0.2 gm square (3-Mg2Si platelets and 0.3 by 0.011.tm (3 1 laths formed insolutionized and quenched A1-0.9Mg-0.6Si. Assuming that the precipitation is at thediffusion controlled growth stage and that the coarsening stage is not yet reached, theprecipitate size, d, can be written as:d f • D •t (4.2)where D is the diffusion coefficient, f is the fractional supersaturation and t is the growthtime (Brown, 1992).The time to produce the same 0.2 p.m (3-Mg2Si precipitates at differenttemperatures has been calculated, as shown in Table 4-9, using D = D o • exp(— CYRT)and assuming that 803 K is the temperature of complete Mg2Si dissolution. It followsfrom the table that the "nose" of the precipitation C-curve occurs close to 773 K. Inreality, it could be at a slightly lower temperature, which can be explained as follows.Above 493 K no GP zones form (Salvo, 1991). On heating the homogenized andquenched material from room temperature at 10 K/rnin., the semicoherent intermediate p'85LCD^-O44: 11O• ——(NJ•VOa b-• • • •*a• •a ••0^10^20^30^40 -' 50itillulkill11111-11111111r11-Figure 4-21. x1000. Precipitation of Mg2Si in the 6061 alloy during annealing (cooling50 K/s). Homogenized 6061 after 30 min. annealing at: a) 773 K; b) 723 K, c) 673 K.I:I86Table 4-9. Kinetics of Mg2Si precipitation calculated from measurements of Mondolfo(1976).Temperature, K 573^(from 673 723 773 798Mondolfo)Fractional supersaturation 0.0104 0.0076 0.006 0.0027 0.0003Mg diffusion coefficient at 573 K 1 80 450 2000 3000Time to reach 0.2 p.m size 1 hour 60 s 15 s 7 s 40 sPinning pressure^on^dislocations(eqn. 4.3), MPa7.6 6.9 6.4 4.9 2.3Drag force on subgrain boundaries(eqn. 2.33) KPa23 17 13 6 0.7phase transforms into the 13 phase at 770, 765 and 757 K for the 6061, 6061/Al 203/10pand 6061/Al203/15p, respectively (Dutta, 1991, Table 2-4). Comparison of Figures 4-21c and b shows Mg2Si rods present after annealing for 30 min. at 673 K, but not afterannealing at 723 K. The rod morphology evidences some degree of coherency betweenmatrix and precipitates. Therefore, the rods are thought to be the 13' -Mg2Si. The criticalenergy for homogeneous f3 precipitate nucleation increases in the absence of the [3' phase,thus, delaying precipitation and pushing the "nose" of the C-curve from approximately773 K (as calculated in Table 4-9 from equation 4.2) to lower temperatures. Qualitativeexperimental observations Table 4-8 suggests that the "nose" is between 723 and 773 K,which is more than 100 K higher than that reported by Mondolfo (1976).4.3.3. Recovery, Grain Growth and Recrystallization in the 6061 AlloyThe 6061 alloy was deformed at strain rates from 0.05 to 15 /s and temperaturesfrom 573 to 823 K, as explained in Chapter 3. Some of the samples were further annealedafter deformation at the deformation temperature or higher temperatures to investigatestatic recrystallization. Precipitate Pinning of Dislocations and Grain Boundaries in the 6061 alloyWhile Mg2Si precipitates are small, they can exert considerable pinning pressureon dislocations, affecting thereby the recovery rates and the material's mechanicalpressure fromprecipitates^ controlled^PresentgrowthpinningDiffusionopticalLoss of^f-? ; r2i2 observationsencyCoarseningf=constr^t 1/3Nucleationresponse. This pinning pressure can be calculated as:G•b^G-13- kfi -2 10^2 • d precipitatewhere 10 is the inter-precipitate spacing and f is the precipitate volume fraction. Thepinning pressure from small precipitates on subgrain and grain boundaries (which iscalled "Zener drag pressure") can be described as:PZ = a y 2.fid precipitate^ (2.33)where y is the boundary energy (0.3 N/m for subgrain boundary and 1 N/m for GB in Al)and a is 3/4 following the original work of Zener. It can now be suggested that,following the precipitate size and volume fraction evolution during annealing, thepinning pressure from precipitates on mobile dislocations and on mobile grain orsubgrain boundaries follows the trend shown in Figure 4-22.TimeFigure 4-22. A pinning pressure evolution during annealing. A-pinning of dislocations,B-Zener drag of boundariesThe assessment presented in Table 4-9 can now be analyzed to answer thefollowing question: in the experimental setup with 1 minute of pre deformation holdingat the deformation temperature, at what temperature interval would the precipitate87(4.3)88pinning be most noticeable during deformation? Table 4-9 suggests as an answer theinterval T=623-723 K. At lower temperatures precipitation is too slow, while at highertemperatures both the precipitate volume fraction is too small and coarsening occurs toofast. Again, the fact that the "nose" of the C-curve may be lowered compared to theassumptions of Table 4-9 due to one-step precipitation of stable P-Mg2Si, may result in aslightly lower temperature interval for the maximum precipitate effects. The verificationof the above assessments will be described in the next section and in sections onrecrystallization in composites and on mechanical response.4.3.3,2. Metallography of Recovery. Grain Growth and Recrystallization in the 6061 Figures 4-23 a - f show the microstructure of samples deformed to a strain of 1 attemperatures 573 K, 723 K and 798 K at strain rates of 0.05 /s and 15 /s. Figures 4-23 gand h show samples deformed at T=723 and 773 K at the highest strain rates of 15 /s.Figures 4-23 i and j show similar samples annealed for 600 s after deformation at thedeformation temperature. A summary of the metallographic observations follows.1. After deformation at T<673 K, the grain boundaries are very irregular withgrains often impinged into each other (Figure 4-23 a, b). After deformation at 723 K atlow strain rates, the grain boundaries become "smoother" (Figure 4-23 c); but at highstrain rates closely spaced deformation lines give the grains the appearance of a very highaspect ratio (Figure 4-23 d). After deformation above 773 K at low strain rates, the grainboundaries are relatively "smooth" and well defined. Bulging of some grain boundaries isoften associated with the formation of large (--6-8 i.tm) subgrains. These subgrains areoptically visible predominantly in the vicinity of the original grain boundaries, as shownin Figure 4-23 e. After deformation above 773 K and high strain rates of 15 /s, the grainboundaries become more irregular than at lower temperature (Figure 4-23 d) which canalso be associated with formation of small optically invisible subgrains in the vicinity ofthe grain boundaries.892. In tests at T>723 K, during annealing after deformation, mostly grain growthand no recrystallization was observed. This is evidenced by an increase in the grain areawith the approximate retention of the aspect ratio (Figures 4-23 d and i, h and j).3. No equiaxed, "typically" recrystallized grains were observed after deformationat a strain rate, =15 /s, to a strain of 1 at 723 K and annealing for 600 s at 723 K(Figure 4-23 i); few recrystallized grains appeared after deformation at 773 K andannealing for 600 s at 773 K (Figure 4-23 j) and none appeared after deformation at823 K and annealing for 600 s at 823 K.4. During annealing at 773 K recrystallized grains were observed only in thesamples deformed at a e >1 /s.The first point underlines the role of recovery as a softening mechanism in mostof the E , T intervals tested. As expected, dynamic recovery has more time to exerteffects on the microstructure at high temperatures and low strain rates. The second pointillustrates domination of recovery over recrystallization as a softening mechanism above723 K. The third point can be explained by an insufficient recovery rate for nucleiformation of recrystallized grains below 773 K and by very intensive recovery above773 K (which decreases the driving force for growth of recrystallized grains). Also, asshown in the previous section, this pinning is most noticeable during deformation atT=623-723 K, which additionally decreases the recrystallization driving force in thatinterval. The forth point can be explained by the fact that at low strain rates recoverydecreases the driving force for recrystallization. At high strain rates there is less time forrecovery to occur, which results in a higher dislocation density after deformation.90a^ bC^d91g^h92Figure 4-23. x100. Recovery and grain growth in 6061 alloy deformed to a strain of 1.a) Deformed at 573 K, E =0.05 /s, air cooled; b) Deformed at 573 K, E =15 /s, air cooled;c) Deformed at 723 K, E =0.05 Is air cooled; d) Deformed at 723 K, E =15 /s, waterquenched; e) Deformed at 798 K, E = 0.05 /s, water quenched; f) Deformed at 798 K,=15 /s, water quenched; g) Deformed at 723 K, E =15 Is and He-quenched;h) Deformed at 773 K, E =15 Is and He-quenched; i) Deformed at 723 K, E =15 /s,annealed at 723 K for 600 s; j) Deformed at 773 K, E =15 Is annealed at 773 K for 600 s.Measurements of grain area and size for the 6061 alloy, defoi Hied to a totalnominal strain of 1 at different temperatures, strain rates and after different annealingtimes at the deformation temperature immediately after deformation, are given in Table4-10. Most of the samples were air cooled; two samples were water quenched.Comparison of the microstructures (fraction recrystallized) in the air cooled specimenand in specimens which were helium quenched after specified holding intervals,established that air cooling from 773 K is equivalent to 8 s isothermal delay before He-93quenching. All structure measurements were done on one quarter of the vertical cross-section of the sample, in the central region with strain e>0.6 (the large area is required tomake more measurements). Thus, depending on the grain size, each value in the Tablerepresents 70-250 grains. The large standard deviation reflects the variability of theresults and the fact that a 3D structure has been examined on a 2D surface.Table 4-10. Grain Size and Shape Evolution in 6061 on Static Annealing afterdeformation to 1.2>E>0.6.T t Nominal Grain area Relative Max. dim. Min. dim. Relative Aspect RelativeK s strain rate, /s sq. micron std. dev.,% micron micron std. dev.,% ratio std. dev.,%723 0 0.05 4560 172 44 3.920 0.05 7830 61 211 56 36 3.87 241800 0.05 8200 76 206 60 50 3.48 2820 1 6940 201 54 3.8120 15 6650 74 207 52 39 4.05 241800 15 11100 110 215 70 48 3.12 24773 20 0.05 5000 62 174 47180 0.05 5700 61 178.5 49.5 491800 0.05 5660 61 176.2 48.5 4520 15 15600 90 236 93 53 2.6 331800 15 19100 97 260 101 52 2.62 29798 600 0.05 8000 100 195 59 57823 600 0.05 11500 59 235 73 56 3.3 3020 1 8940 63 197 69 37 2.91800 1 16300 66 280 80 3.5 240 15 7670 82 223 55 40 4.06 2320 15 8520 65 220 59 37 3.84 28600 15 24000 100 270 112 61 2.53 30It can be inferred from the Table, that:1. There is some grain growth in samples deformed at 823 K; grains in the samplesdeformed at 823 K and quenched are approximately 1.5 times larger than in thesamples deformed at 723 K and quenched. It is unlikely that this growth occurredduring heating to the deformation temperature and 1 min. holding before deformation,because the samples had been homogenized at 838 K for 2 hours prior to testing. Also,Helium quenching followed immediately after deformation. Therefore, the graingrowth occurred during deformation at 823 K.942. The static growth rate is higher after deformation at a strain rate 10 Is than afterdeformation at 0.05 /s.3. The static growth rate is also smaller at lower temperatures, where the grain sizeremains constant, and is equal to that observed after a few minutes after the end ofdeformation.4. As the grains grow, their aspect ratio decreases, but not as significantly as their grainsize increases.The first point is consistent with the non-existent precipitate pinning above thesolutionizing temperature of 803 K. The second point can be explained since at lowerstrain rates greater time is available for dynamic recovery to reduce the dislocationdensity. Higher strain rates should produce higher dislocation densities at the end ofdeformation and immediately after deformation, when most of the grain growth occurs.The third point can be explained by the increasing importance of precipitates in reducingthe grain growth. The fourth point implies that some precipitation occurred during 1 min.pre-deformation holding. These precipitates were lined up by deformation and exhibitnon-isotropic pinning during post-deformation annealing.To better interpret the previous observations, particularly item 4, several 6061samples were heated up immediately after deformation to a higher temperature. Thisincluded deformation at 723 K or 773 K at strain rates 2-15 /s and heating to 798 K for a600 s annealing. Small areas of recrystallized grains appeared in all samples, the size ofthe recrystallized grains being larger in the material deformed at 773 K than in thatdeformed at 723 K (Figures 4-24). Some recrystallized grains appear to be elongated,which is thought to be due to the non-isotropic pinning of the lined-up precipitates.Comparison with the samples annealed at their corresponding deformation temperaturesis given in the Table 4-11.95aFigure 4-24. x100. Grain growth and recrystallization in 6061 alloy heated up afterdeformation at a strain rate 15 /s. Electopolishing in Reagent N2 for 7 time segments of 8s with 1 min. intervals. a) Deformed at 623 K, annealed at 798 K for 10 min.;b) Deformed at 773 K, annealed at 798 K for 10 min.Table 4-11. Sizes and Aspect Ratios for Original and Recrystallized Grains.Tdef Tanneal t Strain Grain area, Relative Aspect Relative Grain area, Relative Aspect Relative Fractionrate original grains std. dev. ratio std. dev. Recryst. grains std. dev. ratio std. dev. recryst.%K K s 1/s sq. micron % % sq. micron % %723 798 600 15 18080 64 2.9 24 930 40 1.31 18 7723 1800 15 11100 115 3.12 24 0798 600 6 17900 76 2.7 19 800 51 1.35 22 5798 600 2 21000 58 2.6 31 760 63 1.53 27 4773 798 600 15 28400 58 2.6 33 1400 47 1.42 20 8773 773 1800 15 19100 97 2.62 29 0798 798 600 0.05 8000 _^100 096It follows from the Table that:1. Deformation at lower temperatures followed by rapid heating to the annealingtemperature favors the appearance of new recrystallized grains compared to annealing atthe deformation temperature.2. As the strain rate increases from 2 to 10 /s, the surface area fraction of smallrecrystallized grains increases from 4 to 7%.These points can be explained in that higher dislocation density and recrystalliza-tion driving force can be achieved after "colder" or after "faster" deformation. Althoughmore intensive recovery during "hotter" annealing decreases driving force for growth ofrecrystallized grains, it also allows more dislocations to sink to subgrain boundaries, thusincreasing the subboundary misorientations and creating more mobile interfaces, which isa necessary step in nucleation of recrystallization. In addition, the pinning force fromprecipitates can be decreased by heating to the higher temperature (where the equilibriumprecipitate volume fraction is lower). A decrease in the concentration of elements in solidsolution by any other means (like consumption in spinel formation, or coarsening intolarger particles) can also decrease precipitate pinning.No quantitative description of static recrystallization in the 6061 alloy has beendone in this research due to the limited temperature interval for recrystallization and thesmall recrystallized volume fractions attained. Sellars and co-workers (1986) observedstatic recrystallization in the 6061 alloy at 673 K (Table 2-8) with the t50% from 180 to1800 s for strains 0.67 or 0.33, respectively. Their different response can be explained bythe thermal history of their material: it was rolled at either 523-573 K or at 673 K, thenannealed for 1 hour at 798 K and air cooled. Reheating after deformation, as well as theprecipitate size and volume fraction were not documented. This suggests thatrecrystallization in their material was particle stimulated and also that less precipitationoccurred during deformation. In other materials similar to the 6061 alloy listed inTable 2-8, recrystallization could also be stimulated by these two factors.974.4. Microstructure of Thermomechanically Processed 6061-AluminaComposites4.4.1. Effect of the Hot Deformation on the Reinforcement DistributionThe MMCs were deformed to a strain of 1, at strain rates from 0.01 to 15 /s and attemperatures from 573 to 823 K. The microstructure of the deformed MMCs is presentedin Figure 4-25. As it can be observed from the Figure, the rigid alumina particles havealigned in the flow direction created by the compressive deformation. The degree of theparticle alignment was characterized by the angle between the particle maximumdimension and the flow direction. The measurements of this angle for the6061/Al203/15p are presented in Figure 4-26. The average value of the angle beforedeformation is 45 degrees, and after deformation it is 30 degrees. This difference of thosetwo values gives the average rotation angle for a particle during deformation of 15degrees.The cluster size and shape was measured for the MMCs similar to how grain sizeand shape was measured for unreinforced composites (section The degree ofclustering, measured as the average cluster size, was not found to significantly change inthe moderately clustered 15% composite and was found to increase from 660 to 900 sq.microns in the most clustered 10% composite. This happened because clusters alignedcloser and even joined in a flow direction. For the same reason, the measured 21 degreesaverage angle between the clusters' maximum dimension and the flow direction wasfound to be different from the similar angle measured for particles as 30 degrees. Thecluster volume fraction and aspect ratio did not change in reproducible manner, and noconclusive evidence on whether clusters deform more or less than the matrix was found.No particle fracture or debonding at the particle/matrix interface has beenobserved at the lowest temperatures 573 K, for the highest strains up to 1.2 and thehighest strain rates of 15 /s.er.98Figure 4-25. x100. Particle distribution in the MMCs deformed at 773 K, at a strain rate1/s to a strain of 1. As-polished. The 6061/Al203/10p (a); the 6061/Al203/15p (b); the6061/Al203/20p (c). The compression direction is horizontal in a) and b) and vertical in c).10090ao70605040302010075^-60^-45^-30^15^0 15^30^45^60^75^90111 For all particlesm For particles with aspect ratio^>2Distribution ofthe same numberof particles beforedeformation99Angle between flow direction and maximum dimension, degreesFigure 4-26. Particle alignment along the flow direction during deformation of the6061/Al203/15p to a strain of 1 at T=723 K, at a strain rate of 15 /s.4.4.2. The Mg2Si Precipitation and Coarsening in MMCsThe Mg2Si precipitation in the MMCs shown in Figure 4-27 is very similar toprecipitation in the 6061 alloy shown in Figure 4-21. However, after 1800 s post-deformation annealing at 773 K, almost no precipitates were observed in the6061/Al203/15p (Figure 4-27 c), few in the 6061/Al203/10p (Figure 4-27 b) and more inthe 6061 alloy (Figure 4-21 a). At lower temperatures, slower precipitation and smallerprecipitate sizes were observed in the MMCs compared to the 6061 alloy (Table 4-12).These effects can be explained by the lower Mg and Si content in the matrix inthe MMCs. The WDX measurements of the matrix composition are presented inTable 4-13. They show a lower drop in the combined Mg+Si content of the precipitatefree matrix after annealing of the MMC (a Mg+Si decrease of 0.15 wt.%) than afterannealing of the 6061 (Mg+Si decrease of 0.29 wt.%). This difference is due to theapproximately 0.2% lower initial Mg content available for precipitation in the MMC,thought to be due to the consumption of Mg for spinel formation at the matrix/alumina100interface, as discussed in section This composition variation effectively results ina decrease of the Mg2Si dissolution temperature for composites from 803 K to 778-783 K, which is supported by the present optical observations and by the literature data.As shown in Table 2-4, Dutta et al. (1991) determined that on heating at 10 K/min thepeak temperatures of the DSC (Differential Scanning Calorimetry) exotherms for13-Mg2Si dissolution decrease by 23 K for 6061/Al203/15p compared to the 6061 alloy.Table 4-12. The precipitate size evolution in 6061 alloy and MMCs during annealing.Where a deviation is indicated, at least 400 counts has been made at a magnification x1600.Material TimeTemperature0^s(Helium quenching)8^s(Air cooling)1800^sannealing6061 alloy773 K <0.2mm 0.2-0.311m 2.1+-11.78+-0.6673 K no pptes no pptes 0.8-16061/Al203/20p773 K no pptes 0.42+-0.13673 K no pptes 0.8+-0.37Table 4-13. Matrix compositions (wt.%) of as-homogenized and annealed MMCs incomparison with the 6061 alloy. Each number corresponds to an average of tenmeasurements.Material and condition Mg Si AlHomogenized and quenched 6061,FeSiAl5 precipitate free matrix 0.92+-0.04 0.45+-0.04 balHomogenized and quenched 6061 annealed at573 K for 30 min.FeSiAl5 and Mg2Si free matrix 0.78+-0.04 0.30+-0.04 balall matrix 0.88+-0.05 0.51+-0.04 balHomogenized and quenched 6061/A1901/20p 0.67+-0.04 0.41+-0.04 balParticle/matrix reaction product 22 5 73Homogenized and quenched 6061/Al203/15pannealed at 573 K for 30 min.FeSiA15 and Mg2Si free matrix 0.56+-0.05 0.37+-0.05 balall matrix 0.65+-0.03 0.46+-0.03 bal101a^ bcFigure 4-27. Precipitation of Mg2Si in 6061\Al203 composites during annealing (cooling50 K/s). a) x1000: 6061/Al203/10p after lmin annealing before deformation at 773 Kb) x400: 6061/Al203/10p after 30 min. annealing after deformation at 773 K;c) x1000, 6061/Al203/15p after 30 min. annealing after deformation at 773 K.1024.4.3. Temperature-Strain Rate Processing Maps for the MMCsFor the testing interval of temperatures and strain rates, the microstructure of eachtest sample was characterized. Such parameters as subgrain size, grain size and shape andfraction of recrystallized grains were examined. Grain size and fraction recrystallizedmeasurements presented a particularly complex task for the MMCs because of theproblems associated with grain boundary etching and lower contrast in the vicinity ofparticles. Therefore, relatively wide classification intervals were used to characterize themicrostructural evolution. The three composites investigated followed closely the sametrends, although each possessed slightly different microstructures after identicalthermomechanical processing. For example, the 6061/Al203/10p deformed to a nominalstrain of 1 at 723 K at a strain rate 15 /s exhibited only few recrystallized grains inclustered regions only, while the 6061/Al203/20p was more than 50% recrystallized.Since there was not enough information to build the processing map for each compositeand the composites behaved in a similar fashion, the temperature-strain rate map wasaveraged for all composites.A microstructural evolution map (temperature-strain rate-microstructure) ispresented in Figure 4-28. All observation were done near the center of the compressedspecimens, to ensure a constant true strain of approximately 1 ± 0.1. The true' localstrain rate and the actual temperature (not the nominal ones2), corrected for deformationheating and other effects, are shown in the map. Two principal domains on the map: thatof recovery and that of recrystallization were quantified as described below.1. This means an actual strain rate, measured from diameter change at mid-height, multiplied by thecorrection coefficients from Figure 4-16 to produce the local strain rate. The true strain and strain rate aremeasured, not the engineering ones. The actual temperature is the average actual value for the testmeasured on the surface of the specimen; it reflects any deformation heating seen at the location of thesurface thermocouple. The actual temperature was not corrected for the spatial location.2. The nominal temperature is that, programmed into the machine. Actual temperature differs fromnominal due to the deformation heating. The nominal strain rate is that calculated from the ram speedprogrammed into the machine. Actual strain rate differs from the nominal one due to machine inertia.1030.05 0.1 0.2^0.5^1 2^5^10 20 50873T, KB It^*C^D^i DynamicX re,It /,‘'9stallization\i873823^I/ A it■A -• -1 /t.'•^4•ttig*541•..^ ,........823773Intensive.4 773723723recovery-, -,--- ^za,y - //z673 _RecoveryII673623573No noticeable subgrain formation6230.05Fraction<10o111A*Legend0.1^ 1^ 10True strain rate, 1/sRecrystallised, %^ Boundaries for25< <75^>75 50% recrystallizationao^0^Air cooled^ D^0.6 s delayI C^20 s delay30 min. delayA^A^10 min. delay^ B^600 s delay2*^* He or water quenched A^1800 s delay50573Figure 4-28. Microstructural evolution map for 6061/Al203/p composites. Up-heating.Continuous boundaries indicate 50% recrystallisation. The dash-dot-dot line(— - - — - -) represents the Humphrey's restriction (2.19) on the critical strain rate forlattice rotations to occur near a particle of 12 pm diameter.1044.4.3.1. Domain of no Subgrain FormationIn the investigated materials only deformation flow lines without any opticallyvisible subgrain formation were observed below 673 K (Figure 4-29 a,b). These flowlines exemplify the inhomogeneity of deformation: when dislocation glide starts in acertain crystal plane, the work of deformation dissipates as heat in that region; this makesit even softer and further promotes flow localization. At 573 K an increase in the strainrate from 0.05 to 15 /s resulted in a decrease of the average distance between flow linesfrom 15 to 12 1.im. This indicates that at the higher strain rate, stress relaxation in oneflow line has less time to propagate in the neighboring regions, which means less flowlocalization among flow lines. Absence of any visible subgrains implies that at the lowertemperatures the subgrains are smaller than the —1 pm resolution limit and/or that theyare not well enough defined and, therefore, do not preferentially etch.The signs of dynamic recovery other than optically visible subgrains, appeared inthe investigated composites at the lowest temperature tested. With an increase in thedeformation temperature from 573 K to 673 K, the curvature of the flow lines aroundparticles became visibly smaller and at 723-773 K the flow lines completely disappeared.This is thought to indicate the onset of recovery via dislocation annihilation. Domain of the Dynamic Recovery via Subgrain FormationAbove 673 K subgrains became optically visible, as shown in Figures 4-30 a, b.They appeared initially along the flow lines around particles. Comparison of the6061/Al203/20p deformed at 673 K at strain rates 0.1 /s and 1 /s, shows that in theformer case subgrains appeared along some flow lines (Figure 4-30 a) and in the latter -along all flow lines (Figures 4-30 b). This indicates a higher flow localization in eachflow line at high strain rates. At higher temperatures, where no flow lines are noticeable,at strains less than 0.2, subgrains appeared first at grain boundaries, as shown in Figures4-30 c, d. At higher strains, subgrain formation close to particles dominated (Figure1054-32 d). For comparison, in the 6061 alloy, subgrains always appeared first alongoriginal grain boundaries, supposedly from the excess dislocations required toaccommodate the deformation.a bFigure 4-29. Flow lines after deformation of the 6061/Al203/20p at 573 K to a strain of 1.a) x100. Deformed at a strain rate of 0.01 /s and air cooled; b) x200: Deformed at a strainrate of 15 /s and air cooled.While competing with DRX at high temperatures-high strain rates, recovery viasubgrain formation remained a major softening mechanism for the unrecrystallizedgrains. These effects are shown in Figures 4-30 e, f, where recrystallized subgrain-freegrains coexist with the original recovered grains, which have equiaxed subgrains inside.106a^ bc^ d107Figure 4-30. Recovery in the composites via subgrain formation. a) x1000. Deformed at673 K, 0.1 Is and air cooled; b) x1000. Deformed at 673 K, 1 /s and air cooled; c) x1000.Deformed at 773 K, 15 /s. Subgrain formation near original grain boundaries. Straininduced grain boundary bulging. Precipitate pinning; d) x400. Deformed at 773 K, 15 /s;e) x1000. Deformed at 773 K, 5 Is and air cooled; f) x400. Deformed at 773 K, 2 Is andHe-quenched. Temperature - Strain Rate Dependence of Dynamic RecoveryMicrographs similar to those shown in Figure 4-30 were used to measure thesubgrain size using a line intersection method. To distinguish large subgrains growing athigh temperatures from small grains (Figure 4-30 f), the first were assumed to be lessthan 10 p.m in size, to have mostly "thin" boundaries and not to have any etched "pattern"on the surface. Following this definition, for example, a large empty space in the grainsurrounded only by small subgrains, which necklace the grain boundary, was notconsidered as a subgrain.Subgrain size was plotted against the Zener-Hollomon parameter, Z, according toequation (2.10), as shown in Figure 4-31 a. The nominal strain rate for the test, not the108true local strain rate was used for calculation of Z. The reason for not using the true localstain rate was that the etching exposed well defined subgrains preferentially near the edgeof the sample and in the regions of low deformation near ram. Also, at highmagnification of x1000 used for subgrain size measurements, it was hard to determineexact location of the observation frame on the specimen.The subgrain size was also plotted as a function of the inverse of the absolutetemperature according to equation (4.4) where strain rate term was neglected as shown inFigure 4-31 b.c1 -1 = a + b • ln(Z) = a + b • 1n(g • exp( Q )) = a + b•ln(e)+ b • Qsu RT RT (4.4)It can be observed from Figure 4-31 that the correlation between 1/d and 1/T ismore statistically significant than that between 1/d and ln(Z) (correlation coefficient andcalculated F-statistics are higher). The slope of the line in Figure 4-31 b equals to b*Q/Rand has a value of 2147. The b•Q multiple has a value of 17.8 kJ/mol.The correlation between 1/d and ln(Z) is weaker, but still more than 99% reliable(calculated F-criterion is larger than the critical F-criterion for 99% reliability). Therelative weakness of this correlation can be partially explained in that many subgraincounts were taken in regions of small deformation, near the edge of the specimen, thusbearing little relationship to the nominal strain rate in the sample. The measured slope,b=0.044, and the intercept, a=-0.686, in the 1/d vs ln(Z) correlation agree reasonablywell with the literature data for aluminium alloys presented in Table 4-14. All otherresults in this Table were obtained by TEM, which included an investigation of the lowerrecovery temperatures and are, therefore, applicable over a wider temperature range.However, the optical observations used in this work provided more data for improvedstatistical reliability. Therefore, both the slope and the intercept are very reliable, asevidenced by their calculated t-criterion exceeding the t-criterion for 99% reliability.Statistical parameters.lid vsln(Z)1/d vs1/TSlope 0.044 2147Standarderror0.006 232t-criterion,calculated7.3 9.25Intercept -0.686 -2.412Standarderror0.145 0.97t-criterion,calculated4.73 2.48Correlationcoefficient0.514 0.646F statistics,calculated49.65 85.58Degrees offreedom47 47critical 7.21 7.21F-criterion3for 99%reliabilitycriticalt-criterion4for^99%reliability2.7 2.710909 -0.3 -0.7 TS 0.60.5-I -•■He-quenchedAir cooled10 min delay•••• IFI 0.4 I[ • •4K• I/ A0.3 - • ♦ I0.2 -• I •■■• • x0 .1^-18^20^22^24^28^28In(Z)a)•+ Helium quencil0.9 - • Ak cool• 10 min. delay0.80.7•0.6^-0.5 -.1•2440.411.•^•1+•A0.3•0.2^-- 0 0••0.1^-00.0012^0.00125^0.0013^0.00135^0.0014^0.00145^0.0015Reciprical temperature^14Cb)Figure 4-31. Correlations between subgrain size, temperature compensated strain rate andtemperature. a) Subgrain size vs Zener-Hollomon parameter (corrected for deformationtemperature rise and using nominal strain rate); b) Subgrain size vs reciprocaltemperature. Each point corresponds to 50 to150 subgrains counted. Measured interval:T=673-823 K, strain rate from 0.05 to 15 /s.3 If the calculated F-criterion exceeds the critical F-criterion value for 99% reliability then with 99%probability the observed high value of correlation coefficient did not occur by chance.4 If the calculated value of t-criterion (ratio of a parameter value to value of its standard deviation)exceeds the critical t-criterion for 99% reliability, then with 99% probability the parameter is significantfor predicting the random variable.110Table 4-14. Dependence of the subgrain size from the temperature compensated strainrate in aluminium alloys (after Wells, 1991).Alloy Temp, K Strain rate, Is a b ReferenceAA1100 473-763 0.05-11.7 -.06 .08 McQueen et al, 1970AA1100 573-823 2 -.2088 .0159 Zaidi et al, 1982AA1100 528-889 0.1-10 -.556 .0656 McQueen et al, 1967AA1100 573-798 1-2 -.2 .01587 Sheppard et al, 1982AA1100 593-889 0.1-10 -.0334 .0545 Jonas et al, 1968AA5456 473-773 not given -.447 .0385 Sheppard et al, 1980AA5083 473-773 0.87-1.6 -3.647 .1370 McShane et al, 1990M575 * 573-773 2 -1.363 .069 Zaidi et al, 19826061/Al203/0-20p673-823 0.05-15 -0.686 .044 Present work*M57S=A1-2Mg-0.26Mn-0.17Si;5456-Al alloy=A1-5.1Mg-0.7Mn-0.18Fe-0.12Cr-0.06Si-0.0012B4.4.3.3. Domain of the Dynamic Recrystallization (DRX)Dynamic recrystallization occurred only in MMCs in the high strain rate - hightemperature region of the processing map (Figure 4-28). The DRX in the6061/Al203/20p and in the clustered regions in the 6061/Al203/10p occurred under thesame strain rate - temperature conditions. However, the fractions recrystallized wasconsistently lower in the 6061/Al203/10p due to presence of the inter cluster regions,where recrystallization was delayed. In Figure 4-28 the differences between thecomposites are averaged in the DRX boundary designated by letter D.An example of DRX in 6061/Al203/10p is shown in Figure 4-32 b.Figures 4 32 b, c show that after deformation to a true strain of 1.2, at a strain rate of 9 /sand high temperatures, limited dynamic recrystallization was visible near the particulatesafter water quenching with a 0.6 s delay. Additional deformation beyond the true strainof 1.2 is expected to produce complete dynamic recrystallization. Thus, at the strain levelemployed (up to 1.2) the transformation in the 6061/Al203/10p at high strain rates andhigh temperatures should be classified as dynamic nucleation and metadynamic growth.Dynamic nucleation of recrystallisation occurs during deformation, while metadynamic111growth proceeds predominantly after deformation. In the 6061/Al203/20p fractiondynamically recrystallized is higher, up to 80% after deformation at T=798 K, at a strainrate of 15 /s and at a strain of 1.2. In this material, the transformation at high strain ratesand high temperatures should be classified as dynamic nucleation and dynamic growth.Only the nucleation stage is considered in this section, while growth is considered in thesection on static effects.From the different recrystallization nucleation mechanisms considered in section2.3.3.1., nucleation in the vicinity of original grain boundaries seems to be supported byFigures 4-30 e and 4-32 a and d. Figure 4-32 a shows the 6061/Al203/10p deformed at723 K, strain rate 2 /s and air cooled. Irregular grain boundaries of the recovered originalgrains indicate grain boundary instability, which, at higher magnifications can be seen inFigures 4-30 c, e and 4-32 d as being associated with bulging of the original GBsoutwards from a well defined subgrain on one side of the boundary. However, thismechanism also operates in the 6061 alloy without causing recrystallization. Therefore, itshould be suggested that another nucleation mechanism is more active in the MMCs. Asdiscussed in section, this other mechanism is thought to be particle stimulatednucleation (PSN).Humphrey's critical strain rate criterion for lattice rotations to occur increaseswith increasing temperature, as indicated schematically in Figure 4-28 by a dash-dot-dotline. In the region to the right of that line lattice rotations and PSN are possible accordingto the criterion. The upper boundary on the DRX domain, imposed by the criterion, wasnot observed in present work because of difficulties associated with machine operationnear solidus. However, to reflect the boundary position, the t50% lines in Figure 4-28 areshown bending to the right at increasing T. Although the kinetics of PSN was not directlyobserved in the present experiments, evidence to support this mechanism was obtained.The initiation of subgrain formation (which is the first stage of nucleation ofrecrystallized grains) in the flow lines around particles (Figure 4-30) agrees with112Humphrey's (1991) predictions. In some cases (Figures 4-27 a, 4-32 d) recrystallizedgrains seem to be clearly associated with large particles. In the clustered materials shownin Figures 4-32 b-d, recrystallized grains nucleate near particles and grow intointercluster regions. Thus, PSN is considered to be a major mechanism introducingrecrystallization in the MMCs studied in this research.The lower boundaries of the recrystallisation domains shown in Figure 4-28 arebelieved to reflect insufficient recovery rates. The reduced recovery does not produce thewell defined subboundaries needed for potential recrystallization nucleation sites.No detailed investigation of MMC processing maps similar to the one presentedin this work has been described in the literature. However, some "stand-alone"observations seem to agree with the presented systematic picture.Castro-Fernandez and Sellars (1988) found that at a strain rate of 5 Is andT>723 K the A1-1.1Mg-lMn-0.48Fe-0.14Si alloy with 5 vol.% of 1.5 p.m particlesrecrystallized during deformation. No dynamic recrystallisation was observed by Shahaniand Clyne (1991) in extruded at 723 K P/M commercial purity Al reinforced with 10 and20% 12 p.m SiC and 10% 12 p.m Al203 (r=16:1, Vram=1.2 mm/s). Dynamic recoveryresulted in retention of the flow lines and —2 subgrain formation. These differentobservations are believed to result from the approximately 0.4% tiny alumina particlesintroduced due to surface oxidation of the powder, which hindered recrystallization.According to McQueen et al., (1984), the Al-5Mg is resistant to recrystallization duringextrusion in the 573-773 K interval. Relatively large (>0.6 p.m) (Fe,Mn)A1 6 particlespresent in the 5083 alloy (A1-4.45Mg-0.74Mn-0.3Fe-0.9Cr-0.15Si) caused dynamicrecrystallisation in torsion tests above 673 K at strain rates of 0.1-1 /s.In the literature there were attempts to quantify the temperature - strain ratedependence of the recrystallized grain size. McQueen et al., (1984) found the size of theDRX grain to vary from 10 p.m at 723 K, ln(Z)=26.9 to 18 pm at 773 K, ln(Z)=24.6.This corresponded to the activation energy Q def=164 idirnol• In the present experiments,. _N 6 -113dFigure 4-32. Dynamic recrystallisation in 6061/Al 203/10p deformed to a strain if 1.2.a) x200. Deformed at 723 K, 2 /s, air cooled. Recovered original grains with irregulargrain boundaries - signs of GB instability; b) x200. Defonned at 823 K, 9 /s, He-quenched. Onset of DRX in clustered regions; c) x100. Deformed at 798 K, 15 /s, waterquenched. Dynamic nucleation and growth; d) x400. The same sample as b). Nucleationnear large insoluble Fe-Si-Al particles and reinforcement. Small new grains surroundedby subgrains that they appeared from are indicated by arrows.114the DRX grain size varied non-systematically and the DRX interval was very narrow;therefore, no similar quantification has been attempted.No visible substructure was found in recrystallized grains (Figure 4-32 c), whileaccording to Zaidi and Wert (1989), dynamically recrystallized grains should possess awell defined substructure. This issue requires further TEM investigation.30 min.delayE 10 min.Lc, delayc00N.,a= Air0c ..).., coolingUNf:Heliumquench 0^0.1^0.2^0.3^0.4^0.5^0.6^0.7^0.8^0.9^1Strainrate, IsLegendHeatingmodeTrue strainT U W V X^Y^ZFractionrecrystallizedT- 0.1 Up-heating I I- OD A 0U- 0.5 Up-heating G J () GI B <10V- 1 Up-heatingW- 2.2 Up-heating 0 Cil c 25X- 6 Up-heating 0 1:11^D 50Y- 6 Down-quenching H M • a E 75Z- 15 Up-heating K N • Ill F 100Figure 4-33. Strain dependence of recrystallisation in the 6061/Al203/15p deformed at773 K and air cooled. Lines are for 50% fraction recrystallized.1154. Critical Strain for RecrystallizationThe 6061/Al203/15p samples were deformed to nominal strains of 0.3, 0.4, 0.6and 1 followed in some experiments by a 10 min. time delay at the deformationtemperature before quenching. For each sample, the strain correction coefficients for thefive points shown in Figure 4-16 were multiplied by the nominal strain in the sample toproduce the true local strain. The fraction recrystallized was assessed in each point.The results for the extent of recrystallisation at a certain strain in differentsamples were very consistent; this indicates that the strain distribution in the sample doesnot change significantly during deformation and that the correction coefficients in Figure4-16, which were derived for a total nominal strain of 1, can be applied to samplesdeformed to other total nominal strains. The points in Figure 4-33 show stages ofrecrystallisation in 6061/Al203/15p samples with various thermomechanical histories.The curved lines correspond to the constant strain rate conditions. All samples were aircooled from 773 K, which, as explained before, is roughly equivalent to an 8 s delay plusquenching. With an increase in the strain rate, the nucleation of recrystallized grainsoccurred earlier. Influence of Matrix Precipitation and RecoveryFigure 4-33 also shows that the down-quenching (cooling in the Gleeble from thesolutionizing temperature 803 K to deformation temperature at a rate 5 K/s) results in theearlier onset of recrystallisation as compared to the up-heating (heating of homogenized,water quenched and naturally aged samples from room temperature to deformationtemperature at a rate of 5 K/s). The following explanation is suggested. In up-heatingtests, the GP zones form during natural ageing; the incomplete reversion (dissolution) ofthese zones during fast heating accelerates P 1 -Mg2Si and 13-Mg2Si formation. On thecontrary, the down-quenching from a higher solutionizing temperature to a deformationtemperature does not allow for GP zone and I3'-Mg2Si formation, delays precipitation of13-Mg2Si and decreases the amount of precipitates in the beginning of precipitation.116Therefore, the precipitate pinning on subgrain boundaries is also decreased, which, inturn, allows for earlier recrystallization nucleation. However, the precipitate coarseningis also delayed, which may retard static grain growth. Not enough data is available tocharacterize the comparative kinetics of simultaneous recrystallization nucleation andprecipitation at both grain nucleation and growth stages. Apparently, the nucleation stageis more important for the overall recrystallization kinetics, because the down-quenchingproduced an experimentally observed extension of the 50% recrystallization domains fordynamic and static recrystallisation to lower strain rates and temperatures (Figure 4-34).The lower precipitate content in the 6061/Al203/20p compared to the 6061/Al203/10p,by analogy with down-quenching, extends the DRX domain for the 6061/Al203/20p (seediscussion of Figure 4-28).As an alternative to a decrease of the pinning force by down quenching, anincrease in a driving force (higher dislocation densities) was achieved for composites bydeformation at lower temperatures where recovery was less intensive. The susceptibilityto recrystallisation also increased; for example, the 50% recrystallisation boundary at798 K expanded from 0.5 to 0.1 /s.The observed effects of precipitation pinning and "colder" pre deformation on thesusceptibility for recrystallization in composites is very similar to their effects onrecrystallization of the 6061 alloy considered in section 4.3.3.The assessment of equations (2.22) and (2.23) give a dislocation energy drivingforce for recrystallization of approximately 20 kPa. For 723 K a precipitate volumefraction, f=0.006 (Table 4-9) and the assessment of the precipitate size, which producesZener drag pressure of the same magnitude, according to equation (2.33), is:d2 .f - 7 5,6GB ' a 2. 0.006 - 0.3 .0.75 = 135 nmprecipitate ^Fp^ 2 .10 4^(4.5)Therefore, to explain the observed effect of precipitation on nucleation ofrecrystallized grains, the maximum precipitate size has to be that given by equation (4.5).T, K8237737238237737231170.05 0.1^0.2^0.5^1^2873 i^I 10^20^50873Legend Fraction Recrystallised, %<10 25«75 >75Boundaries for 50%recrystallization0 0 0^Air coded D,12 0.6 s delayA A A 10 min. delay C, L. 20 s delaytr * *^He or waterquenchedB, f3. 600 s delay0.05^0.1^ 1True strain rate, 1/s10^50Figure 4-34. Extension of recrystallisation domains for 6061/Al203/15p by delayingrecovery or precipitation. Dash-dot lines indicate 50% recrystallisation in up-heating tests(Figure 4-28), Continuous lines indicate 50% recrystallisation in down-quenching tests.Arrow shows heating for a post-deformation anneal to a higher temperature.4.4.4. Mechanical Behaviour of the MMCs44241. mmou_iicw_gcspsnw_to_DRxStress-strain curves for the MMCs produced at strain rates of 1 and 15 /s andtesting temperatures of 573 and 773 K are shown in Figure 4-35. Previousmetallographic analysis has established that at temperatures above 773K and at strain rateof 15 Is dynamic or metadynamic recrystallization have occurred in the MMCs anddynamic recovery in the 6061 alloy; the stress-strain response for these conditions is673623573673623573118shown in Figure 4-35 a. Below 773 K or above 773 K at strain rates below 2 /s dynamicrecovery has occurred in both the MMCs and the 6061 alloy; the stress-strain responsefor these conditions is shown in Figure 4-35 b, c and d. It can be observed from Figure 4-35 that both dynamic recovery (Figures 4-35 b, c and d) and dynamic recrystallization(Figure 4-35 a) produced smooth, steadily increasing stress-strain curve. Dynamicrecrystallisation is generally known to produce a "peak stress" behaviour, as opposed todynamic recovery, which usually produces a smoothly increasing stress-strain curve.In the present experiments, however, due to the inhomogeneity of the strain distributionand, hence, the inhomogeneity of the microstructural evolution in the specimen, nomechanical response reflecting the start of dynamic recrystallization was observed. Theinability of the Gleeble to respond to temperature changes induced by high strain rate andthe strong effect on strength of temperature rise could explain the observed behaviour. Mechanical Response to Precipitation Results of up-heating vs results of down-quenching tests are shown in Figure4-36. Homogenized, water quenched 6061 samples heated (5 K/s) to deformationtemperatures 573-623 K (up-heating results) exhibited a peak stress behaviour (Figure4-35 d; Figure 4-36 b ,c, e). The peak can be explained by pinning of dislocations bysmall f3' or f3—Mg2Si, which precipitated during the up-heating and during pre-deformation holding. The release of pinned dislocations during deformation causes theobserved stress softening. As discussed in section, these precipitates arebelieved to grow from Si clusters which formed during quenching after homogenization,transformed into GP zones at room temperature and incompletely dissolved duringheating. The peak did not appear in the down-quenching experiments, which includedsolutionizing in the machine at 803 K for 1 hour, cooling at 5 K/s to the deformationtemperature and immediate deformation (Figure 4-36 b, c, e). The absence of the peakwas explained by the absence of Si clusters, delayed Mg2Si precipitation and weakdislocation pinning.151030250-• 20PScnN1^12793791 El— 789— 787>^— 785— 763— 781_779— 777— 7757732."eve.",^"z.vr)sza.r.00griorze:v •• ... • • •0.2^0.4^0.6^0.8True strain1000 02 0.4^0.6True strain0.8^ 7600^02^0.4^0.6^0.880 ^70 —SO-504540350790785780775 VE770765-a- 6061/Al203/20p, 773 K, 1/s-4- 6061, 775K, 0.88/s-X- 6061/Al203/15p, 781 K, 0.95 /4- 6061/Al203/10p, 774 K, 1.07 /— Temperature—a— 6061, 778 K. 14.9 /56061/Al203/10p, 781 K, 15.1 /s--n— 6061/Al203/15p, 779 K, 13.4 /s6061/Al203/20p, 783 K, 14.8 /sTemperature— 610—605 6.— 600 20)—595 Ea.)I.-_ 590— 585— 615^250200150100aa- 0-6061/Al203/20p, 591 K, 15 /s-.2-6061/Al203/15p, 598 K, 14.5 Is- 6061/Al203/10p, 597 K, 14.6 Is-A-6061, 593 K,14.8 /s—TemperatureI I^I^I^I^I^II0^0.1 02 0.3 0.4 0.5 0.6 0.7 0.8 0.9True strain119b6061/Al203/15pCC) 13^° ° CO 00 0 0 0 000 000 OD 0O 573K, 1/s• 673K, 1/sX 773K, 1/s• 798K, 1/s•••••••■•••••• • ♦ • AA • AA AA50)00))'/4))))01(0)$))10)=0)))18X0X)40>)*90X>)))•••••••• ••41■41•4■40 ♦ ***NW*00— 58057557002 0.4^0.6True straind0.8Figure 4-35. Mechanical behaviour of the 6061 alloy and the MMCs. Actual temperatureand actual true strain rate for each test is shown in each Figure. The 6061 (a), (b), (c).The 6061/Al203/15p deformed at different temperatures, strain rate 1/s (d).The pinning precipitate size can be assessed from equation (4.3) for pinningpressure on dislocations. By equating the work of external stress for the expanding of adislocation loop and the energy of a dislocation line, the expression (4.6) can be derived.120Neglecting the strength deviation related to the temperature rise during the test (variationin strength due to 5 K temperature change is less than 2 MPa) and taking the stress peaktip equal to 20-25 MPa at T=573-623 K, an assessment of the pinning precipitate size is:G • b • 3117 2.6 .10 • 2 .10 -10 .V0.01r =^ = 28 nm2 . Tp^2 . 20 .10 6(4.6)This assessment is similar in magnitude to the one obtained from the observedinfluence of up- and down-quenching on recrystallization behaviour (equation 4.5).A comparison of Figures 4-36 a and e indicates that the peak stress effect couldbe modified by the machine response at high strain rates; however, in the temperatureinterval T=573-623 K, delayed precipitation always results in a lower strength. With anincrease in temperature to 673 K, the up-heating and down quenching curves becomesimilar (Figure 4-36 f). At 723 K, down-quenching stress-strain curves are even higherthan up-heating curves (Figure 4-36 d, g). That can be explained by the rapid precipitatecoarsening at above 723 K. These effects reflect the C-curve precipitation kinetics of theMg2Si precipitates and require further investigations.In composites, there might be additional effects which eliminate the stress peak indown-quenched samples. Intensive recovery of the "quenched-in" dislocations duringsolutionizing in the machine prior to the deformation temperature decreases the yieldstress of the composite and diffusion rate of Mg atoms. These effects have not beenexamined.Coarsening of precipitates during long holding prior to deformation shoulddecrease the pinning pressure from precipitates and eliminate the peak in up-heatingexperiments. This hypothesis also requires further investigation.50454035gi 30of 25ig 201510501210.802^0.4^0.6True strain^40-II- Up-heating, 599 K, 13 /s--a- Down-quenching, 594 K, 14.6 /s0a•• • • ■•••^•••• • ••• •••••• • • ••-0- Up-heating, 623 K, 0.05 /s-6- Down-quenching, 618 K, 0.05 /80.2^0.4^0.6^0.8Average true strainba180160140JE 120,r 100EX 8060402090807060ri 5°E 4030331000.80^0.2^0.4^0.6True straina• 40N 3°-a- Up-heating, 669K, (los--A- Down-quenching, 672 K, 0.05 /s10Up-heating, 724 K, 0.05 /s-6-Down-quenching, 719 K, 0.05 /s105C403530• 25Si 20• 150.2^0.4^0.6^0.8^1True straind0.6^0.8True straineO0-g 'Up-heating, 673 K, 0.05 Is-6- Down-quenching, 670 K, 0.05 Is0.2^0.4^0.6^0.8^1True strainf0.2^0.4^0.6^0.8^1True straing02^0.4^0.6^0.8True strainh10Figure 4-36. Mechanical response to precipitation. Up-heating vs down-quenching tests.Actual temperature and actual true strain rate for each test is shown in each Figure.The 6061 (a), (b), (c), (d); the 6061/Al203/20p (e), (f), (g), (h).1224.4.5. Static and Metadynamic Recrystallization in the MMCsIn further presentation the terms "dynamic nucleation" (of recrystallized grains)and "dynamic grain growth" (of recrystallized grains) are applied to those processeshappening during deformation. The terms "static nucleation" (of recrystallized grains)and "static grain growth" (of recrystallized grains) are applied to those processeshappening during annealing after deformation. The term "dynamic recrystallization"means dynamic nucleation and significant dynamic grain growth so that fractiondynamically recrystallized is more than 10%. The term "metadynamic recrystallization"means predominantly dynamic nucleation and predominantly static grain growth so thatfraction dynamically recrystallized is less than 10%. The term "static recrystallization"means static nucleation and static grain growth and implies zero fraction dynamicallyrecrystallized.Figure 4-28 indicates that recrystallization occurs in the strain rate interval from0.1 to 15 /s and temperature interval from 723 to 823K. In the interval of strain rates 2-15 /s, the nucleation of recrystallized grains is dynamic (Figure 4-30 e), whereas in theinterval 0.1-1 /s the nucleation is static (Figure 4-32 a). Growth of recrystallized grainsduring deformation is most noticeable at strain rates above 5 /s, so that at a strain rate of10 /s up to 50% of the matrix has recrystallized dynamically, as observed in samplesquenched immediately after deformation (Figure 4-28). However, after deformation at astrain rate of 0.5-5 /s, the growth of recrystallized grains is predominantly static so thatmost of the observed fraction recrystallized is produced during static annealing. Thatstrain rate region includes region of metadynamic recrystallization (from 2 to 5 /s) andpart of the region of static recrystallization ( from 0.5 to 1 /s). The recrystallization in the0.5-5 /s strain rate interval is further quantified.1234.4.5.1. Quantification of recrystallization. The fraction recrystallized was determined from the micrographs of the centralparts of the specimens (these parts underwent strains between 0.9 and 1.2) using a pointgrid area counting procedure (Underwood, 1968). For the 6061/Al203/10p the fractionrecrystallized (X) is plotted as ln(ln( 1/1..x)) vs ln(t) in Figure 4-37. The slope of thecurve represents the n parameter for the JMAK equation (2.17), in this case is n=1.33-1.45. This value can be explained as follows. The as-cast and compressively deformed6061/Al203/10p can be represented as having deformed elongated clusters, where thenucleation starts. The particle stimulated nucleation sites saturate rapidly (see section2.3.3.1) and after that recrystallized grains grow mostly perpendicular to the clusters(Figures 4-32 b and c). That is almost 2D growth (because the clusters are so elongated)where the n value should be approximately 2 (Cahn, 1956). The difference between thisprediction and the experimental results can be explained by the influence of intensiverecovery (section In equation (2.30), recovery lowers n to n•(1-b) (b isintroduced in equation 2.26). For the measured n•(1-b)=1.4 and n approximately 2, avalue of b=1/3 is required. That is in agreement with b=1/3 obtained by Furu et al.(1990) by microhardness measurements on CP aluminum (Figure 2-5). Intensiverecovery also considerably slows the growth rate of recrystallized grains to almost zero.This is consistent with the observation that at strain rates of 0.1 to 0.5 /s recrystallizationis very slow; at 773 K the time for 50% recrystallization is from 10 to 30 min., as shownin Figure 4-28.The application of the JMAK kinetics and the measurement of therecrystallization time exponent, n, permits the calculation of the time for 50%recrystallization, t50%, as shown in equations 2.12 and 2.16. This simplification can donebecause the annealing temperature is the same as the deformation temperature.-3-1I^I^04 5 61.5 —1 —0.5 —..r .....-.■/=..."^-1 ---""C-1.5 --2 —-2.5 —-6-- T_773 K, strain ratel Is--z-- T=773 K, strain rate 2 /s•---- T-773 K, strain rate 6 /s124— 1— 0.9— 0.8— 0.7— 0.6— 0.5— 0.4— 0.3— 0.2— 0.1I I^ I0^ 3In(t)1 2Figure 4-37. Avrami plot for mixed metadynamic/static recrystallization kinetics in6061/Al203/10p.In the temperature-strain rate-microstructure map shown in Figure 4-28, whichwas developed for constant strain conditions, horizontal sections were examined todescribe a constant temperature condition. Thus, the strain rate dependencies for a truestrain of 1.2 at several temperatures were obtained. Similarly, from vertical sections inFigure 4-28, the temperature dependencies for a true strain of 1.2 for several strain rateswere found. Similarly, from the strain-for-initiation-of-DRX map in Figure 4-33, thedependency of taw() on true strain was obtained (movement along each of the Z, Y or Xcurves corresponds to constant strain rate and constant temperature conditions). Fromvertical sections of Figure 4-33, as described in the first step, the strain rate dependenceof t50% was found, for a constant temperature of 773 K at several strains. The results ofsuch calculations are presented in Figure 4-38 and analyzed using equation (4.7).125ICIE11111131111110111111111IXI11011111111E61 I WI-111111b111111111_II MIStrain rate 2/s--.— Strain rate 5/s87^ 7E 5E ,43—0— T=723KT=773A. T-798K065432—a— Strain rate 2.2/s—is— Strain rate 6/s—a— Strain rate 15/s-3^-2^-1^0^1^2^3^0.00125^0.0013^0.00135^0.0014^0.00145In(stra in rate) Reciprocal temperature 1/T, 1/sy5=NMIIESSESIIIIMILIIMEM==MEIMIIMIM131111011gillStrain 0.4--&--MI—0-- Stran 0.66Strain 0.88—1*—KM---.--- Strain 1.28765E 43210-1.5^-1^-0.5In(true strain)0.5 -2^-1^ 0^2In (strain rate)3Figure 4-38. Derivation of parameters for describing recrystallization in 6061/Al203/10p.tso% = 3.1.10' • ez •exp( 293000) ERTwhere x is the strain rate exponent and increases from 1.92 to 2.03 with strain decreasingfrom 1.2 to 0.66;11 is the strain exponent having a value of 5.3.Equation (4.7) is qualitatively the same as equation (2.12) developed byGuttierres et al. (1990). It is applicable only in the mixed region of metadynamic andstatic recrystallization and in the range of parameters where it was derived. This includesstrains of 0.4-1.2, strain rates of 0.5-5 Is and temperatures of 723-788 K. The lower T,and E boundaries for the applicability of this equation are imposed by the paucity of-n(4.7)126recrystallization data obtained beyond these boundaries. The upper strain boundarycorresponds to the maximum strain achieved in present tests. The upper strain rateboundary delineates the region of dynamic recrystallization. The upper temperatureboundary reflects the change in the rate controlling process for dislocation mobility andability to form mobile subboundaries from precipitate pinning below the Mg 2Sidissolution temperature of 778-793 K for the MMCs, to dislocation climb above thattemperature.The results of the present study are compared with literature data in Table 4-15.The higher values of the parameters: x 2 instead of 0.75, Q=293 kJ/mol instead of 180-230 kJ/mol (also Table 2-9) and equal to 5.3 instead of 1.3 could be explained by thepresence of the dynamic recrystallization at the higher temperature-strain rate corner ofFigure 4-28. Equations (2.12, 2.16), on the contrary, describe only purely static effects inwhich fraction recrystallized is zero at t=0.Table 4-15. Parameters of the recrystallization kinetics in the 6061/Al203/p and inaluminum alloys.Material EquationusedStrainrateexponentParametersStrainexponentActivationenergyReferenceX 1 Qdef,kJ/molA1-1Mg-0.16Cu-0.4Fe-0.11Si2.16 1.1 2.7 230 Sellars et al., 1985AA 1100 2.12 0.75 1.3 220 Guttierres^et^al.,19906061/Al201/p 4.9 1.92-2.03 5.3 293 Present work1274.4.5.1. Grain size after recrystallization. Since large particles are very effective at pinning grain boundaries, grains usuallygrow up to an interparticle distance, or up to an intercluster distance in heavily clusteredmaterials. Ideally, if there were no particle clustering, if one grain nucleated at eachparticle and if pinning by the reinforcing particles was strong enough to prevent GBmigration, the grain diameter should be equal to:(1—f ) 3d grain = dparticle^f )In the present experiments, the MMC with the relatively homogeneous particulatedistribution followed equation (4.8). For example, the completely recrystallized6061/Al203/20p obtained after 30 min. annealing after deformation at 6 /s at 773 K hadan average grain diameter of 42+-27 gm. Equation (4.8) predicts an average graindiameter of 26 gm; the difference is thought to be due to particle deviations fromspherical shape and to the initial particle distribution. The latter leaves particle free areasinto which the recrystallized grains grow.McNelley and Kalu (1991) homogenized the particle distribution in a heavilyclustered extruded 6061/Al203/10p by multipass rolling at 723 K, reheating and holdingfor 30 min. at Tdef followed by recrystallization annealing for 1 hour at 803 K after thefmal pass. The resulting grain size decreased from 300 gm (aspect ratio 1.5) in theextruded material to 25-30 gm in the rolled material, in good agreement with equation(4.8).In the present experiments, equation (4.8) did not hold for the heavily clustered6061/Al203/10p. The recrystallized grain size measured in the intercluster regionschanged from 70 to 140 to 230 gm for materials deformed at strain rates 5, 2 and 1 /s,respectively. This can be explained by examining the influence of strain rate onnucleation. At a strain rate of 5 /s "many" nuclei formed and grew during and following128deformation until impingement, whereas at a strain rate of 1 /s, "few" nuclei formed inthe first instances after deformation and then grew into very large grains confined withinthe particle-free intercluster regions.By decreasing the reinforcement particle size, finer grains can be obtained. In anAl/Si3N4/p composite with 1 gm Si3N4 particles, Mabuchi (1991) obtained a 3 gm grainsize, (compared to 2.5 gm grain size predicted by equation (4.8)). which resulted insuperplastic behaviour (480% elongation) in tensile tests conducted at 818 K, i =0.1 /s.The decrease in Si3N4 particle size to 0.2 gm, produced, in spite of some clustering,1 gm grains. This grain size was small enough to further improve superplasticity (620%elongation, i =2 /s, T=833 K).The grain size can also be decreased through multiple nucleation. This theoreticalpossibility was not observed in present experiments.Conclusions1. The as-received 6061/Al203/10p, 6061/Al 203/15p and 6061/Al203/20pmaterials differed in their alumina reinforcement particle size, the degree ofreinforcement clustering and the Mg+Si content in the matrices. The average minimumparticle dimension was 24 gm, 16 gm and 12 p.m for the 20, 15 and 10% particulatereinforced composite, respectively. The degree of clustering, measured as the ratio of theaverage cluster and particle size, varied from 8 to 6 to 2 for the 10, 15 and 20%composites, respectively.2. An approximately 0.5 p.m thick reaction product (reported to be an MgAl2O4spinel) was found at most particle/matrix interfaces. The wavelength dispersionspectroscopy measurements in the 20% composite showed that the Mg content in thematrix decreased by approximately 0.2 wt.% and the Si content decreased by 0.05 wt.%.3. As a result of the lower Mg+Si matrix content, the solutionizing temperaturefor Mg2Si decreased from 803 K for the 6061 to 778-783 K for the 20% composite. Theshortest time for growth of the optically visible precipitates was found between 723 and773 K, which is at least by 100 K higher than the temperature of the "nose" of the C-curve given in literature.4. The strain distribution is inhomogeneous in axisymmetrically compressedcylindrical specimens, with local strains differing by up to a 100% from the averagestrain for the specimen. Optical quantification of the grain aspect ratio permitted thecalculation of local strains at several points in the specimen. These values were only inqualitative agreement with an FEM simulation for a rigid viscoplastic material, but wereconsistent for samples deformed to different average strains. All metallographic data for129130recrystallization analysis were obtained from the part of the specimen where the localstrain approximated the nominal strain.5. In the 6061 Al alloy three distinctly different microstructures were found as afunction of temperature and strain rate. Only deformation flow lines were opticallyobserved below 673 K at strain rates from 0.1 to 15 /s. Above 673 K, dynamic recoverywith optically visible subgrain formation was observed after deformation at strain ratesfrom 0.1 to 15 Is and static recrystallization was observed after deformation at strain ratesfrom 2 to 15 /s. No dynamic recrystallization (nucleation and growth of recrystallizedgrains during deformation) was observed in the 6061 alloy. For the 10 min. annealing atthe deformation temperature after deformation at 773 K, the highest volume fractionrecrystallized of 5% was found after deformation at a strain rate of 15 /s. This isdifferent from observations of t50%=10-30 min. by other researchers on similar materials.The delay of recrystallization in the present work can be explained by the thermal historyof the material. In the present work, fine Mg 2Si particles precipitated during fast heating(5 K/s) to deformation temperature and short (1 min.) pre-deformation holding, whereas,in the other studies the Mg2Si precipitates are believed to have coarsened during longannealing prior to deformation. Coarse precipitates are reported not to pin subboundaries,but to stimulate nucleation. Heating to higher annealing temperatures after deformationwas found to enhance the recrystallization.6. Five distinctly different microstructures were found in the hot deformed 6061Al alloy / alumina particulate composites as a function of temperature and strain rate.Microstructural evolution map (temperature-strain rate-microstructure) was produced fortemperatures ranging from 573 to 823 K and strain rates varying from 0.01 to 15 /s. Thismap includes a region of no optically noticeable dynamic recovery below 673 K. Above673 K, the map includes regions of recovery with optically visible subgrain formation atstrain rates from 0.01 to 10 /s, of static nucleation and growth of recrystallized grainsafter deformation at 0.1 to 1 /s (static recrystallization), of dynamic nucleation of131recrystallized grains and predominantly static growth of these grains after deformationsat 1 to 5 Is (metadynamic recrystallization) and of dynamic nucleation and growth ofrecrystallized grains dining deformation at 5 to 15 /s (dynamic recrystallization).7. At 773 K, dynamic recrystallization was visible after a strain rate of 2 /s in20% composite and after 5 Is in the 10% composite. The enhanced tendency for dynamicrecrystallization in the 20% composite was partially explained by the two times largeraverage reinforcement size and the more uniform reinforcement distribution, ascompared to the 10% composite. The maximum volume fraction of 80% dynamicallyrecrystallized was found in the 20% composite quenched after deformation at 798 K at astrain rate of 15 /s. No dynamic recrystallization was observed in the 6061 alloy in theidentical temperature-strain rate-strain conditions.8. The enhanced recrystallization (both static and dynamic) of the composites wasexplained by Particle Stimulated Nucleation (PSN) and by the lower Mg+Si content inthe matrix; the latter reduces the formation of small pinning precipitates which areknown to restrict recrystallization.9. In the composites, at temperatures from 723 to 788 K, at strains from 0.4 to 1.2and at strain rates from 0.5 to 5 /s, the time, t50%, for 50% recrystallization (static ormetadynamic) was less than 30 min. The recrystallization kinetics in that interval werefound to follow the JMAK equation with n=1.4 for the 10% composite. The discrepancyfrom n=2 for the suggested surface site saturated PSN mechanism was explain byrecovery effects described by equation (2.34). The t50% was best described using anequation of the form:t50% = 3.1.10 -18 • E-x • exp'293000) E-T1\ RTwith x-2 and i=5.3, previously developed by Sellars (1985).13210. Based on the optical observations of both the 6061 alloy and the compositesafter deformation in the 673-823 K interval, the correlation between the subgrain sizeand temperature compensated strain rate was found to be:1 0.686+0.044-1n(Z),in a good agreement with the literature data for aluminum alloys.11. Due to the inhomogeneity of the strain distribution and the associatedinhomogeneity of the microstructural evolution in the specimens, no mechanical responsereflecting the start of dynamic recrystallization (such as a stress peak on the stress-straincurve) was observed. At temperatures above 723 K both dynamic recovery and dynamicrecrystallization produced smooth, steadily increasing stress-strain curves.12. It is proposed that the precipitation of Mg2Si markedly affected the hotdeformation behaviour. The 6061 samples homogenized, water quenched and heated(5 K/s) to the deformation temperatures 573-623 K, exhibited peak stress behaviour inthe stress-strain curve. This was explained by pinning of dislocations by small Mg2Siparticles, which precipitated during heating to and pre-deformation holding (1 min.) atthe deformation temperature. These precipitates are believed to grow from Si clusterswhich formed during quenching after homogenization, transformed into GP zones atroom temperature and incompletely dissolved during heating. In contrast, samplessolutionized in the machine at 803 K for 1 hour, cooled at 5 K/s to the deformationtemperature and immediately deformed did not exhibit the peak stress behaviour. Thatwas explained by the absence of Si clusters and GP zones and the significantly reducedMg2Si precipitation resulting in reduced dislocation pinning. Long annealing atdeformation temperatures before deformation caused coarsening of the Mg2Si, areduction of pinning and did not result in a peak stress behaviour.Future Research Requirements1. In the present research, at the maximum investigated strain of 1.2, strain rate of15 Is and temperature of 798 K, the maximum fraction dynamically recrystallized was80% in the 6061/Al203/20p. It is suggested that at higher strains or strain rates theMMCs may completely dynamically recrystallize. This requires additional research as itrelates to the microstructural evolution during high strains of 3 to 5 in extrusionprocessing.2. The upper temperature boundary of the region of dynamic recrystallization(Humphrey's restriction) has not been observed in the present work due to thetemperature control problems near the solidus and deformation heating at high strainrates. However, the existence of this boundary and its position is both theoretically andpractically important for high temperature processing maps.3. The subgrain size vs temperature compensated strain rate correlation examinedin the present work by means of optical microscopy is in excellent agreement with theliterature data; however, it needs to be validated by TEM work.4. The Mg2Si precipitate size obtained by back-calculation of the initial stages ofthe diffusion controlled growth of these precipitates from the later stages of growth andcoarsening, also requires TEM validation in view of assumed precipitate influence on the"peak" stress mechanical behaviour.5. In the present research, no "peak stress" mechanical behavior was observed inthe region of dynamic recrystallization. That was thought to be due to the inhomogeneityof the strain distribution in the compression specimen. Tensile tests, or tensile tests under133134superimposed hydrostatic pressure (for improved ductility) are required to check thishypothesis.6. The experimentally observed grain aspect ratio in the compressed 6061cylindrical samples exhibited less difference between the aspect ratio obtained in regionsof maximum and minimum deformation than FEM predictions. One suggestedexplanation was that the stress sensitivity of the strain rate used in the constitutiveequation (2.4) was too small. This parameter was obtained by a "best fit analysis" in theinterval of strains, strain rates and temperatures tested so that the strain and strain ratevalues were taken as average for the sample. It is believed, however, that because of thestress being a non-linear function of the strain rate, the integral of stress over the wholeinhomogeneously deformed sample (in FEM) is not equal to the measured value of thestress multiplied by the average sample cross-section. Under the assumption that thereexists a single constitutive equation applicable to the whole range of strain and strain rateconditions obtained in the inhomogeneously deformed sample, it is suggested that moreappropriate parameters for the constitutive equations be determined as follows:a) Find parameters as before and use them as a first approximation;b) Run the FEM to calculate the stress response of he sample to a superimposed(nominal) strain rate;c) Compare the calculated and the experimental stresses and modify theconstitutive equation parameters to get a better fit;d) Repeat the cycle.7. The constitutive equations used for the FEM calculations are derived asmechanical equations of state. They do not account for the thermal history of the materialand its microstructure. A conceptual framework for derivation of more "physicallybased" constitutive equations is suggested in Appendix A.Literature Cited Alpas, A.T., J.D. Embury, D.A. Hardwick and R.W. 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Sci.,17 (1983): 219.Zaidi M.A. and T. Sheppard, Mater. Sci. and Tech., 2 (1986) 938.Zaidi, M.A. and J.A. Wert, "Thermomechanical Processing of Aluminium Alloys." in Treatise onMaterials Science and Technology,  Academic Press, Vol. 31, 1989, 137.141Appendix A. A Conceptual Model for Dynamic Recovery/ Static Recovery and RecrystallizationThe phenomenological descriptions of both microstructural evolution (using theJMAK theory) and mechanical behaviour (constitutive equations) are not completelysatisfactory in that they do not describe in-depth physical processes underlining therecrystallization or mechanical behavior.Constitutive equations were derived as mechanical equations of state (Dieter,1986) 1 . Mechanics does not involve consideration of the energy dissipation and isessentially reversible. This is not the case in deformation processes. Another principalproblem is that stress, strain and strain rate are not similar to the thermodynamicparameters pressure and temperature. In metallurgical language, this means that strain,for example, does not seek equilibrium in different parts of material 2. Thethermomechanical history of the material, including the formation of all kinds of defects,is also not included in constitutive equations, although it affects the mechanicalbehaviour. Subgrain boundaries, for instance, can influence strength according to theHall-Petch equation; diffusional flow of non-equilibrium vacancies can affect matrixcomposition near particles and, therefore, mechanical properties of this region. However,subgrain formation during hot deformation, vacancy generation and all other types ofrecovery are represented in the constitutive equation by one average activation energy.Classic JMAK theory considered nucleation and growth rates in its derivation.Chapter 2 summarizes successful attempts by Furu et al. (1990), Nes and Hutchinson(1989) and Vandermeer and Rath (1990) to relate the growth rate with the dislocationdensity and introduce spatial inhomogeneity and time dependence of the dislocationdensity in static conditions. No attempt, however, was made to indicate physicalmechanisms of dislocation generation or annihilation and to connect the nucleation ratewith the dislocation density. The Monte-Carlo model (Rollett (1992), Humphreys(1992)) was described in section 2.3.5. The model considers an array of points; a randomchange of orientation of a random point changes the total energy of the array; onlyorientation changes producing a decrease of total energy are allowed. The network model(Humphreys, 1992) considers a network of grain boundaries which is seeking to decreaseits total energy by "shrinking" of some boundaries.Under a "physically based model" the microstructure (grain and subgrain size)and mechanical behaviour (stress-strain or stress-steady strain rate) would be describedthrough time evolution of interdependent parameters of dislocation density, vacancyconcentration, grain boundary misorientation, solute concentration, precipitate volumefraction and other "primary" parameters by which the metallurgical state of the materialis described. Since the classic JMAK model, the Monte-Carlo model and the networkmodel do not characterize most of these parameters, they are not physically based.I. "Mechanical Metallurgy", Dieter G.E., McGraw Hill, New York, 1986.2. In fact, residual plastic strain creates residual stresses that tend to relax over time. This relaxationprocess requires sufficient atomic mobility and takes much longer than do externally imposed strains andstresses. Thus, over the typical time of the external stress variation, internal stresses in the material do notequilibrate.142The model of Yada et al. (1987) is partially physically based. It uses thedislocation density as a basic parameter for describing internal stresses and considersdislocation density increase with strain and decrease with time (recovery). The timeevolution of dislocation density, the critical strain for DRX, the fraction dynamically andstatically recrystallized and the size of recrystallized grains are described independentlyfrom each other as phenomenological functions with coefficients dependent on strain,strain rate and temperature. The Trondheim Avrami model. realized on a supercomputer,is also partially physically based. According to Humphreys (1992), it considers up to 10 4potential nucleation sites (any fixed number of nucleation sites is not a "physical"assumption) distributed in any desirable manner. Growth and nucleation rate models areincluded in the model. As an alternative to description of a large number of nuclei andgrains, an approach for describing the mean values of parameters by means of differentialequations was developed by Ghosh (1980) and Lowe and Miller (1984).Ghosh considers the change in mechanical response in cyclical loading of metaldue to internal stresses created by dislocations and their arrangements. Dynamic(dislocation annihilation) and static (subgrain coarsening) recovery were introduced todescribe the time evolution of internal stresses. As a result of dislocation annihilation,internal stresses exponentially approached the flow stress; as a result of subgraincoarsening, internal stresses exponentially approached its unrecoverable value. In bothcases the dislocation density, r, changes as:dp t (A.1)Lowe and Miller consider short and long range internal stresses. The creep strainrate depends on the difference between the applied stress and internal stresses. Short andlong range internal stresses evolve over time, depending on the dislocation densitiesinside subgrains and in subgrain boundaries. These two dislocation densities increaseover time proportional to the difference between the applied and internal stress, and,simultaneously, decrease over time following an Ahrrenius type law. The mathematicalexpression of the model can be found in the paper by Lowe and Miller (1984). Thepresent discussion is a conceptual interpolation of their model which includesprecipitation effects and recrystallization nucleation/growth and a simpler equationformat. All equations describe the rate of approach of a particular parameter to itsequilibrium value as being proportional to the deviation from the equilibrium value.A.1. Driving ForcesThis section describes how, at a given initial stage of precipitation and values ofdislocation density in the grain interiors and dislocation density in subgrain walls, thestatic recrystallization starts and proceeds during annealing. Balances of static recovery,precipitation, recrystallization nucleation and growth are considered. The extent ofnucleation is proportional to the effectiveness of static recovery in creating more mobilehigh-angle subgrain boundaries. The extent of growth is inversely proportional to the rateof recovery, which decreases the dislocation density and, therefore, the driving force forgrowth. Precipitate coarsening decreases precipitate pinning and assists grain growth.The grain growth rate, G, is proportional to the difference between the dislocationdensity driving force, PD, and the Zener drag pressure, Pz:r=m4PD - Pz)^ (A.2)143r=M•(PD — Pz)^ (A.2)The grain boundary mobility term,M h b 2 e, where the activation free•^*energy, AG, for grain growth for the lack of better knowledge can be assumed as equal toQdiffusion or Qdiffusion (1-T/Tmeiting)• Plancks constant, h, and burgers vector, b, aredefined as usual.The Zener pinning force depends on the grain boundary energy, the particlevolume fraction, f, and the particle radius, r:Pz = 74"3^f • 703 • T. (A.3)A.1.1. Precipitation ModelTwo types of particles affect the Zener drag force in the composite materials underinvestigation: the 10-20 p.m alumina reinforcement and the 0.01-2 gm Mg2Si and(Fe,Cr,Mn)SiAl precipitates. The effect of reinforcement can be easily estimated withoutany modeling since it was observed that the grain size stagnates to an average interparticle spacing, 4r/3f (section The (Fe,Cr,Mn)SiAl precipitates do not changetheir size (-2 gm) or shape during heat treatment and exert constant pinning force, whichis relatively small due to their small volume fraction (section 4.3.2) and spacing. Thus,only the 0.01-1 gm Mg2Si precipitates are considered, f being their volume fraction.In the 6061 alloy, f does not exceed 0.6%, but the inter precipitate spacing canalso be very small. As it has been demonstrated by the down-quenching and up-heatingexperiments, the effect of these precipitates on peak flow stress behaviour can be quitesignificant. The model attempts to approximate the limiting conditions of, perfect down-quenching with immediate deformation and perfect up-heating with a long pre-deformation holding time.1. After down-quenching immediate precipitate nucleation is assumed with adiffusion controlled growth rate:df^f dt^tr =^(p • D • t^, with the initial condition f(0)=0^(A.4)where D is the diffusion coefficient and cp is a fractional supersaturation. The exponentialapproach of f to its equilibrium value reflects concurrent decrease of cp to zero. However,tequilib, which determines, how fast the precipitation occurs, is not defined in the model. Itis considered later and can be defined from the experiment.2. The coarsening stage starts in the model after a certain f or r is reached:f = fequb3^3^3r = r +-- Kt^ (A.5)vThe parameter, K, is a complex function of D, T and other parameters. The valueof the parameter v depends on the tails of the particle size distribution (Brown, 1992) and144can in principle be established by the experiment. It seems reasonable to assume that thecoarsening process is not constantly dominated by diffusion controlled growth. Thedissolution of the most closely spaced, smallest particles is of crucial importance for thesubgrain coalescence and for subsequent growth. Two parameters have to be guessedwhen matching the "end" of the diffusion controlled growth and the "start" of coarseningrelationship: firstly, 3*K/v and secondly, the moment when coarsening begins. If thecritical radius of the precipitate (at formation) is assessed to be 5 nm, if the coarseningstarts when the precipitate reaches 50 nm, and if D-10 -13 m2/s, 1,-.2.10-3 in the beginningof precipitation, then K/v should be less than 5.10 -25 .As a result, the combined precipitation model has the following form:df f equilib ) —dt =tequilibdr L • D dt^2 . r^v r 2L = 2 . vC^Cequilib• = 1C equi libf - fequi lib (1 — c eq.„, )r(t = 0) = 5 -10f (t = 0) = 0 (A.6)It should be noted that due to the assumed behavior for f, the precipitation modelis self contained. In fact, dislocations serve as nucleation sites for the precipitates. Thustequilib is dependent on the dislocation density. After running the model, calculations forseveral values of tequilib and K/v can be compared with the TEM observations of r, inorder to define the most reasonable parameter values.The driving force for recrystallization can be expressed via the densities ofdislocations inside the subgrains (equal to the sum of the mobile and immobile dislocationdensities) and dislocations in the subgrain boundaries:it • P sath)* 132 PD =A.2. The recovery processes.This part of the model is equally applicable to static and dynamic stages ofrecovery. The difference occurs only in the dislocation generation.dP mobiledt[= – P mobile a ' VP int ernal • e (Q ) 2-^ e RT )d sub2^ (A.7)The equations for the evolution of each dislocation density are described in thesubsequent section.elinP immobile • b ( 6 external — K 1 Al P int ernal — K 2 A,F7rub p mobile .VP b^ e( Q RT b•b^((A.8)145where the parameters a, 13, 8 (units - m/s) and y (units - m)are subject to fitting; in theabsence of better knowledge a, 13 and 8 may be set to 1 and y may be thought of as anaverage "base length" of the acting dislocation source; drub is the subgrain size. The firstterm if the equation describes the annihilation of mobile dislocation on all internaldislocations; the second term describes the sinking to subgrain boundaries; the third termstands for dislocation generation by bulging of immobile dislocations and is proportionalto the difference of the applied stress and internal stresses both from dislocations andsubboundaries; the last member represents the immobilization of mobile dislocations viaclimb and arrangement into some stable configurations.Recovery also decreases the density of the immobile dislocations in the bulk. It isassumed that this happens via their annihilation only. Immobile dislocations, certainly donot sink to subgrain boundaries and are not generated, but their number can increase dueto immobilization of some mobile dislocations in the immobile dislocation forest:Qannikilaton)dP brtmob  = a Pimmob Pr 1 obile e "^3. P.m.. Pi47nrnob^"dt (A.9)The total amount of dislocations in subgrain boundaries, nsub, evolves due tor annihilation of dislocations within the boundary and also due to sinking of dislocationsfrom the subgrain interiors onto the subboundary. The subgrain size exponentiallyapproaches its equilibrium value.(r2 RT"R; ''b") " P ^ed P sub  =al Psub^e(" ^ddt (A.10)where ppair represents the typical number of dislocations in subgrain boundaries that havea pair dislocation with burgers vector of the opposite sign within the same boundary.Certainly, this is not a very precise treatment, because it does not differentiate betweenedge and screw dislocations. If, on average, the fraction of dislocations that took part insubgrain boundary formation has a pair, then ppair can be written as:2 * • P.biu(T) =C^e(Q7")d(A.11)Hence, the subgrain boundary misorientation angle, 8, can be determined as:e _^ 18011(13s.b^Pp, ;,) (A.12)Initial values of all discussed dislocation densities have to be set at a value differentfrom zero. In an annealed metal typically:P mobile (t = 0 ) = 0P internal^(t = 0 ) = 10 10p pair (t = 0) = 0p sub (t = 0 ) = 10 13^(A.13)Energy ofdislocationinteractionActivation energy forsubGB d' solutionActivation energyfor entrance intosubgrain boundaryDistancedsub , equilbd drub dtd Pbsu dt^VI • tsubgr dissolution(^1Qisfornsatim = a + b • ln E • e RTklY,(d„ — cIsub, „nib )t subgr formation(P sub — °)=146The last equation assumes that the average subgrain diameter is 3 microns with anaverage misorientation angle of 1 degree.The qualitative consequences of the equations written so far are: when recoveryremoves the internal dislocations, ppair becomes constant; therefore, 0 becomes constantas well. The model can be simplified by not considering recovery in subgrain boundaries.This may better reflect subGB dissolution during long annealings, but will lead to anoverestimation of 0. In the model subgrain dissolution is treated further.A.2.1. Subgrain EvolutionThe recovery model is incomplete yet, because the law for subgrain size evolutionis missing. If dislocation density increases drastically during deformation, then formationof the subgrain boundary inside of the initial subgrain may be a faster relaxationmechanism than sinking to the old grain boundaries. Under the assumption that the criticalstage for both competing mechanisms is the climb by —1/2 of the inter-dislocation spacing,it can be shown that new subgrains form when p „ > p • cl,„,2 .For consistency, drub is described in the same manner as f or dislocation densities,so that the rate of restoration of the equilibrium subgrain size is proportional to itsdeviation from the equilibrium value:dsb (t = 0) 0Figure A-1. Interaction of dislocations during subGB formation or dissolution.As the last equation suggests, subgrain size exponentially approaches equilibrium;and time parameter, tsubgr_forntation, determines how fast it happens. An attempt to147calculate this parameter follows. The process of subgrain formation from both mobile andimmobile dislocations involves two major steps, climb (or cross-slip) and sliding (steppingin the dislocation wall). Climb is necessary to space dislocations more or less evenly, whilethe sliding is responsible for putting dislocations into a straight line (Figure A-1). The twoactivation energies shown in the Figure are calculated in literature for several dislocationtypes. The activation energy for climb is assumed to be that for volume heterodiffusion.Now, the tsubgr formation can be expressed via relaxation times of two discussedprocesses:^1 ^1^1 tsubgr formation^tclimb^tsliding^ (A.17)1^b 2tclimb^lip internal • b D (A.18)The first term in (A.17) is the number of jumps to be done during climb, thesecond one is the time of one jumpd.,)^1,,or1^(AG btaiaing = V • (-2)^•^RP internal (A.19)where v is the frequency of diffusion attempts by an individual atom. If the atom isthought of as a harmonic oscillator, then it is making an attempt only when moving in onedirection, towards the barrier; thus, the probability of the right direction is 1/2. If twoindependently fluctuating atoms have to mount the activation barrier together, theprobability of their simultaneous movement in a proper direction is 1/4. The AG is theactivation energy per unit length, which, for the lack of better knowledge, is assumed notto contain any entropy terms and be equal to activation energies shown in Figure A-1. Thelast term in the equation is the squared average "thickness" of the barrier; from Figure A-1it can be seen that this "thickness" is of the same magnitude as the dislocation spacing inthe wall. By analogy, the tsubgr dissolution, which involves only sliding, can be written as:tsubgr dissolutionreinoNtion  a )= v . ('^e RT21 P sub (A.20)It is assumed, that subgrain dissolution starts after a long annealing times, afterrecovery has significantly decreased Pintemal in the bulk and after recovery hassignificantly decreased the number of dislocations in subGBs (ppair•O). As a consequenceof subGB dissolution, the subgrain size increases, and some new dislocations becomemobile:d P bile  = dP sub dt^dtd d,^((I sub — 0) dt^kif • tsubgr dissolutiond p „  = VT, • (P sub — 0 ) dt^subgr dissolution(A.21)(A.22)(A.23)148The equations A.21-A.23 are written following the common assumption that therate of return of a parameter to its equilibrium value is proportional to the deviation fromthe equilibrium. The last equation noes not give a geometric progression, because the timeparameter is rapidly increasing, too.A.3. Nucleation and RecrystallizationA.3.1. Nucleation rateWhen the misorientation angle exceeds, approximately 10° , the subgrain becomesa nucleus. Its growth is described by equation (A.2). The distribution of subgrainmisorientations around an average value, 0, can be assumed as normal, with a standarddeviation of, for instance, 0/2. This allows a nucleation rate Y(t) to be written a rate ofincrease in the number of subgrains having their misorientation angle, 15, exceeding 100 :(151-8 3^d T e l %)Y(t)_ ^d 6,4 .ir • ds,d, dt 0 (A.24)A.3.2. Fraction recrystallizedAs the culmination of the calculations, the volume fraction of recrystallizedmaterial can be obtained, for several annealing times. The usual JMAK equation is usedbut without any restrictive assumptions about nucleation and growth rates:,. (1 i Y (e) j G(r)thr dr1- X(I))= ,^i• (A.25)The goal of the model is to predict the strain, strain rate and temperatureconditions when recrystallization occurs on annealing.A.3.3. Softening due to recrystallization:If growth rate, F, is independent of the grain radius (grain boundary curvature),and in the recrystallized regions all dislocation densities fall to zero, then the ratio of adecrease in the dislocation density to the dislocation density is equal to the ratio of a newlyrecrystallized volume to the total volume. The following two equations consider the casesof "no impingement" and "hard impingement":N2t^ r14 • n •Y(t-.,. ) • JG(z - t * ) • dr^• dt * • G(t)dp — ^r*^. dt ^p1m 3dp^1-edt = P ^ (A.26)1m3r^i r^.2- .14 - r • Y (t * )^f G(r - t * )• dr^- dt * • G(t)0^\t* /These equations can be added to equations A.8 - A.10 with a specific type of dislocationdensity being substituted for p.149Another equation is required to connect the external stress and the microstructurewith the strain rate response. The simplest way to do this is:= p•v•b^ (A.27)A.4.Example CalculationsAs described above, the model includes many assumptions and dozens ofparameters that must be approximated. To obtain some feeling for how the model mightwork, consider the simplest case with only one dislocation density involved, an initialdislocation density equal to 1010 m-2 and constant dislocation velocity. Excluding therecrystallization part, the model is described as:ap = p•(a -Kv-p-)- p-VP . • exp (—QRT )dt= p•v-bwhere p(t=0)=10 10 m-2, K=10, Q=150 Id/ 1, v=103 m/s , b=10-10 m.The integration of these equations produces the following constitutive equation:2 (ln -sri - —1 .1n (I a - exp (4-) - K -Nril = t - consta - exp (-11,-)^Ke (o) = 1000For a given function of the external stress, (JO), equation A-28 can be integratednumerically over time to produce è (t). The thermomechanical history of the materialdetermines p(t) and affects the mechanical response.A.5.Summary.There is no other way to make the constitutive equations reflect the thermohistoryof material except by connecting stress input and strain rate response via themicrostructural state. A model is outlined which is "physically based". Unfortunately, thedescription of each physical process requires long equations and parameterapproximations. After some laws for the microstructural evolution are established, theycan be either modeled on a large (10000) number of sites, or solved simultaneously as asystem of differential equations. The last approach is followed in the present model.Although, the proposed constitutive equations need further development, they have meritin that they consistently based on the assumption that the rate of a parameter restorationto its equilibrium value is linearly proportional to the deviation from the equilibrium value.Another advantage of the proposed model is that both microstructural and mechanicalresponse are directly connected in one model. In an extremely simplified case, the modelcan be analytically integrated to produce a history dependent constitutive equation.Inhomogeneity of stress and strain can be considered by combining the model with FEMsimulations. Some of the model predictions, such as precipitate size and volume fraction,subgrain size and misorientation, dislocation density, grain size and mechanical response,can, in principle, be checked experimentally.(A.28)(A-28)150What the model characterizes: What^the^model^does^notcharacterize:- generation of mobile dislocations, -^probability^distributions^of- dislocation annihilation, parameter values,- sinking of dislocations to existing subGBs, - space non uniformity of parameter- new subGB formation from excess dislocations, values,- dissolution of subGBs during long annealing, - subgrain boundary migration,- formation of nucleus from subGBs, - entropy components in free energy- growth rate of recrystallized grains, terms,- pinning of mobile dislocations by precipitates, -^effect^of^large^second^phase- precipitate diffusion growth and coarsening, particles.- volume fraction of recrystallized material.Symbols:F - velocity of recrystallization boundary, m/s ;M - grain boundary mobility, mkpa• s) ;PD - driving pressure for recrystallization, Pa ;Pz - drag pressure on the moving boundary, Pa;7GB - grain boundary surface energy, J/m2 ;f - current volume fraction of precipitates;r - average radius of precipitates, in m ;fequilib - equilibrium volume fraction of precipitates;L, K, v - do not have clear physical meaning ;41) - fractional supersaturation ;b - burgers vector, in m ;c, cequil - impurity concentration ;a, al, 13, y, 8 - parameters of the model, dimensions are in the text ;p - dislocation densities, in m-2 ;dsub - subgrain size, in m ;Q - activation energies, in kJ ;- fraction of dislocations in subgrain boundaries which have a pair of the opposite sign;8 - misorientation angle, in degrees .CompressiondirectionFlowdirectior50A,0151Appendix B - Quantitative Metallography Programs written for theLeitz Image AnalyzerThree programs in TASIC language were written for the Leitz image analyzer.They are now stored on an 8" disk under their appropriate names. The programs work ininteractive regime and may or may not need manual selection of the objects formeasurements. The first program measures the intercluster or interparticle spacing(depending on magnification) in several directions. The second program measuresparticle/cluster/grain sizes and orientations. The third program measures for each particlethe distance to the closest neighbor. What follows is the description of how the programswork, what commands have to be typed from the keyboard and the program listings, sothat modifications could be done.The programs can be loaded from the 8" diskette. To do this, first find thediskette with the program names on the sticker in the large transparent floppy box, storedon the left of the microscope. Put the diskette into the right drive, DY1, of the computer.After loading a program as explained below, it can be printed out by typing/T, 6on the keyboard. Then put the printer "On-line" and press Enter.B.1. Measurements of the Interparticle SpacingThe program INTER.ILI is measures the intercluster or interparticle spacings inseveral directions, rotated from 0 to 90 degrees from the flow direction (Figure B-1).Figure B-1. Vertical section of the compression specimen.The procedure is as follows (line numbers are given for the listing):- the program generates equally spaced set of parallel lines (lines 37-41);- the image is rotated by 90/n degrees, where n is the number of directionsthat you requested (lines 80-81);- the image is "detected" so that clusters or particles become black, andintercluster spaces remain white (lines 82-86);152- the program checks the size of each particle (line 93) or cluster anddiscards those which area is less then total area of the screendivided by 20000 (as defined in line 33). Particles that are smaller thanthis are believed to be "noise";- the program intersects the set of parallel lines and the "detected" image(line 99-104) and leaves only the pieces of lines lying within the matrix.- pieces, touching the frame are discarded (line 102);- the length of each of these pieces is measured (line 108);- all length measurements are sorted in line 30 into the predeterminednumber of classes (lines 113, 114).flow to make input and obtain output? 1. Put the sample onto the stage of the microscope so that the flow direction isparallel to the long side of the stage. Chose the proper objective lens. It should be *8 forintercluster spacing measurements, as defined by auto focusing procedure in line 70. Thislowest magnification (_*50) yields the lowest error, because fewer long lines touchingthe frame are discarded. For measurements of the interparticle spacing, a magnificationof *200 is more appropriate. For this purpose the *32 lens should be used, and the line 70should be changed into FOC 932,113 . For editing the program, read the Leitz manual.The calibration number should be increased by the same proportion as the magnification.2. Turn on the key on the right of the screen and input the date e.g.: 11-mar-99.3. Press the "stage" button on the function box and move the sample under theobjective by using corresponding arrows. Be sure there is enough space to the left of thelight spot if you want to position several frames on the sample (see below).4. Press the "light" button and then press the "up" arrow until the light intensitycomes to about 580.5. Now focus the microscope, touching only the large focusing wheel.6. Now turn on the "light" button again and press the "*" button. The lightintensity will adjust automatically somewhere around 580.7. Now switch off all lights on the function box.8. Load the program by typing:AJ,DY1:INTER.ILI9. Execute the program in the operating memory by typing:/EWait 15 seconds, until the program invites you by writing Specimen on the screen.Type the name of your specimen, up to 12 symbols. Press Enter.10. Press Enter once more.11. Enter calibration 760. This number is the distance in microns from the leftyellow border on the screen to the right yellow vertical border on the screen.12. Now enter the number of frames. It is better to start better from 1 and checkhow fast the program works. After you input the number of frames, the stage will moveto the end point making 2 steps along the flow direction per one step in the compressiondirection. If the final point resides within the sample, answer "1" to the questionMeander End: OK? If it so happened that the end point is off the specimen, you have torestart the program by pressing CTRL + C. Start again from the step 3.15313. Enter Maximum intercluster spacing; this is the upper limit for sorting of themeasured intercluster spacings. Then enter Number of classes.14. Enter up to 9 answering, How many angles in 0-90 degree interval?15. Being prompted for detection, press button "detection" on the function box. Itis reasonable to set position 7 and window 18-20. Try to repeat the numbers for bettercomparability of different measurements. Be sure, your sample is still in focus, adjustfocus manually if required. Now press "Enter" to run the program further.16. Now you can leave for a while. Normally, it takes 2-3 minutes to analyze 1image. If you ordered 20 frames, 9 angles, the program will need2minlimage*(9+1)images/frame*20frames=6.5 hours.17.After accomplishing the task, the program will ask: Next frame, Intermediateresult or Stop? If you enter "next frame", it will go to the next frame, otherwise it willprint out the results available at that moment. Be sure the printer is "On Line".18. Then you will be offered New measurement, New specimen or Continue.The "new specimen" answer will end the program and all data not printed will be lost.A "New measurement" answer will also cause the loss of all acquired data. If you answer"Continue", the program will return to the previous menu.B.2. Particle Size and Orientation DistributionThe program ORIEN.ILI is measures the following parameters, designated bynumbers, which are also explained in the printout:1-particle area, in square microns;2-maximum particle diameter, in microns;3-minimum particle diameter, in microns;4-aspect ratio,5-angle between maximum particle dimension and flow direction in the sample;6- the same as 5, but for particles with an aspect ratio>2.The procedure is as follows:- the image is "detected" so that clusters or particles become black, andintercluster spaces remain white (lines 52-56);- the prism is rotated by 90 degrees to make the flow direction correspondto the vertical direction on the screen (which is assumed to be the 0direction by the computer; insert before line 59).- the program selects individual particles or clusters and measures theirarea. If this area is less than the threshold limit set in lines 43,44 (1/300of the total screen area) then the program discards this particle. This isdone because particles that are too small may be pieces of broken largeparticles or pieces of diamond embedded during polishing. Therefore,they are believed to be "noise";- the maximum and minimum particle dimensions are measured in thefollowing way: 12 lines separated by 15° are generated starting from 0°in the 0-180° interval. Then 12 corresponding projections of a selected154particle are measured, and the maximum and minimum of them areselected. Certainly, this is not a very precise procedure, but that's whatthe computer can do;- thus, the program output of parameters 5 and 6 has to be understoodin the following way: 7 particles in the parameter range 0-152 means infact that for 7 particles the maximum dimensions are lying exactly at 02to the flow direction. The next rows have to be understood as givingthe number of particles which have max. dimensions lying at exactly 15,30, 45, 60, 75, 90, 105, 120, 135, 150 and 165 degrees from the flowdirection. All data corresponding to parameters >180 ° should be ignoredbecause 180° is the same as 0°. The author should apologize for suchpoorly organized output, but, this is due to the limitations of accessibleRAM - only 6.3 kilobytes;- all length measurements are sorted in line 36 into the predeterminednumber of classes (lines 114, 122).flow to make input and obtain output?1. Put the sample onto the stage of the microscope so that the flow direction isparallel to the long side of the stage. Chose the proper objective lens. It should be *80, asdefined by the auto focusing procedure in line 76. This magnification (--*500) yields thelowest error in measurement, because it allows the best separation of the touchingparticles.2. Turn on the key to the right of the screen and input the date e.g.: 11-mar-99.3. Press the "stage" button on the function box and move the sample under theobjective by using corresponding arrows. Be sure there is enough space to the left of thelight spot if you want to position several frames on the sample (see below).4. Press the "light" button and then press the "up" arrow until the light intensitycomes to about 680.5. Now focus the microscope, touching only the large focusing wheel.6. Now turn on the "light" button again and press the "*" button. The lightintensity will adjust automatically somewhere around 680.7. Now switch off all lights on the function box.8. Load the program by typing:/tJ,DY1:0RIEN.ILI9. Execute the program in the operating memory by typing:/EWait 15 seconds, until the program invites you by writing Specimen on the screen.Type the name of your specimen, up to 12 symbols. Press Enter.10. Press Enter once again.11. Enter calibration 85. This number is the distance in microns from the leftyellow border on the screen to the right yellow vertical border on the screen.12. Now enter the number of frames. It is better to start from 1. After you inputthe number of frames, the stage will move to the end point making 1 step along the flowdirection per 1 step in the compression direction. If the final point resides within thesample, answer "1" to the question Meander End: OK? If it so happened that the end155point is off the specimen, you have to restart the program by pressing CTRL + C. Startagain from the step 3.13. Enter Maximum particle size; this is the upper limit for sorting of themeasured particle sizes. Then enter Number of classes.14. Being prompted for detection, press button "detection" on the function box. Itis reasonable to set position 7 and window 18-20. Chose your own limits if you wish, buttry to repeat some numbers for better comparability of different measurements. Be sureyour sample is still in focus, adjust focus manually if required. Now press "Enter" to runthe program further.15. The program will move to the next frame and focus automatically. Then itwill give control to the pen and pause its execution. With the pen you can press"CONTOUR" on the left side of the screen, draw a line and then either add or erase thecontent of the figure surrounded by this line. Press "ADD" or "ERASE" respectively.This will also switch off the CONTOUR mode. If you made an error and pressed "ADD"or "ERASE" before pressing "CONTOUR", then press "DRAW/SELECT END" toswitch these modes off and be able to turn on the "CONTOUR" again. Do this operationsas many times as necessary. Your last command should be "ADD" or "ERASE". Nowpress the "END PEN CONTROL" in the right bottom edge of the screen. This will runthe program further.16.Wait 1-2 minutes until the program will go to the next frame and repeat step 15.17. After accomplishing the task, the program will ask: Next frame, Intermediateresult or Stop? If you enter "next frame", it will go to the next frame, otherwise it willprint out the results available at a moment. Be sure the printer is "On Line".18. Then you will be offered New measurement, New specimen or Continue.The "new specimen" answer will finish the program and all data not printed will be lost."New measurement" answer will also delete all acquired data. If you answer "Continue",the program will return to the previous menu.B.3. Distance to the Closest Neighbor MeasurementsThe program PARTI.ILI measures the distances from one particle to its closestneighbor and produces a histogram which should be processed further by the user. Beforerunning this program you need to know the average particle size, presumably measuredwith the program ORIEN.ILI. For example, for the three composite materials underinvestigation, namely the 6061 reinforced with 10%, 15% and 20% alumina, the averageparticle areas of alumina particles are 56, 109 and 220 sq. gm respectively.The procedure is as follows:- the image is "detected" so that clusters or particles become black, andintercluster spaces remain white (lines 42-46);- the program focuses automatically on the selected frame (lines 64-75);- the program selects individual particles or clusters and measures theirarea. If this area is less than the threshold limit set in lines 35,36 (1/5000of the total screen area) then the program ignores the particle (line 97).This is done because particles that are too small may be pieces of156broken large particles or pieces of diamond embedded during polishing.Therefore, they are believed to be "noise";- if the particle size is larger than twice the average particle area, it isassumed to be a cluster, therefore its area is divided by the averageparticle area to give the number of particles in the cluster, and it isfurther assumed that all the particles in the cluster touch each other(the distances between them are set to zero, lines 98-100). It is realizedthat this approach has a lot of flaws, but applied consistently, it canquantify the difference between, for example, as cast materials withstrong clustering and deformed material, where some clusters are broken;- if the particle size does not exceed twice the average, than a sufficientlylarge hexagon is ascribed around it (lines 108-110). All particles thatfall into this hexagon are considered in the next step;- the distance between the center of gravity of each particle and itsneighbor measured (lines 122-145). Then, from the part of the distancelying beyond the initial particle boundary, the equivalent diameter of theneighbor is subtracted. The result is taken to be the interparticledistance;- all length measurements are sorted into the predetermined in line 31number of classes (lines 114, 122).How to make input and obtain output?1. Put the sample onto the stage of the microscope so that the flow direction isparallel to the long side of the stage. Chose the proper objective lens. It should be *32, asdefined by the auto focusing procedure in line 76. This magnification (_*200) yields thelowest error in measurement, because it allows the best separation of the touchingparticles on one hand, and the visibility of a sufficient amount of neighbor particles, onthe other.2. Turn on the key to the right side of the screen and input the date in a formated., : 11-mar-99.3. Press the "stage" button on the function box and move the sample under theobjective by using corresponding arrows. Be sure there is enough space to the left of thelight spot if you want to position several frames on the sample (see below).4. Press the "light" button and then press the "up" arrow until the light intensitycomes to about 650.5. Now focus the microscope, touching only the large focusing wheel.6. Now turn on the "light" button again and press the "*" button. The lightintensity will adjust automatically somewhere around 650.7. Now switch off all lights on the function box.8. Load the program by typing:/U,DY1:PARTI.ILI9. Execute the program in the operating memory by typing:/EWait 15 seconds, until the program invites you by writing Specimen on the screen.Type the name of your specimen, up to 12 symbols. Press Enter.15710.Press Enter once again.11.Enter calibration 180. This number is the distance in microns from the leftyellow border on the screen to the right yellow vertical border on the screen.12.Now enter the number of frames. After you input the number of frames, thestage will move to the end point making 1 step along the flow direction per 1 step in thecompression direction. If the final point resides within the sample, answer "1" to thequestion Meander End: OK? If it so happened that the end point is off the specimen, youhave to restart the program by pressing CTRL + C. Start again from the step 3. Theprogram is slow due to the limited 6.4K memory available for it.13.Enter Maximum interparticle spacing; this is the upper limit for sorting ofthe measured particle sizes. Then enter Number of classes. Input the average particle sizemeasured by ORIEN.ILI (see also, the first paragraph of this description).14.Being prompted for detection, press button "detection" on the function box. Itis reasonable to set position 7 and window 18-20. Chose your own limits if you wish, buttry to repeat some numbers for better comparability of different measurements. Be sure,your sample is still in focus, adjust focus manually if required. Now press "Enter" to runthe program further.15.The program will move to the next frame and focus automatically.16.The program will spend from 10 to 20 minutes on a frame with 50 particles.17.After accomplishing the task, program asks: Next frame, Intermediate resultor Stop? If you enter "next frame", it will go to the next frame, otherwise it will print outthe results available at that moment. Be sure the printer is "On Line".18. Then you will be offered New measurement, New specimen or Continue.The "New specimen" answer will finish the program and all data not printed will be lost.The "New measurement" answer will also delete the previously acquired data. If youanswer "Continue", the program will return to the previous menu.


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