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Rotary forming of cast aluminum Roy, Matthew J. 2013

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Rotary Forming of Cast AluminumbyMatthew J. RoyB.E.Sc., The University of Western Ontario, 2005M.E.Sc., Engineering Science, The University of Western Ontario, 2007A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE STUDIES(Materials Engineering)The University Of British Columbia(Vancouver)August 2013c? Matthew J. Roy, 2013ABSTRACTThe application of rotary forming to A356 offers a potential improvement in material use, simpli-fied castings and ameliorated fatigue resistance. To investigate the utility of adopting this processindustrially, an extensive characterization and modelling effort was undertaken.The constitutive behaviour of A356 in the as-cast condition was assessed with compressiontests performed over a range of deformation temperatures (30-500?C) and strain rates (?0.1-10s?1). The flow stress as a function of temperature and strain rate was quantified via an extendedLudwik-Hollomon and Kocks-Mecking framework.The through-process microstructural effects on A356 subjected to rotary forming at elevatedtemperatures was also investigated. This was conducted on material at 350?C with an industrially-scaled, purpose-built apparatus, inducing varying levels of spinning deformation. This was alsoconducted on commercially flow formed material with high levels of deformation at the same tem-perature. Macro and micro-hardness testing was used to track the changes from the as-cast andas-formed states, as well as following a T6 heat treatment. Further EDX analysis indicate that pre-cipitation aspects of heat treatment is not appreciably affected by forming. Forming was found toprincipally affect the eutectic-Si particle size, resulting in a finer particle post heat treatment.An explicit finite element rotary forming model reciprocating experimental forming conditionswas developed incorporating the Ludwik-Hollomon description. This forming model was foundto be computationally expensive; however, demonstrated reasonable agreement with experimentalgeometry and phenomena.In evaluating the effect of forming on fatigue, multiaxial testing of A356-T6 was conductedto apprehend the basic fatigue mechanisms. Endurance limits are found to be generally governedby porosity and maximum principal stress for high cycle fatigue. Uniaxial fatigue tests of bothexperimentally and commercially formed material showed a 30% increase in endurance limits overunformed material, principally through mitigating porosity.iiPREFACEThe following journal submissions have been extracted from the body of work presented in thisdissertation. My supervisor, Prof. Daan Maijer provided experimental insight, results interpretationand editorial support covering all aspects of my research. Aside from my supervisor, and keysecondary contributors, I am the primary contributor to these works:1) Roy M. J., Nadot Y., Maijer D. M., Benoit G., ?Multiaxial Fatigue Behaviour of A356-T6?,Fatigue and Fracture of Engineering Materials and Structures, (2012)2) Roy M. J., Maijer D. M.,?Modeling of As-Cast A356 for Coupled Explicit Finite ElementAnalysis?, Light Metals 2012, (2012)3) Roy M. J., Maijer D. M., Dancoine L.,?Constitutive behaviour of as-cast A356?, MaterialsScience & Engineering, (2011)4) Roy M. J., Nadot Y., Nadot-Martin C., Bardin P.-G., Maijer D. M., ?Multiaxial Kitagawaanalysis of A356-T6?, International Journal of Fatigue, 33 (2011) 823-832Prof. Yves Nadot provided experimental insight, support editorially and in interpretation ofresults for items 1 and 4. Guillaume Benoit provided technical assistance with the experiments foritem 1. Louise Dancoine provide technical assistance in completing the experiments and resultsinterpretation for item 3. Prof. Carole Nadot-Martin and Pierre-Guillaume Bardin provided resultsinterpretation for item 4.Chapter 2 contains material from items 1, 3 and 4. Chapter 3 is based on material drawn fromitem 3. Chapter 5 contains material from item 2. Chapter 6 contains material drawn from item 1and 4. These chapters contain footnotes mirroring the above information.iiiTABLE OF CONTENTSAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiNomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Structure of Al-Si-Mg casting alloys . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Heat treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2.1 Solution treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2.2 Quenching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2.3 Artificial ageing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3 Mechanical properties of Al-Si-Mg alloys . . . . . . . . . . . . . . . . . . . . . . 81.3.1 Effect of DAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3.2 Hardness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.3.3 Behaviour at elevated temperatures . . . . . . . . . . . . . . . . . . . . . 141.4 Fatigue behaviour of A356 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.4.1 The role of defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.4.2 Behaviour in defect-free material . . . . . . . . . . . . . . . . . . . . . . 181.5 Rotary forming and related processes . . . . . . . . . . . . . . . . . . . . . . . . . 191.5.1 Experimental studies of rotary forming . . . . . . . . . . . . . . . . . . . 231.5.2 Finite element analysis of rotary forming . . . . . . . . . . . . . . . . . . 251.6 Scope and objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291.6.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291.6.2 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31iv2 Experimental methods and apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . 332.1 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.1.1 Material employed in constitutive behaviour analysis . . . . . . . . . . . . 352.1.2 Castings used for experimental forming . . . . . . . . . . . . . . . . . . . 352.1.3 Material employed in multiaxial fatigue behaviour . . . . . . . . . . . . . 362.1.4 Commercially formed material . . . . . . . . . . . . . . . . . . . . . . . . 392.2 Experimental forming apparatus and methodology . . . . . . . . . . . . . . . . . . 412.2.1 As-received lathe and modification overview . . . . . . . . . . . . . . . . 412.2.2 Rotary tooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.2.3 Roller and tool stand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442.2.4 Heating system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452.2.5 Rotary DAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462.2.6 Experimental forming methodology . . . . . . . . . . . . . . . . . . . . . 462.3 Material characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502.3.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512.3.2 Optical microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512.3.3 SEM techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522.3.4 Hardness testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552.3.5 Compression testing methodology . . . . . . . . . . . . . . . . . . . . . . 562.3.6 Fatigue testing methodology . . . . . . . . . . . . . . . . . . . . . . . . . 593 Constitutive behaviour of as-cast A356 . . . . . . . . . . . . . . . . . . . . . . . . . . 623.1 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.2 Constitutive equation development . . . . . . . . . . . . . . . . . . . . . . . . . . 673.2.1 Extended Ludwik-Hollomon . . . . . . . . . . . . . . . . . . . . . . . . . 683.2.2 Kocks-Mecking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693.3 Comparison of constitutive expressions . . . . . . . . . . . . . . . . . . . . . . . 733.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744 Characterization of rotary formed material . . . . . . . . . . . . . . . . . . . . . . . 764.1 Microstructure and hardness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.1.1 Experimentally formed material . . . . . . . . . . . . . . . . . . . . . . . 774.1.2 Commercially formed material . . . . . . . . . . . . . . . . . . . . . . . . 824.2 Effects of processing on microstructure . . . . . . . . . . . . . . . . . . . . . . . 854.2.1 Hardness observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 854.2.2 Microstructural observations . . . . . . . . . . . . . . . . . . . . . . . . . 874.2.3 Eutectic particle shape and size . . . . . . . . . . . . . . . . . . . . . . . 904.3 Phase-specific effects of processing . . . . . . . . . . . . . . . . . . . . . . . . . 924.4 Surface defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 944.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 975 Mathematical modelling of rotary forming . . . . . . . . . . . . . . . . . . . . . . . 995.1 Coupled thermomechanical EFA model development . . . . . . . . . . . . . . . . 1005.1.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1015.1.2 Material properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1025.1.3 Initial conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1055.1.4 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1065.2 Material model validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109v5.2.1 Mechanical validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105.2.2 Thermal assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1115.2.3 Effects of time and mass scaling . . . . . . . . . . . . . . . . . . . . . . . 1125.2.4 Maximum scaling factor . . . . . . . . . . . . . . . . . . . . . . . . . . . 1165.3 Preliminary rotary forming modelling . . . . . . . . . . . . . . . . . . . . . . . . 1175.3.1 Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1175.3.2 Mechanical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1195.3.3 Computational requirements . . . . . . . . . . . . . . . . . . . . . . . . . 1205.4 Thermomechanical EFA modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 1215.4.1 Model results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1225.4.2 Geometric comparison to experimental results . . . . . . . . . . . . . . . . 1295.4.3 Surface defect formation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1335.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1346 Fatigue behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1366.1 Multiaxial fatigue characterization . . . . . . . . . . . . . . . . . . . . . . . . . . 1366.1.1 Fatigue test conditions and results . . . . . . . . . . . . . . . . . . . . . . 1376.1.2 Fatigue criteria comparison encompassing natural defects . . . . . . . . . 1376.1.3 Fracture surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1416.1.4 Initiation site observations . . . . . . . . . . . . . . . . . . . . . . . . . . 1436.1.5 Kitagawa analysis of natural and artificial defects . . . . . . . . . . . . . . 1466.1.6 Implications for rotary formed material . . . . . . . . . . . . . . . . . . . 1496.2 Fatigue characterization of rotary formed material . . . . . . . . . . . . . . . . . . 1506.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1537 Conclusions and future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1557.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1557.1.1 Constitutive behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1557.1.2 Rotary formed material characterization . . . . . . . . . . . . . . . . . . . 1567.1.3 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1567.1.4 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1577.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159Appendix A Pyramidal hardness measurements . . . . . . . . . . . . . . . . . . . . . . 170A.1 Relevant formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170A.2 Hardness test methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171A.3 Hardness measurement validation . . . . . . . . . . . . . . . . . . . . . . . . . . 171Appendix B Conversion of ball-type to pyramid hardness values . . . . . . . . . . . . 173viLIST OF TABLESTable 1.1 Various literature compositions and T6 schedules . . . . . . . . . . . . . . . . . 9Table 1.2 Coefficients for property-DAS relationships . . . . . . . . . . . . . . . . . . . . 10Table 1.3 Relative microstructural effects on mechanical properties . . . . . . . . . . . . 12Table 2.1 Composition (%-wt) of modified A356 . . . . . . . . . . . . . . . . . . . . . . 33Table 2.2 Microstructure summary of material employed in the fatigue study . . . . . . . 38Table 2.3 List and description of EFA experiments . . . . . . . . . . . . . . . . . . . . . 50Table 2.4 Fatigue test equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Table 3.1 Compression test characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . 63Table 3.2 Values of fitted coefficients in each material model . . . . . . . . . . . . . . . . 73Table 4.1 Eutectic particle statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Table 5.1 Thermal properties of A356 & AISI?4320 . . . . . . . . . . . . . . . . . . . . 105Table 5.2 Simulation execution acceleration due to time and mass scaling . . . . . . . . . 115Table 5.3 Computational properties of preliminary simulations . . . . . . . . . . . . . . . 121Table 6.1 Test history of all A356?T6 multiaxial fatigue specimens . . . . . . . . . . . . 138Table 6.2 Runout testing summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150Table 6.3 AC-T6 versus formed-T6 Basquin relationships . . . . . . . . . . . . . . . . . . 152Table A.1 ASTM E92-82 repeatability of machines . . . . . . . . . . . . . . . . . . . . . 172Table B.1 HV to HRF and HB conversion coefficients . . . . . . . . . . . . . . . . . . . . 173viiLIST OF FIGURESFigure 1.1 A356 microstructure in the as-cast (AC) condition . . . . . . . . . . . . . . . . 3Figure 1.2 Secondary DAS and grain size versus cooling rate . . . . . . . . . . . . . . . . 5Figure 1.3 Mg2Si in ?-Al pseudo-binary phase diagram . . . . . . . . . . . . . . . . . . 6Figure 1.4 ?y, ?u and ? f versus DAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Figure 1.5 Brinell hardness versus aging conditions and Fe content for A356 . . . . . . . 13Figure 1.6 Yield strength versus Rockwell-F hardness . . . . . . . . . . . . . . . . . . . 14Figure 1.7 A356 flow stress and fracture strain derived from torsion deformation . . . . . 15Figure 1.8 DAS and HIP effects on AC-A356 fatigue life . . . . . . . . . . . . . . . . . . 17Figure 1.9 DAS effect on A356?T6 fatigue properties . . . . . . . . . . . . . . . . . . . . 18Figure 1.10 Spinning process classifications . . . . . . . . . . . . . . . . . . . . . . . . . 20Figure 1.11 Typical spinning defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Figure 1.12 Flow forming configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Figure 1.13 Experimental cast aluminum rotary forming apparatus . . . . . . . . . . . . . 24Figure 1.14 Yield and ultimate tensile stress improvement due to spinning . . . . . . . . . 25Figure 1.15 FEA description of forming after Xu et al. [1] . . . . . . . . . . . . . . . . . . 27Figure 1.16 Outline of research conducted . . . . . . . . . . . . . . . . . . . . . . . . . . 31Figure 2.1 Wedge casting apparatus and geometry . . . . . . . . . . . . . . . . . . . . . 34Figure 2.2 Typical microstructure of compression test specimens . . . . . . . . . . . . . . 35Figure 2.3 Blank cross-section employed in forming trials . . . . . . . . . . . . . . . . . 36Figure 2.4 Multiaxial fatigue specimen locations . . . . . . . . . . . . . . . . . . . . . . 37Figure 2.5 Typical microstructure of multiaxial fatigue specimens . . . . . . . . . . . . . 38Figure 2.6 Blank versus formed cross-section geometry . . . . . . . . . . . . . . . . . . 40Figure 2.7 Commercially formed T6 microstructure . . . . . . . . . . . . . . . . . . . . 40Figure 2.8 Main lathe components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42Figure 2.9 Rotary tooling details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Figure 2.10 Roller and tool stand detail . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Figure 2.11 Heating system detail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Figure 2.12 Rotary DAQ detail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Figure 2.13 Mandrel and blank temperatures recorded during blank preheat . . . . . . . . . 48Figure 2.14 Initial and final cross-sectional geometries of deformed workpieces . . . . . . 50Figure 2.15 Example DAS measurement technique . . . . . . . . . . . . . . . . . . . . . . 53Figure 2.16 Example of automated pore measurement . . . . . . . . . . . . . . . . . . . . 53Figure 2.17 Example of eutectic particle aspect ratio measurements . . . . . . . . . . . . . 54Figure 2.18 Example of manual defect measurement . . . . . . . . . . . . . . . . . . . . . 54Figure 2.19 Hardness profiling apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Figure 2.20 Hardness profile mesh and typical indentation field detail . . . . . . . . . . . . 57viiiFigure 2.21 Depiction of the compression testing apparatus . . . . . . . . . . . . . . . . . 58Figure 2.22 Fatigue specimen types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Figure 3.2 Comparison of experimental flow stress to constitutive expressions . . . . . . . 66Figure 3.3 Extended Ludwik-Hollomon coefficients plotted versus temperature. . . . . . . 69Figure 3.4 Compression test work hardening rate vs. flow stress . . . . . . . . . . . . . . 71Figure 3.5 Saturation and yield stresses versus normalized activation energy g . . . . . . . 72Figure 4.1 ?y to HV relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Figure 4.2 Hardness profiles of AC blank sections . . . . . . . . . . . . . . . . . . . . . . 78Figure 4.3 Comparative hardness profiles of as-deformed axial sections . . . . . . . . . . 79Figure 4.4 DAS measurements of experimentally formed material . . . . . . . . . . . . . 80Figure 4.5 Eutectic distribution in the least deformed EFA workpiece . . . . . . . . . . . . 81Figure 4.6 Comparative hardness profiles of deformed-T6 axial sections . . . . . . . . . . 83Figure 4.7 Commercially formed material hardness profiles . . . . . . . . . . . . . . . . 84Figure 4.8 DAS measurements of commercially formed material . . . . . . . . . . . . . . 84Figure 4.9 HV5 results of AC specimens held at various temperatures and times . . . . . . 87Figure 4.10 Eutectic particle morphology of undeformed specimens held at various temper-atures and times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Figure 4.11 Eutectic particle morphology of as-deformed and deformed-T6 material . . . . 90Figure 4.12 Probability density functions of eutectic particle characteristics . . . . . . . . . 92Figure 4.13 Comparitive microhardness results of ?-Al phase and eutectic . . . . . . . . . 93Figure 4.14 Surface fracture of mid deformed material . . . . . . . . . . . . . . . . . . . . 95Figure 4.15 Surface fracture of peak deformed material . . . . . . . . . . . . . . . . . . . 96Figure 5.1 2D mesh of the blank and mandrel employed for preheating simulations . . . . 102Figure 5.2 Workpiece mesh employed for forming simulations . . . . . . . . . . . . . . . 103Figure 5.3 Preheating simulation boundary conditions . . . . . . . . . . . . . . . . . . . 106Figure 5.4 Model domain and boundary conditions . . . . . . . . . . . . . . . . . . . . . 108Figure 5.5 Material model validation FEA schematic . . . . . . . . . . . . . . . . . . . . 110Figure 5.6 FEA results versus experimental flow stress at forming temperatures . . . . . . 111Figure 5.7 FEA results versus experimental flow stress with strain hardening . . . . . . . . 111Figure 5.8 Final von Mises stress and temperature state found by implicit and unscaledexplicit FEA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Figure 5.9 FEA predicted flow stresses found with time and mass scaling . . . . . . . . . 114Figure 5.10 FEA predicted flow temperatures found with time and mass scaling . . . . . . . 114Figure 5.11 Stress state with varied time and mass scaling . . . . . . . . . . . . . . . . . . 116Figure 5.12 2D and 3D depiction of preliminary FEA model . . . . . . . . . . . . . . . . . 118Figure 5.13 Roller positioning validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 118Figure 5.14 Preliminary model results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120Figure 5.15 Predicted stress state on the surface of least-deformed workpiece during forming 123Figure 5.16 Oblique views of stress state immediate to roller during forming on the least-deformed workpiece . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124Figure 5.17 Stress state on the surface of mid-deformed workpiece during forming . . . . . 126Figure 5.18 Oblique views of stress state immediate to roller during forming on the mid-deformed workpiece . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127Figure 5.19 Contour plots of nodal displacement along the mid-deformed workpiece axis . 128ixFigure 5.20 Simulated equivalent stress distribution on cross-sections of the least-deformedworkpiece during forming . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Figure 5.21 Simulated equivalent plastic strain distribution on cross-sections of the least-deformed workpiece during forming . . . . . . . . . . . . . . . . . . . . . . . 129Figure 5.22 Simulated strain rate distribution on cross-sections of the least-deformed work-piece during forming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130Figure 5.23 Simulated temperature distribution on cross-sections of the least-deformed work-piece during forming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130Figure 5.24 Simulated equivalent stress distribution on cross-sections of the mid-deformedworkpiece during forming . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130Figure 5.25 Simulated equivalent plastic strain distribution on cross-sections of the mid-deformed workpiece during forming . . . . . . . . . . . . . . . . . . . . . . . 130Figure 5.26 Simulated strain rate distribution on cross-sections of the mid-deformed work-piece during forming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Figure 5.27 Simulated temperature distribution on cross-sections of the mid-deformed work-piece during forming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Figure 5.28 Comparison of experimental and modelled formed length of the least-deformedworkpiece . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132Figure 5.29 Cross-sectional comparison of model and experimental results of the least-deformed workpiece . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132Figure 5.30 Comparison of experimental and modelled formed length of the mid-deformedworkpiece . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132Figure 5.31 Cross-sectional comparison of model and experimental results of the mid- de-formed workpiece . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132Figure 5.32 Simulated principal stress magnitude and orientation during forming . . . . . . 134Figure 6.1 Multiaxial fatigue results and criteria for natural defects . . . . . . . . . . . . 139Figure 6.2 Multiaxial fatigue failure types . . . . . . . . . . . . . . . . . . . . . . . . . . 142Figure 6.3 Characteristic fatigue fracture surfaces . . . . . . . . . . . . . . . . . . . . . . 145Figure 6.4 Kitagawa diagrams for different loading scenarios . . . . . . . . . . . . . . . . 148Figure 6.5 AC-T6 versus formed-T6 fatigue results . . . . . . . . . . . . . . . . . . . . . 151xNOMENCLATURERoman Symbols (page introduced) Units?b Burgers vector magnitude of Al (page 69) m?f Time and mass scaling execution acceleration factor (page 113)?d Particle diameter predicted by the LSW model (page 89)?d0 Initial particle diameter employed in LSW model (page 89)? f Endurance limit in tension (page 60) MPa?area Defect size parameter (page 17) ?mBi Biot number (page 112)Fo Fourier number (page 112)a Mechanical property to DAS relationship coefficient (page 9)ACL Crossland fatigue criterion (page 139) MPab Basquin coefficient (page 60)b Mechanical property to DAS relationship coefficient (page 9)Cp Specific heat capacity (page 104) J/kg ?CCy Major yield strength transition coefficient (page 71)cy Minor yield strength transition coefficient (page 71)CMPS Maximum principal stress criteria (page 139) MPaD Instantaneous compression sample diameter (page 58) mmD0 Initial compression sample diameter (page 58) mmE Temperature corrected modulus of elasticity (page 63) MPaFc Clamping force employed in model (page 106) kNfm Mass scaling factor (page 111)ft Time scaling factor (page 111)xig Normalized activation energy (page 69)g0 Initial normalized activation energy (page 69)h Heat transfer coefficient (page 111) W/m2 ?CHHB Brinell hardness (page 12) kg/mm2HRF Rockwell hardness, F scale (page 13)HV0.01 Vickers hardness, 0.01 kg f (page 55) kg/mm2HV5 Vickers hardness, 5 kg f (page 38) kg/mm2J2,a Second invariant of the deviatoric stress amplitude (page 139) MPa2kc Thermal conductivity (page 104) W/m ?Ck1?3 Extended Ludwik-Hollomon strength parameter function coefficients (page 68)kLSW LSW temperature-dependent constant (page 89)kB Boltzmann constant, 1.3806503?10?23 (page 69) m2kg/s2KKLH Extended Ludwik-Hollomon strength parameter (page 68) MPaL Element edge length (page 100) mmm Population mean (page 90)m1?3 Extended Ludwik-Hollomon strain rate function coefficients (page 68)N Fatigue cycles (page 136)n Mechanical property to DAS relationship coefficient (page 9)N f Number of cycles to failure (page 16)n1?3 Extended Ludwik-Hollomon strain hardening function coefficients (page 67)P Probability (page 90)P Radial penetration of roller into workpiece employed in model (page 50) mmp Dislocation interaction parameter (page 69)q Dislocation interaction parameter (page 69)Qc Cooling rate (page 4) ?C/sqH Heat flux (page 111) W/m2qc, f Heat fluxes applied to model workpiece cooling (page 108) W/m2R Radial direction of forming (page 20)RL Load ratio for cyclic loading, ?max/?min (page 16)xiiR1?4 Experimental strain rate ranges (page 61)s Standard deviation (page 90)T Temperature (page 15) ?Ct Time (page 86) sT0 Reference temperature for thermal expansion (page 104) ?CTb Workpiece temperature employed in model (page 106) ?CTm Mandrel temperature employed in model (page 106) ?Ctp Simulated process time (page 108) sTt Extended Ludwik-Hollomon strain rate transition temperature (page 67) ?CT? Sink temperature (page 111) ?CTmelt Liquidus temperature (page 63) Kuo, un, u f Axial/radial roller nose positions employed in model (page 108) mmz Axial direction of forming (page 20)Greek Symbols (page introduced) Units? Coefficient of thermal expansion (page 104) ?C?1? ? Total thermal strain (page 104)? Taylor-Quinney factor (page 108)?? Strain rate (page 14) s?1??0 Absolute strain rate (page 69) s?1??1 Normalization strain rate (page 67) s?1??a Average strain rate obtained during a compression test (page 61) s?1??KM Kocks-Mecking predicted flow stress (page 71) MPa??LH Extended Ludwik-Hollomon predicted flow stress (page 67) MPa?? f Fitted Basquin endurance limit (page 151) MPa? Dendrite arm spacing (DAS) (page 5) ?m? Temperature corrected shear modulus (page 69) MPa?0 Absolute shear modulus (page 69) MPa?o Shear modulus at 300 K (page 63) MPa? Poisson?s ratio (page 63)xiii? Density (page 104) kg/m3? f Crossland fatigue criteria factor (page 139)? True stress (page 14) MPa?1 Maximum principal stress (page 132) MPa?a Tensile stress amplitude under cyclic loading (page 16) MPa? ?f Basquin strength coefficient (page 151) MPa?s Saturation or Voce stress (page 69) MPa?y Yield strength (page 8) MPa?1,max Maximum principal stress during cyclic loading (page 139) MPa?u Ultimate tensile strength (page 9) MPa?H,max Maximum hydrostatic stress (page 139) MPa?VM Von mises equivalent stress (page 118) MPa?s0 Absolute saturation stress (page 69) MPa?a Torsion stress amplitude under cyclic loading (page 136) MPa? f Endurance limit in torsion (page 60) MPa? Strain hardening rate (page 10) MPa? Circumferential direction of forming (page 20)?0 Initial strain hardening rate (page 69) MPa? True strain (page 14)? f True strain at fracture (page 9)?p Plastic strain (page 61)?Eu Eutectic fraction (page 80)xivGLOSSARYLPDC Low Pressure Die CastingHCF High Cycle FatigueDAS Dendrite Arm SpacingHIP Hot Isostatic PressingFEA Finite Element AnalysisEFA Experimental Forming ApparatusRPM Revolutions Per MinuteTC thermocoupleIR-TC infrared thermocoupleMPS Maximum Principal StressSEM Scanning Electron MicroscopyEDM Electro-Discharge MachiningLSW Lifshitz, Slyozov and Wagner coarsening modelMMC Metal Matrix CompositeDRX dynamic recrystallizationDRV dynamic recoveryAC as-castEDX Energy-Dispersive X-ray spectroscopyLVDT Linear Variable Differential TransformerDAQ Data Acquisition systemVHTM Vickers-Armstrong Hardness Test MachineCNC Computer Numeric ControlDPI Dots Per InchRMSE Root Mean Square ErrorECD Equivalent Circle DiameterPDF Probability Density FunctionxvACKNOWLEDGMENTSForemost, I would like to thank my supervisor Prof. Daan Maijer for his support and guidancethroughout the course of this work. Thank you to everyone at CAPTIN; Yongning Wang and ChrisHermesmann for their vision in supporting for this project as well as Dominic Au, Ray DeCenzo andKen Nguyen for helping me to execute it. I am very grateful to Shane Carr for without his donationof equipment, this project would not have had the same scope. I would also like to thank Bill Hayterand Steve Tanahara for helping me to land the equipment and supplying further services. A heartfeltthanks goes to my ENSMA collaborators and hosts, Yves & Carole Nadot, also Guillaume Benoit,Louise Dancoine and Pierre-Guillaume Bardin. I would also like to thank Prof. Warren Poole andDr. Leo Colley for their valuable feedback on A356 characterization, and Prof. Steve Cockcroft fordiscussions on inverse methods and moral support. A big thank you to the engineering techniciansRoss Mcleod, Carl Ng, David Torok and Wonsang Kim for all of their assistance as well as GaryLockhart for his project involvement. Especial thanks to all colleagues and officemates for providinga friendly environment that I was always pleased to work in. I would also like to thank CanadianAutoparts Toyota Inc., the Natural Sciences and Engineering Research Council of Canada (NSERC),Mitacs, Rio-Tinto Alcan and the estate of Cy and Emerald Keyes, without whose generous financialsupport would not permitted this endeavour. Finally, a big thank you to my friends and family, whohave put up with me throughout this.xvi?Was der Vater schwieg, das kommt im Sohne zum Reden; und oft fandich den Sohn als des Vaters entblo?sstes Geheimniss.??F. W. Nietzche, Also Sprach ZarathustraROY FECITxviiCHAPTER 1INTRODUCTIONParticularly in the transportation sector, modern manufacturing is constantly evolving to meet in-creasing demands for higher performance, lighter component weights and reduced ecological im-pact, all with lower costs. Classical near net-shape manufacturing processes for metallic compo-nents such as casting and forging have remained central in addressing these demands. Forging oftenimproves the material properties by imparting work hardening and leaving compressive residualstress on the surface of a component, however, it is cost prohibitive for production of small numbersof parts. The advent of numerically controlled machining centres has diminished the cost of thesetypes of components. However, subtractive manufacturing processes, such as machining, can bevery inefficient in the use of material. Currently, the cost of material waste in machining is offset bythe lack of specialized, component-specific tooling required for short production runs.Rotary forming techniques, such as spinning, shear forming and flow forming have the abilityto produce near net-shape components that optimize material use. These techniques use open dies,or tools, to generate highly localized plasticity to achieve the final shape of the part. By mountinga workpiece on a rotating mandrel, incremental deformation is applied by the tool in the same waya potter shapes clay. This produces dimensionally accurate, axially symmetric components. Thebenefit of these rotary forming techniques is that they may impart the same benefits as forging,albeit with decreased forming loads and more adaptive tooling. As a result, rotary forming has thepotential to be either a stand-alone, disruptive technology or to compliment standard metal turningtechnology.One of the novel applications of rotary forming is aluminum alloy wheel fabrication. Themost cost effective manufacturing technique for these wheels is through Low Pressure Die Cast-ing (LPDC) employing an Al-Si-Mg casting alloy such as A356. These wheel castings are then heat1CHAPTER 1. INTRODUCTIONtreated and then machined to the final size. The marriage of flow forming to standard casting pro-cesses permits a wider range of possibilities than by casting alone. This includes casting the frontface of the wheel including the spokes and hub with LPDC, and then flow forming the remainder ofthe rim [2]. Wheels manufactured in such a manner have the potential to be lighter due to improvedproperties. Further weight savings, up to 20% over a conventionally cast wheel, can be realizedby harnessing a flow forming operation to close hollow spokes [3]. However, rotary forming ofaluminum alloy wheels remains a somewhat expensive operation owed to high initial costs as oper-ational parameters are arrived at by trial and error. As such, it has been limited in application andsuccessful operating parameters are that are arrived at by trial and error are closely guarded tradesecrets. The costs associated with the implementation of rotary forming are further exacerbated bythe necessity to carry out rotary forming of aluminum castings at elevated temperatures.Compared to other material processing technologies such as rolling or extrusion, there has beenlimited academic study of rotary forming processes. This is especially true regarding studies onthe application of rotary forming of aluminum castings. There also is limited data available onthe flow stress behaviour of as-cast A356 at elevated temperatures. Therefore, it is not specificallyknown what impact rotary forming at elevated temperatures will have on mechanical properties,nor on the in-service fatigue performance of components processed in this manner. Moreover, themultiaxial fatigue resilience of this material processed in a standard manner, i.e. processing pathsexcluding rotary forming, has not been previously characterized. There are multiple opportunitiesfor contributions to improved understanding of this industrially relevant material for a wide rangeof applications, however, multiaxial fatigue characterization is particularly pertinent for automotivewheel manufacturers. This is owed to the significant in-service multiaxial cyclic loading thesecomponents endure, outside of regions of the wheels that can be potentially processed by rotaryforming.The following section provides a description of Al-Si-Mg casting alloy structure. Microstruc-tural modifications induced by heat treatment will be discussed, and the overall impact on mechan-ical properties is then presented to appreciate the potential effects of rotary forming on the alloy.2CHAPTER 1. INTRODUCTION1.1 Structure of Al-Si-Mg casting alloysAluminum alloy A356 is a hypoeutectic Al-Si-Mg foundry alloy with an as-cast (AC) microstructurethat consists primarily of aluminum dendrites (?-Al), surrounded by an Al-Si eutectic (Fig. 1.1).Other tertiary phases, such as ?-intermetallics or ?-intermetallics (?-Al5FeSi and pi-Al8FeMg3Si6),may be present due to melt impurities. The ?-intermetallics, appearing as elongated needles withinthe microstructure, are deleterious to mechanical properties. The solidification sequence of thisalloy starts with the nucleation and growth of primary dendritic ?-Al. ?-intermetallics may format this point if Mn and Cr are present [4, 5]. This is followed by the ?-Al-Si eutectic and ?-intermetallics. The remaining liquid, enriched in Si, Mg and Fe, forms Mg2Si precipitates andengages in complicated ternary and quaternary reactions, producing pi-intermetallics [6].Figure 1.1: A356 microstructure in the as-cast (AC) condition displaying DAS, (a) ?-Al, (b)eutectic, (c) intermetallic and (d) a secondary Mg-Si rich region.Overall, the Al-Si-Mg alloy system offers excellent castability, reasonable strength and adequatefatigue resistance. The castability is primarily owed to the ? 7%-wt Si content that enhances thefluidity of the melt. Mechanical properties, including strength and fatigue resistance are influencedby grain/structure refinement, chemical modification and heat treatment. Alloying additions, suchas Al-Ti-B, are used to refine grain size and further improve castability [7]. Chemical modification,achieved through the addition of small amounts of Na and Sr to the melt, changes the morphology3CHAPTER 1. INTRODUCTIONof the eutectic-Si from acicular to more fibrous and refined structures. A356 with additions of Naand/or Sr is referred to as ?modified? and ?unmodified? without. Modified A356 permits eutecticparticles which are both smaller and more spherical after heat treatment [8]. These alloys are rarelyemployed in the AC condition owing to a lack of homogeneity and detrimentally coarse plates of Sipresent in the eutectic. Particularly if ?-intermetallics form, high levels of Fe are also deleterious.Several heat treatment schedules are commercially employed, with the most prominent being T6.Most of these schedules consist of solutionizing, water quenching and then a combination of naturaland artificial aging. Both the duration and temperature at which these treatments are carried outdecide the final mechanical properties.Microstructure refinement, which results in a corresponding strength increase, can be achievedby decreasing the solidification time during casting. By decreasing solidification time, the coolingrate during solidification is increased which results in decreased primary and secondary DendriteArm Spacing (DAS). Fig. 1.2a compares the DAS with cooling rate data provided by various sourcesfor A356 and shows excellent correlation. A reduction in DAS is directly related to decreased grainsize in the material. Many wrought alloys have been found to have mechanical properties correlatedto grain size, due to grain-boundary strengthening according to the Hall-Petch relationship. How-ever, the relatively large and irregular grain structure that is a characteristic of foundry alloys meansthat it is non-trivial to relate strength and cooling rate (Fig. 1.2b).Therefore, the microstructural feature typically used to compare the final mechanical propertiesof Al-Si-Mg alloys is secondary DAS [7, 12, 13]. Directional solidification in commercial cast-ings can produce two principal types of dendritic structure. Columnar dendritic growth is stabi-lized by high cooling gradients, and has a microstructure exhibiting well-defined primary dendrites.Equiaxed structure occurs where gradients are less pronounced, with primary arms often difficult toidentify in particularly coarse material. While tertiary spacing is occasionally used for very coarsematerial [14], secondary DAS is a relatively facile measurement that spans both types of dendriticstructures. For the remainder of this thesis, DAS or ? refers to secondary dendrite arm spacing asshown in Fig. 1.1.With DAS typically on the order of 10-100 ?m, depending on the solidification rate, there aresmaller microstructural features affecting strength. After heat treatment, the typical eutectic-Siparticle size is approximately one order of magnitude less than this, and Mg2Si precipitate occur4CHAPTER 1. INTRODUCTION10?1 100 101 102101102das,?(?m)Cooling rate, Qc (?C/s)FlemingsShabani & MazaheryWang39.78Q?0.31c(a) DAS versus cooling rate100 1010.60.811.21.41.6Cooling rate, Qc (?C/s)Grainsize(mm)A356A357(b) Grain size versus cooling rateFigure 1.2: Secondary DAS versus cooling rate, Qc, for A356 after Flemings [9], Shabani &Mazahery [10] and Wang [11] in (a). Grain size versus cooling rate after Wang [11] in(b).throughout the microstructure on the nanometer scale. Heat treatments applied to these alloys serveto primarily modify the eutectic structure and refine/redistribute the Mg2Si particles. In general,compared to the AC condition, the T6 treatment optimizes strength and ductility and is one of themore commercially common tempers for modified Al-7Si-0.3Mg (A356) alloy.1.2 Heat treatmentAccording to the current ASTM standard, the T6 heat treated condition involves solution treatmentat 540?C for 4-12 hours, quenching in water between 65-100?C, followed by artificial aging (pre-cipitation treatment) at 155?C for 2-5 hours [15]. The solution treatment time may be reducedas required if the melt contains modifiers. The time spent at ambient conditions after quenching,referred to as natural ageing, should be minimized as it reduces the precipitation driving force avail-able for effective artificial ageing. While the current standard does not explicitly mention naturalaging, in previous versions of the same standard, allowances of up to 8 hours at room temperaturewere permitted between the water quench and artificial aging.5CHAPTER 1. INTRODUCTION0 0.5 1 1.5 20100200300400500600700?+Mg2Si?L ?+L540?C1.45%T(?C)Mg2Si (wt %)Figure 1.3: Mg2Si in ?-Al pseudo-binary phase diagram [16]1.2.1 Solution treatmentThe solution treatment is applied to induce three phenomena to occur: dissolution of Mg2Si parti-cles, chemical homogenization and eutectic-Si structure modification. The Mg2Si precipitate thatforms during the last stages of solidification is readily soluble in ?-Al at the typical solutionizingtemperatures, as indicated by the phase diagram in Fig. 1.3, and will dissolve given enough time.In order to maximize the amount of Mg and Si in solution, a solutionizing temperature as closeas possible to the equilibrium eutectic temperature is desirable. A temperature of 540?C is highenough such that incipient melting is avoided at the grain boundaries, which can lead to permanentmechanical strength reduction.In the AC state, solute elements are typically highly segregated due to dendrite formation. So-lution treatment serves to chemically homogenize the casting, thereby improving solid solutionstrengthening. Closset et al. [17] conducted micro resistivity measurements on dendrites in A356in the AC condition and after varying solution times. In the AC condition, it was found that Sicontent was highest at the centre of the dendrite while the Mg content was marginally higher onthe edge of the dendrite compared to the centre. The dendritic distribution of Mg in the AC condi-tion was also confirmed by Colley [18] for an Al-Si-Mg alloy with a near eutectic composition ofAl-11Si-0.22Mg. Closset et al. reported that homogenization was complete after 30 minutes forA356, while Colley reported 3 hours for Al-11Si-0.22Mg. This suggests that while the presence oflarge amounts of Si may influence the distribution of Mg, homogenization of the primary alloyingelements is complete after 3 hours at 540?C regardless of Si content in A356. Colley?s observations6CHAPTER 1. INTRODUCTIONunderscore this point by providing a limiting case. However, Fe-rich intermetallics are quite stableat typical solutionizing temperatures and take relatively longer to dissolve, occasionally remainingafter heat treatment [6, 19].The changes to the eutectic-Si structure imparted by solution treatment also play an impor-tant role in determining the final mechanical properties. While modified Al-Si-Mg alloys containfairly refined fibrous eutectic-Si, this is further refined during solution treatment by the processes offragmentation and spheroidization. The AC fibres break into particles at elevated temperature andgradually spheroidize in order to minimize surface energy of the Al-Si interface. With longer treat-ment times, coarsening occurs. Larger Si particles develop facets and coalesce with other nearbyparticles to minimize surface area in regions of high Si concentration [20, 21].1.2.2 QuenchingFor the quench operation, the water temperature is selected to maximize cooling rate while concur-rently limiting thermal stress development. A high cooling rate is necessary to suppress precipita-tion when cooling from the solution treatment temperature to room temperature. This produces ahigh degree of solute supersaturation as well as retaining a larger number of matrix vacancies. Ifthe cooling rate is too slow, non-uniform precipitation will occur, localized at grain boundaries orsites of high dislocation density. The resulting decrease in supersaturation reduces the maximumyield strength that may be achieved by ageing [22]. The critical temperature range where highcooling rates are required is between 450 and 200?C for most Al alloys and the time spent in thistemperature range during quenching should therefore be as short as possible to avoid preemptiveprecipitation [23].1.2.3 Artificial ageingArtificial ageing is a precipitation heat treatment process. It consists of taking previously solutiontreated components and holding at a static temperature for a period of time. The process is necessaryto precipitate small particles coherent with the surrounding matrix which are finely dispersed parti-cles to resist dislocation glide. In Al-Si-Mg alloys, the supersaturated solid solution (?SSS) resultingfrom the solutionizing process transforms to a stable phase plus a metastable precipitate phase, ?.The rate of precipitation, as well as the precipitate morphology, is dependent on temperature, time,7CHAPTER 1. INTRODUCTIONdegree of supersaturation and diffusivity. At high temperatures, diffusion occurs rapidly even whensupersaturation is low. The inverse is true for low temperatures.The precipitation sequence of Mg2Si specific to an Al-Mg2Si system has been described byEdwards et al. [24]. While A356 contains a significantly elevated level of Si, it is assumed thatthe principal sequence of precipitation in A356 is only marginally affected from that described byEdwards et al. according to:?SSS Mg clusters +Si clustersDissolution ofMg clustersFormation ofMg-Si co-clustersSmall, equiaxedprecipitatesMetastable ???(Mg5Si6 needles)Metastable ?? (Mg2Sirods) and ???Equilibrium ?(Mg2Si platelets)The maximum strength due to precipitation hardening arises when the particle spacing is small.Edwards et al. have identified that the particle morphology coinciding with peak ageing is the??? precipitate, having a nanometer scale, needle-like structure. More recent research by Hasting etal. [25] have shown that the composition of ??? is not just limited to Mg and Si, but may also containup to 20 atomic % aluminum. Further ageing generates equilibrium Mg2Si ? platelets or metastable?? rods and decreases strength, coinciding with an over-aged condition. Colley [18] found that thepeak aged condition was reached after approximately 1 hour at 200?C, 3 hours at 180?C or 8 hoursat 150?C. The time to reach an over-aged condition was found to diminish as the ageing temperatureincreased.1.3 Mechanical properties of Al-Si-Mg alloysTo this point, the structure of Al-Si-Mg alloys has been discussed, along with the aspects of typicalheat treatment. This section will discuss the impact of structure on mechanical properties. This willbe accomplished by tabulating the results of several studies on Al-Si-Mg alloys with variations incomposition and casting methodology to demonstrate the relative impact of structure as character-ized by DAS on mechanical properties. These properties include yield strength (?y) , ultimate tensilestrength (?u), strain to fracture (? f ), as well as hardness. This will be followed by a discussion ofthe behaviour of this material at elevated temperatures. This is necessary to evaluate the potentialimplications for rotary forming on A356.8CHAPTER 1. INTRODUCTION1.3.1 Effect of DASFive studies have been summarized in Table 1.1 and their resulting mechanical properties are plottedversus DAS in Figure 1.4. These studies span a variety of modified versus unmodified alloys over awide range of DAS with varying heat treated conditions. These results are principally for A356, butalso include that of A357, a high strength variant of A356 containing a high amount of Mg. Cast Al-Si-Mg alloys often have property-DAS relationships expressed in terms of a power law equation [26]having the form of:?y, ?u, ? f = a+b? n (1.1)where a, b and n are power law coefficients and ? is DAS. Data corresponding to the T6 and ACconditions have been grouped and a non-linear least squares fitting technique was used to gener-ate the power law coefficients for Eq. 1.1, which are presented in Table 1.2. For all studies, theoverall trends indicate that all properties diminish with increased DAS in both the AC and T6 con-ditions. There is significant variability in the degree to which the fitted expressions represent thedata, quantified principally by Root Mean Square Error (RMSE). The expressions for material inthe T6 condition show an order of magnitude higher RMSE as compared to those for material in theAC condition. The larger variance is attributed to differences in the heat treatment and chemistryamongst the different studies.Table 1.1: Various literature compositions and T6 solutionizing (Sol.), quench (Q) and artifi-cial ageing (AA) schedules employed for mechanical property studies.Reference Composition (wt %) T6 Schedule (?C/hours) Fig. 1.4seriesSi Mg Fe Ti Sr Sol. Q AARan et al. [27] 7.04 0.3 0.17 0.15 - 538/5 70 160/4 IWang [28] 7.0 0.41 0.14 0.13 - 540/20 20 170/6? II.i6.8 0.39 0.13 0.13 0.02 II.iiCeschini et al. [29] 7.0 0.6 0.19 0.17 - 540/20 Not reported IIIBoileau et al. [30] 6.7 0.35 0.05 0.12 0.003 540/5? 93 191/3 IVShabani et al. [10] 6.9 0.33 0.4 - 0.02 Not treated V? Specimens were naturally aged for 20 hours prior to artificial ageing.? Castings were held at 495?C for an hour, then air quenched prior to solution treatment.The data employed for this comparison precludes accurate comparisons between material with9CHAPTER 1. INTRODUCTIONTable 1.2: Coefficients for DAS-property relationships for T6 and AC conditions.Property Condition Coefficient (Eq. 1.1) Fit characteristicsa b n R2 RMSE?y (MPa) AC 81.30 -9.43?10?5 2.43 0.8591 3.205T6 273.94 -1.39?10?2 1.82 0.8691 11.47?u (MPa) AC 177.55 -2.58?10?1 1.12 0.9323 7.397T6 341.90 -1.76?10?2 1.92 0.9614 11.67? fAC -0.0168 0.8360 -0.6191 0.8935 0.0077T6 -0.9155 1.300 -0.0755 0.8735 0.0238equivalent DAS, as it spans a large variety of compositions, microstructural scales and heat treat-ments. However, the following conclusions can be made. Regardless of specific heat treatmentsapplied, there is little change to yield and ultimate strength for DAS less than 40 ?m. Beyond 40?m, the ultimate tensile strength is found to decrease more rapidly with increased DAS than seenwith yield strength, i.e. larger b and n values are observed for ?u versus ?y. AC data shows that theyield strength is increased by nearly three times for small DAS, and does not change significantlyas DAS increases. Based on the fits to the elongation data, for values of DAS less than 40 ?m, heattreatment does not affect the ductility. At higher levels of DAS, the AC material retained ductility,while elongation was exhausted for the heat treated material at DAS values of approximately 100?m.A further review of the impact on mechanical properties of other microstructural factors beyondDAS, such as compositional changes, porosity and eutectic particle morphology is presented in Table1.3. This includes the mechanical properties discussed previously (?y, ?u, ? f ) as well as the strainhardening rate, ?. This data shows that increased amounts of Mg and Si increase yield and ultimatetensile strength and decrease elongation. As demonstrated by Kashyap et al. [31], Fe diminishesall properties, particularly when the content is above 0.2%-wt. Lee [32] found that microporosity(0.2-1 volumetric %) left yield strength unaffected (< 1% change) for material with an estimatedDAS of 25?m. Elongation and ultimate tensile strength, however, were reduced by greater than 50%and 17%, respectively. Boileau et al. [30] used Hot Isostatic Pressing (HIP)1 to reduce or eliminateporosity in specimens with a larger range of DAS than Lee. Boileau et al. found that that yield,1520?C for 3 hours at 105 MPa10CHAPTER 1. INTRODUCTION20 40 60 80 100 120 14050100150200250300das, ? (?m)? y(MPa)  III.iII.iiIIIIVVt6ac(a) ?y20 40 60 80 100 120 140100150200250300350das, ? (?m)? u(MPa)  III.iII.iiIIIIVVt6ac(b) ?u20 40 60 80 100 120 14000.050.1das, ? (?m)? fIII.iII.iiIIIIVVt6ac(c) ? fFigure 1.4: ?y, ?u and ? f versus DAS after (I) Ran et al. [27], (II) Wang [28], (III) Ceschini etal. [29], (IV) Boileau et al. [30] and (V) Shabani & Mazahery [10] with fitted expressionscoinciding with T6 and AC condition.ultimate tensile strength and elongation are only slightly affected. This finding was echoed by Ranet al. [27].Shabestari and Shahri [33] demonstrated that eutectic particle sizes and aspect ratios increasedwith DAS, as well as showing that the number of discrete particles per unit area (distribution) de-creases with DAS. These findings are similar to those of Wang [11], who conducted targeted studiescomparing specimens with the same DAS. Wang also considered the shape and size of the eutectic-Si particles in modified and unmodifed A356 samples. With an aspect ratio of 1 being a perfectsphere, unmodified eutectic particles were found to have an aspect ratio of 2.5, compared to 1.611CHAPTER 1. INTRODUCTIONfollowing modification. Particle size was twice as large in the former compared to the latter. Wangreported a significant increase in the yield strength for A356 with larger particles. Wang did notdemonstrate a significant change in ?u in unmodified material. However, appreciable changes in ?yand ? f were found. Ca?ceres et al. reported similar findings as Wang for ? f [8].Table 1.3: Relative microstructural effects on mechanical properties of Al-Si-Mg alloys in T6condition. ?y, ?u and ? f are presented in addition to strain hardening rate ?, whereavailable.Increase in: ?y ?u ? f ? ReferenceSilicon content NA [31, 34]Magnesium content [11, 31]Iron content NA [31]Porosity NA [27, 32]Eutectic particle conditions ( / with DAS ) [28, 33]Size ( ) ? [8, 11, 28]Aspect ratio ( ) ? [8, 11, 28]Distribution ( ) [11, 33]1.3.2 HardnessMacrohardness measurements are commonly used to empirically quantify the effects of heat treat-ment on strength (?y, ?u) [35]. This is possible through correlation of the flow stress at some levelof strain. The basic quality being measured during a hardness test is the ability of the material toresist local plastic deformation, which is imparted by an indenter with standardized geometry underquasi-static loading. Macrohardness is preferred over microhardness especially for cast aluminumalloys, as larger indents provide an improved sampling of the overall or average microstructuraleffect. Developed as an alternative to ball-type macrohardness measurements such as Brinell orRockwell, the pyramidal diamond Vickers test allows for accurate measurements across a varietyof loads [36, 37]. The hardness from ball-type measurements is sensitive to both indenter geometryand load, while Vickers measurements are sensitive to indentation size, particularly for materialswhich exhibit coarse microstructures.In tracking the effects of Fe and Mn on Al-Si alloys, Tash et al. [4] reported the results of Brinellhardness (HB) measurements for both modified and unmodified A356 in the AC, solutionized andartificially aged conditions. In this study, artificial ageing was performed on several different tem-12CHAPTER 1. INTRODUCTIONAC Sol. 155?C 180?C 200?C 220?C5060708090100110HB  <0.2Mod, <0.2>0.2Mod, >0.2Figure 1.5: A356 HB measurements of AC, solutionized and artificially aged A356 at differenttemperatures after Tash et al. [4]. Ageing was conducted for 4 hours at the indicatedtemperatures. Also shown are results for modified and unmodified material, with lessthan and greater than 0.2 wt% Fe content.peratures for four hours (Fig. 1.5). These results demonstrate that there is an appreciable differencein hardness for the different conditions. For material with low Fe content, in all conditions, themodified material displayed elevated hardness values as compared to the unmodified. This finding,coupled with Table 1.3, indicates that simultaneous refinement of eutectic size and aspect ratio dueto modification are reflected in increased hardness values. However, the unmodified material wasfound to be harder when Fe content was very high (>0.4 wt% Fe) in the overaged condition whichwas attributed to the contribution of significantly harder intermetallics to the overall measurement.Thus it is interesting to note that as Fe content negatively impacts yield strength (Table 1.3), a higherhardness measurement does not necessarily indicate a higher yield strength.A recent study by Tiryakiog?lu et al. [38] tracked both the yield strength and the Rockwell hard-ness (HRF) in samples of Al-7wt%Si-Mg alloys containing varying amounts of Mg. The solutiontreatment in the study was identical for each sample, but the ageing time at 200?C was varied from2 minutes to several days. It was found that there were discrete trends in hardness versus yieldbehaviour correlated to Mg content, which were valid up to the point of peak ageing. Peak hard-ness and the rate with which hardness increased with yield strength was found to increase with Mgcontent. In the overaged condition, there was no discernible difference in the HRF-?y trend withdifferent Mg content. The data from Tiryakiog?lu et al., presented in Fig. 1.6, exhibits a hysteresisassociated with the irreversible thermodynamic change associated with over-aging. This presents13CHAPTER 1. INTRODUCTIONa caveat when comparing hardness to yield strength: hardness values can be correlated to yieldstrength, but the two discrete regimes behaviour for over or underaged must be considered. It ap-pears that for a given composition, there is a distinct relationship for hardness to yield strength untilpeak age is attained.40 50 60 70 80 90100150200250HRF? y(MPa)  0.6-0.2, Overaged0.60.40.2Figure 1.6: ?y versus HRF after Tiryakiog?lu et al. for Al-7wt%Si-Mg alloys plotted accordingto Mg content in wt%. Dashed lines indicate power-law trend fitting.1.3.3 Behaviour at elevated temperaturesEstey et al. [39] measured the constitutive behaviour of A356 in the solutionized condition to pro-vide input for a mathematical model aimed at predicting the distortion in an automotive wheelfollowing heat treatment. Estey et al. performed uniaxial compression tests on AC then solutionizedsamples over a range of temperatures (200 to 500?C) and strain rates (?? =0.001 to 1 s?1) to charac-terize the mechanical behaviour for conditions relevant to the quenching. Besides demonstrating theflow stress (i.e. ? versus ?) behaviour of solutionized A356 at elevated temperatures, the results ofEstey et al. showed that the material demonstrates decreasing work hardening rates as temperatureis increased. Between 400-500?C, near-steady state flow stresses were observed.McQueen et al. [40] compared the mechanical behaviour of both AC A356 and a Si-C reinforcedA356 MMC. Torsion tests targeting temperatures of 300, 400, 500 and 540?C were performed atequivalent strain rates of 0.1, 1 and 5 s?1. The results for A356 are presented in Fig. 1.7. McQueenet al. converted torque-twist measurements to equivalent stress versus strain according to the Fieldsand Backofen method [41]. This methodology requires fitting torque-strain rate and work hardening14CHAPTER 1. INTRODUCTIONcoefficients in order to properly resolve equivalent stresses. The overall trend observed in this datais that ductility (Fig. 1.7b) increases with temperature and decreasing strain rate.A peak flow stress accompanied by a gradual decline with increased strain as depicted in Fig.1.7a would suggest ?classic? dynamic recrystallization (DRX) behaviour [42], as is the case formany fine-grained, precipitate-bearing aluminum alloys. This phenomena clearly manifests in thedata supplied by McQueen et al., however, there is a gradual decline in flow stress as opposed tooscillating flow stress indicative of DRX [43]. McQueen et al. posit that dynamic recovery (DRV)is prominent at elevated temperatures as opposed to recrystallization, with DRV localized in theeutectic phase. The rationale provided is that there is little solute within the ?-Al to provide grainnucleation sites. McQueen et al. also precluded eutectic-Si particles coalescing to further contributeto the strain softening observed, citing their stability. Observations made on the fracture surfaces0 1 2 3 4 5 6020406080100120 300?C, 5 s?1300?C, 1 s?1300?C, 0.1 s?1400?C, 5 s?1400?C, 1 s?1400?C, 0.1 s?1500?C, 5 s?1500?C, 1 s?1500?C, 0.1 s?1?(MPa)?(a) Equivalent flow stress at different T and ??300 350 400 450 500 5500123456T (?C)? f  5 s?11 s?10.1 s?1(b) Fracture strain (? f ) versus temperatureFigure 1.7: A356 equivalent flow stress and strain at fracture for various temperatures andstrain rates derived from torsion testing conducted by McQueen et al. [40].by McQueen et al. suggested that failure at lower temperatures was due to cracks nucleating fromcoarse Si particles and this phenomena diminished at elevated temperatures. The main fractureplanes coincided with the transverse plane of maximum shear stress. Cracks were found to pre-dominantly pass through the eutectic-Si particle/matrix interface as opposed to directly through Siparticles.Kim et al. [44] studied the suitability of a Al-Si-Mg alloy for a casting-forging process. It wasfound that chemical refinement employing titanium boride and Zr was necessary to attain the desired15CHAPTER 1. INTRODUCTIONductility for defect-free processing. The material was deformed at 450?C with tooling surfacesheld at 250?C, presumably to stabilize the workpiece temperature during the forging operation.The authors reported that the aspect ratio of the microstructure was refined consistent with theforging path. After forging and applying a T6 temper, the hardness of the forging was found to haveincreased compared to a unforged component of the same composition and temper.1.4 Fatigue behaviour of A356The uniaxial fatigue behaviour of A356?T6 has been studied by a number of researchers [45?52].These studies clearly established a direct link between microstructure, defects and fatigue resistance.In almost all related studies, casting defects such as intermetallic inclusions, porosity, and oxidefilms have been shown to be present at the origin of the failure. With few exceptions, these studieshave only considered the fatigue behaviour under uniaxial loading. The multiaxial fatigue behaviourof A356?T6 was studied by De-Feng et al. [53] using thin-walled tubular specimens but underloading conditions leading to very low cycle fatigue; as such these results are not directly applicableto HCF conditions. McDowell et al. [54] performed torsional HCF testing, however these tests wereconducted with deformation control, which requires an indirect translation to stress-based criterions.1.4.1 The role of defectsAluminum castings are negatively affected by casting defects such as macro and micro porosity,shrinkages, and oxide films. These defects in the microstructure are stress concentrators and providesites for early crack initiation, thus shortening fatigue life. In some cases, the nucleation step infatigue crack growth may be eliminated if there is a pre-existing flaw. This induces a localizedstress concentration that initiates and speeds crack propagation. Pores act as such crack initiationsites near the surface of the material and the propagation of the crack is decided by both the appliedstresses and the local strength of the material.Boileau et al. reported significant increases in fatigue limit following HIP, as shown in Fig.1.8. Processing in this manner provided an order of magnitude increase in N f for a constant ?aand DAS. This testing was conducted under fully reversed conditions, i.e. the maximum stressmatched the minimum rendering a load ratio RL equal to -1. Gao et al. [55] also found similarincreases in fatigue resistance with HIP-processed A356?T6 material with RL = ?1. While it is16CHAPTER 1. INTRODUCTION30 40 50 60 70 80 90105106107das, ? (?m)Cyclestofailure,Nf  acac+hipexp(13.76 ? 3.14 ? 10?2 ? ?)exp(15.97 ? 3.43 ? 10?2 ? ?)Figure 1.8: DAS and porosity effect on AC fatigue properties demonstrated by Boileau et. al.[30] employing HIP. Fatigue testing was conducted with ?a = 158 MPa and RL =?1.clear that defects are observed at the initiation point on fracture surfaces, very few studies haveidentified the critical defect size that diminishes the fatigue limit for cast and heat treated aluminumalloys. While processing these alloys via a HIP step has been shown to increase fatigue resistance,the changes in behaviour cannot be limited solely to the elimination of pores due to microstructuralchanges caused by the thermomechanical processing. Furthermore, HIP is not economically viablefor many commercial applications. It is therefore necessary to determine a critical defect size, orthe permissible size of a defect before the fatigue endurance limit is affected.Brochu et al. developed a Kitagawa (also referred to as Kitagawa-Takahasi [56]) relationship forrheocast A357. This analysis consisted of comparing fatigue limits to defect sizes that were mea-sured directly from fracture surfaces. The authors employed the Murakami [57] approach whichassumes pores act as cracks and are characterized by the parameter?area. This parameter is de-fined as the equivalent length of a defect projected in 2D onto the fracture surface. Brochu et al.determined that the the critical defect size is 150 ?m under fully reversed tensile loading. Thisexperimental result was larger that the 100 ?m critical defect size suggested by Fan et al. [48] forA356?T6, identified via modelling efforts.17CHAPTER 1. INTRODUCTION1.4.2 Behaviour in defect-free materialIn defect-free cast aluminum alloys, the first cracks are known to initiate either at Fe-rich inter-metallic particles [55], or in the eutectic [54]. In cases where there are no defects or intermetallics,the DAS can be correlated with the fatigue life [30, 54, 55]. Boileau et al. showed that N f can beincreased by an order of magnitude in AC material when DAS is reduced by a third (Fig. 1.8). Gao etal. demonstrated that halving the DAS increased the fatigue limit by 20 MPa in A356?T6 accordingto a Basquin relationship fitted to their data (Fig. 1.9). While the effects of porosity and DAS arenot mutually exclusive, the role DAS plays is less important when the material contains defects.105 106 107406080100120140Cycles to failure, Nf? a(MPa)  ? = 23 ? 4 ?m? = 47 ? 5 ?m1471(2Nf )?0.191374(2Nf )?0.21Figure 1.9: S?N data demonstrating DAS effect on A356?T6 fatigue properties after Gao etal. [55]. Fatigue testing was fully reversed (RL =?1).The main reason that the DAS correlates well with fatigue resistance is the linkage to eutecticparticle condition. Fatigue crack initiation has been found to occur at these particles [54, 58] insamples that are free of defects. Coarse microstructure, as characterized by a large DAS, containslarge, irregularly shaped and spaced eutectic particles which act as stress concentration points withinthe surrounding matrix. In the case of friction-stir processed material, the eutectic particle sizesare significantly refined and fatigue properties were significantly enhanced, resulting in a >80%increase in endurance limit (RL = 0.1) as compared to the AC condition [59].18CHAPTER 1. INTRODUCTION1.5 Rotary forming and related processesRotary forming or spinning is a near net-shape, hot or cold metal-working process for manufacturingseamless, dimensionally precise, rotationally symmetric products. In this process, the workpiece isimpinged between a tailstock and a rotating mandrel. It is then incrementally deformed by contactwith a tool. Usually the tool employed consists of a roller to minimize friction. The mandrel maysupport the workpiece throughout the length of the intended final profile, however, some spinningoperations can be successfully conducted without the benefit of support on the internal diameter.Industrial classification of rotary forming operations spans three discrete categories (Fig. 1.10)based on the change in wall thickness of the component and the internal stresses developed. Interms of wall thickness, spinning induces little to no change while shear forming or cone spinninginduces a uniform change according the sine rule [60, 61], as detailed in Fig. 1.10b. If a flat blankis used, then the final thickness of the product is the starting thickness times the sine of the imposedforming angle. The sine rule can still be applied if the operation is to be conducted on a previouslydeformed component already containing an included angle. In flow forming or tube spinning, thefinal wall thickness may be estimated by conservation of volume if the workpiece wall thickness isreduced uniformly.Depending on the profile, the principal stresses induced in the workpiece by spinning may beeither compressive or tensile. A review of the mechanics of spinning by Music et al. [62] statesthe most desirable stress state under the roller is pure shear, which does not induce any workpiecethickness reduction. This is achieved by balancing the circumferential stresses imposed by theroller with the radial stresses developed through thickness of the workpiece. Moving to largerunbalanced stress states has been shown to cause defects, as shown in Fig. 1.11. Music et al.observed that high circumferential compressive stresses result in buckling of the flange, leading towrinkling in the workpiece flange ahead of the roller. As shown in Fig. 1.11a, these wrinklesdevelop progressively throughout the spinning operation, eventually manifesting as pronouncedlobes at the end of the workpiece. Music et al. state that high radial tensile stresses may induce theformation of circumferential cracks, or cracks which propagate in the R? ? plane. In a review ofrotary forming practices, Wong et al. [63] report that radial cracks, or cracks that propagate in thez?R plane, occur when wrinkles are further worked. These cracks predominantly appear between19CHAPTER 1. INTRODUCTION(a) Spinning (b) Shear forming(c) Flow formingFigure 1.10: Spinning process classifications and final workpiece thickness estimates afterRunge [61]. Spinning induces little change to the workpiece thickness, while shearspinning proceeds according to the sine rule. Final wall thickness in flow forming maybe estimated by conservation of volume.between lobes.Shear forming and flow forming principally cause compressive stresses, predominantly through-thickness. The initial workpiece shape distinguishes the latter and the former processes: nominallya flat blank is employed in shear forming whereas flow forming employs a bushing or tubular blank.The classifications and depictions of each of these processes occasionally overlap in the literature,as shear forming process parameters can be changed to approach those of flow forming. A practicecalled ?overspinning? where the final target thickness is less than that dictated by the sine ruleproduces forming conditions approaching forward flow forming, rendering shear spinning a nominalprocess description.In flow forming, a rotating workpiece mounted on a mandrel is induced to incrementally de-form between a mandrel and a roller traversing the axis of the workpiece (Fig. 1.12). Depending onhow the workpiece is supported, the material can be induced to move in either direction along themandrel as compared to the motion of the roller(s). Flow forming allows for significant and con-20CHAPTER 1. INTRODUCTION(a) Wrinkling (b) Circumferential cracking (c) Radial crackingFigure 1.11: Typical spinning defects reviewed by Music et al. [62] and Wong et al. [63].Originally described by Romanowski [64].trollable thickness reductions axially through the part length by employing combined rolling andextrusion/drawing deformation mechanisms. The coupling of these mechanisms generates plasticstrains that are much larger than would be realized by either mechanism on its own at the sameforming loads [65?67]. In order to improve throughput, most commercial operations employ mul-tiple rollers which operate at the same time in a coordinated fashion. Often these rollers are offsetaxially and radially along the length of the workpiece, having different geometric profiles. Sinceconventional spinning, shear spinning and flow forming process descriptions often overlap [68], thecollective label of rotary forming processes may be used as a less complicated description; this labelwill be employed throughout this thesis.The application of rotary forming results in complicated, highly non-linear tooling and work-piece interactions that are dependent on a myriad of process variables. These process variablesinclude the rates of tooling travel, rotation rate of the workpiece, forming zone geometry, lubrica-tion condition and workpiece material properties. These process variables echo those characterizingstandard metal turning, leading to some researchers attempting to employ rotary forming techniqueson solid cylindrical components [69, 70] with some success.Due to the complexity of the interactions between the part, tool, and mandrel during rotary form-21CHAPTER 1. INTRODUCTION(a) Forward flow forming(b) Backward flow formingFigure 1.12: Flow forming configurations [66].ing techniques, standard approaches to calculate forming loads and material responses using clas-sical analytical techniques, such as plane strain approximations and slab analysis, are not directlyapplicable. Numerous attempts to develop analytical descriptions of flow forming have resulted indifferent formulations for contact area and therefore forming loads [71]. For example, the analyti-cal tooling contact area proposed by Jahazi et al. [72] versus that of Gur and Tirosh [73] are vastlydifferent. Furthermore, they describe forming conditions that do not persist in the process. Theseassumptions are then compounded by the use of simplified representations for flow stresses andfriction. Employing the results obtained by the aforementioned formulations has therefore lead topotentially erroneous conclusions [74]. Developing another analytical description of rotary formingprocesses from a shear spinning perspective, such as that by Chen et al. [75], requires the assump-tion that deformation obeys the sine rule throughout the process and may not be extended to flowforming.Finite Element Analysis (FEA) techniques have been successfully employed to provide betterapproximations of both forming loads and the material response during rotary forming, where ele-ments of spinning and flow forming may manifest. As there is a great deal of literature regarding22CHAPTER 1. INTRODUCTIONthis topic, the focus of the following subsection has been limited to the experimental studies of ro-tary forming on aluminum alloys. For a further review of rotary forming processes, the reader isdirected to literature reviews by Music et al. [62] and Wong et al. [63].1.5.1 Experimental studies of rotary formingExperimental studies on this process conducted at ambient temperatures on wrought aluminumalloys have demonstrated that large amounts of plastic deformation may be imparted. Haghshenaset al. [76] reported that equivalent strains of up to 17 may be imparted to an aluminum workpiece.Applications of this forming technique specifically to cast aluminum alloys have shown the potentialto reduce or eliminate porosity entirely with heavy plastic deformation, significantly improvingfatigue performance. However, due to the lack of ambient ductility, spinning of cast aluminumalloys requires deformation at elevated temperatures in order to achieve a sound product.Mori et al. [77] conducted spinning experiments at temperatures between 350 and 400?C oncast A357 alloy blanks machined from larger castings. A schematic of the experimental apparatusis shown in Fig. 1.13a. It consisted of a stepped mandrel directly driven by a motor with a 2mm thick blank bolted to the face. A steel enclosure surrounded the immediate space around theworkpiece into which air at 700?C was introduced. When the blank was at the intended formingtemperature as identified with an infrared thermocouple (IR-TC), the blank was spun into contactwith a numerically controlled roller actuated in both the z and R directions. Cracking was observedat 350?C in the deformed blank corresponding with the step in the mandrel (Fig. 1.13a). Whenthe temperature was increased to 400?C, cracking was not observed and post-deformation analysisfound that porosity had been eliminated at wall thickness reductions of 25% and greater.While not quantified, it was reported that the DAS was reduced in-line with the wall reductionlevel. As compared to undeformed material, it was reported than an increase in yield strength ofthe deformed material was found after T6 heat treatment (Fig. 1.14). Ductility, as characterized byelongation, was increased by approximately twofold over all deformation levels. However, the spe-cific T6 schedule followed by Mori et al. was not detailed, and therefore it is difficult to differentiatebetween the effects on strength due to deformation and heat treatment.Zhao et al. [79] conducted elevated temperature spinning experiments on strontium modifiedLPDC A356 tubes with a starting wall thickness of 23 mm. At severe wall thickness reductions,23CHAPTER 1. INTRODUCTION(a) Experimental(b) IndustrialFigure 1.13: Experimental apparatus employed by Mori et al. [77] and industrial forming ap-paratus employed by Cheng et al. [78].the dendritic structure was no longer recognizable in some locations. Average dendrite arm spacingwas modified from 37.2 to 23 ?m at wall thickness reductions of 80%. Mechanical testing of thismaterial also showed improvements in the mechanical properties following heat treatment (Fig.1.14). The undeformed material had a hardness of HB =69, which increased to 80 in material with a70% wall thickness reduction. The hardness reported in the undeformed condition matched that ofTash et al. (Fig. 1.5) for material in the solutionized condition suggesting that a non-standard heattreatment was employed. Zhao et al. did not disclose the forming temperature used.Cheng et al. [78] employed a numerically controlled industrial forming apparatus (Fig. 1.13b)to reduce wall thicknesses of blanks made of A356 with a diameter of ?400 mm and a starting wallthickness of ?8 mm. Maximum thickness reduction was reported as 60%. The apparatus consisted24CHAPTER 1. INTRODUCTION0 20 40 60 80 1000.9511.051.11.151.21.25Thickness reduction (%)Normalizedstress  abcFigure 1.14: ?y versus wall thickness reduction for (a) A357-T6 after Mori et al. [77] and (b)A356?T6 after Zhao et al. [79]. Also from Zhao et al., ?u(c). Values are normalized byrespective measurements for undeformed-T6 material.of a mandrel with an actuated tailstock to hold the workpiece in place while being deformed simul-taneously by three rollers. These rollers were offset axially and circumferentially about the formingaxis, z. Cheng et al. found the same effects on microstructure as the two previous studies with aprocessing temperature of 350?C, however, they also observed a small decrease in Rockwell hard-ness of the material in the spun condition (HRF = 90.5? 1.5 versus 89.3? 0.7) post solutionizingfor 6 hours at 540?C and ageing for 3 hours at 155?C. While tensile properties were not reported byCheng et al., according to the data presented by Tiryakiog?lu et al. (Fig. 1.6), this would representa slight decrease in yield strength. This is incongruent with measurements reported by Mori et al.and Zhao et al., which indicate that deformation improves properties with increased deformation.1.5.2 Finite element analysis of rotary formingThe development of rotary forming process models based on material characteristics, process ge-ometry and other operating parameters are highly desirable. This section summarizes the effortsof researchers to address the previously discussed shortcomings of analytical models by employingFEA.25CHAPTER 1. INTRODUCTIONIsothermal finite element analysis of rotary formingThe earliest 3D FEA approaches used to simulate material response during rotary forming wereperformed by Xue et al. [80] and Xu et al. [1]. These models consisted of a 120? section of theworkpiece, with the contact region of the roller pre-defined according to an analytical and experi-mental characterization of a flow forming process provided by Hayama [81]. The commercial FEAsoftware package ADINA was employed by Xue et al., while Xu et al. employed an implicit method.Meshed tooling was employed in the former, while nodal velocities were directly imposed in thelatter. Material response in both studies was implemented on a elastic-perfectly plastic basis, andboundary conditions were identical in both cases. Symmetry boundary conditions were imposedon the edges of the 120? section, which implies three rollers simultaneously in contact on the sameaxial plane, and all nodes on the inner diameter of the workpiece were radially constrained. Thisconfiguration does not accurately reflect the forming conditions in a discrete component as it lacksany description of strain rate effects, nor is the evolution of the elastic loading through the annu-lus of the workpiece described. Furthermore, all diametral growth of material entering the rollerimpingement zone was suppressed due to the radial constraint, which prevents the simulation of acommon phenomena in the flow forming process [82].More recently, Mohebbi et al. [83] developed a geometrically identical model to Xu et al. withthe exception of using a full 360? workpiece, and a single roller. Both the roller and mandrel weremodeled as rigid analytical surfaces, however the same radial boundary conditions imposed by Xu etal. and Xue et al. were retained. The commercial software package ABAQUS Explicit was employedin this work. A Hollomon hardening description for the wrought aluminum alloy was employed.None of the aforementioned studies present quantitative comparisons between experimental andtheir FEA predictions. However, Mohebbi et al. found that their simulated forming loads agreedwith the predictions of an analytical model developed by Hayama [81]. Unfortunately, they did notreport the mean flow stress employed nor the friction factor employed in the analytical formulation.Together, the efforts of Xue et al., Xu et al., Mohebbi et al. and Hayama provide a description ofthe principal deformation modes along principal axes of the workpiece, as shown in Fig. 1.15.Wong et al. [69] used both the implicit and explicit versions of ABAQUS to investigate rotaryforming of solid lead cylinders using flow forming techniques. Wong et al. found that implicit26CHAPTER 1. INTRODUCTIONFigure 1.15: Qualitative description of the simultaneous deformation modes imposed on aworkpiece during tube spinning in the axial (z), radial (R) and circumferential (? ) di-rections, after Xu et al. [1].techniques provided more accurate predictions of forming loads and final deformation based oncomparisons with experimental data. However, it was found that the computational penalty for usingimplicit formulations was excessive, suggesting that explicit formulations are the best approach interms of computational resources used. Using the results of the implicit FEA, it was shown that anexplicit formulation with a large mass scaling factor agreed quite well with the implicit results whileproviding a near ten-fold reduction in computational time. Wong et al. were the first to summarizethe main challenges faced when using FEA to analyze flow forming and related processes [67, 69].They are as follows:? Flow forming is an incremental forming operation, as such only a small portion of the surfaceof the workpiece comes into contact with the roller at any given time. The contact area iscontinually changing as the roller moves leading to difficult contact formulations.? A rotating workpiece induces a computational penalty as all nodal positions are affected dur-ing each time step.? The deformation process has no plane of symmetry, requiring a 3D domain with very highelement counts.All of the aforementioned studies have made comparisons between experiments and simulationson a qualitative basis. Only recently have quantifiable comparisons of experimental measurements27CHAPTER 1. INTRODUCTIONto those from FEA been attempted for rotary forming. The most recent study containing this com-parison was conducted by Wang and Long [84?86] on a conventional spinning process of steelworkpieces. The sole comparison provided was the final thickness of the part versus normalizedpart length, which exhibited 15% error. Owing to the lack of through-thickness reduction inherentin spinning, this error may not reflect the overall accuracy of the model. A model of slit spinning ofaluminum by Zhan et al. [87] found an overall maximum error of 22% in all dimensions, with themaximum discrepancy coinciding with regions of the workpiece having the largest departure fromthe sine rule. The dimensions involved in this comparison were not provided. Huang et al. [88]found that a model of slit spinning under-predicted forming forces by 16%. However, the modelwas inconsistent with the experimental process on which it was based [89] in terms of geometry andmaterial description.All of these preceding studies did not consider the evolution of temperature within the work-piece, employing material descriptions that were based on a single forming temperature. This isparticularly tenuous when considering that a number of these modelling efforts attempt to describethe process for strain rate and temperature dependent materials.Coupled thermomechanical finite element analysis of rotary formingMichel et al. [90] developed a fully coupled explicit model for spin extrusion using MARC. Thespin extrusion process consisted of a combination of flow forming and backwards extrusion, or ahybrid between the Mannesmann2 and flow forming processes. This is the only model reported inthe literature on rotary forming that couples the thermal and mechanical aspects of the process toaccount for the heat generated due to inelastic deformation, or the conversion of strain to thermalenergy. This is characterized as the inelastic heat fraction or Taylor-Quinney coefficient [91], whichis a ratio of strain energy converted to heat during deformation. Heat generation within the work-piece and subsequent transfer to the surrounding environment and to the tooling was considered inthe model. However, frictional heating at the tooling interface was ignored. Michel et al. did notcompare their model against any experimental data, nor document their material description.2Cross-roll piercing process for fabricating seamless pipe28CHAPTER 1. INTRODUCTION1.6 Scope and objectivesWhile the characteristics of A356?T6 have been well documented in the literature in terms of thenet effect of heat treatment on mechanical properties, there is a paucity of data regarding the ma-terial in the AC form. The effect of holding aluminum alloys in the AC condition at the elevatedtemperatures necessary for forming purposes, followed by deformation, has unknown implicationson the final microstructure and mechanical properties of the heat treated material. The propertiesof heat treatable aluminum casting alloys are dependant on microstructural features spanning sev-eral length scales, which are all affected by processing in this manner. Understanding how themicrostructure changes during the different stages of this processing route may help explain themechanical properties of rotary formed cast aluminum reported in the literature.The complexity of rotary forming has precluded the development of effective analytical tech-niques to estimate important process parameters such as forming loads. Rotary forming processmodels employing FEA to accurately determine process parameters and final product dimensionswould increase adoption of the process and reduce the need for costly experimentation. However, todate, studies in this area have used simplistic material models, or have made other incongruous as-sumptions. Furthermore, the surveyed literature indicates that there is a need to improve the materialbehaviour description in rotary forming models and to assess their predictions through comparisonto experimental data.Additionally, there is a scarcity of multiaxial HCF data for A356?T6, including the associatedfracture mechanisms and an experimental basis for a multiaxial fatigue criteria. There is also alack of data regarding the critical defect size required to diminish the endurance limit of A356?T6.This characterization would set a foundation for identifying the specific methods by which rotaryforming improves fatigue resilience.1.6.1 ObjectivesThe objectives of the present work are to investigate the effects of rotary forming on cast alu-minum alloys, specifically, A356 and to develop a model to investigate the evolution of stress state,workpiece deformation and deformation rate. Beyond investigation of the general effects of rotaryforming, the objectives also include augmenting fatigue characterization of A356?T6, to distinguishthe effects of rotary forming on fatigue resilience.29CHAPTER 1. INTRODUCTIONTo achieve these objectives, the following research tasks were identified:? Characterize the flow stress behaviour of AC A356 at various elevated temperatures and strainrates in the AC condition, and ascertain an appropriate constitutive behaviour suitable for FEA;? Develop a simplified Experimental Forming Apparatus (EFA) to produce rotary formed ma-terial with known processing histories, capable of imparting deformation at temperatures in-dicative of a commercial rotary forming process;? Experimentally ascertain the effects of the rotary forming processing route (deformation fol-lowed by heat treatment) on a workpiece;? Develop a process model of rotary forming capable of capturing thermal and deformationhistory of the material, based on the inputs dictated by the EFA;? Study crack growth and the impact of porosity of A356?T6 under multiaxial fatigue condi-tions; and? Characterize the improvement in fatigue resilience of A356?T6 imparted by rotary formingThe research tasks represent substantive and novel contributions based on the literature reviewedpreviously in this chapter. While a significant number of studies have been undertaken to study thedeformation behaviour of A356, all have focused on the material following various thermal treat-ments. Deformation behaviour has been characterized in the AC condition at different strain ratesand temperatures under torsion, however, this was for a select number of conditions. While there areseveral published examples of isothermal FEA models of rotary forming, there have been no fullycoupled thermomechanical models reported and validation has been mostly limited to qualitativeobservations. There has been limited work conducted on tracking the effects of thermomechanicalprocessing on A356 in the AC state. Although many uniaxial studies on the fatigue behaviour ofA356?T6 have been published, an attempt at identifying the critical defect size from a multiaxialfatigue standpoint has not been previously attempted. While an improvement in specific mechan-ical quantities for rotary formed cast aluminum has been reported, there is a paucity of publishedquantitative data on the effects of rotary forming on fatigue properties of any alloy.30CHAPTER 1. INTRODUCTION1.6.2 ScopeThe degree to which the aforementioned research tasks were pursued has been grouped accordingto five main analysis types, as described in Fig. 1.16. This figure also describes the source of eachmaterial type and the processing applied to each material prior to each analysis. These analyses aredescribed in detail below.Figure 1.16: Material and data flow outlining the present work.In order to address the lack of deformation data for A356 at elevated temperatures and strainrates in the AC condition, a large number of isothermal compression tests were conducted in aneffort to develop a comprehensive constitutive equation. The material for this study was sourcedfrom a wedge cast in an apparatus configured to generate specimens with similar microstructureto material cast in a commercial LPDC operation. Analysis of the experimental data was analyzedwithin a constitutive framework, with the end result being an expression capable of describing theflow stress as a function of temperature, strain and strain rate over a wide range of conditions. Thisexpression is necessary for the coupled thermomechanical model.A fully coupled thermomechanical model of a rotary forming operation was developed. Thescope of the model was limited to predicting final part geometries compared to several differentforming experiments. These forming experiments, conducted with the EFA, encompass workpiece31CHAPTER 1. INTRODUCTIONwall thickness reductions ranging from conventional spinning to flow forming. The forming condi-tions imposed by the EFA, combined with the constitutive behaviour description provided the mainmodel inputs.The effect of holding A356 in the AC state at elevated temperatures for forming purposes, fol-lowed by deformation has unknown implications on the final mechanical properties following heattreatment. The properties of heat treatable aluminum casting alloys are dependant on microstruc-tural features spanning several length scales, all of which are affected by processing in this manner.Therefore, the effects of forming operations mirroring those employed with the EFA on the mi-crostructure was characterized, both in the as-formed and T6 condition. This was accomplishedthrough microstructural observations on specimens with various thermomechanical histories, coin-ciding with extensive hardness measurements, Scanning Electron Microscopy (SEM) and Energy-Dispersive X-ray spectroscopy (EDX) analysis.Pursuant to the thermomechanical characterization, the fatigue properties of A356?T6 and ma-terial with varying degrees of deformation in the same heat treated condition were determined.Commercially formed material, in addition to material processed by the EFA, was included in thischaracterization. The commercially processed material embodied significantly more deformationthan that delivered by the EFA. Performance was gauged via uniaxial HCF testing.The current work contributes to understanding the multiaxial HCF behaviour of A356?T6, whichhas seen little attention in the literature. Generating a wide variety of microstructure seen commer-cially, multiaxial fatigue mechanisms were analyzed through fracture surface observations to com-pare against existing uniaxial understanding. Employing a Kitigawa-type analysis, the influenceof casting defects on the HCF behaviour was also examined, permitting the evaluation of a criticaldefect size.32CHAPTER 2EXPERIMENTAL METHODS AND APPARATUS1This chapter details the sources of the materials employed in the present work, along with descrip-tions of the apparatus and the experimental methods used.2.1 MaterialAll of the A356 materials used in this study were sourced from a North American wheel manu-facturer in various states, ranging from melt to LPDC wheels in the AC, T6 and rotary formed-T6conditions. The characteristic composition of all material is given in Table 2.1.Table 2.1: Composition (%-wt) of modified A356, balance Al.Si Mg Fe Ti Na Sr Ni Cu Zn Ca Zr6.714 0.334 0.130 0.124 <0.001 0.014 0.005 0.005 0.002 0.001 0.004A356 in melt form was used to cast wedges using a purpose built apparatus (Fig. 2.1), at thesite of the aforementioned wheel manufacturer. Samples were cut from the wedges for constitutivebehaviour analysis (Type 1) and multiaxial fatigue characterization (Type 2). The wedge castingapparatus consisted of a three part AISI?4320 steel mould (two halves containing a runner andgating system as well as the sides of the wedge cavity) and a water-cooled chill plate which formedthe bottom of the cavity. The mould halves were held together by a combination of clamps and1Portions of this chapter have been published in:? Roy M. J., Nadot Y., Maijer D. M., Benoit G., ?Multiaxial Fatigue Behaviour of A356?T6?, Fatigue and Fractureof Engineering Materials and Structures, (2012)? Roy M. J., Nadot Y., Nadot-Martin C., Bardin P.-G., Maijer D. M., ?Multiaxial Kitagawa analysis of A356?T6?,International Journal of Fatigue, 33 (2011) 823-832? Roy M. J., Maijer D. M., Dancoine L.,?Constitutive behaviour of as-cast A356?, Materials Science & Engineer-ing, (2011)33CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUS(a) (b)Figure 2.1: Wedge casting apparatus and pour type (a) with resulting casting geometry (b).bolts. The casting methodology was altered slightly for each wedge type. For the Type 1 wedge, therunner and gating system was employed and the chill was cooled with 10?C water supplied throughtwo 6.4 mm diameter channels at 3.8 bar. For the Type 2 wedge, the gate system was blocked andthe mould cavity was filled directly with melt, and no cooling water was employed. The motivationfor this wedge geometry was to create a gradient in cooling rate varying with height in the wedge.This methodology was employed to generate material with a range of DAS sizes and defects. Inboth cases, a more refined microstructure was found at the base of the wedge where the coolingrate was the highest as compared to a coarser microstructure at the top where the cooling rate wasthe lowest. The Type 1 wedge exhibited a finer microstructure overall, consistent with commercialLPDC processes, while the Type 2 wedge provided material consistent with LPDC at the base andbecoming coarser with height.LPDC wheels with the same composition as given in Table 2.1 were also provided in several34CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUS(a) (b)Figure 2.2: Typical microstructure of compression test specimens extracted from a Type 1wedge. Low magnification in (a) and higher magnification in (b).conditions. AC wheels were employed as blanks for EFA trials (Section 2.1.2), T6 wheels wereemployed to bolster wedge castings in the multiaxial fatigue study (Section 2.1.3), and commerciallyflow formed wheels in the T6 condition were also supplied for uniaxial fatigue studies (Section2.1.4).2.1.1 Material employed in constitutive behaviour analysisCylindrical compression test specimens, nominally measuring 10 mm in diameter by 15 mm inlength, were extracted from an AC Type 1 wedge. The mean DAS of this material was found to be39.9 ?m with a standard deviation of 7.0 ?m. Gas-based porosity was widely dispersed with a meanpercent area of 0.154% based on micrographic observations. These measurements are characteristicof the cross-section of the wedge where specimens were extracted and are similar to those observedin the wheel castings employed in parallel studies. Figure 2.2 show micrographs of the typicalmicrostructure observed.2.1.2 Castings used for experimental formingAC wheels, produced via a standard LPDC production process, were obtained from the aforemen-tioned North American wheel manufacturer. Blanks suitable for spinning on the EFA were machinedfrom these castings by removing the spokes and hub of the wheel through machining. The blanks35CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUSdid, however, retain the original cast surface in the region that was to be deformed. Employing ablank that could be machined from a wheel casting both eliminated the need for a purpose builtmould to cast blanks and made use of material generated using the industrial process. The resultingblank measured approximately 140 mm axially, had a minimum internal diameter of 330 mm, andan approximate 10 mm wall thickness. Fig. 2.3 shows an axial cross-section of the blank.Figure 2.3: Cross-section of AC blank used with EFA. The blank datum employed is indicatedat z = 0. Fatigue sample extraction region is indicated as well as coupon and circumfer-ential section locations.As discussed in later chapters and sections, these blanks were formed by varying amounts withthe EFA, and characterization was undertaken both prior to heat treatment and afterwards. Hardnessprofilometry was carried out across the entire axial cross-section, and on a 72? circumferential sec-tion. Detailed microstructural analysis and targeted thermal treatments were completed on couponscut sequentially in the circumferential direction from the AC blank. A single undeformed blankand the most heavily deformed workpiece resulting from the forming experiments had uniaxial fa-tigue specimens extracted from axial sections. The fatigue specimens were removed following heattreatment of both components.2.1.3 Material employed in multiaxial fatigue behaviourThe material employed for the multiaxial fatigue study was sourced from both a Type 2 wedge anda LPDC wheel, as shown in Fig. 2.4. The wedge was divided into regions where fatigue specimenswere drawn from based on changes observed in the microstructure. One half of the wedge wasdevoted to multiaxial fatigue specimens (Fig. 2.22), and the other half had a mixture of multiaxial,uniaxial and torsion specimens drawn from it. All specimens were then heat treated to a T6 conditionafter being removed from the wedge block as described in Section 2.3.1. Multiaxial specimens were36CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUS(a)(b)(c)Figure 2.4: Multiaxial fatigue specimen locations in Type 2 wedge (a), extraction points ofmaterial from spokes (c) of an LPDC wheel (b) in the T6 condition.also extracted from the spokes of the LPDC wheel which had the same material composition as thewedge casting. This wheel was received in the T6 condition.The scale of the microstructure showed a marked increase from the bottom of the wedge to thetop (Fig. 2.5) coinciding with the cooling rate differential imposed by the casting practice. Thisis characterized by the measured DAS which increased from the bottom (39.5 ?m) to the top (72.2?m). Average porosity remained relatively uniform throughout the wedge based on the percent area.The peak pore size, as characterized by maximum?area found through metallographic analysiswas 126 ?m. The porosity measurements also show that the middle of the wedge, at a height of89-120 mm, contained a region of elevated porosity as characterized by the maximum pore size.The DAS measured in the wheel specimen (36.7 ?m) was similar to that measured at the bottomlocation in the wedge. The area percent porosity throughout the wedge was uniform (? 0.12%) andapproximate double that measured in the wheel (0.06%). The reduced porosity content is consistent37CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUS(a) (b) (c)Figure 2.5: Typical T6 microstructure and porosity in Type 2 wedge casting. Microstructureat the top of the wedge (a) versus (b) bottom with porosity highlighted, detailed in (c).Table 2.2: Microstructure and porosity summary of material employed in the fatigue study.Standard deviation is provided where applicable.Family Height DAS Mean Porosity HV5(mm) (?m) % Area ?areamax (?m) (kg/mm2)Wheel (W) N/A 36.7 ?8.0 0.0603 59 86.2 ?2Wedge Bottom (A?/B)28.75 39.5 ?7.60.12373678.9 ?558.75 39.7 ?9.1 6188.75 47.6 ?14.0 124Wedge Middle (M)118.75 57.2 ?17.90.124410583.1 ?3144.73 58.5 ?21.0 45174.73 59.7 ?21.2 93Wedge Top (T) 204.73 62.6 ?21.6 0.1232 48 89.0 ?7234.73 72.2 ?28.2 126?Artificial defectswith the degassing practices employed by the wheel manufacturer which substantially reduce thehydrogen content. A range of mean maximum pore diameters was measured in the wedge with thelargest diameters observed in the upper portion of the bottom region (Bottom family, Table 2.2).The increase in pore diameter at this location was a result of the double ladle pouring procedureused to fill the mould cavity where the casting began to solidify between pouring the first ladle andthe commencing to pour the second.38CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUSHemispherical artificial defects were introduced to the middle of the gage sections of six fa-tigue specimens via Electro-Discharge Machining (EDM). In total, two torsion and four uniaxialspecimens were drawn from the bottom of the wedge (family A, Table 2.2) and had artificial de-fects applied post heat treatment with a sink-type machine2. This technique of generating artificialdefects has been qualified in other crack propagation investigations [92, 93]. An example of anartificial defect as it appearing on a fracture surface is shown in Fig. 2.18.2.1.4 Commercially formed materialCommercial wheel castings intended for rotary forming were also produced by the same NorthAmerican wheel manufacturer mentioned previously with the outboard side of the wheel (spoke,hub, etc.) near to net shape, and the inboard side cast with a short, thick wall. This inboard portionwas then formed at elevated temperatures prior to heat treatment. Fig. 2.6 shows the cross-sectionalgeometry of the AC blank and the formed result. After casting and before forming, the blank wasplaced in a holding furnace at 350?C for up to 6 hours. The blank was then placed on a mandrel androtary formed by two diametrically opposed rollers. The path taken by the rollers moves materialdown in the z direction and out from the mandrel to form the inner tire bead of the wheel. Afterforming, the wheel was quenched and then passed through a T6 treatment. All wheels receivedwere in the formed and heat treated condition as well as having undergone some machining. Asingle early prototype AC blank was also obtained.Radius-gauge tensile fatigue specimens were extracted from 4 different locations in the receivedwheels, corresponding to different levels of deformation and orientation. As indicated in Fig. 2.6,specimens were drawn from the hoop or circumferential direction (? ) in locations that encounteredno direct deformation (?H?) and significant deformation (?HD?). A similar approach was taken toremove specimens oriented in the axial direction (?A? versus ?AD?).Preliminary analysis of the microstructure shows that the effects of forming are highly localized.This manifests primarily in changes to the DAS, ranging from lightly compacting the structure oreliminating it entirely, as shown in Fig. 2.7. The microstructure for both the formed-T6 and ACmaterial was characterized and is discussed in greater detail in the following chapters.2Charmilles IsoPulse P2539CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUS(a) AC blank(b) Deformed-T6Figure 2.6: Blank versus formed cross-section geometry showing principal regions affectedby forming as well as location of fatigue samples oriented in the axial (A) and hoop (H)directions.(a) i (b) ii (c) iiiFigure 2.7: Commercially formed T6 microstructure at locations indicated in Fig. 2.6.40CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUS2.2 Experimental forming apparatus and methodologyA scaled rotary forming apparatus was developed to conduct instrumented rotary forming exper-iments. This EFA was constructed based on the geometry of blanks extracted from commercialwheel castings described in Section 2.1.2 and was designed to be flexible enough that differentblanks could be employed through the design of modular tooling in follow-on experiments.The core of the EFA is a Herbert No. 9 capstan lathe (Fig. 2.8a). This lathe was retrofittedwith the necessary systems to be capable of performing repeatable forming experiments at elevatedtemperatures (Fig. 2.8b). All modifications were designed to incorporate commercially availableoff-the-shelf components where possible and custom fabrication elsewhere. The following sectionsdescribe the main components assembled and integrated into the lathe to make this possible.2.2.1 As-received lathe and modification overviewThe received lathe had the following important standard features: a spindle to which a workpiecemay be affixed, a tool stand to hold a turning tool which may be moved along bed rails to encounterthe workpiece, and a tailstock on the same bed rails placed after the tool mount to support long andheavy workpieces. This lathe was also equipped with a mast which engaged a capstan to controltooling and tailstock flexure during heavy turning operations. This feature, plus the overall massof the machine made it a good candidate for conversion to rotary forming operations. Additionalfeatures and components appearing on the lathe are shown in Fig. 2.8a.The lathe is belt-driven by a continuously run induction motor rated at 22.4 kW (30 HP). Theoutput is split with a transmission to drive both the spindle and saddle, giving a range of discretespindle speeds from 19 to 560 RPM. The longitudinal feed, which runs the saddle between thespindle and turret along the z-direction, is proportional to these spindle speeds. As received, thelatitudinal feed which runs the tool in the R-direction was damaged, however manual movement ofall tooling was retained.2.2.2 Rotary toolingThe design of the rotary tooling was conducted in concert with the blank (Fig. 2.3) such that theblank could be extracted from a commercial wheel casting and fit the work envelope of the lathe.The geometry (Fig. 2.3) of the blank represents a compromise between removing segments of the41CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUS(a) Lathe components(b) CAD depiction with additional componentsFigure 2.8: Main lathe components: (1) frame, (2) mast, (3) steady rest, (4) tailstock, (5) toolstand location, (6) spindle, (7) tool slide, (8) saddle, and (9) capstan on the as-receivedlathe in (a) and a CAD depiction in (b) of the same components and additions made forforming purposes.42CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUSFigure 2.9: Depiction of the rotary tooling assembly. The driveshaft connects the main man-drel weldment to the spindle, and is in turn supported by a centre engaging the tailstockplate on the front face. The details of the clamp operation are also shown.wheel perceived as barriers to forming while at the same time providing a clamping feature to hold aportion of the blank to the mandrel and fitting within the work envelope. The geometry of the blankprovided the inputs necessary to further design the tooling to support it through forming, specifically,the clamping system and mandrel. The complete mandrel and clamping system is depicted in Fig.2.9.The main components of the mandrel consist of a slightly tapered, hollow weldment that isattached to a spindle with a hollow driveshaft. The mandrel?s taper was specified to match the taperon the blanks in the clamp region, which was then blended to a smaller taper intended to ease therelease of the blank post-forming. The mandrel weldment is in turn capped by a centering platewhich was brought into contact with a spring loaded ?live? centre3, installed on the tailstock (item4 in Fig. 2.8a). This centering plate, held in place by a series of bolts, also serves to enclose themandrel cavity, which contains a wiring harness for 10 type-K TCs that are welded into the surfaceof the mandrel. Extensions for the TCs are run through the driveshaft and spindle and connectedto the wireless DAQ system described in Section 2.2.5. All components were constructed of AISI?3Ritens number 431-17124; #4 Morse taper, bull nose43CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUS4320 steel and fitted together with grade 12.9 fasteners, allowing the potential for interchangeabletooling for future experiments.The method chosen to hold the blank to the mandrel during forming was to use 3 compressionclamps which force the inner diameter of the blank onto the outer diameter of the mandrel bypushing on the blank flange. The main functional elements of one of the clamps in the clampingsystem are shown in the top right inset of Fig. 2.9. To engage the clamp, first the clamp bracket islocated and fixed to the mandrel with the means of a tapered die pin, passing through the mandrelweldment and the clamp bracket. Clamp element 2 is then fixed perpendicularly to the clamp bracketby a captive shoulder bolt. Afterwards, clamp element 2 is actuated against clamp element 1 witha M16 socket cap screw which passes through the mandrel weldment and threads into the clampbracket. Tightening this bolt induces clamp element 2 to push the engagement block (element 1)against the face of the blank flange. Fixed to clamp element 2 by socket head cap screws, clampelement 3 is brought into contact with the flange opposite to element 1 as the blank approachesthe target forming temperature. Operation of the clamping system requires periodic tightening ofthe M16 socket cap screws as the blank is heated, with the final ?hot? configuration shown in thelower inset of Fig. 2.9. This design accounts for a large range of thermal expansion and maximizesoperator access.2.2.3 Roller and tool standThe tool stand received with the lathe consisted of three main components: a tool holder mountedon a pivot block, which in turn was fixed to a riser communicating with the saddle. This tool standwas originally intended to hold up to four turning tools orthogonal to the workpiece by a locking pinmechanism located in the pivot block. This mechanism was modified such that the tool holder couldbe fixed at arbitrary angles from the R direction by the installation of a jam nut assembly, as shownin Fig. 2.10. A AISI?8620 roller with a diameter of 120 mm and a nose radius of 10 mm was seton an axle with a thrust bearing assembly packed with high temperature grease4. The AISI?4320axle was held in place by a pinch-bolt on a bar held captive by AISI?1035 lateral bracing members,which was then mated to the tool holder. The tool stand angle was fixed at 15? from the R directionfor all experiments. The temperature of the roller remained below that of the mandrel, as it was only4Dow Corning Molykote BR2 Plus44CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUSdirectly heated by contact with the workpiece during the course of forming.Figure 2.10: Roller and tool stand detail.2.2.4 Heating systemIn order to create a flexible heating system which could be scaled as needed, propane heating wasselected as the principal heating method. The heating system consisted of a bank of four propanetorch assemblies that are installed on the mast of the lathe. The torches are held in a frameworkthat permits adjustment of the various torch positions and their distances away from the blank (Fig.2.11). The total heat output of the torch tips employed5 was rated at 82 kW. Propane is suppliedthrough an automotive-type, nominally closed solenoid and regulator at 34.5 kPa, and is distributedto the torches with a manifold containing individual ball valves. The control solenoid permittedrapid cycling of the propane supply, but the torches were lit manually. The final position of thetorches was arrived at by making small adjustments until the blank heated rapidly and uniformly.5Rothenberger/Exact model 313545CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUS(a) Supply detail (b) Torch detailFigure 2.11: Propane heating system.2.2.5 Rotary DAQIn order to monitor instrumentation installed on the rotating tooling and workpieces, a ruggedizedDAQ solution was necessary that could be operated remotely. To meet these needs, a DAQ system wasdesigned to be directly connected to the spindle and spin with the workpiece (Fig. 2.8b). All of theDAQ components are set on a freely rotating shaft mounted to a coupler that directly communicateswith the lathe spindle. Clockwise and counterclockwise angular acceleration/deceleration of theDAQ is dampened with a series of four opposed gas springs, acting about the shaft between the DAQcomponents and the coupler.The electrical components of the system consist of a USB DAQ board6 which is connected to asolid state, small form factor wireless computer. Power for both the DAQ board and the computeris delivered by 12 D-cell NiMH rechargeable batteries. As needed, the computer running loggingsoftware7 is operated remotely to monitor TCs in the mandrel (Fig. 2.9) and blank via a VirtualNetwork Control (VNC) connection during forming operations.2.2.6 Experimental forming methodologySeveral commissioning exercises were undertaken before forming experiments took place. Therotary tooling was installed on the lathe spindle and adjusted until the outer diameter of the mandrel6Measurement Computing 24167National Instruments LabVIEW46CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUSFigure 2.12: Rotary DAQ detail.had 0.5 mm circular runout along the length of the forming region with the tailstock centre engaged.This was measured by a dial indicator after wet polishing the surface with 400 grit Si-C paper. Themandrel surface was preheated to approximately 150?C with the heating system, and was thensprayed with a colloidal graphite coating to aid in blank removal post-forming.A blank was preheated to the same temperature in a box furnace, and the inner diameter wassprayed with refractory-type coating8. This coating was applied to assist in blank removal as wellas to suppress heat transfer between the blank and the mandrel, diminishing blank heating times.The blank and tooling were then allowed to cool to ambient conditions.A single blank had 2 type-K TC junctions peened into the surface, offset on the circumferenceby 30? at different axial locations, and was fitted to the mandrel. These TCs were monitored inconjunction with the other 10 TCs embedded near the surface of the mandrel (Section 2.2.2) to de-termine the characteristic temperature profile through both the blank and mandrel during preheatingand forming exercises. The heating system was engaged, and the mandrel was rotated at ?20 RPM.Heat was applied until clamp element 2 (Fig. 2.9) loosened. The torches were extinguished viathe control solenoid, the clamps were then reseated and tightened before the torches were relit and8Foseco DYCOTE 3247CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUS0 200 400 600 800 1000 1200 1400050100150200250300Time (s)Temperature(?C)  TM1TM2TM3-7TM8TM9TM10(a) Mandrel0 200 400 600 800 1000 1200 1400050100150200250300350400Time (s)Temperature(?C)  TB1TB2(b) Blank(c) TC locationsFigure 2.13: Mandrel and blank temperatures recorded during blank preheat. TC record andaxial location on both mandrel and blank employed for thermal characterization.heating resumed. This continued until a target temperature of 350?C was reached. The clamps werefurther tightened, the heating system was re-engaged and the mandrel was spun at 281 RPM. TheTC record for this exercise is presented in Fig. 2.13, where dashed lines indicate where the mandrelrotation and heating system were disengaged to tighten the clamps, and then heating resumed. Thesolid arrow indicates the point where the mandrel rotation rate was increased from 20 to 281 RPM.This exercise showed that there was little temperature variation in the blank (within 20?C), withthe TC closest to the mandrel interface reading the coldest temperature. The channel exhibitingboth the highest mean temperature and largest heating rate on the mandrel was located immediatelybelow the blank, with temperature and heating rate dropping axially. There was a 1-2?C differencein temperature between the TCs offset circumferentially on the mandrel, and due to this minordifference, the temperature from these TCs has been presented as an average value (TM3-7 in Fig.2.13). Increasing the mandrel speed from the preheating rate of 20 RPM to the forming rate of 281RPM decreased the heating rate in both the mandrel and blank. The mandrel temperature continued48CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUSto increase, while the blank temperature remained nearly constant at the TB2 location over twicethe length of time necessary for forming.Blanks intended for forming did not have TCs installed owing to the interference with forming.Non-contact blank surface temperature measurements were attempted using IR-TCs as per Mori etal. [77] using commercial models9 however it was found that the low emissivity of the blank ma-terial and surface irregularities precluded accurate measurements as compared to a contact method.Therefore, surface temperature measurements of the blank were performed manually with a type-KTC surface probe10 every 3 minutes during heating at TB1 and TB2 locations, as well as imme-diately before and after forming. Preheating the blanks to the target temperature of 360?8?C forforming took between 17-23 minutes. The variance in blank heating time is attributed to mandrelfitment; blanks better conforming to the mandrel surface took longer to heat up as heat transfer tothe mandrel was improved in spite of the refractory-type coating.Once the blank was at the appropriate temperature, the spindle speed was increased to 281 RPMand the roller was brought into contact with the blank at approximately 30 mm per minute. The lon-gitudinal thread-cutting feed screw was then engaged to move the roller axially at a rate of 0.21 mmper revolution with the torches engaged to lessen heat loss. These parameters were selected based oninformation provided on the commercially formed wheels (Section 2.1.4), previous experience withcommercial forming operations [82], the rating of the lathe motor and results of calculations madeduring tooling design. Once the spinning pass was complete, the clamps and blank were removedfrom the mandrel and left to air cool, avoiding potential distortion from quenching.This procedure was repeated to produce three blanks with increasing levels of deformation sum-marily described in Table 2.3 and Fig. 2.14. The specimen with the least deformation (Fig. 2.14b)corresponds to conditions normally seen in spinning operations, and the mid-deformed blank cor-responds to conditions of ?overspinning? as the start of the forming operation was moved axiallytowards the fixed end of the blank (Fig. 2.14c). The peak deformed specimen had two formingpasses applied, one corresponding to the mid-deformed blank and another with a deformation pro-file approaching the conditions of flow forming (Fig. 2.14d). The deformation in all cases was suchthat the inner diameter of the forming region did not contact the mandrel surface for all experiments.9Exergen IRt/c.1X-K-440F/220C and IRt/c.10A10Omega model number 8810849CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUSDuring the course of the process, the workpiece temperature remained above 340?C for all trials.Table 2.3: List and description of EFA experiments based on initial location of roller in termsof the initial axial location and penetration into the workpiece, P.Deformation level Axial forming start (mm) P (mm) PassesLow 100 ?0.01 1Mid 75 ?0.01 1High/peak 75 & 44 ?0.01 & 1 2(a) Undeformed(b) Low level deformation(c) Mid level deformation(d) High level deformationFigure 2.14: Initial and final cross-sectional geometries of workpieces. A depiction of theinitial location of the roller nose is also provided.2.3 Material characterizationMicrostructural changes in the material due to processing and defect features following fatigue test-ing were tracked with several methods. Optical microscopy was used to characterize microstructural50CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUSfeatures in conjunction with multiple image analysis tools. SEM techniques were employed primar-ily in fractography studies and to analyze the effect of heat treatment on precipitation and eutecticparticle changes. Altered mechanical properties due to processing were tracked via extensive Vick-ers hardness tests. Each of these techniques are discussed in greater detail in the following sections.2.3.1 Sample preparationMetallographic specimens from each type of material employed in this research were extractedusing different combinations of bandsaw and Electro-Discharge Machining (EDM) sectioning. Allmetallographic samples were manually polished with 120, 320 and 600 grit Si-C paper. This wasfollowed by two secondary polishing steps with 6 and 1 ?m alumina. Specimen size permitting,final polishing employed a vibratory polishing operation11 at 60 Hz for 180 minutes with 0.06 ?mcolloidal silica. Some samples were mounted in epoxy12 to aid in polishing.While the specific schedule is unknown for the material that was received in the T6 condition,the characteristic T6 schedule performed for all material in the present work is as follows: solu-tionized at 538?C for 3 hours, quenched in water at 60?5?C, and artificially aged at 150?C for 3hours with no natural ageing. Both solutionizing and artificial ageing were performed in separatebox furnaces. A lesser number of small specimens were heat treated for various times and tempera-tures in a nitrate salt bath (60% potassium nitrate, 40% sodium nitrate). These latter samples wereinstrumented with a thermocouple (TC) which was used to continuously monitor the temperatureduring heat treatment.2.3.2 Optical microscopyPhotomicrographs were taken of the metallographic specimens with several different pieces ofequipment. These included:? a Nikon Epiphot 300 inverted microscope and QImaging digital camera, with Clemex VisionPE software;? a Nikon Eclipse MA200 inverted microscope and Nikon DS Fi1 digital camera, with NIS-Elements software;11Buehler Vibromet II12System Three Cold Cure51CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUS? a Leica DM 1LM inverted microscope and Leica DC100 digital camera, with Leica software.Additionally, low magnification images were acquired with a Vickers-Armstrong microscope fittedwith an adapter and a digital SLR camera, as discussed further in Section 2.3.4.Microstructural characterization (DAS, porosity, eutectic-Si particle characteristics) was carriedout on digital images with several software tools including Clemex Vision PE software, Fiji [94] andcustom tools written in MATLAB employing the Image Analysis Toolbox. For wedge characteriza-tion, 2D characteristic measurements of microstructural features were made on a series of imagesrepresenting a composite area greater than 85 mm2. Locations and quantities of measurements madeon formed material are provided in further chapters.DAS measurements were carried out with a program written in MATLAB, shown schematicallyin Fig. 2.15. The program first loaded a micrograph and then accepted the graphical input of thecentre of active secondary dendrite arms. A line of best fit was applied to the arm centres, and thecentres were then projected on this line. The distance between each arm centre on this line wasthen calculated and scaled accordingly for each discrete measurement. This was repeated at allsites where active secondary dendrite arms could be identified, and coincides with the methodologydiscussed in the literature [14].Porosity and defect sizes were characterized by the?area parameter discussed previously inSection 1.4.1. This was accomplished by using one of the aforementioned tools to threshold theimage such that the feature was completely highlighted. The resulting area of the feature was thencalculated based on the number of pixels and scaled accordingly. An example result of this processis provided in Fig. 2.16. In a similar manner, the eutectic particles had their areas measured,and Equivalent Circle Diameter (ECD) was calculated based on this area. Particle aspect ratio wascalculated by applying best-fit ellipses to binarized images of the eutectic, as shown in Fig. 2.17.The aspect ratio was then calculated by dividing the length of the major axis of each ellipse by thelength of the minor.2.3.3 SEM techniquesSEM was carried out on several pieces of equipment. The principal tool employed throughout wasa Hitachi S3000N scanning electron microscope, which was used for general imaging purposes,fractography studies as well as Energy-Dispersive X-ray spectroscopy (EDX). For EDX analysis, an52CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUSFigure 2.15: Example DAS measurement technique, showing 5 discrete arm measurements.(a) Raw image (b) ProcessedFigure 2.16: Example of automated pore size measurement (?area = 29 ?m).Advanced Analysis Technologies detector was employed. This detector has an energy resolution of133 eV and was operated at 2500 to 3000 samples per second with the SEM accelerating voltageat 10 keV. Two other scanning electron microscopes were also employed for fractography studies,including a Hitachi S2300 and JEOL JSM 6400. All were operated in backscatter electron mode,with accelerating voltages ranging from 7 keV to 20 keV.Some polished specimens were deep-etched to examine eutectic Si morphology changes duringpurely thermal and thermal-mechanical processing. This was accomplished by immersing the spec-53CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUS(a) Raw image (b) Binarized (c) Fitted ellipsesFigure 2.17: Example of best-fit ellipses applied to eutectic particles to measure aspect ratio.(a) Raw image (b) ProcessedFigure 2.18: Example of manual defect size measurement carried out on the fracture surfaceof a fatigue specimen containing an artificial defect (?area = 416 ?m).imens in a strong Keller?s etchant composed of 10% HF and 5% HC acid by volume for 50 minutes,as suggested by Colley [18]. These specimens were then imaged via SEM.For tabulating defect sizes employed in the fractography study, a similar process to that em-ployed for the porosity measurements discussed above. However, the SEM images of the fracturesurface did not have the contrast necessary for automated processing. The defects were thereforemanually traced and the result scaled accordingly, as demonstrated in Fig. 2.18.54CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUS2.3.4 Hardness testingChanges in mechanical properties due to thermal and thermomechanical processing were quantifiedvia extensive macrohardness (HV5) measurements, and a lesser number of microhardness (HV0.01)measurements to track changes in the eutectic and ?-Al phases. Macrohardness measurementswere performed on a Vickers-Armstrong Hardness Test Machine (VHTM) which was customized toassist with specimen positioning and measurement processing. Microhardness measurements wereperformed with a Buehler Micromet 3 Micro Hardness Tester. All hardness tests were conducted andvalidated according to the practices detailed in Appendix A. Measurements of indentation diagonalswere accomplished either directly with the filar micrometer on each machine, or indirectly on digitalimages taken of the indentation site employing the analysis tools listed above.The VHTM used for macrohardness measurements was augmented with a custom, Computer Nu-meric Control (CNC) stage (Fig. 2.19). This was accomplished through the design of a double axisrigid stage with ball-screw assemblies driven by high-resolution stepper motors and translator cir-cuits. The translator circuits were in turn controlled by a computer running interpreter programs13.The existing microscope on the VHTM was augmented such that the eyepiece lens and filar microm-eter was replaced with a digital SLR camera14. The camera was controlled with software15 runningon a second computer, employed to image each indentation site. This system provided the abilityto program the stage to repeatedly position a specimen to within 20 ?m accounting for ball-screwbacklash, perform an indentation, and then digitally image the result.In order to create complete hardness profiles of the processed material, blanks with variousprocessing histories were first sectioned, mounted and polished according to the methodology de-scribed in Section 2.3.1. These section profiles were then scanned16 at 1200 DPI. The scans wereprocessed to provide specimen outlines. The outlines were then uniformly meshed with triangularelements, such that the element edge lengths were a minimum of pi times the maximum indent diag-onal of 450 ?m, using a MATLAB script. The resulting mesh was then manually verified and editedsuch that the distance between each node was at least 450pi ?m apart. The nodal coordinates werethen programmed into the stage controller, and indents were placed at each node. The controller13Ability Systems Corporation Indexer LPT and G Code Controller14Canon EOS Rebel T2i fitted with a Martin Microscope MM-SLR15Canon EOS Utility software16Employing a Hewlett Packard ScanJet 4200C55CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUSFigure 2.19: Hardness profiling apparatus consisting of the VHTM with a CNC stage anddigital-SLR camera installed.program was run again following indentation to collect images of each indent. These digital imageswere then processed with MATLAB scripts to generate measurements of the indent diagonals. Thisautomated method of measuring indents was found to agree with manual measurements within 2%over 500 indents.2.3.5 Compression testing methodologyDeformation tests were conducted on a Gleeble17 3500 thermomechanical simulator fitted withisothermal tungsten carbide Iso-T (isothermal) anvils, treated with a nickel-based lubricant18. Thespecimens were deformed by actuating the anvils hydraulically. During each test, the temperaturewas controlled and recorded with a type-K TC mounted to the centre of each specimen. Instanta-neous diametral deformation was measured with a Linear Variable Differential Transformer (LVDT)actuated by quartz mandibles. This arrangement is depicted in Fig. 2.21.17Gleeble is a trademark of Dynamic Systems, Inc., Poestenkill, NY.18Loctite 77124 Nickel Anti-Seize56CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUS(a)(b) (c)Figure 2.20: Hardness profile mesh and typical indentation field detail. The dashed lines in (a)enclose a typical area shown in (b), which shows a typical low resolution micrographfield defined at each node in (c).The specific test procedure followed for each test was:1. The sample was first loaded between the platens with a preload of less than 0.5 kN.2. The hydraulic actuator was retracted by 2 mm to allow for thermal expansion. Pre-load onthe sample was maintained via friction.3. Joule heating was applied to the sample at a rate of 5?C s?1 and then held at the target testtemperature for 60 seconds.4. The sample was deformed at the prescribed deformation rate to target strains of 0.2, 0.4 and0.55 based on the specimens nominal length at ambient temperature. Deformation rates werecalculated based on specimen dimensions at ambient temperatures.5. Based on the prescribed target strain rate, the data acquisition rate from the three transducerswas greater than 200 samples per unit strain during deformation.57CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUS(a)(b)Figure 2.21: An isometric cutaway depiction of the Gleeble the compression test apparatus.The specimen with a TC junction is positioned between the anvils and LVDT in (a). A2D cutaway showing initial and instantaneous diameters D0 and D in (b).At elevated strain rates, heat generated during deformation was greater than could be removed bythe anvils. This caused a slight increase (? 10?C) in the average deformation temperature Ta, andwas more predominant at lower temperatures and higher strain rates. Although the preload at alltemperatures was kept below 0.5 kN, creep occurred at elevated temperatures during the hold stageprior to deformation. While the creep rate differs with temperature, the amount of creep was nearlyidentical from test to test as the pre-deformation heating cycle was the same. Differing amountsof thermal expansion owed to variations in specimen geometry render quantification of the amountof creep prior to deformation intractable. However, due to the low load each sample experiencedsome amount of pre-deformation. This amount of creep is small and has been considered part ofthe thermal expansion included in the initial diameter, D0. Uniform plastic deformation conditionswere assumed to prevail in all cases. Therefore, the instantaneous true strain ? was found from theinstantaneous diameter D according to:? =?2ln DD0(2.1)The instantaneous strain record was then differentiated to provide the instantaneous strain rate, ?? .58CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUS(a) (b) (c) (d) (e)Figure 2.22: Fatigue specimen types: multiaxial (a), torsion (b), straight-gauge uniaxial (c)and radius-gauge uniaxial (d & e).The average strain rate, ??a, is taken as the mean strain rate during deformation, and was only usedto qualify each test. This is also true for the average temperature, Ta, as well. All experimentaldata points of temperature, load, strain and strain rate have been incorporated in the analysis that ispresented in Chapter 3.2.3.6 Fatigue testing methodologyNumerous fatigue sample types were employed to characterize both the multiaxial and uniaxialfatigue behaviour of material with different processing histories. All fatigue tests in the presentwork were conducted under fully reversed loading (RL =?1). These different specimen types werenecessary to facilitate testing with different apparatus and sample sources, as given in Fig. 2.22.Specimen types ?a? through ?c? were drawn from wedge and wheel castings, shown in Fig. 2.4a and2.4c, respectively. Specimen type ?d? was drawn from commercially formed material, as shown inFig. 2.6b. Specimen type ?e? was extracted from EFA workpieces, at locations given in Fig. 2.3.The testing apparatus, testing frequency and applicable loading condition is summarized in Table2.4.The tests which employed the Instron servo-hydraulic apparatus, located in the Laboratory of59CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUSTable 2.4: Fatigue test equipment, operating conditions and specimen typeMachine Frequency (Hz) Sample type (Fig. 2.22) LoadingInstron servo-hydraulic 11 a Tension-torsionAmsler-Vibrophone 45 b, c Tension, torsionSonntag eccentric 33 d, e TensionMechanics and Materials Physics at the ?Ecole Nationale Supe?rieure de Me?canique et d?Ae?rotechnique(ENSMA), were conducted under sinusoidal load control conditions to failure. The Sonntag appara-tus, available in the Department of Materials Engineering at UBC, precluded this type of control, andtherefore testing was conducted under a constant load amplitude as measured with a load cell at thestart of testing. The Sonntag tests were stopped based on a change in elastic response as monitoredby an LVDT and the use of die penetrant for verification. A similar stopping criteria was inherent forthe resonant tests, conducted with the Amsler-Vibrophone machine (located at ENSMA) wherebythe test was stopped when a significant change in resonant frequency was recorded. Specimens thatwere not fractured at the conclusion of testing were cooled with liquid Ni and manually broken forfractographic analysis purposes.The principal utility of the Instron and Amsler-Vibrophone tests was to investigate multiax-ial A356?T6 HCF behaviour. Multiaxial testing was conducted using the step technique originallyoutlined by Maxwell and Nicholas [95], to target the endurance limit (? f , ? f ) at 106 cycles. Bothtension and torsion components were imposed in-phase. With this technique, each specimen under-goes cyclic loading at an initial load level estimated based on previous testing experience. Samplesthat do not fail after 106 cycles are then cycled again at a higher stress amplitude. For speci-mens that failed before 106 cycles without a preceding loading step, the endurance limit was es-timated using a Basquin coefficient, b, of 0.17 based on experimental results found in the litera-ture [47, 55, 58, 96, 97]. For specimens that failed before 106 cycles but after a minimum of oneloading step, the endurance limit was calculated as the average stress amplitude of the failure andprior step.The Sonntag apparatus was used to generate uniaxial S?N or Wo?hler curves, with no steptesting. All data obtained with this apparatus consists of ?runout? results, or results from employinga single load amplitude. The same HCF target of 106 cycles was employed for these uniaxial tests,60CHAPTER 2. EXPERIMENTAL METHODS AND APPARATUSwith minimum loads identified from the multiaxial testing regimen.61CHAPTER 3CONSTITUTIVE BEHAVIOUR OF AS-CAST A3561In order to address the lack of information on the constitutive behaviour of as-cast A356 at elevatedtemperatures across a range of strain rates, a large number of isothermal compression tests were con-ducted according to the methodology described in Section 2.3.5. The data generated with these testssupported the development of a comprehensive constitutive equation. The two main constitutiveframeworks that were considered in developing this equation were an extended Ludwik-Hollomonexpression and a Kocks-Mecking approach. This chapter presents the experimental data, analysisfollowing each constitutive framework, and a discussion of the performance of each.3.1 Experimental resultsIn total, 55 successful compression tests were carried out with a range of temperatures, strains andstrain rates. Temperatures of 30?C, 100?C, and between 200 to 500?C in increments of 50?C andstrain rates of 0.1, 1, 5 and 10 s?1 were targeted. Predominantly in the high strain rate range, thesimulator was not entirely capable of delivering test results without overshooting the target strainor strain rate. Therefore the average strain rates achieved, ??a, are reported. These rates were werecalculated based on the strain versus time information, and are grouped in ranges of 0.06 to 0.11s?1, 0.57 to 0.98 s?1, 3.59 to 5.33 s?1 and 7.58 to 12.24 s?1, which are referred to further as R1, R2,R3 and R4, respectively. Flow curves for each of these strain rate ranges are shown in Figure 3.1,while data for all test conditions is summarized in Table 3.1. The variation in target strain rates andstrains was attributed to thermal expansion and variation in specimen length, therefore the actualplastic strain achieved (?p) as calculated from the LVDT has been reported. A number of additionaltests were performed at the highest target strain rates in each temperature range, however these tests1Portions of this chapter have been published in:Roy M. J., Maijer D. M., Dancoine L.,?Constitutive behaviour of as-cast A356?, Mater. Sci. Eng., A, (2011)62CHAPTER 3. CONSTITUTIVE BEHAVIOUR OF AS-CAST A356were not successful owing to non-uniform deformation and barreling. Tests where these conditionsdeveloped were defined as failed tests and their data is not shown nor used for subsequent analysis.The yield stress for each test (shown in Figure 3.1 as circle symbols on each curve) was foundwith a 0.2% offset method employing temperature-corrected shear and elastic modulii [98], ? andE , according to:? = ?o(1+ T ?300Tmelt)Tmelt?od?dT (3.1)E = 2? (1+?) (3.2)Table 3.1: Compression test characteristics: Ta, ??a, ?y and ?p attained for all tests (continued)(a) ? 30?CNo. Ta (?C) ??a (s?1) ?y (MPa) ?p1 33.4 0.06 97 0.132 36.1 0.07 112 0.373 34.0 0.07 109 0.184 41.0 0.57 114 0.425 38.1 0.71 102 0.196 36.8 0.71 105 0.197 37.5 0.72 113 0.198 33.7 0.74 107 0.149 45.4 3.95 137 0.35(b) ? 100?CNo. Ta (?C) ??a (s?1) ?y (MPa) ?p10 103.7 0.07 95 0.3611 102.4 0.07 104 0.1712 104.3 0.70 120 0.1413 112.4 0.74 102 0.4514 106.9 0.77 106 0.2015 104.7 0.77 117 0.1516 106.6 0.78 111 0.1917 121.5 4.23 121 0.4518 126.9 8.27 117 0.39(c) ? 200?CNo. Ta (?C) ??a (s?1) ?y (MPa) ?p19 201.3 0.08 85 0.1920 199.5 0.08 84 0.3221 204.9 0.72 84 0.3122 203.7 1.10 99 0.2923 188.7 3.86 105 0.2724 201.6 7.58 111 0.27(d) ? 250?CNo. Ta (?C) ??a (s?1) ?y (MPa) ?p25 249.8 0.08 95 0.4226 251.6 0.08 91 0.2027 247.5 0.08 89 0.3328 257.9 0.70 101 0.4429 259.9 4.39 106 0.4030 258.5 8.24 111 0.30(e) ? 300?CNo. Ta (?C) ??a (s?1) ?y (MPa) ?p31 297.8 0.08 90 0.3332 300.5 0.09 85 0.2133 307.6 0.80 101 0.4734 310.2 3.59 108 0.3463CHAPTER 3. CONSTITUTIVE BEHAVIOUR OF AS-CAST A356Table 3.1: Compression test characteristics: Ta, ??a, ?y and ?p attained for all tests(f) ? 350?CNo. Ta (?C) ??a (s?1) ?y (MPa) ?p35 350.1 0.08 60 0.2036 345.3 0.09 65 0.3437 355.0 0.81 71 0.4738 360.6 4.92 84 0.4839 351.9 8.82 81 0.35(g) ? 400?CNo. Ta (?C) ??a (s?1) ?y (MPa) ?p40 400.7 0.09 43 0.2241 396.8 0.09 45 0.3842 404.3 0.83 45 0.5043 407.2 4.28 56 0.4844 407.2 8.59 71 0.3545 408.7 9.17 59 0.3746 404.4 9.68 61 0.15(h) ? 450?CNo. Ta (?C) ??a (s?1) ?y (MPa) ?p47 444.4 0.10 27 0.4148 452.5 0.88 33 0.5249 458.6 5.33 42 0.5350 445.5 10.35 50 0.40(i) ? 500?CNo. Ta (?C) ??a (s?1) ?y (MPa) ?p51 494.9 0.10 17 0.4052 502.3 0.98 24 0.5453 502.6 4.97 32 0.5554 498.8 11.21 39 0.4655 502.8 12.24 38 0.19based on pure aluminum, with T in Kelvin, the temperature dependence of modulus (Tmelt?od?dT ) equalto -0.5, the shear modulus at 300 K (?o) equal to 2.64?104 MPa and ? equal to 0.33. The liquidustemperature of A356 (612.5?C [7]) was employed as Tmelt. A relationship based on pure aluminumis appropriate as the temperature dependence of E for aluminum alloys is relatively insensitive tosolute [99].The flow stress data shows appreciable strain hardening at all strain rates with little strain ratesensitivity until approximately 300-350?C. Above this temperature, there is little to no strain hard-ening and increasing strain rate sensitivity owing to dynamic recovery. This is also demonstrated bythe trend in ?y (refer to Table 3.1). For the low temperature tests, ?y remains relatively insensitiveto strain rate as compared to tests at elevated temperatures. To further demonstrate the change instrain-rate sensitivity, Figure 3.2 shows selected experimental flow stress curves at constant temper-atures for ??a ? R1,R4. For the tests conducted at ? 30 and ? 100?C, ?y for ??a ? R1,R2 was foundto be approximately 108 MPa varying by ?10%. As the systematic error produced by the trans-ducers used in this study is two orders of magnitude lower than this range, the bulk of this varianceis attributed to small variations of DAS, coarse Mg2Si precipitates and segregation in the as-caststructure. Owing to the low area percent and the fact that the applied load will tend to close pores,64CHAPTER 3. CONSTITUTIVE BEHAVIOUR OF AS-CAST A3560 0.1 0.2 0.350100150200250300????a ? R1  Ta = 36.1Ta = 103.7Ta = 199.5Ta = 249.8Ta = 297.8Ta = 345.3Ta = 396.8Ta = 444.4Ta = 494.9Yield(a) R1 = 0.06 to 0.11 s?10 0.1 0.2 0.350100150200250300????a ? R2  Ta = 41.0Ta = 111.5Ta = 204.9Ta = 257.9Ta = 307.6Ta = 355.0Ta = 404.3Ta = 452.5Ta = 502.3Yield(b) R2 = 0.57 to 0.98 s?10 0.1 0.2 0.350100150200250300????a ? R3  Ta = 45.4Ta = 121.5Ta = 191.0Ta = 259.9Ta = 310.2Ta = 360.6Ta = 407.2Ta = 458.6Ta = 502.6Yield(c) R3 = 3.59 to 5.33 s?10 0.1 0.2 0.350100150200250300????a ? R4  Ta = 126.8Ta = 201.9Ta = 258.5Ta = 351.9Ta = 408.7Ta = 445.5Ta = 498.8Yield(d) R4 = 7.58 to 12.24 s?1Figure 3.1: Characteristic experimental flow stresses. Measured stress-strain results for all ??ranges is presented. Average test temperature Ta is reported in ?C.porosity is not considered to influence the compressive strength of the material [39].For comparison, the ?y observed at ? 30?C in this study is half that of this material in the T6condition [100] and twice that of the solutionized condition [39]. The main cause of this differenceis surmised to be the result of the distribution and state of Mg2Si precipitates. In the solutionizedcondition, any precipitates formed during casting have been dissolved and the solute atoms are insolution. This results in a substantively smaller ?y compared to the as-cast condition. The artificialageing step in the T6 process serves to nucleate and grow a more evenly distributed variety of Mg2Siprecipitates as compared to the coarse and randomly distributed variety in the as-cast condition. This65CHAPTER 3. CONSTITUTIVE BEHAVIOUR OF AS-CAST A3560 0.05 0.1 0.15 0.2 0.25 0.3 0.3580100120140160180200220240??  Ta = 103.7, ??a = 0.07??KM??LHYield(a) ? 100?C0 0.05 0.1 0.15 0.2 0.25 0.3 0.3580100120140160180200220240??  Ta = 199.5, ??a = 0.08Ta = 201.6, ??a = 7.58??KM??LHYield(b) ? 200?C0 0.1 0.2 0.3 0.420304050607080??  Ta = 444.4, ??a = 0.10Ta = 445.5, ??a = 10.35??KM??LHYield(c) ? 450?C0 0.1 0.2 0.3 0.4102030405060??  Ta = 494.9, ??a = 0.10Ta = 498.8, ??a = 11.21??KM??LHYield(d) ? 500?CFigure 3.2: Comparison of the experimental flow stress ? to flow stresses predicted by theLudwik-Hollomon ??LH and Kocks-Mecking ??KM constitutive expressions.in turn creates a more effective barrier to dislocation glide, resulting in a higher ?y.For tests conducted at the lowest strain rate, R1, there is evidence of slight strain-softening attemperatures above 300?C (Figure 3.1a), which diminishes at higher temperatures for tests in thesame strain rate range. This behaviour was also observed in the 300?C test for R2 (Figure 3.1b).These results are evidence of the dynamic phenomena known to occur for this alloy system at thesetemperatures, such as recovery [101]. As such, 300?C has been identified as the start temperature forthe transition to strain-rate dependence, the material behaviour may be conservatively characterizedsuch that below 350?C, the material is dislocation interaction dominated. Above this temperature, itis strain rate/diffusion dominated. As there is a temperature/strain-rate range where both dislocation66CHAPTER 3. CONSTITUTIVE BEHAVIOUR OF AS-CAST A356interaction and diffusion processes are both active, a constitutive relationship that traverses these tworegimes will inherently have difficulty describing the flow stress with accuracy in this temperaturerange [102].3.2 Constitutive equation developmentIn general, the phenomenological deformation behaviour of aluminum alloys is dominated by strainhardening at low temperatures, which transitions to a time or strain-rate dependent (creep) re-sponse at elevated temperatures. Models of aluminum casting processes consider the materialas having some elastic behaviour in addition to either time-dependent creep, or plasticity withstrain dependence. The former formulations considered the Sellars-Tegart [103] or Garofalo re-lationships [40,104?106], while the latter [107?109] used extended Ludwik-Hollomon expressions.Constitutive behaviours of AC wrought aluminum AA1050, AA3104 and AA5182 have also beendescribed with a simultaneous combination of time and strain dependence [110] employing theLudwik-Hollomon approach.As standard Sellars-Tegart relationships are not able to effectively describe work hardeningobserved in the current experimental data at temperatures below 350?C, a Ludwik-Hollomon ex-pression was identified as the most suitable phenomenological model to apply to AC A356. Whilebeing quite effective in predicting flow stresses, the main drawback of using phenomenological ap-proaches is that they are only valid within the experimental strain range from which the constitutiveexpression has been derived. Physically-based models, such as the Zerilli-Armstrong [111] whichconsiders grain size or the more general Kocks-Mecking [112?115], employ fundamental materialparameters to predict flow stress. As grain size in cast Al-Si alloys is not typically correlated tostrength as compared to other microstructural features such as DAS, the Kocks-Mecking approachis likely the best physically-based model to apply for AC material. However, this type of approachhas been used primarily to describe materials in the work hardening regime.While the experimental results may be divided into two discernible regimes, from an analysisstandpoint it is necessary to construct an equation or series of equations that successfully predictsthe flow stress across both regimes. The following sections describe the development of two modelsto do so. The analysis was accomplished through linear least squares fitting where possible anda Nelder-Mead technique when non-linear fitting was necessary. The fitting procedure for each67CHAPTER 3. CONSTITUTIVE BEHAVIOUR OF AS-CAST A356approach will be presented initially, after which the results of each model will be discussed. Fittedcoefficients for approach are summarized in Table 3.2.3.2.1 Extended Ludwik-HollomonThe extended Ludwik-Hollomon expression is a phenomenological model that is frequently em-ployed for cast aluminum alloys. In order to capture the simultaneous evolution of both strain hard-ening and strain rate effects with temperature for aluminum, van Haaften et al. [110] proposed anexpression with static fitting coefficients, while other authors [108,109] have employed expressionswhere the fitting coefficients K, M and N are functions of temperature. The temperature dependent,extended Ludwik-Hollomon expression is:??LH = K(T )?N(T )(????1)M(T )(3.3)where ??1 is a normalization strain rate of 1 s?1 . The advantage of this phenomenological approachis that N(T) and M(T ) are both independent functions which when factored from the flow stress,enable K(T ) to be determined via regression.Values of the work hardening parameter, N, were found first via the slope of experimental ln? -ln? curves for each test. The strain-rate term, M, was taken to be the slope of ln? -ln ?? curves builtfrom data at strains between 0.05 and 0.12 with increments of 0.01. The resulting values of M andN versus Ta are shown in Figure 3.3a. The N values plotted versus average temperature demonstratethat there is a near linear trend for all strain rates until approximately 350?C. As mentioned inSection 3.1, above this temperature, diffusional effects become significant. The values of N for??a ? R1 are distinctly negative, while the rest of the strain rates result in N values close to zero.Based on these observations, N(T) was characterized such that:N(T) =?????n1T +n2 T ? Ttn3 T > Tt(3.4)where Tt is the transition temperature (? 350?C) between the two regimes. The constants n1 and n2were found from data corresponding to Ta < 300?C and n3 from Ta ? 300?C. Tt is the intersectionof the two resulting linear expressions.68CHAPTER 3. CONSTITUTIVE BEHAVIOUR OF AS-CAST A356As the physical basis for the trend in the M ?Ta data (Figure 3.3a) is an observed increase instrain rate sensitivity with temperature, a continuous function has been employed to describe M(T):M(T ) = m1T m2 +m3 (3.5)N and M were fit with Eq. 3.4 and 3.5, and then were used to extract values for KLH (Figure 3.3b).The correlation of the strength coefficient with temperature, KLH(T ), was also assumed to be acontinuous function and was found to be best described by:KLH(T ) = k1T 2 + k2T + k3 (3.6)The fitted functions M(T ) and KLH(T ) show good agreement with the calculated M and K valuesbased on experimental values. N(T ) describes the experimental values of N much better in thework-hardening regime as compared to the rate-dependent, with the slowest strain rate data beingpoorly described. Fitted coefficients for each function are provided in Table 3.2.3.2.2 Kocks-MeckingThe Kocks-Mecking hardening model is the most common physically-based approach used to de-scribe constitutive behaviour. The underlying premise of the Kocks-Mecking hardening model is0 100 200 300 400 500?0.1?0.0500.050.10.150.20.25Ta (?C)N,M  N (??a ? R1)N (??a ? R2)N (??a ? R3)N (??a ? R4)N (Ta)MM(Ta)(a) N and M values0 100 200 300 400 500050100150200250300350400T (?C)KLH  KLHKLH(T )(b) KLH valuesFigure 3.3: Extended Ludwik-Hollomon coefficients plotted versus temperature.69CHAPTER 3. CONSTITUTIVE BEHAVIOUR OF AS-CAST A356that the work hardening rate ? = d?/d? approaches zero at some saturation stress, ?s which isa function of strain rate and temperature. As a result, plotting ?/? versus ?/?s creates a mastercurve that is accurate over a large range of hardening such that:??0= f(??s)(3.7)Typically, Eq. 3.7 is assumed to have the form of a linear Voce-type relationship:? = ?0(1? ??s)(3.8)with an integrated form of:? ??s?y ??s= exp(??0??s)(3.9)The saturation stress, ?s, is expressed as:?s = ?s0??0(1?(gg0)1/q)1/p(3.10)which is a function of a normalized activation energy term g, defined as [115]:g = kBT? ?b3 ln??0??(3.11)where ??0 is the minimum strain rate that best converges all data to a single function relating ?s/?to g. Physically, p and q (0 ? p ? 1 and 1 ? q ? 2) in Eq. 3.10 represent the shape of disloca-tion obstacle profiles [114], which in turn decide the values of ?s0 and g0. These constants arephenomenological [115,116] and in the present work have not been tailored to distinguish betweendiscrete obstacles (e.g. precipitates) or grain boundaries. The yield strength, ?y, can also be ex-pressed as a function of g, which renders Eq. 3.9 a ? -? relationship that is a function of strain rateand temperature.Values of ?s were first identified from linear intercepts of experimental ??? data between? = 0 and fully developed yield, ? = ?/20 [115, 117]. The result of this process is demonstratedin Figure 3.4 which shows ?/? versus ?/?s for strain rate ranges R1 and R4. The tabulated ?/?70CHAPTER 3. CONSTITUTIVE BEHAVIOUR OF AS-CAST A356versus ?/?s data demonstrates a continuous function satisfying Eq. 3.7. While the large strain, hightemperature data below ? = ?/20 may be approximated by Eq. 3.8, the overall data distribution isnon-linear. Above ?= ?/20, the data corresponding to small strains and low temperature representsa large initial work hardening rate. The average initial work hardening rate, ?0, across all tests hasbeen identified as 2875 MPa, which is significantly higher than pure aluminum in an annealed statewhere ?0 is in the range of 1120-1720 MPa [118].0.5 0.6 0.7 0.8 0.9 100.020.040.060.080.10.120.140.16?/?s?/?  ? = ?/20? 30? 100? 200? 250? 300? 350? 400? 450? 500Figure 3.4: Compression test work hardening rate versus flow stress. ?/? versus ?/?s for??a ? R1 and R4 at all temperatures is shown. The horizontal line indicates ? = ?/20.Figure 3.5 shows a plot of ?s/? versus g(??a,Ta), and the resulting fitted expressions. Here, thebaseline values of the phenomenological constants identified by Kocks and Mecking [115], p= 1/2,q = 2 and ??0 = 107 s?1 were employed. The constants ?s0/?0 and g0 were determined from they and x intercepts, respectively, of the fitted ?s/? versus g1/q relationship. A sensitivity analysisconducted on the values of p, q and ??0 did not show appreciable improvement of the fit within therange defined by their physical basis.Figure 3.5 also shows the relationship between ?y/? and g. Coinciding with the two regimesidentified in Section 3.1, there is an identifiable threshold value of g, where ?y/? decreases; ?y/?remains constant until this threshold is reached. For larger values of g beyond this transition, ?y/?is taken to approach g0. In order to characterize this transition, a bi-linear function was fitted to data71CHAPTER 3. CONSTITUTIVE BEHAVIOUR OF AS-CAST A356corresponding g1/q > 0.6 and g1/q ? 0.6 for each linear component:?y(g) =????????c1/py g <(cyCy +g1/q0)1/p?(Cy(g1/q ?g1/q0))1/pg ?(cyCy +g1/q0)1/p (3.12)where Cy and cy are constants. The values of all constants are given in Table 3.2.As both ?s and ?y are able to be scaled as a function of temperature and strain rate, an expressionfor flow stress is possible through Eq. 3.9. However, this relationship is incapable of describing alarge portion of the flow stress accurately, owing to the particularly high initial work hardening rate,and the non-linear strain-hardening rate at low temperatures and strains observed in the experimentaldata (Figure 3.4). Having an accurate integrated form is necessary as many commercial FEA codesrequire expressions for equivalent stress and strain. Using a modified equation to describe the ???behaviour [113] has been found to provide a better phenomenological representation of ? versus ?post yield for all conditions such that:??KM =(? 2s +(? 2y ?? 2s)exp(??0??s))1/2(3.13)Both in this expression and in Eq. 3.9, ?0 is taken to be a static value, where ?s and ?y arebased on preselected phenomenological parameters (p, q) for an absolute strain rate of ??0. This0.4 0.5 0.6 0.7 0.80.030.040.050.060.070.080.090.10.11g1/q(?s/?)pand(?y/?)p  ?s?yFigure 3.5: Saturation and yield stresses versus normalized activation energy g, corrected forobstacle profiles by p = 1/2 and q = 2.72CHAPTER 3. CONSTITUTIVE BEHAVIOUR OF AS-CAST A356differs from other approaches taken to assessing these parameters for Al-Mg alloys, which involveregressively solving an objective function [101], and can potentially predict negative flow stresses.The other caveat of using a static value of ?0 is that the slight strain hardening followed by softeningdiscernible at 300?C cannot be captured. However, this phenomena is only pronounced for a smallrange of thermomechanical states. Overall, this approach provides a reasonable description of theentire range of behaviour observed without resorting to scaling ?0.Table 3.2: Values of fitted coefficients in each material model.Model Eq. CoefficientsExtendedLudwik-Hollomon3.4 Tt = 348.8?C n1 =?5.6919?10?4n2 = 0.1892 n3 =?9.2773?10?33.5 m1 = 9.101?10?11m2 = 3.4131m3 = 0.02323.6 k1 = 8.1200?10?4k3 = 407.4k2 =?1.1570Kocks-Mecking3.10 ?s0/?0 = 0.0297 g0 = 1.17983.12 cy = 0.0656 Cy =?0.13613.13 ?0 = 2850 MPa3.3 Comparison of constitutive expressionsFigure 3.2 shows examples of the measured flow stress compared to the predicted flow stressescalculated by the different constitutive expressions. In these calculations, experimental data pointsfor strain, strain rate and temperature are directly substituted into each respective constitutive ex-pression for flow stress. Figures 3.2a and 3.2b demonstrate the characterization of the Ludwik-Hollomon and Kocks-Mecking expressions at temperatures exhibiting strain hardening (100?C and200?C), while Figures 3.2c and 3.2d show the comparison for the strain rate sensitive regime (450?Cand 500?C). Owing to the negligible strain rate sensitivity at 100?C, a single strain rate is presentedcorresponding to R1 in Figure 3.2a, while the latter plots in Figure 3.2 show comparisons to thelowest and highest experimental strain rate ranges, R1 and R4 at each target temperature.At lower temperatures, all applicable relationships describe the experimental flow stress well.The Ludwik-Hollomon fits the data best for these conditions, fitting the data for both strain ratesparticularly well at 200?C (Figure 3.2b). The Kocks-Mecking underestimates the low strain rate73CHAPTER 3. CONSTITUTIVE BEHAVIOUR OF AS-CAST A356flow stress at both 100?C and 200?C, but is acceptable for the elevated strain rate at 200?C. Atelevated temperatures, the Ludwik-Hollomon and Kocks-Mecking expressions are fairly accurate atlow strain rates, but overestimate the flow stress at elevated strain rates.Calculating the sum of the mean difference as well as the RMSE between the predicted andmeasured flow stresses for all tests provides a measure of each models performance. Based on thesemetrics, the Kocks-Mecking slightly underestimates the flow stresses by less than 1% with 3%RMSE and the Ludwik-Hollomon overestimates the flow stress by 2% with 2.5% RMSE. In termsof specific strain rate and temperature ranges best described by each expression, the general trendfor the strain-hardening conditions is that higher error is observed with increasing temperature, withpeak error occurring in the transition regime (300-350?C). Beyond this transition temperature range,the error diminishes with increased temperatures. The accuracy of deformation models using theseconstitutive expressions will therefore be reflected in this behaviour.As this material exhibits a range of temperature and strain rate dependent deformation response,selecting a sole constitutive expression to capture the full range of behaviour observed requirescompromises in accuracy. The extended Ludwik-Hollomon model provides flexibility in a phe-nomenological approach, however requires a large number of fitting coefficients to approximate theflow stress effectively. The physically-based Kocks-Mecking is more efficient in terms of fitting co-efficients, however it requires well characterized yield and saturation stresses. In order to considerstrain dependence, the accuracy of the Kocks-Mecking expression at low strains is dependent on theintegrated form of Eq. 3.7. The Kocks-Mecking expression in the integrated form can only describethe strain-softening behaviour of the material by scaling the initial strain hardening rate accordingto temperature and strain rate. This requires a large number of tests to accurately assess, which mayalso be a limitation when considering inherent material variations.3.4 SummaryThe constitutive behaviour of as-cast A356 has been experimentally characterized through an exten-sive set of compression tests. The data was used to fit both a phenomenological and physically-basedconstitutive expression. The material in the as-cast form shows a diverse range of thermomechan-ical behaviour characteristic of Al-Si-Mg alloys, with a transition from strain-hardening to strainrate dependent behaviour. Below 350?C, the material was observed to strain harden, whereas above74CHAPTER 3. CONSTITUTIVE BEHAVIOUR OF AS-CAST A356this temperature it becomes more strain-rate dependent with increasing temperature. This behaviourposes a challenge for developing a single constitutive expression that accurately describes all ex-perimental results across the temperature and strain rate ranges encompassed experimentally. Asa result, each constitutive expression has differing degrees of accuracy and efficiency in predict-ing flow stress for particular ranges of temperature, strain rate and strain. Specifically, over theexperimental data tested:? The extended Ludwik-Hollomon expression is the most flexible and therefore provides thebest prediction across all temperatures and strain-rates. This expression overestimated theflow stress by an average 2% with a RMSE of 2.5%. This phenomenological approach neces-sitated a large number of fitting coefficients.? The Kocks-Mecking relationship on average slightly underestimated the flow stress by 1%,but exhibited a larger RMSE. Flow stresses for elevated strain and strain rate conditionsshowed better agreement with the relationship. This model is physically-based, and doesnot have as many fitted coefficients as the Ludwik-Hollomon.Based on this analysis, the constitutive expression that most accurately describes AC A356 acrossall temperatures and strain rates is the extended Ludwik-Hollomon expression.75CHAPTER 4CHARACTERIZATION OF ROTARY FORMED MATERIAL1Previous studies on the rotary forming of cast aluminum alloys (Section 1.5.1) have shown improvedmechanical properties following processing, however, they did not provide insight on the underly-ing microstructural changes that lead to these property improvements. The effects of holding the ACmaterial at elevated temperatures for forming purposes, followed by deformation has unknown im-plications on properties following heat treatment. The properties of heat treatable aluminum castingalloys are dependant on microstructural features spanning several length scales and will be affectedby the thermomechanical processing schedule applied. This chapter investigates the microstructureof A356 in the AC condition, following rotary forming operations of varying intensity, and follow-ing heat treatment. This is accomplished through microstructural observations on specimens withvarious thermomechanical histories, as well as concurrent macro and microhardness measurements.4.1 Microstructure and hardnessAs discussed in Section 1.3.2, macrohardness measurements can be used to infer yield strength ofA356. Fig. 4.1 shows selected yield strength versus hardness results reported by Tiryakiog?lu etal. [38] for underaged A356 with low and high levels of Mg, converted to HV. The original data waswas reported as HRF (Fig. 1.6), and was converted according to the method given in Appendix B.A non-linear least-squares fit of the data provided by Tiryakiog?lu et al. shows that ?y = f (HV) canbe described by a power-law relationship, as suggested by Colley [18]. Comparing data providedby Colley for A356 (with DAS equal to 30 ?m) in both the over and underaged conditions showsgood agreement, particularly at lower hardness values. The overall goodness of fit of the power-lawrelationship is greater than 0.95, and the RMSE is approximately 14 MPa over all experimental data.1A version of this chapter is intended for publication in Materials Science and Engineering: A76CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIAL40 50 60 70 80 90 100 110100150200250HV (kg/mm2)? y(MPa)  R2=0.9624RMSE=13.880.4, Tiryakiog?lu0.2, Tiryakiog?lu0.3, Colley0.110 (HV)1.662Figure 4.1: ?y to HV relationship based on converted measurements made by Tiryakiog?lu etal. [38] on underaged Al-7%wtSi-0.2%wtMg and Al-7%wtSi-0.4%wtMg. Data fromColley [18] for over and underaged Al-7%wtSi-0.3%wtMg plotted for comparison.This indicates that this data is sufficient for inferring local yield strength directly from hardnessvalues for the underaged condition.Using the EFA developed at UBC, three workpieces were rotary formed as described in Sec-tion 2.2.6 to varying levels of deformation. Taken from a combination of undeformed and rotaryformed workpieces, 9 sections were analyzed using the hardness profiling methodology describedin Section 2.3.4. Between 950-1350 hardness measurements were performed on each section. Ax-ial and circumferential sections, extracted from a blank, as well as axial sections, extracted fromas-deformed workpieces, were analyzed prior to heat treatment. Axial sections from a blank and theworkpieces were also analyzed following a T6 heat treatment.4.1.1 Experimentally formed materialAs-cast and as-deformed materialFig. 4.2 shows the results of hardness measurements performed on axial and circumferential (72?)profiles taken from the locations indicated in Fig. 2.3. Also shown on the axial section are 11equidistant segment markers to assist in tracking changes through processing. Hardness measure-ments performed on the two profiles showed a similar range of hardness. Axially, the highest hard-ness was found to be at either end of the sample, with the centre being the softest. Circumferentially,a gradient in hardness was observed. The variations in hardness in both directions is thought to be77CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIAL(a) Axial(b) CircumferentialFigure 4.2: Axial and circumferential hardness profiles of the AC blank. Circumferential sec-tion represents a symmetric portion of the wheel from which the blank was machinedfrom.due to differences in DAS and eutectic phase fractions caused by variations in solidification time andthe transport of Si-enriched liquid during solidification.The hardness profiles of each of the as-deformed sections, shown in Fig. 4.3, demonstrate alarge change from the AC condition. In all cases, the mean hardness has dropped significantly. Thepoint of initial roller contact in each specimen and direction of roller travel has been identified withan arrow in Fig. 4.3. In the undeformed regions, the hardness distributions show similar trendsto the AC condition albeit with a reduction in average hardness. Particularly evident in the highlydeformed specimen is a region of elevated hardness appearing immediate to the initial formingsite. Elevated hardness is also observed near the tip of the specimens (segments 10 and 11) inthe deformed regions similar to the AC condition. The remaining positions in the deformed regionsshow increased hardness values relative to the peak hardness when compared with the AC condition.Additionally, the increased hardness values in these areas (segments 8 and 9, 6?9, and 4?9 on thedeformed cross-sections, respectively), are higher at locations closer to the outer diameter. This78CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIAL(a) Low level deformation(b) Mid level deformation(c) High level deformationFigure 4.3: Comparative hardness profiles of as-deformed axial sections. Arrows indicate startof forming.type of hardness distribution has also been seen in the rotary forming of steel [68].In order to track the effects on DAS, five optical micrographs, or fields, were selected at randomalong each of 9 blank/workpiece sections at a depth between 2-3 mm from the outer diameter.Approximately 300 discrete measurements were performed across each of the 5 fields per segment,according to the methodology discussed in Section 2.3.2. The results of this analysis are shown inFig. 4.4.In comparing the results of the AC and deformed material, it appears as though forming hadlittle impact on the mean DAS. Comparing measurements in the most heavily deformed region79CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIAL11 10  9  8  7  6  5  4  3  2  120253035404550SegmentDAS(?m)  ACLowMidHighFigure 4.4: Mean DAS measurements of undeformed blank and deformed workpieces. Arrowsindicate start of deformed section for each specimen. Error bars indicate ? 1 standarddeviation.of each specimen (corresponding to segment 10 and 11) shows a slight decrease in the mean DASwith deformation. Only the highly deformed material showed a consistent decrease in the mean DASmeasurement in all segments affected by forming over the undeformed (AC) material. However, thistrend is not conclusive. A comparison of the mean DAS in the undeformed regions (segments 1 and2) displays approximately the same variance. Generally speaking, it is clear that DAS increases withcross-section thickness in both the AC and deformed material. As larger DAS typically correspondsto lower yield strength and a correspondingly lower hardness value, it is postulated that the causefor elevated hardness in sections 1?3 for all specimens may be related to the presence of elevatedlevels of eutectic phases.To evaluate the link between high hardness and the presence of increased fractions of eutectic,the indentation fields from the axial section of the least-deformed workpiece were reprocessed toquantify the distribution of eutectic. This specimen was the most uniformly polished and thereforehad fields which were best suited for microstructure evaluation of all specimens. The reprocessingcommenced with extracting a subfield absent of the indent. This was followed by determining thegreyscale level for each subfield image separating the eutectic and ?-Al phase. This was accom-plished by differentiating the peak counts of pixels to identify an inflection greyscale value. Anexample is shown in Fig. 4.5. The distributions of hardness (Fig. 4.3a) and eutectic fraction (Fig.80CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIAL4.5d) are quite similar. As such, the condition of the eutectic is a key factor in determining theresulting hardness of this alloy.Heat treated materialAs demonstrated in Fig. 4.6, the range of hardness values measured in each sample after conduct-ing the T6 heat treatment show an overall increase in hardness compared to the AC condition anda dramatic change in the hardness distribution. A comparison of the hardness in the deformed re-gions of each section following the T6 heat treatment indicates decreased hardness with increaseddeformation. The elevated hardness region found at the end of the undeformed specimen, approxi-mately 115 kg/mm2, progressively decreases with deformation to approximately 100 kg/mm2 in thedeformed specimens at the same location. Additionally, the regions of elevated hardness appearingimmediately beyond the start of forming as seen in the as-deformed specimens appears to be elimi-nated. This is particularly evident in the peak-deformed workpiece (Fig. 4.6d vs. 4.3c). Regions in(a) Raw image (b) Normalized histogram (c) Processed image(d) Resulting distributionFigure 4.5: Eutectic fraction (?Eu) distribution in the least deformed workpiece (Fig. 2.14d)in the as-deformed condition.81CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIALdeformed specimens (e.g. segment 1) that were outside the deformation zone exhibit a fractionallyhigher hardness (approximately 5 kg/mm2) than similar locations in the undeformed specimens.This small increase in hardness may be due to increased fragmentation caused by longer coarseningtimes resulting from heating and holding at forming temperatures. According to the HV-?y relation-ship presented earlier (Fig. 4.1), the 15 kg/mm2 difference in hardness between undeformed andheavily deformed material (segment 11) represents a 60.6 MPa drop in ?y.This indicates that regions that saw mechanical and thermal processing were softened by theprocess, while regions which were only processed thermally saw increased hardness.4.1.2 Commercially formed materialThe commercially formed material was analyzed using the same procedures that were applied to theexperimentally formed material. Specimens for this analysis were extracted from an AC blank andfrom a commercially flow-formed wheel following a T6 heat treatment. The hardness profiles of theAC and deformed-T6 conditions are shown in Fig. 4.7. The DAS was measured at select segmentsroughly corresponding to where the dendritic structure could be identified. The measured DAS forboth sections is summarized in Fig. 4.8.The hardness distribution and DAS profile of the AC blank for the commercial flowing processshow similar ranges of values as the AC blank for the EFA in the regions corresponding to segments1?4. However, outside these positions, significantly higher hardness values are observed, partic-ularly near the end or tip of the blank (segment 12). In comparing this result to that of the DASmeasurements, a tentative explanation for this change is due to locally elevated levels of eutecticowed to the coarse microstructure in segments 6?12. This latter point is speculative and based onthe comparison made with the least-deformed experimental specimen; while the indentation fieldspermitted accurate hardness and DAS measurements for the commercial specimens, they were notsuitable for eutectic evaluation.The effect of forming on the microstructure is readily apparent from the decreased DAS in thedeformed regions. DAS measurements on the deformed-T6 sample between segments C and D couldnot be performed because the high level of deformation had broken up the dendritic structure result-ing in the microstructure shown in Fig. 2.7b and 2.7c. Unfortunately, the non-uniform deformationprofile coupled with rough machining prior to heat treatment precludes a quantitative positional82CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIAL(a) No deformation(b) Low level deformation(c) Mid level deformation(d) High level deformationFigure 4.6: Comparative hardness profiles of deformed-T6 axial sections. Arrows indicateforming start point.83CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIAL(a) AC blank(b) Deformed-T6Figure 4.7: Commercially formed material in the AC condition (a) and deformed-T6 in (b).Dashed lines indicate DAS measurement locations (Fig. 4.8).12/I 11/H 10/G 9/F 8/E 7/D 6/C 5/B 4/A 3 2 1101520253035404550SegmentDAS(?m)  acFormedFigure 4.8: Mean DAS measurements of undeformed and commercially formed material. Ar-row indicates forming initiation point. Error bars indicate ? 1 standard deviation.84CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIALcomparison between the samples. However, comparing the DAS measurements at segments 7?12 onthe AC blank with segments D?I on the deformed-T6 workpiece, suggests that forming has reducedthe mean DAS by approximately 50%.4.2 Effects of processing on microstructureIn order to ascertain the effects of holding the AC material at an elevated temperature before forming,coupons (location and size given on Fig. 2.3) were extracted from an AC blank and held at elevatedtemperatures in a nitrate salt bath (described in Section 2.3.1) for varying lengths of time. Sam-ples were left to air cool upon removal from the salt bath, reflecting the EFA procedure. Hardnessmeasurements were made on each sample before the treatment and within 30 minutes of coolingto ambient temperature. The microstructure of select samples was also assessed using optical andelectron microscopy. This work was aimed at determining the effects of holding the material at anelevated temperature (or ageing) prior to forming.The temperatures selected for this investigation were based on potential forming temperaturesand include: 300, 350, and 400?C, as well as the solutionizing temperature of 540?C. Selected tospan the potential breadth of forming operations, target hold times were 2, 10, 20 and 50 minutes.The temperature history of each sample was monitored with a thermocouple. The approximate timeto cool to 100?C for all specimens was 3.5 minutes. Air cooling as opposed to water quenching wasselected as it best matched the procedure employed with the EFA.4.2.1 Hardness observationsThe average hardness and standard deviation for each hold temperature are plotted as a function ofhold time in Fig. 4.9. For all temperatures below 540?C, there is a clear power law drop in hardnessversus hold time, with better agreement at 350 and 400?C. Furthermore, as temperature increases,the standard deviation in the hardness measurements diminishes. This is likely due to the additionaltime at elevated temperature encountered during air-cooling for specimens held for shorter periodsof time. At these temperatures, diffusion mechanisms are active and both Si and Mg have increasedsolubility in the matrix. Apelian et al. [20] reported that the equilibrium solubility of Mg and Si in85CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIALsolid aluminum when both Mg2Si and Si are present as:%-wt Si = 1.69?10?9 ?T 3.19 (4.1)%-wt Mg = 1.45?10?9 ?T 3.16 (4.2)for 310?C< T < 575?C. This implies that the solubility of Mg and Si increase by approximately2.5 times when the temperature is increased from 300 to 400?C. Thus, the potential evolution of theSi-rich eutectic phase and Mg-bearing structures precipitated during casting is enhanced, effectingthe following phenomena:? Coarsening of Mg2Si precipitates that formed during initial casting;? Complete or partial dissolution of small Mg2Si precipitates;? Eutectic spheroidization beyond initial fragmentation; and? Eutectic coarsening beyond spheroidization.The initial casting procedure produces relatively coarse and unevenly distributed Mg2Si precip-itates. Coarsening of these precipitates may occur as Mg and Si transport via diffusion is enhancedwith increasing temperatures or is allowed to occur through longer hold times. This primarily af-fects Mg2Si, but also intermetallics to a lesser extent owed to their stability. These microstructuralchanges significantly decrease the overall mean hardness as precipitation strengthening diminishes.Simultaneously, the AC eutectic structure is also affected. The potential for eutectic Si-phasefragmentation as well as spheroidization is more likely with increasing hold temperatures. Theformer is driven in small part by thermal stress arising from the property mismatch of brittle Siin the Al matrix [119], and more predominantly by diffusion [120]. Spheroidization occurs solelyby diffusion of Si. The changes to eutectic morphology are expected to accelerate with increasedholding temperature. The collective change in hardness due to changes in precipitation and eutecticstructure can be expressed as a function of time t and temperature T :?HV =(?2.93?10?2T +4.21)log t (4.3)86CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIAL100 101 102 1034550556065707580-7.45 log t+73.1-6.16 log t +72.0-4.52 log t +74.1t (s)HV5(kg/mm2 )  300?C350?C400?C540?CFigure 4.9: Comparative HV5 results of specimens initially in the AC condition and after hold-ing at various temperatures and times.While this expression is only valid through the temperatures demonstrating power law behaviour,an extrapolation of this relationship implies that there is no thermal effect on the microstructure(?Hv = 0) below 144?C. The flow stresses presented in Fig. 3.1c show a much higher drop inwork hardening rate between tests conducted at ?120?C and ?190?C as compared to the drop from?45?C to ?120?C. Since diffusive transport is expected to be low at these temperatures, this impliesthat the extrapolated temperature may be when fragmentation of the eutectic commences.In the case of the 540?C results, there is no power law drop in hardness versus time observed aswith the other temperatures. Consistent with samples tested at other temperatures, there was a largeinitial drop observed in the specimen held for 2 minutes. However, the hardness increases fromthis point on. While the eutectic-Si morphology is expected to change as in the lower temperatureconditions, the effects of precipitation are superimposed. With longer temperature holding times,there is a progressive increase in precipitate dissolution, leading to higher levels in solution. Thelow air cooling rate and the potential for natural ageing results in increased hardness with time,coincident with increased levels of dissolution attained at temperature.4.2.2 Microstructural observationsTo examine the effects of hold temperature on the microstructure, the coupons held at each temper-ature for 50 minutes were analyzed via optical microscopy and EDX. These specimens were also87CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIALdeep etched via the methodology given in Section 2.3.3. The results of this analysis, presented inFig. 4.10, show how the Si-eutectic structure evolves with increased holding temperature. Subtlemodification of the eutectic structure is evident from the optical microscopy, while the SEM imagesfollowing deep etching show coarser features with increasing hold temperature. Holding at 300?C,some of the larger eutectic Si branches have rounded and are joined by less refined fiber morphology.Increasing the temperature to 400?C shows a continued evolution of this morphology resulting infewer, thicker branches being observed. At the solutionizing temperature of 540?C, the particles arefully fragmented and spheroidization is evident. The EDX results show that localized Mg-bearingstructures are present up to 400?C. These are expected to be predominantly Mg2Si (outlined inred/orange in Fig. 4.10-4.11); however, intermetallics may also be present. Once the solutionizingtemperature is reached, there is no evidence of these localized Mg-bearing structures. While theEDX observations do not show the evolution in distribution of Mg at 300 and 400?C from the ACstate, the absence of regions containing concentrated Mg in specimens held at 540?C is congruentwith the observations made regarding the macrohardness results (Fig. 4.9).A sample of undeformed material following the complete T6 heat treatment was also analyzedusing this methodology. The results of this analysis are also presented in Fig. 4.10. The distributionof Mg in this sample is approximately the same compared to the sample held at 540?C for 50 min-utes. The eutectic-Si in the T6 sample has also spheroidized to a greater extent and some coarseninghas occurred as characterized by larger and fewer particles with the same field size.This methodology was also applied to analyze deformed material before and after a T6 heattreatment. Specimens were extracted from a location approximately 1 mm from the roller interfacein the sample that experienced the largest deformation in the EFA. The axial location of the spec-imens coincided with the undeformed specimens employed to evaluate the effect of hold tempera-ture/time. The resulting micrographs for this material are shown in Fig. 4.11. Prior to heat treatment,the eutectic-Si particle size appears to have decreased compared to the undeformed specimens andhas been compacted in line with the deformation. There is less evidence of spheroidization havingoccurred, as the Si morphology is observed to be small, short fibers/plates. The EDX maps suggestthat the Mg-bearing structures have consolidated on the edges of the dendrite arms, appearing asplates oriented parallel to the forming direction. The morphology and distribution of these structuresexplains the hardness profiles seen in the spun material prior to heat treatment (Fig. 4.3c), where88CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIAL(a)(b)(c)(d)(e)Figure 4.10: Eutectic particle morphology of undeformed specimens held at various tempera-tures and times, provided by optical images of the microstructure, element maps gener-ated via EDX and SEM images of eutectic particle morphologies following deep etching.This was conducted on specimens in the AC condition (a), held for 50 minutes at 300(b), 400 (c) and 540?C (d) and the T6 condition (e).89CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIAL(a)(b)Figure 4.11: Eutectic particle morphology of as-deformed and deformed-T6 material, pro-vided by optical images of the eutectic microstructure, element maps generated viaEDX and SEM images of eutectic particle morphologies. This was conducted followingdeep etching specimens in the as-deformed (a) and deformed-T6 condition (b). Arrowindicates forming direction.regions of elevated macrohardness were found coinciding with deformed regions. In the deformed-T6 condition, localized Mg is absent as in the case of the undeformed material, however the eutecticstructure differs. While spheroidized, the eutectic particles are found to be appreciably smaller incount and size for equivalent field sizes than those observed in the undeformed material.4.2.3 Eutectic particle shape and sizeThe Lifshitz, Slyozov and Wagner (LSW) coarsening model [121, 122] provides a means of quanti-fying eutectic particle size evolution with time:kLSW =?d 3 ? ?d 30t(4.4)While no data in the present study was collected regarding initial particle diameters, the modeldemonstrates how eutectic particles are dependent on a temperature dependent constant and time.Competitive coarsening driven by diffusion, as described by the LSW model, predicts a steady-statelognormal distribution of particle sizes, centred about ?d, once fragmentation is complete [123]. The90CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIALpresence of these hard Si particles within the softer Al matrix results in a strengthening effect dueto the eutectic phase consistent with Metal Matrix Composite (MMC) theory [40, 124].In order to quantify the effects of different processing paths on the eutectic particles, particleanalysis using optical microscopy was conducted on specimens of AC material solutionized at 540?Cfor 50 minutes, undeformed-T6 material, peak deformed-T6 material and commercially formed-T6material. The particle characteristics were quantified with ECD and aspect ratios measured frombest-fit ellipses. The measurements were then fit to a log-normal Probability Density Function (PDF)according to:P = 1x?2pis2exp(?(lnx?m)22s2)(4.5)where x is ECD or aspect ratio, m and s are the mean and standard deviation of the natural logarithmof x. The resulting statistics in terms of arithmetic mean, mode, m and s2 are summarized in Table4.1 and Fig. 4.12. This analysis indicates that the aspect ratio does not vary significantly betweenthe different processing paths. As the melt was chemically identical for all specimens, a possibleexplanation for this is that the modification technique produces a narrow range of aspect ratios afterfragmentation. Wang [28] showed that the distribution of aspect ratio in modified A356 and A357was nearly identical and otherwise identical unmodified material showed a distinct difference. Aclear difference was noted in the ECD for each sample, with the commercially deformed materialhaving the smallest ECD, followed by the solutionized material, then EFA-T6 and finally the un-deformed material having the largest particle size. The ECD and aspect ratio measurements of theundeformed material are comparable those of Wang et al. [28] for modified A356-T6, and the ECDmeasurements are approximately half of those found for unmodified A357-T6 [28, 38].The results for the solutionized material and the undeformed material in the T6 condition areconsistent with phenomena described in Section 1.2. As reflected in the aspect ratio and ECD mea-surements, the solutionized material did not coarsen to the same extent as the T6 specimen owingto the longer time at temperature for the latter material. Assuming the kLSW coefficient (Eq. 4.4)is the same for both deformed and undeformed material and taking ?d as the mode value, these re-sults indicate that deformation fragments the eutectic-Si to a much greater extent, leading to smallereutectic particle sizes after heat treatment. Increased levels of deformation advance the degree offragmentation, which explains the size difference between the EFA and commercially formed mate-91CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIALTable 4.1: Eutectic particle statistics.Material Statistic Aspect ratio ECD(?m)Mean 1.60 1.81Solutionized Mode 1.40 1.42(Fig. 4.10d) m 0.421 0.511s2 8.20? 10?2 0.162Mean 1.51 2.28T6 Mode 1.35 1.70(Fig. 4.10e) m 0.372 0.728s2 7.43? 10?2 0.195Mean 1.57 2.01EFA-T6 Mode 1.38 1.51(Fig. 4.11b) m 0.403 0.600s2 7.89? 10?2 0.189Mean 1.51 1.63Com. T6 Mode 1.36 1.26(Fig. 2.7c) m 0.373 0.398s2 6.62? 10?2 0.1641 2 3 4 5 600.20.40.60.811.21.4Aspect ratio, ecd (?m)P(m,s2 )  ecdAspect ratioSolutionizedt6efa-t6Com. t6Figure 4.12: PDFs of eutectic particle ECDand aspect ratios.rial. However, it appears that the deformation does not uniformly fragment the eutectic, as deformedmaterial showed marginally higher aspect ratios than undeformed.4.3 Phase-specific effects of processingIn an attempt to ascertain the degree to which processing history effects the primary and eutecticphases, microhardness tests with a low load were employed to selectively test each phase of material.This was conducted on undeformed material with various thermal histories, and the peak deformedmaterial processed by the EFA. Commercially formed material was excluded from this analysisdue to the inability to accurately isolate and test each phase. The results of these measurements,presented in Fig. 4.13, show the relative contribution of each phase to the macro hardness andoverall strength. The mean microhardness and standard deviation of 30 individual measurementsis given for the breadth of conditions presented in the previous section. Indentation locations werechosen such that the plastically affected zone was retained within each phase, as shown in Fig. 4.13band 4.13c.In the AC condition, the eutectic shows a significantly higher hardness as compared to the pri-mary ?-Al phase. The drop in the hardness of the eutectic in samples held at 300 through to 400?Cfor 50 minutes is nearly identical, surmised to be mostly attributed to eutectic fragmentation and92CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIALsome Mg dissolution which increases precipitate coarsening. The decrease in hardness of the pri-mary is identical for specimens in the AC conditions to those for hold temperatures of 300 throughto 350?C, and decreases further to a minimum at 400?C, which can be entirely attributed Mg disso-lution.Below holding temperatures of 540?C, it appears that the hardness in the eutectic stabilizes afteran initial drop, while the peak primary ?-Al phase hardness decreases consistently with temperature.This suggests that the time-dependant decrease in macrohardness (Fig. 4.9) is driven by Mg diffu-sion beyond the initial effects of eutectic fragmentation. In the 540?C case, both the eutectic andprimary phase show increased hardness relative to the other specimens held at lower temperatures.Both benefit from Mg2Si precipitation expected due to slow cooling and eutectic spheroidization.The hardness of the eutectic in the deformed material without heat treatment is approximately thesame as the the specimens held at temperatures below 540?C, and the primary ?-Al phase is some-30405060708090100110120130HV0.01(kg/mm2 )  AC 300?C  350?C  400?C  540?C  Formed T6 Formed,T6 Eutectic?-Al(a) Mean microhardness, ? 1 standard deviation(b) ?-Al, AC(c) Eutectic, T6Figure 4.13: Comparative microhardness of the ?-Al phase and eutectic in various conditions(a). Micrographs demonstrate an example of an indent made in ?-Al in the AC condition(b) and one made in a eutectic region in the T6 condition (c). Dashed circles represent-ing the estimated plastic zone in (b-c) have diameters 2.5? the indent diagonals.93CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIALwhere between the specimens held at 350 and 400?C. This indicates that prior to heat treatment,the majority of the modification in strength can be attributed to changes in microstructure due tothermal effects.Following T6 heat treatment, both the eutectic and primary hardness increase appreciably, withmore effective precipitation and spheroidization. The hardness of the primary ?-Al phase in thedeformed material is approximately the same as the undeformed material, having a mean hardnesswithin a standard deviation of the undeformed. The mean hardness of the deformed material?seutectic phase is 28% less than that of the undeformed, which indicates that the principal cause ofthe hardness decrease observed in deformed samples in the T6 condition (Fig. 4.6) is due to changeslocalized to the eutectic.Overall, these phase-selective microhardness measurements indicate that the primary ?-Al phaseis slightly softer in deformed material, but not appreciably different than that of undeformed ma-terial. This indicates that precipitation strengthening is not greatly affected by deformation. Thesame measurement has type attributed the drop in macrohardness to a significantly softer eutecticphase. It is evident that the condition of the eutectic is a better indicator of hardness, and by virtue,strength of this material as opposed to DAS. This not only includes the shape and size of particlebeyond heat treatment at the micro scale, but also the overall phase fraction on the macro scale.4.4 Surface defectsAs demonstrated in Fig. 4.14 and 4.15, the mid-level and peak deformed EFA workpieces showedsurface defects in the form of cracking on the outer diameter in the deformed regions. Crackingdid not manifest on the least-deformed sample, but was most prominent on the mid-level deformedsample where the highest number of cracks throughout the deformed region were observed. Cracksappearing early in the forming pass alternate between opening counter to the forming direction(A, C) to predominately opening with the forming direction (B, D?U). The cracks at this stage ofdeformation do not extend any further than 140 ?m into the bulk of the material, measured radially,or normal to the forming direction. With the exception of one crack (C) extending up to 320 ?min length along the axis of the workpiece, other cracks are shorter and do not not exceed 200 ?m.The defects observed were larger in scale than those reported by Mori et al. [77], who reporteda maximum size of 60 ?m. Similar to Mori et al., however, cracks were found to predominantly94CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIAL(a) Crack locations(b) MicrographsFigure 4.14: Surface fracture details of mid deformed material. Micrographs are are alignedwith the forming direction moving right to left.penetrate the surface of the sample with an angle of approximately 45? from the radial direction,occurring in eutectic-rich regions.The peak deformed sample embodied two discrete forming passes, with the first pass charac-teristic of the mid-level deformed specimen. This sample also exhibited surface cracks, albeit withfewer, larger cracks than characterized by the mid-deformed specimen, as shown in Fig. 4.15. Itappears that minor cracks created in earlier passes were closed, while larger cracks are deformedalong with the bulk material and are elongated as a result. None of the cracks observed extended anyfurther than 100 ?m into the bulk of the material, however the characteristic axial lengths (a max-imum of 1.2 mm) were much longer than less deformed material. The penetration angle has also95CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIAL(a) Crack locations(b) MicrographsFigure 4.15: Surface fracture details of peak deformed material. Micrographs are are alignedwith the forming direction moving right to left.changed to approach the forming direction, however, cracks were still observed to follow eutectic-rich regions as was seen with the mid-deformed workpiece.This type of localized failure is characteristic to the forming process, as it has been characterizedin other forward rotary forming operations [77, 82]. Cracking or ?fish scaling? in rotary forming iscaused by highly localized shear occurring both ahead of and behind the roller interface. The extentof cracking is dependent on processing parameters and the local strength of material. Both of these96CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIALfactors decide the overall crack morphology. Thus, the brittle eutectic phase appears to be a weakpoint in A356 where cracks initiate.To eliminate cracking, either the forming temperature may be increased, or the forming param-eters altered to avoid high levels of radial shear. Increasing the forming temperature from 350 to400?C was confirmed to arrest the formation of cracks by Mori et al. [77] for similar forming pa-rameters. This is also inline with the torsion testing results of McQueen et al. [40], who reportedsignificant increases in strain to fracture moving from 300?C to 400?C, particularly at lower strainrates. Thus, in addition to temperature, forming speed may be one of the process parameters thatmay be changed to reduce the frequency and severity of surface defects. The effects of furtherparameter changes are discussed in the following chapter.4.5 SummaryRotary forming of A356 at elevated temperatures has shown that the microstructure is affected by anumber of different factors across several length scales. Combined hardness profile and microstruc-tural analysis shows that the DAS has less of an effect on hardness than the distribution and conditionof eutectic-Si phase. Heating the AC material prior to deformation initiates diffusion-driven coars-ening of precipitates and modifies the eutectic structure. An extrapolation of the data from targetedstatic thermal experiments suggest that the AC material is stable up to approximately 144?C. Priorto heat treatment, rotary formed material exhibits a decreased macrohardness in-line with the timespent at elevated temperature, indicating that the decrease in hardness between the AC undeformedstate to the as-deformed state is principally a thermal effect. After heat treatment, there was a smallmacrohardness increase observed in the regions unaffected by forming in the EFA processed mate-rial as compared to unprocessed material with the same heat treatment. This coincided with a largedecrease in macrohardness in heavily deformed regions over unprocessed material due to changesin eutectic particle size.Eutectic particle size and shape analysis showed that rotary forming fragments the eutecticstructure, with particle sizes fragmenting to a greater extent with higher levels of deformation.Furthermore, increased levels of deformation create smaller eutectic particles after heat treatment,which was correlated to lower macrohardness. As a result, it is surmised that flow formed materialin the T6 condition may exhibit decreased yield strength as compared to undeformed material in the97CHAPTER 4. CHARACTERIZATION OF ROTARY FORMED MATERIALsame state, despite smaller eutectic particles observed in the deformed material.Eutectic regions were also observed to coincide with surface defects in the form of cracks foundin EFA processed material. These cracks occurred extensively along the length of the mid-deformedpart, originating and propagating through eutectic-rich regions. Further deformation of the crackedsurface seemed to close some smaller cracks, while elongating others. The cause of these surfacedefects is a combination of forming temperature (affecting the local strength of the material) andprocessing parameters such as forming speed.98CHAPTER 5MATHEMATICAL MODELLING OF ROTARY FORMING1As discussed in Section 1.5.1, rotary forming imparts significant levels of localized workpiece de-formation. The degree of deformation is dependent primarily on tooling and feed-rates, and work-piece geometry as well as deformation history; often the roller(s) will pass over the same workpiecelocation several times to incrementally achieve bulk deformation. This poses several challenges todevelop a model capable of accurately predicting the strain path and overall workpiece deformation.Chief among these challenges is considering the effects of temperature and strain rate on the consti-tutive behaviour, which has not been previously considered. The following sections describe howthese challenges were addressed in developing and applying a coupled thermomechanical model ofthe EFA process detailed in Section 2.2.6.Specifically, the overall model reflecting the EFA process included submodels for workpiecepreheating, forming at elevated temperatures, and cooling once forming was complete. For thepreheating submodel, an axisymmetric domain assumption was made for both the mandrel and theblank. Thermal and mechanical boundary conditions were imposed in order to reflect the geometryand temperature of the workpiece prior to forming. The results from this model were used togenerate a 3D meshed description of the workpiece. Forming of the workpiece was then modelledemploying an adiabatic assumption using rigid analytical tooling to describe the mandrel and roller.The assumption of adiabatic conditions was applied to the workpiece to capture the effects of heatgenerated due to plastic deformation. The use of rigid analytical surfaces to describe the toolingprecludes calculating their temperature history. Once the forming step was complete, cooling ofthe workpiece was simulated to permit direct comparison between experimentally achieved and1Portions of this chapter have been published in:Roy M. J., Maijer D. M.,?Modeling of As-Cast A356 for Coupled Explicit Finite Element Analysis?, Light Metals 2012,(2012)Further material is intended for publication in the Journal of Materials Processing Technology.99CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMINGsimulated geometries at ambient temperatures.5.1 Coupled thermomechanical EFA model developmentIn order to calculate the evolution of stress, strain and temperature within the workpiece duringrotary forming, a fully coupled thermomechanical model was developed using the commercial FEAsoftware package, ABAQUS. With this technique, both the thermal and mechanical states are solvedtogether and are permitted to influence one another via the boundary conditions imposed. A cou-pled thermomechanical model is needed to describe the thermal effects on the mechanical responseand vice versa. Changes in the thermal state have mechanical effects through phenomena such asthermal expansion, and changes in material properties such as diminished yield strength and plas-ticity. Mechanically, heat is generated by the conversion of plastic strain energy, in turn affectingthe thermal state. Coupling the states allows the model to include the interdependent effects in thesolution. As rotary forming involves high levels of localized plasticity, a coupled model providesthe most accurate description of changes to the workpiece during this process.ABAQUS provides both implicit and explicit FEA tools that are capable of performing this typeof analysis. Implicit finite element methods are well suited to modelling quasi-static thermo-mechanical processes such as casting because of the long durations and gradual changes in boundaryconditions. However, dynamic processes with discontinuities in contact and large plastic deforma-tion are better suited to an explicit approach. Explicit approaches rely on a direct calculation ofdependent variables over a given time increment, whereas the implicit approach solves for depen-dent variables expressed in terms of coupled equations. Both involve numerical time integration tosolve for the unknown workpiece displacements and temperatures, which is the basis for the result-ing strains and stresses. A detailed comparison between the two solution techniques in terms of athermomechanical framework has been outlined by Koric et al. [125].Both implicit and explicit techniques were employed in modelling the rotary forming conditionsrealized with the EFA. The initial preheating of the workpiece was predicted using an implicit,2D-axisymmetric model. In addition to predicting the temperature, this model was employed todetermine the geometry of the mandrel and workpiece following thermal expansion. The results ofthis 2D model were then used as initial conditions for an explicit 3D forming model.100CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING5.1.1 GeometryThere are three main components needed to accurately describe the rotary forming process of theEFA: the workpiece, mandrel, and roller. During preheating, only the workpiece and mandrelare involved. Due to the axial symmetry of the mandrel and workpiece during preheating, a 2D-axisymmetric representation was employed. This use of symmetry reduces computational overhead.As discussed in Section 1.5.2, the deformation conditions occurring during rotary forming do notexhibit a plane of symmetry and thus require a 3D representation.The roller geometry was sized according to that employed with the EFA, and was assumed toretain ambient dimensions. The mandrel, which heats up with the workpiece, was sized based ontemperature corrected geometry as described in the following section. The mandrel and roller weredefined as rigid analytical surfaces in order to diminish computational overhead. These surfacesare unmeshed, do not deform, and do not permit heat transfer. Boundary conditions or constraintsto degrees of freedom of these surfaces are applied via a single reference node for each instance,i.e. one reference node for the roller, and one for the mandrel. Using rigid analytical surfaces todescribe the tooling precludes the possibility of deformation, which is a valid assumption based onthe difference in flow stress between tool steel and A356 at forming temperatures.The explicit technique employed for forming simulations requires a mesh which is as uniformas possible. The maximum time increment achieved in explicit FEA is proportional to the shortestpath across any element. Variability in element edge length can needlessly increase the numberof time increments needed to complete a simulation. For irregular geometries, it is not possibleto generate a perfectly uniform mesh and therefore the element edge lengths will vary between aminimum, Lmin, and maximum, Lmax. Meshing strategies for explicit models seek to minimize thedifference between the two lengths. For the preheating model, a 2D section of the workpiece wasdecomposed into quadrilateral elements with a minimum element edge length, Lmin, of 2 mm. Theresulting mesh had 573 nodes and 487 2D-axisymmetric, quadrilateral elements (Fig. 5.1). Fivenodes on this 2D section were designated as tracking nodes to assist in later assigning boundaryconditions. An axial section of the mandrel was meshed with slightly coarser, elements having aLmin close to 4 mm, resulting in 673 nodes and 515 elements. Four tracking nodes were designatedon the surface of the mandrel to track thermal expansion, in addition to the five on the outer surface101CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMINGFigure 5.1: 2D mesh of the blank and mandrel weldment employed for preheating simulations.of the workpiece.The elements for the axisymmetric model featured hourglass control and reduced integration(CAX4RT). While these element options were potentially unnecessary for the preheating simula-tion, they were necessary for later translation of the workpiece mesh from 2D to 3D. In displacement-based FEA, reducing the number of integration points is a standard technique to reduce computa-tional costs, and is often necessary to enable the solution of problems involving large plastic defor-mation. Especially when employing reduced integration, hourglass control is necessary to preventelements from ?locking?. This phenomena occurs when boundary conditions cause elements to de-velop zero stiffness, which may occur depending on deformation and the number of integrationpoints [126]. A more detailed stability analysis of explicit finite elements has been conducted byLing and Cherukuri [127].To generate the mesh for the forming model, the 2D-axisymmetric mesh was revolved aboutits axis of symmetry to form the 3D mesh. In order to minimize the element count, the full 360?section of the workpiece was discretized into 297 circumferential segments, corresponding to theLmax of the 2D mesh (Fig. 5.2). This resulted in 170181 nodes and 144639 brick/hexagonal el-ements (C3D8RT), which inherited the reduced integration and hourglass controls from the 2D-axisymmetric elements. This mesh density was selected primarily on the basis of minimizing thecomputational resources, and the effects of this density will discussed further in Section 5.3.5.1.2 Material propertiesA coupled thermomechanical model requires the definition of both thermal-physical and mechanicalproperties for each of the different materials employed. Thermal-physical properties include density,102CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING(a) 2D section(b) Complete 3D (c) DetailFigure 5.2: Workpiece mesh employed for forming simulations. A detailed view of the 2Dmesh employed for preheating simulations is shown in (a) with an inset showing Lmax.The revolved 3D mesh is shown in (a), constructed from the 2D mesh shown in (a). Adetail view of this 3D mesh is given in (c).103CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMINGspecific heat capacity and thermal conductivity. Mechanical properties include modulus of elasticity,Poisson?s ratio, the coefficient of thermal expansion and a description of the flow stress if plasticityis to be considered. The full set of property data was implemented in both the preheating andforming simulations for the A356 workpiece. Plasticity was considered in the preheating simulationto ascertain appropriate boundary conditions. The material definition of the AISI-4320 mandrel wasonly necessary for the preheating simulation, and did not require a description of plasticity. This isbecause the meshed instance of the mandrel was replaced by an analytical surface in the formingsimulation, and all deformation encountered during the course of preheating was elastic. Materialproperties for both materials was assumed to be isotropic.Most of the FEA of incremental forming in the literature has employed isothermal, quasi-staticmaterial properties as outlined in Section 1.5.2. However, as demonstrated in Chapter 3, the flowstress behaviour of AC A356 is temperature and strain rate dependent. Thus, in the current work,temperature dependent material properties, based primarily on literature reported values (with theexception of the flow stress relationship), were implemented with the goal of quantifying the me-chanical response at elevated temperatures and strain rates.The extended Ludwik-Hollomon behaviour (Eq. 3.3) discussed in Chapter 3 was implementedin the model for A356 via the user subroutine UHARD for the implicit solution (ABAQUS Standard)and VUHARD for explicit cases (ABAQUS Explicit). These subroutines calculate the local flowstress based on the temperature, strain and strain rate at each respective integration point. Thetemperature-corrected elastic modulus and Poisson?s ratio were implemented based on literaturevalues [98], given in Eq. 3.2.The thermal-physical properties of A356 were taken from He?tu et al. [128]. Thermal conduc-tivity and specific heat capacity (kc and Cp, respectively) as a function of temperature were imple-mented in the model using a data table. These functions which are shown in Table 5.1. A constantdensity, ? , of 2670 kg/m3 was implemented as the density of A356 does not change significantlyover the range of processing temperatures. The expression for thermal expansion, ? , given by He?tuet al. is also provided in this table. ABAQUS requires that ? be declared relative to a reference104CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMINGTable 5.1: Thermal properties of A356 and from AISI?4320. Properties for A356 are thoseemployed by He?tu et al. [128] and AISI?4320 properties are from handbook values [129].Cp (J/kg?C) kc (W/m?C) ? (?C?1)A356 898.7+0.4270T 7146+4.150T 2.260?10?7 +(2.39?10?8)TAISI?4320 452.1+0.4740T 43.33?(1.090?10?2)T 6.50?10?7temperature as the total thermal expansion as opposed to differential form [126] such that:? ?(T ) = (T ?T0)?1T?T0?(T )dT (5.1)where ? ?(T ) is the total thermal strain required by ABAQUS at temperature T , with reference tem-perature T0 taken to be 25?C.In order to describe the thermal expansion of the mandrel solely during the preheating phase ofthe process, thermal-physical properties for AISI-4320 were necessary. The values for kc, Cp, and ?were entered in tabular form according to handbook values [129], summarized in Table 5.1. Densitywas taken to be 7850 kg/m3 for AISI-4320, a modulus of 205 GPa and Poisson?s ratio of 0.29 wasprescribed.5.1.3 Initial conditionsAs described in Section 2.2.6, workpieces were preheated to 350?C via propane torches. This pre-heating process was modelled assuming axisymmetry using the implicit solution technique becauseof the long times involved in the heating process. The results from this implicit simulation werethen used as initial conditions for the forming simulation. This included the elastic stress state andtemperatures throughout the workpiece, and the geometry of the workpiece and mandrel after thethermal expansion that occurred during preheating.The resulting geometry and position of the workpiece on the mandrel are shown in Fig. 5.3b.The results of this 2D simulation were then post-processed to map the results onto the 3D meshdepicted in Fig. 5.2b. The displaced coordinates of the tracking nodes on both the mandrel andblank were employed to define tooling positions for the forming simulation. In the case of theblank, the tracking nodes were used to define the initial position of the roller. In the case of themandrel, the tracking nodes were used to define an analytical surface that replaced the meshed105CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING(a) Boundary conditions(b) Resulting deformed meshFigure 5.3: Preheating simulation boundary conditions and resulting deformed workpiecemesh used as initial conditions for forming.instance of the mandrel weldment as discussed previously.5.1.4 Boundary conditionsBoth the preheating and forming simulations require mechanical and thermal boundary conditionsto represent the sequence of steps taken during rotary forming, described in Section 2.2.6. Thermalboundary conditions were necessary to heat the workpiece and mandrel during preheating. Duringforming, the thermal boundary conditions of the workpiece were changed to an adiabatic descriptionand included heat generation due to deformation. The adiabatic state of the blank was then modifiedas boundary conditions were applied to reflect cooling of the workpiece post-forming. Mechanicalboundary conditions were used throughout these stages to control the relative movement of theworkpiece and tooling as well as describe the contact conditions.In the preheating analysis, the mandrel section had node-based constraints applied to the spin-dle end, such that axial movement was suppressed. This causes the mandrel to expand away fromthis constraint as the mandrel temperature increases. This represents the conditions present in theEFA where the mandrel is rigidly fixed to the end of the spindle and expands when heated towardsthe tailstock via the spring-loaded centre. A mechanical contact boundary condition was applied106CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMINGbetween the outer diameter of the mandrel and the inner diameter of the workpiece. Most rotaryforming simulation studies have assumed frictionless contact [80, 83]. However, a recent studyemployed a Coulomb friction coefficient of 0.2 for tooling interactions encountered during unlubri-cated spinning of steel [84]. A Coulomb friction coefficient of 0.1 was assigned in the present workto all surface interactions as some friction was expected in spite of the graphite lubricant employedduring experiments. A 10 kN force (Fc in Fig. 5.3a) was evenly applied to the clamp face of theworkpiece, causing the workpiece to maintain mechanical contact throughout the heating cycle andresulting thermal expansion. The load selected did not induce plastic deformation in the workpiece,but was sufficient to maintain contact.In developing the thermal boundary conditions for the preheating simulation, inverse thermalanalysis using a Levenberg-Marquardt technique [130], was attempted with the experimental TCrecord (Fig. 2.13) and the domain described in Fig. 5.1. This approach was meant to solve forthe time dependent surface flux occurring during flame heating, for use in the preheating modelto predict the heat-up of the workpiece from ambient conditions to the forming temperature. Itwas found that the problem was severely ill-posed owing to the cropped mandrel domain, and thetransient heat transfer between the workpiece and the mandrel. The variability observed in theheating rates between experiments further compounded this analysis. The heat rate variability wasattributed to geometric variance in the workpieces, resulting in non-uniform axial and circumferen-tial contact with the mandrel. It was determined that the heat transfer between the workpiece andmandrel could not be accurately represented with a displacement-based interfacial heat transfer co-efficient. As such, uniform heating conditions were assigned in the preheating model to the mandreland workpiece to reach the measured temperatures of Tm = 220?C and Tb = 350?C, respectively,ramped from 30?C linearly over 20 minutes. These boundary conditions (dTm/dt and dTb/dt) areshown in Fig. 5.3a.Although the meshed instance of the mandrel was replaced by an analytical surface, the me-chanical contact boundary condition between the workpiece and the mandrel employed during pre-heating was retained. An additional contact boundary condition was specified between the rollerand the outer diameter of the workpiece. Adhering to the guidelines set out by Wong et al. [67, 69]to reduce the computational expense discussed in Section 1.5.2, the workpiece was kept stationaryand the roller was moved rotationally about and along its axis. The workpiece was held station-107CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING(a) Forming, axial cross-section(b) Forming, 3D(c) Post-forming, axial cross-sectionFigure 5.4: Model domain and boundary conditions: initial 2D axisymmetric model whichwas then translated to 3D for the forming and post-forming simulations.ary by replacing the distributed force Fc employed in the preheating simulation (Fig. 5.3a) with asurface constraint fixing the location of this surface (Fig. 5.4a).During experiments, the roller was moved into contact with the workpiece radially, and thenset to move across the workpiece. In order to reflect this, the forming simulation had a roller path,starting from a small radial clearance from the outer diameter of the workpiece, that initially movedradially towards the workpiece to make contact and then transitioned to combined rotational andaxial motion. This roller path was calculated based on the geometry and location (on the mandrel)of the preheated workpiece and then implemented in the model via a data table prescribing themotion of the reference node for the rigid analytical surface representing the roller.In implementing the roller path, the tracking nodes corresponding to the surface of the work-piece were used to define geometry to achieve the forming profiles reported in Table 2.3. The initial108CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMINGradial position of the roller nose was determined by linearly interpolating between the coordinatesof the tracking nodes and an initial clearance of 0.1 mm. The initial axial position for each experi-mental condition was found by measuring the axial position of the node representing the start of theformed portion of the workpiece, correcting for dilatation and translating this position to the resultobtained from the preheating simulation. The path of the roller was then set to move first radiallyfrom the initial position uo to point un with a penetration of P = 0.1 mm, while rotating about thez-axis. Upon reaching un, the roller was then moved axially to point u f while rotating about thez-axis. The final axial position of the roller, u f , was defined as the length of the correspondingexperimental workpiece, corrected for temperature, plus 5 mm. This 5 mm clearance was imposedto ensure that the roller moved past the point of contact with the workpiece at the end of the simu-lation. The proscribed axial movement of 0.21 mm per revolution and circumferential movement of281 RPM of the roller matched those employed experimentally. This resulted in simulated formingprocess times (tp) of 61.93 and 87.76 seconds.As mentioned previously, forming models were run adiabatically, to characterize the heat de-veloped due to dissipation or inelastic heat generation without any heat loss from the workpiece. ATaylor-Quinney factor of ? = 0.9 was used.Once the forming pass was complete, the workpiece was cooled down in the model by applyinguniform surface heat fluxes to the surfaces of the workpiece (refer to Fig. 5.4c). A flux of q f =4.3? 103(T ? 25) W/m2 was applied to both the inner and outer surfaces of the workpiece andqc = 6.4?103(T ?25) W/m2 was applied to the clamp surface. With these heat fluxes applied, theworkpiece cooled to ambient temperature in 7.5 seconds. The fluxes and the length of time requiredto cool the formed workpiece do not reflect the experimental conditions where the workpiece wasallowed to air cool for 40 minutes. The heat fluxes were selected to limit the simulation timerequired to reach ambient temperature and to induce no further plasticity in the workpiece. Thiswas conducted in order to compare the experimental workpiece dimensions at ambient temperatureswith those predicted by the model.5.2 Material model validationThe material characterization testing documented in Chapter 3 was modelled both to verify theimplementation of the extended Ludwik-Hollomon constitutive expression. A common method to109CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMINGFigure 5.5: Schematic of the FEA geometry and boundary conditions employed for materialmodel validationreduce computational overhead in explicit FEA is to employ time or mass scaling, which is discussedsubsequently. This model further provided a framework to investigate the effects of this technique.Implicit and explicit solutions of this model were used to validate the constitutive expression withthermal effects directly imposed. Working from these baseline simulations, thermal conditionswere then indirectly specified, and various degrees of time and mass scaling were applied. Thesemodels were used to evaluate the potential effects of scaling on the fully coupled explicit formingsimulation.A 2D axisymmetric model of a compression test was constructed as shown schematically in Fig.5.5 and described in Section 2.3.5. The mesh employed consisted of 1200 2D axisymmetric ele-ments (CAX4RT) with a uniform element length of 250 ?m in each direction (L = Lmax,Lmin). Twomechanical boundary conditions were imposed beyond those inherent due to axisymmetry. First,axial movement of the nodes on the base of the specimen were suppressed, and nodal displacementsu corresponding to the experimental displacement record were imposed on the face opposite to this.This latter boundary condition was implemented on a tabular basis.5.2.1 Mechanical validationIn order to validate the implementation of the material model and the mechanical boundary condi-tions, implicit and unscaled explicit simulations were conducted without considering heat transfer.The results from these simulations were compared against the flow stress measured during com-pression testing. The first test selected (test number 39, Table 3.1) for comparison best reflectedforming conditions, as it was conducted at the highest strain rate at approximately 350?C. A secondtest at approximately the same strain rate, but at a lower temperature that exhibited strain hardeningbehaviour (test number 24, Table 3.1) was also selected.110CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING0 0.05 0.1 0.15 0.2 0.25 0.3050100150??(MPa)ExperimentalImplicitExplicitFigure 5.6: FEA results versus experimen-tal flow stress at forming tempera-tures. Experimental, implicit and un-scaled explicit simulated flow stressesare compared at Ta = 352?C & ?? =8.82 s?1, validating the materialmodel.0 0.05 0.1 0.15 0.2 0.25 0.3050100150200??(MPa)ExperimentalImplicitExplicitFigure 5.7: FEA results versus experimentalflow stress with strain hardening. Ex-perimental, implicit and unscaled ex-plicit simulated flow stresses are com-pared at Ta = 202?C & ?? = 7.58 s?1,further validating the material model.In the same manner that u was assigned from the experimental displacement record, the experi-mental temperature record was directly assigned to all nodes. For the purposes of directly comparingthe simulation to experimental results, strain was extracted from the nodal displacement record atpoint ?X? on the centerline in Fig. 5.5. The average von Mises stress at the integration point ofthe elements along the centerline was extracted. The flow stresses for all simulations are compareddirectly to the relevant experimental flow stresses in Fig. 5.6 and 5.7.These two figures demonstrate that there is no difference between unscaled explicit and implicitsolutions. Furthermore, aside from the flow stress record at low strain, there is reasonable agreementbetween the model results and the experimental flow stresses. The discrepancy at low strain forboth tests is owed to the combined effects of error inherent in the constitutive expression as well aspotential non-uniform deformation occurring during the test.5.2.2 Thermal assessmentAs the previous models had temperatures and displacements applied directly through boundaryconditions, the absence of thermomechanical coupling in this model formulation is insufficient tofully assess the effects of time and mass scaling. To address this, the thermal boundary conditionswere modified. Using the previously discussed compression test data that exhibited work hardening111CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING(Ta = 202?C and ?? = 7.58 s?1, Fig. 5.7), thermal boundary conditions were developed to approx-imate the heat transfer conditions. The initial temperature of 202?C was applied uniformly acrossall nodes, and heat generated due to inelastic deformation was implemented with a Taylor-Quinneyfactor of ? = 0.9. The heat transfer from the sample to the IsoT anvils used in the Gleeble wasapproximated with a heat flux, qH = h(T ? T?), applied to both ends of the specimen (Fig. 5.5),where h = 4?103 W/m2?C and T? = 180?C throughout the simulation.The thermal boundary conditions were established through recursive implicit simulations hold-ing ? constant and modifying both T? and h to establish values close to describing the experimentaltemperature evolution. In reality, these values vary throughout the compression test, however, theseboundary conditions were determined to adequately approximate the heat transfer conditions. Thepurpose of this exercise was not to accurately assess the heat transfer during a compression test, butto increase the degree of thermomechanical coupling to match the potential degree encompassing arotary forming simulation.The flow stresses and temperature response at point ?X? (Fig. 5.5) predicted by models withboth the explicit and implicit formulations were found to be identical. Fig. 5.8 shows the contoursof ?VM and T for the two solution techniques. Throughout the computational domains, the distri-bution of stresses are nearly identical, being within 2 MPa at all points. Temperature contours areindistinguishable. Thus, the explicit simulation with these thermal conditions and the aforemen-tioned mechanical boundary conditions can be used to evaluate the effects of time scaling and massscaling.5.2.3 Effects of time and mass scalingWhile both time and mass scaling strategies are equivalent in terms of reducing computationaleffort, they are quite different in their implementations. Mass scaling seeks to increase the lengthof time increments (?t) by scaling the material density by a factor ( fm) and thereby increasing ?tby decreasing dilatational wave speeds. Time scaling reduces computation time by applying loadsfaster than in actuality, decreasing the total simulated time (tp). Both methods are proportional,where the time scaling factor ft =? fm. In a coupled framework, mass scaling requires the densityof the material and dependent boundary conditions to be scaled. Time scaling requires that materialrate sensitivities and thermal boundary conditions be amended.112CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING(a) Implicit ?VM (b) Implicit T(c) Explicit ?VM (d) Explicit TFigure 5.8: Final von Mises stress and temperature state modelled implicitly and explicitly.Implementing a time scaling strategy is more complicated as it requires both the rate dependencyof the material and the thermal boundary conditions to be modified. The rate dependency may beaccommodated by directly scaling the strain rate in the constitutive behaviour. When applying timescaling to the thermal conditions, the Fourier and Biot (Fo and Bi) numbers in the scaled problemmust remain the same according to:Fo =(kc ft)(tp/ ft)?CpL2 (5.2)Bi =(h ft)Lkc ft (5.3)where the change in process time tp, which is scaled by ft , is accommodated by factoring the con-ductivity kc and boundary heat transfer coefficients, h, to retain the same Biot and Fourier numbers.The baseline explicit model was time scaled by ft equal to 10, 25, 50 and 100. These simula-tions were compared to models with equivalent amounts of mass scaling applied ( fm = 100, 625,2500, and 10000). ABAQUS allows for various implementations of mass scaling such that it is onlyapplied to the mechanical solution and does not affect the thermal characteristics of the model. Al-though selective [131] and variable mass scaling techniques are possible, uniform mass scaling wasemployed. Here, tp was specified directly and the solver increased ? in all elements by the same113CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING0 0.1 0.2 0.3 0.4050100150200??(MPa)Unscaledft = 10fm = 100ft = 25fm = 625ft = 50fm = 2500Figure 5.9: Predicted flow stresses for timeand mass scaling.0 0.1 0.2 0.3 0.4200205210215220225?T(?C)Unscaledft = 10fm = 100ft = 25fm = 625ft = 50fm = 2500Figure 5.10: Predicted temperatures fortime and mass scaling.amount to decrease the dilatational wave speed. As the constitutive expression renders flow stress afunction of temperature, the principal metric to compare the ability of each simulation to track theevolution of stress, strain and temperature was flow stress.A comparison of the predicted flow stresses with various levels of scaling is provided in Fig. 5.9.This comparison shows that flow stresses for both time and mass scaling are similar up to scalingof factors of 25 and 625, respectively, as compared to unscaled results. Increasing time scalingto 50 also agrees well with unscaled results, however, there is a significant departure apparent forequivalent mass scaling. While the flow stresses predicted by the ft = 50 and unscaled simulationare nearly identical, the equivalent mass scaled simulation does not predict the same yield, norpredict the same level of strain. Fig. 5.10 displays the same type of behaviour for the predictedtemperature, with temperatures scaled results departing from unscaled results at fm = 2500.Both mass and time scaling strategies result in significantly shortened computation times. Thiscan be quantified with an acceleration factor, ?f , which is defined as the ratio of unscaled simulationcomputation time to scaled simulation computation time. Table 5.2 provides ?f for each simulationtype and clearly demonstrates the large improvements to computation time that occur with scal-ing. The ft = 10 simulation ran 7.1 times faster and the fm = 100 simulation ran 8.86 times fasterthan the baseline unscaled simulation. Beyond this scaling point, the incremental increase in ?fbecomes smaller for mass scaling as compared to time scaling owed to comparably smaller timeincrements caused by solution instability (locking). This is because locked portions of the domain114CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMINGrequire highly distorted elements elsewhere, which causes Lmin to decrease much more than a stablesolution. However, if the simulation corresponding to ft = 10 is considered to be at the limit of nu-merically stability, then the equivalent mass scaling factor ( fm = 100) provides a 20% improvementin computation time.Table 5.2: Simulation execution time acceleration factor ?f for time and mass scalingft ?f fm ?f10 7.10 100 8.8625 17.72 625 12.0050 44.29 2500 24.01100 95.15 10000 46.71Both time and mass scaling provide a reasonably accurate simulated flow stress at ft = 10 andfm = 100 as compared to the unscaled process (Fig. 5.9). However, a comparison of the von Misesstress contours, shown in Fig. 5.11, with the results from the unscaled model (refer to Fig. 5.8)indicate that the time scaled version is in better agreement than the mass scaled (Fig. 5.11a versus5.11b). However, a single element lying on axis of the specimen (R = 0) has locked in the ft = 10result, which is indicative of numerical instability. This locked element has in turn affected thestress distribution at the midpoint of the domain. This is likely because the domain is sensitive toinstability at this location, as this is where the largest stress and temperature gradients occur in theunscaled simulation (Fig. 5.8c and 5.8d).At ft = 50 and fm = 2500, there is a significant difference between the time and mass scaledversions: the time scaled flow stress matches the unscaled version, while the mass scaled flow stressseverely underestimates the unscaled version. As shown in Fig. 5.11c and 5.11d, the contour plotsof von Mises stress for both scaling factors do not agree with the stress and deformation distributionseen in the unscaled version. Both models show evidence of element locking, with the time scaledversion showing only a few locked elements in the most sensitive portion of the domain. Theextent of element locking in the mass scaled version is on a much larger scale, with only a fewelements in the centre of the domain remaining unlocked. Not only do the locked elements affectthe solution?s accuracy, but also cause the domain?s Lmin to inordinately decrease due to distortedelements elsewhere. This in turn leads to shorter time increments and longer computation times, asshown in Table 5.3.115CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING(a) ft = 10(b) fm = 100(c) ft = 50(d) fm = 2500Figure 5.11: Simulated final von Mises stress state with high and low levels of time and massscaling.5.2.4 Maximum scaling factorAn appropriate scaling factor is dependent on the model formulation both in terms of domain andboundary conditions. Models containing structures with high natural frequencies and quasi-staticloads will be able to accommodate larger scaling factors without much loss in accuracy. As such,isothermal studies of rotary forming that have employed explicit FEA have reported time scalingfactors ranging from ft = 100 for a solid cylindrical lead workpiece [69] to ft = 6 for steel sheet[86]. As demonstrated in the preceding, both time and mass scaling provide reasonable solutionsas compared to the baseline model up to factors of ft = 10 and fm = 100. At these scaling factors,time scaling provided a better match to unscaled simulations. With increasing scaling factors, themodel provided increasingly unstable results, predominantly in the numerically sensitive areas ofthe domain. Mass scaling was found to provide more unstable results as compared to equivalent timescaling. The largest scaling factor with predictions closest to both experimental data and unscaledsimulations was ft = 50. This is in spite of the fact that numerical instabilities were evident in a fewof the elements. As will be shown subsequently, the chance for these instabilities to occur is domaindependent, as ft = 50 was employed for all further simulations.116CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING5.3 Preliminary rotary forming modellingFollowing the verification of the constitutive behaviour within a coupled thermomechanical explicitFEA framework, preliminary modelling of rotary forming was carried out on a simple abstract ver-sion of the EFA process. This preliminary modelling was necessary to examine mesh sensitivityand to assess the computational expense prior to running full-scale models of the EFA process.This preliminary model also permitted verification of the boundary conditions describing the rollermovement. These preliminary models use a simplified workpiece geometry in the form of an annu-lus with approximately the same thickness and (uniform) inner diameter as the EFA workpiece, butone seventh the axial length. These workpiece dimensions allowed the same roller geometry as thefull-scale model to be used in defining the rigid analytical surface. A cylindrical, rigid analyticalsurface was defined for the mandrel to match the inner diameter of the simplified workpiece.5.3.1 Model descriptionBased on the geometry and boundary conditions shown in Fig. 5.12, the model was run three ways:2D axisymmetric and plane strain formulations, and on a fully 3D basis. The analysis consisted ofa single forming step lasting an unscaled time (tp) of 2.21 seconds, with roller movement consistentwith the EFA experiments. The roller was first brought into radial contact with the simplified work-piece at an initial temperature of 350?C. The roller was then moved axially (and circumferentially inthe 3D case) across the outer surface of the simplified workpiece which was held stationary at z = 0.The mandrel had an initial radial clearance of 0.1 mm from the inner diameter of the simplifiedworkpiece. Contact surfaces were defined between the simplified workpiece, the mandrel and theroller with friction conditions mirroring those used in the full-scale forming simulation.For the 2D analyses, the roller reference point started at uo with a radial clearance of 0.1 mmfrom the material at z = 22.5 mm and was then moved radially to penetrate P = 1 mm into thesurface to arrive at un. The roller was then moved axially along the simplified workpiece by 5 mmto u f , deforming the material against the rigid mandrel. For the 3D analysis, the roller was made torotate approximately 34 times (? = 213.774 radians) about the z axis with the same axial and radialdisplacements imposed as in the 2D cases. Fig. 5.13 shows the evolution of the roller position overthe course of each simulation. These boundary conditions were implemented in a tabular fashion,with the simulated result being identical to the tabular values.117CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING(a) 2D(b) 3DFigure 5.12: 2D and 3D depiction of preliminary FEA modelFigure 5.13: Roller positioning validation, as shown by the change in the roller?s radial posi-tion as seen by the reference node. Both 2D and 3D simulations are shown with ?R and?Rsin? series, respectively. The resulting simulated roller position shown by the ?RSim. series and on the inset plot.118CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMINGFour sequentially finer mesh densities were used to describe the simplified workpiece for the2D cases and three for 3D. A uniform mesh (L = Lmax,Lmin) was used in each case, consisting ofquadrilateral reduced-integration elements with hourglass control (CAX4RT and CPE4RT) for the2D cases and equivalent elements (C3D8RT) for the 3D cases. The mesh densities, characterizedby initial element edge length (L) ranged from 5 mm to 0.625 mm for 2D and 5 mm to 1.25 mm for3D.5.3.2 Mechanical resultsThe predicted stress state and deformed shape at time tp for each of the 2D and 3D models of theworkpiece are presented in Fig. 5.14. Here, equivalent stress (?VM) and plastic strain (?p) are shownfor equivalent mesh densities. Little difference is apparent between the 2D descriptions, implyingthat the diameter of the workpiece is sufficiently large to support a plane strain assumption. Thedifference in the stress and strain state between the 5 and 2.5 mm mesh cases is very apparent, sug-gesting that a 5 mm element edge length is too coarse. The difference between 2.5 and 1.25 mmmesh cases is significantly more muted, suggesting that element edge lengths less than 2.5 mm ad-equately discretizes the domain. This was confirmed by the 0.625 mm 2D simulations (not shown),which displayed similar results to the 1.25 mm case. Even at the finest mesh density, there is noevidence of elements locking in the same manner as was seen previously with the compression testsimulations. This indicates that the time scaling factor employed is appropriate for these conditionsand domain.For all mesh densities, however, there is a significant difference between the 2D and 3D results.In the 3D instances, deformation is highly localized at the roller interface. Here, the material iscarrying larger load both in terms of shear and ?VM compared to the 2D cases. This is due to thelarger plastically affected zone predicted in the 2D approximations, which extends approximately2.5 mm into the material directly beneath the roller, compared to approximately half that for the 3Dpredictions. Another appreciable difference is the material pileup ahead of the roller in the 3D case,which is absent in the 2D. Comparing the 3D model results, it appear that the element edge lengthmust be 2.5 mm or smaller in order to predict this phenomena.Based on the results from these simulations, modelling rotary forming with a domain similar tothat of the EFA process requires a 3D description. Both 2D and 3D modelling efforts dictate that119CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING(a) ?VM(b) ?pFigure 5.14: Preliminary model results with axisymmetric (left column), plane strain (centre)and 3D (right) domains having different mesh densities; L = 5 mm in (i), L = 2.5 mmin (ii), and L = 1.25 mm in (iii).mesh with a characteristic element edge length of 2.5 mm is required, with finer mesh providingmore coherent results.5.3.3 Computational requirementsThe resulting memory footprint and solution times using a single processor are given in Table 5.3for each of the simulations. This data shows that solution times sharply increase when moving tothree dimensions, as the 3D model with finest mesh took 66 hours to complete. It is importantto note that this computation time reflects approximately 30 hours per second of simulation, evenwith an aggressive time scaling factor. The cause is twofold: both the problem size, measured interms of memory requirements, and the number of floating point operations increase with a largernumber of solution variables as the critical time step decreases. The latter is also the reason for120CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMINGTable 5.3: Computational properties of preliminary simulations.L (mm)2D 3DSolve time (s) Size (MB) Solve time (s) Size (MB)Axisymmetric Plane Strain5 26.0 22.0 0.238 2.03 ?103 25.22.5 70.0 61.0 0.403 3.53 ?104 1.75 ?1021.25 3.37 ?102 3.32 ?102 1.20 2.37 ?105 1.33 ?1030.625 2.45 ?103 2.34 ?103? 3.70 NA NA? Used to benchmark the effects of additional processors.the axisymmetric simulations taking marginally longer to complete than equivalent plane strainformulations; the boundary conditions produced a minimum element length Lmin that was slightlysmaller during the course of the axisymmetric deformation.In an effort to gauge the improvement in solution times by employing multiple processors, theL = 0.625 mm plane strain model was run with multiple processors on a multicore computer. Inthese tests, the domain was split across 2 to 8 processors with shared memory. Additional pro-cessors did improve the solution times appreciably. Moving to two processors showed a 104%improvement, but the rate of improvement showed diminishing returns with additional processors;moving from 7 to 8 processors only displayed a 2% improvement. This is due to increased com-munication overhead as ABAQUS holds all element calculations on a single processor, and passesnode-based calculations on to each processor. The net result is that a finely meshed 3D domainrequires significant computational resources, and despite a high level of time scaling and additionalprocessors, results in very long solution times for very short simulation periods.5.4 Thermomechanical EFA modellingFollowing the development and verification of the modelling methodology, full-scale, coupled ther-momechanical models of the EFA process were run to analyze the forming conditions achieved inthe experiments. The application of this modelling methodology to the EFA process provides alarge amount of information regarding the process including the ability to track the evolution of thestress state, strain rate, and temperature in the workpiece during forming. The results of the formingmodel reflecting the mid-deformed and least-deformed workpiece will be presented as an exampleof the model capabilities. These results will be followed with a comparison of the final workpiece121CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMINGgeometries generated experimentally and those predicted with the model. Finally, the stress stateimposed on the workpiece during mid-level deformation will be presented and discussed within thecontext of surface defect formation.5.4.1 Model resultsThe forming model provides a great deal of insight into the overall process. One facet is the evo-lution of the stress-state and deformation of the overall workpiece during forming. This is demon-strated in Fig. 5.15, which shows the distribution of the equivalent stress on the surface of theleast-deformed workpiece at the start, midpoint and end of forming. This corresponds with theroller at un, at the midpoint of the roller travel, and just prior to the roller leaving the surface of theworkpiece. In this figure, the workpiece has been rotated such that axis of symmetry of the roller isparallel with the centerline of the workpiece, affording an orthogonal view of the workpiece alongits axis during forming. This orientation is similar to the orientation describing the qualitative stressdistribution used by Xu et al. [1], as shown in Fig. 1.15.At the start of forming, the equivalent stress is highly localized about the centerline of the work-piece, and close to being symmetric about the centerline of the workpiece. The bulk of the formingzone, identified by the regions of elevated stress (greater than 125 MPa), is directed circumferen-tially along the path of the roller, with the maximum contact stress appearing slightly ahead of thecenterline. At the midpoint of forming, the stress state has evolved such that the majority of theforming zone remains ahead of the roller, however, significant stresses have evolved elsewhere onthe surface. The region ahead of the roller through to the end of the workpiece shows significant loaddirected axially. At this stage in forming, the overall bounds of the circumferential region carryingan elevated load has increased dramatically from the start of forming. At the end of forming, thestress state returns to being highly localized immediately beneath the roller, ahead of the centerline.Fig. 5.16 shows an oblique view of the workpiece at the same stages during forming presentedin Fig. 5.15. Also shown in this figure are the nodes that are reported as being in contact with theroller at each stage. At the start of forming, a faint ridge can be seen due to the initial contact of theroller, with a relatively small roller contact footprint. At the midpoint of forming, this ridge is morevisible and contact has extended to include a small pileup of material ahead of the roller, whichresults in a larger contact region. The region ahead of the roller in the axial direction demonstrates122CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING(c) End (b) Midpoint (a) StartFigure 5.15: Predicted equivalent stress state (?VM) on the surface of the least-deformed work-piece during forming.slight diametral growth, coinciding with the high axial stress levels as compared to behind theroller. At the end of forming, the contact patch has diminished in accordance with the dissipationof material pileup. In this last stage, the formed regions behind the roller exhibit ridges attributed tonon-uniform pileup dissipation as the roller location progressed.Orthogonal views of the deformation and stress states occurring in the mid-deformed workpieceat similar stages during forming are presented in Fig. 5.17. Overall, the stress magnitude is sig-nificantly higher than seen with the least-deformed workpiece, coinciding with a more aggressiveforming profile. Like the least-deformed workpiece, the peak stresses on the surface of the work-123CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING(a) Start(b) Midpoint(c) EndFigure 5.16: Oblique views of the simulated equivalent stress state immediate to the roller onthe surface of the least-deformed workpiece. Inset shows nodes in contact with theroller.124CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMINGpiece occur slightly ahead of the centerline at all forming stages. At the start of forming, the stressstate is similar to the least-deformed workpiece in that the contact stress is approximately axiallysymmetric about the centerline of the roller. However, this stress state embodies a much larger re-gion of stress projected towards the fixed end of the workpiece, which is attributed to bending stresscaused by the roller contact. Midway through forming, the stress state has changed dramatically tobe quite disparate from the least-deformed workpiece. This is attributed to the workpiece bucklingand forming a convex flange ahead of the roller. Two regions of elevated stress appear on the cir-cumference. One aligned with the centerline of the roller, and the other appearing on the flange,behind the roller circumferentially and ahead of the roller axially. At the end of forming, the stressreturns to being localized to the vicinity of the roller, however, the axial length shows a large degreeof irregularity around the circumference than that seen in the least-deformed workpiece.Oblique views of the mid-deformed workpiece at the same forming stages are shown in Fig.5.18 in conjunction with the nodes in contact. This shows that the same number of elements are incontact with the roller as the least-deformed workpiece at comparable forming stages. However, thisis the sole similarity. The initial ridge formed by roller contact at the start of forming is much morepronounced. Beyond the formation of the flange midway through forming, the surface previouslyencountering the roller is much more irregular and a small region of pileup is seen at the edge ofthe flange closest to the roller. At the end of forming, the flange has collapsed, and the edge ofthe workpiece shows localized irregularities. The ridges seen in the least-deformed workpiece thatwere attributed non-uniform pileup dissipation are much more exaggerated in this forming case.However, the ridges in the mid-deformed case are much less radially consistent than in the least-deformed workpiece. Clearly, the simulation predicts significantly less uniform deformation thanobserved in the least-deformed workpiece, with the workpiece wrinkling as the flange buckles.Two orthogonal views of the mid-deformed workpiece at the last stage of forming is providedin Fig. 5.19 with contours showing the predicted axial displacement. This result highlights thenon-uniform distribution of axial deformation, in particular the formation of lobes that are apparentat the end of forming. This phenomena is discussed further in the next section. To further examinethe evolution of other process variables beyond stress and displacement, cross-section views of thesimulated workpieces immediately underneath the roller have been extracted at each stage of theforming process. An example of one of these locations is shown in Fig. 5.19.125CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING(c) End (b) Midpoint (a) StartFigure 5.17: Simulated equivalent stress state (?VM) on the surface of the mid-deformed work-piece during forming.Contours of equivalent stress, equivalent plastic strain, strain rate, and temperature on the cross-sectional planes at each of the three stages in forming of the least-deformed workpiece are shownin Figs. 5.20 - 5.23, respectively. The equivalent stress in the least-deformed workpiece (Fig. 5.20)at the start of forming shows that the region of elevated stress is localized directly beneath theroller and does not extend very far through-thickness. As forming progresses, the stress distributionevolves ahead of the roller, staying predominantly localized to the outer diameter of the workpieceas the workpiece bends to conform with the forming profile. The distribution of plastic strain (Fig.5.21) mirrors the stress profile, with a peak of 0.7 on the outer diameter and 0.3 on the inner. Thestrain rate distribution (Fig. 5.20) which encompasses both elastic and plastic strain rates, has a126CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING(a) Start(b) Midpoint(c) EndFigure 5.18: Oblique views of the simulated equivalent stress state immediate to the rolleron the surface of the mid-deformed workpiece. Inset shows nodes in contact with theroller.peak located at the roller interface at the start of forming. Midway through forming, the peak strainrate has shifted to being slightly ahead of the roller and midway through the workpiece thickness.This is attributed to the combined effects of surface deformation and bending. The peak rate stays atapproximately 4-4.5 s?1 for most of the forming pass, rising to 7 s?1 briefly at the end. Reflectingthe relatively low amount of strain imparted to the workpiece, the temperature has only increasedby approximately 10?C (Fig. 5.23).Contours of equivalent stress, equivalent plastic strain, strain rate, and temperature on the cross-127CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING(a) Axial view (b) Normal to axisFigure 5.19: Contour plots of nodal displacement along mid-deformed workpiece axis, corre-sponding to Fig. 5.17c and 5.18.sectional planes at each of the three stages in forming of the mid-deformed workpiece are shown inFigs. 5.24 - 5.27, respectively. The equivalent stress state occurring radially in the mid-deformedworkpiece (Fig. 5.24) demonstrates a much higher load both on the outer and inner diameter thanthe least-deformed workpiece. This is likely due to bending stresses developed as soon as the rollercontacts the workpiece. As forming progresses, the stress state evolves ahead and to a lesser extent,behind the roller. The highest stress appears in the middle of the workpiece, differing from theleast-deformed workpiece as the deformation in mid-deformed workpiece is dominated by bending.The distribution of equivalent plastic strain (Fig. 5.25) is primarily localized on the outer and innerdiameter of the workpiece at all forming stages. This is similar to the least-deformed workpiece,albeit peak strains are an order of magnitude higher. Additionally, at the midpoint of forming, anappreciable plastic zone has developed on the edge of the flange, well ahead of the roller, which isattributed to the start of buckling in the flange. At the end of forming, the flange region exhibits thelargest amount of strain caused by the combination of buckling and roller contact during forming.The strain rate (Fig. 5.26) distribution is similar to that observed in the least-deformed workpiece,128CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING(a) Start(b) Midpoint(c) EndFigure 5.20: Equivalent stress distributionon cross-sections of the least-deformed workpiece at differentforming stages.(a) Start(b) Midpoint(c) EndFigure 5.21: Equivalent plastic strain dis-tribution on cross-sections of theleast-deformed workpiece at differentforming stages.however, the magnitude is approximately 4 times that seen owing to the large amount of buckling.As there was significantly higher amounts of strain applied, the temperature increase is significantlyhigher, with the peak temperature increasing by 40?C (Fig. 5.23).5.4.2 Geometric comparison to experimental resultsIn order to gauge the effectiveness of the model to predict the final shape of the workpiece, the resultsof the model after cooling the deformed workpiece to room temperature have been compared in twomanners. First, predicted workpiece lengths are compared over the entirety of the circumference.Second, the predicted workpiece cross-sections are compared through thickness with correspondingexperimental profiles (Fig. 2.14c and 2.14d).Fig. 5.28 shows variation of the predicted axial length of the work piece around the circum-ference for the least-deformed case. The model data shows that there are four discrete minima andmaxima appearing about the circumference of the part, corresponding to faint lobes (illustrated inFig. 5.19). The measured extents of the least-deformed workpiece have been plotted as dashed129CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING(a) Start(b) Midpoint(c) EndFigure 5.22: Strain rate distribution oncross-sections of the least-deformedworkpiece at different formingstages.(a) Start(b) Midpoint(c) EndFigure 5.23: Temperature distribution oncross-sections of the least-deformedworkpiece at different formingstages.(a) Start(b) Midpoint(c) EndFigure 5.24: Equivalent stress distri-bution on cross-sections of themid-deformed workpiece at differentforming stages.(a) Start(b) Midpoint(c) EndFigure 5.25: Equivalent plastic strain dis-tribution on cross-sections of themid-deformed workpiece at differentforming stages.130CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING(a) Start(b) Midpoint(c) EndFigure 5.26: Strain rate distribution oncross-sections of the mid-deformedworkpiece at different formingstages.(a) Start(b) Midpoint(c) EndFigure 5.27: Temperature distribution oncross-sections of the mid-deformedworkpiece at different formingstages.lines for comparison. The solid line coincides with the overall length of the experimental cross-section (Fig. 2.14c) presented in Chapter 4. The experimental workpiece did not exhibit lobes asthe minimum and maximum length were offset circumferentially by 180?. However, with the exper-imental workpiece measuring 149.25?0.55 and the simulated 148.43?0.62, the agreement betweenthe model and experiment is within the length of an element.Fig. 5.29 compares shape of the experimental cross-section (solid outline) with that predictedby the model (mesh) at location of the maxima (on lobe) and minima (off lobe). The model predictsthe development of a convex shape axially along the outer diameter, where as experimental profileis slightly concave. Both predicted profiles exhibit approximately the same amount of error in de-scribing the experimental cross-section, with the inner radius being approximately 4.5 mm smallerat the midpoint of the deformed region than found experimentally.Fig. 5.30 presents the same comparison as Fig. 5.28 for the mid-deformed workpiece. For themid-deformed conditions, the circumferential variation in length predicted by the model is muchmore pronounced, demonstrating much larger lobes. The final length of the experimental workpiecewas 162.15?0.65 mm, where as the model predicts a length of 155.15?3.15 mm. The model131CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMING0 90 180 270 360147.5148148.5149149.5150150.5Circumferential location (?)Axiallength(mm)  Cross-sectionExperimental extentsSimulationFigure 5.28: Final axial length of the leastdeformed workpiece compared to ex-perimental measurements.(a) On lobe(b) Off lobeFigure 5.29: Cross-sectional comparison ofmodel and experimental results forleast-deformed workpiece.0 90 180 270 360152154156158160162164166Circumferential location (?)Axiallength(mm)  Cross-sectionExperimental extentsSimulationFigure 5.30: Final axial length of the mid-deformed workpiece compared to ex-perimental measurements.(a) On lobe(b) Off lobeFigure 5.31: Cross-sectional comparison ofmodel and experimental results formid-deformed workpiece.does not predict the overall part length for the mid-deformed conditions nearly as well as the leastdeformed forming profile. This is also reflected in the comparison of the experimental cross-sectionwith model predictions at the on and off lobe positions (Fig. 5.31). The on lobe position agrees withthe experimental cross section for the majority of the length, with the exception of the very end ofthe workpiece. The off lobe position departs significantly, predicting an inner radius approximately9 mm smaller at the midpoint of the deformed region.The primary cause for the large discrepancy between the model prediction and the experimental132CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMINGresults for the mid-deformed workpiece can be attributed to limitations in the model. The modelcurrently predicts localized deformation, but does not predict material fracture. Experimentally,surface cracks were observed on the outer diameter of the workpiece (documented in Section 4.4).Incorporating the prediction of surface cracking in the model would affect the bending stressessignificantly as the overall part stiffness would decrease. This would in turn modify the flangebuckling phenomena. Based on the experimental results, this had the effect of diminishing wrinklingand limits the formation of lobes.However, the model does shows reasonable agreement with the experimental geometry in thecase of the least deformed workpiece. It also permitted a fair prediction of the radial cross-sectionof the mid-deformed workpiece on lobes. The lack of agreement elsewhere for the mid-deformedworkpiece can be attributed to cracking. This shows that the the basic deformation mechanism hasbeen successfully modelled.5.4.3 Surface defect formationIn a study of rotary forming of cast aluminum, Mori et al. [77] demonstrated experimentally thatsurface cracks similar to those found in the present study occurred in regions of high levels of strain.These levels of strain were identified with a strain rate independent model. In reviewing the resultsof torsion testing conducted by McQueen et al. [40], fracture in A356 was observed to occur atstrains of 1 and 1.5 at 300 and 400?C, respectively (Fig. 1.7), for strain rates up to 5 s?1. Thetorsion tests also showed that the equivalent stress at fracture was seen to increase with higher strainrates.Based on this information, the forming model can be used to explain the lack of surface cracksappearing in the least deformed workpiece. The peak strain predicted by the model for this work-piece was 30% less than the fracture strain identified by McQueen et al., at approximately the sametemperature and strain rate conditions. In the case of the mid-deformed workpiece, the model pre-dicts equivalent plastic strains of 1.5 or more during early forming, prior to the flange buckling.Furthermore, the predicted strain rate is significantly higher than the range employed by McQueenet al., which would decrease the fracture strain to a greater extent. However, strain and strain ratealone are not sufficient to predict local failure.Fig. 5.32 shows a contour plot of the the principal stress (?1) magnitude occurring on a cross-133CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMINGFigure 5.32: Simulated ?1 magnitude and orientation from the forming direction immediate tothe roller on the z?R plane. The depicted state was extracted from the mid-deformedsimulation, at a quarter way through the axial travel of the roller.section of the mid-deformed workpiece immediately below the roller. Overlaid on the contour plotis a quiver plot showing the projection of ?1 onto the z?R plane, with origins located at integrationpoints. In this figure, the length of each arrow (quiver) represents the principal stress magnitude.This state reflects 17.5 mm of axial roller travel, or approximately 25% through the forming profile,coinciding with a position halfway between those shown in Fig. 5.24-5.27. The region in contactwith the roller demonstrates a high degree of compressive stress, however the element immediatelybehind the roller shows a nearly zero stress state at the surface. The stress state is increasinglytensile moving towards the inner diameter. The crack morphology shown in Fig. 4.14 matches thisstress disparity, as annotated by the black dashed line.Attributing this precise mechanical state to categorically identify the conditions necessary forcrack development during forming is speculative at best. This is because the experimental basis forthe material model employed does not extend to encompass the strain and strain rate predicted bythis simulation, as well as being limited by the data available regarding fracture conditions. Themodel does, however, provide a framework to include further data with which forming parametersmay be modified to conclusively mitigate this phenomena from occurring.5.5 SummaryThe various thermal and mechanical processing steps involved in EFA processing have been mod-elled as a coupled thermomechanical process in ABAQUS. This consisted of an implicit submodelfor preheating the workpiece to forming temperatures, as well as explicit submodels of the forming134CHAPTER 5. MATHEMATICAL MODELLING OF ROTARY FORMINGoperation at elevated temperatures and final cooling to room temperature. The overall modellingeffort contributes significantly to the overall understanding of rotary forming as a whole; hereto-fore, strain rate and temperature dependency in modelling efforts have not been considered in rotaryforming, much less for A356.The model development commenced with validating the extended Ludwik-Hollomon?s expres-sion within ABAQUS, both implicitly and explicitly. The explicit implementation had thermal bound-ary conditions changed to develop a thermal gradient in the deformation model based on unequalrates of heat generation due to inelastic deformation and conduction. This baseline model was thenused as a metric to compare both time and mass scaling strategies. Time scaling was shown to pro-vide reasonable solutions up to factors of ft = 50, which significantly reduced explicit simulationcomputational overhead.A simplified abstraction of the EFA process was then used to validate boundary conditions, ex-amine minimum mesh requirements and accompanying computation resources. The minimum meshrequirements identified had elements with lengths less than 2.5 mm, and the computational penaltyfor further mesh refinement was excessive. Each bisection of the element length resulted in solutiontimes increasing by an order of magnitude. Parallelization proved to provide little improvementto the solution time as the problem size grew with mesh density, resulting in large communicationoverhead between processors.The overall model results show that the local effects of the roller interface dominate throughoutforming, and that the strain rates achieved are significantly higher than those used to fit the constitu-tive material behaviour. Changes in material state, manifesting with the evolution of strain rate andtemperature produce non-uniform deformation in the form of wrinkling and the formation of lobes.Comparing the geometry of the lightly deformed workpiece with that predicted by the model showsreasonable agreement with the experimental geometry, demonstrating that the model successfullydescribes the basic deformation mechanism. Comparing the results for the mid-deformed workpieceshowed that the model did not predict the geometry nearly as well. It has been speculated that thiswas due to the inability of the model to predict cracking. As additional data on cracking of A356 athigh strain rates and strains at elevated temperatures becomes available, this model may provide theability to modify forming parameters such that rotary forming defects may be avoided.135CHAPTER 6FATIGUE BEHAVIOUR1As covered in Section 1.4, there are a multitude of factors which affect the High Cycle Fatigue(HCF) resilience of A356?T6. Most studies conducted in this area have focused on uniaxial loadingconditions, leaving a knowledge gap with regards to the effects of multiaxial loading. The effectsof multiaxial loading on fatigue resilience of A356 will be assessed prior to characterizing theeffect of rotary forming on fatigue resilience. Fully reversed tension, tension-torsion and torsionfatigue tests were performed and combined with fracture surface observations to analyze the fatiguemechanisms. Basic fatigue criteria were also evaluated within this loading regimen. Kitagawa-typeanalysis has been performed for the three loading cases, and an estimate of the critical defect sizefrom a multiaxial loading standpoint is defined. The uniaxial HCF fatigue resilience of heat treatedrotary formed material is then presented in light of these investigations.6.1 Multiaxial fatigue characterizationAs described in Section 2.1.3, A356?T6 from a variety of sources has been employed to characterizethe multiaxial fatigue behaviour. This included material from wedge and wheel castings with a rangeof DAS and porosity sizes, with some specimens containing artificial defects.1Portions of this chapter have been published in:? Roy M. J., Nadot Y., Maijer D. M., Benoit G., ?Multiaxial Fatigue Behaviour of A356?T6?, Fatigue and Fractureof Engineering Materials and Structures, (2012)? Roy M. J., Nadot Y., Nadot-Martin C., Bardin P.-G., Maijer D. M., ?Multiaxial Kitagawa analysis of A356?T6?,International Journal of Fatigue, 33 (2011) 823-832136CHAPTER 6. FATIGUE BEHAVIOUR6.1.1 Fatigue test conditions and resultsIn total, 32 fatigue samples of A356?T6 with various geometries were tested according to the stepmethodology described in Section 2.3.6. The specimen name, final step loading condition, extrac-tion location and number of cycles to failure employing the step method for each sample is summa-rized in Table 6.1. The resulting number of steps to failure for each specimen are also provided.For example, specimen W1 underwent 106 cycles at ?a =80 MPa without failure, as calculatedat the surface of the specimen. The stress amplitude was increased by 5 MPa to ?a =85 MPa, whereit also withstood N = 106 cycles. The stress amplitude was increased again by 5 MPa to ?a =90MPa and the sample failed after N f = 7.22?105 cycles on the 3rd loading step.While the results obtained from this testing are not endurance limits from a statistical standpoint,step testing is the only technique that permits the evaluation of an ?endurance limit? for a naturaldefect of unknown size. The term ?endurance limit? is defined as the stress level at fracture afterone million loading cycles. In the majority of the fatigue tests, failure occurred after at least oneloading step. There were two instances of specimens arriving at the same endurance limit albeitwith different numbers of steps. Samples W4 and M2 failed at ?a = 90 and ?a = 52 MPa after 5and 2 loading steps, respectively. Specimens T1 and T2, both from the top of the wedge, failed at?a, ?a = 65 MPa after 5 and 2 loading steps, respectively. Furthermore, specimen T3 was conductedas a run-out test and failed after 908 kilocycles with the same loading amplitude as T1 and T2.Owing to the non-ferrous nature of this material, these results indicate that A356?T6 is not sensitiveto the coaxing effect [132, 133]. It is asserted that the step testing method was able to ascertain theendurance limit for 106 cycles to within 5 MPa.6.1.2 Fatigue criteria comparison encompassing natural defectsGrouped according to family, Fig. 6.1a depicts ? f versus ? f for each specimens containing naturaldefects (i.e. specimens with artificial defects, family A have not been plotted). Based on the ob-served decrease in DAS from top to bottom of the wedge, the general trend identified in Fig. 6.1ais that specimens with the largest DAS exhibit the lowest endurance limit. However, specimensextracted from the wheel (W family) show a lower endurance limit than the wedge material at atension/torsion ratio slightly below pure torsion. This is in spite of having a smaller overall DAS.This difference is less than the range of results shown by the pure torsion testing of the wheel spec-137CHAPTER 6. FATIGUE BEHAVIOURTable 6.1: Test history of all A356?T6 multiaxial fatigue specimens.Specimen Loading (MPa) Steps N f (?105)?area (?m)Label Type? ?a ??a Number MPa/stepW1 a 0 90 3 5 7.22 59?W2 a 0 85 1? NA 3.00 59?W3 a 45 78 1? NA 8.35 59?W4 a 90 52 5 5 1.45 59?W5 a 70 70 2 5 1.05 59?B1 a 50 87 2 5 1.18 59?B2 a 90 52 2 5 2.04 59?B3 a 70 70 2 5 0.76 90?B4 b 0 70 2 5 3.98 39?B5 a 0 100 3 10 1.51 30?B6 a 0 110 2 10 8.83 38?M1 a 50 87 2 5 2.31 90?M2 a 90 52 2 5 4.01 90?M3 a 95 0 3 5 0.79 90?M4 a 65 65 2 5 2.46 514M5 a 70 70 3 5 5.26 53?M6 b 0 60 2 10 3.25 531M7 b 0 55 1? NA 2.27 90?M8 b 0 60 4 10 2.61 90?T1 a 65 65 5 5 4.24 112?T2 a 65 65 2 5 1.29 265T3 a 65 65 1? NA 9.08 300T4 a 60 60 1? NA 4.05 496T5 c 90 0 5 10 6.63 310T6 b 0 50 1? NA 7.33 265T7 b 0 50 2 10 4.84 372A1 c 90 0 1? NA 4.24 398A2 c 90 0 3 10 1.29 514A3 c 80 0 4 10 9.08 740A4 c 70 0 2 10 5.26 760A5 b 0 70 4 10 4.84 465A6 b 0 50 2 10 6.63 708?As calculated on the surface of the specimen.?Fig. 2.22. Tension-torsion specimens W1, W2, B5 and B6 were tested in pure torsion; M3was tested in pure tension.?Failed before 106 cycles during the first step?Estimated based on the maximum?area in Table 2.2138CHAPTER 6. FATIGUE BEHAVIOUR0 20 40 60 80 100020406080100? f(MPa)?f (MPa)  WBMT(a) Endurance limits grouped by family0 20 40 60 80 100020406080100? a(MPa)?a (MPa)  StepFailureCrosslandmps(b) Experimental results vs. criteriaFigure 6.1: Fatigue testing results: endurance limit grouped by material family type and testpoints compared to Crossland and MPS criteria. Note that only specimens with naturaldefects were included in this analysis.imens, and therefore the material from the wedge performed on par with that from the wheel. Fig.6.1b plots the ?a versus ?a data for all of the loading scenarios (Table 6.1) independent of familytype. While the tension and tension-torsion tests are tightly grouped, the specimens tested underpure torsion exhibit a greater range of results with ?a at failure between 50 and 110 MPa. Withthe exception of pure torsion, comparing the maximum endurance limit at all ratios of tension andtorsion, ? f and ? f for RL =?1 are approximately equidistant from the origin for all ratios of tensionto torsion.Under pure torsion loading, the straight-gauged tension-torsion type ?a? specimens exhibited ahigher endurance limit compared to the torsion type ?b? specimens. The defect population assess-ment of different positions in the wedge (Table 2.2) showed that the largest range of defect sizeswas observed in the middle of the casting. This location is where ?80% of the samples loadedunder pure torsion were extracted from. During the torsion tests, it was also observed that multipleshear cracks were active at the same time, with the dominant crack not appearing until late in thetest. The fractographic observations for this loading condition (Section 6.1.3) combined with theporosity measurements preclude specimen configuration being responsible for scatter. As the ten-sion and combined loading cases produced tightly grouped results, the scatter seen with pure torsion139CHAPTER 6. FATIGUE BEHAVIOURappear to be loading-dependent. However, this specific loading condition may be unimportant as thecombined effects of loading and geometry on components will create local multiaxial stress statesdifferent from pure shear.As an exploratory effort to ascertain a basic multiaxial fatigue criteria, the maximum endurancelimit from all data sets containing natural defects (i.e. each specimen family) at each tension/torsionratio was determined to characterize the behaviour for A356?T6. The extracted endurance limit datawas compared to the Crossland and Maximum Principal Stress (MPS) fatigue criteria. The Crosslandcriterion was selected owing to its similarity with other stress-based critical plane approaches underconstant amplitude [134?136]. The MPS criterion has been applied as it is relatively simplisticand is often used to assess brittle materials. These criteria were applied to the entire dataset ofexperimental results, since this is representative of the microstructural differences expected in alarge cast component.Crossland [137] proposed that the second invariant of the deviatoric stress and the maximumhydrostatic stress are the main parameters determining fatigue resilience:?J2,a +? f ?H,max 6 ACL (6.1)where J2,a is the second invariant of the deviatoric stress amplitude and ?H,max is the maximumhydrostatic stress. The constant ? f is a function of the endurance limit in pure tension and torsionand ACL is the endurance limit in pure torsion. Using the mean ? f = 89 MPa and ? f = 67 MPabased on data given in Table 6.1, ? f and ACL were determined to be 0.54 and 67 MPa, respectively.The MPS criterion asserts that the maximum principal stress must be below a critical thresholdsuch that:?1,max ?CMPS (6.2)where CMPS is taken to be the average tensile endurance limit, ? f = 89 MPa.These two criteria are plotted versus ?a and ?a in Fig. 6.1b. Both the Crossland and the MPScriteria underestimate the measured endurance limit for combined loading. It should be noted thatthe Crossland criteria approaches the MPS criteria under tension. Depending on the expected vari-ance in the pure torsion, these results may show that the Crossland criterion is overly conservative.140CHAPTER 6. FATIGUE BEHAVIOURThe Crossland criterion is reliant on the determination of an accurate endurance limit under puretorsion, which experimentally showed significant scatter. Therefore, the MPS criterion is the best ofthe two criteria to describe these results [55, 59].6.1.3 Fracture surfacesA representative summary of the fracture surfaces formed for each type of loading for specimenswith natural defects is presented in Fig. 6.2. Under pure tension (Fig. 6.2a), the fracture plane wasfound to always be normal to the direction of applied stress and thus, coincident with the maxi-mum principal stress (?1,max) plane. Specimens from both the wheel and wedge casting exhibitedthis behaviour indicating that this observation is independent of microstructure. Furthermore, SEMobservations on gauge section material far from the initiation site did not reveal any other cracks.Thus, multiple initiation sites did not manifest under pure tension, regardless of microstructure.Under combined tension-torsion loading, the fracture surface features are similar to pure tensionincluding regular fracture planes with no bifurcation (Fig. 6.2b) regardless of the sample location.SEM observation of the gage section far from the fracture surface reveals only small secondarycracks less than 50 ?m long. The orientation of the fracture surface in Fig. 6.2d is shown by thefracture surface normal. In this combined loading case where ?a = ?a, the fracture surface normalis oriented 27? from the axis of the specimen. With the maximum principal stress acting at 31? fromthe specimen axis, the fracture surface normal is close to being parallel with this direction. Thisdifference of 4? is the largest discrepancy observed over the 18 multiaxial specimens tested. Thus,the orientation of the macroscopic fracture plane under combined loading conditions correlates tothe loading condition. More specifically, the fracture plane correlates to the maximum principalstress (?1,max) direction. Therefore, the tension component of the loading must play a major role indetermining the path of crack propagation.Under pure torsion, the failures surfaces observed were very different and showed no similar-ities to that of pure tension or combined tension-torsion loading. Fig. 6.2c is an example of thefracture surface observed. The tortuous fracture surface has two major crack planes activated: onealigned with the axis of the specimen and the other one perpendicular to this axis. This highlightsthe difficulty in finding a unique initiation site on the fracture surface. Macroscopic observationsconfirmed by SEM analysis indicate that there are many different initiation sites over the periphery141CHAPTER 6. FATIGUE BEHAVIOUR(a) Pure tension (b) ?a = ?a (c) Pure torsion(d) Crack plane orientation (e) Secondary cracking under torsionFigure 6.2: Multiaxial fatigue failure types: pure tension (a), combined tension-torsion, ?a =?a (b) and pure torsion (c). Macroscopic crack plane orientation for combined tension-torsion (d). Secondary shear crack on the gage section of a torsion sample far from thefracture surface (e).of the gage section and that different crack planes link together to form the final fracture surface.Remarkably, there is no evidence of macroscopic cracks growing in the direction normal to the?1,max in the pure torsion scenario. For this loading condition, the crack path is governed by shearas opposed to principal stress. A clear demonstration of the dominance of shear is shown in Fig.6.2e where cracks propagate in shear mode from early in the fatigue life to the final failure. Thevery long crack observed in Fig. 6.2e was observed to propagate throughout the test under shearmode III and showed no evidence of bifurcation under mode I. When bifurcation did occur on thissample, a new crack plane extended from the original mode III shear plane and linked with anothermode III shear crack in the opposing activated shear plane. The sample shown in Fig. 6.2e exhibited142CHAPTER 6. FATIGUE BEHAVIOURmore than ten other cracks similar to the one depicted, and additional smaller cracks observed inboth shear mode III planes.The fractographic observations indicate that the fracture morphology is independent of the sam-ple family. Therefore, the microstructural features and the defect characteristics, such as DAS andaverage pore diameter (Table 2.2) do not dictate crack paths under multiaxial loading. The overrid-ing observation from the following analysis is that the macroscopic crack path is governed by ?1,maxunder multiaxial loading except for pure torsion where shear mode III dominates. This observationfor pure torsion is at odds with the general mechanical analysis performed in Section 6.1.2 whichasserted that the MPS criteria provided the closest description of the multiaxial fatigue results.6.1.4 Initiation site observationsThere are various multi-scale microstructural features that can cause fatigue initiation in A356?T6 [54, 55, 138]. Defects such as gas pores, shrinkage pores, oxides and inter-metallic particles caninitiate fatigue cracks. At smaller length scales and in the absence of larger-scale defects, the fatigueproperties are dominated by the primary ?-Al and eutectic characteristics. SEM observations wereperformed on each sample tested in this work to identify fatigue crack initiation sites and to examinethe crack propagation surfaces.The analysis performed on each sample followed a systematic methodology to reproduciblyidentify initiation sites and crack surface features. The methodology employed was as follows:? Optical microscopy was employed to observe the fracture surface and identify the fatigue andfast-fracture zones. The fast-fracture zone refers to that portion of the crack surface whichdeveloped in the last fatigue cycles.? Observations of the fatigue zone were conducted using SEM to determine the initiation site(within 1 mm2) where river marks on the fracture surface converge.? If a clear defect was identified, the size of the defect was measured using the?area parameteron the fracture surface. This is performed regardless of the position of the defect relative tothe gage surface.In a number of samples, the initiation site could not be accurately identified or characterized. Thiswas true for pure torsion samples with multiple initiation sites, but also for multiaxial tests where143CHAPTER 6. FATIGUE BEHAVIOURmodel III shear cracking lead to fretting damage of fracture surfaces.Due to the readily available tensile fatigue data for A356?T6, only two specimens were testedunder these conditions. Each of these specimens exhibited a gas or shrinkage pore as the initiationsite for the fatal crack. The first, M3 (Table 6.1), had a endurance limit of 90 MPa and contained agas pore with an equivalent diameter of 88 ?m at the initiation site. The other specimen, T5, had ashrinkage pore with an ECD of 370 ?m (Fig. 6.3a) at the initiation site and exhibited a endurancelimit of 85 MPa. Similar to pure tension, the combined tension-torsion samples exhibited fracturesurfaces that were easily characterized. Fig. 6.3b-6.3e are examples of typical defects that initiatedthe fatal crack. Fig. 6.3b shows the fracture surface of sample B3 that had a ? f of 68 MPa. Theinitiation area on this specimen was readily identified, but a root initiating defect could not be found.Fig. 6.3c is the fracture surface for sample W5, which had the same endurance limit as B3. Thefracture surface is less clear but it was possible to identify the initiation area where no clear defectswere observed. The fracture surface instead shows friction-generated oxide associated with crackpropagation. Fig. 6.3d reveals a 500 ?m pore just below the surface of specimen M4. Remarkably,the endurance limit for M4 was 63 MPa, which is close to the highest value observed. This may becaused by the root defect location relative to the surface of the sample. When a propagating crackdoes not intersect the sample surface, it is not under ambient environmental conditions, but undervacuum instead. This effect has been investigated in a cast Al-Si-Cu alloy [139] where the fatiguelife under vacuum when a surface defect is present is the same as when failure initiates from aninternal defect of the same size. These observations have also been confirmed with nodular castiron [140]. Therefore, a fatigue assessment of A356 should account for the position of the defectwith respect to the free surface as there is different damage accumulation dependant on whether thedefect lies on the surface or within the bulk. Fig. 6.3e shows a typical shrinkage pore at the surfaceof specimen T4. In this case, a 500 ?m pore decreased the ? f to 51 MPa. This result suggests thata surface pore is more detrimental to the fatigue life than a subsurface pore of the same size. Theenvironmental effect is not the only factor in this case because the morphology of the defects maybe different.The fracture surfaces of the samples tested in pure torsion were much more difficult to analyzethan the pure tension samples. As shown in Fig. 6.2c, the macroscopic topology of the surface isvery complex with two perpendicular mode III cracks activated and multiple initiation sites. Initia-144CHAPTER 6. FATIGUE BEHAVIOUR(a) T5 (b) B3(c) W5 (d) M4(e) T4 (f) T7Figure 6.3: Characteristic fatigue fracture surfaces: specimen T5 (? f = 85 MPa), B3 (? f , ? f =68 MPa), W5 (? f , ? f = 68 MPa), M4 (? f , ? f = 63 MPa), T4 (? f , ? f = 51 MPa) and T7(? f = 45 MPa).145CHAPTER 6. FATIGUE BEHAVIOURtion is spatially distributed and as a result, the fracture surface is a combination of different cracksthat have coalesced to cause final failure of the sample. Thus, it was difficult to identify a singleinitiating feature. However, when the fracture surface was less tortuous, there were features thatcould be analyzed (Fig. 6.3f). For these samples, it was non-trivial to separate the fatigue zone fromfinal failure zone. Fig. 6.3f shows three features that are presumed fatigue initiation sites. The fea-ture closest to the centre of the specimen is clearly porosity with an equivalent diameter of 265 ?m,located well away from the surface. The second and third features are possibly oxide film(s), but thefeatures have been destroyed by damage/oxidation of crack surfaces under mode III propagation.Under cyclic torsional loading, it is apparent that fatigue mechanisms are related to small, dif-fuse damage. This suggests that samples tested under pure shear conditions are more susceptible todistributed porosity as compared to the other loading scenarios. The pure torsion tests were also theonly specimens tested that experienced no hydrostatic stress. For steel, it has been shown that puretorsion leads to small distributed shear cracks on the surface of the sample while the other loadingstates cause more localized fatigue damage [141, 142]. However, when a crack in steel initiates ona shear plane, it bifurcates into mode I propagation after a relatively short length (100 - 300 ?m).In the present study, the pre-bifurcation crack length was much larger: on the order of millimetersas shown in Fig. 6.2e. This is important as crack deflection and bifurcation increase the overalldamage tolerance for a material. It is surmised that there are few eutectic-Si particles of the correctsize, shape and orientation that provide the necessary impetus for crack bifurcation in A356-T6.6.1.5 Kitagawa analysis of natural and artificial defectsWhile Section 6.1.4 focussed on the methodology of initiation site observation and qualitative ob-servations, this section aims to apply a quantitative assessment of the impact of defects on theendurance limit. This includes specimens with small, natural defects, as well as those with largerartificial defects applied, as described in Section 2.1.3. The experimental fatigue test results are pre-sented in Fig. 6.4 in the form of Kitagawa diagrams for each of the loading cases. These diagramshave both loading amplitude versus defect size at each step, as well as the endurance limit versusdefect size corrected for step testing as outlined in Section 2.3.6. For specimens where the initiationsite was unidentifiable, the initiating feature was estimated as the maximum?area of porosity foundvia metallography. The use of these results in the Kitigawa analysis is thus speculative. For speci-146CHAPTER 6. FATIGUE BEHAVIOURmens where there were multiple initiation sites, the largest identifiable defect closest to the surfacewas characterized. The results of the defect size assessment for each specimen are summarized inthe final column of Table 6.1.Tensile resultsFig. 6.4a presents the experimental Kitagawa relationship under pure tension. In all samples, theinitial defect size was readily identifiable on the fracture plane that was found to be perpendicular tothe direction of the maximum principal stress. The primary finding from the tensile Kitagawa curveis that the critical defect size is relatively large: specimens T5, A1 and A2 have very little impacton the endurance limit (8% reduction). These tensile specimens show that the material appears tobe sensitive to defects only when?area is greater than than 500 ?m.Specimen M3 displayed an oxide-related defect at the origin of the crack linked to subsurfaceporosity. Specimen T5 failed due to a 400 ?m pore that intersected with the surface of the sample(6.3a), while specimen A1 failed due to a 398 ?m artificial defect. Since specimens T5 and A1demonstrated the same endurance limit, it is concluded that the area parameter is able to correlatedifferent types of defects, independent of the nature of the defect. Nevertheless, this finding shouldbe verified with larger defects having a greater impact on the endurance limit. In terms of artificialdefects, fracture surfaces for specimens A2, A3 and A4 were very similar to A1, showing that theartificial defect was unmistakably the initiation point.Combined tension-torsion resultsThe combined tension-torsion Kitagawa diagram, presented in Fig. 6.4b, includes results for spec-imens with natural defects only. The macroscopic fracture surfaces were similar to those of thetensile specimens: a flat surface in a plane perpendicular to the direction of the maximum principalstress with clear, identifiable initiation sites excepting specimen B3 (Fig. 6.3b). For the specimenstested, the Kitagawa diagram suggests there is a small influence by large defects such as in specimenM4 (Fig. 6.3d), exhibiting a large 500 ?m subsurface pore. Below this size, there is no apparentinfluence of defects on the endurance limit.The origin of the failure on sample T4 was a shrinkage void near the surface of the specimen. Itis of interest to highlight that specimen M4 has approximately the same endurance limit (?67 MPa)147CHAPTER 6. FATIGUE BEHAVIOUR0 200 400 600 800020406080100M3T5 A1 A2A3A4?area (?m)?(MPa)  Failure (?f )No failure (?a)Artificial defects(a) Tension0 100 200 300 400 500 600405060708090W5B3T1M5 T2T3T4M4?area (?m)?=?(MPa)  Failure (?f , ?f )No failure (?a, ?a)(b) Tension-torsion0 200 400 600 800020406080100120B5B4W1W2M7B6T6 T7A5M6A6?area (?m)?(MPa)  Failure (?f )No failure (?a)Artificial defects(c) TorsionFigure 6.4: Kitagawa diagrams for different loading scenarios.and?area parameter as specimen T4 (514 versus 496 ?m), reinforcing the independence of defecttype and dependence of defect size characterized by?area on the overall fatigue life.Torsion resultsThe Kitagawa diagram for the torsion specimens, shown in Fig. 6.4c, is similar to the others inthat there was an observable effect on endurance limits with increasing defect sizes. The exper-imental points presented below 100 ?m are for specimens that were unsuccessfully classified byfractography. The data for these specimens has been separated along the horizontal axis based onthe porosity assessment of their location in the wedge to render individual tests identifiable. As theendurance limits vary from 55 to 95 MPa for specimens with unidentifiable defects, the Kitagawa148CHAPTER 6. FATIGUE BEHAVIOURdiagram under torsion exhibits a large amount of scatter as compared to the tensile results.The main complication in identifying defects in the sub 100 ?m range is the tortuous nature ofthe fracture surface, as shown in Fig. 6.2a and described in Section 6.1.4. Cracking was activatedon two planes of maximum shear such that the final fracture surface reveals multiple initiationsites. While multiple initiation sites could explain the scatter seen in the Kitagawa plot, carefulexamination of the fracture surface at each suspected initiation point did not always result in anidentifiable defect. An attempt to link the presence of porosity to the multiple initiation sites wasmade with specimens B4, M7, T6 and T7 by metallography performed on sectioned and polishedfracture surfaces. There was little to no deviation found from the porosity measurements given inTable 2.2. In light of these findings, the critical defect size is difficult to assess. Specimens withidentifiable defects show a definite decrease in endurance limit beyond 300 ?m, which is smallerthan under tension. As is the case with the tensile testing, this critical defect size should be clarifiedby other tests on samples containing 300 ?m or larger artificial defects.6.1.6 Implications for rotary formed materialUp to this point, the fatigue behaviour has been discussed for A356?T6 processed in a standardmanner which contained a variety of different defects. The fracture mechanism due to multiaxialloading was seen to be proximate for all loading scenarios aside from pure torsion. This mechanismconsisted of cracks initiating at defects, and propagating orthogonal to the direction of maximumprincipal stress. Kitigawa analysis showed that the endurance limit does not change significantlywith defects in the size range of approximately 100?400 ?m as characterized by the?area = pa-rameter.High levels of deformation characteristic of rotary forming has the potential to reduce the meandefect size. In a formed workpiece, defects would be completely eliminated proximate to the outersurface, due to highly localized deformation. Moving away from the roller interface into the bulk ofthe material, large defects would have their overall size decreased less than the critical defect sizeidentified by the Kitigawa analysis. Smaller defects also have the potential to be mitigated such thatcrack propagation rates are significantly slowed. Since this crack propagation is largely dependenton MPS, the uniaxial fatigue testing results of rotary formed material discussed in the subsequentsection is extensible to multiaxial conditions.149CHAPTER 6. FATIGUE BEHAVIOUR6.2 Fatigue characterization of rotary formed materialAs outlined in Section 2.3.6, a series of runout fatigue tests was conducted on fatigue samplesextracted from rotary formed materials to investigate the effects of processing on fatigue properties.These tests were conducted on samples from commercially flow formed material, as well as thepeak deformed and undeformed EFA material, each with a T6 temper. The load level for these testwas selected to achieve a fatigue life of 106 cycles in each sample. Stress-life (S?N) data fromthese tests was augmented with results provided by Bhatnagar [143] for fatigue samples extractedfrom undeformed-T6 LPDC wheel sections, corresponding to locations similar to ?AD? in Fig. 2.6band having the same DAS as the EFA material. A summary of the tests conducted is presented inTable 6.2 and the resulting S?N data is shown in Fig. 6.5. Geometry for each specimen type isgiven in Fig. 2.22, with type ?d? results plotted in Fig. 6.5a, and type ?e? in Fig. 6.5b.Table 6.2: Runout testing summary: specimen types, condition and quantity employed in therunout fatigue study.Type Condition Quantity SourcedAC-T6 55 Bhatnagar [143]4 (A)Fig. 2.6bCommercially 24 (AD)formed-T6 4 (H)4 (HD)eAC-T6 15 Fig. 2.3EFA formed-T6 12In the case of the commercially formed material (Fig. 6.5a), specimens were extracted fromfour discrete locations, ranging from axial and circumferential/hoop orientations (?AD? and ?HD?,respectively) in a highly deformed region to their lightly deformed counterparts (?A?, ?H?). Therewas negligible difference in the results that could be attributed to orientation as compared to thoseobtained for the ?AD? specimens. At least two out of the four ?A? specimens had fatigue livesmatching or exceeding ?AD? specimens. There is also little difference between heavily deformedcircumferential orientations, with an ?H? specimen failing before an ?HD? specimen at ?a = 125MPa, and the opposite occurring at ?a = 110 MPa. However, there were few ?H? specimens ascompared to ?A? specimens and therefore little conclusions can be made regarding the effect of150CHAPTER 6. FATIGUE BEHAVIOUR104 105 106 1076080100120140160180Nf? a  acAADHHD??f (ac)??f(a) Commercial104 105 10680100120140160180Nf? a  acExp.??f (ac)??f(b) Experimental104 105 1066080100120140160180Nf? a  IIIIIIIV??f (ac)??f(c) CombinedFigure 6.5: AC-T6 versus formed-T6 S?N curves. Commercial results employing type ?d?specimens in (a), and experimental type ?e? in (b). Commercial and experimental resultsare combined in (c): AC type ?d? in I, AC type ?e? in II, formed type ?d? in III and formedtype ?e? in IV.deformation and orientation within the scatter of the results. Regardless, the S?N data of theformed material specimens clearly shows an elevated endurance limit over the undeformed materialfor all conditions, particularly approaching the low-cycle fatigue regime.The EFA material (Fig. 6.5b) also shows improved fatigue properties following processing overthe undeformed variant. Specimens with ?a between 110 and 120 MPa showed approximatelythe same range of fatigue lives as the commercially formed material. The same was true for ?aof 160. Other EFA specimens with similar ?a to the commercially formed material show fatigue151CHAPTER 6. FATIGUE BEHAVIOURlives within 2 orders of magnitude. The undeformed material, however, showed significantly higherendurance limits at similar fatigue lives than that used for the commercially formed comparison.This may be because of the difference in specimen sizes; larger specimens are more likely to containhigher numbers of large defects that affect the endurance limit, and potentially create multiple crackinitiation points. The specimens taken from material deformed with the EFA had gauge diametersthat were approximately 30% smaller than the commercial.In order to quantify the impact of forming on the fatigue behaviour, the measured fatigue datawas fit to Basquin [99, 144] relationships according to:?? f = ? ?f(2N f)?b (6.3)where ?? f is the stress amplitude necessary to arrive at N f cycles to failure, ? ?f is a fatigue strengthcoefficient and b is the Basquin coefficient. The Basquin coefficient, b = 0.17, was the same valueused to correct the endurance limits acquired via step testing (Section 2.3.6). The results of thefitting procedure are summarized in Table 6.3, including values for ? ?f , fitting statistics and thefitted Basquin endurance limit evaluated at N f = 106 cycles as the key HCF life indicator.Table 6.3: AC-T6 versus formed-T6 Basquin relationships.Type Fig. 6.5c Condition ??f R2 RMSE ?? f??106series (MPa) (MPa)dI AC-T6 851.14 0.7441 21.69 72.25III Commercially 1270.02 0.8629 166.7 107.80formed-T6eII AC-T6 985.49 0.8322 15.90 83.64IV EFA formed-T6 1215.16 0.8850 17.32 103.15d & e I & II AC-T6 880.56 0.7454 21.49 74.75III & IV Formed-T6 1256.70 0.8703 17.04 106.67The results of this fitting exercise show that the HCF endurance limit for the commercially flowformed material increases by 33% over the undeformed material, and similarly, a 19% increase isrealized for the EFA material. Combining the undeformed and formed sample sets, the predictedendurance limit is increased by 30% after forming. Departure of the data from the Basquin relation-152CHAPTER 6. FATIGUE BEHAVIOURship, quantified both in terms of R2 and RMSE, is also greatly diminished for formed materials, forthe combined sample sets. The undeformed EFA relationship shows a higher fatigue limit and theRMSE is lower than that of the relationship fitted to Bhatnagar?s data from undeformed-T6 LPDCwheel sections. This is likely due to the larger sample set combined with the increased likelihoodof acquiring endurance limiting pores in larger specimens. In the case of the EFA formed material,the RMSE is slightly higher than that of the commercially formed material and has a lower fatiguelimit. The commercial forming process imparted significantly higher amounts of deformation thanthe EFA process, and it is likely that porosity was correspondingly mitigated.However, porosity-driven effects cannot solely explain the significant increase in endurancelimit of the flow formed material. The changes in the eutectic structure imparted by forming likelyplays a role as well. As previously discussed, larger eutectic particles with elevated aspect ratiosinduce diminished elongation. The forming process produces eutectic with smaller and rounderparticles post heat treatment; this observation combined with S?N data suggests that fatigue char-acteristics are also affected. In general, brittle materials show greater increases in crack growthrates over wider ranges of stress intensity factors [145], and the additional ductility afforded by theformed material?s eutectic may reduce crack propagation rates. Furthermore, as eutectic particledebonding dominates crack growth in this material [49], eutectic particle refinement increases thenumber of particles that require debonding, and introduces more chances for path deflection.6.3 SummaryUndeformed A356?T6 specimens with a wide range of microstructure were tested under multiaxial,full reversed loading conditions. Tests completed with a variety of tension-torsion ratios were usedto evaluate endurance limits and were compared to classical fatigue criteria. These mechanical re-sults showed large scatter for pure torsion loading conditions. Fatigue cracks were found to initiateeither on casting defects (gas or shrinkage based porosity and oxides) or inside the microstructure.Both scales are in competition for the localization of cyclic plastic deformation that induces theinitiation of the crack that leads to failure. The distance to the free surface as well as the mor-phology are important parameters. This study has provided the following conclusions for A356?T6processed in a standard manner:? The experimental results demonstrate average endurance limits of ? f = 89 MPa and ? f = 67153CHAPTER 6. FATIGUE BEHAVIOURMPa.? Standard criteria like Maximum Principal Stress (MPS) and Crossland provide mostly conser-vative estimates of the experimental endurance limits. However, MPS provides the closest fitto the mechanical results.? Cracking mechanisms are very different depending on the loading type. Under pure torsionthe material shows multiple initiation sites and long mode III/I shear crack propagation. Thebifurcation to mode I is not observed at the end of the fatigue life. Under tension or combinedloading the initiation is shorter and more localized such that crack propagation starts directlyin mode I.? The defect size necessary to affect the endurance limit is relatively large. The critical de-fect size ranges from 300 ?m for pure torsion to 500 ?m for pure tension and combinedtension-torsion. This suggests such that an overall critical defect size necessary to diminishthe multiaxial endurance limit is 400 ?100 ?m.In the case of rotary formed material, a comparison of runout S?N data showed the overall HCFendurance limit was improved by 30% over undeformed material. The commercially processed ma-terial showed a 33% increase in endurance limit, and the EFA material showed a 19% improvement.As the commercially processed material was deformed to a much higher extent than that with theEFA, this implies that increased levels of rotary forming improves the fatigue properties of the ma-terial accordingly. The cause for this increase is primarily attributed to the mitigation of porosity.A secondary cause may be attributed to the refinement of eutectic particles induced by processing,which in turn slows crack propagation.154CHAPTER 7CONCLUSIONS AND FUTURE WORK7.1 ConclusionsThe present work served to experimentally investigate rotary forming of A356 at elevated tem-peratures, and documented the development of a model reciprocating these experiments focussingon predicting workpiece deformation. The development of this model necessitated a constitutivebehaviour description that was developed through experimental thermomechanical testing. Thethrough-process microstructural impact of rotary forming on this material was examined, includ-ing the implications for final heat treatment. In order to investigate the effect on fatigue resilienceimparted by this process, the existing understanding of A356?T6 fatigue behaviour was augmentedto account for multiaxial loadings. These findings were then extended to experimental uniaxial fa-tigue observations of rotary formed material. Specific conclusions for each aspect of this work arepresented in the proceeding.7.1.1 Constitutive behaviourThrough extensive compression testing, the constitutive behaviour of AC A356 has been experi-mentally characterized for a range of strains, temperatures and strain rates. The material displayeda diverse range of thermomechanical behaviour characteristic of Al-Si-Mg alloys, with a transitionfrom strain-hardening to strain rate dependent behaviour occurring at approximately 350?C. Abovethis temperature, the material was found to be entirely rate-dependent for all strain rates tested.Over the experimental data tested, a Ludwik-Hollomon expression was found to better predict flowstresses than with a Kocks-Mecking type expression.155CHAPTER 7. CONCLUSIONS AND FUTURE WORK7.1.2 Rotary formed material characterizationThe microstructure of three experimental rotary formed workpieces with increasing levels of de-formation have been compared to commercially formed and unprocessed material in both the ACand T6 condition. It was found that changes to DAS imposed by forming have little effect on me-chanical properties as characterized by macrohardness measurements. Select thermal treatment ofAC material inferred that the AC structure is unstable at temperatures beyond 144?C, and with ef-fects accelerated by higher temperatures. This instability is characterized by structural changes ineutectic-Si and Mg2Si precipitate. Rotary forming at elevated temperatures was found to inducefragmentation of eutectic-Si particles prior to heat treatment, resulting in smaller eutectic particlesizes as compared to undeformed material with the same heat treatment. Precipitation strengthen-ing has been found to be relatively unaffected by heat treatment. Eutectic regions were found to bethe propagation paths for cracks on the outer diameter during forming which were apparent undermoderate to heavy deformation.7.1.3 ModellingA comprehensive coupled-thermomechanical model of an experimental rotary forming process wasdeveloped, containing submodels to describe changes in the workpiece during initial heating, form-ing and final cooling of the component. This model was executed with boundary conditions reflect-ing a workpiece with light and moderate deformation. It was found to predict process characteristicssuch as the evolution of temperature, strain and strain rate and stress state within the workpiece. Thepredicted final workpiece geometry provided by the model showed reasonable agreement with thelightly deformed experimental workpiece where no cracking was observed. The geometry predic-tions of the final moderately deformed workpiece did not agree with experiments to the same degreeas the lightly deformed case. As surface cracks were observed in this workpiece, the primary causefor this discrepancy is attributed to the inability of the model to account for damage evolution. Alsoin this latter case, the predicted strain rates were found to be in excess of those with which the mate-rial model was based. However, as there was good agreement with the lightly deformed workpiece,the the basic deformation mechanism of this process has been successfully modeled.156CHAPTER 7. CONCLUSIONS AND FUTURE WORK7.1.4 FatigueMultiaxial HCF step testing of undeformed A356?T6 has found endurance limits of ? f = 89 MPaand ? f = 67 MPa. These endurance limits were not seen to vary with DAS, and were more sensitiveto porosity. A Maximum Principal Stress (MPS) fatigue criterion better described the results ascompared to a second invariant based criterion, such as Crossland. Fractographic observationsshowed that the crack growth mechanisms under pure torsion were different as compared to tensionor combined loading. In the two latter cases, the fracture plane was orthogonal to the maximumprincipal stress direction, which reinforces the MPS criterion. While Kitigawa analysis showedinconclusive results for specimens with small defects, larger defect sizes necessary to diminish theendurance limit for this material was found to be 300 ?m for pure torsion to 500 ?m for pure tensionand combined tension-torsion.Runout stress-life (S?N) data of experimentally and commercially formed material as com-pared undeformed material showed significantly improved fatigue resilience. Elevated increases inendurance limit were found with increased levels of deformation imparted by the process, with anoverall increase in endurance limit of 30%. The cause for this increase is primarily due to mitiga-tion of porosity. A secondary cause has been proposed to be eutectic-Si morphology changes whichslow crack propagation.7.2 Future workThe current work spans a great deal of fundamental aspects regarding the use of cast aluminumalloys, in particular, A356. The following items have been identified to extend the current workspecifically for rotary forming of cast aluminum alloys at elevated temperatures:? In describing the constitutive behaviour, the effects of holding the casting at elevated temper-atures for a long period of time should be included. This is necessary to account for ageingoccurring prior to forming.? As the model predicted elevated strain rates for a lightly deformed workpiece, commercialapplications with higher levels of deformation may encompass strain rates approaching ma-chining. Therefore, material characterization should extend to examining the constitutivebehaviour to account for strain rates beyond 10 s?1 at elevated temperatures.157CHAPTER 7. CONCLUSIONS AND FUTURE WORK? Continued development of the EFA to allow for controlled tooling movement such that form-ing passes can be undertaken such that simultaneous axial and radial tool movements arepossible. This could be possible through the augmentation of the apparatus with a numericalcontrol system similar to that employed to perform the hardness profiles with the VHTM. Thisaugmentation would closer reflect a commercial process.? In order to more accurately predict the final geometry of a rotary formed workpiece by FEA,fracture behaviour at elevated temperatures should be investigated. This could be extended toallow for the determination of forming limits for this process.? It is recommended a more accurate description of thermal boundary conditions be imple-mented to improve the process model. This could be arrived at by further instrumentationinstalled on the EFA. For further modelling validation efforts from a mechanical perspective,the EFA roller assembly and mandrel could be instrumented with strain gauges to measureforming loads.? FEA forming models would be ameliorated with a greater domain resolution than employedin the current study. However, the computational penalties will have to be addressed eitherthrough customized code, or specialized hardware to account for the degree of coupling in-herent in the process.? Harnessing the model to evaluate the effects of this process on the in-service performance atthe component level, such as the impact of retained stress.The computational challenges posed by this process with current FEA techniques are the mostpoignant. If these challenges are addressed, then a large barrier will be removed for more widespreadadoption of this process by industry.158BIBLIOGRAPHY[1] Y Xu, S.H Zhang, P Li, K Yang, D.B Shan, and Y Lu. 3D rigid-plastic FEM numericalsimulation on tube spinning. Journal of Materials Processing Technology, 113(1-3):710 ?713, 2001. (Cited on pages viii, 26, 27, and 122.)[2] Giorgio Mufatto. Flexible procedure for flow forming light alloy wheels and the relativemachine. EU patent EP1389501 A1, 02 2004. (Cited on page 2.)[3] Katsunori Yoshimura. Method of manufacturing light-alloy wheel for vehicle and the wheel.EU patent EP2377690 A1, 10 2011. (Cited on page 2.)[4] M. Tash, F.H. Samuel, F. Mucciardi, and H.W. Doty. 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Fatigue & Fracture of Engineering Materials &Structures, 30(10):932?946, 2007. (Cited on page 146.)[143] M. Bhatnagar. Mathematical modeling of the fatigue life following rim indentation test inaluminum alloy wheels. Master?s thesis, The University of British Columbia, 2010. (Citedon page 150.)[144] O. H. Basquin. The exponential law of endurance tests. Proceedings of ASTM, 10:625?630,1910. (Cited on page 152.)[145] R.O. Ritchie. Mechanisms of fatigue-crack propagation in ductile and brittle solids.International Journal of Fracture, 100(1):55?83, 1999. (Cited on page 153.)[146] ASTM International. Annual Book of ASTM Standards, volume 3.01. American Society forTesting and Materials, Philadelphia, 2011. (Cited on page 170.)[147] ASTM International. Annual Book of ASTM Standards, volume 3.01. American Society forTesting and Materials, Philadelphia, 2008. (Cited on pages 170 and 171.)[148] ASTM International. Annual Book of ASTM Standards, volume 3.01. American Society forTesting and Materials, Philadelphia, 2007. (Cited on page 173.)169APPENDIX APYRAMIDAL HARDNESS MEASUREMENTSThis appendix serves to outline the methodology and experiment considerations needed for accuratehardness measurements. These are the practices that were followed in setting up and calibratingall hardness measurement related equipment to deliver results found in this thesis, as well as theconversion from other hardness values reported in the literature to Vickers measurements.The ASTM E384-11e1 [146] specification applies to both Vickers and Knoop pyramidal inden-tation, although there is a pre-existing, Vickers-only specification that is available as well [147].A.1 Relevant formulasA hardness value is measured by the ratio of force F required to produce an indent with a givensurface area of A. The HV number has the force given in kg/mm2, with DPH (Diamond PyramidalHardness) numbers being reported in N/mm2. The area of an indent is given as a function of thediagonal lengths and the included angle of the indenter tip, ? , which is 136?0.5?:A = d22sin(?/2) =d21.8544 (A.1)Therefore, the Vickers hardness, HV in kg/mm2 is equal toHV =FA= 2Psin(?/2)d2 =1.8544Fd2 (A.2)where P is the load in kg f . In base SI units, or the DPH number:HV =FA= 0.1891Fd2 (A.3)170APPENDIX A. PYRAMIDAL HARDNESS MEASUREMENTSwhere F is given in Newtons and d in millimeters.A.2 Hardness test methodologyThe specimen was placed on a holder that did not allow any rocking or lateral movement to preventerroneous readings and potentially damaging the diamond. The diamond was periodically checkedfor damage via a microscope focussed on the bottom of an indentation and measuring the apparenttip of the indent with a filar micrometer. The diamond was not used if the apparent tip was largerthan 5% of the overall diagonal [147]. The microscope/measurement apparatus was verified to beable to measure indent diagonals within ? 5% or half a ?m, whichever was bigger. The indenter tipwas periodically cleaned with ethyl alcohol and lens paper.In all cases, the unmounted thickness of the specimen was 1.5? the diagonal of the indent. Thiswas done to avoid an intersection of the plastically affected zone of the indentation site with thesupport, or the ?anvil effect?.The analysis surface was be finished such that the diagonals were clearly defined/ Cold-finishingwas employed exclusively as to not temper or work harden the surface during preparation. In allcases the specimen was supported such that the indentation surface was parallel within 1?.In all cases, the indentation centers were be placed at least 2.5? a diagonal apart. This was doneto avoid the indentation-affected zone that surrounds each indent from interfering with results. Thiswas verified by creating a grid of indents that were slightly less than 5? apart, and then indents wereplaced directly between them to see if the hardness was affected. This was validated via statisticalmethods.A.3 Hardness measurement validationThis section summarizes ASTM E92-82(2003) ?Standard Test Method for Vickers Hardness ofMetallic Materials?, Section B, ?Verificiation of Vickers Hardness Testing Machines? [147]. Thisparticular methodology only applies for hardness machines that are used for routine testing usingstandardized gauge blocks of known hardness, the specification also covers machines that are usedcontinually in a laboratory setting. Also note that this standard applies to machines applying loadsof 1 kg f to 120 kg f . For loads less than this, this section only serves as a general guideline.? A minimum of five Vickers hardness readings shall be taken on at least three blocks having171APPENDIX A. PYRAMIDAL HARDNESS MEASUREMENTSdifferent levels of hardness with the test force applied with a dwell of 12 seconds.? For each block, let d1,d2 . . .d5 be the arithmetic means of each indentation diagonal arrangedfrom smallest to largest.? The repeatability is given as R = d5 ?d1.? The error for each block is given as ?d?d where d = (d1 +d2+ . . .d5)/5 and ?d is the reportedmean diagonal on the gauge block.The machine is considered calibrated if the repeatability and error are within the following limits.The repeatability must be satisfied by the conditions in Table A.1, and ?d and d should not differby more than 2% or 0.5 ?m, whichever is greater. If the repeatability of the machine or error areTable A.1: ASTM E92-82 repeatability of machinesBlock Hardness Range R must be100 to 240, inclusive > 4% of d240 to 600, inclusive > 3% of d> 600 > 2% of doutside of the prescribed tolerances, then the machine must be calibrated before further use. Ifthe repeatability of the machine is acceptable, but the error is outside of the prescribed limit thenstatistical methods may be used to correct the data. Note that under optimal conditions, the accuracythat can be expected is the equivalent of 4% of the Vickers hardness number of a standardizedreference test block. As a last resort, the reduction in accuracy can be established via statisticalmethods.172APPENDIX BCONVERSION OF BALL-TYPE TO PYRAMID HARDNESS VALUESBall-type indentation to measure the hardness of material is load-dependent. This means that the re-sult obtained with a ball-type indentor with a given load will not be the same if the load is increasedor decreased. Furthermore, different load scales are necessary to test both soft and hard materi-als. The ASTM E140-07 standard [148] provides hardness values spanning Brinell, Rockwell andVickers hardness measurements for both hard and soft materials. While the load used for Vickersmeasurements for hard materials is given, the load is not provided for soft materials. It is assumedthat the load used for Vickers measurements in this case were in-line with those for Rockwell andBrinell. The conversion for Rockwell-F (HRF 60 kg, 1.59 mm diameter steel sphere) to HV forcartridge brass is given as:HV =(a+b ?HRF + c ?H2RF+d ?H3RF)?1(B.1)For the conversion from a 500 kg, 10 mm ball diameter Brinell hardness (HB 10/500/15) to HV:HV = a+b ?HBS (B.2)Conversion coefficients for each of the two preceding expressions are given in the following table.Table B.1: HV to HRF and HB conversion coefficientsCoefficient HRF HBa 2.95966?10?2 -5.60725b ?1.03725?10?4 1.19007c ?2.31669?10?6 -d 1.12203?10?8 -173

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