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

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EXTRUSION OF ALUMINA PARTICULATE REINFORCED METAL MATRIX COMPOSITES By WEI CHANG CHEN B. A. Sc. M. Sc. M. A. Sc.  Beijing University of Iron and Steel Technology University of Science and Technology Beijing University of British Columbia  A THESIS SUBMITthD IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES METALS AND MATERIALS ENGINEERING We accept this thesis as conforming to the required standard  THE UNWERSITY OF BRITISH COLUMBIA December 1994 © Wei Chang Chen, 1994  1983 1986 1991  In presenting this thesis in  partial fulfilment of the requirements for an advanced  degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  (Signature)  fr14TEf1FiL  Department of The University of British Columbia Vancouver, Canada Date  DE-6 (2188)  Fd. 24 95 -  5’ii.  U  ABSTRACT  Alumina particulate reinforced metal matrix composite is a new kind of material, which has wide potential applications in automobile industry. The study of its physical nature during extrusion process is essential to optimize the process which may improve its mechanical properties and increase its productivity to finally reduce its cost and make it more competitive to other materials. Constitutive equations were developed for the alumina particulate reinforced metal matrix composites (Duralcan materials) based on the hot deformation tests on a ‘Gleeble 1500’ machine.  Plant trials were conducted for the same materials in both a laboratory  extrusion device at Kingston R & D Center (KRDC), and an industrial extrusion press at Universal Alloy Corporation, California.  Different temperatures and extrusion ratios with  different ram speeds were adopted during extrusion. Low speed cracking was observed at the front end of some extrudates, which has not been observed with the unreinforced aluminum alloy (AA6061). Microstructure change with particle fracture and particle distribution was studied using an optical microscope and an image analyzer in the deformation zone of a billet and the extrudates from the plant trials. The extrusion processes have been simulated with the aid of a finite element model. The plant trial data were used to validate the model predictions. The model predictions at both a macroscopic and a microscopic level were correlated with microstructural changes. /lOp and 6061/A1 3 0 2 /20p were 3 0 2 Extrusion Jimit diagrams for both composites of 6061/A1 developed with low speed cracking boundaries included for the press at UAC.  The  mechanism of the low speed cracking was proposed based on the FEM and SEM analysis.  111  Although low-speed cracking was proposed to be associated with void formation in the surface layer of the extrudates, the voids were not significant to the effect of tensile properties, because the elastic modulus, the yield stress and the ultimate tensile strength measured from extrudates of the plant trials at KRDC did not decline at extrusion ratios from 10 to about 30.  Minimization of void formation in the composites was discussed and  recommendations have been provided for optimization of the extrusion of the alumina particulate reinforced MMCs.  iv  This page left blank intentionally  V  TABLE OF CONTENTS  ABSTRACT TABLE OF CONTENTS  v  TABLE OF TABLES  xi  TABLE OF FIGURES  xiii  NOMENCLATURE  xix  ACKNOWLEDGEMENTS  xxii  DEDICATION  xxiii  Chapter 1 INTRODUCTION 1.1 Characteristics of Metal Matrix Composites  1 1  1.2 Fabrication of Particulate Reinforced Metal Matrix Composites 1.3 Processmg and Applications of Particulate Reinforced MMCs  4  1.3.1 Secondary Deformation Processing  4  1.3.2 Applications  5  Chapter 2 LiTERATURE REVIEW 2.1 Extrusion Process 2.2 Extrusion Related Defects of Particulate Reinforced MMCs (PRMMCs) 2.2.1 Extrusion Related Defects 2.2.2 Hot Workability of PRMMCs 2.3 Development of Extrusion Limit Diagrams  6 6 8 9 14 17  2.3.1 Peak Pressure  18  2.3.2 Temperature Rise  19  2.4 Finite Element Analysis of An Extrusion Process  21  2.4.1 Finite Element Analysis of an Extrusion Process  21  2.4.2 Development of an Extrusion Limit Diagram Using FEM  22  vi 2.4.3 Fracture Criteria for Monolithic Metals  24  2.5 Finite Element Analysis of the PRMMC  25  2.5.1 Multilevel Finite Element Method  29  2.5.2 Particle Fracture Model during Deformation  31  2.5.3 Microscopic Analysis of PRMMCs under Larger Deformation  33  Chapter 3 SCOPE AND OBJECTIVES  34  3.1 Scope and Objectives 3.2 Methodology Chapter 4 EXPERIMENTAL  37  4.1 Gleeble Tests 4.2 Plant Trials at UAC, Anaheim  40  4.2.1 Extrusion Procedure  40  4.2.2 Extrusion Data  44  4.3 Pilot Extrusion at KRDC, Kingston  50  4.3.1 Extrusion Procedure  50  4.3.2 Extrusion Data  52  4.4 Extrusion Surface Defects 4.5 Effect of Extrusion Conditions on the Mechanical Properties  58  4.5.1 Tensile Tests  58  4.5.2 Property Changes after Extrusion  58  Chapter 5 MODELING EXTRUSION OF THE PRMMCs 5.1 Mathematical Model of the Extrusion Process 5.1.1 Finite Element Model  64 64 64  5.1.1.1 Flow Formulation  64  5.1.1.2 Boundary Conditions  68  5.1.2 Input Data  70  5.1.3 Finite Element Solution  70  vu 5.2 Sensitivity Analysis of the Model  72  5.3 Extrusion Process Simulation 5.3.1 Processing Conditions  75  5.3.2 Model Predictions  76  5.3.2.1 Deformation Behavior  76  5.3.2.2 Temperature Distribution  84  5.3.2.3 Comparison of Predictions with Measured Data  86  5.4 Validation of Model Predictions  89  5.5 Summary  92  Chapter 6 MICROMECHANICAL ANALYSIS OF THE PRMMC DURING LARGE  94  DEFORMATION 6.1 Obstacles and Challenges of Micromechanical Analysis of the PRMMCs 6.1.1 Particle Phenomena  94  6.1.2 Matrix Phenomena  95  6.1.3 Modeling Constraints  95  6.2 Micromechanical Analysis during Plane Strain Compression 6.2.1 Twin-Particle Model 6.2.2 Multiple-Particle Model 6.3 Micromechanical Analysis during Cylindrical Compression 6.3.1 Single-Particle Model  96 98 104 106 107  6.3.1.1 Material Flow of a Cylindrical Specimen Containing a Particle  109  6.3.1.2 Effect of Particle Shape  115  6.3.2 Twin-Particle Model  120  6.3.2.1 Effect of Reduction  121  6.3.2.2 Effect of Particle Spacing  121  6.4 Model Validation 6.5 Conclusions  126 126  ‘In  Chapter 7 PARTICLE FRACTURE OF THE PRMMC DURING EXTRUSION  128  7.1 Specimen Preparation for the PRMMCs  129  7.2 Macroscopic Examination of Metal Flow in the Deformation Zone  130  7.3 Particle Fracture during Extrusion  134  7.3.1 Qualitative Microstructure Analysis  134  7.3.1.1 Particle Deformation Behavior in the Deformation Zone  134  7.3.1.2 Microstructure Analysis of the Extrudates  140  A. Comparison of Microstructure in Longitudinal and Transverse Sections  141  B. Comparison of Microstructure for 606 l/A1ZO3/20p and 606 l/A1 /lOp 3 O 2  143  7.3.2 Image Analysis of Particle Distribution in Extrudates  146  7.3.2.1 Homogeneity of Particle Distribution  146  7.3.2.2 Particle Size  149  7.3.2.3 Aspect Ratio of Particles  154  7.3.2.4 Particle Orientation  156  7.4 Modeling Particle Fracture during Extrusion  157  7.4.1 Particle Fracture Probability at High Temperature  157  7.4.2 Particle Fracture Model during Extrusion  158  7.4.3 Application of the Model  160  7.5 Discussion 7.5.1 Microstructure Comparison before and after Extrusion  162 163  7.5.1.1 Comparison of Particle Distribution before and after Extrusion  163  7.5.1.2 Particle Size Refmement after Extrusion  168  7.5.2 Particle Fracture Modes during Extrusion  168  7.5.3 Correlation between Particle Fracture and Bulk Deformation Behavior  170  7.6 Summary Chapter 8 ORIGIN OF LOW SPEED CRACKING DURING EXTRUSION OF THE PRMMCs  173 177  ix 8.1 Microstructure Examination of Low-speed Cracks  177  8.2 Particle Behavior and Microscopic Damage  180  8.2.1 Particle Fracture  180  8.2.2 Void Formation  183  8.3 Effect of Processing Parameters on Low Speed Cracking  186  Effect of Ram Speed  189  Effect of Billet Temperature  193  Effect of Die Temperature  197  Effect of Friction at Die Interface  198  Effect of Extrusion Ratio  200  Effect of Volume Fraction of the Composites  202  8.4 Mechanism of Low Speed Cracking  204  8.5 A Preliminary Criteria for Low Speed Cracking  206  Chapter 9 EXTRUSION OF THE PRMMCs  210  9.1 Development of Extrusion Limit Diagram  211  9.1.1 Using Empirical Equations  211  9.1.2 Using Finite Element Method  215  9.1.2.1 Application of the Finite Element Model  215  9.1.2.2 Comparison of Extrusion Limit Diagrams  217  9.2 Extrusion Limit Diagram with Low Speed Cracking Boundary  220  9.2.1 Low Speed Cracking Boundary  220  9.2.2 Effect of Extrusion Ratios  222  9.2.3 Extrusion Limit Diagram with Low Speed Cracking Boundary  223  9.3 Extrusion of the PRMMCs  224  9.3.1 Minimization of Microstructural Damage during Extrusion  225  9.3.2 Improvement in Particle Distribution and Size Refinement  229  9.3.3 Quality and Productivity of the PRMMCs  231  x  Chapter 10 CONCLUDING REMARKS  234  10.1 Summary and Conclusions  234  10.2 Future Work  236  REFERENCES  237  x  TABLE OF TABLES  Table 1.1  illustration of the principle factors linked with the aspect ratio  Table 2.1  Microstructure observed in the particulate reinforced composite before  2 13  and after extrusion Table 4.1  Material constants for the constitutive equation of the Composites  40  Table 4.2  Extrusion programs for the 7” press at UAC  41  Table 4.3  Billet temperatures immediately prior to extrusion at UAC  43  Table 4.4  Plant trial conditions at KRDC  51  Table 4.5  Billet dimensions of each test at KRDC  53  Table 4.6  Measured test data of the plant trials at KRDC  53  Table 4.7  Extrudate data from plant trials at UAC  57  Table 4.8  Tensile test results of extrudates from the plant trials at KRDC  59  Table 5.1  Some data for sensitivity analysis of the FEM model  72  Table 5.2  Processing Conditions for Two Simulations  76  Table 6.1  Simulation conditions for plane strain deformation  97  Table 6.2  Simulation conditions for cylindrical compression test  107  Table 6.3  Particle sizes studied  109  Table 6.4  Comparison of model predictions with measured data  126  Table 7.1  Polishing procedure for Duralcan materials at KRDC  129  Table 7.2  Polishing procedure used at UBC for Duralcan materials  130  Table 7.3  Extrusion conditions of the Trial S92-3 of 6061/Al /20p 3 0 2  131  Table 7.4  List of examined extrudates with two different cross-sections  141  Table 7.5  Statistical results for volume fraction distribution of the two composites  147  Table 7.6  Statistical results for the quantitative metallography  153  Table 7.7  Average number of parts fractured from a single particle in  159  /20p 3 0 2 606 l/A1 Table 7.8  Comparison of model predictions with measured data  162  Table 8.1  Tensile stress in particles and matrix at different reductions  182  xli Table 8.2  Standard conditions for parametric study  188  Table 9.1  Constants in Eq. (9.1) for the composites  211  Table 9.2  Extrusion conditions for the specimens examined under an SEM  225  xIn  TABLE OF FIGURES  Figure 2.1  7 10  Figure 2.3  Schematic of a forward extrusion process Tensile elongation to fracture against strength for A356 alloy and its composites with different volume fractions of SiCp before and after extrusion at different extrusion temperatures of 400°C and 600°C Strain dependence of fractured particle of 606 1/SiCp MMCs  Figure 2.4  A schematic extrusion limit diagram  18  Figure 2.5  23  Figure 2.6  Schematic extrusion limit diagram with low speed cracking Finite element model used by Aradhya et al  Figure 2.7  Master mesh for generating different microscopic morphologies  Figure 2.8  The crack morphologies generated by the FEM study for different overall fraction of the angular Zr0 2 with transformation (a) FEM mesh with local refinement during a plane-strain upsetting; (b) Stress distribution along the line PQ (Eh=l% calculated with ABAQUS)’  27 29  Figure 2.2  Figure 2.9  15  26  30  Figure 3.1 Figure 4.1  Methodology for the extrusion of alumina particulate reinforced MMCs Schematic of the Gleeble test set-up  36 38  Figure 4.2  Schematic of extrusion setup for Duralcan trials  42  Figure 4.3 Figure 4.4  Typical load-stroke curve with variation of ram speed (S92-3) Die temperature increase during extrusion (S92-3)  45  Figure 4.5 Figure 4.6  Effect of homogenization on extrusion force (S92-3 and S92-4) A weak correlation of increasing ram speed with increasing die temperature during extrusion (S92-5)  46  Figure 4.7 Figure 4.8  Effect of billet temperature on extrusion force (S92-5 and S92-6) Effect of billet length on extrusion force during extrusion (S92-3 and J94-12)  47  Figure 4.9  Effect of volume fraction on extrusion force (606 1/A1203/1 Op: J94-3, and 606 l/A12O3/2Op: J94-7)  48  Figure 4.10  Effect of extrusion ratio on extrusion force (J94-4, J94-lO, J94-15)  49  Figure 4.11  Schematic drawing of the extrusion press at KRDC  Figure 4.12  Typical load-stroke curve during extrusion at KRDC (K-7)  52 54  Figure 4.13  55  Figure 4.14  Variation of ram speed at the press pressure limit (K-li) Low speed cracking at the front end of two extrudates  Figure 4.15  Schematic of a tensile test specimen  Figure 4.16 Figure 4.17  Tensile property under different extrusion ratios  58 60  Elongation of the composites as a function of extrusion ratio  61  Figure 4.18  /lOp for different extrusion ratios 3 O 2 (a) Tensile property change of 6O6l/A1  62  during  46  extrusion  47  48  56  xiv with a true volume fraction from 7.0% to 7.4%; (b) Tensile property change of 606 l/A1 /2Op for different extrusion ratios with a true volume fraction 3 O 2 from 19.2% to 19.8% Figure 4.19  Corresponding elongation values at different extrusion ratios for both composites  63  Figure 5.1  Schematic of an extrusion press  65  Figure 5.2  Initial finite element mesh for the billet and its surrounding tools  68  Figure 5.3  Sensitivity of load stroke curve to the number of elements in the billet  74  Figure 5.4  Sensitivity of the maximum temperature to the number of elements in the  74  billet Figure 5.5  Material flow near the end of upsetting stage  78  Figure 5.6  Effective strain distribution near the end of upsetting stage  78  Figure 5.7  Velocity distribution in the billet after a ram displacement of 40.7 mm in the large extrusion press; length of arrow is proportional to velocity  79  Figure 5.8  Velocity distribution in the billet after a ram displacement of 26.7 mm in a small extrusion press; length of arrow is proportional to velocity  79  Figure 5.9  Mean stress distribution in the billet at a ram displacement of 40.7 mm in the  81  large extrusion press (negative values denote compressive stresses) Figure 5.10  Mean stress distribution in the billet at a ram displacement of 26.7mm in the  82  small extrusion press (negative values denote compressive stresses) Figure 5.11  Effective strain distribution of the billet in the small press  83  Figure 5.12  Effective strain rate distribution of the billet in the small press  84  Figure 5.13  Temperature distribution in the large extrusion press  85  Figure 5.14  Temperature distribution in the small extrusion press  85  Figure 5.15  Comparison of predicted force with measured data (large press)  87  Figure 5.16  Comparison of predicted force with measured data (small press)  87  Figure 5.17  Comparison of predicted temperature with measured data (large press)  Figure 5.18  Comparison of FEM force with measured data corrected for extrusion press  88 91  compliance according to Eq. (5.26); large press Figure 5.19 Figure 6.1 Figure 6.2 Figure 6.3 Figure 6.4  Comparison of FEM force with measured data corrected for extrusion press  91  compliance according to Eq. (5.26); small press Initial fmite element meshes for each object of plane strain deformation  97  Initial finite element mesh around two particles  98  Effective strain distribution at a reduction of 49% Localized effective strain distribution around two particles at different reduction  100 102  xv Figure 6.5 Figure 6.6 Figure 6.7 Figure 6.8 Figure 6.9 Figure 6.10 Figure 6.11 Figure 6.12  Effective stress in the particles at different reductions Localized effective strain distribution at a reduction of 1%  103  Localized effective stress distribution at a reduction of 1% Localized mean stress distribution at a reduction of 1%  105  Initial mesh and location of a particle in a cylindrical specimen  108  Effective strain distribution in the cylindrical specimen with and without a particle at a reduction of 65%  110  Effective strain distribution around the particle at a reduction of 65% Effective strain distribution along the center line of the specimen under  111  105 106  112  different reductions Figure 6.13  Effective stress distribution in the cylindrical specimen with and without a  112  particle at a reduction of 65% Figure 6.14  Effective stress in the matrix and in the particle at a reduction of 65%  113  Figure 6.15  Mean stress distribution in the cylindrical specimen with and without a  114  particle at a reduction of 65% Figure 6.16  Mean stress distribution both in the matrix and in the particle at a reduction of  115  65% 118  Figure 6.18  Effect of particle shape on damage factor at a reduction of 65% Effect of particle shape on strain distribution at a reduction of 65%  Figure 6.19  Effect of particle shape on effective stress variation during compression  120  Figure 6.20  Effective strain distribution under different reductions with an initial particle  122  Figure 6.17  119  spacing of 120 p.m Figure 6.21  Mean stress distribution in the matrix and in the two particles under different reductions with the initial particle spacing of 120 p.m  123  Figure 6.22  Effect of particle spacing on strain distribution at a reduction of 65%  125  Figure 6.23  Comparison of predicted value with measured data  125  Figure 7.1  Metal flow of a billet in a container  131  Figure 7.2  Schematic positions for the pictures taken with low magnification  132  Figure 7.3 Figure 7.4  Metal flow in the deformation zone during extrusion Schematic positions for the pictures taken for micro examination  133 134  Figure 7.5  Typical particle distribution in the Locations 1 -9  137  Figure 7.6  Schematic of examined extrudate specimen  Figure 7.7  /2Op at an 3 O 2 Typical characteristics of particles after extrusion of 606 1/A1 extrusion ratio of 34  141 142  Figure 7.8  /lOp at an 3 O 2 Typical characteristics of particles after extrusion of 6O61/A1 extrusion ratio of 34  144  xvi Figure 7.9  Histogram of volume fraction for 6061/Al 03/lOp 2  148  Figure 7.10  Histogram of volume fraction for 606 1/AlO3/20p  148  Figure 7.11  Histogram of the particle diameter for Sample B3 of 6061/A1z0 /20p 3  150  Figure 7.12  Histogram of the particle diameter for Sample B6 of 6061/A1 /lOp 3 O 2  151  Figure 7.13  Histogram of the particle area for Sample B3 of 606 1/AI /20p 3 O 2  152  Figure 7.14  Histogram of the particle area for Sample B6 of 6O6l!A1 /lOp 3 O 2 Histogram of the aspect ratio for Sample B3 of 606 l/Al /20p 3 0 2  152  Figure 7.16  Histogram of the aspect ratio for Specimen B6 of 606 1/A1 /lOp 3 0 2  155  Figure 7.17  Histogram of orientation of the particles with respect to extrusion direction for the Sample B3 of 6061/AlO f20p 3  156  Figure 7.18  Histogram of orientation of the particles with respect to extrusion direction 03/lOp 2 for the Sample B6 of 6061/A1  157  Figure 7.19  161  Figure 7.20  Fracture probability variation in the deformation zone Particle size reduction during extrusion  Figure 7.21  Microstructure of 606 1/AlO /l0p before and after extrusion 3  164  Figure 7.22  Microstructure of 606 1/A1 /20p before and after extrusion 3 0 2  165  Figure 7.23  Variation of maximum and minimum alumina particle dimension  166  Figure 7.24  Aspect ratio of alumina particles of 6061/A1 I2Op in back end of a billet 3 O 2 and in extrudate  167  Figure 7.25  Orientation of alumina particles of 606 1/A1 /20p in back end of a billet and 3 O 2  167  Figure 7.15  155  162  in extrudate Figure 7.26  A schematic diagram for three particle-fracture modes during extrusion  170  Figure 7.27  Effective strain rate distribution in the deformation zone  171  Figure 7.28  Mean stress distribution in the deformation zone  171  Figure 7.29  Shear stress distribution during extrusion  Figure 8.1  Void formation near a low speed crack tip of J94-14 of 606 1/A1 /20p in 3 0 2 longitudinal section  173 179  Figure 8.2  /lOp in 3 O 2 Void formation near a low speed crack tip of J94-1 lB of 606 1/A1  179  longitudinal section Figure 8.3  Tensile stress in a particle under plane strain condition at a reduction of 10%  182  Figure 8.4  Tensile stress distribution in the matrix and around particles  185  Figure 8.5  Tensile stress distribution in the monolithic material at a reduction of 10%  185  Figure 8.6 Figure 8.7  under plane strain condition Temperature distribution of billet and die at steady state extrusion Tensile stress (ar) distribution at the die interface zone Effect of ram speed: (a) Maximum temperature in the die land zone during  Figure 8.8  187 188 190  xvii  Figure 8.9  extrusion; (b) Maximum tensile stress in the die land zone during extrusion Temperature distribution on both side of the die interface at a ram  191  displacement of 30mm Figure 8.10  Effect of ram speed on strain distribution through radius direction  192  Figure 8.11  Effect of ram speed on stress distribution (az) through radius direction Effect of ram speed on effective strain rate variation in extrudate  192  Figure 8.13  Effect of initial billet temperature:(a) Max. temperature in the die land zone during extrusion; (b) Max. tensile stress in the die land zone  194  Figure 8.14  Thermal gradient on both sides of the die interface under different billet temperature  195  Figure 8.15  Effect of initial die temperature: (a) Maximum temperature in the die land zone during extrusion; (b) Maximum tensile stress in the die land zone during  196  Figure 8.12  193  extrusion Figure 8.16  Thermal gradient on both sides of the die interface under different initial die temperatures  197  Figure 8.17  Effect of friction condition at die interface: (a) Maximum temperature in the die land zone during extrusion; (b) Maximum tensile stress in the die land  199  zone during extrusion Figure 8.18  Thermal gradient on both sides of the die interface under different friction  200  condition at die interface Figure 8.19  Effect of extrusion ratio (a) Maximum temperature in the die land zone  201  during extrusion; (b) Maximum tensile stress in the die land zone during extrusion Figure 8.20  Thermal gradient on both sides of the die interface under different extrusion  202  ratios Figure 8.21  Effect of volume fraction: (a) Maximum temperature in the die land zone  203  during extrusion; (b) Maximum tensile stress in the die land zone during extrusion Figure 8.22  Thermal gradient on both sides of the die interface under different volume fraction  204  Figure 8.23  Variation of E value during different conditions but same extrusion ratio  208  Figure 8.24 Figure 9.1  Variation of E value during extrusion at different extrusion ratios Extrusion limit diagram at an extrusion ratio of 28 for 6061IAl /20p for the 3 O 2  208 213  Figure 9.2  press at KRDC Extrusion limit diagram at a ram speed of 12.5mm/s for 606 1/Al /20p for 3 0 2  213  the press at KRDC  xviii Figure 9.3  Extrusion limit diagram for 606 11A1 /20p at an extrusion ratio of 34 for the 3 0 2  214  Figure 9.4  large press at UAC Extrusion limit diagram for 6061/A1 110p at an extrusion ratio of 34 for the 3 0 2  214  Figure 9.5 Figure 9.6  large press at UAC Extrusion limit diagram for 606 l/A1 /20p for the press at KRDC 3 0 2 The limit diagram for 6061/A1 /20p for the press at UAC 3 0 2  216  Figure 9.7  Comparison of the extrusion limit diagram for 6061/A1 /20p for the press 3 0 2  218  Figure 9.8  at KRDC using different techniques Comparison of the extrusion limit diagram for 6061/A1 /20p for the press 3 0 2  219  Figure 9.9  at UAC using different techniques The extrusion limit diagram for both 6061/A1 /lOp and 6061/A1 3 0 2 /20p 3 0 2  219  Figure 9.10  using the empirical equation technique Low speed cracking boundary for the extrudate of 6061/A1 120p at an 3 0 2  221  Figure 9.11  extrusion ratio of 13 Low speed cracking boundary for the extrudate of 6061/A1 /20p at an 3 0 2  221  Figure 9.12  extrusion ratio of 34 Low speed cracking boundary for the extrudate of 6061/A1 /20p at an 3 0 2  222  217  extrusion ratio of 52 Figure 9.13  Effect on extrusion ratios on low speed cracking boundary during extrusion of 606 l/A1 /20p 3 0 2  223  Figure 9.14  Extrusion limit diagram of 606 1/A1 /20p for the press at UAC with low3 0 2  224  speed cracking boundaries Figure 9.15  Voids in the surface layer of an extrudate of 606 l/A1 /2Op at an extrusion 3 O 2  227  Figure 9.16  ratio of about 34 without low speed surface cracking (front end of J94-14) Voids in the surface layer of an extrudate of 6O6l/AI I1Op at an extrusion 3 O 2  228  Figure 9.17  ratio of about 28 with low speed surface cracking (front end of K-6) SEM image observed in the surface layer of the extrudate at an extrusion  230  ratio of about 34 without low speed surface cracking (back end of J94-14)  NOMENCLATURE A, B, C, E,  Experimental constants  F, a, b Cross section of a billet area, m 2 (t), C 1 C (t) 2  Time-dependent constant in temperature analysis Product of fracture stress and fracture strain of a material, MPa  c,  specific heat, J/kg-K  [C]  Heat capacity matrix  d  Diffusion distance, m  D  Volume equivalent particle diameter, jim  1 D  Mean refined volume equivalent particle diameter, jim  DB  Initial billet diameter, m Inside diameter of a container, m Extrudate diameter, m  B, E 0  Elastic modulus of a solid phase, GPa Overall stiffness of a press, kN/mm  B  Product of max. tensile stress and max. effective strain during extrusion  1 F  Surface traction on velocity boundary  {f)  Residual of the nodal point force vector  0 h  Initial width of the gap between two cracked particles, pm  J  Mechanical equivalent of heat  k  Thermal conductivity, W/m-° K  K, 1 KK ,  Penalty constant, and material constants  [Ks], [Kc]  Stiffens matrix, and heat capacity matrix  0 L  Initial billet length, m  D, 1  L  Instantaneous length of a billet measured from the dead metal zone, m  ii  Die land length, m  LR  Length of a discard  n  Stress exponent  xx n  Average number of parts fractured from a single particle  N, N  Number of broken particles, and number of total particles  P  Extrusion load, N  Pf  Extrusion force at the end of stroke, kN  p  extrusion pressure, MPa  ph  Pressure required for matrix intrusion into the gap of cracked particles, MPa Particle fracture probability;  1  Average particle fracture probability rate over cross section in deformation zone  Po  Fraction of porosity in a solid phase  4  Heat generation rate, WIm  Q  Hot deformation activation energy, 3  Qb,  Q  Activation energies for surface and bulk diffusion  { Q)  Heat flux vector  R  Extrusion ratio  R  Gas constant, JImol-°C  1 R  Radius of cross section in deformation zone during extrusion  S  Surface area, m 2  Sa, Sm  Adjusted and measured ram stroke, respectively  ST  Total ram stroke, m  t  Time, s  T, { T }  Temperature and the matrix of its nodal values,  0  K  Summation of temperature differentiation with spatial coordinates Temperature differentiation with time v, v ,v 1 3  velocity component  VB  Ram speed, rn/s  V  Volume, m 3  x  Material constant depending on internal structure  Z  Zener-Holloman parameter, s 1  AD/D  Mean particle size reduction after extrusion  xxi AT  Temperature rise in extruded product, °K  ATD  Initial temperature difference between the billet and the chamber or die, °K  At  Time incremental, s  { Av }, Avj  First-order correction of the velocity at previous step Material constant, MPa’; and particle aspect ratio;  f3 1,  Time integration factor Constant in particle fracture model, tm 3  ii  Strain Fracture strain of a material eN, 60, CJ,  Fracture strain of void nucleation, growth, and linkage  max  Maximum effective strain during extrusion  e., e, e  Strain rate, effective strain rate, and volume strain rate, Critical strain rate for dislocation accumulation in front a particle, Heat generation efficiency Semi angle of extrusion; degree Angle of dead metal zone, degree Functional for the deformation body  p  density, kg/md  a,  Flow stress, yield stress, MPa  ,  m, 3  1 a  Effective stress, mean stress, and principle stress, MPa Fracture stress of the composites  a CTz  Tensile stress in X-direction in plane strain compression, and in the extrusion direction, MPa  Sub- and Superscripts: s  denotes the steel for tools  c  denotes the composite for the billet  t  time  xx  ACKNOWLEDGEMENTS  I would like to express my sincere appreciation to Drs. Indira Samarasekera, Keith Brimacombe, Bruce Hawbolt, and Chris Davies for their supervision throughout the whole course of this project. Without their support, my dream of obtaining a Ph.D. would never have come true. Appreciation is extended to Alcan International Ltd. for providing test specimens, technical help and discussions.  Thanks to Mr. William (Bill) Dixon of  Duralcan USA, and Dr. David Lloyd, and Mr. Chris Cabryel, of Alcan International Ltd. for their help with the extrusion trials. Thanks are also extended to Dr. Stuart MacEwen for his help and discussion of finite element modeling of the extrusion process. Thanks for financial support go to the industrial partners in the Metal Matrix Composite Pre competitive Research Consortium: Mean International Ltd., Ontario Hydro Ltd., Sherritt Gordon Ltd., Pratt and Whitney Canada Inc., Inco Ltd. and NSERC, and also to the Ontario Center for Materials Research, through whose auspices the consortium was set up.  Thanks to Ms. Mary Mager for her assistance in using the SEM. Thanks to Professor Tara Chandra from University of Wollongong for his interest  to this project. A great help from Dr. Warren Poole in this department is very much appreciated. I would also like to thank all my fellow students in this department for their discussion and friendship. Finally, I would like to take this opportunity to express my appreciation from the bottom of my heart to my mother, and my wife, Xiaoli (Shelly). Without their love and emotional support, this Ph. D. project could never be finished.  xxili  DEDICATION  To my mother  Chapter 1 Introduction  1  Chapter 1 INTRODUCTION  1.1 Characteristics of Metal Matrix Composites Metal Matrix Composite (MMC) research was initiated in the 1960’s. It is particularly attractive in applications when the following improvements over monolithic materials are required: Easily designed and tailor-made material; Improved strength/density ratio; Improved stiffness/density ratio; Improved wear resistance; Improved high temperature mechanical properties; Adjustable physical properties (coefficient of thermal expansion, diffusivity, elastic modulus). : 111 Among the important MMC systems, the following are of interest /Al and A1 3 0 2 A1 /Mg; 3 0 2 SiC/Al Boron/Aluminium; Carbon/Aluminium. MMC research initially focused on continuous fiber reinforcements which give very high stiffness and strength. Most of the continuous reinforcements are very expensive and have low workability owing to fiber fracture; they have found applications primarily in aerospace and military. In order to avoid the problems of high cost and low ductility, there  Chapter 1 Introduction  2  has been considerable interest in discontinuous reinforcements such as short fibers, whiskers and particles.  The advantages  of discontinuous reinforcements over continuous  reinforcements can be seen in Table 1.1t21. Since particulate reinforced MMCs can be processed by conventional metal working methods or techniques to produce all forms of semifinished products, they become more attractive from a cost perspective. Another decisive factor, especially for small industry, is that parts made of particulate reinforced MMCs behave almost isotropically, and are therefore much simpler to use in design.  Although the strength and elastic modulus of particulate  reinforced composites are inferior to those of continuously reinforced composites, the low cost, high workability and isotropic properties render them suitable for a wider range of applications, especially in automobile production.  Table 1.1 fllustration of the principle factors linked with the aspect ratio (where V’ denotes the advantage and ‘x’ the disadvantage) Advantages  Discontinuous  Continuous  Reinforcement  Reinforcement  Isotropy Orientable Properties  x x  Formability, Ductility  x  Fabrication Costs  x  Material Cost  x  Recyclability  x  Reinforcement Efficiency  x  Chapter 1 Introduction  3  1.2 Fabrication of Particulate Reinforced Metal Matrix Composites In discontinuously reinforced metal matrix composites, the reinforcements are generally ceramic in nature and can either be added to the matrix as discrete elements or fonned in situ in the matrix.  Reactivity with the matrix during fabrication and service,  differences in coefficient of thermal expansion (CTh) between the matrix and reinforcements, and cost/performance in the finished product are the critical selection criteria used for the reinforcements. Alumina and silicon carbide powder (greater than 1 micron in size) have been chosen primarily for the reinforcement, as these materials represent a good compromise between density, property improvement, and cost. However, alumina is about 5-10 times cheaper than silicon carbide powder (SiCp) and 10-100 times cheaper than alumina or silicon carbide filaments . Moreover, alumina has a higher stability than silicon carbide in aluminum 131 alloys, such as the 2xxx, 6xxx, and 7xxx series.  Lower manufacturing cost provides a  potential for large scale production of a competitively priced product. In fact, the MMC that is closest to a commercial breakthrough is an aluminum matrix composite with discontinuous, particulate ceramic reinforcements (SiC and A1 . 1 ) 3 0 2 41  It is being fabricated in several  different ways: Foundry processes, where particles (or whiskers) are inserted into the molten metal by mechanical stirring, and the product is cast into an ingot of desired shape or size; Powder metallurgy process, where metal powders and reinforcements are blended cold, compressed and bonded by diffusion; Squeeze casting, where the molten metal is pressure infiltrated into a preform of fibers;  Chapter 1 Introduction  4  Spray deposition technique, where deposition of atomized liquid metal along with particulate is employed to fabricate MMC ingots. The attraction of ingot casting is the potential for producing MMC billets suitable for utilization on the large scale equipment currently employed for fabrication of monolithic alloys.  This approach will capture economies of scale, and is being used at Alcan  International Limited, Canada, Duralcan, USALS], and Hydro Aluminium, Norway’.  Melt  viscosity limits the volume fraction of the reinforcement to approximately 25 volume percent. Alcan Aluminium Ltd. has commissioned a 25 million lb/yr facility in Quebec for the production of composites for Duralcan in Canada in 1990151. The scale-up of the casting process to larger sizes presents challenges related to: a) the effects of the solidification rate on the ingot cell size, and b) attendant particle-pushing to the last regions to freeze. A cast route which could have more homogeneous particle distribution in a cast product of particulate reinforced metal matrix composites is sought. In addition, since matrix-reinforcement reaction is a critical issue in some MMC systems, large ingots which have longer solidification times result in increased exposure of the reinforcement to the molten metal.  1.3 Processing and Applications of Particulate Reinforced MMCs 1.3.1 Secondary Deformation Processing Many discontinuously reinforced metal composite products require subsequent deformation processing via rolling, extrusion, or forging to achieve the final shape, irrespective of how the primary ingot is produced. Dural Aluminium Composites Corporation (Duralcan), has developed necessary technologies to produce a range of ceramic particle reinforced MMCs by the molten metal route. Their products have been used to produce cast  Chapter 1 Introduction  5  shapes, forgings and a wide range of extruded solid and hollow shapes. The main thrust of their extrusion development has focused on 6061 and 2014 alloys, reinforced either with silicon carbide or alumina at 10  -  20 volume percentage.  Significant improvements are  achieved in the elastic modulus and strength, although ductility is reduced.  The elastic  modulus is increased by up to 40%, and the minimum increase in tensile strength is 20%’. However, defects such as surface tearing are observed during extrusion, which affect the quality of the final MMC products. To improve the quality of MMC products , a better 571 understanding of how deformation processing influences the microstructure and properties in these materials is needed. 1.3.2 Applications Metal matrix composites (MMCs) are now used in, or being considered for use in, a variety of applications in the military, aerospace, automotive, and other commercial areas. Automotive applications include automotive drive shafts, cylinder linings, brake rotors’ ; 81 other applications include bicycle frames and components, and tire introduction of the MMCs into actual applications is still sparse.  . 91 studs’  However, the  No true high volume  applications exist to date. To promote further use of MMCs, some fundamental changes must take place. The cost of the composites must be reduced, probably by improving the manufacturing processes. A better chemical and physical understanding of the MMCs must be developed so that designers can use the material with confidence.  Chapter 2 Literature Review  6  Chapter 2 LITERATURE REVIEW 2.1 Extrusion Process Extrusion is a forming technique widely used in the aluminium industry to produce shapes of complex cross section. The extrusion process can be classified into three broad categories’°’ depending on the direction of extruded material movement relative to the punch. i) Forward extrusion: material flows in the same direction as the motion of the punch; ii) Backward extrusion: material flows in a direction opposite to the motion of the punch; iii) Side extrusion: material flow is perpendicular to the direction of motion of the punch. In the forward aluminium extrusion process, cylindrical billets are preheated to a temperature, between 300°C and 5000C, at which point they are transferred to the heated container of an extrusion press (Figure 2.1).  The container is generally heated to a  temperature, 30-50°C lower than the billet in order to compensate for cooling during billet transfer. A load is applied to one end of the billet via a ram and dummy block, forcing material through a die of a shape and size calculated to give the dimensions of the final cooled product. The die is also heated, and sits on top of a number of support components, collectively known as the stack. The die may be classified into shear or flat face die, conical, parabolic and streamlined types, the difference among them being the mathematical representation of the surface or material path lines. In a shear die, a dead metal zone exists and a shearing band is formed between the dead metal zone and the deformation zone. In a conical die, the material path line is a linear function; in the parabolic die ( convex or concave) it is a parabolic function (second order equation); and in the streamlined die a cubic function has been used. The conical die, which is relatively easy to design and manufacture, is fairly  Chapter 2 Uterature Review  7  well known. In this case, material flow is more uniform than for the shear (or flat face) die. However, the conical die may induce some rigid body rotation near the die exit due to abrupt changes of material flow at that point. The parabolic die (convex type) has a smooth entry but the exit is sharp, creating rigid body rotation and discontinüities in the velocity distribution. Dies having both smooth entry and exit are referred to as streamlined dies with the implicit assumption that the matedal path lines coincide with the improved die surfaces. Streamlined dies have been shown to be suitable for processing “difficult to extrude” metal al1oys . 101 However, the shear die type is still widely used for the extrusion of aluminium and its alloys in  industry, probably because of its simple design and low cost.  1 2 3 4 5 6  -  -  -  -  -  -  Billet Container Die Extrusion Stem Dummy block Die holder  Figure 2.1 Schematic of a forward extrusion process Press sizes range from lab scale- 200 ton maximum load, 60mm container I billet diameter- to industrial-size presses of up to and greater than 10,000 ton load capacity, with billet diameters of 250mm. Extrusion ratios (upset billet area to extrudate area) of between  Chapter 2 Literature Review  8  10:1 and 200:1 are typical; associated extrusion speeds, measured at material exit, can range from less than 0.5mlmin. to lOm/min. or greater. The process is stopped short of all the material exiting the die; the portion of billet remaining in the container is known as the discard, the extruded material as the extrudate. The extrudate may either be air cooled, or quenched with water sprays. It is also important to note that hydrostatic extrusion is a nearly-ideal friction-free process. Low frictional forces in hydrostatic extrusion permit the use of lower die angles and high extrusion ratios, both of which lead to higher hydrostatic stress and therefore to conditions which suppress fracture  .  The uniform deformation near the surface, caused by  low friction, reduces the danger of surface cracking and fracture can be suppressed by extruding at high fluid pressure. Therefore, brittle materials were the prime target for the application of the hydrostatic extrusion . Embury et al. [t121 have suggested application of 1131 the hydrostatic extrusion process for MMC processing to increase its fonnability. Unfortunately, the complexity of the production process leads to a higher cost of the product.  2.2 Extrusion Related Defects of Particulate Reinforced MMCs (PRMMCs) There is a considerable interest in the forming of metal matrix composites (MMCs), in particular, for controlling the deformation parameters so as to avoid defects or microstructural damage.  Of the various forming processes, extrusion has received considerable attention.  Not only does the large compressive hydrostatic component of the stress facilitate the imposition of large strain, which homogenizes the particle distribution and heals particle fracture during the process, but it also causes axial alignment of discontinuous reinforcements. DURALCAN® composites have been manufactured by hot, direct (forward) extrusion ® Owned by Alcan Aluminum Corporation  Chapter 2 Literature Review  9  (lubricated and unlubricated) and also by hydrostatic extrusion. Hot direct extrusion with shear-face dies without lubrication is the simplest, the cheapest and the most widely used method. Alternative processes involving conical-entry dies, with or without lubrication, are not presently being considered, owing to the difficulty of obtaining a high-quality surface finish. In an exceptional study, using a conical die, Selseth and Lefstad 141 found that when extruding the AA6061/SiCp (SiCw) MMCs produced by the powder metallurgy (P/M) route, the necessary extrusion force was about 30% higher compared to a shear-face die. The ‘p’ and ‘w’ notations stand for particle and whisker reinforcement, respectively.  2.2.1 Extrusion Related Defects Although hot extrusion of casting products appears to homogenize the particle distribution, clustering (defined as the aggregation of particles) and banding are still evident due to an insufficient extrusion mtio . The study by Uoyd’ 1 ’ also indicated that although 53 the tensile elongation of a permanent mould cast composite test bar (Cast A356 -15% SiC) is around 1%, which is much lower than the unreinforced alloy (Cast A356) as shown in Fig. 2.2. Alter extrusion at an extrusion ratio of 70:1 under different temperatures (e.g. at 400°C and 600°C for A356-lO%SiC and A356-20%SiC), the composite elongation is comparable to or better than the unreinforced as-cast alloy (Cast A356). However, it is lower than the alloy in extruded conditions. During extrusion, surface defects such as surface tearing and cracking appear; some of these defects are known to occur during extrusion of unreinforced materials, while some others are specific features on the MMCs only. These defects will significantly affect the extrudability of particulate reinforced MMCs.  Chapter 2 Literature Review  10  Elongation to Fracture versus Stress A356— SiC 0.30 0.25  I:: A  A  240  260  I  280  o *356  vv A  I  A  AA  I  300 320 340 Stress (MPa)  10%SIC (600) V P356 20%SiC (600) V *356-i 5%SiC (600) • Extruded A356  I  360  -  C) *356  -  -  *356  -  I  380  400  i0%SiC (400) 20%SiC (400)  A Cast P356-i 5%SIC  •  Cast *356  Figure 2.2 Tensile elongation to fracture against strength for A356 alloy and its composites with different volume fractions of SiCp before and after extrusion  1531 at different extrusion temperatures of 400°C and 600°C Extrudability refers to the maximum attainable speed of the billet without surface defects occurring during extrusion. Based on the early extrusion trials done by Hams et al. , 171 it was found that (i) two kinds of defects occurred during extrusion of 6061 and 2014 with alumina reinforced MMCs, and (ii) their behavior was very different from unreinforced alloys. Firstly, considerable surface tearing occurred at the front end of the extrusion at low extrusion speeds, which persisted over the entire extruded length. However, the intensity of tearing usually reduced with increasing extrusion speed, and on occasion, disappeared completely at intermediate speeds. Secondly, a further increase in speed resulted in the onset of edge and surface cracking which differed from the low speed cracking. These cracks were similar in appearance to a type commonly encountered with conventional aluminium extrusions. It was  Chapter 2 Literature Review  11  reported that two types of crack mechanisms exist for speed-limiting cracking of Al-Mg-Si alloys. The first type initiated at the die/extrudate interface, and occurred because the matrix was not strong enough to withstand frictional force at the die. The second type initiated at subsurface weaknesses, and was assumed to be due to incipient melting. Obviously, both types of tearing mechanisms are temperature dependent and are initiated in a region close to the die/extrudate interface. Therefore, the temperature distribution resulting from heat losses and the temperature rise during extrusion needs to be examined. Although both types of high speed cracking occurred in both monolithic alloys and the MMCs, low speed tearing which should be designated as the third type, appeared only in the MMCs (Brusethaug et al. ). This 61 tearing was characterized by deep notches extending from the surface into the material. A probable explanation of the mechanism for the third type was given by Hams et a1. 7 as follows: In the initial stages of extrusion, the die was colder than the extrudate.  Metal  adhering to the die bearing land during this phase was immediately chilled and its flow stress increased. This may create conditions which were energetically favorable for subcutaneous fracturing, so that the material in contact with the bearing remained stationary, while the subsurface material continued its forward motion. Further increase in pressure broke the bond between the bearing and adhered material; this material then moved across the bearing surface. The entire periphery did not move in unison; different segments breaking away at different times. New material adhered to the die bearing land and consequently the extrudate surface retained this debris. The process was repeated in the classic stick-slip mode until conditions were energetically favorable for continuous movement of material across the bearing surface. This low speed tearing introduces a minimum extrusion speed for the MMCs.  Chapter 2 Literature Review  12  Obviously, this mechanism needs to be refined, because it does not include the interaction between particles and matrix materials. ’ in Europe for three different 4 Another trial was conducted by Selseth and Lefstad aluminium composites.  They investigated the extrudability of discontinuously reinforced  p in an AIMgSi matrix. The 3 O 2 aluminium alloys. The composites were SiCp, SiCw and A1 silicon carbide particle (SiCp) reinforced MMC was fabricated by mixing AIMgSi powder (AA6061) and SiC particles of size 4j.tm, while the alumina particle  ) reinforced MMC (AI p 3 O 2  p of size of 3Opm into the molten AIMgSi (AA6082). The 3 0 2 was fabricated by stirring the A1 volume fractions of particles or whiskers were all 20%. In the tests, a conventional shear-face die was used, and the extrusion ratios were 22 and 39. In some of the experiments a disc of unreinforced material was clad in front of the bifiet.. This markedly reduced the tendency towards high speed surface tearing, thus increasing the maximum extrusion speed. Their experimental results showed that the composite containing the finest SiC particles (4pm) could be extruded to solid rod at an extrusion speed of 250mm/s, while the alumina particle reinforced MMC was extruded at a speed of only 83mm/s. Because the matrix materials of 3 particle reinforcement were quite similar, the 0 2 AA6061 for SiC particles and AA6082 for Al relatively poorer extrudability for the alumina particle reinforced MMC was related to the . As described earlier, in 41 difference of microstructure of the MMCs by Selseth and Lefstad’ p reinforced MMCs, there were some particle clusters especially at lower volume 3 AlzO fraction, such as lOvol% and l5vol%, which were not discovered in SiCp reinforced materials made by the P/M route. The material with the least clusters, yielded the best surface quality. This could be the reason for its poor extrudabiity. However, the effect of different particle  Chapter 2 Literature Review  13  size for AI p (3Otm) and SiCp (4j.tm) MMCs should also be considered, because it is also 3 O 2 important to the deformation and fracture behavior.  Table 2.1 Microstructure observed in the particulate reinforced composite before and after extrusion (where V denotes the observation of the defect. Material State  Defects  *  may not be taken as defects.) MMCs  Unreinforced Matrix Alloy  Porosity, voids As-cast  Cluster, stringers Surface cracks Particle fracture Debondmg at particle/matrix interface  Deformed  Near interface Matrix Fracture  (Extruded)  Low speed surface cracking High speed surface cracking: 1) at die/extrudate interface 2) at subsurface of billet Rotation and migration of particles*  Obviously, the ability of material to withstand high strain rates is vital to the extrudability of the composite. Higher strain rates may cause fracture of the extruded material at the extrudate surface and also result in an overheating in the low melting zone at the sub surface of the extrudate, giving hot shortness during extrusion. All the defects observed in ascast and extruded materials are summarized in Table 2.1. Therefore, it is essential to analyze the process to establish the optimum operating conditions to produce defect-free products. It  Chapter 2 Literature Review  14  is worth pointing out that the rotation and migration of particles during extrusion of MMCs produced by the melt-casting route will be beneficial to the particle distribution.  2.2.2 Hot Workability of PRMMCs Hot workability relates to the ability of a metal or alloy to be deformed under conditions of high temperature ((T> 0.6TM), where TM is the melting point of the material in Kelvin), and relatively high strain rates (0.1 to 1 s_i ) without forming cracks . The two ” 1 characteristics that govern hot workability are strength and ductility.  Since for a given  material, different strains are attained prior to fracture depending on the process, workability of a material is affected by both the material itself and the external processing conditions, i.e.:  2 (process, friction) Workability = f (material) x f where  .,  (2.1)  is a function of the basic ductility of the metal and f 2 that of the external factors  which modify the basic ductility. The formula clearly implies that the accumulation of internal damage which leads to fracture is closely related to the deformation and restoration processes operative during hot working. In particulate reinforced metal-matrix composites, the aim has been to combine the beneficial stiffness of ceramics with the superior ductility and toughness of metals. However, this combination produces lower ductility and toughness in composites as compared to the matrix alloy. In order to maximize these properties, it is necessary to understand the local micromechanical failure modes and their relation to macroscopic toughness. As mentioned above, these local failure modes are also dependent on the processing details and, for the MMCs, on the matrix trealment and its effect on the interface. In general, the failure modes in the particulate reinforced MMCs can be due to one or more of the following: Particle fracture;  Chapter 2 Literature Review  15  Debondmg at particle/matrix interface; Near interface matrix fracture; General fracture mechanism of the matrix of the MMCs as the same as that of the unreinforced matrix alloy’’. The study by Lloyd’ ’ showed that, for the SiCp reinforcements, fracture occurs in the 53 larger size fraction of the particulate population. Fig. 2.3 shows the strain dependence of fractured particles for 6061-10 and 2Ovol%SiCp at room temperature. o 6061—20%SIC  6061— 10% SIC  400  30o  0.  0  0  ,  1  2  3  4  ;  5  ,  6  7  cx  V  8  I  1  V  I  I  9 1011 121314  Figure 2.3 Strain dependence of fractured particle of 606 1/SiCp MMCs 531 It is evident that the extent of particle cracking is lower in the lOvol%SiCp composite, which is not surprising considering the lower particle content in this composite. The rate of particle cracking with strain is also lower. It is interesting to note that less than 5% of the  16  Chapter 2 Literature Review  total particle population has cracked at fracture of the composite. However, it is apparent that particle cracking is initiated at low strains. In spite of this, the voids created do not grow sufficiently during subsequent straining to affect the final fracture strain; the strain of fracture does not correspond to the strain for particle cracking.  Similar behavior has also been  3 composites. This indicates that there is a critical amount of damage 0 2 observed in 606 l/A1 developed at large strains.  The damage is in the form of voids associated with particle  clusters, together with the occasional cracked particles. The voids have not grown extensively in the tensile stress direction. This is generally the case in unreinforced alloys. This also suggests that the growth strain is negligible in comparison with the nucleation strain, and that void nucleation is primarily a result of matrix failure within closely spaced particles. The reason for this behavior is related to the deformation response of the particle clustered region relative to the rest of the composite. Within clusters, the far field applied stresses are no longer controlling. Actually, higher-stiffness particles constrain the deformation of the matrix adjacent to them, and this results in a complex triaxial stress being developed in the matrix within the cluster. Obviously, the triaxial stresses are important because a triaxial tensile stress enhances both void nucleation and void growth. To consider the effect of the degree of the triaxial tensile stress, a ratio of mean stress to effective stress, aJ was adopted. Uoyd found that the unreinforced alloys have a significant loss in elongation with increasing triaxiality, while the composites are relatively unaffected. This is consistent with the idea that the fracture of the composite is controlled by the intrinsic triaxiality generated at particle clusters, and these dominate any imposed far field stress state. Thao et al  have reported  that as the temperature increases the void formation due to interface debonding at the ends of particles in tensile direction becomes dominant comparing to particle fracture which is  Chapter 2 Literature Review  17  dominant at low temperature. Lloyd ’ also pointed out that due to the importance of particle 53 size on the deformation and fracture behavior of the composite, particle size must be limited to maximize strength, and minimize fracture. It has been indicated that using particles of around 10 microns with a tight size distribution, reduces the propensity for particle fracture, which occurs most readily in coarse particles. However, a small particle size may result in more clusters which are harmful for the fmal properties of the MMCs.  2.3 Development of Extrusion Limit Diagrams Modeling of extrusion has, at a practical level, been focused on the use of empirical equations  and  analytical  solutions  to  predict  optimum  operating  . 1555 conditions  Consequently, the determination of extrudability has been based on extrusion press-side measurements and property I quality requfrements. The extrusion process is governed by the imposed variables, temperature, strain rate (speed), and strain (reduction ratio) and their interaction with the characteristics of the material.  The significance of each of these  parameters will be determined by several factors, such as surface quality, minimum microstructural damage if there is any, excessive pressure requirement, etc.. Meadows and 63 showed that the bounds of extrudability may be calculated theoretically, and Cutler’ demonstrate this on a diagram showing maximum tolerable extrusion pressures and surface incipient melting plotted on the axes of extrusion speed against temperature for a certain extrusion ratio, as schematically shown in Fig. 2.4. The constant pressure boundary line is determined by the extrusion press limit, but is a function of extrusion ratio, temperature and strain rate. The incipient melting boundary line is depicted according to the temperature at the die land interface, which is a function of initial extrusion temperature, extrusion ratio, ram speed, friction coefficient at interfaces, etc..  18  Chapter 2 Literature Review  Such limit diagrams have been developed to include structural 591 and property ’ 8 . Sheppard 5 features’ 1 reviewed these and other developments, and found that most prior research has been oriented to the prediction of a peak or maximum load required of the press,  and the prediction of temperature rise due to extrusion deformation.  Speed  Extrusion Temperature Figure 2.4 A schematic extrusion limit diagram  2.3.1 Peak Pressure The simplest equation for estimation of peak pressure during extrusion is expressed as, p=a(a+bInR)  (2.2)  where a is the flow stress of a material, R is the extrusion ratio, and a and b are constants. The above equation needs to be modified to include friction effects; assuming that sticking friction condition prevails during extrusion which was widely adopted by researchers in , the above equation is changed to, 55 aluminium extrusion industry’ p  =  a[(a+blnR)+  4L]  (2.3)  where L is an instantaneous length of the billet measured from the dead metal zone and Dc is the inside diameter of the container.  Chapter 2 Literature Review  19  At high temperature, the flow stress of a material is a function of strain rate and temperature, and may be characterized by a hyperbolic sine equation, (2.4)  Z = e exp() = Asinh(aa) where Z is Zener-Holloman parameter, and A, a,  Q  and n are material constants. Inserting  Eq.(2.4) into Eq.(2.3), a general equation for peak pressure during extrusion can be derived:  (xn  A  (2.5)  AD  where B, C, E, F are constants for a specific press. The mean strain rate formula adopted in this study is expressed as, (2.6)  _4vDtanq —  2 ” 3 (DaDE)  where DB and DE are diameters of the billet and the extrudate, respectively, vB is the ram speed and q is the semi angle of the deformation zone outlined by the shear zone in unlubricated shear die extrusion, expressed as , 1 p=54.1+3.45lnR  (2.7)  Based on some plant trials, the above four constants for the extrusion press can be estimated, and the constant pressure boundary line in a limit diagram can be delineated using Eq.(2.5).  2.3.2 Temperature Rise A general analytical equation for temperature rise during extrusion was derived by Castle and Sheppard’ 651 based on a thermal analysis including the billet, and the sunounding  tools. AT  =  (O.9PvBt  —  2 (t)) I ATDC  1 (t)) C  (2.8)  Chapter 2 Literature Review  20  where P is the extrusion force, ATD is the initial temperature difference between the billet and  (t), and C 1 the container or die, C (t) are heat flow coefficients and t denotes extrusion time. 2 671 claimed that ‘for high conductivity aluminum alloys, this form of temperature Sheppardt increase may be sufficiently accurate for practical use’. In aluminum extrusion practice, it is common for there to be little or no temperature difference between the billet and the surrounding toolstM]. However, the generation of heat internally will establish a temperature differential. Therefore, in the calculation of temperature rise, the initial temperature difference between the billet and the tools could be ignored. The above equation then becomes, AT =  =  PvBt / 9 . 0  PvBt/ 9 O.  1 (t) C  (2.9)  t” +(K 1 (K 2 2 213 )t +(K 4 +K 33 )t” +K 5 +K t) 11  All the constants are expressed as below, K1 2 K  —  —D)(kSPSCPS)lI ic(D 2 12 )112 )213 l (18kSDB (p C 8  =  3 =.lD(l8ksD(p$Cps)2)hI3 K 4 K  =  -  l (1 8kSDR (pC 8  )1/2 )213  ((p,C,)2)hI3 1 =.l D 18k 5 8 K  (2.9a) (2.9b) (2.9c) (2.9d) (2.9e)  (2.9f) where ID is the deforniation zone depth between the pressure pad and the dead metal zone, l 11 K  is the die land length,  =  ‘p is the  pCCPCRvB1tD  /4  angle of dead metal zone, p, k, C, are thermal properties of a  material, and the subscripts s and c denote the steel for tools and the composite for the billet, respectively.  Chapter 2 Literature Review  21  2.4 Finite Element Analysis of an Extrusion Process 2.4.1 Finite Element Analysis of an Extrusion Process Modeling of an extrusion process for detennination of punch pressure, stress/strain distributions, material flow pattern, etc., is of extreme importance to the manufacturing process designer for a number of reasons. It provides valuable information, not only for enhanced design of work tools and process parameters, but is also useful for improving existing extrusion methods or even inventing new routes. Various kinds of extrusion processes have been analyzed for monolithic materials by the finite element method at a macroscopic leve1 , using both the Solid Approach and the 14361 Flow Approach. The Solid Approach treats the solid as an elastic-plastic material during forming. The significant shortcoming is its complex formulation and the computing cost . 291 In contrast, the Flow Approach considers the materials to behave as a non-Newtonian viscous fluid. A typical shortcoming of this approach is that it cannot represent many of the subtleties of elastic-plastic constitutive laws; hence it does not provide information on residual stresses and also does not solve directly the displacements’ . 29331 For extrusion problems, depending on the type of model, the transient and steady-state components of the process can be analyzed.  The transient portion is of interest if peak  pressure and the deformation behavior at the beginning of the extrusion need to be examined. For the steady-state situation, the deformation behavior of the head end and the tail end of the billet cannot be analyzed; only the deformation behavior in the deformation zone can be investigated. The Eulerian description is suitable for this analysis with the Flow Approach. In the Eulerian description, the mesh is stationary while the material flows through the  Chapter 2 Literature Review  22  deformation zone during deformation. However, for non steady-state (transient) problems, the total Lagrangian or updated Lagrangian description is preferable and is adopted by using the Solid Approach or Flow Approach. In a non steady-state process, such as at the initial stage of the extrusion process, the Lagrangian description suffers from major drawbacks when the workpiece endures large or localized deformation and also when the work tools, namely the punch and the die, have complex shapes or sharp edges. This may be attributed to the fact that, in the Lagrangian description, the fmite element mesh remains embedded in the material and moves with it. Lack of control over the grid motion often results in excessively distorted elements, thus deteriorating the quality of the finite element solutions.  Continuing the  simulation beyond certain levels of deformation becomes impossible in many cases, on account of entangled or non-convexed elements. Therefore, various remeshing schemes have been attempted to overcome these obstacles . 391 Another approach is the application of an Arbitrary Lagrangian-Eulerian description (ALE) to industrial metal forming simulation.  In Arbitrary Lagrangian-Eulerian  description, the mesh moves at a different velocity from that of the material. The description is a hybrid between the Lagrangian and Eulerian descriptions, i.e., if the mesh moves at the same velocity as material, it is termed Lagrangian, and if the mesh velocity is zero, it is Eulerian. However, it is difficult to choose an appropriate mesh velocity; and it appears that remeshing is required during large deformation.  2.4.2 Development of an Extrusion Limit Diagram Using FEM The above described semi-empirical equations in Section 2.3 for development of extrusion limit diagrams result in mean values for the variable. One recognized ’ drawback 69 of the semi-empirical approach is the problem of analyzing the close inter-relation of the  Chapter 2 Literature Review  23  process variables- flow stress, strain rate and temperature. The intractability of the situation can lead to a large number of experiments being required. A more attractive, and increasingly accessible approach is the use of fmite element . Grasmo et al. have used a finite element model to simulate the extrusion 41 techniques° of an Al-Mg-Si alloy, AA6060. The model considers the material to behave like a fluid and does not include predictions during the billet upsetting phase.  However, it is the most  practical and complete model of extrusion developed to date using FEM techniques. Nevertheless, there is little literature using a finite element technique to develop extrusion limit diagrams. For the extrusion of particulate reinforced composites, low speed cracking should be included in the limit diagram. However, no work has been found for the low speed cracking. Dixon  (91  proposed that the low speed cracking boundary is a function of extrusion ratio as  schematically shown in Fig. 2.5. The low speed cracking boundary can be determined by a series of plant trials. Alternatively, a finite element model can also be employed to determine this boundary provided a suitable criterion is inserted into the model.  Extrusion Speed  Extrusion Temperature Figure 2.5 Schematic extrusion limit diagram with low speed cracking’ ’ 5  Chapter 2 Literature Review  24  2.4.3 Fracture Criteria for Monolithic Metals Some fracture criteria for cold and hot working have been established to rationalize the data which are available for different test geometry, i.e., Stress Criterion; Strain Criterion, Plastic-Work Criterion . The Stress Criterion was based on the fact that cracking in metal 1491 working was recognized to be associated with induced tensile stresses, even in processes such as forging in which the stresses are predominantly compressive. The importance of the tensile stresses was indirectly confirmed by the large increase in apparent ductility when materials are deformed under hydrostatic pressure. The tensile fracture of conventional alloys is considered in terms of the microvoid coalescence model (MVC) in which the fracture strain expected is the sum of the nucleation strain, the void growth strain until void coalescence occurs, and the fmal linkage strain, £L G+eL 8 LF—eN+  (2.10)  Usually e, is considered to be small relative to the other terms, therefore the fracture strain is expressed as: eF—EN-f-CG  (2.11)  However, in working operations, it is likely that both shear and tensile stresses play a part, since there is evidence that localized flow by shear is required to initiate cracks which are then propagated by tensile stresses. A Strain Criterion has also been suggested by some 1501 based on the total strain, but difficulties arise since the total strains vary markedly workers in different processes. Therefore, it is reasonable to assume that any criterion should be based on some combination of stress and strain rather than on either of these quantities separately. There are indications that the total plastic work to fracture may be an important factor (Plastic-Work Criterion). Cockcroft and Latham proposed that fracture occurs in a ductile  Chapter 2 Literature Review  25  material when, for a given temperature and strain rate, the plastic work done by the highest tensile stress reaches a specified limit . 1511  s:”Gl  I)d = C  (2.12)  Cockcroft and Latham successfully applied the criterion to cold working but did not test it for hot working. Sellars et 491 al.’ tested the above equation and concluded that the equation could be a reasonable criterion for hot working as well as for cold working, but claimed that further data is required to test it more rigorously for hot working.  2.5 Finite Element Analysis of the PRMMCs In modeling monolithic metal forming, some approximations are always made, such as constant volume of material, isotropy, coincidence of the axis of principle stress and strain, no influence of hydrostatic pressure and equivalent response to tensile and compressive loads. For the MMCs, these assumptions are not entirely valid. Therefore, a micro-material model needs to be developed to characterize the particle and the material behavior on a microscopic scale due to microstructural characteristics and their influences on properties. However, there is little published work on the microanalysis of mechanical working of the MMCs at elevated temperature. The micromechanical analysis of the particulate reinforced MMCs associated with thermal phenomena and simplified loading conditions are discussed to review the current methodology of the MMC deformation analysis. A few studies have been attempted for the micromechanical analysis of materials, 140421 and particulate reinforced MMCs including fiber , but most of them are based on a 143 unit cell model with idealized boundary conditions. Aradhya et al.’ ’ analyzed a simplified 45 MMC structure under tensile loading, as shown in Fig. 2.6.  Chapter 2 Literature Review  26  y  B  E1 Aluminium  SIC  j  C>  I  A  0  1.-rn  0 7/)//  m A =  b  =  I ,)/,/9///)///  A  mesh size interparticle distance particle Length particle width  Figure 2.6 Finite element model used by Aradhya et Based on a two-dimensional  AIISiCp composites and the  below a certain  and  critical  the  element model, the  effect of different volume  properties were investigated. In unifoimly distributed,  finite  their analysis,  aspect  ratio  the particle  was taken  volume fraction of SiCp  mechanical  fractions size was  properties of  of SiCp on  6061  the tensile  assumed to be 4Ojim  and  to be unity. The model predicted that,  (25%),  the matiix  yielded at slightly lower stresses compared to the unreinforced  material  material  in the composite under  the tensile  loading conditions. This is obviously contrary to the experimental results which indicate that  the 0.2% yield stress of composite is invariably higher than the unreinforced matrix alloy. The apparent discrepancy  between the FEM and the experimental results was explained by the fact  that the properties of the  unreinforced matrix material were used in the model to describe the  matrix material in the MMCs. The  UTS  values predicted by  FEM were  much lower than the  Chapter 2 Literature Review  27  experimentally observed. The discrepancy between the elastic modulus prediction by FEM and experimentally measured values also existed, and the maximum difference was about 12% at volume fraction  =  0.4. In spite of this, the unit cell model with idealized assumptions in a  MMC micromechanical analysis, such as, uniform distribution of second phase particle with regular particle shape, idealized boundary conditions, etc. can give a pre1iminwy insight of the microscopic behavior of the MMCs, although it is far from reality. A more flexible discretization for different volume fractions of particulate reinforcements was developed by Ramakrishnan et al. 1 using a master mesh, as shown in Fig. 2.7.  Figure 2.7 Master mesh for generating different microscopic morpho1ogies’’  Chapter 2 Literature Review  28  In their finite element analysis, some important aspects associated with the transformation induced plasticity in 2 .-Zr0 were analyzed. These aspects included: (i) an 3 0 A1 estimation of the residual stress in the second phase, arising during post fabrication cooling, which affected the critical stress for transfonnation; (ii) the constitutive behavior of the material during the dilatational transformation of Zr0 2 and (iii) the crack deflection due to the transformation. The study was conducted for angular and spherical shapes of second phase particles and also for varying volume fractions of the second phase. The crack morphologies generated by the FEM study for different overall fractions of the angular Zr0 2 are shown in Fig. 2.8, based on the assumption that the particle/matrix was perfectly bonded. Because the master mesh model represents more closely the real situation of the MMCs (with randomly distributed second phase particle and its random shapes, angular or spherical) than regular arrangement of the reinforcements with idealized shapes, such as spherical, cylindrical, square, etc. assumed by other unit cell fmite element models described above, the comparison of analytical solutions they derived assuming a spherical shape for the second phase particles with the results obtained through the simulation showed very good agreement. However, no experimental validation was provided due to the difficulties for a master mesh model to satisfy all the real boundary conditions. Moreover, in their study, since no large deformation was involved, the mesh size and its arrangement were not altered during the simulation. But for large deformation of the MMCs, the mesh which represents the matrix would distort, while the mesh representing the reinforcement would not distort due to its higher stiffness. Therefore, a remeshing technique has to be applied. It is evident that the master mesh model cannot be adopted on a microscopic scale in the extrusion process, because a large number of elements would be required and remeshing would be difficult.  However, microscopic  Chapter 2 Literature Review  29  mechanical analysis could be conducted based on an idea of multilevel finite element analysis duiing large deformation with some simplifications.  a  Volume fraction of Zr02 = 0.05  4111144 —  w 4  VOIUIM fraction of ZO2 = 0.1  -  %cv Volume fraction of Z,0 2 = 0.2  Volume fraction of Z,0 2 = 0.3  FIgure 2.8 The crack morphologies generated by the FEM study for different overall fraction of the angular Zr0 2 with transformation  23.1 Multilevel Finite Element Method Multilevel finite element analysis was first proposed by Kopp et al. 1471 in the simulation of metal forming processes to optimize the computation time. At Level 1 (Global Analysis) integral parameters such as the required force and requited work are computed using a coarse FEM mesh At Level 2 (Local Analysis), an optimized number of elements is used to determine continuum mechanics parameters like stress, strain and temperature; Microscopic phenomena are simulated at Level 3 (Microscopic Analysis), using special micromaterial elements and thermodynamic models. The method has been applied to an upsetting  Chapter 2 Literature Review  30  problem. The results from Level 1  size  estimation of the  of plant  are  sufficient to provide reasonably accurate data for the  needed  or the forming schedule of a process.  analysis  formability of a workpiece is concerned, a more detailed Moreover, the results from Level 2 are useful in microstress or thermodynamic evolution, such as, microscopic  a ceramic  material element,  particle  in  analysis  at Level  When the  (Level 2) is required.  3.  recrystallization, etc.,  3,  At Level  either  is of interest. Using a  the stress concentration around a second phase particle, such as  the MMC5,  can also  locally refining the  be estimated by  finite element  mesh as shown in Fig. 2.9(a).  ——  —  a macroscopic stress  —b microscopic stress 1  eE  :  ‘4, (‘4  .100 a  Ifl  HH  ------  .L._._  0  10i2 25mm (a)  Figure 2.9  20 10 (1 distance tram ingot center (b)  P  (a) FEM mesh with local refinement during a plane-strain upsetting;  4 ’ t47 (b) Stress distribution along the line PQ (e=1% calculated with ABAQUS) The  results using  a multilevel finite element system  concentration due to second phase particles are shown in Fig. of second phase particles  along the line PQ shown in Fig.  to  calculate  2.9(b), based on the  2.9(a).  Figure 2.9(b)  the  stress  distribution  shows that the  Chapter 2 Literature Review continuum-mechanics based solution  31  ( Level 2: macroscopic stress) yields a normal stress  (curve a), while substitution of the micro-elements (Level 3: microscopic stress) produces a stress curve (curve b) in the same figure with spikes at the positions of micro-elements. Obviously, the substitution of micro-element (or second phase particles in real materials) changes the local stress in the matrix. For metallurgical microanalysis, FEM results from Level 3 are needed to study microstructure evolution during hot deformation.  2.5.2 Particle Fracture Model during Deformation Finite element analysis at level 2 can reveal the macroscopic deformation behavior of the MMCs during extrusion. However, criteria quantifying the microstructure (fracture) at level 3, based on the deformation behavior, are required. Brechet et al.  (75-76]  assumed that the  probability of fracture of a particle, p, is a function of area-equivalent particle diameter, D, and strain, c, at room temperature as below. (2.13) where  f  is a constant and the probability is defined as the ratio of the number of cracked  particles to total number of particles.  Their experimental data had verified the linear  relationship between the fracture (percentage of particles cracked) and the imposed level of strain by compressing a sample of Al(A356)-20%SiC. The model did not consider the shape of a particle (including aspect ratio). As observed in the microstructure in extrudates of alumina particulate-reinforced metal matrix composites, equiaxed particles crack less easily. To take aspect ratio into account, the probability of a particle cracking can be expressed as: (2.14) Dae) 1 Pf = 1 —exp(— where a is the aspect ratio of a particle and is a constant (= l.6x10 43 p.m ) . It is noted that Eq. (2.14) is consistent with the experimental data from Brechet et a1 . Actually, if the 761  Chapter 2 Literature Review  32  exponential term in Eq. (2.14) is less than 1, Eq. (2.14) could be approximately expressed as Eq. (2.13).  Because the above equations are valid for room temperature, it is not clear  whether or not the criteria apply to high temperature deformation such as the hot extrusion process. At high temperature, plastic relaxation around particles is easier due to possible dislocation climb, and work hardening is not dominant, while the strain rate is more sensitive to flow stress. Due to the compressive stress state in the hot extrusion process, particle cracking could be the dominant fracture mode. Humphreys and Kalu 771 have investigated the low temperature transition of a second phase particle behavior in a model material of Al-Si alloy. At low temperature, there is an accumulation of dislocations at the particles, whereas at high temperatures climb is possible with the consequence that there is no stress build-up. Consequently there will be very little particle damage or interface decohesion. They proposed that at high temperature the critical strain rate below which stresses will not accumulate is given by: cc  =  2 +K 2 exp(—Qb IRT)/ Td 3 Ki exp(—Q / RT)ITd  where K K are material constants, 1 and 2  Q  (2.15)  and Qb are the activation energies for bulk and  surface diffusion, d is the diffusion distance, and T is the absolute temperature. They also pointed out that with appropriate adjustments to the constants, the above equation may be used with some confidence to predict the effect of second-phase particles on the mechanical behavior of alloys at elevated temperature. Based on the above analysis, it would be feasible to neglect the strain effect because of less work hardening, but add the strain rate and temperature effect to account for the probability of a particle fracture at high temperature. Therefore, the strain rate compensated  Chapter 2 Literature Review  33  variable, Z = eexp(Q / RT), should be introduced to consider the probability of a particle fracture during deformation at high temperature. Moreover,  of fractured particles by  intruding matrix materials into the gap of two halves has been observed in deformed materials with superimposed hydrostatic pressure. The pressure, Ph’ required for the matrix material to : 751 intrude into the cracks is expressed ast ph(e)=a ‘  2 3  D ln(D I h ° ) e )1 0 3h ) 0 ln(D1h  [—+—(  (2.16)  —  where h 0 is the initial width of the gap of the crack and  is the flow stress of the matrix. It  is evident that easier ‘healing’ could occur at high temperature if this equation is applicable. 2.5.3 Microscopic Analysis of PRMMCs under Larger Deformation It is known that a microscopic analysis of the PRMMC during industrial extrusion process is impractical. The multilevel system can be applied to the analysis of particulate reinforced MMC during large deformation in laboratory tests, although a specific microelement material model is required on a microscopic scale to induce its anisotropy. At the macroscopic level, the MMCs are assumed to be isotropic and the continuum plasticity theory is used. The deformation behavior of the MMCs can be characterized and the fonnability of the MMCs can be analyzed by using a modified Plastic-Work Criterion. At a microscopic level, micromechanical analysis of the MMCs under large deformation can be conducted by a single particle model (micro-element material model) and a multiple particle model to be described in later section. In this study, the behavior of a particle during a cylindrical compression and a plane strain test will be analyzed at both the macroscopic and microscopic level, to help understand the microstructural evolution of the PRMMC during large deformation (including extrusion) at high temperature.  Chapter 3 Scope and Objectives  34  Chapter 3 SCOPE AND OBJECTIVES  Particulate reinforced MMCs are attractive for many applications in the automotive industry. However, the demand has been limited owing to the cost and insufficient knowledge of the behavior of the MMC materials. Many discontinuously reinforced MMC products require deformation processing via rolling, extrusion, or forging to achieve the final shape. Issues associated with these processing schedules include equipment capabilities, die wear due to the abrasive nature of the reinforcements and the influence of deformation conditions on microstructure and properties. To meet the goal of increased productivity with high quality and reduced costs, a better understanding is needed of how deformation processing influences microstructure and properties in these materials.  3.1 Scope and Objectives From the literature review, it appears that the extrusion process is the widely used and one of the most economical secondary processing routes for particulate reinforced MMCs. It may also improve the mechanical properties of the material. The scope and objectives of this study are: 1) To conduct compression tests using a Gleeble® machine to develop constitutive equations for the PRMMCs. The constitutive law will be adopted in the fmite element model; 2) To better understand the deformation behavior of the alumina particulate reinforced MMCs during extrusion with the aid of a finite element model, DEFORM® level;  ®  Gleeble is a registered trade mark of Dynamic Systems, Inc., New York, USA.  ,  at macroscopic  Chapter 3 Scope and Objectives  35  3) To conduct extrusion plant trials to examine the microstructural evolution (e.g., particle fracture and size refinement) and the mechanical property change of the MMCs under different extrusion conditions; the plant trial data, such as extrusion force and temperature measurement will be used in validation of the finite element model predictions and the model predictions as well as plant trial data will be applied to the development of an extrusion limit diagram; 4) To establish a correlation between deformation parameters and the low speed surface cracking by microstructural examination and the finite element analyses at both macroscopic and microscopic levels.  3.2 Methodology An integrated approach has been adopted for this study: Gleeble compression tests were conducted to develop the constitutive law of the alumina reinforced metal matrix composites.  The constitutive law has been adopted in the finite element analysis of the  extrusion process. Extrusion plant trials were conducted and the plant trial data were used in validation of the finite element model predictions. Microstructural evolution for the extrusion billet and extrudates was examined using an optical microscope and an image analyzer. A correlation between deformation variables (e.g., ram speed (strain rate), extrusion ratio and temperature), and composite failure (including surface cracking) was established based on an SEM surface crack examination and the FEM analyses. The effect of extrusion conditions on the mechanical property change was investigated by conducting tensile tests of the extrudates.  Extrusion limit diagrams for the material were finally developed for the purpose of industrial production. The overall conception of the project is schematically shown in Figure 3.1.  ®  DEFORM is a registered trade mark of Scientific Forming Technology Corporation, Columbus, Ohio.  Chapter 3 Scope and Objectives  36  Gleeble Tests Micromechanical  I Constitutive L.aw  AnalYSis  Particle Size Refinement  Load stroke curve, Extrusion  Limit  Product  Analys Deformation  iafE Low Speed Cracking,  Development  Model Validation  Behaviour  Effect of  Extrusion Conditions  Figure 3.1 Methodology for the extrusion of alumina particulate reinforced MMCs  37  Chapter 4 EXPERIMENTAL Laboratory tests and plant trials were conducted to better understand the behavior of the alumina particulate reinforced metal matrix composites during processing. Constitutive equations for three different volume fractions, 10%, 15% and 20%, of the MMCs were developed based on cylindrical compression tests using a Gleeble® machine. The constitutive equations will be used in extrusion process simulation with the aid of a fmite element model. Two plant trials were conducted on a small press in the Kingston Research and Development Center (KRDC), and a large industry press at Universal Alloy Corporation (UAC), Anaheim, for two different volume fractions, 10% and 20%, of the composites. The extrusion data such as load-stroke and die temperature will be used for validation of a FEM model prediction and development of extrusion limit diagrams. Microstructure evolution of the composites during extrusion will be examined using microscopes and correlated with the tensile properties measured from the extrudates of the KRDC plant trials.  4.1 Gleeble Tests 3 with three different volume fractions from 10% to 20% 0 2 Specimens of 6061/A1 were machined from cast billet stocks into cylinders of 10mm diameter by 15mm long. The specimens were homogenized at 565°C for 2 hours to improve the as-cast structure, to reduce segregation and precipitates and large dispersoids.  Compression testing was  conducted using a Gleeble® 1500’ thermomechanical simulator.  The specimens were  resistance-heated at 5°C/s to test temperatures in the range of 400°C to 525°C, held at that temperature for one minute, and then deformed to a true strain of 1.0 at a nominal strain rate of 0.05, 0.1, 1, or l0s-. Graphite shims were inserted between the specimen and ram to  Chapter 4 Experimental  38  prevent excessive barreling (Figure 4.1).  The test conditions chosen were based on the  extrusion conditions adopted in industry for the unreinforced aluminum alloys. The hot working behavior of many conventional alloys has been characterized with an empirical equation derived from creep laws. The equation which is most applicable over the range of strain rates and temperature encountered of monolithic alloys during hot f8J• 1 • working is the hyperbolic sine constitutive equation (Equation 4  Figure 4.1 Schematic of the Gleeble test set-up Z = eexp(Q I RT)  =  Asinh(xa)  (4.1)  where Z is the Zener-Hollomon parameter (the temperature compensated strain rate), strain rate,  Q  C  is  is activation energy, R is the universal gas constant, T is the absolute  temperature, a is the flow stress and A, cz, and n are constants. It is noted that the equation is strictly valid only over the steady state regime of deformation and as such, it may not be  Chapter 4 Experimental  39  applicable to the low strain range where transient behavior is observed.  However, some  workers have empirically applied the equation over the whole strain range of a test with a reasonable fit of the dat? . Typically during analysis for the equation constants, a is set to 9 an arbitrary value and the other parameters are calculated using plots In { sinh( a a)) against  me  to determine n, and ln{sinh(a a)) against l/T to determine  Q.  The method of  unconstrained variables was used in this study to analyze the data for the four parameters in the constitutive equation. This method, based on a procedure first shown by Sheppard and ’ 80 Wright  ,  allows all four of the equation constants to vary during iteration to a solution,  rather than fixing a, as is common in most other work. For the data analysis, true strain was calculated from transverse extensometer readings of the variation of specimen diameter during compression. The flow stress for the analysis was calculated at a strain of 0.5 in the steady state regime. The nominal strain rate was obtained from the recorded value over a strain range of 0.35 to 0.65, because it varied at the beginning and at the end of the deformation. The temperature used for the analysis was also the absolute value at a strain of  0.5. The values of the four parameters in the hyperbolic sine equation were determined through iteration by minimizing the absolute difference between the measured flow stress and the predicted flow stress. The values of each material constant for the composites are compared with those for the unreinforced parent alloy in Table 4.1. It is noted that the four hi. 8 constants were determined for the best fit of the experimental datat  The correlation  coefficient between the predicted and the experimental data for each volume fraction is also listed in Table 4.1 for reference. It is seen that a good correlation has been obtained between the predicted flow stresses and the experimental data.  Chapter 4 Experimental  40  1 Table 4.1 Material constants for the constitutive equation of the Composites Material  Q(kJ/mol-K)  A(s’)  a(MPa-’)  n  6061  197.5  2 1.97x10’  0.036  4.11  Correlation Coefficient 0.997  /lOp 3 0 2 6061/A1  216  4 9.42x10’  0.023  5.24  0.988  60611A1203115P  210  2 9.77x10’  0.034  4.00  0.992  /20p 3 0 2 6061/A1  220  4 4.45x10’  0.024  4.41  0.987  4.2 Plant Trials at UAC, Anaheim 4.2.1 Extrusion Procedure Two plant trials were held at Universal Alloy Corp., Anaheim, on the Duralcan composite and its unreinforced material. Two billets each of 6061, 6061/A1203/1OP and /20p were extruded in the first plant trial in September, 1992 ( designated as 3 0 2 6061/A1 /2Op bifiets were homogenized. 3 ‘S92’, hereafter). Only the 6061 and one of the 6061/AlO /lOp 3 The remaining three billets were extruded in the as-cast state. The two 606 l/AlO billets were 508 mm (20”) long and all the others were 304 mm (12”) long. The diameter of all the billets were 178 mm (7”) in the second plant trial in July, 1994 (designated as ‘J94’, /lOp, and 8 of 606l/AlO3I2Op, were extruded using 3 0 2 hereafter). 22 billets, 14 of 6061/A1 4 different dies. They were all prehomogenized at about 570°C for four hours. The length of all 22 billets was 381mm (15”), and the diameter of all the billets was also 178 mm (7”). Details of the extrusion condition are listed in Table 4.2.  Chapter 4 Experimental  41  Table 4.2 Extrusion programs for the 7” press at UAC Test No.  Material  Billet Dimension  Die Diameter  (L (mm) x D(mm))  (inch)  Pretreatment  S92-1  6061  305x178  1.25  Homogenized  S92-2  6061  305x178  1.25  Homogenized  S92-3  3 0 2 606l/A1 / 20p  508x178  1.25  Homogenized  S92-4  I2Op 3 O 2 606 iIA1  508x 178  1.25  as-cast  S92-5  /lOp 3 O 2 606l/A1  305x178  1.25  as-cast  S92-6  3 0 2 6061/A1 / l0p  305x178  1.25  as-cast  394-1  /iOp 3 O 2 6061/A1  381x178  2  Homogenized  394-2  3 0 2 6061/A1 / lOp  381x178  2  Homogenized  394-3  6061/A1O3/l0p  381x178  2  Homogenized  394-4  /iOp 3 O 2 606lIAl  381x178  2  Homogenized  394-5  /2Op 3 0 2 606l/A1  381x178  2  Homogenized  394-6  /20p 3 0 2 6061/A1  381x178  2  Homogenized  394-7  /20p 3 0 2 606l/A1  381x178  2  Homogenized  J94-8  /lOp 3 0 2 6061/Al  381x178  1.25  Homogenized  394-9  /lOp 3 0 2 606l/A1  381x178  1.25  Homogenized  394-10  IlOp 3 O 2 606 lIAl  381x178  1.25  Homogenized  J94-1 1  /lOp 3 0 2 6061/A1  381x178  1.25  Homogenized  394-1 lb  /iOp 3 O 2 6061/A1  381x178  1.25  Homogenized  394-12  /2Op 3 O 2 606l/A1  38 lxi 78  1.25  Homogenized  394-13  /20p 3 0 2 606 l/A1  381 xl 78  1.25  Homogenized  394-14  /20p 3 0 2 606 l/A1  381 xl 78  1.25  Homogenized  194-15  /lOp 3 O 2 606l/A1  381x178  1  Homogenized  394-16  /lOp 3 O 2 606l/AI  381x178  1  Homogenized  394-17  /lOp 3 O 2 6O6l/A1  381x178  1  Homogenized  394-19  /2Op 3 O 2 606l/A1  381x178  1  Homogenized  394-20  /20p 3 O 2 6061/A1  381x178  1  Homogenized  394-ha  /lOp 3 O 2 6061/A1  381x178  1.5  Homogenized  394-18  3 0 2 606h/Al / lOp  381 x 178  1.5  Homogenized  Chapter 4 Experimental  42  A schematic diagram of the press setup at UAC is shown in Fig. 4.2.  Billets were  preheated in a gas fired, three-zone, chain belt furnace. Initially the three zone temperatures were set to 12 1°C, 32 1-343°C and 466°C, but the preset temperature of the last zone was adjusted according to the required extrusion temperature, which is 420°C to 520°C. Billets resided in the furnace for typically 40 min., although, a billet only progressed when the preceding one was withdrawn. Contact thermocouples in each measure billet temperature for furnace control (Fig. 4.2).  fire zone were employed to  The final zone temperature was  recorded in the data spreadsheet as the fmal billet temperature in the furnace.  These  temperature measurements have the potential to be inaccurate as they were taken directly a flame had impinged on the billet surface.  after  Further temperature measurements were taken  from both the front and the back end of a billet using a hand-held K-type thermocouple immediately before the billet entered the transfer mechanism (Table 4.3). Container, die Product runout table  Press hydraulics  -  • Z2 I  I  I  I  I  I  I  I  Billet loading  Z3  •  I  I  -  Billet transfer mechanism  Il  ‘I Il  Il  Thermocouples  Three-zone gas firing furnace  Figure 4.2 Schematic of extrusion setup for Duralcan trials  -  I  -  —  -  -  —  -  Die preheatingi box  Chapter 4 Experimental  43  Table 4.3 Billet temperatures immediately prior to extrusion at UAC Test No.  Material  Preset Temp.  Temp.@front  Temp.@back  (°C)  (°C)  (°C)  S92-1  6061  427  452  454  S92-2  6061  427  424  438  S92-3  I20p 3 O 2 606 1IA1  427  429  429  S92-4  /20p 3 606l/A1O  427  391  391  S92-5  /l0p 3 0 2 606l/A1  427  393  410  S92-6  /lOp 3 0 2 6061/A1  427  431  443  J94-1  /lOp 3 O 2 60611A1  466  424  426  J94-2  /l0p 3 0 2 6061/A1  493  399  399  J94-3  OlOp 2 606l/Al  477  459  516  J94-4  /l0p 3 0 2 606l/A1  493  516  519  J94-5  !20p 3 0 2 606l/A1  477  452  457  J94-6  /20p 3 0 2 606 l/A1  477  444  460  J94-7  /20p 3 0 2 606l/A1  488  458  516  J94-8  /l0p 3 0 2 6061/A1  488  463  521  J94-9  /lOp 3 0 2 606l/A1  488  479  507  J94-10  /lOp 3 0 2 606l/A1  488  482  496  J94-11  /l0p 3 0 2 6061/A1  468  446  457  J94-llb  IlOp 3 O 2 6061IA1  468  434  483  J94-12  /2Op 3 O 2 6061IA1  468  423  460  J94-13  /20p 3 0 2 60611M  491  471  507  J94-14  /20p 3 0 2 6061/A1  491  461  514  394-15  OillOp 2 606l/Al  491  488  503  394-16  /lOp 3 O 2 6061/A1  491  498  465  J94-17  /lOp 3 O 2 6061/A1  510  487  529  J94-19  /2Op 3 606l/A1O  510  484  503  J94-20  606 l/A1 /2Op 3 O 2  477  457  474  194-ha  3 0 2 6061/A1 / l0p  466  451  495  J94-18  3 0 2 60611Al 1 h0p  466  451  457  Chapter 4 Experimental  44  It is seen from Table 4.3 that the temperature distribution is uneven for most of the billets at the end of heating. Ambient temperature was recorded at 28oC, rising to 38 to 49°C near the press. The total transfer time from furnace to the start of extrusion was 30 to 45 seconds. The pressure pad, or ‘dummy block,’ which was transferred along with the billet, was preheated to around 49 to 92°C (three measurements were made). The die was preheated to a setup temperature of about 427°C in a die box, whereas the bolster, upon which the die sits, was placed in the stack at ambient temperature. The die assembly would have lost heat because the thermocouple had to be inserted after removal of the assembly from the die box. However, this is of little importance as we have a continuous record of the die temperature. The container temperature was set to heat up to 4270C, but temperatures measured at the inlet part of the container with a hand-held device indicated a variation of 277 to 348°C. The press is a 3000T horizontal press with no extrudate quenching capability. Extrusion speed was manually controlled by a pulley system, and varied significantly for the establishment of good extrudate surface conditions. A thermocouple was inserted in the die to a position approximately 1.6 mm away from the die bearing surface, and it seemed to give a good response to billet loading and extrusion. The container has an inside diameter of 184 mm. The pressure pad is 89 mm long with a flange at the contact end of 186 mm diameter by 12.7 mm, the rest being 178 mm diameter. All the tools were H13 steels, except for the 1.5inch die used in the second plant trial of J94-1 la and 394-18, which was ceramic material.  4.2.2 Extrusion Data During extrusion, the load, ram speed and die and container temperatures were recorded. A typical load-stroke curve, with the variation of ram speed, is shown in Fig. 4.3 for the extrusion of Trial S92-3. The peak pressure is reached at the end of the filling-up  45  Chapter 4 Experimental  stage, when the billet is about to break through the die aperture. Then the extrusion force falls until the pad reaches the dead metal zone, due to the decrease in billet length and  consequent reduction in friction force at the container interface. The reason for the variation in extrusion speed greater than about lmnils are due to operator actions: the process was surface quality driven with all other factors being subservient. One operator stood at the press exit and directed the actions of another operator who was manipulating the speed control. When surface cracking appeared at the front end of the extrudate, the ram speed was increased. The increase in die temperature during extrusion is mainly because of heat conduction from the hotter billet (Fig. 4.4). The friction heat at the die interface also heats up the die temperature. After contacting each other, heat conduction occurs between the billet and the die, which causes the steep die temperature increase at the beginning. The die temperature tends to level off when the steady state is reached.  z a, 0 LL  12000  5  10000  4  8000  3  6000  0  Co  I-.  w  4000 1  2000  0  0 0  50  150 100 Ram Displacement (mm)  200  250  Figure 4.3 Typical load-stroke curve with variation of ram speed (S92-3)  Chapter 4 Experimental  ! 2  •  46  12000  460  10000  ‘..,‘j  A’2C  80006000  .—‘  •400j  —0--Load  —a— Die Temp.  -  Q 0  • 370  4000’  340  2000 0  I  0  50  -310  I  I  200 150 100 Ram Displacement (mm)  250  Figure 4.4 Die temperature increase during extrusion (S92-3)  I  16000  F— Homo (S92-3) I.  14000  —0— Unhomo (S92-4jj  12000 10000 8000  6000 4000  2000  0  0  50  I 100  I 150  I 200  250  Ram Displacement (mm)  Figure 4.5 Effect of homogenization on extrusion force (S92-3 and S924)  Chapter 4 Experimental  47  460  6  430  370  Die Temp  300 200 Ram Displacement (mm)  100  0  i—310  I  I  0  400  500  Figure 4.6 A weak coffelation of increasing ram speed with increasing die temperature during extrusion (S92-5)  I —a-- 431°C (S92-6)  1—0—  16000  C  r. .—  12000  393°C (S92-5)  8000 4000 0 0  I  I  I  I  100  200  300  400  500  Ram Displacement (mm)  Figure 4.7 Effect of billet temperature on extrusion force (S92-5 and S92-6)  5  Chapter 4 Experimental  48  16000 12000 8000  —a-- 305 mm (S92-3) —a-- 381 mm (394-12)  400()  50  0  100  150  200  250  300  Ram Displacement (mm)  Figure 4.8 Effect of billet length on extrusion force during extrusion (S92-3 and 394-12)  12000  ‘-‘  —a— 20% (194-7) —0—10% (J94-3)  10000-  8000 6000 .4000.2000 01 0  I  I  50  100  150  I  I  200  250  300  Ram Displacement (mm)  Figure 4.9 Effect of volume fraction on extrusion force during extrusion (606 l/A12O3/lOp: 394-3, and 606 l/A12O3/2Op: 194-7)  Chapter 4 Experimental  49  15000 12000 9000 .6000  3000 0 0  50  100  150  200  250  300  Ram Displacement (mm)  Figure 4.10 Effect of extrusion ratio on extrusion force (J94-4, 394-10, J94-15) A higher load is required for extrusion of the non-homogenized billets (both /l0p billets of S92-5 and -6 and 6061/A1203/20P of S92-4, Fig. 4.5). This higher 3 0 2 6O6l/A1 load is related to the microstructure of the non-homogenized materials, which contain segregated elements, precipitates and large dispersoids. A weak correlation between increasing ram speed and a delayed increase in die  temperature at the thermocouple position was observed, as shown in Fig. 4.6. This is because an increase in ram speed leads to a higher strain rate and a higher stress, which results in a higher rate of heat of deformation. Consequently, a higher billet temperature due to higher extrusion speed causes an increase in die temperature. A higher load is also needed for extrusion of lower temperature billets, because of the higher flow stress at lower temperatures (Fig. 4.7). The extrusion pressure is dependent only on the flow stress when the extrusion ratio is constant.  The increase in extrusion force  Chapter 4 Experimental  50  associated with an increase in billet length (Fig. 4.8) is due to friction at the container interface; the friction force at the container interface is proportional to the billet length. Figure 4.9 shows that the extrusion force increases with volume fraction of reinforcement because the composite with a higher volume fraction of the particle has a higher flow stress. However, the similar value of the extrusion force for both volume fractions at steady state is due to high initial temperatures of the billet at the back ends, (5 16°C, see Table 4.3), in addition to temperature rise due to heat of deformation, which results in a similar flow stress for both volume fractions. The effect of extrusion ratio on extrusion force, shown in Fig. 4.10, confirms that a higher extrusion ratio leads to a high extrusion pressure. The influence of extrusion ratio and billet length on extrusion force are also well explained by Eq. (2.2-5). A higher initial bifiet temperature was also tested (e.g., J94-17, J94-19) to try to observe the incipient melting, but it failed because of low maximum ram speed of the press. •The control device consists of a pulley rig which opens or closes a valve in the hydraulic system. This accounts for the fluctuations of less than about lmmls: the press does not have very good speed control, and the maximum speed which can be realized is less than 10mm/s.  4.3 Pilot Extrusion at KRDC, Kingston 4.3.1 Extrusion Procedure A total of 14 extrusion tests were performed at Kingston Research and Development /20p) under 3 0 2 /lOp and 60611A1 3 0 2 Center, Kingston, with two volume fractions (606 1/A1 different extrusion conditions, as listed in Table 4.4. The microstructure of the extrudates were examined for different extrusion conditions. The extrusion data recorded were used  Chapter 4 Experimental  51  both in validation of a finite element model and in development of extrusion limit diagrams of the composites. The test number is designated hereafter as ‘K-’, as shown in Table 4.5.  Table 4.4: Plant trial conditions at KRDC 606 1/Al 20 3/ lop V =  1 T  1 R  = =  606 l/Al03/2Op Vl  0.8-0.9 mm/s  400°C, T 2  500°C  1 T  =28,R 2 lO,R = 3 64  1 R  =  = =  =  0.8-0.9 mm/s  400°C, T 2  =  500°C  =28,R 2 l0,R = 3 64  The billets were in the as-cast condition. The billet was typically 76 mm long and 53 mm diameter. All the billets were preheated in an electric furnace for about three hours to achieve a uniform temperature. The temperature of an instrumented billet of 6061 aluminum  alloy in the furnace was monitored and controlled using a thermocouple. The die and the pressure pad were heated at the same time. However, the container was heated separately by three heaters around the outer surface of the container along its axial length (Fig. 4.11). The set-up temperature for the container was 500°C, but the air temperature measured in the container was -.410°C. The ambient temperature was recorded at 24°C. Before extrusion, the die was first inserted into the container from the bottom, then the billet was loaded from the top within 5-10 seconds; finally, the pressure pad was placed on the top of the billet before the stem began to press it. The press is a lOOT vertical machine. A schematic drawing of the press set-up is shown in Fig. 4.11. During extrusion, load, ram speed, and ram position were recorded by a data acquisition system at a rate of 1 Hz. Unfortunately, no thermocouples were inserted into either the die or the container to record the temperature variation during extrusion. Only the billet temperature was measured before it was loaded into the container by a hand-held device.  Chapter 4 Experimental  52  Extrusion speed could not be controlled very well at high speeds (—4mmls). Therefore, a ram speed of about 1 mm/s was adopted. Only one extra test was conducted at a ram speed of about 3.0mm/s with 6 l/Al2O3/lOp. All the extrudates were air cooled. The O surface finish of most of the extrudates was acceptable, except for K-b, which exhibited severe die land lines and K-il which showed slight low speed cracks. More details on the low speed cracking will be described in Section 4.4.  Figure 4.11 Schematic drawing of the extrusion press at KRDC  4.3.2 Extrusion Data The dimensions of the billets and the extrudates after extrusion were measured (Table  4.5). The container had an inside and outside diameter of 57mm (2.25”) and 111mm (4.375”) respectively, and its length was 203mm (8”). The pressure pad was 19.05mm (3’74) long with a flange at the contact end of 57mm (2.25”) diameter by 3.18mm (1”18), the rest being 53mm (2.09”). The outside diameter of the die was the same as the inside diameter of the container. The die land lengths were 2.48mm, 1.73mm, and 4.15mm for the 1”/4, 3”18, and 5”/8 dies, respectively. All the other data are listed in Table 4.5.  Chapter 4 Experimental  53  Table 4.5 Billet dimensions of each test at KRDC Trial No.  K-i K-2 K-3 K-4 K-5 K-6 K-7 K-8 K-9 K-b K-il K-i2 K-13 K-14  MMC (vol%) 20% 20% 10% 10% 10% 10% 20% 20% 10% 10% 20% 20% 10% 10%  Billet Dimension (mm) 50.80x87.0 50.80x87.0 50.80x87.0 50.80x87.0 / 50.85x86.40 50.76x88.13 50.82x85.91 50.66x58.61 50.90x59.02 50.75x84.42 50.78x90.89 50.51x87.37 50.67x86.90  Die Size (inch) 5’78 5U18  5’I8 5”18 I 3”18 3I8 1”14 1”/4 3”/8 3”18 578 578 578  Extrudate Diameter (mm) 15.74 15.75 15.75 15.75 I 9.72 9.72 6.42 6.40 9.72 9.46 15.875 15.75 15.75  Discard Thickness (mm) 3.0 2.6 1.5 3.0 / 4.0 11.3 6.0 1.8 2.0 5.0 6.0 4.0 5.5  Table 4.6 Measured test data of the plant trials at KRDC Ram Speed Material TB(Meaq’d TC(sethn’) (mmls) (vol%) (°C) (°C) K-i 20% 464 500 0.8-0.9 K-2 20% 464 500 0.8-0.9 K-3 10% 464 500 0.8-0.9 464 0.8-0.9 K-4 10% 500 / 430 K-5 10% / 496 0.8-0.9 K-6 10% 500 0.8-0.9 K-7 20% 467 500 0.8-0.9 482 500 K-8 20% 0.8-0.9 442 K-9 10% 500 0.8-0.9 418 475 K-b 10% 0.8-0.9 400 475 K-il 20% 0.8-0.9 435 475 K-12 20% 0.8-0.9 10% 436 475 K-13 2.70 475 10% 436 K-14 where TB and TC are billet and container temperature respectively.  Trial No.  Remark no crack no crack no crack no crack / no crack no crack no crack no crack die line surface crack no crack no crack no crack  54  Chapter 4 Experimental  Figure 4.12 shows a typical force-displacement response and coffespondmg ram speed for test K-7. The extrusion data has the same characteristics as the data from UAC, Anaheim, and the salient features are provided below:  i) The typical load-displacement curve for direct extrusion is shown in Fig. 4.12. The first stage is upsetting of the billet to fill the container, followed by a characteristic “break through pressure”, which leads to a steady state region with decreasing force due to decreasing friction.  I  1200  1 0.8  900  0.6  600  a) a)  0.4’ 300  0.2  0 0  20  40 60 Ram Displacement (mm)  0 80  Figure 4.12 Typical load-stroke curve during extrusion at KRDC (K-7) ii) the ram speed was controlled at approximately lmmls, except for those trials in which the extrusion force exceeded the press limit, such as trials K-8, K-b, K-il, K-i2. When the extrusion force exceeded the press limit (lOOT), the ram slowed down automatically to keep pushing the billet through the die aperture, until the extrusion force required became less than the press limit, and then the ram speed increased again (Fig. 4.13).  Chapter 4 Experimental  55  iii) Other features, similar to those in the plant trials at UAC, were also observed, e.g., a higher extrusion force was obtained at either a lower extrusion temperature, a higher extrusion ratio or a larger volume fraction of the particle.  1200  1.5  -  •  f  cF  0 0  I 20  I  A )  600x 3o0  1.2  I  0.9 0.6  —a-Force —a--Speed  0.3  I  60 40 Ram Displacement (mm)  80  Figure 4.13 Variation of ram speed at the press pressure limit (K-il)  4.4 Extrusion Surface Defects During the above two plant trials, the extrudates generally had a good surface finish. However, low speed cracks were observed at the front end of some extrudates from the plant trials at UAC when the ram speed was relatively low. This phenomenon disappeared if the /20p 3 0 2 ram speed was increased. It occurred more frequently in the extrudates of 6061/A1 /lop. The higher the extrusion ratio, the more severe the cracking. Figure 3 0 2 than in 606l/A1 2Op with different extrusion ratios of 13, 34, 52 606l/A1 / 3 0 4.14 shows extrudates of 2 I1Op with the extrusion ratio of 34 3 O 2 progressing from the ruler side; an extrudate of 6061/A1 is also shown at the right for comparison. It was interesting to note that low speed cracking happened much more frequently in the plant trials at UAC, Anaheim, than in the plant trials at  Chapter 4 Experimental  56  KRDC, Kingston. However, there was no low speed cracking in any extrudate when the ram speed was above 6mm/s at any extrusion ratio at UAC. The length of each extrudate covered with low-speed cracks for the plants trials at UAC was measured and is listed in Table 4.7. The mechanism of low speed cracking will be analyzed in Chapter 8 based on finite element analyses and microstructural examination.  Figure 4.14 Low speed cracking at the front end of two extrudates Some minor defects were also noticed in the composite materials. These were due to agglomerates of alumina particles showing at the surface and were statistically likely, assuming that the agglomerations were unifonnly distributed through the casting. Die lines were evident on all extrudates. These were present in all extrusions and cannot be countered with current technology. Some chatter crazing was observed on the last extrudates of each die. This defect was due to build-up of material on the die surface. Severe die wearing was evident, as shown by measurement of extrudate diameter from each die (Table 4.7). No high  Chapter 4 Experimental  57  speed cracking was observed, because the initial bifiet temperature and the ram speed for both plant trials were not high enough.  Table 4.7 Extrudate data from plant trials at UAC Test No.  Material  Nominal Die Dia.  Extrudate Dia.  (mm) 31.75  (mm)  Coverage of low speed cracks at front end of extrudates  /  slight(mm) not available  severe(mm) not available  S92-l  6061  S92-2  31.75  31.98  not available  not available  S92-3  6061 120p 3 0 2 606l1A1  31.75  32.00  not available  not available  S92-4 S92-5  606l1A1 1 3 0 2 20p /lOp 3 O 2 606l/A1  31.75 31.75  32.00 32.03  not available not available  not available not available  S92-6  606l/A1 / 3 0 2 lOp /l0p 3 0 2 6061/A1  31.75  32.03  not available  /lOp 3 O 2 606l/A1  50.80 50.80  50.95 51.18  not available 0 0  0  394-3  /lOp 3 0 2 606l/A1  50.80  50.93  0  0  394-4  /lOp 3 O 2 6061/A1  50.80  50.95  0  394-5  /20p 3 0 2 606l/A1  50.80  51.10  0 102  J94-6 194-7  6061/Al / 3 0 2 2Op /20p 3 0 2 6061/Al /lOp 3 0 2 6061/Al  51.13 51.03 31.75  229  J94-8 194-9  50.80 50.80 31.75  0 0 0  6061/Al O 2 illOp /l0p 3 0 2 606l/A1 /lOp 3 0 2 6O6l/A1  31.75  31.75  31.75 31.75  31.78 31.85  76 114  31.75 31.75  31.95  394-12  6O61/A1 / 3 O 2 1Op 120p 3 0 2 606l/A1  3810 406  31.98  457  394-13  /2Op 3 0 2 6061/A1  31.75  J94-14 J94-15 394-16  6061/A1O3/20p /lOp 3 0 2 6061/A1 /l0p 3 0 2 606l/A1  31.75 25.40 25.40  32.00 32.13 25.40 25.43  127 381 51  2286 0  394-17  606l/Al / 3 0 2 l0p /20p 3 0 2 6061/Al  25.40 25.40 25.40  25.44 25.53 25.78  203 127  0 0  127 2286  0 4318  38.10 38.10  38.10 38.10  0 0  0 0  J94-l J94-2  394-10 J94-11 J94-llb  J94-19 194-20 394-ha 394-18  6061/AlO / 3 20p /hOp 3 O 2 6O6h/A1 IlOp 3 O 2 606l/Al  38 0  0  0  0 0 3048 0 356 102  Chapter 4 Experimental  58  4.5 Effect of Extrusion Conditions on Tensile Properties of Extrudates Plant trials have been conducted at different extrusion conditions. It is known that mechanical properties of the PRMMCs are improved after extrusion compared to the as-cast  state. However, the effect of extrusion conditions on the mechanical property change is not clear yet.  4.5.1 Tensile Tests To investigate the tensile property change of the composites, four double-shoulder tensile specimens were machined from each extrudate of the plant trails at KRDC, Kingston, for tensile strength measurement and for elastic modulus evaluation for each condition. All the specimens were in T4 heat treatment condition before testing, i.e., 1 hour holding at  550°C, followed by quenching and aging at room temperature for 48 hours or more. A schematic of the tensile test specimen is shown in Fig. 4.15. The tests followed the ASTM standard procedure’° . 21  Figure 4.15 Schematic of a tensile test specimen  4.5.2 Tensile Properties under Different Extrusion Conditions From the tensile tests, 0.2% offset yield strength, ultimate tensile strength (UTS), elastic modulus, and %-elongation, were all recorded for the extrudate obtained from the two different extrusion ratio tests performed at KRDC, Kingston. The mean value of the tensile  Chapter 4 Experimental  59  data from four samples tested for each condition is listed in Table 4.8. Unfortunately, only the standard deviation for tensile elongation is available. The exact extrusion ratio for each test  was obtained based on the measurement of the extrudate diameter after extrusion. The variation of the values is mainly due to the change of die for each test. The tensile property change of the 6061/Al IlOp for different extrusion ratios is shown in Fig. 4.16(a). It is 3 O 2 evident that the elastic modulus, yield stress, and ultimate tensile strength do not show a significant increase for extrusion ratios up to approximately 27. However, for ratios above 27, the properties increase slightly. The same is true of the extrudates of 6O6iIAl /20p 3 O 2 (Fig. 4.16(b)). A corresponding decreasing trend is evident in the elongation of the extrudates for both composites (Fig. 4.17). Although scattering of the data exists, the change in value of the elongation seems larger than the standard deviations (i’able 4.8).  Table 4.8 Tensile test results of extrudates from the plant trials at KRDC  Triai#  (%)  (°C)  ExtrusicJE Ratio (GPa)  Yield (MPa)  -  UTS (MPa)  E1opgJ JStand. Dev. (%)  606 1/A1 /20p 3 0 2 K-i  19.8  484  10.40  99.9  188.0  290.0  8.7/1.0  K-2  18.0  484  10.40  97.7  179.0  276.0  10.2/0.4  K-12  19.2  435  10.23  99.0  183.0  287.0  8.9/0.7  K-7  18.0  467  27.30  97.3  179.0  283.0  10.0/0.4  K-il  19.8  400  28.80  100.5  187.0  290.0  7.5/0.7  1 lop 3 0 2 606 11A1 K-13  9.0  436  10.28  81.5  160.0  276.0  15.7/1.0  K-14  7.0  436  10.35  76.6  156.0  274.0  20.0/1.3  K-3  7.4  484  10.40  79.8  163.0  277.0  17.0/0.3  K-4  7.4  484  10.40  80.1  158.0  274.0  16.0/0.6  K-6  8.8  496  27.34  79.0  168.0  287.0  15.0/1.0  K-b  7.0  418  27.42  80.4  161.0  281.0  17.0/1.2  K-5  7.0  430  28.44  84.3  179.0  296.0  12.0/1.7  Chapter 4 Experimental  300  6_.  60  —  —  —  —  _  250  —  —  —  —  —  —  —  —  —  —ii----E-Modulus(GPa) -  -  x  -  Yield Stress (MPa) UTS(MPa)  200  x  150  100 50 10.00  I  I  I  15.00  20.00 Extrusion Ratio  25.00  30.00  /lOp 3 0 2 (a) 606 1/A1  300 250 200  —  a  a  —  a  —  —  —  S  —  —a----- B-Modulus (OPa) X Yield Stress (MPa) - UTS (MPa)  .  -  -  -  -z  .  150  100 50 10.00  I  I  I  15.00  20.00  25.00  Extrusion Ratio  I20p 3 O 2 (b) 606 1IA1 Figure 4.16 Tensile property under different extrusion ratios  30.00  61  Chapter 4 Experimental  20 17  a  14  T-10%  11 8\ 5. 10.00  I 15.00  20.00  25.00  30.00  Extrusion Ratio Figure 4.17 Elongation of the composites as a function of extrusion ratio The tensile properties are dependent on the volume fraction of the particle, as seen by comparing the data of 6061/Al2OillOp and 6061/Al Oil2Op. It is evident that a higher volume 2 fraction results in a higher yield strength, UTS, and elastic modulus, but a lower elongation value. Therefore, the true volume fraction in each extrudate tested should be deteniiined, because under the same nominal volume fraction of 10 and 20% the true volume fraction may  vary from specimen to specimen.  By dissolution of the matrix of the extrudates, more  accurate volume fraction for each extrudate tested was obtained, as listed in Table 4.8 with the tensile properties. It is seen that for the extrudates of 6O6lIAlzOil2Op, the true volume lOp, it changes 6061/A1 / 3 O fraction varies from 18% to 19.8%, while for the extrudates of 2 from 7.0% to 9.0%.  The evaluation of the property change at different extrusion ratios  should be conducted at the same true volume fraction (rather than a nominal value, as plotted in Fig. 4.16 and Fig. 4.17). The results of the tnais of K-i, K-12, and K-il with a narrower  range of volume fraction from 19.2% (K-12) to 19.8% (K-i, K-12) were re-plotted for  Chapter 4 Experimental  62  /lOp, the trials of 7% volume 3 O 2 Oil2Op in Fig. 4.18(a) and 4.19. For the 6061/A1 2 6O6lIAl fraction (K-14, K-b, K-5) to 7.4% (K-3, K-4) were adopted, as shown in Fig. 4.18(b) and Fig. 4.19. The effect of extrusion ratio on mechanical properties are shown in Fig. 4.18(a)  and (b) for yield strength, UTS, and the elastic modulus, and Fig. 4.19 for the %-elongation. It is seen that for 606 1/A1 /2Op the elastic modulus, the yield strength and the UTS increase 3 O 2 very little with increasing extrusion ratios from 10 to 28 (Fig. 4.18(a)).  However, for  /lOp, a slight increase in the elastic modulus, yield strength and UTS are shown in 3 0 2 606l/A1 Fig. 4.18(b).  The elongation of both composite materials decreases with an increase in  extrusion ratio, while a more gradual decrease is seen for the 606l/Al Oil2Op than for the 2 /lOp. However, it is worth pointing out that the small variation of the tensile 3 606lIAlzO strengths and the elastic modulus could be within the range of their standard deviation. Unfortunately, the values are not available at the moment. 325 1III  —  —  —  —  a  —  —  —  a  a  a  —  —  a  275  —---UTS (MPa)  225  Yield (MPa)  —  —  —  —  E  175 E (GPa) 125  75. 10  15  20 Extrusion Ratio  25  30  Figure 4.18(a) Tensile property change of 606 l/AlO /2Op for different extrusion ratios 3 with a true volume fraction from 19.2% to 19.8%  Chapter 4 Experimental  63  300 —  —  —  —  —  —  .  —  —  —  —  ----.-----.  —  —  —  UTS (MPa)  —  .  —  —  —  —  0  250  a 200  Yield (MPa)  x W  E  2  150  X  E (GPa)  100 A  50 10  I  I  I  15  20 Extrusion Ratio  25  30  I1Op for different extrusion ratios 3 O 2 Figure 4.18(b) Tensile property change of 6061/A1 with a true volume fraction from 7.0% to 7.4% 20  17  4  o  14  N  — —  —  —  — —  — — — 6061/A1203/lOp  0  0  11  6061 /A1203/20p  8’  5  10  I  I  15  20  25  30  Extrusion Ratio Figure 4.19 Coffesponding elongation values at different extrusion ratios for both composites  ChapterS Modeling the Extrusion of the PRMMCs  64  Chapter 5 MODELING THE EXTRUSION OF THE PRM[VICs  The literature review suggests that little work has been carried out on the analysis of a transient extrusion process at high temperature and none for the extrusion of the PRMMCs. To better understand the extrusion process, one test from each plant trial was simulated with the aid of a finite element package, DEFORM®’ , by applying the alumina PRMMCs as a 821 monolithic material. The plant trial data were then used to validate the model predictions. The results during hot extrusion will help to understand particle fracture and surface cracking.  5.1 Mathematical Model of Extrusion Process 5.1.1 Finite Element Model 5.1.1.1 Flow Formulation DEFORM® is based on a Flow Formulation approach with a penalty function procedure using an updated Lagrangian procedure’ . The choice of the package was dictated 831 by two factors: the requirement that it should be capable of modeling large scale hot deformation (strains of up to four and greater), and the need to predict loads over the whole range of deformation (i.e. under transient and steady-state conditions).  It contains an  automatic re-meshing feature, which facilitates the modeling of transient large deformation processes, such as are found for extrusion processes. In this study, the model consists of four objects to be simulated in the extrusion press: billet, pressure pad, container and die, as schematically shown in Fig. 5.1.  The ram and stack were ignored, as was the elastic  deformation of the extrusion presses, for the purposes of this work. Because of the large plastic deformation associated with the process, the billet material was assumed to behave as a  ChapterS Modeling the Extrusion of the PRMMCs  65  rigid-plastic material, whereas the other three objects were defined as being rigid in computation and only the billet was involved in deformation to which the flow formulation applies. FORCE APPLIED  CONTAINER  II  PRESSURE PAD  —  IEX11WDATh  I  STACK COMPONENTS  Figure 5.1 Schematic of an extrusion press  Based on the virtual work-rate principle, the following variational equation was . 831 obtained & dV—JF d S=O v =Ja6cdV+JKe3e 1  (5.1)  1 is the traction specified on the surface where V is the flow domain of the billet, and F boundary 5;  defined as:  and  are effective stress and effective strain rate, respectively, which are  ChapterS Modeling the Extrusion of the PRMMCs  66 (5.2)  = (aa..)’  2”’  (5.3) Due to incompressibility, the rate of volumetric straining should be zero, i.e.: (5.4) To preserve the incompressibility condition valid in the deformation analysis, a term of 0.5K  ,  where K is a very large constant, _108 or called penalty constant, was introduced ,  into the virtual work principle functional to guarantee the volume constancy (second term in Eq. (5.1)).  This is called the Penalty Function procedure, which is widely used in finite  analysisL The mean stress, or the hydrostatic stress, which is defined l. element deformation 83 as the mean of three normal stress components, am, obeys the following equation based on : 831 the penalty function procedure am  (5.5)  Ke 2 =4  The compatibility between the strain rate, C.  1 (v +v,) 1 = ,  and the velocity, v, is defined as:  (5.6)  where the comma between the ‘i’ and ‘j’ denotes differentiation with respect to spatial coordinates. The deviatoric stress, a, is related to stress, a, and the mean stress, am, as follows: a=a—öjjam  (5.7)  where ö is the Kronecker delta. According to the Levy-Mises theory, the constitutive law 831 can be expressed as follows: 3_  .  .  a =(—a/E)e  (5.8)  ChapterS Modeling the Extrusion of the PRMMCs  67  Equation (5.1) can be converted to a series of non-linear algebraic equations by a  normal FEM discretization procedure, resulting in:  acIv(acI) av,  —  (5.9)  av,  Linearization of this equation was achieved by Taylor expansion near an assumed solution  point v  =  0 (initial guess), resulting in, v  +[  3 L=, Av av 1 av 3  =  (5.10)  0  where Av is the first-order correction of the velocity v . Equation. (5.10) can be written in 0 matrix form, (5.11)  [K]{zv}={f) where [Kj is the stiffness matrix, { Av } is the velocity correction term, and  [f) is the residual  of the nodal point force vector. Since the PRMMCs are extruded at high temperature, heat transfer occurs throughout all the objects due to different initial temperatures and internal heat of deformation in the billet and friction heat at the interface. The governing equation for the heat transfer is: , +q—pc T=O 1 kT,  (5.12)  where the first term of the equation is the heat transfer rate, with the comma denoting differentiation with respect to spatial coordinates and with the repeated subscript meaning summation; k denotes thermal conductivity. The second term is the rate of generation of heat arising from deformation, which is obtained from the following well known formula:  q=iGe —.  (5.13)  where r is the efficiency of conversion of deformation energy to heat, and is assumed to be in  the range of 0.90 to 0.95, depending on the material being formed. Thus heat transfer and  ChapterS Modeling the Extrusion of the PRMMCs  68  deformation heating are coupled in the simulation. However, this heat generation rate term only applies to the billet, because all the surrounding tools are assumed to be rigid. The third term in Eq. (5.12) is the rate of accumulation of internal energy. Eq. (5.12) can be discretized following a traditional Galerkin fmite element method and written in matrix fonn as : 11 [C]{T)+[K]{T}  =  (5.14)  {Q}  where [C] is the heat capacity matrix, [Ks] the heat conduction matrix,  [Q)  the heat flux  vector, [T] the vector of the nodal temperature and {T) the vector of the nodal temperature  change with time. 5.1.1.2 Boundary Conditions Four objects were discretized into a series of 4-node iso-parametric elements (Fig. 5.2). Due to axisymmetry, an axisymmetrical slice of the press setup was analyzed with a 2-D model. The basic variables: velocity and temperature, were linear within each element. The 0.240  0.046  -0.149  [343  -0.537  -0.731  -0.926  -1.120  0.0  12.0  24.0  36.0  48.0  60.0  Radius (mm)  Figure 5.2 Initial finite element mesh for the billet and its surrounding tools  ChapterS Modeling the Extrusion of the PRMMCs  69  4-node iso-parametric element was used because it made remeshing . 821 ’ 137 easiei Due to limitation of the DEFORM® model, heat was oniy conducted between the billet and the surrounding tools.  However, interface heat transfer between various tools, e.g.,  between pressure pad and container, between container and die, was ignored (Fig. 5.2). The thermal boundary condition between the billet and the tools is expressed as: = h(TBS  —  T)  at interface boundary  (5.15)  where k is the thermal conductivity of the bifiet, and TB , and 8 8 TT are interface temperature of the bifiet and its contacted tool (pressure pad, container, and die), respectively; h is the heat transfer coefficient at the interface. For surfaces of all objects which are exposed to air, such as, a part of surface of the billet at the die aperture, the thermal boundary condition is expressed as: = hair(T&  —  T.j  at surface boundary exposed to air  (5.16)  At the center line of the billet, due to axisymmetry, the heat transfer rate is zero. kTB =0  at the center line of the billet  (5.17)  At the outer surface of the container, because of the induction heater, the surface temperature was kept constant as measured, i.e.,  T =7  at outer surface boundary of the container  (5.18)  For simplicity, the outer surfaces of the pressure pad and the die were assumed to be exposed to the air, as in Eq. (5.16), due to cold ram and die stack. The mechanical boundary conditions of the deformed billet to be satisfied are as follows: at the center line of the billet, the velocity in the radial direction is zero; Vr  =0  at the center line of the billet  (5.19)  At the container and the die interfaces, the velocity normal to the boundary, v, is zero, while the velocity normal to the interface at the pressure pad is equal to the ram speed.  ChapterS Modeling the Extrusion of the PRMMCs v =0 v  =  70  at the container and die interface  (5.20)  at the pressure pad interface  (5.21)  (t) 0 v  In addition, a friction stress was applied to the interface between the billet and the surrounding tools as stress boundary conditions. The shear factor friction law, t=mk, was adopted in hot deformation, where t is the friction stress, m the shear factor, and k the shear strength of the  . The free surface at the bottom end of the billet and the free surface of the extrudate 1831 billet have no surface traction.  5.1.2 Input Data In common with observations made by , 851 sticking friction conditions were ’ 1M others assumed to prevail at the interfaces between the billet and the container, and the billet and die, i.e., m=1, for the shear factor friction law, t=mk. For the interface between the pressure pad and billet, a shear factor of m=0.7 was assumed due to the cold pad’ . The heat transfer 831 K, based on the laboratory work 2 coefficient at these interfaces was assumed to be 200kW/m on aluminum alloys by H1ady . A hyperbolic sine constitutive equation developed using the 1861 Gleeble® machine was employed in the model to calculate the effective stress in Eq. (5.8). The thermophysical properties of the billet (the PRMMCs) and the tools (H13) used in the heat transfer model were all temperature dependent, except for the density of the material, which was assumed to be constant . 11181  5.1.3 Solution Procedure The convergence of the scheme requires consistency and stability. The consistency requirement ensures that as the size of the elements tends to zero, the approximation equation (5.14) will represent the exact diffeintial equation (5.12) and its boundary conditions  (Equations 5.15-5.16), and is satisfied by an approximation of the type,  ChapterS Modeling the Extrusion of the PRMMCs  T+ The term  and t  =  =  T + tt[(l  —  (5.22)  f3) 1 + f T+]  f is a time integration factor used  t + tt,  71  to average temperature over time, at time t  and varies between 0 and 1. For unconditional stability,  =  f should be greater  0 L 5 841, than • and in the current model a value of 0.75 was chosen. The total number of  elements in the billet was 1000 at the upsetting stage, and increased to 1250 afterwards. For the surrounding tools (e.g., the pressure pad, the container, and the die), the number of elements in each rigid object was from 200 to 400, since only a heat transfer analysis was conducted. Because most of the deformation occurred in the die region after the upsetting stage, the elements of the mesh at the die exit zone were refined relative to the size of the elements under the pressure pad, to achieve a more accurate solution. The solution of the velocity and temperature field was obtained alternatively by direct iteration followed by a modified Newton-Raphson method.  The convergence criteria for  velocity and extrusion force had to be satisfied for further temperature calculation in the same  time step, viz.: for velocity •  .  .  V  II vii  1 (=0.5x10 e  .  ), where  (vTv)1fl, and v is a vector, and for extrusion force  I lvii etc. is an error norm, defmed as ). 2 e (=0. lxlO  After the  temperature of all the objects was calculated, the geometry of the bifiet was updated based on nodal velocities. The velocity solution was iterated again at a new step. The simulation proceeded in this maimer until a negative determinant of Jacobian matrix was encountered in one distorted element, which indicated that the mesh had been severely distorted. Therefore, remeshing was conducted over the whole billet. However, the distribution of the new mesh density was similar to that of the old one prior to remeshing; in this way remeshing errors  ChapterS Modeling the Extrusion of the PRMMCs  72  were minimized due to interpretation. The stroke step, As,  (=  V  At, where  VB  is the ram  speed, and At is time step), adopted for the simulation was 0.25mm during the upsetting stage,  and 0.05mm after that. The simulation was terminated when the extrusion reached the ‘steady state’ region.  5.2 Sensitivity Analysis of the Model A sensitivity analysis in mathematical modeling should be conducted if values of some parameters are uncertain. In our study, the parameters, such as friction shear factor, m, heat transfer coefficient, h, at the interface, and heat generation efficiency, r), are reasonably well known as described in previous sections.  However, the number of elements affects the  accuracy of the results, therefore, a sensitivity analysis was conducted, with 500, 750, 1000,  and 1250 elements in the billet. Because the surrounding tools were only involved with heat transfer, the number of elements in each tool (pressure pad, container and the die) were kept unchanged in the sensitivity analysis. The simulation and boundary conditions used in the model were the same as described in the above sections. The thermophysical properties for the surrounding tools (H 13) and the billet of 6061/AI /20p were obtained from Duralcan 3 O 2 181 as mentioned in Section 5.1.2. The other input data are listed in Table 5.1. USA’  Table 5.1 Some data for sensitivity analysis of the FEM model Billet temperature, T  425°C  Container temperature, Tr  395°C  Die temperature, T  395°C  Pressure pad temperature, Ti,..  70°C  Extrusion ratio  34.0  Billet dimension  4178x305mm  ChapterS Modeling the Extrusion of the PRMMCs  73  Because the peak extrusion force and the maximum temperature of the billet during extrusion is crucial to the development of extrusion limit diagrams, the effect of the number of elements in the bifiet on these two maximum values were studied. The maximum temperature  was usually reached in the die land zone because of severe deformation at the die throat. This will be seen clearly in the section of model predictions (Section 5.3.2.2).  The extrusion  process of the large press at UAC, Anaheim, was simulated with four different number of elements.  Each simulation was stopped when the steady state was reached at a ram  displacement of 25 mm for the sake of CPU time. The load-stroke curves predicted for the four different numbers of elements are shown in Fig. 5.3.  It is evident that the load is  insensitive to the number of elements in this range. The effect of the number of elements on the maximum temperature is shown in Fig. 5.4. It is seen that when the number of elements increases, the curves of the temperature converge; although in the range of the number of elements from 500 to 1250, the differences between them are all quite small and within 5°C. This may result from the fact that although the total nuiñber of elements in the billet are different, the mesh size in the die exit zone for all the cases is fine enough to become insensitive to the peak load and the maximum temperature prediction.  However, a small  number of elements in the billet, e.g., 500, may cause other problems, such as an interference of billet mesh with the rigid die boundary at the die exit corner.  This could affect the  prediction of the effective strain rate and the stress at that corner. Hence, in industry process simulation, 1250 elements were used in the billet after the upsetting stage and the mesh was refined with a higher mesh density in the die exit zone to achieve a higher accuracy of the results (based on the fact that severe deformation occurred in the die exit zone) while only  1000 elements in the billet were adopted in the upsetting stage.  ChapterS Modeling the Extrusion of the PRMMCs  12000  74  -  100001250  0  8000-  —-—-1000 750 500  6000 4000  2000 0. 0  I  I  5  10  I 15  25  20  Displacement (mm)  Figure 5.3 Sensitivity of load stroke curve to the number of elements in the billet 465-  455..  445  1250 1000 —-—-750 500  14’  I  1  435  I  425 20  I 21  I 22  23  I 24  I 25  26  Displacement (mm) Figure 5.4 Sensitivity of the maximum temperature to the number of elements in the billet  ChapterS Modeling the Extrusion of the PRMMCs This sensitivity analysis was conducted for the large press.  75 However, the results  should also be applicable to the small press because the extrusion ratios for both presses which  are going to be simulated in the subsequent section are similar at approximately 30. Therefore the element size in the billet of the small press would be about 10 times smaller when the same number of elements was applied, because the deformation zone of the billet in the large press  was about 10 times larger than that in the small press.  5.3 Extrusion Process Simulation 5.3.1 Processing conditions The extrusion process simulation was conducted for one test from each plant trial: S92-3, for the large scale industrial machine, and K-7, for the laboratory press. In the first case, a homogenized billet of approximately 17 8mm diameter by 305mm was heated to 429°C in a continuous, gas fired furnace. The billet temperature at the furnace exit was recorded using a hand-held probe. The time to transfer the billet from the furnace to the press was around 40 seconds. The extrusion container was heated to a nominal temperature of 425°C, and the die to 336°C and the pressure pad to 70°C. The die was a flat faced die, with an aperture diameter of 32mm. A thermocouple was embedded in the die 1.6mm away from the die bearing, in order to record the temperature change during extrusion. The billet for the second press was substantially smaller, around 51mm in diameter by 88mm in length, and was heated to 467°C in an electric muffle furnace. The delivery time of the billet from the furnace to the press was around 10 seconds. A flat-faced die with an aperture diameter of 10mm was employed. The die and pressure pad were heated in the same furnace as the billet; however, no continuous die temperature monitoring was conducted. The container was heated to 475°C by an induction heater placed around the  ChapterS Modeling the Extrusion of the PRMMCs  76  outside surface of the container. The details of the process conditions of the two plant trials simulated are summarized in Table 5.2 for clarity.  Table 5.2 Processing Conditions for Two Simulations Parameter  S92-3, at UAC  K-7, at KRDC  TB  429°C  467°C  T  425°C  475°C  336°C  467°C  Tp  70°C  70°C  Ram Speed  —2.6mm/s  0.9mm/s  Transfer Time  40 sec  10 sec  Extrusion Ratio  34  28.0  Billet Dimension  Ø178x305mm  Ø51x88mm  No. of Elements in Billet  1250  1250  5.3.2 Model Predictions Each of the extrusion trials was simulated from the start of extrusion until the steady state was reached after the peak pressure. The deformation behavior of the billet as well as the thermal history of each object, was predicted during extrusion. Material flow, stress state, strain and strain-rate distribution in the deformation zone, and also the temperature distribution in all the objects were characterized.  The predicted extrusion load and die  temperature were compared with the measured data.  5.3.2.1 Deformation Behavior After the billet was loaded into the container, there was a gap between the billet and the inside surface of the container due to the smaller billet diameter than the inside diameter of the container (Fig. 5.2).  When the pressure pad pressed the billet, it commenced  upsetting, and the container was gradually filled up. Figure 5.5 shows the material flow near  ChapterS Modeling the Extrusion of the PRMMCs  77  the end of the upsetting stage. The arrowheads are the nodal velocities starting at node positions in the finite element mesh of the billet. The length of the arrow is proportional to the value of velocity.  The apparent ‘wavy’ nature of the velocity arrows is due to the  positioning of the nodes in the finite element mesh. It is seen that the gap between billet and the container had almost been filled, only the bottom-right part at the die-container corner remained to be filled up with the billet material flowing towards the corner. At the same stage, the part of the billet at the die aperture had been pushed into the die throat with a contact with the die bearing land, and apparently the material velocity in the die exit increased. The effective strain distribution at this stage was still relatively small with the large values concentrated at all the corners, such as die-container corner and die exit corner (Fig. 5.6). As the extrusion proceeded, the die-container corner was filled up, and then all the material would flow towards the die aperture. A break-through pressure (the peak point in the load-stroke curve) was necessary for the billet to be pushed through the die land. After passing the peak pressure, the so-called ‘steady-state’ deformation began, although the extrusion force decreased due to the drop in friction force at the container interface. The velocity fields at the steady state are shown in Fig. 5.7 and Fig. 5.8 for both large and small presses. The velocities of the material at the die exit were significantly higher than those in the container because of the high extrusion ratio.  The ‘dead metal zone’ at the corner  between the die and the container was present in both instances (see also Figures 7.1 and 7.3). Although a tendency of material flow still appeared in the dead zone, the value of velocity at each node in the dead metal zone was close to zero(again, the apparent ‘wavy’ nature of the velocity arrows is due to the positioning of the nodes in the finite element mesh).  Chapter 5 Modeling the Extrusion of the PRMMCs  78 Velocity 3 (mm/s)  -15.0  V  V  —  TV,  V  V  yyyy  VVVVVVVV VV V \\\V  1  1,  -55.0  0.00  6.00  y  J  (  450  V  -  12.00  18.00  24.00  1 30.00  Radius (mm) Figure 5.5 Material flow near the end of upsetting stage -15.0  -  ‘  ? NL._  Eff. Strain Billet  —3——  A O.50000E41 Bx 0.000 C 0.35000 oo.5oooo E. 065000 F o.eOOoo  -35.0  0,  z  0.00  6.00  12.00  18.00  24.00  30.00  Radius (mm) Figure 5.6 Effective strain distribution near the end of upsetting stage  ChapterS Modeling the Extrusion of the PRMMCs  p p  4250  79  Velocity 217.8 (mm/s)  V  p  p  F  ‘p  ‘P p  P P,  ‘P  E E 01 0,  p  p  P  P 4.500  P  P  P.  P  -3.750  p  -4000  -4250  50.5  10  1000  753  Radius (mm)  Figure 5.7 Velocity distribution in the billet after a ram displacement of 40.7 mm in the large extrusion press; length of arrow is proportional to velocity  -7200  -7.700  ‘ , , , , , 1?VVVP7ppp P p pP vVPr?p,ppppPPp, Pp P p P P?PVVPppPpPPPPp P ,,ppppppppp, PP Pp P p P Pr,, PPPPPPPPP,,,rrP  ;;‘  Velocity 81 (mmls) V F  ,,rP P V  Pp?p  p,,PPpPPPP,,,p  E E 0)  -8200  PPPPp, p pP PppppP p • ppm frppP FFFftP  0,  I  F  p P p  P  F F F  F  P  p  p  P  A  F  P  F a a  4.700  -9200  12.00  1800  24.00  30.00  Radius (mm)  Figure 5.8 Velocity distribution in the billet after a ram displacement of 26.7 mm in a small extrusion press: length of arrow is proportional to velocity  ChapterS Modeling the Extrusion of the PRMMCs  80  It is worth pointing out that, in the finite element large deformation analysis, an absolute dead metal zone could not exist, because otherwise the nodal strain-rate in that zone would become zero, which could result in a numerical difficulty. For this, in our study, a limit strain-rate was defined which was io times less than the mean effective strain-rate over the deformation zone. If the calculated nodal strain-rate was less than the limit strain-rate, then the limit value replaced the corresponding nodal value, and the zone was taken as ‘rigid’. The mean stress is representative of the stress state because it is defined as the mean of all the normal stress components: if the mean stress is negative, a compressive stress state is dominant. However, if the mean stress is positive, there must exist at least one dominant tensile stress component. Fig. 5.9 and Fig. 5.10 show the mean stress distribution at steadystate during extrusion. It is evident that the stress state in the deformation zone is almost all in compressive except in the surface layer near the die land. The absolute value of the mean stress in the container decreases from the pressure end to the die exit, which implies that the billet tends to be in tension in the extrusion direction when approaching the die exit, due to elongation. The positive value in the surface layer apparently is due to two factors: firstly, the material flows faster in the center zone than in the surface layer, which has been technique° ; and secondly, friction stress at the die land confirmed by an experimental 1 surface exists. By comparing Figures 5.9 and 5.10, it is seen that the mean compressive stresses are significantly higher in the larger press, as would be expected due to the lower initial temperature of the billet and higher ram speed. However, a common feature for both presses is the negative value of the mean stress in the deformation zone and positive value in the surface layer at the die land area. The significance of the negative mean stress is that it may  ChapterS Modeling the Extrusion ofthe PRMMCs  81  help minimize the microstructural damages (e.g., potential void formation due to decohesion  and particle fracture) during extrusion of the MMCs. However, the existence of a tensile stress component in the surface layer in the die land  area  might contribute to the source of low  speed cracking, which is a specific feature of extrusion of the particulate reinforced MMCs. This will be discussed in more detail in Chapter 8. Mean Stress (MPa) B(et  -2.750  A= -335.00  8= -310.00  C= -285.00 D= -260.00  E= 23500 F=-210.00 G= -185.00 H= -160.00 1= -135.00 J= -110.00  -3050  K- -8000 L=-60.000 M= -35.000 N= -10.000 0= 15.000  -3350  -3.650  -3.950  4.250 40.0  60.0  100.0  Radius (mm) Figure 5.9 Mean stress distribution in the billet at a ram displacement of 40.7 mm in the large extrusion press (negative values denote compressive stresses) Although the mean stresses  are quite  different, the effective strain near the die is in the  range of about 4- 5 for both presses, as expected because of their similar extrusion ratios. A typical effective strain distribution is shown in Figure 5.11 for the small press at a ram displacement of 26.7mm. The annular strain pattern in the extrudate is  also as  would be  expected from a qualitative assessment of extrusions which shows a recrystallized  ring after  ChapterS Modeling the Extrusion of the PRMMCs  82  . The corresponding effective strain rate distribution is shown in Fig. 5.12 for the 91 extrusion’ small press. It is seen that the strain rate distribution is confined in the die throat zone, and its form is similar to predictions made by Chen, Oh and Kobayashi t1201 for extrusion through conical dies. The maximum strain rate is reached at the die exit corner where extrudate Mean Stress (MPa)  2  Biliet  -0.500  A= -270.00 B= -245.00 C. -220.00 D= -195.00 E= -170.00 F=-145.00 G=-120.00 H= -95.000 1= -70.000 J= -45.000 K= -20.000 50000  -0.600  I :i:  -0.700  -0800  -0.900  -1.000  0.00  6.00  12.00  24.00  18.00  30.00  Radius (mm)  Figure 5.10 Mean stress distribution in the billet after a ram displacement of 26.7mm in the small extrusion press (negative values denote compressive stresses) surface forms from both the shear zone and a small volume of dead zone at the bottom of the  ’ and 187 die . 71 This feature is in accord with other observations, both experimental ” 1 interface 201 ” 172 FEM  .  The maximum strain rate is in the range of values typical of those found in  651 and similar to the maximum strain rate of about 21.5 s ’ t63 extrusion , 4 for the small press, estimated using another empirical equation  (5,23)1611.  However, the mean strain rate  Chapter 5 Modeling the Extrusion of the PRMMCs  83  calculated using an empirical equation (5.24) [61) is only 2.4s. The low value estimated by the second empirical equation results from the assumption that the deformation is homogeneous throughout the billet. This restriction does not apply to the finite element analysis, which consequently predicts a higher mean effective strain rate of 13.7s , which probably more 1 accurately reflects the deformation of the billet. Furthermore, the empirical equation (5.24) cannot take into account the large-scale variations in ram speed observed during the trials, whereas the finite-element analysis is ideal for this situation. max  —  —  Em  (5.23)  VBR 6 DE  (5.24)  4Dvtanq ‘3I2 si.BLE)  —  2  LII. Strain BIet  -0.650  -0.720  A= 0.90000 8= 1.7000 C= 2.5000 D= 3.3000 E= 4.1000 F= 4.9000  %....  -0860  0.930  -1.000  -  0.00  5.00  10.00  15.00  20.00  I  25.00  Radius (mm)  Figure 5.11 Effective strain distribution of the billet in the small press  84  Chapter 5 Modeling the Extrusion of the PRMMCs  Eff. Stn Rt (us)  -8.000  A= 0.0000 B= 3.0000 C= 6.0000 0= 9.0000 E= 12.000 F= 15.000 G= 18.000 H= 21.000  E E 0) ci  -8.500  -8.750  -9.000  0.00  3.00  6.00  9.00  12.00  15.00  Radius (mm)  Figure 5.12 Effective strain rate distribution of the billet in the small press 5.3.2.2 Temperature Distribution Because the flow stress of the composites is very sensitive to temperature, the temperature drop during transfer of the billet from the furnace to the container was also included in the simulation based on the measurement of the delivery time (Chapter 4). At the beginning of the extrusion, due to the cold pressure pad and lower initial die temperature of the large press, a ‘cbilling’ effect exists at both ends of the billet, which consequently heats up the pressure pad and the die by heat conduction through the interface. After the upsetting stage, the bifiet temperature exhibits the effect of deformation heating toward the die entry, although in the larger billet, this is more pronounced because of its lower initial temperature (Figures 5.13 and 5.14).  Chapter 5 Modeling the Extrusion of the PRMMCs 2  x  -3250  Temperature  (C)  )  -  \  -3.450  4.650  85  -  A=  405.00  8= 415.00 C- 425.00 0=435.00  E= 445.00 F= 455.00 G= 465.00 11=  475.00  Cr A= 400.00 8= 405.00 C- 410.00 0= 415.00  De A= 330.00 8=345.00  -3.850  C-  360.00  0= 375.00 E=  390.00  F= 405.00  4.050  G= 420.00 H= 1= J=  435.00 450.00 465.00  -4.250  0.0  25.0  50.0  75.0  100.0  125.0  Radius (mm) Figure 5.13 Temperature distribution in the large extrusion press 2  Temperature (C)  8d A=  447.00  8=453.00 C-  459.00  0=  465.00  E= 471.00  F= 477.00  -0.700  A=  440.00  8=446.00 C-  452.00  E=  464.00  0=458.00  E .850  A  De  :c  -1.000-  —1.150  -  A=  360.00  C-  400.00  0=  4200  E=  440.00  F=  460.00  —  0.0  15.0  30.0  45.0  60.0  Radius (mm) Figure 5.14 Temperature distribution in the small extrusion press  ChapterS Modeling the Extrusion of the PRMMCs  86  Temperature increases of approximately 70°C and 23°C were predicted for the large press and the small press, respectively, because of the heat of deformation. This is again due to the low initial temperature of the billet and higher ram speed of the large press, which increases the flow stress and the strain rate, resulting in a higher rate of heat generation. The maximum temperature of about 484°C and 479°C for the large and small presses, respectively, is reached at the surface of the extrudate in the die land zone. The maximum temperature of the die is about 10°C less than the maximum value in the billet due to the thermal resistance at the die interface. Because the thermal diffusivity of the die material (H 13) is about 7 times less than that of the 606 l/A1 /20p, a much larger thermal gradient exists in the die land than 3 O 2 in the extrudate. The more pronounced thermal gradient in the die land for the large press is a result of the difference in initial die and bifiet temperatures while the large thermal gradient in the extrudate of the large press is due to the larger diameter of extrudate and the higher ram speed, which results in a more pronounced adiabatic heat effect. 5.3.2.3 Comparison of Predictions with Measured Data Load / stroke predictions are compared with measured data for displacement beyond the peak load in Figures 5.15 and 5.16. The agreement is good during the upsetting stage, and within 10% at the higher loads in both instances. However, the load increase at the end of the upsetting stage is faster in the FEM prediction than in the measured data, especially for the small press, in which a larger shift in the peak load appears. This might be due to the assumption of rigid tools in the FEM model, while in reality there always exists deformation of the press. The large shift in the peak load might be partly due to the capacity of the small press (lOOT) which was almost fully loaded in the test, while the 3000T capacity of the large press meant it was only half used. Therefore the compliance of the press has to be estimated.  87  ChapterS Modeling the Extrusion of the PRMMCs  14000  Measured  12000 ‘10000V  FEM  8000 .  6000  :t 2000 0 0  I  20  10  I  I  30  40  Ram displacement (mm) Figure 5.15 Comparison of predicted force with measured data (large press) 1200 1000 Measured 800  ‘FEM  C)  600 C  L  400 200 0 0  I  I  10  20  30  Ram dislacement (mm) Figure 5.16 Comparison of predicted force with measured data (small press)  ChapterS Modeling the Extrusion ofthe PRMMCs  440  88  Measured  420  FEM  U 0  380  a a  360 •5 340  a  a  a  a  320 300-  I  10  0  20  30  40  Ram displacement (mm) Figure 5.17 Comparison of predicted temperature with measured data (large press) The predicted temperature at the thermocouple position of approximately 1.6 mm away from the die bearing  in  the die for the larger press (Figure 5.17) is within 10°C of the  measured temperature over the range of the simulation, although it does not follow the variation closely. The model seems to have overpredicted the temperature after the peak load has been achieved, but the difference is still less than three percent. Actually, the discrepancy between the predicted and the measured temperature could also be due to the assumption of initial uniform die temperature and the error of the thermocouple position because the thermocouple was inserted into the hole in the die after the die was put into place before extrusion. It is worth pointing out that the reason for fewer predicted points in the upsetting stage in the FEM curve (Fig. 5.17) is that fewer time steps with predicted results  Chapter 5 Modeling the Extrusion of the PRMMCs  89  were saved to prevent a big size (could be up to 300MB) of the output database file during simulation. However, the load value was saved automatically for each step in the model.  5.4 Validation of Model Predictions Model predictions must be evaluated in the light of the fact that the boundary conditions in some areas were not precisely defined, and this may affect the results. The friction between the billet and container or die surfaces was assumed to be sticking friction but was not measured. Furthermore, the temperature field in the billets extruded through the large-scale press was not accurately known, due to the constraints imposed by the conditions under which the trial was conducted. In addition, the temperature at the die in the smaller press was not recorded.  The prediction of the forces required for extrusion is most  susceptible to temperature variations. Finally, it must be recognized that the simulation is a two-dimensional simulation, and any results should be treated with caution, although for the axisymmetrical case considered here, errors are likely to be low. Notwithstanding these limitations, the modeling has resulted in a reasonably accurate prediction of load and temperature rise. Furthermore, predictions in the upsetting stage are difficult with a fluid-flow type model°’, but in this work the agreement between predictions and measured data was very good. The ability to predict forces in the upsetting stage has a concatenation effect in that it influences the subsequent predictions of, for example, temperature and strain. Load predictions resulting from the finite-element analysis are close to the values measured from each press, although the prediction for the larger press is considerably closer to the measured value. The predicted sharp rise in load after upsetting of the billet does not accurately follow the measurements (the scale of the abscissa in Figs. 5.15 and 5.16 distorts  ChapterS Modeling the Extrusion of the PRMMCs  90  the difference however). This is not an anomaly of the model, as mentioned before, but rather is a consequence of defming the die, container, and pressure pad as rigid objects during the simulation.  In reality, the components are not rigid, but this assumption was needed to  complete the simulation in a reasonable CPU time.  Thus, the model predicts only the  response of the material, whereas the instruments on the press read the response of the whole system. It is known that the difference between the length of a billet before extrusion and the length of the remained butt end after extrusion is the real displacement the billet experienced during extrusion.  If the press (assuming the billet is rigid-plastic) were rigid, then the  recorded ram stroke would be exactly the same as the real displacement. Therefore, the difference (a total elastic deformation of the press) between the real displacement and the recorded ram stroke was used as a simple examination of the contribution of machine compliance to the load-stroke curve.  For the lOOT press, the total elastic deformation,  including the elastic deformation of the bifiet, was obtained to be 5.27mm for the given test. The maximum ram stroke was reached when the final ram speed approached zero. Considering the measured extrusion force at the maximum ram stroke for that given test, F = 1 808kN, an overall elastic deformation constant for the press was calculated as: 0 = Ff/(ST (L E 0 LR)) = l53kN/mm -  -  (5.25)  Applying this constant to the measured stroke, the adjusted stroke excluding the elastic deformation, as simulated by DEFORM® , can be obtained as: 0 (mm) Sa(t) Sm(t) F(t)1E  (5.26)  where Sa(t) and Sm(t) are the adjusted and measured ram stroke, respectively; F(t) is thç extrusion force, and t denotes extrusion time.  Chapter 5 Modeling the Extrusion ofthe PRMMCs  91  14000  Measured  12000  FEM  z 10000 ‘1.)  ° I  8000  °  6000  I  .  4000,, :1  0  20  10  30  40  Ram displacement (mm) Figure 5.18 Comparison of FEM force with measured data corrected for extrusion press compliance according to Eq. (5.26); large press 1200  1000 z -  • Measured • i  FEM  800  0  600 •0  400 200 1 0L  0  I  I  10  20  30  Ram displacement (mm) Figure 5.19 Comparison of FEM force with measured data corrected for extrusion press compliance according to Eq. (5.26); small press  Chapter 5 Modeling the Extrusion of the PRMMCs  92  Another way to calculate the E 0 is to measure the unloading slope of the extrusion force-stroke curve. The average E 0 for the larger press is measured as 2777kN1mm from four tests. Corrections to the measured data accounting for the machine compliance align the measurements with the simulation (Figures 5.18 and 5.19).  In principle, the reverse is  possible: the simulation could include an elastic component in order to better model the specific extrusion press under investigation, at the expense of simulation time. The variation in the load prediction, after the peak load has been reached (Figures 5.15 and 5.16), is due to a node in the bifiet losing contact with the die and a consequent drop in the extrusion force. The software attempts to compensate for this node unpinning, causing the observed behavior. The prediction could be improved in a number of ways, although any benefit derived from eliminating the small variation (less than 10%) would itself be canceled out by the large increases in CPU time required to achieve the following solutions. Either the mesh at the die throat could be further refmed by increasing the number of elements, or the Arbitrary Lagrangian-Eulerian (ALE) method could be used, though there is no guarantee that a re-meshing would not be required; furthermore, the mesh velocity would be difficult to determine. In addition, it is unlikely that in either case the proximity of the prediction to the measured data would be altered.  5.5 Summary A model has been developed and verified to simulate the extrusion of PRMMCs. The model is a bulk forming model with the material assumed to be monolithic with the properties of the composites. Both the transient and steady state parts of extrusion were modeled. A description of the bulk extrusion of this MMC has been presented and shown to be valid for the prediction of extrusion loads, and consequently deformation in the billet during extrusion.  ChapterS Modeling the Extrusion of the PRMMCs  93  Load predictions resulting from this model agree to within ten percent of the measured value, and in the upsetting stage, to a higher accuracy. Temperature predictions agree to within less than three percent. Slight discrepancies between the model and measurements in the region of maximum rate of change in load have been accounted for by elastic deformation of the press components.  The model is useful for macroscopic analysis, such as the development of  extrusion limit diagrams, but cannot correctly predict deformation on the scale of the particles. However, the stress, temperature, and strain distributions can be related to the propensity for particle fracture and/or void formation.  Chapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation  94  Chapter 6 MICROMECHANICAL ANALYSIS OF THE PRMMC DURING LARGE DEFORMATION  6.1 Obstacles and Challenges of Micromechanical Analysis of the PRMMCs In recent years, micromechanical analysis of particulate reinforced MMCs has been 81 ° 1105 conducted  to better understand the MMC’s response during either thermal or  mechanical changes.  However, almost all of the finite element analysis on particle behavior  of the MMCs were based on the unit cell model with simplified boundary conditions, as described in the literature review (Chapter 2).  The characterization of behavior of the  particulate reinforced MMCs under large deformation conditions has received little attention, probably because of the obstacles stated below.  6.1.1 Particle Phenomena It is the presence of particles that results in the improvement of properties of the MMCs in many aspects. However, the particles have some specific features in real MMCs: (a) the shapes of particles in the MMCs are not regular rectangles or circles as assumed by some investigators in two-dimensional unit cell models; (b) the size of the particles varies widely from a few microns to 50p.m or even more for the Duralcan® composites; (c) it is known that large particles tend to fracture more easily than small particles; (d) more importantly, the distribution of the particles in as-cast MMCs fabricated by the molten route is not uniform but contains clusters and voids due to solidification; and micro-fracture initiates more easily within clusters during deformation. Therefore, to account for particle behavior under large deformation with the aid of a finite element model, the shape and size of the  Chapter 6 Microstructural Analysis of the PRMMC during Large Deformation  95  particles and clusters should be taken into account. However, because the average dimensions of a particle (up to 501.tm) in the MMCs are significantly (—10k times) smaller than those of the workpiece (e.g. 10 mm), if the deformation of the particles in the MMCs were studied, at least 108 elements would be necessary for a two dimensional analysis with the element size close to a particle dimension. Obviously, this is impractical from a computational stand point. Then the question is, how can a micromechanical analysis of the MMCs be conducted with a traditional finite element model? 6.1.2 Matrix Phenomena  The MMCs are not simply a mixture of the particles and the matrix. In fact, the interactions of a second phase particle with the matrix during deformation is very complex. It is known that additional phenomena will occur, such as (a) precipitation of fine particles formed by chemical reaction between the particles and matrix alloy; (b) interface bonding and  its strength; (c) residual stress due to mismatch of the thermal expansion coefficient between the particle and the matrix; (d) strain induced dynamic recovery and particulate stimulated nucleation for recrystallization; (e) fracture of particle and decohesion of the interface, rotation and migration of the particle during deformation, etc., The question is, how could a  finite element model take those factors into consideration?  6.1.3 Modeling Constraints To investigate the micromechanical behavior of the MMCs, a physical constitutive  equation (not like the phenomenological one as developed in Chapter 4) needs to be developed by combining microscopic variables and macroscopic process parameters. Although a few simplified physical constitutive equations have been developed, they are incomplete. Hence, how can a physical constitutive equation be developed which includes all  Chapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation  96  the factors or at least the most dominant (if known) ones influencing the dynamic behavior of the MMCs by combining both the macroscopic and microscopic process parameters? If it were developed, could it be applied to a multiaxial stress state during processing by validating only through uniaxial compression and/or tensile testing? It seems impractical to overcome all these obstacles by the available plasticity theory and computation technology.  6.2 Micromechanical Analysis during Plane Strain Compression Under the above mentioned circumstances, it is therefore impractical to conduct micromechanical analysis of the MMCs during industrial extrusion. Nevertheless, a laboratory plane strain test was simulated to analyze the behavior of particles during hot deformation. To simplify the analysis, a twin-particle model and a multiple-particle model were adopted with each particle size of 40x40 p.m 2 in the planar cross section. In the twin-particle model, two particles were arranged such that the particle movement in the lateral direction perpendicular to the loading direction could be analyzed. In the mode1, the matrix around the particle behaves as a monolithic material with the deformation properties of the composite, and the particle has its own properties and flows along with the matrix during deformation. The DEFORM®, as described in Chapter 5, was adopted for the micromechanical analysis. The initial setup of the plane strain test simulation with finite element meshes for each object is shown in Fig. 6.1. Because the particle size is only 40p.m 2 , the element size around the particles is tremendously refined.  The detailed finite element mesh around the two  particles is shown in Fig. 6.2 for the twin-particle model. For a plane strain test simulation, only a half of the set was analyzed due to its symmetry. The friction shear factor, m, and the heat transfer coefficient, h, at the interface between the specimen and the anvil were assumed  Chapter 6 MicrostructuralAnalysis ofthe PRMMC during Large Deformation  97  to be 0.7 and 200 , 1861 respectively. The test simulation conditions are listed in Table K 2 kW/m 6.1. The nominal strain rate is 0.05/s. The total reduction was about 50%.  Table 6.1 Simulation conditions for plane strain deformation Object Name (No.)  Material  Size  Temperature  Number of  (mm)  (°C)  Elements  Upper Anvil (#1)  718 (rigid)  8.64x3.0  445  100  Specimen (#2)  606 l/AI /2Op 3 O 2  25.4x10  450  2500  (rigid-plastic) Bottom Anvil(#3)  718(rigid)  8.64x3.0  445  100  Particle (#4)  3 (elastic) 0 2 A1  40x40 urn 2  450  18-36  14.00  10.60  -  720  E >3.80  0.00  3.40  6.80  X (mm)  10.20  13.60  17.00  Figure 6.1 Initial finite element meshes for each object of plane strain deformation  Chapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation  98  6.2.1 Twin Particle Model For the twin-particle model, one particle was located at the center line of the specimen, therefore only half of the particle was considered due to symmetry. The other particle was initially located 4Otm apart in the lateral direction( see Fig. 6.2). The interface between the particle and the matrix was assumed to be perfectly bonded. The elastic modulus of the particle was 450 GPa; the Poisson ratio was 0.25, and the coefficient of thennal expansion was 7.7x10 1°C with the reference temperature of 450°C, based on data in the 4 literature for the same kind of MMC’ . 1  5.150  5.100  5.050  >-  5.000  4.950 0.000  0.050  0.100  0.150  0200  X (mm) Figure 6.2 Initial finite element mesh around two particles The effective strain distribution in the specimen at a reduction of about 49% is shown in Fig. 6.3(a) and (b) with and without particles, respectively. From the figure, it is seen that the overall effective strain distributions for both cases are quite similar, but deformation  Chapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation  99  localization occurs around the particles. This is because only two particles are considered in the micromechanical analysis. The localized effective strain is shown more clearly in Fig. 6.4 as a function of reduction. Fig. 6.4 (a) shows the effective strain distribution around two particles at a reduction of 10%. It is seen that the highest strain is concentrated in the middle of the two particles (Contour line ‘C’), and the strain around the two particles is at about the same level (contour line ‘B’). As the reduction increases, the particle located outside the center line is pushed away by matrix material along the flow direction. The distance between the two particles becomes about 130J1m (Fig. 6.4(b)). As a result, the effect of clustering is decreasing, although the highest strain is still concentrated between the two particles (Contour line ‘F’). At a reduction of about 49%, two closely distributed particles are pushed apart from an initial spacing of 40tm to more than 300J1m (Fig. 6.4(c)). It is seen that a low strain zone (contour line ‘F’) appears close to the particle. The highest strain is obtained outside the low strain zone both parallel and perpendicular to the loading direction (Contour line ‘H’). This indicates that as the reduction increases, the interaction between two particles becomes weak, and each particle plays its own part in the material during deformation.  Obviously, the  migration of particles in real composites helps break the clusters formed in casting and improves the homogeneity of particle distribution after secondary processing. Especially, in extrusion processing, due to large deformation, fractured particles can be separated by shear deformation and healed by compressive hydrostatic pressure. The effective stress in the particles at two different reductions of 10% and 49% is shown in Fig. 6.5. It is seen that the stress level is much higher than that of the effective stress in the matrix, which is about 6OMPa. This is partly due to the assumption of plane strahi deformation, in which the strain in the third direction is constrained to be zero. Therefore,  c c  Chapter 6 Micro structural Analysis ofthe PRMMC during Large Deformation  9.80  6.60  -  -  E >3.40  EU. Swain ObedS 2 A= 0.00000E.00 B= 0.30000 C=0.60000 0=0.90000 E=12000 F=1.5000 G= 1.8000 1-1= 2.1000 1= 2.4000  C  020  -3.00-  3.40  0.00  6.80  10.20  13.60  17.00  X (mm)  (a) Twin particle model  -0.020  -0.340  E E >-0.660  -  EU. Strain Obed 12 A= 0.00000E*00 B= 0.30000 C= 0.60000 0=0.90000 E= 12000 F=1.5000 G=18000 H= 2.1000 1= 2.4000  DE C  -0.980  —1.300  0.00  3.40  6.80  1020  X (mm)  13.60  17.00  (b) homogeneous MMCS  Figure 6.3 Effective strain distribution at a reduction of 49%  100  Chapter 6 Microstructural Analysis of the PRMMC during Large Deformation  4900  Objedl2 A= 0.00000E.00 8=0.30000 C= 0.60000 0=0.90000 E= 12000 F=1.5000 G= 18000  -  H= aiooo 1= 2.4000  4.580  -  E 4.420  4260  4.100  ._—  0.000  0.160  0320  X (mm)  I 0.480  I 0.640  I 0.800  (a) at a reduction of 10% 3.620  3.546  Eff. Slrain Objed # 2 A= 0.00000E.e00 8=0.30000 C= 0.60000 0=0.90000 E= 12000 F= 1.5000 G= 1.8000 H= 2.1000 1= 2.4000  0  ,DCES 3.460  3.380  3.300  —  0.000  0.080  0.160  X (mm)  0240  (b) at a reduction of 30%  0.320  1 0.400  101  Chapter 6 Mjcrostructural Analysis of the PRMMC during Large Deformation  ::  Eff. Strain  2.850  2.490  102  Object # 2 A= 0.00000E÷00 8= 0.30000 C= 0.60000 D= 0.90000  =2.4000  -  2.370  2250  -  0.000  0.160  0.320  0.480  X (mm)  0.640  0.800  (c) at a reduction of 49% Figure 6.4 Localized effective strain distribution around two particles  at different reductions even a very small strain in the third direction could lead to a large stress because of high elastic modulus of the particle. It is also interesting to see that the value of the effective stress  in the particles increases as the reduction increases. Besides the effect of matrix defonnation, this could be also due to the build-up of thermal stress in the third direction when temperature in the particle changes during deformation. The larger value of the effective stress in the particles at a small reduction during large defonnation confirms that particles could fracture at a early stage of deformation, if the fracture stress of the particle is reached.  Chapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation  Elf. Stress (UPa) 4 (right) A= 40.000 8= 80.000 C= 120.00 0= 160.00 Ex 200.00  4.700  objedl  4.620  E >-  4540  Ot*d 1 5 (dr hne) A= 40.000 8= 80.000 C= 120.00 0= 160.00 E= 200.00  -j) .  4.460  4.380  -  4.300  I  0.000  0.080  0.160  0240  0.320  0.400  X (mm)  (a) at a reduction of 10% Elf. Stress (UPa) Obed 1 4 (right) A= 40.000 8=80.000 C= 120.00 0= 160.00 E= 200.00  2.750  2.670  Object 15 (dr ne) A= 40.000 8=80.000 C= 120.00 0= 160.00 E= 200.00  2.590  >-  2.510  2.430  2.350 0.000  0.080  0.160  0.240  X (mm)  0.320  0.400  (b) at a reduction of 49% Figure 6.5 Effective stress in the particles at different reductions  103  Chapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation  104  6.2.2 Mulliple-Particle Model To consider the effect of clustering of particles in a composite, a four-particle model was developed with two more particles added to the twin-particle model, as shown in Fig. 6.6. Due to the presence of more hard-to-deform elastic particles in this model, remeshing for the matrix around four particles becomes very difficult. Therefore, a total reduction of only 1%  was considered. The effective strain distribution in the cluster zone in Fig. 6.6 shows that a higher strain zone (Contour line ‘B’) appears in the middle of two particles in both the loading  and the lateral directions in the planar cross section; however, a lower strain zone (Contour line ‘A’) exists in the center of four-particle cluster. This is because at the early stage of deformation, four particles act as a cluster; therefore, the center of the cluster is hardly deformed. The effective stress distribution in both particles and the matrix is shown in Fig. 6.7.  Considering the stress distribution in the matrix, it is seen that a low stress zone  (Contour lines ‘D’) exists in the center of the four-particle cluster. Again, the effective stress in the particles are more than 4 times higher than that in the matrix, which is similar to the twin particle model as described above. The mean stress distribution in the matrix shows a  tensile stress state in the zone between the two particles in the lateral direction (Fig. 6.8), whilst the stress state between the two particles in the loading direction is compressive. The stress state in each particle is quite similar a tensile stress component exists at the top and the bottom surface of each particle (the locations of contour line ‘E’ in each particle) due to the positive value of the mean stress, which could be a potential site for cracking.  Chapter 6 Microstructural Analysis of the PRMMC during Large Deformation  Eff. Strain ot4edl 2 A= 0.0150 B= 0.0350 C= 0.0550 D= 0.0750 E= 0.0960  5200  5.100  5.000  >-  4.900  4.800  4.700 0.000  0.070  0.140  0.210  0280  0.350  X (mm)  Figure 6.6 Localized effective strain distribution at a reduction of 1% Eff. Stress (MPa) Objedl 2 A= 10.000 8=20.000 C= 30.000 0=40.000 E= 50.000 F= 60.000  5.075  5.025  Objedl 4 -17  A= 80.000 8=120.00  4.975  E >-  C- 160.00  0=200.00 E= 240.00 F. 280.00  4.925  4.875  4.825  0.000  0.050  0.100  X  0.150  0200  0250  (mm)  Figure 6.7 Localized effective stress distribution at a reduction of 1%  105  Chapter 6 MicrostructuralAnalysis ofthe PRMMC during Large Deformation  106  Mean Stress (MPa) Object # 2 A= -130.00 8= -90.000 C= -50.000 D= -10.000 E= 30.000  5.050  5.000  F= 70.000  Object #4 #7 A= -70.000 8= -50.000 C= 40.000 -  E  E4.g50  D= -10.000 E= 10.000 F= 30.000  4.900  4.850 0.000  0.050  0.100  X  (mm)  0.150  0200  Figure 6.8 Localized mean stress distribution at a reduction of 1%  6.3 Micromechanical Analysis during Cylindrical Compression Although a unit cell model in plane strain  condition has been widely adopted by  researchers for particle analysis at a microscopic level, obviously the particle model is not representative of a real three dimensional particulate, but instead of an infinite bar in the third  direction (perpendicular to the plane). Therefore, it would be ideal to develop a threedimensional model. However, the large number of elements needed for 3-D analysis, as mentioned in Section 6.1, would be impractical from the perspective of computation costs. Hence a laboratory axisymmetric cylindrical compression test was simulated by inserting particles at the center line of the specimen. As a result, the shape of a particle is either  Chapter 6 Microstructural Analysis of the PRMMC during Large Deformation  107  cylindrical or spherical in 3-D due to axisymmetry. The simulation conditions are listed in Table 6.2.  Table 6.2 Simulation conditions for cylindrical compression test Object Name  Material  Size  Temperature(°C)  No. of Elements  718 (rigid) /2Op 3 O 2 6061/A1 (rigid-plastic) 718 (rigid) 3 O 2 AI (elastic)  20x20mm  449  150  410x15mm  450  2500  420x20mm  449  150  20.440im  450  18-36  (No.)  Upper Anvil (#1) Specimen (#2) Bottom Anvil (#3) Particle (#4)  The initial finite element mesh of a specimen including particles is shown in Fig. 6.9(a). Again, the element size around the particle was tremendously refined, as shown in Fig. 6.9(b) for a single particle and Fig. 6.9(c) for a twin-particle model. The nominal strain rate for the test is 0.05/s, and the nominal strain is 1.0. The other boundary conditions are the same as in  the plane strain simulation. 6.3.1 Single Particle Model A single-particle model refers to a cylindrical specimen under large hot deformation containing only one particle at the center line. For the cylindrical compression test, only an axisymmetrical plane was analyzed due to its axisymmetry. The particle had to be in the  center line because otherwise it would become a ring. Two extreme shapes of a particle were considered, i.e., a cylinder and a sphere in three dimensions. Four different particle cases were studied. The particle size for each single-particle model adopted is listed in Table 6.3.  Chapter 6 Microstru ctural Analysis of the PRMMC during Large Deformation  108  16.00  12.80  9.60  E  6.40  -  320  0.00  0.00  2.00  4.00  6.00  10.00  8.00  Radius (mm) (a) initial finite element mesh in a specimen  7.600  7.600  7.550  7.550  —4  I  %I  j_...4  %  V  E  7.500  4-  C) 0,  7.500  :i:  7.450  7.400  7.450  0.000  0.050  0.100  Radius (mm) (b) mesh around a particle  0.150  7.400  0.000  0.050  0.100  Radius (mm) (c) mesh around the twin particles  Figure 6.9 Initial mesh and location of a particle in a cylindrical specimen  0,.150  Chapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation  109  Table 6.3 Particle sizes studied Case  Comp-1  Comp-2  Comp-3  Comp-4  Shape  Cylinder  Cylinder  Sphere  Cylinder  Size($Imxlim)  40x40  420x20  42O  ct20x80  Aspect Ratio  1.0  1.0  1.0  4.0  6.3.1.1 Material Flow of a Cylindrical Specimen Containing a Particle The effective strain distribution in a cylindrical specimen with and without a particle is shown in Fig. 6.10(a) and (b) for a reduction of 65%. It is evident that the overall strain distributions for two specimens are very similar, but a larger strain is reached near the particle due to strain localization. Details of the local strain distribution around the particle are shown in Fig. 6.11 for the 40x40im particle. In the loading direction, it is seen that a low-strain zone appears at both the top and the bottom of the particle; however, a high strain zone shows up adjacent to the low strain zone. This is because during compression, matrix material near the center line flows towards the particle which is located at the center of the specimen; and material changes its flow direction when it approaches the particle due to the high elastic modulus of the particle.  A dead metal zone thus forms around the cylindrical surface.  Effective strain variations along the center line in the loading direction for different reductions are shown in Fig. 6.12. It is seen that, as the reduction increases, the non-uniformity of strain distribution becomes more severe. The effective stress distribution for both cases, with and without particles, is shown in Fig. 6.13(a), and (b). Again, the overall distributions of the effective stress are quite similar to each other; but stress localization occurs around the particle (Fig. 6:14). A maximum effective stress of around 260 MPa in the particle is reached, which is almost 4 to 5 limes larger than that of the matrix. The corner of the particle is a  Chapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation  110  region of high stress concentration, which implies that the corners are the potential crack initiation sites. This prediction is consistent with the phenomenon of corner fracture of a sharp particle observed in microstructure during extrusion (see Fig. 7.5).  Mean stress  distributions in the deformation zone of the matrix for both cases show that compressive stresses prevail during compression, except in the bulge zone, where a tensile hoop stress exists which might lead to surface cracks at the bulge surface under some conditions (Fig. 6.15(a) and (b)). The mean stress distributions in both the matrix around the particle and in the particle are shown in Fig. 6.16, in which a tensile stress component (positive value) appears in the upper and the bottom zone in the particle.  Efi. Strain Object # 2 A= 0.20000 8= 0.53000 0=0.86000 D= 1.1900 E= 1.5200 F= 1.8500 G= 2.1800 H= 2.5100 1= 2.8400 J= 3.1700 K= 3.5000  6.00  4.50  E E 3.00 0)  z 1.50  0.00 0.00  2.00  4.00  6.00  8.00  10.00  Radius (mm)  Figure 6.10 Effective strain distribution in the cylindrical specimen at a reduction of 65%: (a) monolithic  Chapter 6 Microstructural Analysis of the PRMMC during Large Deformation  E E  Eff. Strain Object# 2 A= 0.20000 B= 0.53000 C= 0.86000 D= 1.1900 E= 1.5200 F= 1.8500 G= 2.1800 H= 2.5100  3.00 0) 0)  J= 3.1700 K= 3.5000  6.00  4.50  1= 2.8400  1.50  0.00 0.00  2.00  6.00  4.00  8.00  10.00  Radius (mm)  Figure 6.10 Effective strain distribution in the cylindrical specimen at a reduction of 65%: (b) with a particle  Eff. Strain Objed 1 2 A= 0.20000 B= 0.53000 C= 0.86000 D= 1.1900 E= 1.5200 F= 1.8500 G= 2.1800 H= 2.5100 1= 2.8400 J= 3.1700 K= 3.5000  2.710  E E  2.670  C)  a, z  2.630  2.590  2.550  0.030  0.060  0.090  0.120  0.150  Radius (mm)  Figure 6.11 Effective strain distribution around the particle at a reduction of 65%  111  Chapter 6 Microstructural Analysis of the PRMMC during Large Deformation  112  3 2.5 Cl)  2 1.5 1 0.5  4-  x  0  10  8  6  4  2  Distance from Surface of the Bottom Anvil (mm)  Figure 6.12 Effective strain distribution along the center line of the specimen under different reductions  Eff. Stress (UPa) Objed#2 A= 20.000 8= 24.000 C= 28.000 D= 32.000 E= 36.000 F= 40.000 ( 44 14= 48.000 1=52.000 J= 56.000 K= 60.000  600  450  6 6 -  300  1.50  0.00 0.00  2.00  4.00  6.00-  8.00  10.00  Radius (mm)  Figure 6.13 Effective stress distribution in the cylindrical specimen at a reduction of 65%: (a) monolithic without a particle  12  Chapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation  En. Stress (UPa) Object 1 2 A= 20.000 8= 24.000 C= 28.000 0=32.000 E= 36.000 F= 40.000 G= 44.000 H= 48.000 1= 52.000 J= 56.000 K= 60.000  6.00  4.50  E 3.00 0) :i: 1.50  0.00 0.00  2.00  6.00  4.00  8.00  10.00  Radius (mm)  Figure 6.13 Effective stress distribution in the cylindrical specimen at a reduction of 65%: (b) with a particle Eff. Stress (UPa) Object I 2 A= 20.000 8= 24.000 C= 28.000 0= 32.000 E= 36.000 F= 40.000 G= 44.000 H= 48.000 1= 52.000 J= 56.000 K= 60.000  2.710  E E  2.670  a  0) 0) 2.630  Object 1 4 A= 20.000 8= 60.000 C= 100.00 0=140.00 E= 180.00 F= 220.00 G= 260.00 H= 300.00 1= 340.00 J= 380.00 K= 420.00  2.590  2.550  0.030  0.060  0.090  0.120  0.150  Radius (mm)  Figure 6.14 Effective stress both in the matrix and in the particle at a reduction of 65%  113  Chapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation  (  6.00  4.50  N \  -  I=-14.000  ç  3.00  J= 3.0000 K= 20.000  r  a,  Mean Stress (UPa) ‘ Objed#2 A=-150.00 B= -133.00 C= -116.00 D= -99.000 E= -82000 F= -65.000 G=-48000 H=-31.000  :i: 1.50  0.00  I 4.00  I 2.00  0.00  I 6.00  10.00  8.00  Radius (mm)  (a) monolithic without a particle  6.00  4.50  E E  I b  r  I  i-  Mean Stress (UPs) Objed#2 A= -150.00 B= -133.00 C= -116.00 0.. -99.000 E=-82.000 F.. -65.000 G=-48.000 H=-31.000 I.. -14.000 J=3.0000 K= 20.000  1.50  0.00 0.00  I 2.00  I 4.00  I 6.00  I 8.00  10.00  Radius (mm)  (b) with a particle Figure 6.15 Mean stress distribution in the cylindrical specimen with and without a particle at a reduction of 65%  114  Chapter 6 Microstructural Analysis of the PRMMC during Large Deformation  Mean Stress (MPa) Object#2 A= -150.00 8= -133.00 C=-116.OO 0= -99.000 E= -82.000  2.710  2.670  -  C) 2.630  2.590  2.550  -  -  ) /  /  ‘  F=-65.000 G=-48.000  /  /  s(  115  3= 3.0000 k=20.000 Object #4 A=-150.00 8= -127.00 C= -104.00  Y-N:  F= -35.000 G= -12.000 H= 11.000 1= 34.000 .1= 57.000 K= 80.000  -  0.000  0.030  0.060  0.090  0.120  0.150  Radius (mm)  Figure 6.16 Mean stress distribution both in the matrix and in the particle at a reduction of 65% 6.3.1.2 Effect of Particle Shape Different particle shapes were analyzed during the compression test, as listed in Table 6.3. A damage factor was modified based on the plastic workfracture criterion proposed by Lathem and Cockcroft 1511 , and was used to compare the effect of particle shape on the stress and strain state at a reduction of 65% during compression (Fig. 6.17)(a)-(d)). Df=f(-)d where a 1 is the maximum principal tensile stress,  (6.1)  is the effective stress, and d is the  effective strain increment. As described in the literature review, in cold forming operations, it was found that failure of a monolithic material at some point occurs when the damage factor reaches a critical value. This criterion, together with finite element modeling, has been used  Chapter 6 Microstructural Analysis of the PRMMC during Large Deformation  116  extensively to predict the occurrence of damage during cold forming’ . Sellars et al. 91 ”° 49 49 tested the above equation and concluded that the equation could be a reasonable criterion for hot working as well as for cold working, but further data is required to test it more rigorously for hot working. By comparing the above fracture criterion to both the Stress Criterion and the Strain Criterion described in the literature review, Syu and Ghosh 11121 confirmed that the proposed fracture criterion is the best for the development of forging limit diagrams for particulate reinforced MMCs in laboratory upsetting tests.  Figure 6.17 shows that the  maximum value of the damage factor near the particle with the an aspect ratio of 4 is about twice as large as that near the spherical particle; a greater value of the damage factor is predicted for the larger cylindrical particle than for the smaller particle. These results indicate that a spherical particle gives rise to the least damage potential in the surrounding matrix  material, and non-regular particles, such as the particle with an aspect ratio of 4, have the largest effect. For the equiaxed particles, larger particles have a more severe effect on the matrix damage than the small ones, especially at the corners (Fig. 6.17). Figure 6.18(a) shows the effect of particle shape on the effective strain variation along the center line near the particle at a reduction of 65%. It is shown again that severe localized strain occurs around all the particles, with the particle of the largest aspect ratio having the highest strain and the spherical particle, the smallest The effective strain along the horizontal mid-plane is shown in Fig. 6.18(b). It is evident that the strain near the spherical particle is quite uniform compared to the case with no-particle. However, a significant strain drop was predicted in the radial direction near the interface of particles of 2Ox8Oj.im and 4Ox4Ojim.  Chapter 6 Microstructurat Analysis of the PRMMC during Large Deformation  Damage  2.750  Obed$ 2 A= O.00000E.00 8= O.38000E-01 C= 0.76000E-01 0=0.11400 E= 0.15200 F= 0.19000 G=022800 H= 026600 1=0.30400 3=0.34200 K= 0.38000  2.710  2.670  Z2630.  2.590  2.550  -  0.000  0.030  0.060  0.090  0.120  0.150  Radius (mm) (a) ‘3i40x4() (cylinder) Damge Obed # 2 A= 0.00000E+00 8= 0.38000E.01 C= 0.76000E-01 0=0.11400 E= 0.15200 F= 0.19000 G=022800 H=026600 =0.30400 3=0.34200 K= 0.38000  2.710  2.670  0) 2.630  -  2.590  2.550  -  0.000  0.030  0.060  0.090  0.120  Radius (mm) (b) 420x20 (cylinder)  0.150  117  Chapter 6 Microstructural Analysis of the PRMMC during Large Deformation 2.750  Damage Objecll2 A= 0.00000E+00 8= 0.38000E01 C= 0.76000E-01 D= 0.11400 E= 0.15200 F= 0.19000 G=022800 H= 026600 1=030400 .3= 0.34200 K= 0.38000  2.710  2.670  -  E .2’ 0)  -  2.630  2.590  2.550  0.000  0.030  0.060  Radius  0.090  0.120  0.150  (mm)  (c) cI2O (sphere) 2.710  Damage Obied 1 2 A= 0.00000E+00 8= 0.38000E-01 C= 0.76000E-01 0=0.11400 E= 0.15200 F=0.19000  -  2.670  0)  2.630  H= 026600 1= 0.30400 .3=0.34200 K= 0.38000  -  2.590  2.550  I  0.000  0.030  0.060  0.090  0.120  0.150  Radius (mm) (d) c120x80 (cylinder)  Figure 6.17 Effect of particle shape on damage factor at a reduction of 65%  118  Chapter 6 Microstructural Analysis of the PRMMC during Large Deformation  3.75  -  .  -  3.25 .  C’, V  No Particle Cylinder 40x40 Cylinder 20x20 Sphere 20 Cylinder 20x80  -.  —  2.75  a  2.25  .  C.)  119  1.75 1.25 0.75 2.6  2.7  2.65  2.75  2.8  2.85  2.95  2.9  3  Distance from surface of the bottom anvil (mm) (a) along the center line of the specimen (40x40 etc are the particle size in microns)  2.25  C’,  a)  >  4’  I  1.45  ‘I I  1.05 0.65  0.25  o—a-__ a-’  O—-  O 7 /1  1.85  o  I  —  0  No Particle Cylinder 40x40 Cylinder 20x20 Sphere 20 Cylinder 20x80 I  I  0.2  0.4  0.6  0.8  Distance from center line to the bulge surface (mm)  (b) along the mid-plane in radial direction (40x40 etc are the particle size in microns) Figure 6.18 Effect of particle shape on strain distribution at a reduction of 65%  1  Chapter 6 Microstructural Analysis of the PRMMC during Large Deformation  450  120  +  400  +  +  +  +  +  +  +  350 300  °  Cylinder 40x40  A  Cylinder 20x20  A  0  250  Sphere 20  A  0  200  +  Cylinder 20x80  150 •  100 50  I  20  30  40  50  60  70  Reduction (%) Figure 6.19 Effect of particle shape on effective stress variation during compression (40x40, 20x20, 20, and 20x80 are all the particle sizes analyzed in microns) The effective stress in the particle is not so sensitive to the reduction for all the four particle shapes, as shown in Fig. 6.19; however, the particle shape itself affects the stress value quite significantly, from about 125MPa for the spherical particle (‘Sphere 201.Lm’), to 425MPa for the highest aspect ratio particle (‘Cylinder 20x80p.m’ in Fig. 6.19). The values for the cylindrical particles with an aspect ratio of unity are quite close. Therefore, it is concluded that the particle fracture is sensitive to the shape of particles, especially for those  with a larger aspect ratio, while the size of equiaxed particles is less important. 6.3.2 Multiple Particle Model The characterization of single particle behavior during cylindrical compression might only apply to the situation in which particles are separated by a large distance relative to their  Chapter 6 Microstructural Analysis of the PRMMC during Large Deformation size.  121  However, for the particulate reinforced MMCs fabricated by a cast route, particle  aggregations, or clusters, are always present. Therefore, a multiple particle model is needed, in which twin cylindrical particles with a particle size of 40x40 located at the center line of the compression specimen were studied. 6.3.2.1 Effect of Reduction Particle spacing changes during compression, as predicted in plane strain compression in Section 6.2. For a starting particle spacing of 120 jim in the center line, the effective strain distribution is relatively uniform at a reduction of 33%, and its characteristics are quite similar to that of a single particle model (Fig. 6.20(a)). However, at a reduction of 65%, deformation around the particle becomes more severe.  A localized strain zone extends in the radial  direction as a result of material flow (Fig. 6.20(b)). The maximum value around the particle is larger for the twin-particle case than that for the single particle, which indicates that more severe deformation occurs for the multi-particle situation. The mean stress distribution in each particle at a reduction of 33% (Fig. 6.2 1(a)), also shows similarity to the single particle model (Fig. 6.11) due to the large spacing, although the values of stress are different. The mean stress distribution around the particle under this reduction is relatively uniform at a level of -12 MPa to -44 MPa. At a reduction of 65% (Fig. 6.21(b)), the value of the mean stress changes from -44 MPa to -300 MPa; also a large mean stress gradient appears in the gap between the two particles, which implies a complex tn-axial stress state. 6.3.2.2 Effect of Particle Spacing Three different initial particle spacings of 20, 40, and 120pm were studied. The effect of particle spacing on strain values along the center line of the specimen are shown in Fig. 6.22(a). It is seen that the strain reaches a maximum at a point about half a particle size above  Chapter 6 MicrostructuralAnalysis of the PRMMC during Large Deformation  122  the particle, and the maximum values for each spacing are not much different, with the smallest spacing being the largest. The minimum strain value is located at the right top of the particle, with the smallest value for the largest spacing (120 jim). In the zone between two particles, obviously, the larger the spacing, the larger the strain. This is because for large spacing the matrix deformation is increased. Figure 6.22(b) shows the strain distribution along the radial direction in the mid-plane between the two particles. It is seen that a smaller particle spacing (20.un) leads to less deformation in the gap.  Elf. Strain Object 41 2 A= 0.20000 B= 0.53000 C= 0.86000 D= 1.1900 E= 1.5200 F= 1.8500 G= 2.1800 H 2.5100 1= 2.8400 J= 3.1700 K= 3.5000  5.200  5.150  5.100  E 0) 0)  5.050  5.000  4.950  0.000  0.030  0.060  0.090  0.120  0.150  Radius (mm)  Figure 6.20 Effective strain distribution at different reductions with a starting particle spacing of 120 jim: (a) 33%  Chapter 6 Microstructural Analysis of the PRMMC during Large Deformation  2.710  Elf. Skan Obje #2 A= 0.20000 B= 0.53000 C= 0.86000 D. 1.1900 E= 1.5200 F 1.8500 G= 2.1800 H= 2.5100 I 2.8400 .1= 3.1700 K= 3.5000  2.670  2 -C 0)  2.630  2.590  2.550  0.030  0.060  0.090  0.120  0.150  Radius (mm) Figure 6.20 Effective strain distribution at different reductions with a starting particle spacing of 120 pm: (b) 65% Mean Stress (MPa) Obje I 2 A= -300.00 B= -268.00 C= -236.00 0= -204.00 E= -172.00 F= -140.00 G= -108.00 H= -76.000 1= -44.000 .J=-12.000 K= 20.000  5.150  5.100  2 0)  Obel 4# 5 A= -120.00 B= -102.00 C= -84.000 0= -66.000 E= -48.000 F= -30.000 G= -12.000 H= 6.0000 1= 24.000 J= 42.000 K= 60.000  5.050  5.000  4.950  0.030  0.060  0.090  0.120  0.150  Radius (mm) Figure 6.21 Mean stress distribution in the matrix and in the two particles under different reductions with the initial particle spacing of 120 pm: (a) 33%  123  Chapter 6 Microstructural Analysis of the PRMMC during Large Deformation  Mean Stress (UPa) Objed# 2 Am -300.00 8= -268.00 Cm -236.00 0= -204.00 E. -172.00 Fm -140.00 Gm -108.00 H. -76.000 1 -44.000 .3. -12.000 K= 20.000  2.710  E E  2.670  0) 0) 2.630  2.590  2.550  124  -  D  0.000  0.030  0.060  I  I-  0.090  0.120  -  I  Obed1 4# 5 Am -120.00 B. -102.oo C. 84.000 0. -6&000 E= -48.ooo F= -30.000 G= -12.000 H= 6.0000 1= 24.000 .3= 42.000 K. 60.000  0.150  Radius (mm)  Figure 6.21 Mean stress distribution in the matrix and in the two particles under different reductions with the initial particle spacing of 120 pm: (b) 65% 3.5 3 V 0 V  x o  2.5 c]  2  No Particle 20Microns 40 Microns 120 Microns  X<  ‘.4-  1.5  0  1  I  2.6  2.65  2.7  I  I  I  2.75  2.8  2.85  I  2.9  Distance from surface of the bottom anvil (mm)  (a) along the center line of the specimen  2.95  3  Chapter 6 Microstructural Analysis of the PRMMC during Large Deformation  125  2.2  I  2 1.8 1.6  No Particle 20 Microns —x— 40 Microns —D —l20Microns  I  .  1.4 1.2  0.4  0.2  0  I  I  0.6  0.8  Distance from center line to the bulge surface (mm)  (b) along the mid-plane between two particles in radial direction Figure 6.22 Effect of particle spacing on strain distribution at a reduction of 65%  10  I I  Measwed  z  FEM  8  6  4  zzz 2  0  0  2  3  4  5  6  9  Displacement (mm) Figure 6.23 Comparison of predicted value with measured data  10  1  Chapter 6 Microstructural Analysis of the PRMMC during Large Deformation  126  6.4 Model Validation For validation of the model predictions, the final geometry of the simulated cylindrical test specimen was measured. Table 6.4 shows the final maximum diameter measured and predicted during compression, which suggests barreling. Table 6.4 Comparison of model predictions with measured data  It is seen that the predictions are in very good agreement with the measured data. This can be further validated by comparison of the load-displacement curve for the monolithic model with the measured data (Fig. 6.23).  6.5 Conclusions Based on the above micromechanical analysis, some conclusions can be drawn on particle behavior in MMCs during large hot deformation. 1) Large deformation leads to more severe localized deformation around the particle, and also to particle rotation and migration. The particle migration during large deformation helps break clusters and heal the fractured particles; 2) The stress value in a particle is not very sensitive to strain during hot deformation. Therefore, particle fracture may occur at a very small strain, if the stress in a particle is large enough; 3) The shape of a particle has a large effect on fracture of both the particle and its surrounding matrix under large deformation, and particles with sharp corners and large aspect ratios have the greatest propensity to fracture;  Chapter 6 Microstructural Analysis of the PRMMC during Large. Deformation  127  4) Particle fracture is not very sensitive to the size of equiaxed particles; however, it is known that the probability of particle fracture is a function of the probability of finding a flaw in the particle and the probability of activating a flaw. Apparently, larger particles may have a high frequency of flaws. Because this effect has not been considered in this work, it is still  true that large particles may have higher probability to fracture during large deformation. 5) Small particle spacing results in a complex stress state in the cluster zone. However, as the particle spacing increases, the interaction between particles decreases. The tensile stress generated in the interparticle zone in the flow direction may cause void formation during deformation or promote void growth if the voids are present while the hydrostatic  pressure may help stop void formation and growth. 6) Localized particle deformation does not affect the macroscopic performance of the material. Therefore, a phenomenological constitutive law of the MMCs characterizes the macroscopic behavior of the material.  128  Chapter 7 PARTICLE FRACTURE OF THE PRMMC DURING EXTRUSION Commercial exploitation of MMCs is dependent on the reproducibility of properties  and achieving high productivity at minimum cost. Thus, controlling the fracture of particles during extrusion of the PRMMCs is of interest. Particle fracture is a potential defect if associated with void formation: notably the modulus of the resultant extrudate could be deleteriously affected. However, if void formation is suppressed, then benefits in terms of mechanical properties may result from the increased homogeneity of particle distribution, and  from a decrease in particle size. The fracture of particles during cold deformation has been extensively investigated 8951 but the systematic examination of fracture during hot ’ t7778 over the past few years  deformation has received little attention. Furthermore, deformation to high strain at low temperature has been limited by the low failure strain of the MMCs. Therefore, there are features of low temperature deformation which are expected to relate to deformation under conditions characteristic of extrusion. Particle fracture occurs owing to the inability of the material to accommodate local stresses. Fracture at low temperature is related to strain, 61 (see also Section 8.2 for the micromechanical analysis) ratio 7 ’ particle size, particle aspect 175 . The superimposed hydrostatic pressure during deformation extends ” 1 and volume fraction . Under such circumstances matrix 90911 the ductility, and effectively inhibits void foniation” material may also flow into the voids between fractured particles under large deformation.  To elucidate the nature of particle fracture during the hot extrusion process, the microstructure of the composite in the deformation zone and of the extrudates of  Chapter 7 Particle Fracture of the PRMMC during Extrusion  129  /lOp and 6061/A1 3 O 2 6O611A1 /20p was examined, i.e., particle distribution, size refinement, 3 O 2 and orientation and migration of particles were characterized.  7.1 Specimen Preparation for the PRMMCs A specimen of area about lOxlO cutting wheel blade.  was cut using either a hack saw, or a TiV  The specimen was mounted and polished in an automatic polishing  machine. The detailed polishing procedure adopted at KRDC, Kingston, is listed in Table 7.1.  Table 7.1 Polishing procedure for Duralcan materials at KRDC Step 1  Paper/Cloth SiC paper  Grit Size  Time  (jim)  (mm.)  Grit 120  until  Lubricant  Load  Remark  (N) water  100  flat  Struer’s blue  80-  flat with less  lubricant  100  scratches  Struer’s blue  100  more shinny  100  less scratches  100  very few scratches  100  clean boundary  flat 2  Petrodisk  15  10  Diamond plate 3  Perforated  15  10-15  cloth  4  Perforated  lubricant 3  10  cloth 5  Pan W  lubricant 3  5  polishing cloth 6  OP Chem. fmal polishing cloth  Struer’s blue Struer’s red lubricant  0.05  1-2  Colloidal Si0 2 suspension  around particles  11001 was adopted for the automatic Another polishing procedure modified from Newell polishing machine at UBC, as listed at Table 7.2. A very clean background resulted following polishing for both procedures, which was necessary for microstructural analysis, especially  Chapter 7 Particle Fracture of the PRMMC during Extrusion  130  image analysis. The last step was quite effective to clean the boundaries between the matrix and the particles.  Table 7.2 Polishing procedure used at UBC for Duralcan materials Step  Paper/Cloth  Grit Size  Time  (pm)  (miii.)  Lubricant  Pressure  Remark  (psi)  1  SiC Paper  180  3  Water  30  overall flat  2  SiC Paper  320  3  Water  30  flat  3  SiC Paper  500  3  Water  30  flat with less scratches  4  SiC Paper  1000  3  Water  30  less scratches  5  Texture Paper  6 tm  10  Diamond  30  few scratches  30  very few  suspension 6  Texture Paper  3 .tm  5  DPsuspension  7  OP Chem. final polishing cloth  0.05 urn  1-2  Colloidal 2 Si0  scratches 30  clean boundary around particles  suspension  7.2 Macroscopic Examination of Metal Flow in the Deformation Zone Macro-examination of metal products can reveal the grain size and shape as well as 03/20p from the trial of 2 fabricating or casting defects. An end-of-extrusion billet of 6061/A1 S92-3, 184 mm in diameter, was sectioned by a hacksaw along the extrusion direction. The extrusion conditions are listed in Table 7.3 for convenience. Mixed-acid etchants are excellent for revealing grain size, shape, and contrast. The 3 etchant used for the composite was a mixed solution of lOmi HC1 (concentrated), 3Oml HNO 961 The solution was mixed just before use. The 3 FeCl 0, and 5g . 2 (concentrated), 2Oml H  Chapter 7 Particle Fracture of the PRMMC during Extrusion  131  longitudinal section of the billet was first ground on SiC paper (Grit 60  -  600), and then was  immersed at room temperature into the solution for a few seconds, rinsed in cold water, and repeated until the desired effect was obtained, as shown in Fig. 7.1. Table 7.3 Extrusion conditions of the Trial S92-3 of 6061/A1 /20p 3 0 2 Billet Temperature (°C)  429  Billet Diameter (mm)  178  Extrudate Diameter (mm)  32  Extrusion Ratio  33.6  --------;  .  c;_____•_•  Figure 7.1 Metal flow of a billet in a container A dead metal zone existed at the corner between the die and the container, and a shear zone showed up between the dead metal zone and the deformation zone. The accumulation of the metal at the corner of the pressure pad and the container was probably due to the sticking friction at the container interface. Some porosity was also observed at the etched surface.  132  Chapter 7 Particle Fracture of the PRMMC during Extrusion  More detailed metal flow of the billet was examined by an optical microscope with a magnification of 50X. The zones examined in the billet are schematically shown in Fig. 7.2.  Pressure Pad End  4  Deformahon Zone  2’. 5 Sheai Zone  8  ‘.6  9  3  i  -. -  I  -  -  Dead Zone  I  Die Exit Figure 7.2 Schematic positions for the pictures taken with low magnification The metal flow at each location is shown in Fig. 7.3.  At Location 1, the matrix  material has accumulated due to sticking friction at the interface between the billet and the container. A localized material flow pattern near the gap between the pressure pad and the container is revealed in Fig. 7.3 (Location 1). At Location 2, in the shear zone, the metal flow along the shear boundary is clearly shown. However, in the dead metal zone there is little metal flow (Location 3). At Location 4, only a small tendency of metal flow in the downward direction can be seen. Metal flow lines are clearer in Location 5, in the deformation zone; here the flow lines approach the horizontal direction near the die interface (Location 6). At the center line of the deformation zone, due to axisymmetry, metal flows close to the extrusion direction, and the tendency increases from under the pressure pad (Location 7) to the die entry (Location 9). Locations 4 and 7, under the pressure pad, a hard-to-deform zone exists.  At  Chapter 7 Particle Fracture of the PRMMC during Extrusion  Eii  Figure 7.3 Metal flow in the deformation zone during extrusion  133  Chapter 7 Particle Fracture of the PRMMC during Extrusion  134  The metal flow pattern shown here is consistent with experimental observation by other researchers , and also, qualitatively, with the velocity vector distribution of the FEM 1211 model prediction in Chapter 5.  7.3 Particle Fracture during Extrusion A microscopic study of particle fracture and particle distribution was conducted both qualitatively, using an optical microscope, and quantitatively using an image analyzer. The dynamic behavior, such as recoveiy and recrystallization, which occurs in the hot extrusion process, is beyond the scope of this project. 7.3.1 Qualitative Microstructure Analysis  7.3.1.1 Particle Deformation Behavior in the Deformation Zone The other half of the butt-end was divided into several small sections on a cutting machine with a Ti-V wheel blade, and 9 samples from the longitudinal section, with an area of about lOxlO  2  ,  were polished at UBC for micro-examination. The location of the 9  samples in the billets inside the container are schematically shown in Fig. 7.4.  Pressure Pad End 7  1  4  Deformation Zone 8  5  2  6  3—  Sh&ir Zone Dead Zone  -  9  Die Exit Figure 7.4 Schematic positions for the pictures taken for micro examination  Chapter 7 Particle Fracture of the PRMMC during Extrusion  135  The particle distribution and particle fracture behavior for each sample, located in different zones, was investigated under an optical microscope. At Location 1, the upper right corner of the billet where there is contact with the pressure pad and the container, a “particlefree” zone (with a small number of particles) was formed (see Figs. 7.1 and 7.3). This is the result of accumulation of the matrix material near the gap between the pressure pad and the container: during extrusion, as the pressure pad pushes the bifiet forward, the matrix material adheres to the container, while the particles in the subcutaneous layer of the billet were pushed forward. As a result, matrix material accumulated at the corner. Very few particles were trapped in this ‘particle-free’ zone. Beside this large ‘particle-free’ zone, more particles were found but still with lower local volume fraction compared to other locations, as shown in Location 1, Fig. 7.5(a). Roughly a 1-mm thick particle-free layer at the billet surface was observed at Location 2 (r  =  ). The formation of this layer was again a result of adhesion with the container. At 0 R  the intersection of the shear boundary and the container interface (See Fig. 7.1), part of this layer began to flow into the shear zone along the shear boundary to form a particle-free band during extrusion.  it is this particle-free band that outlined the dead metal zone in the  macroetched butt-end (Fig. 7.1). In the adjacent zone, severe particle fracture was evident due to large shear deformation (Location 2, Fig. 7.5 (a)).  Most of the particles were  orientated along the shear direction. All the large particles that did not crack were found to have a regular shape with an aspect ratio close to unity, which implies that equiaxed particles are harder to fracture even with a larger diameter(Location 2, Fig. 7.5 (a)).  This result  confinns the predictions of the effect of particle shape on particle fracture in the micromechanical analysis in Chapter 6. With a —1 mm thick particle-free layer being also  Chapter 7 Particle Fracture of the PRMMC during Extrusion  136  present at the billet surface in the dead metal zone (Location 3), a conclusion can be drawn  that during hot extrusion of particle reinforced MMCs, a particle-free layer is formed at the interface of the billet and container because of adhesion, and part of the matrix material in this layer flows into the shear zone to form a particle-free band in the shear direction. In the dead metal zone, all the particles were distributed with no preferred orientation and had a similar spatial disthbution to those in the as-cast composites. Fractured particles were occasionally observed but not separated as in the shear deformation zone, i.e., the particles were just cracked (Location 3, Fig. 7.5(a)). Mid-way between the container interface and the center line of the billet  (r  Ro/2)  under the pressure pad (Location 4), it was observed that fewer particles were fractured due to formation of the ‘hard-to-deform’ zone, and particle clusters also remained (Location 4, Fig. 7.5(b)). Fewer clusters, but more fractured particles, were observed in the region below the ‘hard-to-deform’ region, as deformation increased. Particles were orientated towards the direction of metal flow (No. 5, Fig. 7.5(b)). At Location 6, which included both a part of the deformation zone and a part of the dead metal zone, a ‘particle-free’ band was also observed in the shear zone with more particles present than in the up stream band. Due to the low local volume fraction of the particles in this band, no extensive particle fracture was observed. However, in the adjacent zone, more fractured particles were found due to the large shear deformation, as seen in Location 6, Fig. 7.5 (b). Moreover, particles in the shear zone tended to align in the shear direction. At the top surface zone around the center line (r  =  0) of the billet (Location 7), some  particle clusters remained, as observed at Location 4, with similar particle distribution to the as-cast products. However, fractured particles in clusters were observed occasionally because  Chapter 7 Particle Fracture of the PRMMC during Extrusion  137  Figure 7.5 (a) Typical particle distribution in the Locations 1, 2 and 3 (‘P.C.’= particle cluster ‘P.F.Z.’=particle-free zone; ‘P.P.B.’—particle-free band; ‘S.D.’=shear direction)  Chapter 7 Particle Fracture of the PRMMC during Extrusion  Figure 7.5 (b) Typical particle distribution at the Locations 4,5 and 6 (‘P.C.’ particle c1uster ‘P.F.Z.’=particle-free zone; ‘P.F.B.’—particle-free band; ‘S.D.’=shear direction)  138  Chapter 7 Particle Fracture of the PRMMC during Extrusion  139  iF1  N ,  Figure 7.5 (c) Typical particle distribution at the Locations 7,8 and 9 .D.’= extrusion direction) 4 (‘P.C.’= particle cluster; ‘PEZ.’—particle-free zone; ‘P.F.B.’=paiiicle-free band; B  Chapter 7 Particle Fracture of the PRMMC during Extrusion of local tn-axial stresses (Location 7, Fig. 7.5 (c)).  140  The most obvious characteristics at  Location 8 were the alignment of the particles and the formation of particle-free bands along the extrusion direction. This is due to axisymmetnic material flow which forces particles to align in the extrusion direction and also elongates the particle-free zones in the cast material to form the ‘particle-free’ bands (Location 8, Fig. 7.6(c)). It was interesting to note that although some cracks in the deformation zone align along the flow direction due to shear stress, other cracks perpendicular to the flow direction were observed, especially for those particles with a large aspect ratio. This is a result of load transfer from the matrix to the particle along the flow direction, which generates tensile stresses in the particle (See Chapter 8). If the tensile stress exceeds the fracture stress of the particle, it cracks perpendicular to the flow direction. Near the center line at the die entry, alignment of particles and particlefree bands along the extrusion direction were even more obvious. However, at positions off the center line, particles were aligned not in the extrusion direction, but in the flow direction. Near the die throat, more small particles were found which implies severe particle fracture due to shear deformation (Location 9, Fig. 7;5(c)). It is worth pointing out that all the features described above in the deformation zone are a summary of an overall examination of the sample at each location. However, they all could not be shown in one typical picture for each location, as in Fig. 7.5.  7.3.1.2 Microstructure Analysis of the Extrudates Two samples of each extrudate were cut from both the front end (named “F’) and the back end (named “B”). Caution was taken when each piece was sectioned along the extrusion direction using a Ti-V wheel blade, as shown in Fig. 7.6. All the specimens were polished at UBC following the procedure listed in Table 7.2.  The particle distribution in both the  Chapter 7 Particle Fracture of the PRMMC during Extrusion  141  transverse section (perpendicular to the extrusion direction) and the longitudinal section (parallel to the extrusion direction) was examined by an optical microscope. The samples examined are listed in Table 7.4.  Extrudate Sample  Transverse  Longitudinal  Figure 7.6 Schematic of examined extrudate specimen  Table 7.4 List of examined extrudates with two different cross-sections Sample  Cross  6061  Name  Section  Alloy  (W6A20)  (W6A1O)  S92-2  592-3  S92-6  Trial No.  606 11A1203120P 60611M203110P  Front End  Transversal  F2-T  F3-T  F6-T  Front End  Longitudinal  F2-L  F3-L  F6-L  Back End  Transversal  B2-T  B3-T  B6-T  Back End  Longitudinal  B2-L  B3-L  B6-L  A. Comparison of Microstructure in Longitudinal and Transverse Sections Based on the optical microscopic examination of transverse and longitudinal sections /20p, some typical characteristics of the particle distribution 3 of the extrudates of 606l/AlO in the transverse section of the specimen are summarized: (1) particles were randomly oriented, i.e., with no preferred orientation; (ii) particle size was non uniform;  Chapter 7 Particle Fracture of the PRMMC during Extrusion  (a) Transverse  (b) Longitudinal I2Op 3 O 2 Figure 7.7 Typical characteristics of particles after extrusion of 606 l/AI at an extrusion ratio of 34  142  Chapter 7 Particle Fracture of the PRMMC during Extrusion  143  (iii) many small particles were observed; (iv) particles were quite uniformly distributed.  The particle distribution in the transverse  section with some of the above features is shown in Fig. 7.7(a). In the longitudinal section, some salient features are summarized as: (i) most of the particles with a large aspect ratio were aligned in the extrusion direction; (ii) fractured particles were found in clusters; (iii) equiaxed particles (i.e., aspect ratio of the particle is close to unity) were harder to crack; (iv) for the situations where a single particle positioned between two large particles, the middle particle had a high tendency to fracture; (v) more extensive particle fracture was observed in the longitudinal section; however fractured particles seemed to have healed with intrusion of the matrix material into the resulting gap under high hydrostatic pressure, or because fractured pieces were shifted by local metal flow during shear deformation; (vi) most of the cracks (the gap between two fractured parts) were in the extrusion direction. This was due to the fact that particles were fractured in the shear deformation zone and finally rotated into the extrusion direction, if these cracked parts had not been shifted sufficiently far apart. A typical particle distribution with some of the above features is shown in Fig. 7.7(b).  B. Comparison of Microstructure for 6061/A1 110p 3 0 2 /20p and 6061/A1 3 0 2 For the extrudates of 6061/Al /lOp, similar characteristics of particle fracture to 3 0 2 the 606 11A1 /20p were also recognized (Fig. 7.8), such as: 3 0 2 (i) particles were also randomly oriented in transverse section, but aligned in the extrusion direction in the longitudinal section;  Chapter 7 Particle Fracture of the PRMMC during Extrusion  (a) Transverse  (b) Longitudinal IlOp 3 Figure 7.8 Typical characteristics of particles after extrusion of 606 lIAlzO at an extrusion ratio of 34  144  Chapter 7 Particle Fracture of the PRMMC during Extrusion  145  (ii) multiple fracture was observed from large particles with a high aspect ratio and those in clusters. The salient features of the microstructure of the extrudates of 606 1/AlO3/10p compared to 6061/Al203/1OP are: (i) particle size was much smaller than that in the 606l/A1O3/20p, and the size distribution  was more uniform; (ii) large particle-free zones in the transverse section and particle-free bands were more frequently observed in the longitudinal section due to the small volume fraction and non uniform distribution of particles in the cast billet. The ratio of the length to the width of the bands in the longitudinal section was measured under the microscope and found to lie in the range of 20 to 27, which is comparable to the extrusion ratio of 34. This implies that the formation of the particle-free bands are most probably due to elongation of the particle-free zone in the as-cast billet;  (iii) more clusters remained after extrusion; (iv) although the aspect ratio change is not as obvious, most of the small particles have an aspect ratio close to one. For the extrudates of the aluminum alloy, 6061, many precipitates were present, most of which were MgSi. It was found that the size of the precipitates was around one micron  and they were quite uniformly distributed throughout each section.  In the longitudinal  section, the precipitates were aligned in the extrusion direction. These precipitates were also present in the composite extrudates, though not visible at the magnification shown in Fig. 7.7  and 7.8.  Chapter 7 Particle Fracture of the PRMMC during Extrusion  146  7.3.2 Image Analysis of Particle Distribution in Extrudates An image analyzer was used to quantify the particle size and orientation. The particle size was measured in terms of particle area and maximum and minimum diameter.  The  particle area was defined as the cross sectional area of a particle on the polished surface, while the maximum and minimum diameter were defmed as the longest and the shortest dimension of a particle on the polished surface, respectively.  In addition, particle aspect ratio and  orientation were also measured. The particle aspect ratio was defmed as the ratio of the maximum diameter to the minimum diameter, and the orientation of a particle was determined by the angle from the direction of its longest axis with respect to a specified direction, e.g., the extrusion direction in the longitudinal section. Thus, if the angle was zero degree, the particle was considered as aligned in the extrusion direction. A total of more than 2000 particles were measured for a relative error in the measurements of less than ±5% with 95% confldence . 971 7.3.2.1 Homogeneity of Particle Distribution The homogeneity of particle distribution is difficult to characterize quantitatively. However, the variation of local volume fraction in the composites could be a measure of the uniformity of particle distribution. A particle-free zone results in a zero local volume fraction, while a field full of clusters might approach 100% local volume fraction in extreme conditions. Apparently, a uniform distribution of particles would lead to a small range of variation in the local volume fraction. The local volume fraction from position to position was measured using a Letiz Image Analyzer. A total of 500 fields were examined. The local volume fraction varied from 5% to 29% for the extrudates of 6061/Al 110p. The frequency of local volume fractions in the 3 0 2 range of 1% to 30% is shown in the histogram in Fig. 7.9 for the extrudate of  Chapter 7 Particle Fracture of the PRMMC during Extrusion  147  /lOp for both the transverse and the longitudinal sections. The mean volume 3 O 2 606 1/A1 fraction for the transverse section and longitudinal section were calculated to be 12.48% and 14.52%, respectively. The corresponding standard deviations were 2.34% and 3.52%, and the relative coefficients were 0.1875 and 0.2424, respectively, which is defined as the ratio of the standard deviation to the mean value. Obviously, the distribution of the particles in the 606 l/A1 03/lOp composite is non-uniform, and the non-uniformity in the longitudinal section 2 is even more than in the transverse section based on the standard deviation and relative coefficient values. This is due to the band formation in the longitudinal section. The histogram of the volume fraction for the extrudate of 606 l/A1O3/20p in Fig. 7.10 shows that the variation of local volume fraction varied from 13% to about 35%. The mean values of the volume fraction in the transverse and longitudinal sections are 24.52% and 24.45%, respectively, while the corresponding standard deviations are 3.74% and 4.05%, with the relative coefficients being 0.1525 and 0.1656, respectively.  The values of relative  coefficients indicate that, firstly, the particle distribution for the 6061/A1203/20P is more /l0p (Table 7.5); secondly, the particle distribution in the 3 uniform than in the 606l/A1O transverse section is more uniform than in the longitudinal section for both volume fractions. However, all the measured values of the volume fractions were larger than the nominal values, as the designation indicates. Table 7.5 Statistical results for volume fraction distribution of the two composites  606 1/A1203120P  / lOp 3 0 2 606 1/A1 Mean Value  Standard Deviation  Relative  0.188  24.52  3.74  0.152  0.242  24.45  4.05  0.166  Mean Value  Standard Deviation  Relative  Transverse  12.48  2.34  Longitudinal  14.52  3.52  Section  (%)  (%)  Coeff.  (%)  (%)  Coeff.  Chapter 7 Particle Fracture of the PRMMC during Extrusion  148  9O 80  •B6-T  70  0B6-L  60  50  I  I -:  1357911131517192123252729  Volume Fraction (%) /lOp 3 0 2 Figure 7.9 Histogram of volume fraction for 606 1/Al  60 50 40 30  11  13  15  17  19  21  23  25  Ii  27  B3-T  L0 B3-L  11, 1 n 29  31  33  35  Volume Fraction (%) Figure 7.10 Histogram of volume fraction for 606l/A1O3/2Op  37  39  Chapter 7 Particle Fracture of the PRMMC during Extrusion  149  7.3.2.2 Particle Size To evaluate the particle size variation in the composites after extrusion, the dimensions of a particle in terms of its area, maximum and minimum diameter (dimension) were measured. The details of the measurements with statistical analysis are listed in Table 7.6. A. Particle Diameter The histograms of the maximum diameter and minimum diameter for B3 (Back end of  I2Op) and B6 (Back end of 3 O 2 the extrudate S92-3: 6061/AI /lOp) are shown in Figs. 7.11 and 7.12. 3 O 2 606 l/A1  the extrudate S92-6:  From Fig. 7.11, it is seen that the  variation of the maximum diameter in a total count of about 2000 particles in B3 is from 50.0 .Lm to 3.3p.m, while the minimum diameter varies from 1.67pm to 44pm. However, the mean values of both the maximum and minimum diameter are larger in the longitudinal section than  /lOp (B6), in Fig. 7.12, it is 3 0 2 in the transverse section, as seen in Table 7.6. For 60611A1 seen that the range of the variation of the maximum diameter is from about 3.tm to 28j.tm and the minimum diameter from 1.3Jm to 15pm, which is almost half of the values of the particles I2Op (B3 and F3). Similar to the 20% composite, the mean values of both the 3 O 2 in 606 1IAI maximum and minimum diameter of the particles are larger in the longitudinal section than in the transverse section for the 10% composite, as seen in Table 7.6. B. Particle Area The variation of particle area may reflect the particle size distribution in the composites more directly. Figure 7.13 shows the particle area distribution for the same count of particles in the extrudate of 606 l/A1203120P at the back end. It is seen that there is a large —l6jim to 480 urn variations in the particle area, from 2 . 2  Again, the mean value of the  particle area in the longitudinal section are larger than those in the transverse section, which is  Chapter 7 Particle Fracture of the PRMMC during Extrusion  150  200 180 160 140  • B3-T E  120  D  100  B3-L  iiIl  880  1.67  11.69  6.68  16.7  21.71 26.72 31.73 36.74 41.75 46.76  Maximum Particle Diameter (Micron Meter) (a) Max. Diameter  400 350  300  250  Ln.L  200 0150 100 :  0  1.67  6.68  9  11.69  16.7  I  -  21.71 26.72 31.73 36.74 41.75 46.76  Minimum Particle Diameter (Micron Meter) (b) Miii. Diameter 0il20p 2 Figure 7.11 Histogram of the particle diameter for Sample B3 of 606 l/A1  Chapter 7 Particle Fracture of the PRMMC during Extrusion  151  350 300  250  1Iii  200  8150 ma  1.33  D1B&L  3.99 6.65  12  9.31  14.6  17.3  20  22.6  25.3  27.9  Maximum Diameter (Micron Meter) (a) Max. Diameter  600  ii  500  200  1C 1.33  3.99  ILi ,I [I  6.65  •B6-T  9.31  11.97  14.63  17.29  19.95  Minimum Diameter (Micron Meter) (b) Min Diameter IIOp 3 O 2 Figure 7.12 Histogram of the particle diameter for Sample B6 of 6061/AI  22.61  Chapter 7 Particle Fracture of the PRMMC during Extrusion  350 300 250 200  I11111L I  16  49  81  152  •B3-T DB3-L  liii  1  114 146 179 211 243 276 308 341 373 406 438 471  Part1ce Area (Square Micron Meter) /2Op 3 O 2 Figure 7.13 Histogram of the particle area for Sample B3 of 606 l/A1  450 400 350 300  I I•B6-T [IB6L  50 C 2  8200 150 100  i9  8.6 26  43  I hhl1r-thI  60  78  95  ‘ti -i -i  —i  i  112 129 147 16.4 181 198 216 233 250  Particle Area (Square Micron Meter) /lOp 3 0 2 Figure 7.14 Histogram of the particle area for Sample B6 of 6061/A1  Chapter 7 Particle Fracture of the PRMMC during Extrusion  153  Table 7.6 Statistical results for the quantitative metaflography MMC  No. of  Particle Area  Max.Diameter  Min.Diameter  Particles  ) 2 (.tm  (pm)  (pm)  Mean Value Location 4 inFig.7.4 (S92-3) Location 7 inFig.7.4 (S92-3) B3-T  2259  179.79  2256  161.63  2282  134.09  B3-L  2508  174.07  F3-T  3269  136.90  F3-L  2020  161.59  B6-T  2137  34.37  B6-L  2245  44.16  F6-T  1965  31.20  F6-L  3004  38.54  Mean Std. Dev. I Value Rel. Coeff 140.21 21.61 / 0.780 132.43 20.83 / 0.819 122.52 17.97 I 0.914 143.27 19.57 I 0.823 124.37 18.62 I 0.908 140.19 20.17 I 0.868 24.67 8.75 I 0.718 33.34 10.17 I 0.755 22.04 8.64 I 0.706 35.54 8.99 I 0.922  Std. Dev. / Rel. Coeff 9.94 I 0.460 9.73 / 0.467 9.47 / 0.527 11.23 / 0.574 9.60 / 0.516 10.65 / 0.528 3.72 / 0.425 4.27 I 0.420 3.66 I 0.424 4.56 I 0.507  Mean Value 12.12 11.23 10.07 11.43 10.14 11.50 5.55 6.16 5.13 5.71  Std. Dev. / Re!. Coeff 5.99 I 0.494 5.73 / 0.510 5.24 / 0.520 6.73 I 0.589 5.20 I 0.513 6.44 / 0.560 2.19 I 0.395 2.45 / 0.398 2.06 / 0.401 2.72 / 0.476  Aspect Ratio Mean Value 2.01 2.12 2.00 1.99 2.07 1.99 1.77 1.87 1.92 1.75  Std. DevJ Re!. Coeff 0.59 / 0.294 0.66 I 0.311 0.56 / 0.280 0.55 / 0.276 0.62 / 0.300 0.57 / 0.286 0.47 I 0.266 0.54 / 0.289 0.57 I 0.297 0.47 / 0.269  Note: ‘Rel. Coeff.’ in the table is a relative coefficient which is defined as the ratio of standard  error to the mean value.  Chapter 7 Particle Fracture of the PRMMC during Extrusion due to the re-orientation of particles along the extrusion direction.  154 The variation of the  particle area for the 6061/AlO3/lOp is from 8.6p.m 2 to around 2 20Oim (Fig. 7.14). The mean value of the particle area is about 4 times less than that of the 6061fAlO3I20p (Table 7.6). This is principally due to different initial range of particle sizes adopted in the fabrication of the composites.  7.3.2.3 Aspect Ratio of Particles The aspect ratio of a particle is defmed as the ratio of its maximum dimension to its minimum dimension.  The distributions of aspect ratio in the two samples with different  volume fractions are shown in Figs. 7.15 and 7.16. It is seen that the variation of the aspect ratio is from 1.2 to 4.5 for both materials.  The mean aspect ratio in extrudates for the  /20p is around 1.99 to 2.07, while the aspect ratio for the 6061/Al 3 0 2 6061/A1 /lOp is 3 0 2 around 1.75 to 1.92 (Table 7.6), which confirms the observation that more particles have an aspect ratio close to unity in 6061/A1203/1OP. The relative coefficients (Table 7.6) of the particle size (e.g., area, diameters) are generally smaller for 6O6l/Al /lOp than for 3 0 2 /20p, which also confirms that the particle size is more uniform in extrudates of 3 0 2 6061/A1 /20p, because the particle size is smaller. 3 0 2 606 l/AlO3/l0p than in 606 l/A1  Chapter 7 Particle Fracture of the PRMMC during Extrusion  155  350 300  • B3-T  250 200  B3-L  8150  I  I  0.15  I  I  I  I  1.05  0.6  1.5  I  I  1.95  II1Ih:  2.4  2.85  3,3  4.2  3.75  Aspect Ratio /20p 3 Figure 7.15 Histogram of the aspect ratio for Sample B3 of 606 1/AlO  • 400 •B6-T 300 ÷...  []B6-L  250  8150 100 I  I  I  I  -H -Ii  I  0.2 0.5 0.8 1.1  1.4 1.7  2  2.3 2.6 2.9 3.2 3.5 3.8 4.1  Aspect Ratio Figure 7.16 Histogram of the aspect ratio for Specimen B6 of 6061/AlO3/10p  4.4  156  Chapter 7 Particle Fracture of the PRMMC during Extrusion  7.3.2.4 Partide Orientation Orientation of the particles with respect to extrusion direction was also analyzed with the Leitz Image Analyzer. The extrusion direction was set to be 0° or 180°. The entire range from 0° to 1800 was divided into 12 groups, with the group width being 150. The frequency of the particle orientation with respect to its maximum dimension in the different groups for the extrudates is shown in Figs. 7.17 and 7.18. It is obvious that particles in the transverse section have no preferred orientation, because the frequencies (counts) of the orientation for each class are similar. However, higher frequencies of the particle orientation in 0 to 300 and 165 to 1800 were measured in the longitudinal section, which means the particles in the  longitudinal section are aligned in the extrusion direction. These measurements are consistent  with the microscope observations (Figs. 7.7 and 7.8). 600  500 -4-  400  C  300 (-) 200 100 0 15  30  45  60  75  90  105  120  135  150  165  180  Orientaion w.r.t. Extrusion Direction Figure 7.17 Histogram of orientation of the particles with respect to extrusion direction /20p 3 0 2 for the Sample B3 of 606 l/Al  Chapter 7 Particle Fracture of the PRMMC during Extrusion  157  450 400 350 300 250 200 150 100  8  50  0  15  30  45  60  75  90  105  120  135  150  165  180  Orientation w.r.t. Extrusion Direction Figure 7.18 Histogram of orientation of the particles with respect to extrusion direction IlOp 3 for the Sample B6 of 606l/AlO  7.4 Particle Fracture Model during Extrusion 7.4.1 Particle Fracture Probabifity at High Temperature Particle fracture has been observed during the extrusion process; and this results in particle size refinement. There are two factors which are known to determine particle fracture and its influence on material properties in service: local stress ( related to imposed strain at low temperature), and hydrostatic pressure, which is obviously of importance during , (see also 1 extrusion. At low temperature the probability of fracture is correlated to str in’ Eq. 7.1), whereas, at high temperature it is expedient to correlate fracture to the Zener Holloman parameter and its time effect, as it is the Zener-Holloman parameter that determines the flow stress of the matrix material during hot extrusion.. e) =1—exp(D a Pr 3  (7.1)  Chapter 7 Particle Fracture of the PRMMC during Extrusion  158  If the particle fracture process is stochastic, then the fracture probability can be derived to predict the particle size refinement during hot extrusion. pf  =  D3aZ)dt) 1 1_exp(J(_3  (7.2)  where f3 is a constant with the unit being [1/jim ], and detennined by quantitative 3 microstructure analysis; D is the volume equivalent particle diameter, [jim]; particle aspect ratio; and Z = eexp(Q/RT), [us].  (X  is the mean  It is noted that dt considers the  accumulation effect of particle fracture in the extrusion process. The term —3 aZ reflects 3 D 1 the flow stress level, which controls the particle fracture process, and also represents the fracture rate during extrusion [b03j• In the subsequent section, this fracture probability will be applied to the hot extrusion process to calculate the particle size refinement.  7.4.2 Particle Fracture Model during Extrusion It was observed that particles undergo multiple fracture. Hence, the assumption that a 761 may require re-evaluation for a ’ 75 halves particle fractures into two approximately equal , model of particle fracture under extrusion conditions. In the case under evaluation, it would seem that this assumption denies the evidence of a large increase in small particles.  To  estimate the average number of parts formed from a single particle fracture event, a total number of around 50 counts of a single particle fracture event was made for both transverse and longitudinal section of an extrudate. The number of parts fractured from a single particle event (including a fracture event in a cluster) was recorded. Therefore, the average number of parts, n, formed from a single particle fracture event, is simply; (7.3) n=  N  Chapter 7 Particle Fracture of the PRMMC during Extrusion  159  where N is the number of counts, 50 in this case as mentioned above and N 1 is the number of parts counted from each fracture event.  It was found that a large single particle often  fractures into two parts with one part twice the area of the other one. However, a particle in a cluster often is crushed into 3 or more parts with equivalent size. With respect to different extrusion ratios, more fractured particles were observed at a high extrusion ratio.  The  average number of parts from a single fracture event for different sections of an extrudate at different extrusion ratios is listed in Table 7.7. It is seen that more parts are formed from a single particle fracture event in an extrudate at a higher extrusion ratio than at a lower extrusion ratio. This also implies that the higher the extrusion ratio, the larger the particle size reduction.  Table 7.7 Average number of parts fractured from a single particle in 6061/A1 /20p 3 0 2 Extrusion ratio  Longitudinal  Transverse  Both in  ofanExtrudate  (‘L’)  (‘T’)  ‘L’and’T’  64.00 (K-8)  2.78  2.44  2.63  28.80 (K-li)  2.52  2.18  2.37  10.23 (K-12)  2.42  2.22  2.24  The particle fracture probability, Pp is a function of temperature and strain rate, and is also associated with the deformation time. To determine the final fracture probability of particles at the die exit during extrusion, an integration over the deformation zone is necessary, i.e., =  af(r,z)dt t J(—i D 1 ocZ)dt = J  (7.4)  Chapter 7 Particle Fracture of the PRMMC during Extrusion  160  where af provides the fracture rate, which varies both in the radial direction, r, and in the extrusion direction, z, over the deformation zone of the billet. To simplify the numerical calculation, an average fracture rate over a cross section of the billet in the deformation zone during extrusion was determined first, i.e., the fracture rate was integrated over a cross sectional area at a certain depth, z, in the deformation zone, and was divided by the cross sectional area to obtain an average as described below. (75)  —  p=f 2af(r,z)rdr/R  where R 1 is the radius of the deformation, which is outlined by the shear zone boundary. It varies from the initial radius of the billet (R ) at the back end of the deformation zone, to the 0 radius of the extrudate (RE) at the die exit. If one assumes that a particle with a volume equivalent diameter, D, is fractured into n equally sized particles during extrusion, the volume equivalent diameter of each fractured piece is DI Th. particles, N  Because the number of broken  is the total number of particles in the  is equal to Pf * N, where  deformation zone, the mean refined particle diameter can be derived as: —  3 (D/)  —  113  —  1 (1+(,-1)p)” 3  D  (7.6)  Then, the particle size reduction at that stage is defmed as:  %=-x1OO%  (7.7)  7.4.3 Application of the Model From an image analysis of the extrudate from Trial S92-3 at UAC, Anaheim, the mean particle diameter, Dime, in the extrudate was found to be 12.41pm; while the mean size of the particle,  at the back-end of the bifiet was 13.07p.m. The mean value of the maximum  Chapter 7 Particle Fracture of the PRMMC during Extrusion  161  diameter of the particles, was 18.77tm and 21.22tm for the extrudate, D , and the billet, 1 respectively. Using Eq. (7.6), the overall fracture probability was estimated as 12.20%, and consequently the constant fi in the fracture model (Eq. 7.2) is 3.07x10 ]. Both 3 [1/pm 21 the mean particle size (diameter) and the mean value of the maximum diameter are predicted  using the DEFORM results for temperature and strain rate in the deformation zone (Table 7.8). It is evident that there is good agreement between the mean particle diameter and the mean value of the maximum particle dimension. The probability variation at each time step through the deformation zone was estimated using Eq. (7.2). Figure 7.19 shows that a maximum fracture probability is reached near the exit of the die aperture. This indicates that the most severe particle fracture occurs near the die throat by severe shear deformation due to choke of metal flow into the die aperture, which is consistent with the microstructural examination in the deformation zone. The corresponding mean particle size reduction is shown in Fig. 7.20. 100  ‘0.12 a  80 S.  60-  -  -  -  I  I I I  0  I  I  a  20 a  I  330  345  3.4  I 360  0.04 0.02  Die Throat I  .  0.06€  I  I  0315  0.08  I I  40-  0.1  I  a  Shear B’dary Probability  *  I I i—-  375  390  Depth into Deformation Zone (mm) Figure 7.19 Fracture probability variation in the deformation zone  •0 405  Chapter 7 Particle Fracture of the PRMMC during Extrusion  162  100  -  ShearB’daryl MeanDia.  8O E E  S.—  -  13.3 13.1  -12.9  60  40 125  20  --  12.3  Die Throat 0315  I  I  330  345  360  375  390  Ct i  12.1  405  Depth into Deformation Zone (mm) Figure 7.20 Particle size reduction during extrusion Table 7.8 Comparison of model predictions with measured data Mean Particle Diameter Reduction D(im)  1 mLm) D  Red (%)  pf  Measured  13.07  12.41  5.02  12.20  Model  13.07  12.39  5.19  11.02  Average Maximum Particle Dimension Reduction Doinax(i.Lm)  1 13 D m)  Red (%)  Measured  21.22  18.77  11.55  32.48  Model  21.22  17.64  1687  33.36  7.5 Discussion The particle distribution has been examined during the extrusion process. However, some questions remain.  What is the influence of the extrusion process on particle  Chapter? Particle Fracture of the PRMMC during Extrusion  163  distribution? How is a particle fractured during deformation, and what is the correlation between extrusion deformation behavior and the particle fracture?  7.5.1 Microstructure Comparison before and after Extrusion 7.5.1.1 Comparison of Particle Distribution before and after Extrusion Porosity and voids have been considered to be the most detrimental defects in cast  . 61 products  In cast PRMMC products, other defects, such as surface defects (cracks),  agglomeration and clustering may also be present. In the microstructure study conducted by Kalu and McNelley’ , it was found that Al 541 3 particles were clustered in the as-cast lOvol% 0 2 material provided by Duralcan. Similar features were found in 6061/A OillOp, shown in Fig. 2 7.2 1(a). The distribution of the particles was more uniform in a higher volume fraction, e.g., I2Op composite, as shown in Fig. 7.22(a). 3 O 2 6O61IA1  The non-uniformity is a result of  entrapment of the particles in the interdendritic regions during solidification.  These are  potential sites for crack formation in service because a complex tn-axial stress state is easily established in clusters (see Fig. 6.8 in Chapter 6). The microstructures of a transverse section of the lOvol% and 2Ovol% composites after extrusion at a ratio of 34 at UAC, are shown in Fig. 7.21(b) and Fig. 22(b), respectively. It is quite obvious that the homogeneity of particle distribution is improved after extrusion, especially for 606 i1Al /iOp, although some clusters still remain in the transverse section, 3 O 2 while extrusion bands are evident in the longitudinal section. The number of small particles increases as a result of particle fracture during extrusion.  This is more obvious with  quantitative particle size analysis using the image analyzer. Evidently, heavier extrusion ratios improve the homogeneity of particle distribution. However, a larger extrusion ratio at a relatively low temperature may introduce voids in the surface layer of extrudates due to tensile  Chapter 7 Particle Fracture of the PRMMC during Extrusion  (a) Before extrusion  (b) After extrusion 1 before and after extrusion lOp l/A / 3 0 Figure 7.21 Microstructure of 606 2  164  Chapter 7 Particle Fracture of the PRMMC during Extrusion  (a) Before extrusion  (b) After extrusion I2Op before and after extrusion 3 O 2 Figure 7.22 Microstructure of 606 1IAI  165  Chapter 7 Particle Fracture of the PRMMC during Extrusion  166  0.25  • back  0.2  Q extrud.  o 0.15  o.iJ]  V  I  0.0: I  I  0-5 5-10 1015  1520  2025  2530  ‘iii 3035  3540  4045  45- >50 50  Size class (microns) (a) Maximum alumina particle dimension of 6061/A1 /20p 3 0 2  0.45 0.4 0.35 0.3 0.25 0.2 0.15  o.i  0.0  in back end of a billet and in extrudate  • back Llextrud.  ri 0-5  [  -  510  1015  Iri _ _ 1 l -  15- 2020 25  25- 30- 3530 35 40  40- 45- >50 45 50  Size class (microns) (b) Minimum alumina particle dimension in 606 l/A1 /20p 3 O 2 in back end of a billet and in extrudate Figure 7.23 Variation of maximum and minimum alumina particle dimension  Chapter 7 Particle Fracture of the PRMMC during Extrusion  167  0.14  I  0.12 > 0  a) z  a)  back  O extrud.  0.1 0.08  0.06  .  0.04 0.02 i]I11IIII[  0  Aspect ratio class Figure 7.24 Aspect ratio of alumina particles of 606 1/A1 /20p 3 0 2 in back end of a billet and in extrudate  0.4  0.35 > 0  back  0.3  extrud.  I)  z 0.25 a) a)  > ..  0.2  0.15 0.1 0.05 0 0-15  15-30  30-45  1-i 45-60  60-75  Angle to extrusion direction (degrees) /20p 3 0 2 Figure 7.25 Orientation of alumina particles of 606 11A1  in back end of a billet and in extrudate  75-90  Chapter 7 Particle Fracture of the PRMMC during Extrusion  168  stress, which may cause deterioration of the mechanical properties of the MMCs, based on the 19295 studies on the materials at low temperature  1221•  7.5.1.2 Particle Size Refinement after Extrusion To quantify the change in particle size during processing, the particle size distribution at two locations was analyzed, at the back end of the billet (Locations 4 and 7 in Fig. 7.4), and from the longitudinal section of the extrudate. The statistical results shown in Table 7.6 reveal that the variables characterizing particle size, such as particle area, maximum and minimum dimension, and even aspect ratio, are greater at Locations 4 and 7. The smaller relative coefficients of particle size at Locations 4 and 7 indicate that the particle size distribution is more uniform in the material before extrusion; in other words, some particles fracture into smaller pieces during extrusion. This can also be seen through the distribution of the maximum and minimum particle dimensions (Figure 7.23(a)-(b)). The increase in number of small particles is quantified. The decrease in mean aspect ratio of particles is accompanied by a rise in the class of particles with an aspect ratio close to one, as shown in Figure 7.24. The orientation distribution of particles is distinct in Figure 7.25. 7.5.2 Particle Fracture Modes during Extrusion The tendency for the particle size distribution to skew towards lower size classes is in accord with observations of material deformed at low temperature under hydrostatic ’ (Fig. 7.23(a) and (b)). Such observations are indicative of the comminution of 76 pressure ’ (Comminution mode in Fig. 7.26(a)). It is also noted that in the transverse section 98 particles of the extrudate there appear to be substantially more small particles than in the longitudinal section: this is, in part, an effect of particle re-orientation. It was observed that fractured pieces healed due to the low flow stress of the matrix material and high hydrostatic pressure  Chapter 7 Particle Fracture of the PRMMC during Extrusion  169  encountered during extrusion, which results in matrix material being forced into . 901 ’ 175 cracks This feature is the major difference between low strain/low temperature and large strain/high temperature behavior. However, at high temperature, under tensile stress, the PRMMCs tend to form voids behind the particles’ . This will be discussed in more detail in subsequent 1011 chapters. Particle re-orientation during extrusion may also have an effect on the propensity of particles to fracture.  It was interesting to note that most of the cracks in the particles  (fracture gap) were parallel to the flow direction, and particles seem to be most affected when they lie parallel to the extrusion direction in the longitudinal section of the extrudate. This may be caused by the shear stress acting on the particles under high hydrostatic pressure (Shear mode in Fig. 7.26(b))’ . 991 The skewing of the aspect ratio data (Fig. 7.24) suggests that particles with a large aspect ratio are more likely to fracture during extrusion.  From the microstructure  examination, some cracks were observed perpendicular to the flow direction for those particles with a large initial aspect ratio. The fracture may result from tensile load transfer between the matrix and the particle due to its large initial aspect ratio. A tensile mode of particle fracture was therefore proposed during extrusion (Fig. 7.26(c)).  This is also a  fracture at low temperature in the loading direction , and is retained at high temperatures. 761 Based on the above analysis, three basic modes are proposed for particle fracture during extrusion, i.e., the comminution mode, the shear mode and the tensile mode (Fig. 7.26). Particle fracture during extrusion is a very complex phenomenon. Not only does a single mode function, but particle fracture may be affected by a combination of two or even three modes at the same time, especially for particles in a cluster.  However, from  Chapter 7 Particle Fracture of the PRMMC during Extrusion  170  microstructural examination, the shear mode may be more applicable in the shear deformation zone, where most of the deformation occurs; the tensile mode may be more effective at the position where elongation is very severe, such as near the die exit zone; and the comminution  w  mode may occur anywhere in the deformation zone for a single particle, but most probably in clusters where large compressive tn-axial stresses are present.  U  (a) Comminution mode  U  (b) Shear mode  ‘I,  (c) Tensile mode  Figure 7.26 A schematic diagram for three particle-fracture modes during extrusion  7.5.3 Correlation between Particle Fracture and Bulk Deformation Behavior To understand the particle fracture during extrusion, the deformation behavior of the composite billet was analyzed with the aid of DEFORM® as described in Chapter 5. A typical effective strain rate distribution near the die exit area at a steady state is shown in Fig. 7.27.  Chapter 7 Particle Fracture of the PRMMC during Extrusion -7.750  X )  171  1  Etf.StnRl(1/s)  -  Billet  A. 0.0000 8= 3.0000  C- 60000 0— 8.0000 E. 12.000  -8.050  F. 15.000  Gm 18.000 lb 21.000  -8.350  -8.950  -9250 6.00  0.00  I 18.00  12.00  I 24.00  I 30.00  Radius (mm) Figure 7.27 Effective strain rate distribution in the deformation zone Mean Stress (MPa) Billet  2 -0.500  A— -270.00  8= -245.00 C. -220.00 0= -19500 E= -170.00 F. -146.00 G. -120.00 lb  -0.600  E E 0,  -0.700  .800  —1.000  1= -70.000 J-45.000 K. -20.000  -  1= 5.0000  -  I  —  0.00  6.00  12.00  I  18.00  I  24.00  30.00  Radius (mm)  Figure 7.28 Mean stress distribution in the deformation zone  Chapter 7 Particle Fracture of the PRMMC during Extrusion  172  It is seen that the highest strain rate is reached at the die throat, where metal flow was choked. Therefore, most severe particle fracture could occur in this choked zone. This is also consistent with the particle fracture probability prediction in Section 7.4.3. The mean stress (hydrostatic stress) corresponding to the strain rate state is shown in Fig. 7.28. It is evident that over most of the bifiet, the stress state is in compression (negative value), and a very high hydrostatic pressure exists in the deformation zone. Comminution of a particle or particles in a cluster could result under such a large hydrostatic pressure which may also heal the fractured particle under the large deformation during extrusion (Comminution mode). However, near the die exit zone, tensile stresses appear, especially at the die-bearing interface, which is due to high elongation of the billet and the friction stress at the die interface. These tensile stresses could lead to particle fracture (Tensile mode), or voids behind particles. FEM model predictions confirm the existence of a large shear zone during extrusion, as shown in Fig. 7.29.  In this shear zone, velocity gradients appear from the dead metal zone to the  deformation zone. As a particle flows along the shear direction, the shear deformation forces the particle to rotate into the flow direction (which finally leads to an alignment of the particles along the extrusion direction). However, if the stress in the particle from both the shear and the hydrostatic pressure is large enough, the particle could fracture (Shear mode); healing could consequently occur if the matrix material intrudes into the gap of the crack under high hydrostatic pressure or the fractured pieces were shifted apart because of the t velocity gradient under large deformation” presented in this chapter.  .  Evidence of particle fracture and healing are  Chapter 7 Particle Fracture of the PRMMC during Extrusion  2  -ooo  173  RZ Stress (MPa)  /  Billet  I  A. -20.000 B. -12.000 C-4.0000 0. 4.0000  I  -0.500  .  (  I  -0.600  -0.700  -0.900  —1.000  iz.ooo  F. 20.000 G. 28.000  H. 36.000  -  -  ——  0.00  I  6.00  I  12.00  I  18.00  I  24.00  I  30.00  Radius (mm)  Figure 7.29 Shear stress distribution during extrusion  7.6 Summary Macro- and micro-exmiination of a billet during extrusion sheds light on the metal flow pattern and particle fracture. It was found that the particles fractured in the severe shear deformation zone at the die throat, but most fractured parts healed in the extrudates due to the high temperature and large hydrostatic pressure, which has also been confirmed by Duralcan USALIOSI. Some major findings are summarized below.  Chapter 7 Particle Fracture of the PRMMC during Extrusion  174  (i) Due to adhesion friction between the billet and the container in hot extrusion, a particle-free layer was formed at the interface, and the particle -free matrix material flows into the shear deformation zone to form a particle-free band in the extrudates in the extrusion direction. In this zone, very few particles reside, and therefore there was less fracture of the particles; (ii) More obvious particle alignment along the flow direction was observed in the severe deformation zone than in the dead metal or hard-to-deform zone under the pressure pad. The formation of the particle-free bands along the extrusion direction was obviously due to the elongation of the particle-free zone in the as-cast material during extrusion.  The  frequency of particle fracture depended on deformation conditions. In the deformation zone, more fractured particles were observed than in the dead metal zone, but most severe particle fracture occurred in the shear deformation zone at the die throat. The fractured parts were healed due to the low flow stress of the matrix material at high temperature and the large hydrostatic pressure. However, clusters in the hard-to-deform zone under the pressure pad, or even in the dead metal zone, showed evidence of particle fracture due to the comminution effects. In the dead metal zone, some particles were cracked, but not separated, due to small deformation; (iii) Most of the single particles that fractured had a large aspect ratio or sharp corners. Equiaxed particles were much harder to fracture; all the large particles which remained unfractured in different zones had an aspect ratio close to unity; (iv) Many cracks in particles were in the flow direction due to shear deformation, but some cracks perpendicular to the flow direction were also observed, especially in particles  Chapter 7 Particle Fracture of the PRMMC during Extrusion  175  with a large aspect ratio. This was probably due to the tensile stress in the particle in the flow direction. The size and distribution of the particles in the extrudates have also been examined using both an optical microscope and an image analyzer. Comparing the transverse section with the longitudinal section, some important features are: (i) Orientation of the cracks in the transverse section was randomly distributed. However, many of the cracks in the particles in the longitudinal section were either parallel or perpendicular to the extrusion direction. Most of the particles with an aspect ratio greater than one were aligned in the extrusion direction; (ii) Particles with a different aspect ratio were observed in both the transverse and the longitudinal sections. Larger particles especially with sharp corners or large aspect ratios, and those in clusters, fractured more easily. More small particles were found in the transverse sections than in the longitudinal section, partly because of re-orientation of particles during extrusion; While comparing the extrudate of 6O6l/AlO3/lOp to that of 6O6lIAl /20p, it was 3 O 2 found that:  O3I2Op. 2 (i) Particles were much smaller in 606 l/AlO /l0p than in 606 1IA1 3 However, the particle distribution was less homogeneous in 606l/Al /lOp than in 3 0 2 606 l/A1 /20p, i.e., more clusters and more particle-free bands remained in the extrudates 3 0 2 of 606 1/A1 /lOp; 3 0 2 /lOp was less than that in 3 0 2 (ii) The mean aspect ratio of particles in 6061/A1  606 1/A1 /20p. 3 0 2  Chapter 7 Particle Fracture of the PRMMC during Extrusion  176  Quantitative metallography and statistical analysis were conducted using an image analyzer. The particle dimensions, such as minimum and maximum dimension, area, aspect ratio, and particle orientation were quantified at different positions in the deformation zone. The most salient points are: (i) Particle alignment along the extrusion direction was confirmed. Particle fracture during extrusion leads to more smaller particles. The average aspect ratio of the particles after extrusion is around 1.74 to 2.07 with more uniform size distribution in 606l/AlO3/l0p than in 606 1/AlO3/20p. The mean size of the particles in the longitudinal section is larger than in the transverse section due partly to re-orientation of particles during extrusion. However, the particle distribution is more uniform in the transverse section than in the longitudinal section; (ii) The four-fold difference in size of particle area in the extrudates between 6061/AlO3/l0p and 606l/AlO3/20p is mainly due to a difference in initial particle size of the composites. The change in particle size, size distribution, homogeneity, and orientation, and healing of the ‘damage’ which accompanies a fracture event, may all have benefits for the in-service mechanical properties of extruded components. However, the influence of particle fracture on mechanical properties, the correlation between the particle size and the deformation parameters, and the mechanism of the low speed cracking, need to be clarified.  Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs  177  Chapter 8 ORIGIN OF LOW SPEED CRACKING DURING EXTRUSION OF THE PRMMCs The particle fracture analysis presented in the previous chapter revealed the improvement in homogeneity of particle distribution and particle size refinement after extrusion. This could be beneficial with respect to mechanical properties of the composites. However, low speed cracking was observed in the plant trails at UAC, which is specific to the composite material. It is essential to explore the mechanism of the low speed cracking during extrusion.  8.1 Microstructure Examination of Low-speed Cracks As observed in the plant trial at UAC, low speed cracking occurred at the front end of extrudates in most of the trials. Although some explanation for the low speed cracking was proposed by researchers, as described in Chapter 2, it was incomplete because the interaction between the particles and the matrix were not considered. To study the mechanism of low speed cracldng, extrudates with severe low speed cracks were cut and polished to examine both longitudinal and transverse sections. The samples were cut from the front end of the extrudates of J94-14 and J94-20 of 6O61IA1 I2Op with very severe low speed cracking, and 3 O 2 J94-1 lB of 6O61IAl I1Op with slight cracking. The polishing procedure of Table 7.2 was 3 O 2 followed by using an automatic polishing machine at UBC. The samples were examined under an SEM, because it is harder to investigate void formation by using an optical microscope, due to its low depth of field. Before examination, a very thin film of Au-Pd was sputter coated on the surface of the polished specimens for about 4 minutes for 6O61IAl I2Op, and 3 O 2  Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs  178  /lOp samples. As a result, good contrast between the particles 3 O 2 about 3 minutes for 606l/A1  and the matrix was obtained with little electronic charging of the A1 3 particles. Under the 0 2 SEM, it was found that the low speed cracks penetrated into the surface layer, and that extensive voids existed around the low speed crack tips in all three samples, as shown in Fig. 8.1 for J94-14. It is seen that most of the voids were associated with particles and located at the two ends of particles in the extrusion direction (orientation of particles with large aspect ratio in the picture). The same phenomenon was also observed around the crack tips of 3941 lB for 6061/A1 /lOp, as shown in Fig. 8.2. This is due to the tensile stress state in the 3 0 2 matrix between particles in the flow direction, as predicted by the micromechanical analysis in Chapter 6. It is interesting to note that more severe low speed cracking was observed in 394-14 of /lOp, although the initial billet temperature of 3 O 2 /20p than in 394-1 lB of 606 l/A1 3 O 2 6O61IA1 J94-14 was higher at 461°C than 434°C used for J94-11B, as listed in Table 4.3. This is due to the fact that the lower volume fraction results in higher ductility of the composite, while the fracture behavior is controlled by exhaustion of matrix ductility due to the constraints on . A high volume fraction of second 1 matrix plastic flow by the elastic reinforcing particles’ phase particles results in more severe constraints of the matrix flow around the particles during extrusion, although the 6061IA1 /lOp composite has a less uniform distribution than 3 O 2 the 606 l/A1 /2Op composite, as described in Chapter 7. 3 O 2  Crushed particles were also  observed at the surface which form the minor defects observed in the extrudate surface. Cracked particles in clusters remained without evidence of healing, although interface decohesion seems to be dominant in the surface layer.  Chapter 8 Origin of Low Speed Cracking during Extrusion of the PRMMCs  Figure 8.1 Void formation near a low speed crack tip of 394-14 of 2 1 in longitudinal section il20p 6061/A 0  Figure 8.2 Void formation near a low speed crack tip of J94-1 lB of 606 1/A1 /lOp in longitudinal section 3 0 2  179  Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs  180  8.2 Particle Behavior and Microscopic Damage The above microstructure indicates that the low speed cracking is associated with particle behavior and its consequent microscopic damage, such as particle fracture and void formation. Therefore, particle behavior and its constraints to the plastic flow of the matrix material becomes important. Micromechanical analysis of particle behavior under both the plane strain and the cylindrical compression has been conducted in Chapter 6. All the particle models (Single-, Twin- and Multiple-particle Model) predict a localized deformation behavior around the particle, although the overall deformation behavior of a specimen with and without a particle are quite similar to each other.  it is the localized deformation that intrinsically leads to  dynamic microstructural evolution (such as particle fracture, void formation, etc.) during extrusion.  8.2.1 Particle Fracture At a microscopic level, the predicted localized matrix flow in the vicinity of large alumina particles, especially at both the sharp ends of angular particles and in the vicinity of particle clusters, was confirmed for alumina particulate reinforced metal matrix composites by Ferry and Munroe in the form of shear bands in the matrix around the particles, based on their . They also found that large particles and 111 microstructural study in Al/A1O 3 composites” those with a high aspect ratio had the greatest propensity to fracture during deformation. Some particles fractured into very fine (1-2 tIm) pieces and redistributed along the shear band during deformation. These observations are also consistent with the single-particle model prediction of different shapes of a particle during cylindrical compression and with the prediction of particle migration in the plane strain simulation. The interaction between the  Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs particles and the matrix is mutual:  181  the particles in a cluster and those with an irregular  morphology force the matrix to deform in a highly constrained manner (localized deformation), and the highly deformed matrix material inversely affects the particle behavior, e.g., the rotation and migration of the particle, and consequently the stress state in the particle. Therefore, matrix flow and particle behavior are very much temperature dependent. If the temperature is low, the matrix work-hardens more easily and the stress in the particle will be higher, which in turn leads to particle fracture. Because the flow stress of the matrix at low temperature is high, the cracked parts are harder to heal by intrusion of matrix material into the gap. In contrast, at high temperature, due to the low flow stress, there is little work hardening and the matrix flows more easily around the particle. Consequently, the stress in the particle is low and the particle is harder to fracture. Even if a particle fractures, the cracked parts heal easily by matrix intrusion into the crack under hydrostatic pressure, or the two cracked parts are separated away by shear deformation, as observed in extrusion processing. A tensile stress was predicted in a particle with an aspect ratio of 2 under plane strain conditions at a reduction of 10%, as shown in Fig. 8.3. This is consistent with the proposal of the ‘Tensile mode’ of particle fracture during extrusion, i.e., if a particle moves in the matrix flow direction, a tensile stress is generated in the particle. The larger the aspect ratio, the higher the tensile stress, and consequently, the higher the propensity to fracture. This is also predicted by study of particles with different aspect ratios under a plane strain condition, which have some similar deformation characteristics to the extrusion process (Table 8.1). The table shows that generally a particle with a large aspect ratio has a higher internal tensile stress in the flow (x) direction. However, as the reduction increases, the tensile stress  Chapter 8 Origin of Low Speed Cracking during Extrusion of the PRMMCs  182  This is because the interparticle spacing increases, and subsequently, the  decreases.  interaction between the two particles becomes weaker. Table 8.1 Tensile stress in partides and matrix at different reductions Aspect  Object No.  Reduction: 10%  Ratio  (Material)  Mi  A.R.=1  A.R.=2  Reduction: 30%  Reduction: —50%  Max.  Miii.  Max.  Miii.  Max.  (MPa)  (MPa)  (MPa)  (MPa)  (MPa)  (MPa)  #2(Matrix)  -50  42  -51  30  -64  38  #4(Particle off C.L.)  -8  83  -28  89  -45  72  #5(Particle @ C.L.)  -4  89  -18  69  -34  50  #2(Matrix)  -131  125  -60  54  -57  34  #4(Particle off C.L.)  9  158  -12  84  -26  55  #5ParticIe @ C.L.)  56  170  8  92  -24  54  X Stress (UPa) Objed #4 (dght)  4.600  A. 8= C= D=  4.570  4.540  E  -  4.510  _______  (I  E= 70.000  F  EE>E  L  4.450  Figure 8.3 Tensile  0.030  stress in a  0.060  0.090  X (mm)  particle under plane  strain  0.120  F. 85.000 G= 100.00 H. 115.00 I. 130.00 4=145.00 K. 160.00 Objed #5 (dr line) A. 10.000 8=25.000 C. 40.000 D. 55.000 E= 70.000 F. 85.000 G= 100.00 H. 115.00 1= 130.00 4= 145.00 K= 160.00  4.480  0.000  10.000 25.000 40.000 55.000  0.150  condition at a reduction of 10%  Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs  183  8.2.2 Void Formation Voids have been observed with an SEM in the surface layer of some extrudates with severe low speed surface cracking, as described in Section 8.1. It was found that voids were more frequently present at the ends of two closely spaced particles which were aligned in the extrusion direction. The void formation could be explained by the local stress state owing to the presence of the particles. Figure 8.4 shows the tensile stress (ar) distribution around the particles at a reduction of 10% under the plane strain condition. A high tensile stress zone is generated between two particles in the x-direction. A smaller spacing (20j.tm) between the two particles with a large aspect ratio leads to a higher value of the tensile stress in the interparticle zone (see contour line value of ‘J’ of 104 MPa in Fig. 8.4(b) and compared to the contour line ‘G’ of 28MPa in Fig. 8.4(a) for a particle spacing of 40pm). A high tensile stress value is also predicted for the multiple-particle model at a reduction of 1% (see contour line ‘E’ of 6OMPa in Fig. 8.4(c)). This implies that in the matrix material within closely spaced particles, such as within a cluster, it is easier to initiate voids. The predictions are consistent with the results obtained by Poole et 11 a!. 13-1 14J It is interesting to note that the tensile stress component in the x-direction in the center zone of the monolithic material with no particles present is less than 6MPa, although all the other simulation conditions are the same, as shown in Fig. 8.5.  Chapter 8 Origin of Low Speed Cracking during Extrusion of the PRMMCs  X S1m1 (UPa) ObdI 2 A= -20.000 8= -12.000 Cs 4.0000 0= 4.0000 Es 12.000 F= 20.000 G= 28.000 H= 36.000  4.650  4.600  E  4.550  >(0 4.500  4.450 0.000  0.050  0.100  X (mm)  0.150  0200  (a) Twin-particle model with a unity aspect ratio at a reduction of 10% X Qrese (UPa) Objed 1 2 A= -130.00 8= -104.00 C= -78.000 0= -52.000 Es -26000 F= 0.0000 G. 26.000 14= 52.000 1= 78.000 .1= 104.00 K= 130.00  4.650  4.600  E  4.550  >-  4.500  4.450  0.000  0.050  ‘I  0.100  X (mm)  0.150  0200  (b) Twin-particle model with an aspect ratio of 2 at a reduction of 10%  184  Chapter 8 Origin of Low Speed Cracking during Extrusion of the PRMMCs  X Streu (UPa)  5.060  Cbed#2 A -4000 8. .15.000 C. 10.000 0-35.000 E. 60.000  5.000  E  4.960  E  >-  4.900  4.850  I  0.100  0.050  0.000  i  %  0.200  0.150  X (mm)  (c) Multiple-particle model with a unit aspect ratio at a reduction of 1% Figure 8.4 Tensile 0.020  _.  E E  -0260  xO  -  stress  distribution in the matrix and around particles  1 Stress (UPa) X Objed 1 2 A- -30.000 8= -24.000 C. -18.000 0= -12.000 E= 4.0000 F= O.00000E+00 G= 6.0000 H. 12.000 1= 18.000 J. 24.000 K= 30.000  -  >-0.540  —1.100  -  I  —  0.00  2.80  Figure 8.5 Tensile  5.60  I 8.40  11.20  14.00  X (mm)  stress  distribution in the monolithic material  at a reduction of 10% under plane  strain  condition  185  Chapter 8 Origin of Low Speed Cracking during Extrusion of the PRMMCs  186  Therefore, even though the monolithic stress state is compressive, a local tensile stress component around particles may exist. It is the local tensile stress behind a particle in the flow direction which leads to void formation, as observed in the extrudates.  The hydrostatic  pressure helps to stop void formation and growth during extrusion which explain why the elastic modulus of the extrudates does not decline as the extrusion ratio increases.  8.3 Effect of Processing Parameters on Low Speed Cracking From the microscopic analysis in the above section, it is known that low speed cracking is related to the presence of a tensile stress both in the particle and in the matrix, which might lead to particle fracture and void formation, respectively.  However, the  microscopic behavior must be related to the macroscopic extrusion parameters, such as extrusion temperature, speed and the material itself. The temperature is, however, affected by many factors such as ram speed, initial billet and die temperature and die material, etc.. An effort has been made to explore the origin of low speed cracking during extrusion with the aid of the finite element model, DEFORM’.  I2Op and the die near the 3 O 2 The temperature distribution of both the billet of 606 1IA1 die exit zone, during extrusion at steady state, is shown in Fig. 8.6. The simulation conditions are listed in Table 8.2. It is evident that the billet temperature is increased to about 460°C from the initial value of 425°C due to the heat of deformation for an extrusion ratio of 34; and the die interface also heats up due to heat conduction. Obviously, the thermal diffusivity of the die material is also very important to the temperature distribution in both the extrudate and the die interface. Figure 8.7 shows the tensile stress builds up at the die land area in the extrudate during extrusion. All the other zones in the billet are in a compressive stress, which  Chapter 8 Origin of Low Speed Cracking during Extrusion of the PRMMCs  187  may help prevent void growth or crack formation. Apparently, both the temperature and tensile stress in this die land zone are crucial to the low speed cracking. As described in the last section, the fracture behavior of the composite is controlled by exhaustion of matrix ductility due to the constraints on matrix plastic flow by the elastic reinforcing partic1e”’. Therefore, the lower the billet temperature in the die land zone, the lower the matrix ductility. On the other hand, the larger the tensile stress generated in the surface layer in the die land zone, the higher the propensity .for void formation due to local tensile stress near the ends of particles in the extrusion direction, especially for those closely distributed particles (e.g., particle cluster), based on the micromechanical analysis conducted in Chapter 6.  Tenipefature (C)  aa  4.000  A 426.00 B 426.00 C. 432.00 0-438.00 E 444.00 F. 450.00 G= 456.00 H. 462.00 I- 468.00  4.300  I  Die  4.600  A. 378.59  8. 389.56 C. 400.52  0- 411.49  E. F. G. H.  4.900  445 433.42 444.38 455.35  1. 466.31  4200  4.500 0.0  30.0  60.0  90.0  120.0  150.0  Radius (mm)  Figure 8.6 Temperature distribution of billet and die at steady state extrusion  Chapter 8 Origin of Low Speed Cracking during Extrusion of the PRMMCs  188  Table 8.2 Standard conditions for parametric study Ram speed:  1mm/s  Initial billet temperature:  425°C  Friction shear factor at the container and die interface:  m=1 (sticking)  Friction shear factor at pressure pad interface:  m=0.7  Initial die temperature:  395°C  Billet diameter  178mm (7”)  Contain inside diameter:  184(7.25”) 34  Extrusion ratio:  2  ZSkees(MPa)  -2.750  A— -420.02 B -359.45 C= -296.89 D=-238.32 E -177.75 F— -1 17.18 G. -56.616 H 3.9517 1= 64.519  \ \ \  -3.050  \ -3.350  4959  250  -  0.0  -  30.0  60.0  90.0  Radius (mm)  120.0  150.0  Figure 8.7 Tensile stress (as) distribution at the die interface zone To determine the effect of extrusion variables on the temperature and the tensile stress /20p was conducted for 3 0 2 in the die land zone, a systematic study of the extrusion of 606 1/A1  Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs  189  all the process parameters, such as ram speed, initial billet temperature, initial die temperature, frictional condition at the die interface, extrusion ratio and the billet materials. The standard simulation conditions are listed in Table 8.2.  Effect of Ram Speed Figure 8.8(a) and (b) show the effect of ram speed on the variation of the maximum billet temperature and the maximum tensile stress in the extrudate in the die land zone during extrusion. Figure 8.8(a) shows that the temperature increases much faster at the speed of 6mm/s than at 1mm/s. This is because a higher speed results in a higher heat generation rate, and also the higher speed reduces the time of heat transfer from the extrudate to the die, which generates a steeper thermal gradient near the die interface, as shown in Fig. 8.9. Tensile stress, az, (where Z denotes the extrusion direction) in the die land zone decreases during extrusion, because of the temperature rise (Fig. 8.8(b)). A higher ram speed results in a sharper decrease in the stress value because of the higher heat generation rate. Apparently, the tensile stress value is quite sensitive to the extrusion temperature. Figure 8.9 shows that the temperature distribution through the whole radius of the extrudate is higher for the ram speed of 6mm/s, and also that the thermal gradient is greater at the interface, due to the shorter heat transfer time. On the other side of the die interface, the thermal gradient is even greater because of the lower thermal diffusivity (the thermal diffusivity of H13 is about 7 times lower than that of the composite material). Again, because of the shorter heat transfer time, the thermal gradient is greater for the ram speed of 6mm/s and the inside temperature of the die is even lower than that of the ram speed of 1mm/s.  Chapter 8 Origin of Low Speed Cracking during Extrusion of the PRMMCs  190  520 —  500 U ‘‘  —  480  /  460 440-  /  —  —  —  /  ///1Z6.5  1.0 mm/s  420 20  —  —  22  24  28 26 Ram Displacement (mm)  30  32  (a) Maximum temperature in the die land zone during extrusion  85  I 75  1.Omnilsl ‘6.5mmIsj  C’,  C,, ‘1)  65  55 30 28 26 24 22 20 Ram Displacement (mm) (b) Maximum tensile stress in the die land zone during extrusion Figure 8.8 Effect of ram speed  32  Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs  191  525  500 U 0  1)  475  450  425  400 0  5  10  15  20  25  30  Distance from the Center of extrudate (mm) Figure 8.9 Temperature distribution on both side of the die interface at a ram displacement of 30mm Figure 8.10 shows the effective strain distribution through the whole radius of the extrudate at the die exit. It is seen that the strain distribution is not sensitive to the ram speed,  because the strain is more dependent on extrusion ratio. The distribution of stress component in the extrusion direction  (az) along the radius of extrudate, indicates that the stress is  compressive near the center and gradually becomes tensile near the surface of the extrudate (Fig. 8.11). Obviously, in a surface layer of more than a quarter of the radius of the extrudate there exists a tensile stress in the extrusion direction. The existence of the tensile stress state in the surface layer may promote void formation if the temperature of the billet at the surface in the die land zone is low; this may fmally lead to low speed cracking, as was observed.  Chapter 8 Origin of Low Speed Cracking during Extrusion of the PRMMCs  192  4. 1OmmJs  36  2.8  -  2.4 I 4  2 0  I 8 Distance from the Center Line (mm)  I 12  16  Figure 8.10 Effect of ram speed on strain distribution through radius direction  60  -  I  I—  4020 U  —  —  1.0mm/si  6.5mm/si  — 0 0  0-  -  0  0 0  20 o  0  -.  z  •0  I.—  0  0  -60 0  4  8 Distance from the Center Line (mm)  12  Figure 8.11 Effect of ram speed on stress distribution (az) through radius direction  16  Chapter 8 Origin of Low Speed Cracking during Extrusion of the PRMMCs  193  8 —  6  —  —  1.0mm/s 6.5mm/s  4, 2  0  4  8 12 Distance from the Center Line (mm)  16  Figure 8.12 Effect of ram speed on effective strain rate variation in extrudate A big difference in effective strain rate is expected because of the different ram speeds (Fig. 8.12) but near the exit of the die land, the strain rate is concentrated only within the surface layer. Effect of Billet Temperature With all the other conditions kept the same, the effect of initial billet temperature on the tensile stress in the extrusion direction and the temperature rise was studied (Fig. 8.13(a) and (b)).  Thus the higher the initial temperature, the higher the extrusion temperature.  However, the temperature rise is lower for the higher initial billet temperature (—20°C) than for the lower initial temperature  (— 40°C); because of the lower flow stress and the low heat  generation obtained for the higher billet temperature. Correspondingly, the maximum tensile stress in the extrusion direction (CT) is lower, as shown in Fig. 8.13(b). A 75°C increase in  Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs  194  520  500  5°C  L) 0  E  500  460 a  a  a  •  •  —  —  a  a  •  •  •  —  e  a  —  a  —  440 S ,  420 20  I  I I  I I  22  24  I I  I  26 28 Ram Displacement (mm)  30  32  (a) Max. temperature in the die land zone during extrusion  85 75  .  65  ..  -  a  —  a  0  I  a  55 45 35  :  20  22  24  b  —  —  425 °C 500°C  a  26 28 Ram Displacement (mm)  30  32  Figure 8.13 Effect of initial billet temperature: (b) Max. tensile stress in the die land zone  Chapter 8 Origin of Low Speed Cracking during Extrusion of the PRMMCs  195  550 -  -  -  525  425 °C 500°C  into Billet  475 S  0  0  S  into Die  S  450Interfac  Die 425  a 0  I  0  5  10  15  20  25  30  Distance from the Center of extrudate (mm)  Figure 8.14 Thermal gradient on both sides of the die interface under different billet temperature billet temperature results in a drop of maximum tensile stress of  3OMPa. It is obvious that  the effect of billet temperature on the maximum tensile stress is quite significant. It is known that a higher tensile stress may increase the propensity ofvoid formation at high temperature . Therefore, temperature control is important to eliminate 1011 in particulate reinforced MMCs low speed cracking during extrusion. On the other hand, at a lower initial billet temperatures, the tensile stress in the extrusion direction in the surface layer of the extrudate decreases more rapidly because of the higher heat generation rate due to the high flow stress (Fig. 8.13(b)). Because the ram speeds are the same for both cases, the thermal gradient in the extrudate is about the same (Fig. 8.14). However, on the die side, the thermal gradient is larger for the lower initial bifiet temperature of 425°C, because the temperature rise is higher.  Chapter 8 Origin of Low Speed Cracking during Extrusion of the PRMMCs  196  530  I C-)  0  -  -  -  I  500°C-395°C 500°G470°C  I  480  .  20  I  I  24  22  I  I  26 28 Ram Displacement (mm)  30  32  (a) Maximum temperature in the die land zone during extrusion 65 60  -  500°C-395°C 500°C-470°C  55 50  -  . ..  45 40  35 20  I  I  22  24  I  I  26 28 Ram Displacement (mm)  I  30  (b) Maximum tensile stress in the die land zone during exirusion Figure 8.15 Effect of initial die temperature  32  Chapter 8 Origin ofLow Speed Cracking during Ertrusion of the PRMMCs  197  550 -  -  530  —‘  U  :  5 10  -  500°C-395°C 500°C-470°C  — _  _  _  .  —  _  _  =  =  —  =  —  —  —  —  into Billet  490  intoDie  470 Die 4500  I  I  5  10  15  Interfac 20  I 25  30  Distance from the Center of extrudate (mm) Figure 8.16 Thermal gradient on both sides of the die interface  under different initial die temperatures Effect ofDie Temperature From the above analysis, it can be seen that the tensile stress is very sensitive to the temperature of the extrudate in the die land zone. Because the die temperature is not very well controlled in the plant thai at UAC, the sensitivity of die temperature was also analyzed (Fig. 8.15). Die temperatures of 395°C and 470°C were used with the same initial billet temperature of 500°C. From Fig. 8.15(a), it is seen that, because of the lower initial die temperature of 395 °C, the maximum defonnation temperature of the extrudate is about 15°C lower than that of the die temperature of 470 °C, and the extrusion temperature is even below  its initial temperature of 500°C at the end of the upsetting stage (at a ram displacement of  Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs about 21mm) due to the cold die ‘chilling’ effect.  198  As a result, the tensile stress of the  extrudate in the surface layer within the die land zone is higher (Fig. 8.15(b)).  The  temperature distribution in the cross section of the extrudate is more uniform than that on the die side because of the higher thermal diffusivity. The lower initial die temperature results in a steeper thermal gradient on the die side(Fig. 8.15). Effect of Friction at Die Interface With sticking friction confmed to the container interface, the sensitivity of two extreme friction conditions was studied with the friction shear factor being set at 0 and unity, respectively.  It is worth pointing out that in DEFORM®, when considering the sticking  friction condition, the relative velocity between two objects in contact is not restricted; in contrast, a shear stress with an equivalent value of shear strength of the deformed material, is . Therefore, although a sticking friction condition was specified, the 1831 applied at the boundary nodes of the deforming finite element object (billet) in contact with the stationary object (tools) are still movable. Figure 8.17 shows the sensitivity of the friction condition at the die interface. Without friction heating at the die interface, the maximum temperature of the extrudate during extrusion is lower than, but very close to, the value of the extrudate temperature with friction. This is because the die land length is only about 2 to 3mm; and thus the contribution of friction heating is very small.  The small effect of friction on the  temperature rise can also be seen from the thermal gradient on both sides of the die interface, as shown in Fig. 8.18. However, the difference in tensile stress related to the two different friction conditions is quite obvious (Fig. 8.17(b)). It is interesting to note that even with no friction condition applied at the die interface, the tensile stress still exists. This indicates that  Chapter 8  470  Origin of Low Speed Cracking during Extrusion of the PRMMCs  199  -  460 U 0 ‘450  /  /  I  — -  _I.  —  •  —  —  —  440  —  m=1  430420 20  ‘  I  22  24  I  I  30  28 26 Ram Displacement (mm)  32  (a) Maximum temperature m the die land zone during extrusion  90 80  —  m=1 70 z  r5O  50 40  I  I  20  22  24  28 26 Ram Displacement (mm)  (b) Maximum tensile stress in the die land zone during extrusion Figure 8.17 Effect of friction condition at die interface  30  32  Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs  200  475  463 c-) 0 ‘—  451  427  415 0  10  5  15  20  25  30  Distance from the Center of Extrudate (mm) Figure 8.18 Thermal gradient on both sides of the die interface  under different friction condition at die interface the tensile stress build-up in the die land zone is not only due to friction, but also due to matérial flow itself, because metal flows faster at the inside layer of the extrudate than at the outside layer and also there is no back pressure applied onto the front end of the extrudate. Therefore, it is this velocity difference that causes the tensile stress at the die exit. Severe friction conditions simply make the situation worse. Effect ofExtrusion Ratio A temperature rise of the billet under smaller extrusion ratios is expected to be lower if all other conditions are kept the same. At an extrusion ratio of 13, the extrudate temperature rise is only about 15°C compared to 45°C for an extrusion ratio of 34. About 30°C difference has been predicted for the extrusion ratio of 13 and 34(Fig. 8.19(a)). Because of the relatively  Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs  201  470  —  R=13 R=34  ,—  C-) o  450  -  —  —  —  —  —  0’  E 430  410 20  /  /  I  I  I  25  30 Ram Displacement (mm)  35  40  (a) Maximum temperature in the die land zone during extnision  85  20  25  30 Ram Displacement (mm)  35  (b) Maximum tensile stress in the die land zone during extrusion Figure 8.19 Effect of extrusion ratio  40  Chapter 8 Origin of Low Speed Cracking during Extrusion of the PRMMCs  202  525 -  R=13 R=34  -  500 U  0  —  2  475  4—  into Billet  into Die  450 •  —  —  _  a  a  a  a  a  a  a  a  a  425  a  a  —  Die  •  —  —  —  400 10  0  -10  20  30  40  Distance from the Center of Extrudate (mm) Figure 8.20 Thermal gradient on both sides of the die interface under different extrusion ratios higher heat generation rate for the higher extrusion ratio, a greater thermal gradient is predicted for both sides of the billet and the die, as shown in Fig. 8.20. The tensile stress is  higher initially for the higher extrusion ratio, but decrease rapidly because of the rapid temperature increase (Fig. 8.19(b)).  Effect of Volume Fraction of the Composites /2Op. The effect of 3 O 2 The sensitivity analysis conducted above was for the 606 l/A1 10% and 20% volume fraction of the PRMMCs was also conducted for a similar sensitivity analysis (Fig. 8.21).  As expected, a high volume fraction of particles results in a higher  temperature rise due to the higher flow stress (Fig. 8.21(a)). The tensile stress is also greater  Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs  203  470  460  -  /  f /  c_) 450-  — — —I.  —  —I I—  —  —  I” 1/ Il  440  —  —  —  —  10%vol 20%vol  /I  430  j  I  420  20  I  I  30  32  2462830 Ram Displacement (mm)  32  22  24  28 26 Ram Displacement (mm)  (a) Maximum temperature in the die land zone during extrusion 80  (b) Maximum tensile stress in the die land zone during extrusion Figure 8.21 Effect of volume fraction  Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs  204  470  460  ‘—‘  450  I  430  420 0  5  10  15  20  25  30  Distance from the Center of extmdate (mm) Figure 8.22 Thermal gradient on both sides of the die interface  under different volume fraction for the larger volume fraction material. This means that the decrease in flow stress due to temperature rise cannot compensate for the effect of a larger volume fraction of the reinforcement. The difference in thermal diffusivity of different composite materials can be seen from the thermal gradient in the extrudate, although it is quite small.  The higher  thermal diffusitivity of 6061/A1ZO3/lOp results in a slightly flatter temperature distribution through the radius of the extrudate (Fig. 8.22).  8.4 Mechanism of Low Speed Cracking Based on the analyses described in the above sections, it is believed that the low speed cracking is induced by both the low ductility of the composite and microstructural damage  Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs  205  (such as voids including decohesion and unhealed cracks) during extrusion as follows: 1) at the beginning of extrusion, the die temperature is lower than that of the billet, so a ‘chilling’ effect occurs at the front end of the billet when it is in contact with the ‘cold’ die. The lower temperature results in lower ductility of the composites; and 2) the extrudate surface is generated from two distinct regions of the composite: the deformation zone of intense shear, decorating the dead metal zone, which is the major contribution and the smaller deformation volume near the die throat, moving along the die face . With the presence of particles t1171 which constrain the surrounding matrix deformation, especially at low temperature, severe defonnation near the die throat may lead to matrix failure at the particle interface (void formation) and particle fracture in particle clusters in the composite during extrusion. The tensile stress generated in the die land zone may not only leave the cracked particle unhealed, but also promote the void growth. When the fraction of the voids reaches a certain value, the voids may link each other to result in a tearing at the extrudate surface within the die land length, due to low ductility at low temperatures. At high extrusion speed, because the heat generation rate of deformation is greater, and also because the thermal diffusivity of the die material (H13 and the ceramic die) is about 7 to 10 times lower than that of the composites, the temperature at the die interface increases very rapidly (See Fig. 8.8). However, at low speed, the heat generation rate is lower and the heat has time to diffuse through the die, due to the relatively longer extrusion time (Fig. 8.9). Therefore, if either the initial bifiet temperature or initial die temperature is low, the matrix within the particles is constrained much more than at higher temperature, because the flow stress is much higher at lower temperature (see also Figs. 8.13 and 8.15). Voids are easier to form and grow under tensile stress (see also Figs. 8.4 and 8.5). Therefore, low speed cracks  Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs  206  appear. Apparently, all the extrusion conditions that may result in lower billet temperature and higher tensile stress in the surface layer of the extrudate in the die land zone may lead to low speed cracking during extrusion, such as lower initial billet and die temperature, low ram speed, higher extrusion ratio, higher friction condition at the die interface, and also high volume fraction of the particle reinforcement.  This is consistent with the plant trial  observations at UAC and at KRDC, Kingston. At UAC, more severe low-speed cracking in the 606 l/Al Oil2Op composite at higher extrusion ratio (1” and 1.25” die) has been found; 2 and the low-speed cracking disappeared when the ram speed was increased. However, only one extrudate with low-speed cracking was found in the trials at KRDC, in which the ram speed was considerably lower than the set value of 0.9mm/s. This occurred when the press limit was exceeded due to low initial billet temperature of 400°C.  At a ram speed of  —0.9mm/s. low speed cracking always appeared in the plant trials at UAC. However, no low speed cracking was observed in the plant trials at KRDC. This is because the die and the billet were heated at the same time in a furnace at KRDC, and the temperature of the container was even higher than that of the billet. The ‘stick and slip’ observed, is due to the fact that when voids link to form a crack, the tensile stress generated is released. This process repeats itself as long as the temperature of the billet remains low and also the tensile stress is sufficiently high to promote void formation in the extrusion process.  8.5 A Preliminary Criteria for Low Speed Cracking It is clear now that the onset of low speed cracking is controlled by both the fracture stress and fracture strain (ductility) of the material. Therefore, a preliminary fracture criterion is proposed for the low speed cracking during extrusion based on the idea of the plastic-work : 5t1 criterion  Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs c 2 E—a  GF6F  =CF  where (Yz is the maximum principle stress, and  207  (8.1)  is the maximum tensile strain obtained  during extrusion, which is defined as the strain induced under a tensile stress, while  GFEF  is  the product of the fracture stress and tensile fracture strain of the material. The low speed cracking is induced by local failures of the composite, related to the local tensile stress and strain.  However, because it is difficult to know the local tensile stress and strain, the  monolithic tensile stress and strain are used in the criterion. Since the fracture strain of a material is also dependent on the process itself, a tensile strain is used, although it is hard to determine its value in an extrusion process. Apparently, if the product of the maximum tensile stress and the maximum tensile strain in the composites exceeds a critical value, which is the product of the fracture stress and strain, low speed cracking would occur. The reason to use a product instead of a single stress (Stress Criterion) or strain (Strain Criterion) is because the onset of low-speed cracking is induced by the combination of those two factors, i.e., the microdamage would be induced for a certain strain (fracture strain) within particles, and the tensile stress would promote the void growth to link voids to form the low speed cracks for a certain stress value (fracture stress). According to Eq. (8.1), the effect of a variation of the product (E) of the maximum tensile stress and the maximum extrusion strain in the extrudate (rather than the difficult to obtain tensile strain) during extrusion under different conditions, but for the same extrusion ratio of 34, was shown in Fig. 8.23. J94-12 has the highest value of B, because it has the lowest temperature of 423°C. The higher starting value of E of J94-13, with higher initial  Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs  208  450  420  194-12 J94-13 194-14  -..  —  390 4-  360  330  300 24  I 28  I  I  I  32  36  40  Ram Displacement (mm) Figure 8.23 Variation of E value during different conditions but same extrusion ratio 530 194-6 394-14  480  J94-20  430 380 330  -  280  230 24  I 28  I 32  =  -  *  -  -.  I 36  Ram Displacement (mm) Figure 8.24 Variation of E value during extrusion at different extrusion ratios  I 40  Chapter 8 Origin ofLow Speed Cracking during Extrusion of the PRMMCs  209  billet temperature of 47 1°C, must be related to the lower initial die temperature. Although the starting values of E for both J94-12 and J94-13 are higher, they decrease more rapidly than those in 394-14. This implies that the low speed cracking would disappear in the extrudate earlier than noted in J94-14. This is consistent with the low speed cracking ranges at the front end of each extrudate, with J94-14 having the longest low speed cracking length and J94-13 the shortest (Table 4.7). The variation of E during extrusion for different extrusion ratios, is shown in Fig. 8.24. Apparently, the highest extrusion ratio of J94-20 has the highest E value with the longest low speed cracking range in its extrudate. 394-6, with the smallest extrusion ratio, has the lowest E value and the shortest cracking range (Table 4.7).  Although the E value variation  corresponds qualitatively with the low speed cracking, the determination of the Cf value is difficult, because it is dependent on temperature, strain rate, and the process itself. However, in the plant trials at UAC, the large variation of ram speed would result in both strain rate and temperature fluctuations in the deformation zone. One way to determine the product of ae is to conduct a series of tests (e.g., collar tests) in the laboratory at different temperatures and strain-rates to measure the fracture stress and strain. However, it would still be difficult to specify the fracture stress and strain at the crack position; and moreover, the applicability of the laboratory test results to the industrial process would need to be verified.  210  Chapter 9 EXTRUSION OF THE PRIVIMCs  It is conceivable that the unique properties of particulate reinforced MMCs will ensure their place in automobiles and other applications by the year 2000 or before . 11151  As  mentioned in the literature review, MMCs can be applied in the manufacture of the automobiles in several areas, such as drive shafts, brake rotors, engine blocks and cylinder liners, connecting rods and pistons, tire studs, etc. Although, of the mentioned parts, only the drive shafts and the connecting rods are produced through extrusion processing, the. manufacturing technologies, involving control of consistent material quality and hightolerance tube extrusion techniques, etc., are critical to the successful implementation of drive shafts in high-volume automotive applications. Quality aspects of the MMCs of concern to the customer for application in the auto industry include specific stiffness, fatigue life, wear . However, different parts have 181 resistance, tailorable properties (e.g., thermal expansion) different quality requirements. Taking the drive shafts for example, the high specific modulus of MMCs is a veiy cost-effective improvement. Although the elastic modulus reduction occurs during low temperature defonnation because of damage by particle fracture, especially for metal matrix composites with a high volume fraction (e.g., 20%)  [995.h161,  it has been  confirmed that the hot extrusion process does not reduce the elastic modulus and tensile strength. Instead, it may increase the tensile properties due to an increase in the homogeneity of the particle distribution and particle size refinement. Fatigue life of the composites could also be affected by thennomechanical processing (e.g. hot extrusion). Improvements in the fatigue strength of MMCs, compared to parent alloys are reported, but a lower specific fatigue strength for 606lIAlO3I20p compared to 6061 is also seen, which could depend  Chapter 9 Extrusion of the PRMMCs  211  critically on both the method of testing and the quality of the composites’ . 81  Therefore,  acceptable process windows for reliably producing higher quality and high-volume production of the MMCs are yet to be defmed.  9.1 Development of Extrusion Limit Diagram 9.1.1 Using Empirical Equations The empirical equations used for the development of extrusion limit diagrams have been described in Section 2.3 in the literature review. For convenience, two main equations are listed below in Eq. (9.1) and (9.2). The extrusion pressure can be estimated using Eq. (9.1), which is related to the press parameters (e.g., R, L, Dc) and the extruded material properties (e.g.,  (X,  n, A). From the plant trial data at KRDC, and at UAC, the four constants  in Equation (9.1) have been estimated for both the extrusion presses (Table 9.1). (9.1)  p=!{B+CinR+Elfl..+FQ.)(....L)} an A AD  Table 9.1 Constants in Eq. (9.1) for the composites  Small Press at KRDC for 606 l/A1 /20p 3 O 2 Large Press atUAC for 606 1/A1 /20p 3 0 2 Large Press atUAC for 6061/A1 1l0p 3 0 2  B  C  E  F  36.07 17  16.8 147  -43.9526  40.6549  Correlation Coeff. 0.9882  291.0946  214.6415  -205.3810  218.3884  0.9804  443.0187  260.1046  -211.9300  205.3414  0.9381  A good correlation was obtained between the measured peak load and the prediction by the above equation. Hence the pressure limit line in a limit diagram can be delineated, at least tentatively, using Eq.(9. 1), based on the press limit . 15551  Chapter 9 Extrusion of the PRMMCs  212  With respect to the bifiet temperature rise during extrusion, the following equation (see also Eq. 2.9) is used, based on an assumption that there is little or no temperature difference between the billet and the surrounding tools’ . This assumption is valid for the 631 plant trial at KRDC, because both the die and the billet were heated at the same time in the same furnace. However, the die temperature in the plant trial at UAC was significantly lower than that of the billet.  For simplicity, in the calculation of temperature rise, the initial  temperature difference between the bifiet and the tools was ignored, while the internal generation of heat establishes a temperature differential, AT = 0.9PvBt I C 1 (t)  =  t” + (K 1 (K 2 +3 3÷3 )?’ + (K 4 K )t” + t) 5 K 11 K O.9PvBt I 2  (9.2)  Based on Eqs. (9.1) and (9.2) for peak pressure and temperature rise, extrusion limit diagrams can be developed for the Duralcan® composite materials extruded in the small press at KRDC and the large press at UAC.  Figure 9.1 shows a limit diagram at a constant  extrusion ratio of 28 for 606 1/A1 /20p for the press at KRDC. Due to the low capacity of 3 0 2 the press (—l000kN), the operating window for extrusion processing is small. Figure 9.2 shows a limit diagram for the same material at a constant ram speed of 12.5mmJs (maximum speed for the press at KRDC). A ram speed of 35mm/s for Duralcan® material processed at an extrusion ratio of 25 and 14mm/s for SiCp reinforced composites (matrix alloy: A357) at an extrusion ratio of 36 has been reported in industrial extrusion practice’ ’ 9 ’.  A limit diagram for 2 606l/A1 ! 3 O 2Op for the large press at UAC under an  extrusion ratio of 34 is shown in Fig. 9.3. It is seen that, due to the large capacity of the press (3000 tons), the process window is much larger than that at KRDC. This indicates that the pressure limit for the large press at UAC is not a problem for extrusion of the composites at high temperature.  Chapter 9 Extrusion ofthe PRMMCs  213  60 50  Extrusion Ratio: 28  F.  40 30  1  4 j  20 10  Pressure Limit  0 420  Incipient Melting i  440  460  480  500  540  520  Extrusion Temperature (°C) Figure 9.1 Extrusion limit diagram at an extrusion ratio of 28 for  /20p for the press at KRDC 3 0 2 6061/A1 8  6  350  Ram Spee& 12.5mm/s  375  400  425  450  475  500  525  Extrusion Temperature (°C) Figure 9.2 Extrusion limit diagram at a ram speed of 12.5mm/s for  6061/A1 / 3 0 2 20p for the press at KRDC  550  575  Chapter 9 Extrusion of the PRMMCs  214  125 100  ‘g  0  -  04  Cl)  0  75  Pressre Limit  Incipient Melting  50 25 I  I  250  I  I  450 400 350 Extrusion Temperature (°C)  300  500  550  /20p at an extrusion ratio 3 0 2 Figure 9.3 Extrusion limit diagram for 606 1/Al of 34 for the large press at UAC 400  300  ressure Limit  200  Incipient Melting  l00  0  200  I  I  250  300  450 400 350 Extrusion Temperature (°C)  500  550  /lOp at an extrusion ratio 3 0 2 Figure 9.4 Extrusion limit dIagram for 606 11A1 of 34 for the large press at UAC  Chapter 9 Extrusion of the PRMMCs  215  An extrusion limit diagram for  I1Op was also developed for the large press 3 O 2 606l/A1  at UAC using the empirical equations (Fig. 9.4). It is evident that the process window of /lOp is even larger than that for 606 l/A1 3 0 2 6061/A1 /20p due to its lower flow stress. 3 0 2  9.1.2 Using Finite Element Method 9.1.2.1 Application of the Finite Element Model Extrusion limit diagrams are usually developed using the above empirical equations, based on extrusion plant trials. The assumptions and simplification of heat transfer analysis for derivation of the empirical equation for temperature rise during extrusion may lead to inaccuracy of the processing window. Moreover, to have an accurate load prediction, a small number of plant trials are necessary to determine the coefficients in Eq. (9.1). Obviously, this approach is not cost effective. As computation technology advances, extrusion limit diagrams can also be developed using the fmite element technique. Based on the fmite element predictions, a relationship between temperature rise and billet temperature and extrusion speed may be obtained, AT=fI(T,vB)  (9.3)  Similarly, a relationship between peak pressure and the two variables can also be established: (T,vB) 2 P=f  (9.4)  With the aid of DEFORM, extrusion of the composite material was simulated at different ram speeds and different initial billet temperatures. The ram speed varied from 1 to  50 mm/s for the press at KRDC and 1 to 75mm/s for the press at UAC; while the initial billet temperature changed from 400°C to 550°C for the press at KRDC (because of its low load capacity) and 300°C to 570°C for the press at UAC. The initial die temperature was assumed to be 30°C less than that of the billet, while the container temperature was the same as that of  Chapter 9 Extrusion of the PRMMCs  216  the die. The temperature of the pressure pad was 70°C. The interface friction was assumed to be sticking between the billet and the die, and between the billet and the container, while a friction shear factor of m=0.7 was assigned to the interface between the billet and the pressure pad, due to its lower temperature. The heat transfer coefficient at the interfaces was assumed to be 2O0kW/m°C . 18  All the other boundary conditions were the same as described in  Chapter 5. The incipient melting point of 5 82°C for the 6061/A1 /20p composite material 3 0 2 was used , and was taken as the limiting boundary for the incipient melting line in the 155571 extrusion limit diagram. An extrusion limit diagram for 606 1/A1 120p for the small press at KRDC was thus 3 0 2 developed, as shown in Fig. 9.5.  Correspondingly, the extrusion limit diagram for  606 11A1203/20P for the press at UAC is shown in Fig. 9.6. Again, the processing window for the press at UAC is much larger than that for the press at KRDC. 160  I  120  80  40  0 375  425  475 Extrusion Temperature (°C)  525  /20p for the press at KRDC 3 0 2 FIgure 9.5 Extrusion limit diagram for 606 1/A1  575  Chapter 9 Extrusion of the PRMMCs  217  125 100  j75 Incipient Melting  Pressure Limit  50 25 0 250  300  I 450 350 400 Extrusion Temperature (°C)  500  550  Figure 9.6 The limit diagram for 606 1/A1 /2Op for the press at UAC 3 0 2 9.1.2.2 Comparison of Extrusion Limit Diagrams The extrusion limit diagrams for 606 l/A1 /2Op for the press at KRDC and UAC by 3 O 2 both the empirical-equation technique and the finite element method are shown in FIgs. 9.7  and 9.8.  The pressure limit lines in the diagram from both techniques are quite close,  especially in the limit diagram for the press at KRDC. This is expected because the empirical  pressure equation (9.1) was determined using the plant trial data. The discrepancy between the pressure limit lines obtained by the two techniques in the diagram for the press at UAC is due to the low boundary temperature of about 250-300°C, because this temperature is beyond  the valid extrusion temperature range of 390°C  -  485°C used to determine the empirical  equation (9.1). This might result in inaccuracy of the pressure prediction by the empirical equation (9.1). The difference between the two incipient melting lines is more obvious. This is mainly due to simplification of heat transfer analysis for the temperature rise estimation in  Chapter 9 Extrusion of the PRMMCs  218  the empirical equation (9.2), because the FEM model considered coupled thermal and mechanical phenomena for both the billet itself and the suffounding tools during extrusion to steady state. The model predictions have been validated by comparison with the measured data in Chapter 5. Limit diagrams for both the 2 6061/A1 1 3 0 l0p and the 2 6061/Al O ’2Op using the empirical equations are shown in Fig. 9.9. It is seen that the processing window for the 6061/A1 1 3 0 2 20p is totally within the window of 6061/A1 /lOp. This is due to the lower 3 0 2  /lOp. It thus can be concluded that the safe processing conditions 3 0 2 flow stress of 606 1!A1 for 606 1/A1 /20p are also safe for the processing of 606 / 3 0 2 2 1/A1 3 0 lOp.  160 140  Extrusion Ratio: 28  ._120  ----FEM Empirical Equation  100 80 60 40 Pressure Limit  20 0  -  375  395  -  r  415  -  frf Incipient Melting i  -  435  455  475  495  515  535  555  Extrusion Temperature (°C)  /2Op for 3 0 2 Figure 9.7 Comparison of the extrusion limit diagram of 606 1/A1 the press at KRDC using different techniques  575  Chapter 9 Extrusion of the PRMMCs  125  219  1 ;  FEM --  .  75’  :  50  --  I I  Empncal  —  Incipient Melting  I  25 .:‘PreureLimft 0 250  I .450  300  350 400 Extrusion Temperature (°C)  500  550  Figure 9.8 Comparison of the extrusion limit diagram of 606 2 1/A I 3 O 2Op 1 for the press at UAC using different techniques  200 20% 15O  I: 200  Pressure L \tMe  250  300  350 400 450 Extrusion Temperrature (°C)  500  6061 / 3 0 lO /A1 p and Figure 9.9 The extrusion limit diagram for both 2 1/A 0 y’2O1 606 2 p using the empirical equation technique  550  Chapter 9 Extrusion of the PRMMCs  220  9.2 Extrusion Limit Diagram with Low Speed Cracking Boundary As observed in the plant trial at UAC, low speed cracking occurs at the front of extrudates in most of the trials. It is veiy important to delineate the boundaries of low speed cracking in the extrusion limit diagram for safe processing. Although a preliminary fracture criterion for the low speed cracking has been proposed in Chapter 8, it is still difficult to predict the low speed cracking by including a low speed criterion in the finite element model. Fortunately, substantial data on low speed cracking during the plant trial at different extrusion conditions has been generated, and the boundaries of low speed cracking can be delineated by processing the data.  9.2.1 Low Speed Cracking Boundary During extrusion in the plant trial at UAC, the ram speed varied from less than 1mm/s to about 6mm/s, and the coverage of low-speed cracks on the surface of the extrudates changed from a few centimeters to more than 6 meters under different extrusion speeds and temperatures (Table 4.7). Because the billet temperature changes during extrusion, due to the heat of deformation, to track the billet temperature change, DEFORM was applied to the cases exhibiting long coverage of low-speed cracks through the extrudates (e.g., J94-6, J9412, J94-13, J94-14, J94-20). The varying extrusion temperature and ram speed were traced from the front end of the extrudates exhibiting low speed cracks, toward the back end, until they disappeared. Then the data points traced from the recorded ram displacement were divided into two groups, the one associated with low speed cracking (termed as ‘Fail’), and the other without low speed cracks (termed as ‘Safe’). Thus the low speed cracking boundary of the extrudates of 606 1/Al /20p under the same extrusion ratio can be delineated, as 3 0 2 shown in Figs. 9.10 to 9.12 for three different extrusion ratios.  Chapter 9 Extrusion of the PRMMCs  221  8 R=13  —‘6  a  a 394-5-s •: J944.f 394-6-s ‘. x 394-7-f oJ94-7-s — Boundary  0  o  Safe  (/2  2  :&. :e.*.  Fail  *.  .  t  I  I  0  445  450  455  465  460  470  475  Extrusion Temperature (°C) Figure 9.10 Low speed cracking boundary for the extrudate of  I20p at an extrusion ratio of 13 3 O 2 606 lIAl 8 x S91-3-f o S91-3-s A 194-12-f 394-12-s X 394-13-f o 394-13-s + 394-14-f a 394-14-s Boundary  R=34  6  0  Safe 4 Fail AZ4  A  0420  a  I  450  480  510  Extrusion Temperature (°C)  Figure 9.11 Low speed cracking boundary for the extrudate of OJ2Op at an extrusion ratio of 34 2 606 l/A1  540  Chapter 9 Extrusion of the PRMMCs  222  8 R=52  z 394-19-f *  -  Safe  A  4 Fail  394-19-s 394-20-f 394-20-s Boundary  A  420  440  460  480  500  520  540  560  Extrusion Temperature (°C) Figure 9.12 Low speed cracking boundary for the extrudate of  /20p at an extrusion ratio of 52 3 0 2 606 1/A1 In the legend of Figs. 9.10 to 9.12, the symbol ‘-f and ‘-s’ denote ‘fail’ and ‘safe’, respectively for each extrudate. Due to less data being available for the 606 1/A1 /lOp, the 3 0 2 low speed boundary could not be delineated.  9.2.2 Effect of Extrusion Ratios The effect of extrusion ratio on the low speed cracking boundary is shown in Fig. 9.13. It is noted that to understand the effect of the extrusion ratio, the ram speed should be converted into extrusion exit speed, which is multiplied by the extrusion ratio. It is seen that as the extrusion ratio, R, increases, the low speed cracking boundary shifts toward high extrusion speed and higher temperature. This is consistent with the observation of the plant trial results, that is, more frequent low speed cracking occurred when the extrusion ratio was increased. The trend of the low speed cracking boundaries indicates that at a low extrusion  Chapter 9 Extrusion of the PRtfMCs  223  ratio, temperature has a larger effect than the ram speed, and vice versa at a high extrusion ratio. This is because at low extrusion ratio, the temperature rise of the billet due to the heat of deformation is low, and at a high extrusion ratio, because of higher exit speed, the adiabatic effect becomes more significant.. 350 ri  300  m R=13-safe  250  Safe  R=34-fail  200  a  R=13-fail  *  R=34-safe  .  R=52-fail  150  A  Increasing R  A  R=52-safe  100 50  Fail  c 0  Low Speed Cracldng Boundary  0 420  450  480 Extrusion Temperature (°C)  510  540  Figure 9.13 Effect on extrusion ratios on low speed cracking boundary /20p 3 during extrusion of 606 1/A1O 9.2.3 Extrusion Limit Diagram with Low Speed Cracking Boundary The boundaries of low-speed cracking at different extrusion ratios are incorporated with the extrusion limit diagram developed using the FEM technique, as shown in Fig. 9.10.  However, because of the limited range for the low speed cracking, only a part of the extrusion limit diagram is presented to clarify the low speed cracking boundaries. The high speed boundary refers to the incipient melting line obtained from Fig. 9.6. It is evident that an increase in either temperature or extrusion speed is beneficial to preventing occurrence of the  Chapter 9 Extrusion of the PRMMCs  224  low-speed cracking. The boundary line shifts towards the high speed cracking line (high speed boundary) as the extrusion ratio increases to reduce the size of processing window. However, because no low speed cracking was observed at a ram speed of -6mm/s in the plant trials at UAC, 6mm/s is the minimum ram speed for the 7-inch press at UAC for extrusion of the PRMMCs at the extrusion ratio of 52.  600  500 ,  —  High Speed High Speed Boundary  R=13  400  R=34  c 300  —  100 0  R=52  Increasing R  Fail  \  Low Speed Boundary  Fail  I  I  420  Safe  450  510 Extrusion Temperature (°C) 480  540  570  Figure 9.14 Extrusion limit diagram of 606 l/A1 /20p for the press at UAC 3 0 2 with low-speed cracking boundaries  9.3 Extrusion of the PRMMCs Particle fracture, with its size refinement and particle redistribution during extrusion, has been examined in Chapter 7. The origin of low speed cracking observed in the plant trials has been explored with the aid of both macroscopic and microscopic finite element models in Chapter 8. It is therefore essential to minimize the potential microscopic damage, such as unhealed fractured particles and interface decohesion, which might lead to macroscopic low  Chapter 9 Extrusion of the PRMMCs  225  speed cracking on the extrudate surface, and also to improve the quality of the PRMMCs by optimizing the extrusion processing conditions for maximum productivity.  9.3.1 Minimization of Microstructural Damage during Extrusion The extrudates from two plant trials at KRDC and UAC were cut and polished. The specimen from the plant trial at KRDC was cut from the front end of the extrudate, K-6, and polished at KRDC following the procedure listed in Table 7.1; the specimens from the plant trial at UAC were also cut from the front end of the extrudates, 394-14, 394-20, with severe low speed cracks visible on the surface, and J94-l 1B, with slight low speed cracks, and polished at UBC following the procedure in Table 7.2. The extrusion conditions for the four specimens are listed in Table 9.2. The polishing samples were examined under an SEM for microstructure comparison. It seemed that some voids were present in the surface layer for all extrudates. The voids in the specimen from UAC were recognized as the origin of the low speed cracks, as shown in Fig. 9.15 from J94-14; while voids in K-6 specimen were associated with clusters, as shown in Fig. 9.16 for both the longitudinal and transverse sections.  Table 9.2 Extrusion conditions for the specimens examined under an SEM Trial #  Material  Temp.  Extrusion  (°C)  Ratio  Billet Din. (mm)  Remark  394- 14  20%  461 (Front)  34  178  Severe cracking  394-20  20%  457 (Front)  52  178  Severe cracking  J94-11B  10%  434 (Front)  34  178  Slight cracking  K-6  10%  496(Front)  28  51  No cracking  In the longitudinal section, again, most of the voids were formed at two ends of aligned particles in the extrusion direction, although some were also associated with particle fracture. The voids in the transverse section were randomly located around a particle or in a  Chapter 9 Extrusion of the PRMMCs  226  cluster. The voids observed in the surface layer of the front-end extrudates could be due to the following reasons: i) some voids could have been in the as-cast materials, not removed by extrusion, especially those in clusters. Any processing route in which the ceramic particles are not fully separated is susceptible to voids. In the cast materials, the voids are located between the particles (e.g., in clusters). Therefore there is more likelihood of seeing voids in the as-cast ,  6O6l/A1 / 3 O 2 lOp because of the smaller particle size and its tendency towards particle clustering. This kind of void could be removed by either improving the particle distribution during the melt fabrication or breaking the clusters during extrusion. ii) Voids form when a fractured particle was not healed by intruding the matrix material into the cracked gap. Most of these voids would be avoided by high hydrostatic pressure during extrusion at high temperature. iii) Voids may also form by interface decohesion. Decohesion is encouraged by weak . The 1231 interfaces, such as obtained by spinel formation, MgA1 , at the particle interfacet 4 O 2 generation of tensile stress in the surface layer of the extrudate in the die land area would lead to void formation, if either the tensile stress is higher or the interface was weak enough. Therefore, the tensile stress should be minimized by controlling all the possible extrusion parameters studied in Chapter 8, e.g., higher initial temperature of billet and die, high ram speed, low friction at the die interface. Elimination of spinel formation at the particle interface by increasing the magnesium content in the matrix alloy has been 231 studied and new matrix , formationU during l alloys could also be sought with a better 1 ductility 2 ’ 21 and free of spinel 23  primary processing.  die was A In addition, a better die design, such as stream line 2  recommended to minimize the fracture behavior during extrusion of MMCs. However, it is  Chapter 9 Extrusion of the PRMMCs  227  (a) Transverse  ‘I  (b) Longitudinal Figure 9.15 Voids in the surface layer of an extrudate of 606 1/Al2Oil2Op at an extrusion ratio of about 34 with low speed cracking (front end of J94-14)  Chapter 9 Extrusion of the PRMMCs  228  (a) Transverse  (b) Longitudinal Figure 9.16 Voids in the surface layer of an extrudate of 6061/A1 110p 3 0 2 at an extrusion ratio of about 28 with low speed cracking (front end of K-6)  Chapter 9 Extrusion of the PRMMCs  229  unclear whether the use of a stream line die may sacrifice the improvement of particle  distribution obtained by the flat face die extrusion, or increase the tendency of low speed cracking due to die interface friction. The adoption of a hydrostatic extrusion process 761 ’ 11112 is certainly helpful to suppress void formation, although the production cost could become a concern. It is interesting to note that no obvious voids were present in the surface layer of the extrudates cut from the back end without visible low speed cracks on the surface, as shown in Fig. 9.17 for J94-14. This is mainly due to different extrusion temperatures and different ram speeds for the extrudates from the plant trials at UAC. Taking J94-14 for an example: at the front end, the extrusion temperature is about 460°C at a ram speed of about 1mm/s. However, at the back end, the extrusion temperature is about 5 5-60°C higher than that at the front end because of heat of deformation at a raised ram speed of about 6mm/s. Because microstructural damage, such as particle fracture and/or void formation, may affect the elastic modulus of the 995 composites the variation of values of the extrudates , 1 ” obtained under different extrusion conditions provide information on the effect of microstructural damage. The correlation between Young’s modulus, E, of a hardened cement paste and the porosity P 0 was described as follows: E=E 0 exp(—xP ) 0  (9.5)  where E 0 is the modulus of the solid phase without any pores and x is a material constant i. 4 dependent on the internal structureElO  This may also be applicable to the composite  materials during extrusion, where E is the elastic modulus of the composites after extrusion and E 0 is a standard elastic modulus which is a function of matrix alloy, reinforcement material and volume fraction of the reinforcement for a specific MMC. Hence the change in elastic  230  Chapter 9 Extrusion of the PRMMCs  modulus of the composites for different extrusion conditions should reflect the existence of significant voids in the extrudates as a result of particle cracks, interface debonding, etc. For the extrudates from KRDC, the elastic modulus as well as yield strength and the UTS for two different extrusion ratios (10 and 28) were tested, with little difference being found (See Fig. 4.18). This indicates that the void formation is not significant based on Eq. (9.5), although the elongation was sacrificed probably due to the presence of voids and/or the slight increase in the tensile strength.  Obviously, the high hydrostatic pressure in the  deformation zone helped suppress the void formation and growth during hot extrusion. However, it should be pointed out that at a higher temperature it seems likely that the lowest melting point phases could melt, leading to void formation. The low melting point phases must be associated with particles which were found at the dendrite extremities in the as-cast state.  Figure 9.17 SEM image in the surface layer of the extrudate in longitudinal section at an extrusion ratio of about 34 without low speed surface cracking (back end of 394-14)  Chapter 9 Extrusion of the PRMMCs  231  9.3.2 Improvement in Partide Distribution and Size Refinement It is well known that at room temperature the elastic modulus deteriorates as strain increases, due to particle . 94 This is because the fractured particles were not ’ 7576 fracture healed at room temperature. However, in the hot extrusion process, the stress state in the deformation zone is tn-axial compressive, except in the surface layer of the extrudate in the die land area where the stress component in the extrusion direction is tensile.  The  compressive stress state results in two beneficial effects: firstly, void formation and growth is largely suppressed; secondly, most of the fractured particles were healed due to both severe shear and compressive deformation, because there is no oxidation in freshly formed surfaces 1-12,75-76]. 1 Reduction in particle size is known to be associated with an increase in the yield strength of composite materials. This decrease in size, in conjunction with the increased homogeneity of the particle distribution and reduction in aspect ratio, is expected to improve the fracture toughness. The healing of fractured particles will allow the material to attain its maximum potential elastic modulus. However, it could be balanced by the void formation if the secondary processing, e.g., extrusion, was not well controlled. A slight increase in the elastic modulus of the composites with an increase of the extrusion ratio (from the tensile tests) indicates that a large extrusion ratio should be beneficial to the improvement of mechanical properties, if and only if the voids can be minimized.  9.3.3 Quality and Productivity of the PRMMCs Based on the above analysis, for a better quality control, a high extrusion temperature with a high absolute reduction would be suggested for the processing of the PRMMCs because of the following reasons:  Chapter 9 Extrusion of the PRMMCs  232  i) the increase in temperature improves the matrix flow due to lower flow stress, which, in turn, results in a series of beneficial effects: a) a lower tensile stress in the surface layer of the extrudate in the die land zone, which also leads to a lower local tensile stress at the ends of a particle, which could become a source of interface decohesion; b) a lower particle fracture probability based on the particle fracture model; c) easier to heal the gap between fracture particles due to matrix flow; d) more importantly, an increase in the ductility of the composite materials, which is the one of the controlling factor for fracture behavior of particulate reinforced MMCs ; 11221 ii) a higher absolute reduction is likely to result in a larger movement of particles in the deformation zone during extrusion which helps break clusters to improve the particle distribution; the clusters are always the source of potential damage, as presented in the micromecharncal analysis of the PRMMCs in Chapter 6 and Chapter 8. A higher extrusion speed is also recommended for extrusion of the PRMMCs. This is mainly due to: i) a higher extrusion speed will eliminate the low speed cracking, as described in Chapter 8; ii) it also helps the break-up of the particle clusters in the shear deformation zone; the cluster acts as a harder zone during deformation whose effect decreases as the strain rate ; 11 increases iii) more importantly, the higher extrusion speed will result in a larger productivity of the composites, which reduces the production cost, and consequently makes the product more competitive. Certainly, the high productivity is constrained by the high speed defects (such as void formation due to low melting phases, and high speed cracks on the surface). For this reason,  Chapter 9 Extrusion of the PRMMCs  233  the composites should be processed within the high speed boundary of the extrusion limit diagram developed.  Chapter 10 Concluding Remarks  234  Chapter 10 CONCLUDING REMARKS  10.1 Summary and Conclusions To convince customers to use Duralcan® materials, high quality product must be produced with a competitive price. A complete physical and chemical understanding of the product is essential for better quality and higher productivity. Hence, two extrusion plant trials were conducted on the Duralcan® materials; and the extrusion processes in two different presses have been simulated with the aid of a finite element model, DEFORM®. The plant trial data were used to validate the model predictions. Particle fracture and size refmement were observed in microstructural examination of the composites during extrusion. The finite element model predictions at both macroscopic and microscopic level were correlated with microstructure changes.  IlOp and the 3 O 2 Extrusion limit diagrams for both the 6O61IA1  /20p were developed by both an empirical technique and the finite element 3 O 2 606 11A1 technique, and modified with the low speed cracking boundary which is specific to the PRMMCs. The mechanism of low speed cracking was studied with the aid of the finite element model and the SEM analysis. The major findings from this study are summarized as follows: 1) Particles fractured during extrusion with accumulation of smaller particles in extrudates. Three particle fracture modes were proposed, i.e., comminution mode, shear mode, and tensile mode. Most of the fractured particles were healed under large hydrostatic pressure and shear deformation at high temperature.  Chapter 10 Concluding Remarks  235  2) Particles are aligned in the extrusion direction with formation of extrusion bands, especially in the 606lIAl I10p. Voids were observed in the surface layer of the extrudates 3 O 2 with low speed cracks, and also in those extrudates with severe particle clusters, especially the  606l/A1 / 3 O 2 lOp.  The causes for void formation could be three-fold:  i) retained from the as-cast material, especially for those in clusters; ii) unhealed particle fracture in the surface layer at relatively low temperature; iii) weak particle interface under high local tensile stress at the ends of the particles, especially for those in clusters in the surface layer of the extrudate. These voids can be avoided by controlling the processing parameters in both the primary and secondly processing routes. The hydrostatic pressure generated during flat-face die extrusion may help suppress void formation and growth. This is why the elastic modulus and other tensile strengths (e.g., yield stress, and the ultimate tensile strength) do not decline under an extrusion ratio of about 30, although the elongation is sacrificed. The improvement in homogenization of particle distribution and the particle size refinement after extrusion allow the maximum potential increase of tensile properties and also the fracture toughness, if the void formation can be suppressed by generation of a high hydrostatic pressure and low tensile stress in the surface layer as obtained in higher temperature extrusion. 3) The safe processing window for the extrusion of the Duralcan materials was squeezed towards the high temperature side by the low speed cracking boundary. The low speed cracking, observed at the front end of extrudates, is believed to be induced by low ductility of the materials and void formation and growth at relative low temperature under tensile stress in the die land zone. Both the low speed cracking and the void formation can be suppressed by increasing the initial billet and die temperature and the extrusion speed within  Chapter 10 Concluding Remarks  236  the limit of the high speed cracking boundary (incipient melting line) with better quality and larger productivity of the PRMMCs.  10.2 Future Work To better understand the physical and chemical nature of the composites, the following work is suggested based on the above study. 1) Because the origin of the low speed cracking is associated with void formation, a quantitative analysis of the fraction of voids formed under different temperature and strain rate is beneficial for a more accurate control of the processing parameters, such as temperature and extrusion speed, to improve quality (to minimize voids and obtain more homogenized particle distribution at a finer and a more uniform particle size level) and productivity; 2) A fracture criterion for low speed cracking or potential microstructural damage during extrusion needs to be developed and verified.  The fracture criterion can then be  incorporated into the finite element model to cost-effectively develop extrusion limit diagrams for different materials. 3) An effective technique is required at the fabrication stage to improve both the particle distribution and the bonding strength between the particles and the matrix to prevent potential interface decohesion. New choices of matrix alloys with higher ductility but free of spinel formation are needed. A better design of the die to have improved quality and higher productivity of the extruded products should also be studied. New processing technologies which produce defect free products with lower production costs should be explored.  References  237  REFERENCES  [1] Chawla, K.K.: ‘Composite Materials, Science and Engineering’, Material Research and Engineering (MRE), Springer-Verlag, 1987. [2] Caron, S.; Masounave, J.: A Literature Review on Fabrication Techniques of Particulate Reinforced Metal Composites, Proc. of mt. 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