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Sintering behaviour of cupronickel alloy powder Bala, Sathish Rao 1976

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SINTERING BEHAVIOUR OF CUPRONICKEL ALLOY POWDER by SATHISH RAO BALA B . S c . , U n i v e r s i t y o f M y s o r e , Ind ia (1966) B . E . , Ind ian I n s t i t u t e o f S c i e n c e , B a n g a l o r e , Ind ia (1969) M . A . S c . , The U n i v e r s i t y o f B r i t i s h C o l u m b i a , Canada (1972) A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS OF THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department o f METALLURGY We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE bWTVERSITY OF BRITISH COLUMBIA J u l y , 1976 0 Sathish Rao Bala, 1976 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f M e t a l l u r g y The U n i v e r s i t y o f B r i t i s h Co lumbia V a n c o u v e r 8, Canada Date Ju ly 15, 1976 P A R T A ABSTRACT Studies have been made of both the. solid state and supersolidus sintering characteristics of spherical cupronickel powders. Observations were made of the structural changes and shrinkage rates in specimens sintered in vacuum and in hydrogen. It was concluded that the early stage of solid state sinter-ing (up to one hour at 1200°C) was dominated by Nabarro-Herring creep. Calculations of the stresses at necks during sintering were consistent with the proposed mechanism. No solute segregation to necks occurred during sintering, contrary to earlier observations by Kuczynski with other copper alloys. When pre-sintered cupronickel powder ( 68 ym) aggregates were heated to a temperature above the equilibrium sol idus, melting was nucle-ated f i r s t at high angle grain boundaries (necks) and particle surfaces (voids). Most melting was intragranular, nucleated at interdendritic sites of above-average copper content. Solid-liquid equilibrium was established in less than one minute at the supersolidus temperature. The dihedral angle in the system was less than or equal to zero. i i Growth of solid grains during supersolidus sintering obeyed a parabolic rate law consistent with a model of growth due to phase boundary reaction-controlled solution and precipitation. Shrinkage during supersolidus sintering proceeded in several distinct stages. Prior to attainment of equilibrium; i.e. within the f i r s t minute above the solidus (Stage 1), contraction could be attributed to a melting and melt accommodation sequence, plus flattening by the the local operation of solution and precipitation. Beyond this (Stages 2 and 3) a l l densification was attributed to solution-precipitation, including grain growth. In the final stage of shrinkage (Stage 3) the rate of con-traction was controlled by the rate of escape of gas from closed pores. Comparisons have been made between the supersolidus sintering of cupronickel and the liquid-phase sintering of iron-copper. The processes are seen to have l i t t l e in common. P A k T B ABSTRACT Porous cupronicKe! spec imens with zero to 50 per cent porosity by volume have been prepared from loose prealloyed cupronickel powders by solid s t a t e and supersol idus s i n t e r i n g techniques. Young's Modulus (E) and strength values at low s t r a i n s were determined in compression tests. Porosimetry and metallography were used to establish the continuity, size and shape of the pores. In specimens sintered to > 93% of solid, the pores were essentially a l l closed and e q u i a x e d , and the grains could not be identified with the original powder particles. In this density range, the elastic modulus v a r i e d with fractional p o r o s i t y (P for closed pores) according to E = E 0 ( l - 2 P c ) which for cupronickel is c o n s i s t e n t with the predictions of several pub-lished theoretical analyses based on elasticity theory. Between about 93 and 92% of solid density there was a drop in the elastic modulus associated with the appearance of major amounts of inter-connected, irregular-shaped porosity. With decreasing density below 92 iv per cent of solid, pores increased in number but not in average size. For the range of 92 to 62% of solid, the eiastic modulus was below that pre-dicted from published analysis. However, over the whole range of density, the results fitted reasonably well to the relationship E = E 0 ( l - 2P) where P is the total fractional porosity. This is a special case of a Rule of Mixtures dependence wherein the loose powder aggregate prior to sinter-ing has an i n i t i a l porosity of 0.5 and has zero strength until sintered. The result is discussed in terms of the theoretical variation of the load-carrying neck area with porosity in sintered material. A similar approach is taken to analyse the results of offset strength measurements. V TABLE OF CONTENTS P A R T A Page * i i x i i * * " xxv.i Chapter 1 INTRODUCTION 1 1.1 Solid State Sintering . . . 1 1.1.1 Pure Metal Powders 1 1.1.2 Prealloyed Powders 7 1.2 Liquid Phase Sintering . 8 1.3 Supersolidus Sintering . . 14 1.4 Scope of the Present Research 15 2 EXPERIMENTAL 16 2.1 Choice of Alloy for Experimental Work 16 2.2 Preparation and Characteristics of Powders 17 2.3 Cleaning and Homogenisation of Powder 18 ABSTRACT . . . . LIST OF TABLES . LIST OF FIGURES. ACKNOWLEDGMENTS. v i Chapter Page 2.4 Preparation of Cast Cupronickel Specimens 18 2.5 Preparation of Powder Specimens 23 2.6 Sintering Procedures 24 2.6.1 Vacuum Sintering 24 2.6.2 Superkanthal Furnace Practice 25 2.6.3 Thermocouple Calibration . . . . . . . . . 29 2.7 Experimental Difficulties in Studies of Supersol idus Sintering 30 2.8 Dilatometric Experiments 31 2.8.1 Description of the Apparatus 31 2.8.2 Procedures in Dilatometer Runs 34 2.8.3 Advantages and Limitations of the Technique 38 2.9 Optical Metallography 39 2.10 Microprobe Analysis 43 2.11 Scanning Electron Microscopy 48 2.12 Density Determinations. . 48 3 RESULTS. , 50 3.1 Phase Equilibria in Cupronickel 50 3.1.1 Published Phase Diagrams 50 3.1.2 Effect of Impurities in Cupronickel. . . . 52 3.1.3 Thermal Data from Quenching Experiments. . 54 3.2 Structure and Homogeneity of Presintered Specimens 66 3.3 Sintering Behaviour 68 v i i Chapter Page 3.3.1 Sintering at 1200°C . 68 3.3.2 Supersolidus Sintering in Vacuum 71 3.3.3 Sintering in Hydrogen at 1200-1273°C . . . 82 3.3.4 Sintering at 1273°C in Hydrogen 87 3.3.5 Sintering at Temperatures Above 1273°C . . 100 3.4 Dilatometer Results 100 3.4.1 Qualitative Observations on the Progress of Shrinkage 100 3.4.2 Anisotropy of Shrinkage in Dilatometer Runs 105 3.4.3 Calculated versus Measured Density Changes. . 106 3.4.4 Metallographic and Microprobe Analyses 110 3.4.5 Effect of Powder Particle Size 124 3.5 Behaviour of Cast Cupronickel 124 3.5.1 Structure of Cast and Homogenised Specimens 124 3.5.2 Liquid Formation on Heating Above the Sol idus 128 4 DISCUSSION 134 4.1 Solid State Sintering Behaviour of Loose Powders 134 4.1.1 Sintering in Real versus Model Systems 134 4.1.2 Observations of Early Sintering Kinetics 135 4.1.3 Structural Changes During Sintering. . . . 138 v i i i Chapter Page 4.1.4 Possible Mechanisms of Early Shrinkage 142 4.1.5 Segregation of Solute During Sintering 154 4.2 Melting Behaviour of Cupronickel 160 4.2.1 The Partial Melting of Metals and Alloys 160 4.2.2 The Partial Melting of Cast Cupronickel 163 4.2.3 The Partial Melting of Sintered Cupronickel 164 4.2.4 Attainment of Solid-Liquid Equilibrium 168 4.3 Grain Growth During Supersolidus Sintering 172 4.3.1 Mechanisms of Growth 172 4.3.2 Growth Law for the Present Results 176 4.4 Shrinkage During Supersolidus Sintering 182 4.4.1 Possible Stage 1 Shrinkage Mechanisms 184 4.4.2 Role of Coalescences and Bridges 192 4.4.3 Possible Shrinkage Mechanisms in Stage 2 and 3 195 4.4.4 Transition from Stage 2 to Stage 3 . . . . 198 4.4.5 Kinetics of Shrinkage 200 4.4.6 Summary. 209 4.5 Comparison of Supersolidus and Liquid Phase Sintering 211 5 CONCLUSIONS 215 REFERENCES . ' 218 ix TABLE OF CONTENTS P A R T B Page ABSTRACT i v LIST OF TABLES x i v LIST OF FIGURES n l l i Chapter 1 INTRODUCTION 227 1.1 Review of Previous Work 227 1.1.1 Elastic Constants for Porous Materials . . 227 1.1.2 Strength of Porous Materials 234 1.2 Scope of the Present Work ...... .. . . . . . . 239 2 EXPERIMENTAL PROCEDURE . . . ._. . 241 ,v 2.1 Compression Test Specimens and Technique. . . . • .•'••">' 241-2.2 Heat Treatment and Retesting 243 2.2.1 Homogenisation 243 2.2.2 Resintering 244 2.3 Estimation of Open and Closed Porosity. 246 X Chapter Page 3 RESULTS AND DISCUSSION 248 3.1 Microstructure versus Density 248 3.2 Young's Modulus 258 3.2.1 Elastic Modulus versus Density 258 3.2.2 Interpretation 268 3.3 Plastic Flow Behaviour. 275 4 CONCLUSIONS. . 283 REFERENCES 285 x i LIST OF TABLES PART A Table Page 2.1 Chemical Analysis of Cupronickel Powder Fractions 17 2.2 Thermocouple Calibration Against Melting Point of Pure Copper 30 2.3 Intensity Ratios for the Cu-Ni System Obtained from the MAGIC Programme 44 2.4 MicroDrobe and Chemical Analyses on a Presintered Cupronickel Powder Specimen 46 2.5 Microprobe and Chemical Analyses on Relatively Homogeneous Cupronickel Specimens 47 3.1 Effect of Oxygen and Silicon on the Melting Points of Copper and Nickel 53 3.2 Quenching Experiments and Results . . . 56 3.3 Data for Sintering Experiments at 1200°C 69 3.4 Data for Supersolidus Sintering Runs in the Centorr Furnace. All Runs at 1260°C. . 77 3.5 Oxygen Content of Cupronickel Specimens Sintered at 1200°C and /I260°C in the Centorr Furnace 81 3.6 Data for 30-Minute Sintering Runs at 1200-1273°C in Hydrogen, Part I. 200 x 230 Mesh Powder 83 x i i Table Page 3.7 Data for 30-Minute Sintering Runs in Hydrogen, Part II. 170 x 200 Mesh Powder 84 3.8 Data for 1273°C Sintering Runs in Hydrogen 91 3.9 Quantitative Metallographic Data for Specimens Sintered at 1273°C in Hydrogen 92 3.10 Measured Shrinkage Values for Dilatometer Specimens 104 3.11 Density and Grain Size of Dilatometer Specimens as a Function of the Temperature Attained During the Run 108 3.12 Liquid Distribution in Dilatometer Specimens 118 3.13 Data for Experiments with Cast Cupronickel 129 4.1 Compressive Stresses at the Neck for Various Fractional Interpenetration, According to Leary. 147 4.2 Diffusion Data for Cupronickel Alloy at 1200°C 156 4.3 Dendrite Spacings, Pool Diameter and Pool Spacings of Cast Cupronickel and Sintered Cupronickel 170 4.4 Grain Size Values for Supersolidus Sintered Specimens at Temperatures Other than 1273°C . 179 4.5 Experimental Data Used in Arrhenius Plots of Figure 4.18 180 4.6 Shrinkage Produced by Melt-Accommodation Models 188 4.7 Slopes Obtained by the Linear Regression Method for Different Stages of Sintering at 1273°C 205 4.8 Experimental Values of A and B in the Assumed Relation £f = A + B(.t - t T ) 0 - 5 209 x i i i LIST OF TABLES PART B Table Page 1.1, Prediction of Elastic Constants for Porous Materials . .y. . . . . . . . . .;; 2 1.2 Quantities Used in Skorokhod's Model . . . 6 1.3 Empirical Expressions for the Tensile Strength of Porous Materials 9 3.1 Data for Compression and Xylene-Impregnation Experiments 23 3.2 Treatment Numbers and the Symbols Used in the Figures 26 3.3 Elastic Constants for Cu-Ni Alloys, at Room Temperature 38 3.4 Predicted Values of E for Sintered Cupronickel 40 3.5 Contact Area, Density, and Young's Modulus for Ideal Cubic Packing of Spherical Cupronickel 46 3.6 Values of o°, and b 1 in Equation 3.8 . . 56 xiv LIST OF FIGURES PART A Figure Page 2.1 Scanning electron micrograph of 200 x 230 mesh (68 ym) cupronickel powder, x235 19 2.2 Scanning electron microqraph of 68 ym cupronickel particle, xlOOO 19 2.3 As atomised powder, x250, (a) 68 ym powder and (b) 49 ym powder 20 2.4 Composition versus distance plots for as cast and homogenised cupronickel alloy 22 2.5 Thermal cycle for solid-state sintering in the Centorr furnace 26 2.6 Thermal cycle for supersolidus sintering in the Centorr furnace 26 2.7 Superkanthal furnace assembly. Radiation cage and specimen suspension shown separately 27 2.8 Thermal cycle for supersolidus sintering in the superkanthal furnace. 36 2.9 The dilatometer 32 2.10 Thermal cycle for supersolidus sintering in the dilatometer 36 2.11 A typical- continuous linear dimensional change curve obtained from a .dilatometer 37 XV Figure Page 3.1 The Cu-Ni phase diagram according to Hansen, and Feest and Doherty 51 3.2 The Cu-Ni phase diaqram showing the predicted solid state miscibility gap 51 3.3 The Cu-Ni phase-diagram derived from quenching experiments and probe analyses 57 3.4 Specimen Q22, sintered at 1262°C for 30 min. in hydrogen and quenched; (a) x!20 & (b) x760 58 3.5 Specimen Q20, sintered at 1264°C in hydrogen for 30 min. and quenched; (a) x!20 & (b) x760 59 3.6 Specimen Q19, sintered at 1266°C in hydrogen for 30 min., and quenched; (a) xl20 & (b) x760 60 3.7 Specimen Q18, sintered at 1268°C in hydrogen for 30 min. and quenched; (a) xl20 & (b) x760 61 3.8 Specimen Q 4 2 , sintered at 1273°C in hydrogen for 30 min. and quenched; (a) xl20 & (b) x760 62 3.9 Specimens sintered at 1273°C in hydrogen and quenched, xl20; (a) 047, 5 min., & (b) Q45, 15 min 63 3.10 Copper and nickel x-ray intensity lines superimposed on the absorbed electron image of particle necks in Q22; scanning paths are (a) throuqh the neck, and (b) across the neck; xlOOO 64 3.11 Copper and nickel x-ray intensity lines superimposed on the absorbed electron image of particle necks i n . 020; scanning paths are (a) through the neck & (b) across the neck; xlOOO 64 3.12 Internal structures of as-homogenised particles in a presinter (R66) revealinq grain boundaries, twins and microporosity; x270 67 xvi Figure Page 3.13 Composition versus distance plots for as-received and homogenised 68 ym cupronickel powder particles 68 3.14 Density, densification parameter and rr- versus V o isothermal sintering time for 68 ym cupronickel powder sintered at 1200°C . 70 3.15 Specimen R4, sintered at 1200°C for one hour in vacuum; (a) x270 & (b) x740 72 3.16 Specimen R14, sintered at 1200°C for 5 hours; (a) x270 & (b) x740 73 3.17 Specimen R16, sintered at 1200°C for 10 hours; (a) x270 & (b) x740 74 3.18 Microstructure of the section of R70 after etching with Carapella's reagent. Reveals annealinq twins, x270. . . . 75 3.19 Cu and Ni x-ray intensity lines superimposed on absorbed electron images in 68 ym cupronickel powder specimens' sintered at 1200°C for one hour in hydrogen and quenched; (a) Ql, xlOOO; (b) Q2, xlOOO & (c) Q3, x500 76 3.20 Cupronickel specimens sintered at 1260°C in a vacuum of ~10 - 5 torr, for (a) 10 min. (R60) and (b) 30 min. (R62); xl20 79 3.21 Cupronickel specimens sintered at 1260°C in a vacuum of ~10~2 torr for (a) zero min. R(58), and (b) 5 min. (R52). Specimens helium treated at the end of the runs; xl 20 79 3.22 Cupronickel specimens sintered at 1260°C in a vacuum of ~10-2 torr for (a) 10 min. (R57) & (b) 30 min. (R51). Helium treated at the end; xl20 8 0 3.23 CupronickeT specimens sintered at 1260°C in argon for 30 min; (a) as received powder (R63) and (b) cleaned in hydrogen (R64); xl20 80 x v i i Figure Page 3.24 Density and densification parameter versus sintering temperature for 30 min. runs in hydrogen. 85 3.25 Linear coalescences between particles, as shown at 'C , in specimens sintered (solid state) at (a) 1260°C (Q14) and (b) 1262°C (Q22) for 30 min.; x385 88 3.26 (a) Liquid pools (P), interparticle liquid (as at B), and the shape change of particles at liquid f i l l e d clusters in cupronickel specimens sintered at 1264°C for 30 min. (Q20); x385 88 3.27 Specimen Q19, sintered at 1266°C for 30 min. showing the presence of dense regions and different amounts of penetration of liquid; x385 89 3.28 Specimen (Q18), sintered at 1268°C for 30 min. reveals the presence of large grains, linear coalescences and partial penetration of liquid; x385 89 3.29 Absorbed electron images and x-ray intensity traces showing the presence of liquid at the neck region and the absence of liquid at particle surfaces and at the pore periphery; (a) Q47, x3600, (b) Q47, xlOOO and (c) Q20, xlOOO 90 3.30 Density versus time for supersolidus sintering at 1273°C in hydrogen 93 3.31 Densification parameter versus time for supersolidus sintering at 1273°C in hydrogen 93 3.32 Cupronickel specimens sintered at 1273°C in hydrogen for (a) zero min. (Q38), (b) 5 min. (Q31), (c) 10 min. (033) and (d) 15 min. (Q29); xl20 94 3.33 Cupronickel"specimens sintered at 1273°C in hydrogen for (a) 30 min. Q(28), (b) 45 min. (Q36) and (c) 60 min. (Q66); xl20. 95 3.34 The amount of liquid as pools, and the real grain size, versus time of sintering at 1273°C in hydrogen 97 x v i i i Figure Page 3.35 Scanning electron micrographs of cupronickel specimens sintered at 1273°C in hydrogen for (a) zero min. (Q38), (b) 5 min. (Q31), (c) 10 min. (Q33) and (d) 15 min. (Q29); xl20 98 3.36 Scanning electron micrographs of specimens sintered at 1273°C in hydrogen for (a) 30 min. (Q28), (b) 45 min. (Q36) and (c) 60 min. (Q66); xl20 99 3.37 Bottom section of the specimen sintered at 1285°C for 5 min. in hydrogen. Reveals the segregation of liquid; (a) xl2 and (b) x!45 101 3.38 Corrected r^- versus time plots for 81 ym cupronickel powder. . .° 103 3.39 Sintered dimensions of specimen LVDT 56 . 107 3.40 Density versus time for dilatometer runs 109 3.41 Portion of the longitudinal section of dilatometer specimens (81 ym powder), x7; (a) LVDT 60, (b) LVDT 54, (c) LVDT 49, (d) LVDT 59 and (e) LVDT 55 I l l 3.42 Portion of the longitudinal section of dilatometer specimens, x7; (a) LVDT 56, (b) LVDT 61, (c) LVDT 29, (d) LVDT 62 and (e) LVDT 32 (49 ym) 112 3.43- Results of microprobe surveys across dilatometer 3.46 specimens, Shows composition of nickel-rich solid 113-versus distance from centre 116 3.47 Microstructure of LVDT 59. On the diametral axis (line M) shown in Figure 3.41 .d, at locations (a) surface and (b) 2mm from the surface, x760 119 3.48 Same as Figure 3.47, for locations (a) 4mm from the surface and (b) near the central hole, x760 120 3.49 Microstructures at Region A in Figure 3.41; (a) LVDT 49, (b) LVDT 59, (c) LVDT 53 and (d) LVDT 55, x67 122 xix Figure Page 3.50 Microstructures at Region A in Figure 3.42; (a) LVDT 56, (b) LVDT 61, (c) LVDT 29, and (d) LVDT 62, x67 123 3.51 Linear shrinkage versus time, from start of contraction, for runs 29, 32, 34 . . . . . I 125 3.52 Linear shrinkage versus time, from start of contraction, for runs 30, 31 , 35 126 3.53 As cast cupronickel alloy, (a) x26 and (b) x!20 showing dendritic segregation 127 3.54 As homogenised, cast cupronickel alloy; (a) x26 and (b) xl20 130 3.55 Cast cupronickel specimen SPLS 2, heated at 1273°C for "zero" minutes in hydrogen and quenched; (a) x268 and (b) x.120 130 3.56 Cast cupronickel, SPLS 3, heated at 1273°C for 15 min. and quenched; (a) x268 and (b) x!20 131 3.57 Cast cupronickel SPLS 4, Heated at 1273°C for 30 min. and quenched; (a) x26 and (b) xl20 131 4.1 Relative density versus sintering time at 1000°C for fine spherical carbonyl nickel powder, from Tikkanen arid Yla'ssari 136 4.2 Relative density versus sintering time for solid state sintering. Data of Calow and Tottle for copper, and present data for cupronickel 137 4.3 Volumetric shrinkage versus sintering time for copper (Clark et al.) and for cupronickel (present results) 139 4.4 Volumetric shrinkage data for copper and nickel (Tikkanen and Makipirtti) and for cupronickel (present results) 139 XX Figure Page 4.5 Linear .shrinkage data of Shumaker and Fulrath for solid state sintering of Cu and Ni powder compacts in the S.E.M .'; 140 4.6 Interdiffusion coefficient versus i for 50-50 weight per cent cupronickel alloy 145 4.7 Two sphere model for solid-state sintering with complete penetration 149 4.8 "Deformation-Mechanism Map" for nickel as derived by Ashby. 150 4.9 ^Cu~^Cu v e r s u s ^ o r C u P r o n ' ' c ' < e l alloy powder 158 4.10 Relative interfacial energy as a function of composition in the Al-Sn system 161 4.11 Thickness of the melted shell on a 68 micron spherical particle as a function of the volume fraction melted .166 4.12 Composition profile in a f i n i t e slab due to diffusion out of ;the slab 171 4.13 Concentration distributions at various times in the sheet -£ < X i < £ with i n i t i a l uniform con-. centration C 0 and surface concentration Cj 171 4.14 Grain size data for 1273°C sintering runs plotted as ( d s 2 - d o 2 ) versus time. 177 4.15 Grain size data for 1273°C sintering runs plotted as ( d s 3 - d 0 3) versus time 177 4.16 Grain size data for 1273°C sintering runs plotted as (d s - d o ) 2 versus time 178 4.17 Grain size data for 1273°C sintering runs plotted as ( d ^ - d o 1 * ) versus time. . 178 4.18 Arrhenius plots of grain growth data, Log K versus reciprocal absolute temperature 181 xx i Figure Page 4.19 Log plot of linear shrinkage versus time data for 1273°C sintering experiments. Different 'stages' of sintering revealed by slope changes 183 4.20 Optical micrographs showing the formation of clusters in dilatometer specimens; (a) LVDT 49 and (b) LVDT 55; x24 186 4.21 Accommodation models .189 4.22 Contact flattening and shrinkage by solution-precipitation 191 4.23 Pores within clusters (B) and at bridges (A). . . 194 4.24 Contribution of grain growth to closure of large pores 194 4.25 Shrinkage of bridged array of particles 196 4.26 Replots of linear shrinkage data from dilatometer runs: 29, 35, 62 201 4.27 Same as Figure 4.26, for dilatometer runs 30 and 34 202 4.28 Same as Figure 4.26, for dilatometer runs 31 and 32 203 4.29 Schematic plot showing contribution of components J and K to total linear shrinkage observed in super-solidus sintering after stage la . 206 4.30 Experimental data from stage 2 of LVDT. Run 35 plotted as linear shrinkage versus square root of time 207 4.31 Log plot of stage 3 shrinkage data corrected to make origin coincide with slope change between stage 2 and 3 . . . .210 x x i i LIST OF FIGURES PART B Figure Page 1.1 (a) Contact area vs. porosity plots; (b) relative strength vs. porosity plots for ideally packed sintered spheres as calculated by Knudsen 239 2.1 Apparatus for compression tests on porous sintered Cupronickel 242 2.2 Cu and Ni x-ray intensity lines superimposed on absorbed electron images of supersolidus sintered cupronickel specimen (Q42), showing the variation in composition 245 2.3 Schematic diagram of the composition distribution in supersolidus sintered cupronickel showing the sinusoidal distribution of composition in the intra- , v dendritic region . . . .... . ' .7. .. 245 3.1 Amount of open and closed porosity versus density for sintered cupronickel specimens .253 3.2 Amount of open and closed porosity versus total porosity for copper powder 254 3.3 Specimen sintered in solid state to density of 61 .4% solid (R4), x73 255 3.4 Specimen sintered in solid state to density of 65.5% of solid (R14), x73 . 255 3.5 Specimen sintered in solid state to 85.4% of solid density (R36), x73 256 x x i i i Figure Page 3.6 Specimen sintered above solidus to 86.6% of solid density (Q31 ), x73 2 5 6 3.7 Specimen sintered above solidus to 92.3% of solid density (Q30), x73 257 3.8 Specimen sintered above solidus to 97.4% of solid density (Q28), x73 257 3.9 Specimen sintered above solidus, then homogenised 45 days at 1000°C (R49), x73 25? 3.10 Supersolidus sintered and homogenised structure (R59), x80 259 3.11 Supersolidus sintered and homogenised without prestrain (Q75), x80 260 3.12 Supersolidus sintered and homogenised without prestrain (Q77), xl4 260 3.13 Same as Figure 3.5 (R36), x80 261 3.14 Supersolidus sintered and resintered after a prestrain (Q39), xl4 . . . . 261 3.15 Young's Modulus versus density for porous sintered cupronickel 2 6 3 3.16 Elastic constants for Cu-Ni alloys . . . . . . . . . . . . . . 265 3.17 Young's modulus versus density for porous sintered cupronickel. Experimental data and theoretical predictions 267 3.18 High density portion of Figures 3.15 and 3.17. . . . . . . . . 269 3.19 Typical stress-strain curves for sintered cupronickel powder specimens .• 276 xx iv Figure Page 3.20 0.02% offset flow stress in compression versus density. 278 3.21 Same as Figure 3.20 but for 0.2% offset flow stress 279 3.22 Same as Figure 3.20 but for 0.6% offset flow stress 280 3.23 Flow stress at 1% total strain versus density 281 XXV ACKNOWLEDGMENTS The author wishes to express his sincere gratitude to Dr. John Lund for his advice and assistance during the course of this investigation. Helpful discussions with other faculty members and fellow graduate students, particularly the candidate's Ph.D. committee members, Dr. A.CD. Chaklader, Dr. E.B. Hawbolt and Mr. R.G. Butters, are also gratefully acknowledged. Special thanks are expressed for the generous assistance given by many members of the department technical staff, particularly Messrs. B.N. Walker, J. Walker, A. Lacis, E. Klassen and P. Musil. Financial assistance was received in the form of an assistant-ship under National Research Council of Canada grant number A-2449, and is gratefully acknowledged. xxvi l a P A R T A STUDIES OF SOLID STATE AND SUPERSOLIDUS SINTERING Chapter 1 INTRODUCTION 1.1 Solid State Sintering The published literature is rich in reports of both experimental and theoretical studies of the sintering of metals in the solid state. The application of much of the previous theoretical work to practical sintering situations is not highly productive, however, for two major reasons: a) The p a c k i n g of p a r t i c l e s and t h e i n t e r n a l p o r e morphology i n r e a l powder b o d i e s d e v i a t e i n i m p o r t a n t ways from t h o s e used i n model e x p e r i -ments and a n a l y s e s . T h i s i s p a r t i c u l a r l y t r u e f o r i r r e g u l a r shaped p a r t i c l e s o r f o r p r e -compacted powders. b) Most, and perhaps t h e b e s t , o f t h e p r i o r work has been devoted t o p u r e , s i n g l e component metaI s y s t e m s . In p r a c t i c e , a l m o s t a l l powder m e t a l l u r g i c a l a p p l i c a t i o n s a r e t o a l l o y s o f two o r more major components, and i m p u r i t i e s a r e a l s o commonly i n v o l v e d . 1.1.1 Pure Metal Powders Three successive, but overlapping stages have been distinguished in the course of sintering: 1 2 a) F o r m a t i o n of necks between p a r t i c l e s , and neck g r o w t h . P a r t i c l e s bond t o g e t h e r a t c o n t a c t s i n t h e e a r l y s t a g e o f s i n t e r i n g w i t h o u t l o s i n g t h e i r i d e n t i t y and w i t h o u t moving c l o s e r t o g e t h e r . b) F u r t h e r neck growth, accompanied by t h e approach o f p a r t i c l e c e n t r e s ( d e n s i f i c a t i o n ) , and p r o -g r e s s i v e l o s s o f p a r t i c l e i d e n t i t y . c) Pores become i s o l a t e d and s p h e r i c a l . In t h e p r o x i m i t y of g r a i n b o u n d a r i e s , pores s h r i n k and a r e e v e n t u a l l y e l i m i n a t e d . In t h e absence of g r a i n b o u n d a r i e s , f u r t h e r pore s h r i n k a g e s t o p s . Material transport mechanisms which have been cited for the sin-tering processes include: viscous creep, plastic flow, volume self-diffusion, grain boundary diffusion, surface diffusion, evaporation-condensation and recovery-recrystallisation. All of these mechanisms may either simultaneously or individually aid bonding and neck growth. Of these, viscous creep, plastic flow, volume diffusion and possibly grain boundary diffusion can account for the approach of particle centres; i.e. contribute to densification. In the case of metals, viscous flow can also be associated with self-diffusion in accordance with the "diffusional creep" model of Nabarro-Herring [1,2]. Since the important work of Kuczynski [3], several analytical approaches have been taken to predict neck growth and densification in powder aggregates as a function of sintering temperature and time. The The equations governing neck growth in model experiments are: approaches are based on different models of material transport. n \ = F(T)t m or r \ n f •= F(T)t a m-n 3 Transport Mechanism n m p = n-m F(T) Authors Ref. Viscous or plastic flow 2 1 1 3Y/2n Frenkel 4 Evaporation conden-sation 3 1 2 f 9 T i f l - Y Pol* [ 2 M RT J Kuczynski 3 7 3 4 - Pines 5 Lattice diffusion 5 4 2 1 3 3 RT K Dy Y Q RT Kuczynski Ki ngery and Berg Pines 3 6 5 Surface diffusion 7 3 4 56 Y 8 6 n RT Us Kuczynski Rockland 3 7 - - > 6£n ^ ~ t Pines 5 5 3 2 1 3 2 Cabrera Schwed Schwed 8 9 9 Grain boundary diffusion 6 2 4 96 DG y w kT Coble 10 Equations for mid-point approach in the sphere-sphere model are as follows: a) Viscous flow 17 = 1 e \ w 2 ( K i n g e r y a n d B e r g [ 6 ] ) 4 b) Volume Diffusion (i) Grain boundary as vacancy sinks AL L 0 [2 Y Dv a) RT a : 0.5 t 0 ' 5 (Coble [10]) (1.2) 3^ 2" RT a 3 0.4 t 0 , 4 (Ichinose and Kuczynski [11]) (1.3) flO*^" Y Du Q] RT a-0.4 t 0 ' 4 (Kingery and Berg [6]) (1.4) 31 Y ft. D, i\z RT a a 0.46 t 0 , 4 6 (Johnson and Cutler [12]) (1.5) 3 n x 80 Y ft DY 8 a 3 RT 0.8 t 0 , 8 (Kingery & Berg [6]) (1.6) ( i i ) Particle Surface as vacancy sinks [40 Y D „ ft]0"8 AL = L 0 ~ 8 v " R T l F t0 , 8 (Kingery & Berg [6]) (1.7) AL r - = 0 (Ichinose and Kuczynski [11]) L n (1.8) 5 c) Grain boundary diffusion (50 w Y ft D, ^ 0.31 AL Lo 7 IT RT a1* (Johnson and Cutler [12]) (1.9) f3 Dr y w] 0.33 .0.33 (Coble [10]) (1.10) where AL the change in length L 0 = the original length a = the radius of the particle n x = the coordination number Y = the surface free energy of the particle ft = the atomic volume w = the grain boundary thickness n = the viscosity of the substance R = the gas constant T = the absolute sintering temperature t = the isothermal sintering time Dy = the lattice diffusion coefficient Dg = the grain boundary diffusion coefficient D = the surface diffusion coefficient s x = the neck radius M = the molecular weight k = Boltzmanns constant 6 = the surface thickness P 0 = the equilibrium vapour pressure 6 Based largely on observations in wire, two-sphere and sphere-plate model experiments [13,14,15], i t was concluded that surface di f -fusion was of primary importance in the earliest stage of sintering, that volume diffusion was more significant in the intermediate stage, and that grain-boundary diffusion was dominant in the final stage (isolated pore removal). Experiments with powder aggregates, rather than models, provide conflicting evidence of the general applicability of the above conclusions. More recently, Johnson [16,17,18] has provided a more practical treatment of sintering in which he considers the operation of a l l mechanisms simultaneously rather than in isolation. Again, however, the quantitative predictions are s t r i c t l y applicable only to regular arrays of particles of simple shape. There are conflicting opinions about the participation of dis-locations (plastic flow) in the densification of powder agglomerates during sintering. It has been suggested that the surface tension stresses at the neck region cause dislocation creep. However, Wilson and Shewmon [19] reached the conclusion that steady state creep by dislocation motion is impossible since the condition 2y > G0b (where b is Burgers vector and G0 is the shear modulus), for dislocation generation, can never be satisfied. Tikkanen et at. [20] noticed the existence of numerous twins in sintered nickel (from loose powder) and claimed that this observation strongly supported the theory that dislocations (plastic flow) are effective con-tributors to the densification process. In a study of sintering using hot stage electron microscopy Easterling and Thb'len [21] concluded that dislocations play l i t t l e or no part in sintering in the absence of an 7 external load. Similar observations were reported from previous work on the sintering of iron and aluminum spheres by Easter!ing and Tholen [22]. In a recent paper Ashby [23] has discussed the possibilities of dislocation involvement in sintering. He suggests that " a l l the dislocation segments in the neck region climb, becoming curved, until they reach a con-figuration such that they are in static equilibrium. In climbing, the dislo-cations release matter which joins the neck." Ashby described this as a "transient creep" mechanism which would be involved in the very early stage of sintering. There is general agreement that i f an external stress is applied then there is a significant contribution from dislocations to the densifica-tion process. . 1.1.2 Prealloyed Powders When a prealloyed powder mass of homogeneous composition is sintered in the solid state, neck growth and densification might be expected to proceed by mechanisms similar to those described above for a pure metal. However, the components of the alloy may not diffuse to the necks at the same rate, whether material transport is by surface or volume diffusion. Thus at least in the early stage of sintering, when the vacancy gradient is large due to the small neck radius, a greater concentration of the faster diffusing atoms may be generated in the neck area. Kuczynski et dl. [24] observed this phenomenon occurring in the sintering of solid solution alloy wires. For Cu + 8 at. % In wire, indium diffused prefer-entially to the neck and formed an indium rich phase on the neck surface. In the case of Cu + 4.5 at. % Ag alloy wires, sintered at 920°C for 10 minutes and 2 hours, a silver rich area was found only in the specimens sintered for 10 minutes. It was argued that after longer times, there was 8 rediffusion of the solute atoms. Silver + 10 at. % Cu alloy wires sin-tered at 830°C for 10 minutes showed Cu rich neck regions. This may be attributed to the observation that in dilute solutions of copper and silver, the diffusion coefficient of the solute is greater than that of the solvent. If the prealloyed powder particle contains two or more phases in equilibrium at the sintering temperature, the progress of sintering may be further influenced, e.g. by restrictions on grain growth or grain boundary mobility. 1.2 Liquid Phase Sintering An alternative, and often effective approach to the manufacture of alloy parts by powder metallurgy is to sinter a powder mixture (a) above the melting point of one or more minor components of the mixture, or (b) at a temperature,where some liquid will eventually form when alloy phase equilibrium is established. The technique is applied commercially to relatively immiscible systems such as copper-lead (for bearings) and tungsten-copper (for electrical switch contacts), and to partially-miscible systems such as iron-copper (for machine parts) and tungsten carbide-cobalt (cutting tools). In these cases, liquid is usually present throughout the sintering cycle. However, the procedure is also sometimes applied to a miscible mixture, in which case liquid is present only for the period during which the liquid species enters into solution in the more abundant solid. An example of the latter case is the sintering of a Cu - 10 wt. % Sn mixture at a temperature just above the melting point of t i n . The tin rapidly diffuses into the copper to form a porous solid (bronze) body. 9 The structural and dimensional changes which take place under conditions of liquid-phase sintering are determined largely by the rela-tive energies of the solid-vapour (y s v)> liquid-vapour (Y l v)» solid-liquid (Y s l) and grain boundary (Y g b) interfaces in the system being sintered. Wetting of solid particles by the liquid is defined by the contact angle, 6, which is given (from sessile droplet equilibrium) by: SV " YSL cos 9 = — — Y LV Systems for which 6 > 90°, described as non-wetting, are of no practical interest since the liquid would be ejected from a solid-liquid aggregate. For 9 = 0 ° the liquid w i l l spread throughout the aggregate, tending to cover a l l solid surfaces. At intermediate values of contact angle, the liquid tends to collect at solid-solid necks. For any system with 6 < 90°, there will be a capillary pressure which acts as a hydro-static compressive stress on the aggregate. Equilibrium of surface tensions requires that the liquid makes an angle with the solid at a grain boundary given by Ypn • <J> = 2 arc cos = Dihedral angle. (1.11) In a system with a zero dihedral angle, the liquid will completely penetrate grain boundaries (at least those high angle boundaries for which Yq B is above a c r i t i c a l value). This condition correspond to 2 < i.e. two solid-liquid interfaces can replace a solid-solid interface. When <J> > 0, grain boundaries are not completely penetrated. Thus, a solid network ("skeleton") must exist. 10 Several mechanisms [25] have been proposed to account for the dimensional (density) change in an aggregate which is sintered in the presence of a liquid phase. 1. Rearrangement If solid particles are dispersed in a wetting (6 < 90°) liquid, they can slide past one another. The capillary stress which exists in a wetting system might tend to encourage particles to move into closer packed arrays. A substantial densification could occur by this mechanism alone i f enough liquid were present. Kingery [26,27] has estimated that an array of spherical solid particles can be completely densified by rearrangement i f 35 volume per cent of a completely wetting liquid is present. It is important to note that i t is a necessary condition for rearrangement that the dihedral angle be zero. Otherwise, a solid skeleton will exist. There are several systems of commercial interest in which this condition apparently prevails at least temporarily during sintering, including WC - Co and Fe - Cu. Kingery has treated the rearrangement process in terms of viscous flow, and has predicted that the tii..e dependence of shrinkage, will be given by ' TT a t 1 + y where 0 < y « 1 (1. (V 0 and AV are the original volume and change in volume of the powder aggregate.) 11 A more complex analysis was reported by Cech [28], but the pre-dictions are similar to those of Kingery. There are several reported verifications of the above time-dependence of shrinkage, although some investigators [25,29] have reported much higher-order dependence. 2. Solution-Precipitation Several mechanisms of shrinkage during liquid-phase sintering have been proposed which involve solution of the solid by the liquid at some locations followed by re-precipitation of solid at other locations. Price et al. [30] observed both rapid solid particle growth and rapid densification in the liquid phase sintering of w-Ni-Cu alloys. They attributed these effects to the selective dissolution of small particles (small radius of curvature) with precipitation onto the larger particles. While this process, which has become known as the Heavy Alloy mechanism [31], can adequately and quantitatively explain particle growth, i t is not obvious that i t can account for any densification. This criticism of the Price et al. model has been recorded by Parikh and Humenik Jr. [32], and by Kingery [27]. An alternative solution-precipitation mechanism was proposed by Kingery [27]. At contacts, between solid particles, or at near contacts with a thin liquid film separation, there is a local concentration of the capillary stress in wetting systems. This increases the chemical potential of the solid, and thus i t s solubility in the liquid, at or near the con-tacts. Solid dissolves locally and is precipitated at less stressed regions. The mechanism predicts two effects; (a) densification associated with the approach of particle centres, and (b) shape changes of the solid particles 12 such as to allow more efficient f i l l i n g of space. Both of these effects are generally observed in wetting systems. From an anlysis of his model, Kingery derived the following relationship for spherical particles: Vo where 'a' is the mean particle radius and 'C is a constant which includes DV> Y L V and T. For diffusion rate-control of the process, x = - -| and z = ^ . If the rate controlling step is a phase-boundary reaction, x = -1 and z = ^ . The constant is different for the two cases. Kingery also treated theoretically the case of prismatic shaped particles such as can develop during the sintering of WC - Co and TiC - Ni. Attempts to verify experimentally the Kingery model of densifi-cation by solution-precipitation are complicated by the fact that the process is commonly preceded or accompanied by rearrangement. Kingery's analysis of his own experiments with Fe-Cu [33], WC-Co [34] and of pub-lished data for TiC-Ni-Mo [35] led him to conclude that solution-precipi-tation was diffusion rate-controlled in the three systems. P r i l l et at. [36] later reanalysed the same data and concluded that a phase boundary reaction was rate-controlling. 3. Coalescence For systems with <}> > 0, solid state sintering mechanisms can operate within the solid skeleton even when a liquid phase is present. 13 Thus even in the absence of interfacial energy relationships which promote rearrangement or solution at contacts, densification of the aggregate can proceed. Even in a wetting system with <f> = 0, some adjacent solid particles may be crystallographically oriented with respect to each other such that a low angle, low energy solid boundary is established which is not wetted by the liquid. "Particle growth" i s commonly observed during liquid phase sinter-ing, in systems for which the dihedral angle is zero or positive. With zero dihedral angle, the growth can be largely attributed to the Heavy Alloy mechanism discussed above. However, there is experimental evidence that growth can also result from quite different processes described as "coales-cence." Warren [37] distinguishes between two types of coalescence. a) Agglomeration-particles retain their identity i n i t i a l l y and are separated by contiguous boundaries. This process is essentially solid state sintering within a cluster of particles, with grain boundaries i n i t i a l l y at necks. In the later stages of sintering of the agglomerate, the particles lose their identity, voids become isolated, and grain boundaries migrate. Thus an apparent particle "growth" has occurred. Agglomeration is expected to be important only in systems with positive dihedral angle. b) "True" coalescence in which two or more single crystal par-ticles of similar crystallographic orientation combine to form a single particle. Coalescence processes are not as effective in producing net shrinkage (densification) of a powder mass as are rearrangement and particle 14 shape-change processes. Thus, in liquid phase sintering systems for which <J> > 0, densification proceeds at relatively low rates. It should be noted that for some systems, dimensional changes during liquid phase sintering are complicated by other factors such as a) dissolution of liquid in the solid, causing progressive expansion of the solid particles and reduction in the amount of liquid available, and b) changing interfacial energies as a result of alloying during sintering. Only for the simplest of systems i t is possible to characterise the progress of sintering in terms of the theoretical models described above. 1.3 Supersolidus Sintering If an alloy powder mass is sintered at a temperature above the solidus of the alloy, liquid forms and equilibrium is more or less rapidly established. This process, described as supersolidus sintering [38], appears to be a special, or "ideal" case of liquid phase sintering. Liquid will be present throughout the sintering cycle. In general, i t can be expected that the system will be completely wetting with a zero dihedral angle. Conditions are thus i n t r i n s i c a l l y favourable for rapid and effective den-sification of the powder mass by rearrangement and solution-precipitation processes. As a means of fabricating alloy parts of high density from pre-alloyed powder, supersolidus sintering has an obvious potential, a fact which appears to have gone unrecognised until very recently. Preliminary studies of supersolidus sintering applied to high carbon steels and copper nickel alloy powders were reported by Cambal et at. [38] and Lund et at. 15 [39,40]. There are some recent indications that the process is being applied commercially to aluminium alloy powders [41], although no data have been reported to describe the amount of liquid used or the effect of the liquid on sintering kinetics. It is likely that the use of supersolidus sintering temperatures for aluminum alloys was at least partially motivated by the d i f f i c u l t y of breaking down oxide films between particles when solid state sintering was attempted. 1.4 Scope of the Present Research Supersolidus sintering is of considerable engineering interest, yet has never previously been examined in depth. A primary objective of this investigation was to study the rates and mechanisms of contraction in the process, and.to compare these with conventional liquid phase sintering. Some studies of solid state sintering of a solid solution alloy powder were also undertaken, for several reasons: a) The s i n t e r i n g b e h a v i o u r o f s o l i d s o l u t i o n powders has r e c e i v e d l i t t l e p r e v i o u s a t t e n t i o n . C a r e f u l s t u d i e s o f s t r u c t u r a l changes a r e o n l y r e p o r t e d f o r model e x p e r i m e n t s , n o t a b l y i n t h e work o f Ku c z y n s k i [ 2 4 ] w i t h w i r e models. b) In t h e s i n t e r i n g of a s o l i d s o l u t i o n , m a t e r i a l t r a n s p o r t may be m a n i f e s t e d i n b e h a v i o u r which cannot be seen i n a p u r e , s i n g l e component system. Thus, f u r t h e r i n s i g h t i n t o s o l i d s t a t e s i n t e r i n g mechanisms might be p r o v i d e d by e x a m i n a t i o n o f s o l i d so I u t i o n s i n t e r i n g . c) Some s o l i d s t a t e s i n t e r i n g i n e v i t a b l y o c c u r s on h e a t i n g t o s u p e r s o l i d u s t e m p e r a t u r e s . The s t r u c -t u r e d e v e l o p e d a t t h i s s t a g e can s i g n i f i c a n t l y a f f e c t t h e b e h a v i o u r when l i q u i d f o r m s . Moreover, o b s e r v a t i o n s o f t h e t r a n s i t i o n from s u b s o l i d u s t o s u p e r s o l i d u s s i n t e r i n g may p r o v i d e c l u e s as t o t h e s i n t e r i n g mechanisms i n v o l v e d . 16 Chapter 2 EXPERIMENTAL 2.1 Choice of Alloy for Experimental Work Many binary solid solution systems were considered prior to choosing the alloy to be used in the present work. The following char-acteristics were desirable: a) Low vapour p r e s s u r e a t t h e t e m p e r a t u r e s r e q u i r e d f o r s u p e r s o l idus s i n t e r i n g . b) . Low r e a c t i v i t y w i t h a i r a t ambient t e m p e r a t u r e s and w i t h s i n t e r i n g atmospheres and c o n t a i n e r s a t e l e v a t e d t e m p e r a t u r e s . The o x i d e s o f t h e com-ponents s h o u l d be r e a d i l y reduced a t moderate t e m p e r a t u r e s i n hydrog e n . c) A s o l i d u s - I i q u i d u s t e m p e r a t u r e i n t e r v a l o f 50 t o I00°C [ 3 8 ] . d) Phase e q u i l i b r i u m d a t a a v a i l a b l e i n t h e l i t e r a t u r e . e) No s o l i d s t a t e t r a n s f o r m a t i o n s , o r l i q u i d - s o l i d r e a c t i o n s which c o u l d o b s c u r e , on c o o l i n g , t h e s t r u c t u r e p r e s e n t a t t h e s i n t e r i n g t e m p e r a t u r e . A s i m p l e isomorphous system was p r e f e r r e d . On the basis of these c r i t e r i a , the copper-nickel alloy system was selected for the present study, and the specific alloy chosen for conversion to powder was 50% copper, 50% nickel by weight. 17 2.2 Preparation and Characteristics of Powders A bulk alloy of nominal composition 50% copper, 50% nickel by weight was supplied to the Federal-Mogul corporation for custom atomisation. Inert gas was specified as the atomising medium in order to obtain a) dominantly spherical powder particles, and b) freedom from major oxida-tion or other contamination of the alloy. The as atomised powder a l l passed a 50 mesh (Tyler, 250 ym) screen, and was mostly minus 100 mesh. The chemical analyses of several particle size fractions are shown in Table 2.1. A l l reported analyses for copper and nickel are the Table 2.1 Chemical Analysis of Cupronickel Powder Fractions Mesh No. Chemical composition in weight per cent (U.S. Std.) Cu Ni Si * P * S Co 170 x 200 49.85 49.96 0.13 — - -200 x 230 49.81 50.06 0.09 — - 0.010 270 x 325 49.85 49.93 0.08 - - --500 a l l * 49.82 50.16 - 0.0023 0.0026 0.009 Ledoux and Company. Others Can Test Ltd. average of two or more determinations. Spectroscopic analysis on as-received powder revealed the presence of 0.001% Al , 0.001% Ag, 0.005% Mg, 0.01% Fe, 0.05% Co and 0.1% Si by weight. The silicon content, verified by chemical analysis (Table 2.1) reflects the use of silicon as a deoxidant. Most of the powder particles were spherical, with small accretions as shown 'in Figure 2.1. Also, some agglomerates of the spherical 18 particles were seen. The surface of the particles was rough due to dendritic solidification of the melt, as shown in Figure 2.2. Optical metallography revealed a cored dendritic .structure, and both large pores and microporosity as shown in Figure 2.3. 2.3 Cleaning and Homogenisation of Powder Prior to use in sintering experiments, batches of powder were cleaned by heating in hydrogen or cracked ammonia for up to 12 hours at 600°C. Some re-oxidation of powders undoubtedly occurred during prepara-tion of specimens for sintering. Where sintering was conducted in hydrogen, the low-temperature cleaning treatment was probably superfluous. In the case of vacuum sintering experiments, the amount of oxygen in the specimens at the start of heating was significant, as discussed in a later portion of the thesis. Above about 600°C in a reducing atmosphere the extent of sintering was such that the particles of powder could not be readily separated. Preliminary experiments were conducted to establish conditions for homogenisation of the powders. It was found that the cored microstruc-ture disappeared visually when the powder was heated for one hour at 900°C, and this procedure was applied as a "Presintering" treatment in all cases except where specifically noted otherwise. 2.4 Preparation of Cast Cupronickel Specimens The coarsest screen fraction of the cupronickel alloy powders was melted under hydrogen in an alumina (alundum) crucible using induction F i g u r e 2 . 2 . S c ann i n g e l e c t r o n m i c r o g r a p h o f 68 ym c u p r o n i c k e l p a r t i c l e . (Rough s u r f a c e due to d e n d r i t i c s o l i d i f a c t i o n o f the m e l t ) , x lOOO. 20 F i g u r e 2 . 3 . A s - a t o m i s e d powder. x250 (Cored d e n d r i t i c s t r u c t u r e , po re s and s e g r e g a t i o n - f r e e c r u s t ) ; (a) 68 ym powder , (b ) 49 ym powder 21 heating-in a graphite susceptor. The molten alloy was solidifed in the crucible by applying a water cooled copper c h i l l to the bottom end of the alundum crucible. In this manner, 1 cm diameter x 5 cm long bars were cast. One of the as cast alloy specimens was analysed for microsegrega-tion on the electron beam microprobe analyser, with the results shown in Figure 2.4. Inhomogeneities of composition along any line through a cast structure can be approximated to a Fourier summation of sinusoidal varia-tions. This yields, from the solution of Ficks second law, an expression [42] 772 5 t cm as an approximation for the redistribution of solute during an homogeni-sation anneal, where, c = the variation from the average concentration at the point £, c = the i n i t i a l maximum variation from the average concentration, l = the distance between a region of maximum concen-tration and an adjacent region of minimum concentration, D = the interdiffusion coefficient at the homogenising temperature, t = the time for the desired degree of homogeneity. Assuming the average composition to be 50 wt. % copper and using values of 4.8 x 10" 1 1 cm2/sec. for D [43,44] at 1000°C and 0.01 cm for % 2 2 D i s t a n c e , p.m. Figure 2.4. Composition versus distance plots for as cast and homogenized cupronickel alloy (from Microprobe Analysis). 23 in Equation (2.1), a time of 270 hours was calculated to reduce the con-centration variation to 0.01 of the maximum variation in the cast cupro-nickel at 1000°C. Accordingly, cast specimens were homogenised at 1000°C for 12 days. The electron microprobe analysis of the as homogenised cupronickel revealed a composition variation of ±1 weight per cent of the average composition as shown in Figure 2.4. Also, average compositions of 49.9 wt. % Cu for the top portion and 49.8 wt. % Cu for the bottom portion of the homogenised casting indicated that the castings exhibited l i t t l e or no macrosegregation along their length. The chemical analysis of as homogenised cupronickel is given below: Cu 49.46 wt. % > Ni 50.10 wt. % Si 0.23 wt. % Al 0.05 - 0. 06 wt. % • (Can Test Ltd.) Co 0.02 - 0. 07 wt. % B ~ 0.05 wt. % J 0 0.0003 wt. % (Ledoux) 2.5 Preparation of Powder Specimens As-cleaned powders were poured into recrystallised alumina crucibles of 1.3 cm inside diameter. By adding approximately 25 gms of the powder in several increments, and tapping the crucibles between additions, a column of powder was obtained with 50.0 ± 0.02 per cent of the density of the i 24 solid alloy. The maximum packing density that could be achieved by tapping 200 x 230 mesh powder was 53 per cent of the theoretical density. The loose powder columns were then pre-sintered for one hour at 900°C in a vacuum of 0.4 x 10~5 torr. This treatment produced cylinders which were strong enough to sustain handling when removed from the crucibles. 2.6 Sintering Procedures 2.6.1 Vacuum Sintering Homogenisation, solid state sintering and some supersolidus sin-tering experiments were done in a Centorr vacuum furnace. The furnace assembly consisted of a water cooled cylindrical copper chamber with internal tungsten screen heating elements located concentrically in the chamber. Two W/3% Re - W/25% Re thermocouples located close to the heating elements were connected to a temperature control unit. A Pt - Pt/10% Rh thermocouple was conducted to the specimen through a seal in the l i d of the vacuum chamber. The furnace chamber could be pumped to a vacuum of 10"7 torr. There was also an access for the controlled introduction of gases to the chamber. Crucibles of dimensions 25 mm diameter x 100 mm t a l l could easily be accommodated inside the furnace. Several runs were made to calibrate the furnace for power settings and temperature control. It was possible to control the temperature at a desired level within ±3°C. A maximum temperature variation of ±2°C along the length of a 12 mm diameter x 38 mm long specimen was detected. 25 Cupronickel powder columns were presintered in the vacuum furnace with the thermocouple tip embedded in the top of the powder column. At the end of the presintering treatment the temperature was raised. The standard thermal cycle for a solid state sintering run is shown in Figure 2.5. After completion of a run, the power to the furnace was switched off and the sintered specimen was allowed to cool inside the furnace. A vacuum of ~10~5 torr was maintained throughout the cycle. In the case of supersolidus sintering, the cupronickel powder columns were presintered in a s p l i t alumina crucible. They were further sintered isothermally at a supersolidus temperature for a desired interval of time. A vacuum of 10"2 torr was maintained during most of the thermal cycle, which is shown in Figure 2.6. However, when the furnace was switched off, helium gas was simultaneously introduced into the furnace chamber at one atmospheric pressure and the specimen was cooled with the helium atmosphere inside the furnace. For a few runs, the complete supersolidus sintering cycle was completed either in a vacuum of greater than 10~5 torr or in an atmosphere of argon gas instead of vacuum and helium. 2.6.2 Superkanthal Furnace Practice The superkanthal furnace consisted of a vertical alumina tube heated externally by means of two molybdenum d i s i l i c i d e heating elements as shown in Figure 2.7. The bottom end of the alumina tube was immersed in a quenching medium. The top end of the tube could be closed with a water-cooled brass l i d . The l i d contained a gas inlet tube, two thermocouple access holes and a central hole to accommodate a wire supporting the specimen. 26 Figure 2.5. Thermal cycle for solid-state sintering in the Centorr furnace. Figure 2.6. Thermal cycle for supersolidus sintering in the Centorr furnace. 27 • Brass rod Slide block » -Gas inlet —Brass lid -Mo support wire k—W-Re thermocouple Specimen -Radiation cage -MoSig heating elements -ALjOg tube -Quenching medium Figure 2.7. Superkanthal furnace assembly. Radiation cage and specimen suspension shown separately (top right). 28 The upper ends of thermocouple and support wires were attached to a slide block. The thermocouple wires also supported a radiation cage. The radiation cage consisted of two molybdenum sheet discs separated by three 50 mm long alundum thermocouple sheaths and molybdenum wires. The specimen was hung inside the cage by a molybdenum wire passing through a central hole in the top disc. The specimen could be lowered into the quench bath through a central hole, 18 mm in diameter, at the bottom disc of the cage. Since the specimen support wire and thermocouple wires were attached to the slide block, the cage along with the specimen could be lowered to, or raised from, the constant temperature-hot zone of the furnace. The temperature control thermocouple, made up of Pt and Pt/13% Rh wires, was located at the high temperature zone of the furnace touching the outer surface of the alumina tube. The furnace was calibrated in pre-liminary runs. Any desired temperature could be obtained and maintained within ±2°C by controlling the power input and by using the temperature, control. There was a constant temperature zone of greater than 35 mm length in the furnace tube. A presintered cylinder from the vacuum furnace was removed from the s p l i t crucible. A hole, 1.5 mm in diameter was dr i l l e d radially near one end of a cylinder to allow a support wire to be fastened to the specimen. Alloying of the wire with the specimen was prevented by using an alumina thermocouple sheath. Another hole, 3 mm in diameter and 12 mm deep, was d r i l l e d axially at the top end of the presintered powder cylinder to act as a seat for the thermocouple hot junction. Contact 29 between the thermocouple and the specimen was prevented by using a closed-end alumina sheath. The cage, along with the presintered powder cylinder, was hung at the colder top end of the furnace tube. The furnace tube was flushed with dry helium gas. After a few minutes, dry hydrogen was passed through the furnace at a constant rate and the helium flow was discontinued. The cage and specimen were lowered to the constant temperature zone. Specimens were sintered at the desired temperatures in hydrogen for various intervals of time. At the end of isothermal sintering the specimen was either raised to the colder top end of the furnace or lowered into the quench bath. For quenching experiments, 10 mm diameter x 20 mm long presintered cupronickel cylinders were used. At the end of the isothermal sintering the wire supporting the specimen was cut to allow the specimen to f a l l freely into the iced-brine solution kept at the bottom of the furnace tube. Visible heat (colour) in the specimens was found to subside in less than 5 sees in the quenching medium. Also, as-homogenised cast cupronickel specimens, 10 mm in diameter x 25 mm long, were heated isothermally in an atmosphere of hydrogen and then quenched into iced-brine solution by the same procedure. The thermal cycle for superkanthal runs is as shown in Figure 2.8. 2.6.3 Thermocouple Calibration For calibration of a Pt-Rh thermocouple the melting point of pure nickel was employed. Sherritt Gordon nickel powder, 99.90% pure, was melted in an alumina crucible using induction heating. Cooling of the nickel was followed with both a recorder and a potentiometer. In several runs, 30 the thermal arrests occurred at temperatures in the range of 1453 to 1455°C. The melting point of nickel can be taken as 1455°C [45]. The calibration of a W/3% Re -W/25% Re thermocouple was done in a similar way. In this case 99.999% pure copper was melted using the superkanthal furnace. Both metling and freezing arrests were observed with the results given in Table 2.2. An average of 1082^0 was obtained as the melting point for copper compared with a published value of 1084°C [45]. The thermocouple was further calibrated against the Pt-Pt/10% Rh thermocouple between 1000 and 1500°C. The temperatures measured using W-Re thermocouple were within ±^ -°C of those measured using the Pt-Pt/Rh thermocouple. Table 2.2 Thermocouple Calibrations Against Melting Point of Pure Copper (W/3% Re - W/25% Re Thermocouple) Melting Freezing Potential :, mV Temp. °C Potential, mV Temp. °C 19.880 1083 19.840 1081 19.885 1083 19.850 1081 19.890 1083 19.850 1081 2.7 Experimental Difficulties in Studies of Supersolidus Sintering To follow the course of supersolidus sintering was int r i n s i c a l l y d i f f i c u l t for reasons which include the following: 31 a) Loose powder a g g r e g a t e s have low t h e r m a l c o n d u c t i v i t y . b) L i q u i d forms o v e r a range o f t e m p e r a t u r e i n an a I Ioy. c) The m e l t i n g p r o c e s s i s d i f f u s i o n - c o n t r o l l e d and hence a s i g n i f i c a n t t i m e i s i n v o l v e d t o e s t a b l i s h phase e q u i l i b r i u m even a t c o n s t a n t t e m p e r a t u r e . d) The i n i t i a l d e n s i f i c a t i o n o f a powder a g g r e g a t e i s t h e most r a p i d . e) The e q u i l i b r i u m amount o f l i q u i d i s v e r y s e n s i t i v e t o t e m p e r a t u r e . If the rate of heating is kept low the compact may heat uniformly but the amount of liquid will change over the interval between the solidus and any chosen isothermal supersolidus sintering temperature. This makes i t impossible to analyse the kinetics of shrinkage for any given liquid content or temperature. Conversely, i f an attempt is made to reach the desired temperature quickly, two other problems arise: a) Large t e m p e r a t u r e g r a d i e n t s a r e g e n e r a t e d a c r o s s the specimen and m e l t i n g s t a r t s f i r s t n e ar t h e s u r f a c e . b) The amount of l i q u i d formed a f t e r s h o r t i n t e r v a l s o f t i m e i s not t h e e q u i l i b r i u m amount. 2.8 Dilatometric Experiments 2.8.1 Description of the Apparatus The dilatometer, shown in Figure 2.9, consisted of a quartz tube held vertically by means of a lava block pedestal at the bottom and a steel frame at the top. The top end of the quartz tube was closed with a water H 2 gas Transducer Water cooled collar Alumina rod Silica glass tube nduction coil J-Silica discs at both ends of powder compact Alumina tube Lava block - Thermocouple Figure 2.9. The Dilatometer. 33 cooled, hollow brass collar. The brass collar supported a transducer (linear variable differential transformer, or LVDT) which could be held at any vertical position using a screw attached to the steel frame. An axial hole through the LVDT acted as a gas inlet tube to the quartz tube. The iron core of the LVDT was attached to a 20 cm long x 1.6 mm diameter alumina rod. A thermocouple, made of W/3% Re - W/25% Re passed through a central hole in the ceramic (lava) pedestal block. The thermocouple pro-jected approximately 6.3 mm above the top surface of a smooth s i l i c a disc placed on top of the pedestal block. The presintered specimen, with a central hole deep enough to accommodate the thermocouple hot junction, sat firmly on top of the s i l i c a disc. A second s i l i c a disc covered the top surface of the specimen. The alumina rod from the LVDT core was placed centrally on top of this s i l i c a disc. The iron core along with the alumina rod and the s i l i c a disc weighed roughly 9 gms. An alundum sleeve placed between the specimen and the quartz tube acted as a heat insulator and shield. A high frequency induction coil was located concentrically outside the quartz tube. The whole assembly of the dilatometer was supported on a screw jack and hence could be moved vertically for adjustment of specimen position relative to the induction c o i l . The LVDT was connected to a Daytronic model - 300 BF signal conditioner and amplifier. The output of the amplifier was continuously recorded using a Honeywell chart recorder. The recorder was calibrated to give a maximum recording sensitivity of 0.0025 inch per inch of chart in the mV. direction using a feeler gauge of known thickness. 34 The thermocouple was connected to cold junction compensating leads and then to the Phillips induction furnace control unit. The control unit contained a thermocouple chart recorder with a f u l l scale deflection of 25 mV. Separate measurements of the specimen temperatures were also made using a potentiometer with an accuracy of 0.01 mV. By further c a l i -bration of the potentiometer i t was possible to measure the temperature at the thermocouple to an accuracy of ±i°C. Hydrogen was employed for a l l cleaning and sintering in the dilatometer furnace. Bottled hydrogen was passed through a palladium catalyst chamber and then through "Drierite" and phosphorus pentoxide columns. 2.8.2 Procedures in Dilatometer Runs Cupronickel powder was tapped into a small alumina crucible to obtain a powder column approximately 15 mm diameter by 20 mm high and with 50 per cent of the theoretical density. The crucible and contents were heated in a tube furnace at 1000°C for one hour in an atmosphere of hydrogen. This provided cleaning and some homogenisation. The presinters thus obtained were removed from the crucibles. Both ends of the cylinders were machined to be f l a t and parallel. The densities of the machined specimens were determined from weight and dimensions. An axial hole, 2.3 mm diameter x 9 mm deep, was d r i l l e d at one end of each cylinder to serve as the thermocouple well. The specimen was again weighed. The presinter was placed on the s i l i c a disc at the top of the pedestal block. It was then further cleaned and homogenised at 1000°C for one hour, in an 35 atmosphere of clean and dry hydrogen, using induction heating in the dilatometer. The specimen was cooled to room temperature and the weight and dimensions were again measured. With the specimen returned to the dilatometer, the LVDT was zeroed and the recorder was calibrated. The specimen was heated to the sintering temperature in dry hydrogen in two steps according to the cycle shown in Figure 2.10. The i n i t i a l power input was such that 1200°C was attained in approximately 4 minutes. At that moment the power input was increased to reach 1273°C rapidly. The input was thereafter controlled manually as necessary to maintain the temperature at 1273°C within ±1°C. The specimen was held at this temperature for varying times up to about 10 minutes. At the end of the sintering treatment the induction unit was switched off and the specimen was cooled to room temperature in the dilatometer i t s e l f . A typical dilatometric chart is shown as Figure 2.11. After cooling, the weight and the length of the specimen were determined. The change in length during sintering, as measured by calipers agreed closely with the value recorded from the LVDT. Calibration runs were also conducted to determine the contribution of expansion and contraction in the specimen support assembly members during a dilatometer experiment. A solid steel cylinder was used as a heat susceptor instead of a powder presinter. The alumina rod from the LVDT was passed, through an axial hole in the steel cylinder, to rest on the s i l i c a disc at the top of the pedestal block. The thermal cycle was typical of a dilatometer run, Figure 2.10. The thermal expansion curve obtained for the support assembly was used to correct the dilatometer curves obtained from powder specimens. 36 Figure 2.8. Thermal cycle for supersolidus sintering in the superkanthal furnace. Figure 2.10. Thermal cycle for supersolidus sintering in the Dilatometer. Figure 2.11. A typical continuous linear dimensional change curve obtained from a Dilatometer run. 38 During dilatometer runs, a copper deposit was formed on the s i l i c a discs at the ends of the specimen. Weight loss measurements indicated that up to 0.08 per cent of the specimen was lost by evaporation in the longest dilatometer runs. Even i f this loss was assumed to be pure copper, i t would not have produced a composition change of greater than 0.16 per cent in the copper and nickel contents of the alloy. Since this is well within the limits of accuracy of analytical determinations, no effort was made to correct for evaporation losses. 2.8.3 Advantages and Limitations of the Dilatometric Technique The dilatometric technique employed in the present work had a number of advantages over that used for other studies of sintering (par-ticularly liquid phase sintering): a) By u s i n g d i r e c t HF i n d u c t i o n h e a t i n g t h e tempera-t u r e g r a d i e n t s a s s o c i a t e d w i t h t h e low t h e r m a l c o n d u c t i v i t y of a l o o s e powder mass were p a r t i a l l y r e d u c e d . b) H e a t i n g and c o o l i n g r a t e s were r a p i d u s i n g d i r e c t i n d u c t i o n . c ) C o n t i n u o u s o b s e r v a t i o n However, data generated by quantitative significance for several o f s h r i n k a g e was p r o v i d e d . the technique were of restricted reasons: a) " S k i n " h e a t i n g e f f e c t s o c c u r i n d i r e c t HF i n d u c -t i o n which i n t r o d u c e a r a d i a l g r a d i e n t i n tempera-t u r e and i n t h e sequence o f m e l t i n g a c r o s s a specimen. b) The l i n k a g e s between specimen and d i l a t o m e t e r a r e heat s i n k s which c o n t r i b u t e t o an a x i a l t e m p e r a t u r e g r a d i e n t . The d i l a t o m e t e r " s e e s " d i m e n s i o n a l changes a t t h o s e l o c a t i o n s where t h e h e a t - s i n k e f f e c t s a r e g r e a t e s t . 39 2.9 Optical Metallography 2.9.1 Mounting, Polishing and Etching An epoxy resin mixture of 90 wt. % Epon 828 and 10 wt. % diethylenetriamine, was used for mounting specimens. Most of the porous sintered specimens were soldered to copper wires prior to mounting. They were then immersed in the resin and the assembly was placed inside a desiccator. The desiccator was evacuated using a forepump for five minutes to remove air from the pores of the specimens. When air was re-introduced into the desiccator the resin was forced into the continuous pores. This procedure was reasonably effecient in impregnating the pores with resin. The specimen, along with the resin, was poured into silicone rubber moulds with the copper wire projecting. After curing of the resin, specimens were ground and polished to 1 micron diamond. trolyti c etching was found to be superior since i t removed some of the fine polishing scratches from the surface of the specimen. The chemical etchant used was Carapella's reagent [46]; The composition and conditions of use for the electrolytic etch [47] were as follows: Both chemical and electrolytic etching were practiced. Elec-Ferric Chloride Cone, hydrochloric acid Ethyl alcohol Time at 20°C 5 gms, 2 ml, 99 ml, 3 sec - 2 min. Chromic oxide Glacial acetic acid D i s t i l l e d water Age Voltage Cathode Temperature Time 25 gms, 133 ml, 7 ml, > 6 months, 6 volts, Stainless steel, 16°C, 2-15 minutes. 40 2.9.2 Quantitative Metallography Estimates of grain size were made using the linear intercept method [48]. For a composite containing gas (pores), liquid, and solid, the mean linear intercept d s" in the solid is given by d = (2.2) • s where P s = the proportion of solid n = the number of solid grains in an intercept of length I. It has been pointed out that the mean linear intercept d $" is less than the true mean diameter of the grains in the plan of sectioning, d •', and that the mean diameter of the grains in a planar section, is less than the true mean diameter of the grains in the aggregate, d . According to derivations presented elsewhere [49,50] d s = 1.675 d s" (2.3) Woodhead [51] suggested that i f the mean linear intercept is based on an observation involving n grains, then the relative error, <t>l3 of the mean intercept can be given by 0.49] 0- 5 (2.4) In the present work, lines 8.8 cm long were used to determine the mean intercept in micrographs of porous sintered specimens. The grain 41 size was estimated from counts of more than 500 mean intercepts using four or more micrographs, and using the expression: H - 1-675 x I x p s " n x Mx where p = the fractional density of the specimen Mi = the magnification of the micrograph. The error involved in these determinations was approximately 3% according to Equation (2.4). Estimates of "liquid" content in specimens were made using the point count method [51]. The basic principle of the method is that the volume fraction of a phase is given by that proportion of a regular array of points, placed on a micrograph, that f a l l on the phase. It is impor-tant that the spacing of the points on a rectangular grid be large with respect to the microstructural features. In sintered specimens regions which were liquid at the sintering temperature were appreciably higher in copper content than those regions which had remained solid. Conventional etching attacked the copper-rich areas preferentially, giving them a dark appearance in the microstructure. Since these areas could not always clearly be distinguished from porosity, the point count method was used to evaluate the total dark area in photo-micrographs, and the known porosity content was then deducted. A one inch grid containing 36 points, regularly spaced, was superimposed on the micro structure. The choice of magnification was such that the spacing of the points on the rectangular grid was large compared to that of the dark features. The volume fraction, p H, of the dark region is given by 42 7T (2.6' where n^ is the number of points occurring in the dark region and n 2 is the total number of points in the microstructure. The equation given by Gladman et al. [52] for the standard deviation of the volume fraction in relation to the number of points used in the point-counting method is 0P 10.5 P d(l - P d)/n 2 (2.7) d Standard deviations of 0.0032-0.0061 were observed in the e s t i -mation of the liquid content in cupronickel. The mean diameter, dp', of spherical particles in a plane of section is related to the true mean volumetric diameter of the particles, d p, by [53] dp'- = Tin dp (2.8) The value of d 1 was obtained directly by averaging the diameter of many particles seen in photomicrographs. Some sintered specimens exhibited macroscopic variations in porosity content, associated with thermal gradients during sintering. In these cases, estimates of both porosity and liquid-phase content were made at localised regions of metallographic specimens or on photomicrographs of those regions, using the Quantimet instrument. 43 2.10 Microprobe Analysis To study phase compositions and gradients in sintered specimens a JE0LC0 JXA-3A electronprobe microanalyser was used. a) A t h i n f i l m o f ca r b o n was e v a p o r a t e d on t o p o l i s h e d specimens t o p r e v e n t c h a r g e b u i l d - u p and t o g i v e b e t t e r c o n d u c t i v i t y . b) An o p e r a t i n g v o l t a g e o f 25 KV was used w i t h an e l e c t r o n beam d i a m e t e r o f I urn. c) A l i t h i u m f l u o r i d e c r y s t a l was used i n t h e x - r a y s p e c t r o m e t e r . d) Ni K and Cu K x - r a y i n t e n s i t y c o u n t s f o r 10 a a 7 seconds were r e c o r d e d . Repeated 10-second c o u n t s were t a k e n a t t h e same specimen s i t e , o r a f t e r moving t h e specimens i n s t e p s o f 1.25 urn. e) C o n t i n u o u s s c a n s were a l s o made a t a specimen speed o f 100 urn per m i n u t e . f ) Background c o u n t s were o b t a i n e d on specimens and s t a n d a r d s by moving t h e s p e c t r o m e t e r one degree o f f t h e peak b e i n g measured. g) I n t e n s i t y r a t i o s were o b t a i n e d from t h e c o u n t s o b t a i n e d f o r t h e specimen and t h e s t a n d a r d s a f t e r b e i n g c o r r e c t e d f o r "dead t i m e " and background. The i n t e n s i t y r a t i o was f u r t h e r c o r r e c t e d f o r f l u o r e s c e n c e enhancement. No c o r r e c t i o n f o r a t o m i c number was n e c e s s a r y s i n c e c o p p e r and n i c k e l a r e a d j a c e n t s p e c i e s i n t h e P e r i o d i c Table". S i m i l a r l y , no a b s o r p t i o n c o r r e c t i o n was a p p l i e d because t h e a b s o r p t i o n c o e f f i c i e n t s f o r cop p e r and n i c k e l a r e c l o s e l y s i m i l a r . Conversion of intensity ratio into weight fraction was performed directly by an IBM 370 computer using the MAGIC Programme [54]. The weight fraction could also be obtained from a back-calculation method using the MAGIC Programme. In this case assumed weight fractions of Cu and Ni were converted into corresponding intensity ratios corrected only for dead time and background. The intensity ratios obtained for 0.1, 0.2, 0.3, etc. up 44 to 0.9 weight fraction copper in nickel are given in Table 2.3. The variation of the ratio within an interval of 0.1 weight fraction was essentially linear. Thus a l l intensity ratios could be converted into weight fractions by simple interpolations within intervals of 0.1 weight fraction over the whole range of compositions. Table 2.3 Intensity Ratios for the Cu-Ni System Obtained from the MAGIC Programme Weight Fraction Intensity ratio (K a-Ratios) Cu Ni Cu Ni 0.9 0.1 0.8964 0.1079 0.8 0.2 0.7936 0.2129 0.7 0.3 0.6917 0.3157 0.6 0.4 0.5905 0.4169 0.5 0.5 0.4902 0.5168 0.4 0.6 0.3906 0.6154 0.3 0.7 0.2918 0.7130 0.2 0.8 0.1938 0.8096 0.1 0.9 0.0965 0.9052 Probe calibrations were carried out using as standards homogeneous solid-state sintered or cast-cupronickel specimens, for each of which reliable chemical analyses had been obtained from an independent laboratory. In the acquisition and treatment of probe data, the following procedures were adopted: 45 a) Not less than five sets of 10-seconds counts were taken in the probe survey of a given specimen. b) The mean concentrations of copper and nickel were adjusted ' proportionally to total 99.9 weight per cent. The justification for this procedure is that: ( i ) c o p p e r and n i c k e l x - r a y c o u n t s were made s i m u l t a n e o u s l y a t any g i v e n specimen s i t e ; t h u s , f l u c t u a t i o n s i n such o p e r a t i n g c o n d i -t i o n s as beam c u r r e n t would a f f e c t the c o u n t s f o r both s p e c i e s i n t h e same d i r e c t i o n , c h e m i c a l a n a l y s e s showed t h a t t h e c o p p e r p l u s n i c k e l c o n t e n t o f t h e m a t e r i a l s under s t u d y was c l o s e t o 99.9 per c e n t , any r e s i d u a l s e g r e g a t i o n i n homogenised specimens c o u l d a l t e r t h e Cu:Ni r a t i o a t a s p e c i f i c specimen s i t e , but t h e a v e r a g e r a t i o o v e r many s e t s o f c o u n t s would be t h a t o f t h e b u l k , as r e p r e s e n t e d by t h e c h e m i c a l a n a l y s i s ; and no i m p u r i t y phases were d e t e c t e d i n t h e m a t e r i a l s a n a l y s e d . The degree of reproducibility of the microprobe results was indicated by surveys on a single homogenised presinter specimen on seven different occasions (actually on 5 different days). The results are con-tained in Table 2.4.which also shows the application of the above-mentioned normalising procedure to the probe data. The averages of the seven copper and nickel determinations were compared with the chemical analysis also given in the table. The variance of the results is 0.6 per cent of the absolute value for each element. Table 2.5 contains probe and chemical analyses from several sintered and cast cupronickel specimens of relatively high homogeneity. ( i i ) ( i i i ) ( i v ) 46 Table 2.4 Microprobe and Chemical Analyses on a Presintered Cupronickel Powder Specimen (sintered 900°C for 1 hour, from 200 x 230 mesh powder) Determination Computed wt. % from Microprobe Normalised wt. % Microprobe Chemical Analysis wt. % Cu a b c d e f g Average Variance 50.64 50.60 49.57 50.88 50.35 49.89 50.38 Ni Cu 50.32 50.16 50.16 50.10 50.30 50.30 49.69 50.1 50.2 49.7 50.3 50.0 49.7 50.3 50.0 ±0.6 Ni Cu 49.8 49.7 50.2 49.6 49.9 50.2 49.6 49.9 ±0.6 49.81 Ni 50.06 Can Test Ltd. Combined with those in Table 2.4, these results indicate that a high pro-portion of individual probe analyses for copper and nickel can be expected to f a l l within a range of 1.2 per cent about the "true" analyses. Statis-t i c a l l y , this is a simple, and conservatively high estimate of the variance in the data. A more rigorous treatment of the variance is neither jus-t i f i e d by the size of the statist i c a l sample, nor required for purposes of the present investigation. It should be noted that in some of the super-solidus sintering experiments to be discussed, progressive trends in 47 Table 2.5 Microprobe and Chemical Analyses on Relatively Homogeneous Cupronickel Specimens Material Treatment Microprobe Analysis, wt. %, Normalized Chemical Analysis, wt. %* Cu Ni Cu Ni SPLS 2 Cast & Homog. 49.9 50.0 49.46 50.10 SPLS 3 -do- 49.8 50.1 -do- -do-SPLS 4 - do- 50.0 49.9 -do- -do-Q22 sinter 49.9 50.0 49.81 50.06 Ql sinter 49.9 50.1 50.1 50.0 49.8 49.8 -do- -do-R66 presinter 49.9 50.0 -do- -do-R67 -do- 50.3 49.6 -do- -do-R24 sinter 50.1 49.8 -do- -do-R14 sinter 49.8 50.1 50.1 49.8 -do- -do-R16 sinter 50.2 50.1 49.7 49.8 -do- -do-* Can Test Ltd., Vancouver. 48 composition change with changes in experimental conditions could be pre-dicted from known phase equilibria in the copper-nickel system. In nearly all cases, the results of microprobe analyses were consistent with the predictions. These observations added confidence to the above estimates of variability in the results of individual microprobe surveys. 2.11 Scanning Electron Microscopy An ETEC autoscan scanning electron microscope coupled with an ORTEC model 6200 multichannel analyser was used for both surface topology studies and x-ray energy analyses. 2.12 Density Determinations The lattice parameter of the cupronickel alloy powder was deter-mined by the precise x-ray diffraction method [55]. Powder of 200 x 230 mesh, previously heated at 900°C in an atmosphere of cracked ammonia for one hour, was used to obtain x-ray diffraction patterns. The value of o o 3.5630 A obtained agreed closely with 3.5636 A reported by Coles [56] for an alloy of 50.09% Cu, 49.81% nickel by weight. From the present value of the parameter, the theoretical density of the cupronickel alloy was cal-culated to be 8.96 gm. cm - 3. The density of a sintered specimen was obtained using two methods: a) From a c c u r a t e measurements of the w e i g h t and d i m e n s i o n s o f s p e c i m e n s . b) By w e i g h i n g o i l - i m p r e g n a t e d specimens i n w a t e r and i n a i r C57_|. 49 A previously-weighed specimen was suspended in Dow Corning F-l-0173 flui d (dimethyl polysiloxane; specific gravity at 25°C = 0.968 gm. c c - 1 and viscosity at 25°C = 100 centi stokes) using a fine thread. The specimen was heated in the f l u i d at 82 ± 5°C for 4 hours and cooled to room tempera-ture while s t i l l immersed. The specimen was carefully wiped with f i l t e r paper to remove excess oil from the surface. The weight was then determined in air and in d i s t i l l e d water, and the density calculated in the usual manner. Densities were measured on many compacts using both methods, and the results agreed to within ±0.5 per cent. Densification during sintering can be represented in different ways; e.g. a) as an absolute or fractional increase in density b) as volumetric specimen shrinkage, rr- (AV = the change in volume, V0 = the original volume), c) as linear shrinkage, ^ (AL = the change in length, L 0 = L o the original length); valid only i f shrinkage is isotropic), d) as "densification parameter," [58] given by .,. ,. , s i n t e r e d d e n s i t y - qreen d e n s i t y d e n s i f i c a t i o n parameter = -it — ;—-, r-r1 - ; r-~-. t h e o r e t i c a l d e n s i t y - green d e n s i t y The densification parameter can vary between zero and one and represents the densification which has occurred as a fraction of that theoretically possible. It is a useful property in situations where the i n i t i a l ("green") density of the powder specimen is a variable in the experiments. Chapter 3 RESULTS 3.1 Phase Equilibria in Cupronickel 3.1.1 Published Phase Diagrams for Cu-Ni Hansen [59] published in 1958 a copper-nickel equilibrium phase diagram derived from the thermal analysis results of earlier investigators. The solidus curve had been determined by several independent sets of cooling-curve data, which agreed reasonably well with each other. The Hansen diagram is shown with dashed lines in Figure 3.1. Feest and Doherty [60] in 1971 redetermined the solidus and liquidus curves in the copper-nickel system using more sophisticated experimental and analytical techniques (described in Section 3.1.3 below) than had been available prior to 1958. The results are plotted in Figure 3.1 (with solid lines). In particular, the solidus curve was found to be substantially higher than indicated by Hansen, Feest and Doherty a t t r i -buted the large discrepancies between their solidus temperatures and those in Hansen's diagram to errors inherent in dynamic thermal-analysis experi-ments when applied to systems that are subject to non-equilibrium s o l i d i f i -cation. It should be noted, however, that the solidus temperatures of 50 51 1 | : 1 , , r WEIGHT PERCENT. NICKEL The Cu-Ni equilibrium phase diagram. _-Feest and Dahcrly Figure 3.1. The Cu-Ni phase diagram according to Hansen and to Feest and Doherty. °c 1500 2600 F 1400 2500 F 1300 23O0F 1200 21 OOF 1100 300 500 F 200 10 20 Cu-Ni Copper-Nickel Atomic Percentage Nickel 30 40 .50 60 70 80 Cu 10 20 30 40 50 60 70 Avinash D. Kuikami Weight Percentage Nickel 90 r | 1 r~ r - ' 1 - 1 r 1455° L • K l i t 1084 .5 ° Ji mi 3 2 2 ° 3 5 8 ° . • a, CURI TEMPER4TU RE a,+a2 \ a 2 80 90 Ni Figure 3.2. The Cu-Ni phase diagram showing the predicted solid state miscibility gap. 52 copper alloys are dramatically lowered by minor amounts of certain impurities, notably oxygen and sulphur. It is possible that some of the earlier studies were conducted with less pure raw materials. Thermodynamic data predict that there is a tendency toward clustering in the solid state in the copper-nickel alloy system (Oriani et al. [61]), and the occurrence of some clustering was reportedly con-firmed by x-ray and neutron diffraction experiments [62,63]. The solid miscibility gap shown in Figure 3.2 was calculated by Elford et al. [64], but has not been experimentally verified because of the low temperatures involved. 3.1.2 Effect of Impurities in Cupronickel The major impurities in the cupronickel powder were (a) oxygen, originating mainly from superficial oxidation of the alloy powder particles in a i r , and (b) si l i c o n , used as a deoxidant in melting prior to atomisa-tion of the alloy. As indicated in Table 3.1, these impurities can have a significant effect on the melting temperatures of pure copper and pure nickel, and thus might be expected to lower the solidus and liquidus temperatures of a cupronickel alloy. An attempt was made to establish the solidus temperature of the cupronickel powder by differential thermal analysis (DTA). A DuPont Model 900 Instrument was used with a 1600°C furnace c e l l . Since Pt - Pt/Rh thermocouples were involved, a hydrogen-rich atmosphere had to be avoided. Heating rates were 10 or 20°C per minute. Powders were cleaned in hydrogen prior to DTA work, but some oxidation undoubtedly occurred at ambient 53 Table 3.1 Effect of Oxygen and Silicon on the Melting Points of Copper and Nickel [59,46] Sol lite wt. % Lowering of Melting Temp. °C Cu Ni Liquidus Solidus Liquidus Solidus si 1 icon 0.10 1.5 4.3 1.0 3.3 0.23 3.3 10.0 2.3 8.1 oxygen 0.001 0.05 5 0.1 1 0.005 0.2 18 0.3 5 0.100 0.5 18 0.6 10 0.020 1.0 18 1.2 15 temperatures while the powders were handled and charged into the instrument. Initial runs were made with a helium atmosphere in the DTA c e l l . In several heating runs, the indicated solidus temperature of the alloy ranged from 1244 to 1250°C. While these temperatures are in good agreement with the solidus at 50 Cu - 50 Ni in Hansen's phase diagram, they are at least 20°C lower than the solidus in the Feest and Doherty diagram. The helium atmosphere in the DTA furnace cell was diluted with small concentrations of hydrogen for subsequent heating runs. Traces of hydrogen in the atmosphere increased the apparent solidus to 1255°C; with s t i l l more hydrogen the indicated solidus was 1266°C. At this juncture, i t was apparent that the effective solidus temperature of the cupronickel alloy powder was a c r i t i c a l function of impurity content, particularly with respect to residual oxygen. The data in Table 3.1 suggest that 200 ppm 54 of oxygen could lower the solidus temperature of the alloy by 15 to 18°C. Separate gravimetric studies showed that superficial oxidation of pre-cleaned cupronickel powder could result in at least this level of oxygen contamination after only minutes of exposure to air at ambient temperatures. Since i t was impractical to duplicate in the DTA furnace the sintering atmospheres used in the present work, i t was decided to evaluate the solidus and liquidus temperatures of the cupronickel alloy powder on the basis of quenching experiments in an actual sintering furnace, as described below. 3.1.3 Thermal Data from Quenching Experiments Quenching experiments were conducted in conjunction with quantitative metallographic and microprobe analyses. This approach was essentially the same as that used by Feest and Doherty to establish complete solidus and liquidus curves in Figure 3.1; viz. a) P r e s i n t e r e d specimens were s i n t e r e d ( h e i d f o r f i v e o r more m i n u t e s , u s u a l l y 30 m i n u t e s ) a t a s e r i e s o f t e m p e r a t u r e s , some o f which were above the s o l i d u s . The s i n t e r i n g was done i n dr y hydrogen, under c o n d i t i o n s i d e n t i c a l t o t h o s e which a p p l i e d t o o t h e r s i n t e r i n g s t u d i e s i n t h e s u p e r k a n t h a I - f u r n a c e . b) The specimens were quenched i n t o i c e d w a t e r from each of t h e s i n t e r i n g t e m p e r a t u r e s . c) The c o m p o s i t i o n s of t h e u n i f o r m n i c k e l - r i c h r e g i o n s o f t h e quenched specimens; i . e . t h o s e r e g i o n s which were s o l i d a t t h e s i n t e r i n g t e m p e r a t u r e , were d e t e r m i n e d by m i c r o p r o b e a n a l y s i s f o r s e v e r a l e x p e r i m e n t s . d) The volume f r a c t i o n s o f n i c k e l - r i c h and c o p p e r -r i c h r e g i o n s i n quenched specimens were a s s e s s e d 55 by q u a n t i t a t i v e m e t a l l o g r a p h y on e t c h e d specimens o r p h o t o m i c r o g r a p h s o f the specimens. These f r a c t i o n s were r e l a t e d t o t h e w e i g h t p r o p o r t i o n s o f s o l i d and l i q u i d phase p r e s e n t a t t h e s i n t e r i n g t e m p e r a t u r e . The results are presented in Table 3.2 and have been used to prepare the phase diagram of Figure 3.3. Figures 3.4 to 3.9 are photomicrographs of the structures typical of quenched specimens. Copper-rich areas were selectively attacked by the etchant and appeared darker in the microstructure. No evidence of melting could be found in specimens sintered at 1262 ± 2°C or lower tempera-tures, either visually in the microstructures or by microprobe analysis, Figure 3.4 and 3.10. Since a 1262°C specimen was cycled in the furnace between 1260 and 1264°C, i t can be concluded that the solidus temperature of the homogeneous cupronickel alloy powder was > 1264°C. Melting had occurred in a 1264 ± 2°C specimen.: The evidence for this was both metal!o-graphic (Figure 3.5) and analytical (Figures 3.11). Thus the solidus temperature for 49.9% copper was narrowly defined as 1265 or 1266°C. The value of the solidus has two sources of uncertainty. The actual temperature of a specimen at the time of the quench was known only to ±2°C. Also, individual quantitative probe analyses are accurate to ±0.6 per cent (Section 2.10). The solidus curve for the cupronickel powder (in dry hydrogen) was found to be at the lower limit of the range of scatter in Feest and Doherty's experimental data (Figure 3.1), and lay 7 to 8 degrees below the curve drawn by Feest and Doherty through their data points. It is unlikely that oxygen was present, after presintering and sintering in dry 56 Table 3.2 Quenching Experiments and Results Run Quenching Temperature and Variation During Run °C Time at Temp. Composition of Nickel Rich Areas (solidus) wt. % Ni Estimated Liquid Content at Temp.** wt. % Liquid Calculated min. vol. % wt. % Q14 1260 + 0.5 1 .5 30 ND NIL NIL NIL Q22 1262 + 2 30 50.0 NIL NIL NIL Q20 1264 + 2 30 50.2 V. small V. small 0 Q19 1266 + 2 30 50.6 2.9 . 3.7 3 6 ± 2 Q18 1268 + 2 30 50.8 4.8 5.8 4 9 ± 2 Q47 1273 + 2.5 0.5 5 52.4 17.7 21.2 15 7 ± 2 Q45 1273 + 2.5 0.0; 15 52.9 20.7 21 .7 19 1 ± 2 Q42 1273 + 2.5 0.0 30 52.9 20.5 21.1 19. 1 ± 2 Q46 1273 + 2.5 0.5 5 ND 17.5 20.4 ND Q44 1273 + 2.5 1.0 15 ND 20.3 21.2 ND Q43 1273 + 2.5 1.0 30 ND 21.1 21 .6 ND Electron beam microprobe analysis, normalised 99.9% copper pi us nickel. Quantitative Metallography. 1370 I 1 1 1 r-—r 1 r——i 1 1 — i — i 1 r 1170 1 1 1 1 1 1 1 1 1 1 1—•—' 1 1 • ' ' » 29 33 37 41 45 4 9 53 57 S i Cu NICKEL WEIGHT % Ni " F i g u r e 3.3. The Cu -N i p h a s e - d i a g r a m d e r i v e d f rom q u e n c h i n g e x p e r i m e n t s and probe a n a l y s e s . 58 Figure 3.4. Specimen Q22, sintered at 1262°C for 30 min. in hydrogen and quenched. (Reveals the absence of liquid); (a) xl20 and (b) x760. (b) Figure 3.5. Specimen Q20, sintered at 1264°C in hydrogen for 30 min. and quenched. (Reveals clearly the presence of liquid); (a) xl20 and (b) x760. Figure 3.6. Specimen Q19, sintered at 1266°C in hydrogen for 30 min. and quenched. Intraparticle liquid pools were revealed as shown at P; (a) xl20 and (b) x760. Figure 3.7. Specimen Q18, sintered at 1268°C in hydrogen for 30 min. and quenched, (a) x!20 and (b) x760. 62 (b) Figure 3.8. Specimen Q42, sintered at 1273°C in hydrogen for 30 min. and quenched. (Linear coalescences indicated at 'C 1), (a) xl20 and (b) x760. 63 Figure 3.9. Specimens sintered at 1273°C in hydrogen and quenched, xl20; (a) Q47, 5 min. and (b) Q45, 15 min. 64 Figure 3.10. Copper and nickel x-ray intensity lines superimposed on the absorbed electron image of particle necks in Q22. (Reveals no noticeable liquid.) Sanning paths are: (a) through the neck, (b) across the neck, xlOOO. (a) (b) Figure 3.11. Copper and nickel x-ray intensity lines superimposed on the absorbed electron image of particle necks in Q20. (Reveals the presence of liquid.) Scanning paths are: (a) through the neck, (b) across the neck, xlOOO. 65 hydrogen, in quantities sufficient to affect the solidus significantly. The lower curve for the present results can probably be attributed at least partially to the presence of approximately 0.1 weight per cent silicon in the alloy (see Section 3.1.2). It was not possible to establish accurately the liquidus curve for the cupronickel alloy powder on the basis of the present data. How-ever, i t is reasonable to use the liquidus curve derived experimentally by Feest and Doherty, because: a) This liquidus differs l i t t l e , in the composition range of interest, from that of Hansen's diagram, possibly indicating that i t is relatively insensitive to minor impurity content, (b) within the limits of accuracy of quantitative metallography, the position of the liquidus is consistent with the amounts of liquid observed at several different supersolidus sintering temperatures, and (c) the effect of si l i c o n on the liquidus temperature of cupronickel can be expected to be much less than its effect on the solidus based on the data for copper and nickel in Table 3.1. It should be noted that the phase equilibria indicated in Figure 3.3 can be applied only to cupronickel powder which is sintered in dry hydrogen at one atmosphere. For vacuum and argon sintering experiments in the Centorr furnace, the effective solidus temperatures were substantially lower (as indicated in Section 3.3.2), probably due to the presence of a : significant amount of residual oxygen in specimens at the sintering tempera-tures. However, no attempt was made to establish the solidus or liquidus curves quantitatively for these conditions of sintering. 66 3.2 Structure and Homogeneity of Presintered Cupronickel Powder Specimens It was d i f f i c u l t to reveal the two dimensional microstructure of presintered specimens since the necks in such specimens were weak, and particles were pulled out of the mount while polishing. Since the density of the original powder column was increased from 50.0 to only 51.2 per cent of solid in the presintering treatment, the presintered structure can probably be assumed to be representative of the original packing. The d i s t r i -bution of powder particles in a section of the presinter is as shown in Figure 3.41.a. Clustering of powder particles and bridges are quite evident. Some homogenisation occurred in the powder particles during the presintering treatment and the cored structure was transformed to a uniform grain struc-ture as shown in Figure 3.12. The mean grain size was 18 urn compared with a mean particle diameter of 68 ym. Each particle contained interdendritic microporosity and twins. Figure 3.13 shows the results of microprobe surveys on the cupro-nickel powder as-received and after presintering for one hour at 900°C. Maximum concentration variations about the mean were reduced, by presintering, from about 10 per cent to one per cent by weight. Applying Equation (2.1) from Section 2.4, and using I = 0.0004 cm (from Figure 3.13 for the as-received powder), the derived value of D is 1.04 x 10" 1 1 cm2 s e c - 1 . This is in good agreement with the value of 9 x 10" 1 2 cm2 sec" 1 obtained from data published by Brunei et al. [65]. It should be noted that further homogenisa-tion of the alloy would have occurred in the course of heating to sintering temperatures in the range of 1200 to 1265°C. Moreover, in the previous determination of solidus and liquidus temperatures from quenching experiments, specimens had resided at 1260 to 1273°C for periods of 5 to 30 minutes. The amount of residual microsegregation in the solid after this treatment could not be detected within the limits of accuracy of individual probe analysis. 67 Figure 3.12. Internal structures of as-homogenised particles in a pre-sinter (R66) revealing grain boundaries, twins and micro-porosity, x270. 68 i i — r - T - — r z 4 0 Cupronickel (68/U.m)- Separate particles O As received • Homogenised for one hour ot 9 0 0 ° C 1 1 1 I I i » 20 40 Distance , /x.m. J 1 1 L 60 Figure 3.13. Composition versus distance plots for as-received and homogenised 68 urn cupronickel powder particles (Microprobe data)-3.3 Sintering Behaviour 3.3.1 Sintering at 1200°C Table 3.3 contains the sintering conditions and results for experiments in which 68 urn cupronickel powder specimens were sintered in the solid state at 1200°C for varying periods up to 10 hours. Results for density versus time are plotted in Figure 3.14. Typical of the sintering behaviour of loose metal powders, the rate of sintering was i n i t i a l l y rapid and decreased with increasing time. Typical microstructures of specimens sintered at 1200°C are revealed in photomicrographs, Figures 3.15 to 3.18. The following observa-tions are noted: Table 3.3 Data for Sintering Experments at 1200°C Spec. No. Cleat n'ng Time to reach 900°C min. Time to reach 1200°C from 900°C mi n. Sintering time hrs. Density % of theoretical Density variation % A Densification parameter % AV Vo % atm. time hrs. R69 C. NH3 12 42 10 0 53.7 0 0 R71 12 36 9 0 53.2 _ 0 0 R68 12 60 35 0.5 57.5 8.6 7.0 R70 12 34 8 0.5 57.0 _ 7.5 6.1 R3 1 55 30 1.0 60.7 _ 15.5 11.9 - R4 1 56 44 1.0 61.1 <1.4 16.3 12.4 R7 1 58 24 1.0 61.3 <1.5 16.8 12.7 R9 1 36 30 1.0 61.3 <1.7 16.8 12.7 . R24 6 44 21 2.5 62.1 _ 18.5 13.8 R35 4 37 19 2.5 63.5 <3.3 21.5 15.7 R36 4 39 16 2.5 63.0 <2.4 20.4 15.1 R37 4 36 16 2.5 63.3 <2.7 21.1 15.5 Rll 6 64 17 5.0 64.7 <4.0 24.1 17.3 R12 6 68 23 5.0 67.1 <0.2 29.2 20.3 R14 6 50 21 5.0 65.5 <1.3 25.8 18.3 R15 6 51 17 5.0 63.7 <2.3 21.9 16.0 R16 6 47 12 10.0 67.2 _ 29.5 20.4 R17 1 56 17 10.0 66.3 _ 27.5 19.3 R18 f 1 65 18 10.0 66.8 _ 28.6 19.9 R19 6 45 13 10.0 66.2 - 27.3 1-9.2 Q49+ H2 12 23 * 4 0.5 57.6 8.8 7.1 Q50+ H-2 12 23 5* 0.5 57.5 - 8.6 7.0 *time to reach 1200°C from 100°C superkanthal practice A i n the calculation of densification parameter, the "green" density was taken as 53.5% of theoretical, corresponding to the density achieved when 1200°C was f i r s t reached (zero time) 70 67 o I-63 59 V) c <u O 55 O o - f o Solid-State Sintering (68/i.m., 1200 °C) > 0 24 03 <u E o o Q_ c o 16 £ 8 o c Q 0 © -.4T A ~ o ~ -o o A / / / -O— D.P. AV Vo 4 T i m e , 6 H o u r s 8 l—~T J L J L 0 Figure 3.14. Density, densification parameter and ~ versus isothermal v o sintering time for 68 ym cupronickel powder sintered at 1200°C. 71 b) A marked i n c r e a s e i n t h e g r a i n s i z e r e s u l t e d from h e a t i n g a t I200°C compared t o 900°C (compare F i g u r e 3.12 w i t h 3.15). In specimens s i n t e r e d f o r 5 o r more h o u r s , a l m o s t e v e r y p a r t i c l e had become a s i n g I e " c r y s t a I . A n n e a l i n g t w i n s ( r e v e a l e d o n l y by a p p r o p r i a t e e t c h i n g , as i n F i g u r e 3.18) were found i n most g r a i n s . c) Some of t h e necks which had d e v e l o p e d between p a r t i c l e s were l a r g e o u t of a l l p r o p o r t i o n t o o t h e r s and were much l a r g e r than e x p e c t e d i n r e l a t i o n t o t h e b u l k d e n s i f i c a t i o n which had o c c u r r e d ( e . g . the necks a t 'A' i n F i g u r e s 3.16 and 3.17). T h i s phenomenon was a s s o c i a t e d w i t h r e l a t i v e l y dense c l u s t e r s ( F i g u r e s 3.16 and 3.17). d) No p a r t i c l e s were e v e r o b s e r v e d which had a di m e n s i o n g r e a t e r t h a n 74 ym (200 mesh) i n the p l a n e of p o l i s h . There i s t h e r e f o r e no e v i d e n c e o f p a r t i c l e growth by c o m p l e t e c o a l e s c e n c e o f p a r t i c l e s a t I200°C. Moreover the ave r a g e p a r t i c l e d i a m e t e r , d e t e r m i n e d by q u a n t i t a t i v e m e t a l l o g r a p h y on specimens s i n t e r e d between 0 and 10 hours was 68 ± 2 ym. The neck regions of several 1200°C sintered specimens were care-f u l l y surveyed in the microprobe analyser to determine i f there was any evidence of segregation of one of the alloy components at the necks. Similar studies were performed on specimens which were sintered at 1200°C and quenched directly. No evidence of segregation was found in any specimen at any location. Figure 3.19 show typical x-ray intensity traces super-imposed on absorbed electron image photographs for several necks. 3.3.2 Supersolidus Sintering in Vacuum The f i r s t supersolidus sintering experiments were conducted at 1260°C in the Centorr furnace at pressures of 10"5 to 10"2 torr; Table 3.4. 72 Figure 3.15. Specimen R4, sintered at 1200°C for one hour in vacuum; (a) x270, (b) x740. 73 Figure 3.16. Specimen R14, sintered at 1200°C for 5 hours. (Reveals that al l particles as essentially single crystals, very large necks at 'A' and dense clusters), (a) x270, (b) x740. (b) Figure 3.17. Specimen R16, sintered at 1200°C for 10 hours. Similar to Figure 3.16; (a) x270, (b) x740. 75 Figure 3.18. Microstructure of the section of R70 after etching with Carapella's reagent. Reveals annealing twins, x270. (b) (c) Figure 3.19. Cu and Ni x-ray intensity lines superimposed on absorbed electron images in 68 urn cupronickel powder specimens sintered at 1200°C for one hour in hydrogen and quenched. (Scanning path is across the neck. Reveals absence of segregation); (a) Ql, xlOOO; (b) Q2, xlOOO; (c) Q3, x500. Table 3.4 Data for Supersolidus Sintering Runs in the Centorr Furnace. All Runs at 1260°C, with 200 x 230 Mesh Powder Spec. No. Clear ing Time to reach 900°C min. Homog. atm. Vac. Torr Time to reach 1260°C from 900°C min. Sintering cycle Sintered Density atm. Time hrs. atm. Press. Torr Time min. End Treatment g cm- 3 % of Theroet. R58 H2 4 35 i o - 2 10.9 vac i o - 2 0 He at 1 atm. 6.18 69.0 R59 H 2 12 39 i o - 2 12.9 vac i o - 2 0 He at 1 atm. 6.17 68.9 R52 H2 4 34 i o - 2 12.7 vac i o - 2 5 He at 1 atm. 7.64 85.3 R53 H 2 4 38 i o - 2 14.5 vac i o - 2 5 He at 1 atm. 7.88 88.0 R54 H 2 4 37 i o - 2 14.7 vac i o - 2 5 He at 1 atm. 7.60 84.9 R55 H2 4 34 1.5 x 10"6 14.16 vac 0.2 x IO"5 5 vac 7.87 87.9 R56 H 2 4 36 i o - 2 18.3 vac i o - 2 10 He at 1 atm. 8.67 96.8 R57 H2 4 37 i o - 2 20.7 vac IO"2 10 He at 1 atm. 8.63 96.4 R60 H2 12 37 10~5 11.5 vac 0.4 x IO"5 10 vac 7.44 83.1 R48 H2 4 33 0.4 x 10"5 12.5 vac 0.4 x IO"5 15 He at 1 atm. 8.71 97.2 R49 H2 4 34 IO"2 12.0 vac i o - 2 15 He at 1 atm. 8.65 96.5 R61 H2 12 33 0.3 x IO"5 11.5 vac 0.6 x TO"5 15 vac 7.63 85.2 R50 H2 4 36.5 TO"2 12.0 vac i o - 2 30 He at 1 atm. 8.60 96.0 R51 H2 4 33 IO"2 13.0 vac IO"2 30 He at 1 atm. 8.45 94.4 R62 H2 12 29 10"e 10.4 vac 0.4 x 10"5 30 vac 8.60 96.0 R65 H2 12 50 io - 2 10.25 Ar. 760 30 Ar. 7.40 82.6 R64 H 2 12 46 IO"2 12.75 Ar. 760 30 Ar. 7.08 79.0 R63 as rec ei ved 35 IO"2 13.90 Ar. 760 30 Ar. 8.08 90.1 78 The rate at which densification occurred at 1260°C suggested that a sub-stantial amount of liquid had formed. It was subsequently revealed by DTA work (Section 3.1.2) that the solidus temperature of the alloy powder varied with the atmosphere in which i t was heated and with the amount of residual oxygen in the system. Photomicrographs of typical sintered specimens are reproduced in Figures 3.20 to 3.23. The following observations are significant: a) specimens sintered and cooled in a vacuum of 10"5 torr contained larger pores than those which were sintered in vacuum but cooled under 1 atmosphere of helium (compare Figures 3.20 and 3.22), b) specimens sintered and cooled in argon (at 1 atmosphere) did not achieve high densities, even after 30 minutes at 1260°C, and exhibited large pores after sintering (Figure 3.23), and c) owing to the slow cooling rate of specimens in the Centorr furnace, the boundaries between regions which had been liquid (copper-rich) and solid (nickel-rich) were not readily defined by metallography. It was therefore not possible to define quantitatively the amount of liquid which was present during sintering.' However, there were qualitative indications that the amount of liquid formed was far from uniform for al l the runs. The above observations are consistent with the presence of sufficient oxygen in the vacuum sintering specimens to result in appreciable lowering of the solidus temperature of pure cupronickel and the evolution of oxygen gas at intraparticle voids during sintering. Although the powders were cleaned in hydrogen, they were exposed to air during the preparation of specimens, and they were not thereafter heated in a reducing atmosphere. Oxygen analyses were performed on a number of the sintered specimens. The results in Table 3.5 indicate that as much as 20-200 ppm of oxygen was 79 Figure 3.20. Cupronickel specimens sintered at 1260°C in a vacuum of -TO-5 torr, for (a) 10 min. (R60) and (b) 30 min. (R62), x 120. (a) (b) Figure 3.21 Cupronickel specimens sintered at 1260°C in a vacuum of ~10 - 2 torr for (a) zero min. (R58) and (b) 5 min. (R52). Specimens helium treated at the end of the runs, xl20. 80 (a) (b) Figure 3.22. Cupronickel specimens sintered at 1260°C in a vacuum of ~10 - 2 torr for (a) 10min. (R57), (b) 30 min. (R51). Helium treated at the end, xl20. (a) (b) Figure 3.23. Cupronickel specimens sintered at 1260°C in Argon for 30 min, (a) as received powder (R63); (b) cleaned in hydrogen (R64), xl20. 81 Table 3.5 Oxygen Content of Cupronickel Specimens Sintered at 1200 and 1260°C in the Centorr Furnace Spec. No. Sintering * Oxygen, ppm Spec. No. Si ntering * Oxygen ppm Rl s 17 R50 SS 19 R3 s 12 R53 ss 29, 87 R5 s 292 R54 ss 26 R12 s 86 R55 ss 18 R13 s 115 R56 ss 15 R20 s 323 R59 ss 56 R29 s 181 R60 ss 33 R31 s 212 R61 ss 23 R40 ss 13 R62 ss 17 R41 ss 36, 35 R63 ss 17 R42 ss 19, 15 R64 ss 36 R43 ss 28, 14 R65 ss 33 R44 ss 15 R66 ps 27 R46 ss 14 R67 PS 25 R47 * ss 21 R48 ss 12 s - solid state sintering at 1200°C ss - supersolidus sintering at 1260°C ps - presintered at 900°C 82 s t i l l present after sintering, and that there were appreciable differences in the amount of residual oxygen between specimens in the series. For reasons indicated above, these early supersolidus sintering experiments, could not be interpreted quantitatively. However, they provided a basis for the design of later experiments. Metallography on the specimens also provided some early insight into the mechanisms of super-solidus sintering. 3.3.3 Sintering in Hydrogen at 120Q-1273°C As noted in Section 3.1.3, the solidus temperature of the cupro-nickel powder when heated in dry hydrogen was 1265 ± 1°C. A number of sinter-ing experiments were conducted in the superkanthal furnace with a hydrogen atmosphere, and at temperatures in the range of 1200°C to 1273°C. All speci-mens were held for 30 minutes at temperature. Data and results for runs with 68 urn powder are in Table 3.6 and for runs with 81 urn powder are in Table 3.7. The sintered densities and the densification parameters as a func-tion of sintering temperature are plotted in Figure 3.24. The data show that: a) W i t h i n t h e t e m p e r a t u r e regime.where no l i q u i d formed, d e n s i f i c a t i o n d u r i n g s i n t e r i n g was l i m i t e d and was not s t r o n g l y t e m p e r a t u r e dependent. b) Specimens s i n t e r e d a t t e m p e r a t u r e s where l i q u i d fqrmed d u r i n g t he s i n t e r i n g c y c l e showed e x t e n -s i v e d e n s i f i c a t i o n , t o a degree which depended s t r o n g l y on the t e m p e r a t u r e (amount o f l i q u i d f o r m e d ) . c) Under c o n d i t i o n s o f s u p e r s o l i d u s s i n t e r i n g a t a g i v e n t e m p e r a t u r e , t h e r e was l i t t l e d i f f e r e n c e i n the d e n s i f i c a t i o n of 68 urn and 81 um powder specimens. In t h e s o l i d s t a t e , t h e c o a r s e r powder specimens d e n s i f i e d s l i g h t l y l e s s f o r a g i v e n s i n t e r i n g t r e a t m e n t . Figures 3.25.a and b are photomicrographs from specimens sintered at temperatures between 1230 and 1262°C. Table 3.6 Data for 30-Minute Sintering Runs at 1200-1273°C in Hydrogen Part I. 200 x 230 Mesh Powder Density of the presinter = 51.2% of theoretical Spec. No. .Sintering 'Temp. °C Time to reach temp, min. Temperature f l actuations °C End Treatment % theoretical density Densification parameter % Grain Size* ym + -Q49 1200 4.0 2.5 2.5 F 57.6 8.8 Q50 1200 5.0 2.5 2.5 F 57.5 8.6 71 Q51 1230 4.5 2.5 2.5 F 59.6 13.1 75 Q59 1230 5.0 2.5 2.5 F 59.5 12.9 Q61 1260 5.0 2.5 3.0 F 63.1 20.7 Q62 1260 6.0 2.5 2.5 F 63.8 22.2 Q14 1260 11.0 0.5 1.5 Q 64.2 23.0 73 Q21 1262 4.5 2.0 2.0 Q 61.6 17.4 71 Q22. 1262 10.0 2.0 2.0 Q 62.4 19.2 73 Q20 1264 4.5 2.0 2.0 Q 75.9 48.2 87 Q19 1266 7.0 2.0 2.0 Q 78.1 52.9 88 Q16 1268 4.0 2.0 2.0 F 82.7 62.8 Q17 1268 10.0 2.0 2.0 F 86.2 70.3 Q18 1268 5.0 2.0 2.0 Q 82.6 62.6 115 Q15 1273 11.0 1.0 1.5 F 95.4 90.1 147 F = Furnace cooled Q = Quenched into iced brine * = Assuming solid and pores only Table 3.7 Data for 30-Minute Sintering Runs in Hydrogen Part II. 170 x 200 Mesh Powder Density of the presinter = 51.2% of the theoretical density Spec. No. Sintering temp. °C Temperature f1uctuation °C Time to reach the temp, min. End Treatment % theoretical density Densification parameter % + -Q69 1250 1.5 3.0 4.25 F 58.1 9.9 Q70 1253 2.0 3.0 4.75 F 58.5 10.8 Q71 1256 2.0 1.75 9.00 F 59.0 11.8 Q72 1259 2.0 2.0 6.60 F 59.9 13.3 Q73 1262 2.0 0.5 8.25 F 67.5 30.1 Q74 1265 1.5 1.5 5.92 F 73.4 42.8 Q75 1268 2.0 1.0 8.75 F 85.1 68.0 Q76 1270 2.0 1.0 5.95 F 94.7 88.6 Q77 1273 1.0 1.0 8.60 F 97.5 94.6 0 0 IOOI 90 o 80 cu -C H 85 70 </> 5 60 O 81 O 68/im. Sintering Period 30 min. o — o y 8 , / e 1 o / o o o o/ o / J 7 50 100 80 0) | 60 o 40 o Q_ c o o u = 20 (/) c cu Q 1210 o I 0 P o/o / -I / 6 o/ P i o o o 1230 T e mperature, 1250 ° C. 1270 F i g u r e 3 .24. D e n s i t y and d e n s i f i c a t i o n p a r a m e t e r v e r s u s s i n t e r i n g t e m p e r a -t u r e f o r 30 -m inu te runs i n h y d r o g e n . 86 a) Powder p a r t i c l e s become s i n g l e c r y s t a l s a f t e r o n l y 30 mi n u t e s a t I230°C o r h i g h e r t e m p e r a t u r e s , whereas s e v e r a l hours a t I200°C were n e c e s s a r y t o e l i m i n a t e i n t e r p a r t i c l e h i g h a n g l e b o u n d a r i e s . b) E v i d e n c e was found f o r l i n e a r c o a l e s c e n c e between some p a i r s o f n e i g h b o u r i n g p a r t i c l e s (as a t "C" i n F i g u r e 3.25), and t h e f r e q u e n c y o f o b s e r v a t i o n s o f c o a l e s c e n c e i n c r e a s e d w i t h s i n t e r i n g t e m p e r a t u r e i n th e range I230-I262°C. The t y p e s and s i g n i f i c a n c e o f c o a l e s c e n c e e n c o u n t e r s a r e d i s c u s s e d l a t e r i n t h e t h e s i s . c ) The a p p a r e n t s i z e and s i z e d i s t r i b u t i o n o f p a r t i c l e s i n specimens s i n t e r e d a t t e m p e r a t u r e s up t o and i n c l u d -ing I262°C d i d not i n c r e a s e w i t h s i n t e r i n g t e m p e r a t u r e . Typical optical microstructures of specimens which had been sin-tered at or above 1264°C are shown in Figures 3.26 to 3.28 and also in pre-vious Figures 3.5 to 3.9. The following observations were made: a) L i q u i d was p r e s e n t ( a t s i n t e r i n g t e m p e r a t u r e s ) a t two l o c a t i o n s i n the specimens; ( i ) between, n e a r - n e i g h b o u r s o l i d p a r t i c l e s ; i . e . f o r m i n g " n e c k s " a t l o c a t i o n s c o r r e s p o n d i n g t o t h e h i g h a n g l e g r a i n b o u n d a r i e s seen i n s o l i d s t a t e s i n t e r e d s p e c i m e n s , and ( i i ) as i n t r a p a r t i c l e " p o o l s " o f e s s e n t i a l l y s p h e r i c a l shape ( a t P i n F i g u r e s 3.6 and 3.26, f o r exampIe). b) L i q u i d a t p a r t i c l e s u r f a c e s remote from necks c o u l d n o t be d e t e c t e d by m i c r o p r o b e a n a l y s i s ( F i g u r e 3.29) o r by o p t i c a l m e t a l l o g r a p h y . c) L i q u i d had not c o m p l e t e l y p e n e t r a t e d a l l necks between s o l i d p a r t i c l e s . D i f f e r e n t amounts of p e n e t r a t i o n a r e seen a t B i n F i g u r e 3.26 and a t D i n F i g u r e 3.27 and 3.28. d) With i n c r e a s i n g s i n t e r i n g t e m p e r a t u r e (amount o f l i q u i d p r e s e n t ) f o r a f i x e d s i n t e r i n g t i m e , t h e a v e r a g e g r a i n s i z e i n c r e a s e d r a p i d l y as shown i n T a b l e 3.6. e) C o a l e s c e n c e e n c o u n t e r s ( s o l i d necks) between n e i g h b o u r -ing p a r t i c l e s were f r e q u e n t l y o b s e r v e d i n specimens which' were s i n t e r e d a t t e m p e r a t u r e s s I i g h t l y above t h e s o l i d u s . Necks formed by c o a l e s c e n c e were n o t p e n e t r a t e d by l i q u i d a t t h e end o f t h e s i n t e r i n g c y c l e . P a r t i a l p e n e t r a t i o n o f l i q u i d a t necks (see ( c ) above) 87 c o u l d r e s u l t i f c o a l e s c e n c e was i n p r o g r e s s when t h e specimen was c o o l e d . f ) In the p r e s e n c e o f a l i q u i d phase a t the s i n t e r -ing t e m p e r a t u r e s , t h e r e was a marked change i n shape o f t h e s o l i d p a r t i c l e s from s p h e r i c a l t o p o l y h e d r a l . Even a t I264°C, where v e r y l i t t l e l i q u i d (0.9% by w e i g h t ) had been formed, t h i s shape change was o b s e r v e d a t t h e more dense ( l i q u i d f i l l e d ) c l u s t e r s w i t h i n t h e a g g r e g a t e ( e . g . F i g u r e s 3.26 and 3.27). A f t e r 30 minutes a t I273°C, when d e n s i f i c a t i o n had p r o g r e s s e d t o an advanced d e g r e e , r e - s h a p i n g o f t h e s o l i d p a r t i c l e s was g e n e r a l ( F i g u r e s 3.9 and 3.28). 3.3.4 Sintering at 1273°C in Hydrogen In another group of experiments, the duration of sintering at a single supersolidus temperature, 1273°C was varied from "zero" to 60 minutes in an effort to examine the kinetics of densification and the progress of structural changes. Again, all sintering was conducted with 68 pm powder in the superkanthal furnace, in a dry hydrogen atmosphere, according to the conditions in Table 3.8. Results for densification are plotted in Figures 3.30 and 3.31. Essentially complete densification was obtained after one hour at 1273PC. Figures 3.32 and 3.33 are photomicrographs typical of specimens from this series of runs. Using quantitative metallographic techniques, estimates were made of the size and distribution of copper-rich (liquid phase) and nickel-rich (solid) areas in the specimens. These results are collected in Table 3.9. The observations can be summarised as follows: a) A t t h e s i n t e r i n g t e m p e r a t u r e , l i q u i d was p r e s e n t both a t i n t e r p a r t i c I e and i n t r a p a r t i c I e s i t e s . 88 Figure 3.25. Linear coalescences between particles, as shown at 'C, in specimens sintered (solid state) at (a) 1260°C, (Q14) and (b) 1262°C, (Q22) for 30 minutes, x385. (a) (b) Figure 3.26. Liquid pools (P), interparticle liquid (as at B), and the shape change of particles at liquid f i l l e d clusters in cupronickel specimens at 1264°C for 30 min. (Q20); x385. 89 Figure 3.27. Specimen Q19, Sintered at 1266°C for 30 min. showing the presence of dense regions and different amounts of pene-tration of liquid (as at 'D'), x385. Figure 3.28. Specimen Q18, sintered at 1268°C for 30 min. reveals the presence of large grains, linear coalescences and partial penetration of the liquid (as at 'D'), x385. 90 Cu wt. % 47-6 47-8 52-3 52-Ni wt. % (a) (b) (c) Absorbed electron images and x-ray intensity traces showina the presence of l i q u i d at the neck region and the absence of liquid at particle surfaces and at the pore oeriuherv t»\ nA7 X3600, (b) Q47, xlOOO, (c) Q20, xlOOO p e n P h e r ^ ^ Q47, Table 3.8 Data for 1273°C Sintering Runs in Hydrogen (0-60 Minutes at Temperature) 68 urn Powder Spec. No. Time to reach 1273°C min. Temperature fluctuation Sintering time min. End Treatment % theoretic density • + -Q37 11.0 - - 0 F 72.8 Q38 11.0 - - 0 F 76.4 Q31 9.0 2.5 0.5 5 F 86.6 Q32 10.5 2.5 0.0 5 F 83.7 Q30 12.0 2.5 1.0 10 F 92.3 Q33 7.5 2.5 1.0 10 F 89.6 Q29 8.0 2.5 2.5 15 F 95.5 Q34 7.0 2.5 2.0 15 F 94.8 Q28 6.0 2.5 2.0 30 F 97.4 Q35 8.5 2.5 2.5 30 F 97.3 Q39 10.0 1.0 2.5 30 F 91.8 Q40 9.0 2.5 2.0 30 F 98.1 Q27 9.0 2.5 2.0 45 F 97.3 Q36 11.0 2.5 2.0 45 F 98.3 Q65 11 .0 1 .5 1.0 60 F 99.1 Q64 11 .5 1 .5 1.0 60 F 100.0 Q66 5.0 2.5 2.5 60 F 100.0 Q46 7.0 2.5 0.5 5 Q 86.0 Q47 5.0 2.5 0.5 5 Q 83.5 Q44 11.0 2.5 1.0 15 Q 96.0 Q45 9.0 2.5 0.0 15 Q 95.6 Q42 13.0 2.5 0.0 30 Q 97.1 Q43 11.0 2.5 1.0 30 Q 97.5 Measured change in dimensions Ad do AL_ Lo Densification parameter A L / L o Us i ng po = 74.6% Using Po = 53.5! 0.121 0.098 0.139 0.152 0.174 0.165 0.181 0.181 0.188 0.166 0.188 0.188 0.103 0.085 0.110 0.134 0.137 0.133 0.173 0.161 0.164 0.151 0.174 0.154 41.5 49.2 71.2 64.9 83.4 77.6 90.3 88.8 94. 94. 82, 95. 94. 96. 98.1 100.0 100.0 69.9 64.5 91.4 90.5 93.8 94.6 ,4 .2 .4 ,9 .2 3 0 0 0.046 0.036 0.064 0.056 0.073 0.071 0.078 0.078 0.063 0.080 0.078 0.080 0.082 0.085 0.085 0.044 0.036 0.074 0.073 0.077 0.078 0.088 0.100 0.127 0.120 0.140 0.134 0.147 0.145 0.150 0.150 0.139 0.152 0.150 0.152 0.153 0.155 0.155 0.126 0.120 0.148 0.147 0.150 0.150 F = Furnace cooled Q = Quenched into iced brine d = Diameter L = Length Table 3.9 Quantitative Metal!ographic Data for Specimens Sintered at 1273°C in Hydrogen Spec. No. Sintering time min. Liquid pool daimeter dP urn Grain size* dP = "s urn Average planar diameter, urn No. of pools counted Wt. % 1iquid as pools n d N d ^ Wt. % liquid at grain boundary True grain size*** d s urn pool d^ grain dp n Q38 0 10.3 74 8.4 60.4 278 24.4 - 0 74 Q31 •5 11.5 93 9.4 75.9 237 16.5 2 92 Q33 10 14.1 102 11.5 83.3 194 16.8 3 101 Q29 15 15.2 118 12.4 96.4 152 11.4 9 114 Q28 30 15.1 147 12.4 120.0 122 5.9 14 139 Q36 45 15.4 174 12.6 142.0 114 4.1 16 164 Q66 60 17.1 194 14.0 158.0 59 2.1 18 182 Q32 5 84 2 83 Q30 10 115 3 114 Q35 30 146 14 140 Grain size assuming pore and solid only ( uncorrected). The number of grains, N, counted are 22. *** Grain size assuming liquid, solid and pore. True grain size. no 93 100 r o 9 0 cu xz ^ 8 0 «/> c 0) Q 7 0 ~i 1 1 1 1 i r - — — - 9 " " 8 " 9 / /0 i o J L Supersolidus Sintering (68/xm., 1273 °C) J L 2 0 3 0 4 0 T i m e , m i n . 5 0 6 0 Figure 3.30. Density versus time for supersolidus sintering at 1273°C in hydrogen. 100 CD CD I 8 0 o Q_ c o o 6 0 o CO c CD Q T~ "T / I — " i r — 8 o 0 4 0 ' db L i r 8 " - Q Q - ^ ! J 1 1 J I L J L I 0 2 0 3 0 4 0 T i m e , m i n . 5 0 6 0 Figure 3.31. Densification parameter versus time for supersolidus sinter-ing at 1273°C in hydrogen. 94 and (d) 15 min. (Q29). Clustering is evident in (aj, x!20 Cupronickel specimens sintered at 1273°C in hydrogen for (a) 30 min. (Q28), (b) 45 min. (Q36) and (c) 60 min. (Q66). Coalescence is evident at 'C in (a), xl20. 96 b) A f t e r " z e r o " time a t I273°C; i . e . l i q u i d p r e s e n t d u r i n g o n l y t h e i n t e r v a l o f t i m e r e q u i r e d t o h e a t from 1265 t o I273°C, most o f t h e l i q u i d was e v i d e n t l y p r e s e n t as i n t r a p a r t i c I e p o o l s . A t h i g h m a g n i f i c a t i o n s , t h e r e was e v i d e n c e o f l i q u i d between a d j a c e n t p a r t i c l e s , but more l i q u i d was i n t h e p o o l s . Owing t o g a l v a n i c e f f e c t s i n e t c h i n g , t h e c o p p e r - r i c h • ( I i q u i d ) r e g i o n s a r e a t t a c k e d s e l e c t i v e l y and can be e x p e c t e d t o appear d i s p r o p o r t i o n a t e l y l a r g e i n t h e m i c r o s t r u c t u r e . However, t h i s e f f e c t a p p l i e s t o both i n t e r p a r t i c I e and i n t r a p a r t i c I e r e g i o n s . c) With i n c r e a s i n g t i m e a t I273°C, t h e i n t r a p a r t i c I e p o o l s i n c r e a s e d s l o w l y i n s i z e but d e c r e a s e d r a p i d l y i n number, and e v e n t u a l l y r e p r e s e n t e d o n l y a minor f r a c t i o n o f t h e t o t a l amount o f l i q u i d p r e s e n t a t t h e s i n t e r i n g t e m p e r a t u r e ( F i g u r e 3.34). d) The mean p l a n a r s p a c i n g o f n e a r e s t n e i g h b o u r i n t r a -p a r t i c l e p o o l s a f t e r z e r o m i nutes a t I273°C was 13 ym w i t h i n a g i v e n p a r t i c l e . A f t e r l o n g e r s i n t e r -i n g t i m e s t h e p o o l s were c o n c e n t r a t e d near t h e v o l u m e t r i c c e n t r e s o f t h e s o l i d p a r t i c l e s ( F i g u r e 3.33) . e) The s i z e o f t h e s o l i d p a r t i c l e s which e x i s t e d a t the s i n t e r i n g t e m p e r a t u r e i n c r e a s e d s t e a d i l y w i t h t i m e a t t e m p e r a t u r e ( T a b l e 3.9 and F i g u r e 3.34). f ) S o l i d p a r t i c l e s underwent s u b s t a n t i a l shape change, from s p h e r i c a l t o p o l y h e d r a l , w i t h i n c r e a s i n g t i m e a t I273°C. W i t h i n p a r t i c l e c l u s t e r s , some p a r t i c l e s had a l r e a d y begun t o change shape when I273°C was reached on h e a t i n g ; i . e . a f t e r z e r o t i m e a t t e m p e r a t u r e . g) There was e v i d e n c e o f c o a l e s c e n c e ( f o r m a t i o n o f s o l i d n e c k s ) between some p a i r s o f p a r t i c l e s a f t e r a l l t i m e s a t I273°C (as a t 'C i n F i g u r e s 3.3.a o r 3.8.a). h) A f t e r z e r o t i m e a t I273°C, pronounced c l u s t e r i n g o f t h e s o l i d p a r t i c l e s i n h i g h - d e n s i t y r e g i o n s was e v i d e n t ( F i g u r e 3.32.a). V o i d s were p r e s e n t which were a t l e a s t as l a r g e as t h o s e which e x i s t e d in t h e o r i g i n a l l o o s e powder a g g r e g a t e o r which e x i s t e d a f t e r s i n t e r i n g i n t h e s o l i d s t a t e (compare F i g u r e s 3.4.a and 3.32.a). S c a n n i n g e l e c t r o n m i c r o g r a p h s which s u p p o r t s e v e r a l o f t h e above o b s e r v a t i o n s a r e reproduced i n F i g u r e s 3.35 and 3.36. O O Q_ to O 24* \ \ \ U V I 6 L Ox o 3 cr >P 8 . c 0) i 1 r ~— i 1 1 1 1 1 1 r Supersolidus Sintering (68 / im., 1273 °C) s X 'XX — - X L -L I I J i • ' 220 180 E <u n 140 CO c o o 100 60 J L 1 I 1 1 1 1 r - 1 1 1 r o -• -0 ' o _ x r J I L J I I I » l I 0 10 20 30 4 0 Time , min. 5 0 60 Figure 3.34. The amount of liquid as pools, and the real grain size, versus time of sintering at 1273°C in hydrogen. Figure 3.35. Scanning electron micrographs of cupronickel specimens sin-tered at 1273°C in hydrogen for (a) zero min. (Q38), (b) 5 min. (Q31), (c) 10 min. (Q33) and (d) 15 min. (Q29), x!20. 99 (b) (c) Figure 3.36. Scanning electron micrographs of specimens sintered at 1273°C in hydrogen for (a) 30 min. (Q28), (b) 45 min. (Q36) and (c) 60 min. (Q66), xl20. 3.3.5 Sintering at Temperatures Above 1273°C 100 A few specimens were sintered in hydrogen at 1280°C and 1285°C, for which the phase diagram (Figure 3.3) indicates that the amount of liquid present was 29 and 38 per cent by weight, respectively. Densifica-tion proceeded rapidly, but problems were encountered with sagging of the specimens under their own weight and some physical segregation of liquid at the highest temperature (Figure 3.37). The following observations are noted: a) Specimens a c h i e v e d - 96 per c e n t o f s o l i d d e n s i t y a f t e r 5 m i n u t e s - o r l e s s o f s i n t e r i n g a t 1280 o r I285°C. b) A p p r e c i a b l e p a r t i c l e growth o c c u r r e d i n o n l y 5 minutes a t I285°C. c) The i n t r a p a r t i c I e l i q u i d p o o l s formed a t I285°C were l a r g e r than t h o s e ;formed a t lower s u p e r -s o l i d u s t e m p e r a t u r e s . 3.4 Dilatometer Results 3.4.1 Qualitative Observations on the Progress of Shrinkage A typical continuous linear dimensional change curve obtained from a dilatometer run is presented in Figure 2.11. The curve clearly shows a) i n i t i a l t h e r m a l e x p a n s i o n d u r i n g t h e c o u r s e o f h e a t i n g t o t h e s o l i d u s t e m p e r a t u r e , b) r a p i d net s h r i n k a g e f o r a s h o r t p e r i o d a f t e r r e a c h i n g t h e s o l i d u s t e m p e r a t u r e , f o l l o w e d by s l o w e r n e t s h r i n k a g e a t a s t e a d i l y d e c r e a s i n g r a t e , and c ) f i n a l t hermal c o n t r a c t i o n d u r i n g t h e c o u r s e o f c o o l i n g t h e specimen t o room t e m p e r a t u r e . 101 Figure 3.37. Bottom section of the specimen sintered at 1285°C for 5 min. in hydrogen reveals the segregation of liquid, (a) xl2, (b) xl45. 102 This last component of the dilatometer curve includes s o l i d i f i -cation shrinkage. From the previous results for the effect of temperature on densification i t follows that: ( i ) s o l i d s t a t e s i n t e r i n g s h r i n k a g e d u r i n g t h e c o u r s e of h e a t i n g t o t h e s o l i d u s t e m p e r a t u r e i s n e g l i g i b l y smaI I and ( i i ) r a p i d n e t s h r i n k a g e s t a r t s t o o c c u r a t t h e s o l i d u s t e m p e r a t u r e even though t h e t e m p e r a t u r e a t t h e c e n t r e o f a specimen was noted t o be about I0°C below the s o l i d u s a t t h a t s t a g e i n a d i l a t o m e t e r r u n . On this basis shrinkage curves were calculated by adding the appropriate thermal expansions to the observed decrease in length of the specimens. Corrected shrinkage curves thus obtained for a number of dilatometer runs are given in Figure 3.38. The times at which the final sintering temperature was reached at the thermocouple are indicated on the curves. Actual times to attain the isothermal sintering temperature from the start of observed net shrinkage are given in Table 3.10. Some specimens held for more than about 12 minutes (e.g. LVDT 62, curve 12 in Figure 3.38) exhibited "sagging." This is believed to be the consequence of overheating of specimens. The thermocouple wires became alloyed with cupronickel and thus their thermoelectric properties were altered. 103 104 Table 3.10 Measured Shrinkage Values for Dilatometer Specimens Total Shrinkage Time min. Measured Corrected Maximum . AL . t — from Lo LVDT Spec No. • Average AL Lo Average Ad do Shrinkage Time at 1273°C min. LVDT 54 0.025 0.0214 0.0247 0.0012 -LVDT 49 0.125 0.0613 0.0742 0.0234 -LVDT 53 0.200 0.0597 0.0808 0.0324 0.140 LVDT 59 0.200 0.0847 0.0972 0.0456 0.180 LVDT 58 0.300 0.0871 0.0962 0.0442 0.190 LVDT 55 0.550 0.0980 0.1093 0.0651 0.125 LVDT 57 0.850 0.1072 0.1232 0.0633 0.180 LVDT 56 3.350 0.1222 0.1260 0.0866 0.190 LVDT 61 5.150 - - 0.1036 0.160 LVDT 29 10.280 0.1519 0.1490 0.1201 0.260 LVDT 35 11.430 0.1450 0.1490 0.1176 0.330 LVDT 62 21.10 - - 0.1809 0.190 105 3.4.2 Anisotropy of Shrinkage in Dilatometer Runs The vertical specimen surfaces and corners were the f i r s t regions to be heated in the high frequency induction furnace. Temperature gradients were generated in the early stages of supersolidus sintering, aggravated by the relatively low heat transfer rate through the porous bodies. The early gradients caused non-uniform dimensional changes, and the i n i t i a l cylindrical shape of a specimen became and remained distorted. Using calipers, the final dimensions of a sintered specimen were measured at a number of positions, as indicated in Figure 3.39. Ratios of the average change in length and diameter to the original dimensions are given in Table 3.10. Also, the maximum linear shrinkages obtained from dilatometer plots are given in the same table. The following observations may be made from the data: a) D i m e n s i o n a l changes d u r i n g s u p e r s o l i d u s s i n t e r i n g a r e not i s o t r o p i c ; i n n e a r l y a l l runs t h e r e was more n e t d i a m e t r a l s h r i n k a g e than l e n g t h s h r i n k a g e . b) The n e t average d e c r e a s e i n l e n g t h measured on s i n t e r e d specimens was s i g n i f i c a n t l y g r e a t e r t h a n t h a t d e t e c t e d by d i l a t o m e t r y . The d i l a t o m e t e r o b s e r v e d changes i n specimen l e n g t h o n l y a t t h e c e n t r e o f t h e long a x i s o f t h e specimen, which was t h e l a s t p a r t o f t h e specimen t o a t t a i n the s i n t e r i n g t e m p e r a t u r e . From both of the above observations i t was clear that shrinkage data derived directly from dilatometer plots were of restricted quantiative value. However, the nature of the anisotropy and non-uniformity of sinter-ing shrinkage in the dilatometer were comparable from one run to another. Thus, the trends observed in shrinkage with variations in time, temperature, particle size, and other factors in the dilatometer experiments were significant. 106 3 . 4 . 3 Calculated Versus Measured Density Changes Finally densities of sintered dilatometer specimens were determined by (a) the oil-impregnation method, and (b) measurements of weight and average dimensions. Owing to the non-cylindrical shape of the specimens after sintering (Figure 3 . 3 9 ) , the values from impregnation tests were the more accurate. Results are given in Table 3 . 1 1 , together with values of density calculated from the dilatometer data, on the assumption of homogeneous and isotropic shrinkage in the specimens, using the releationship: p % = 1 _ 3AL Po x 100 ( 3 . 1 ) where p 0 = the i n i t i a l density of the presinter, p = the final sintered density, AL = the change in length, Lo = the i n i t i a l length at P o -The results are compared in Figure 3 . 4 0 , from which i t may be observed that: a) The degree o f d e n s i f i c a t i o n i n d i c a t e d by d i l a t o m e t r i c measurements o f l i n e a r s h r i n k a g e i s c o n s i s t e n t l y lower than t h a t which a c t u a l l y o c c u r r e d . b) The a b s o l u t e d i s c r e p a n c y does n o t change a p p r e c i a b l y w i t h t i m e of s i n t e r i n g , i n d i c a t i n g t h a t i t p r o b a b l y has i t s o r i g i n s i n the v e r y e a r l y s t a g e s of s u p e r s o l i d u s s i n t e r i n g . Vertical axis o.f dilatometer ' _ > Front View 0-515 in 0-492 in 0-489 in 0-491 in 0-510 in c do O a> 6 o> o ID 6 c fO o 6 c to •x-6 0 519 in 0-490in 0-490 in 0-490in 0-513 in Side View Figure 3.39. Sintered dimensions of specimen LVDT 56. Table 3.11 Density and Grain Size of Dilatometer Specimens as a Function of the Temperature Attained During the Run Spec No. • Time of Sintering min. Derived (from dilatometer data) Density I % theoretical Measured Temperature at the termination of run °c Grain size ym Density II % theoretical Density III % theoretical LVDT 60 0 54.2 54.2 ND _ 81 LVDT 54 0.025 54.3 60.4 60.8 1258 _ LVDT 49 .0.125 58.6 68.0 68.0 1264 81 LVDT 53 0.200 60.2 69.0 71.3 1276 89 LVDT 59 0.200 62.9 72.6 72.8 1273 88 LVDT 58 0.300 61.6 71.6 72.4 1273 LVDT 55 0.550 66.8 75.0 75.6 1274 96 LVDT 57 0.850 66.8 78.8 80.5 1274 LVDT 56 3.350 72.7 80.8 83.6 1273 99 LVDT 61 5.150 78.9 NO 89.5 1273 110 LVDT 29 10.280 84.6 88.0 90.1 1273 129 LVDT 35 11.430 81.2 87.1 88.4 1273 LVDT 62 21.100 ND ND 96.6 1274 -I - Calculated from AL/Lo obtained from dilatometer II - Calculated from weight and average dimensions III - Measured by oil impregnation method * - Zero time was taken at the start of shrinkage ND - not determined o 00 0 0 9 0 o cu 80 .c H . 7 0 >•» to c cu 3 60 1 1—I—I I I I I i 1 — i — n — T T 1 1 1—I I I I I • — M e a s u r e d O ~ From Dilatometer Data Particle Size 81 /xm. 5 0 001 .CT o J I I I I I I I J I I ' » I » 01 T i m e , m i n . J J U J L I Figure 3.40. Density versus time for di1atometer runs. n o 3.4.4 Metallography and Microprobe Analyses on Dilatometer Specimens Dilatometer specimens were sectioned for their f u l l length along a diameter and through the thermocouple well (Figures 3.41 and 3.42). As noted earlier, cooling in the dilatometer was rapid, and i t could be assumed that l i t t l e adjustment of composition in the solid portion of a specimen occurred during cooling. This assumption was justified by comparisons of probe results for specimens which had been quenched from 1273°C in the superkanthal furnace (Section 3.1.3) with those for specimens cooled in the dilatometer from the same temperature after sintering for times sufficient to ensure that equilibrium had been established prior to cooling. Both metallographic examination and microprobe analysis were carried out at various locations in the specimens along the two lines M and C as shown in Figure 3.41.d. The "solid" (nickel-rich) regions in the microstructure were analysed in the probe at 500 ym intervals along each line, with the results plotted in Figures 3.43 to 3.46. Each plotted composition is the result of averaging five sets of counts in the probe taken at 1.5 ym intervals within a single solid particle. At low magnifications, Figures 3.41 and 3.42, i t was evident that at the top and bottom of the specimens, adjacent to the ceramic discs in the assembly, densities were lower than elsewhere. Additionally, for times up to 0.2 minutes from the start of observed shrinkage, there were density gradients between the outer surface of a specimen and the thermo-couple well. Higher magnification photomicrographs revealed that there were substantial gradients in the amount of liquid present in specimens Figure 3.41. Portion of the longitudinal sections of dilatometer specimens (81 um powder), x7. Revealing presintered and inhomogeneous sintered structures. The lines C and M show the paths of electron probe microanalyses; (a) LVDT 60 (as homogenised); (b) LVDT 54; (c) LVDT 49; (d) LVDT 59; (e) LVDT 55. (a) (b) (c) (d) (e) Fiaure 3 42. Portion of the longitudinal sections of dilatometer specimens, x7 (particle size 81 ym except ' (e)), revealing the sintered structures; (a) LVDT 56; (b) LVDT 61; (c) LVDT 29; (d) LVDT 62; (e) LVDT 32 (49 ym). ro 113 5 4 50 -c 54 5 0 t 54 5 0 h — i 1 1 1 1 1 1 1 1 1 r r |G Thermocouplt Well Outside of Specimen t> ' Y ? ' Y LVDT 54 - M — I 1 1 1 1 I I I ' i i • -| 1 1 1 1 1 1 1 1 1 1 • * 4 * LVDT 49 -M _ i i i i r i i i • • 1 • " i i 1 1 1 1 1 1 1 1 1 r * * * * * T <} } • $ ^ ^ LVOT 53-M -I 1 L 1 1 | _J | I I I I 2 4 6 8 10 12 Distance , 500 /xm. Intervals Figure 3.43. Figures 3.43 to 3.46. Results of microprobe surveys across dilatometer specimens shows composition of nickel-rich solid versus distance from centre (thermocouple well). — i r — p - — " i 1 1 1 1 1 1 1 r |d Thermocouple Well Outside of Specimen > <r- A * T <p T . I LVDT 59-M I I I I -J I I I I I I L 54 50 — i 1 1 1 r — r - — i i 1 1 1 r * * A * * ? <j> LVDT 59-C L l _ J L I 1, I I I — _ J I I l _ 54 50 ~ r 1— — i 1 1 1 1 1 i 1 1 r LVDT 55-M - J —J 1 1 1 I I I I I I I 54 50 ~ i 1 1 1 1 1 1 1 1 1 1 r A * ^ * M A * ? A M * 54 50 LVDT 55-C I I 1 I I i » t i 2 4 6 8 10 12 Distance, 500 fim. Intervals Figure 3.44. 54 50 115 1 1 1 1 1 1 1 1 1 1 1 1 — |4 Thermocouple Well Outside of Specimen > LVDT 56-M — I J J _J 1 1 I I I I i i 5 4 a* ^ 5 0 _-5 4 a> 54 h 50 h i 1 — ~ i " i 1 r ~ — i 1 1 r y * Y LVDT 56-C J 1 1 — — i — I I I i i i i i T ~— i T — r — — ! 1 1 1 1 1 r M M M M .y 50 T LVDT 61-M L —I 1 J 1 1 1 1 1 1 I L ~ l 1 1 ~I 1 1 1 1 1 1 1 — r l i A Y Y 9 * LVDT 61-C - I — — I 1 1 1 — — i 1 i • i » i 2 4 6 8 10 12 Distance , 500 yum. Intervals Figure 3.45.. 116 1 1 1 T 1 1 1 1 1 1 '—I 1— 54 f\ Thermocouple Well Outside of Specimen > O 5 0 I LVDT 29-M I 1 _J J- 1 I 1— L_ » ' i I o o 0 o 0 o 0 ° o T ~ 1 1 1 r ~ 1 ~1 1 1 1 r-o 54 o o o o o O ° o 00 50 f- LVDT 29-C -I _ J I — J -L_ I _L _L_ I I I L T 1 1 i 1 ! 1 1 1 1——r 54 50 o ° . o ° o O o ° 0 o LVDT 62-M J l _ L_ L_ _J I J I I I L T — i — T - — i 1 1 1 j - — i 1 1 r ° o o ° o o o o o o 0 o LVDT 62-C -L _L _ _ l I 1 I L J ™ J _ I I 54 5 0 2 4 6 8 10 12 D i s t a n c e , 500 / im. Intervals Figure 3.46. 117 heated for shorter periods in the dilatometer. These gradients alone could account for the above mentioned discrepancy between the densification of specimens indicated by LVDT data and that found by direct measurements of bulk density (Table 3.11). Microprobe analyses further revealed that substantial gradients in liquid content existed in the short-term specimens (Table 3.12). More-over, i t was evident that constitutional equilibrium had not been estab-lished through these specimens. The temperatures reached at the thermo-couple when the runs were terminated are given in Table 3.11. Specimen LVDT 59 had reached 1273°C at the thermocouple, and at equilibrium there would be ~ 16 per cent liquid present at this temperature; yet both metallography and the probe surveys showed that very l i t t l e liquid was present near the centre of the specimen (Figures 3.47 and 3.48). The scatter bars shown in Figures 3.43 to 3.45 represent two sources of error in the probe analyses: a) The e r r o r i n i n d i v i d u a l probe a n a l y s e s p r e v i o u s l y e s t a b l i s h e d as ±0.6 p e r c e n t . b) A " s a m p l i n g " e r r o r a s s o c i a t e d w i t h inhomogeneity i n t h e s o l i d p a r t i c l e s , e s t i m a t e d as ±\% ( o f th e a b s o l u t e c o m p o s i t i o n ) f o r s h o r t run specimens, but n e g l i g i b l e f o r l o n g - t i m e specimens such as LVDT 29 and LVDT 62. Gradients in the composition of solid across a dilatometer specimen arise from two sources: 1) Temperature g r a d i e n t s a s s o c i a t e d w i t h i n d u c t i o n h e a t i n g and w i t h t h e r e l a t i v e l y low h e a t t r a n s f e r r a t e t h r o u g h a porous specimen. 2) D i f f e r e n c e s i n t h e t i m e a v a i l a b l e f o r d i f f u s i o n i n t h e s o l i d t o approach e q u i l i b r i u m . Table 3.12 Liquid Distribution in Dilatometer Specimens wt. % liquid at 500 urn intervals from the central hole No. Central hole 1 2 3 4 5 6 7 8 9 10 11 12 LVDT 54 0-10 0-5 0-8 0-5 0-8 0-5 4-14 0-10 16-26 5-15M LVDT 49 0-5 0-5 0-5 0-8 0-5 0-5 1-11 0-8 11-21 22-32 4-14 7-17M LVDT 53 7-17 0-5 0-5 '1-11 0.5 0-5 9-19 0-5 0-5 11-21 5-15 13-23M LVDT 59 5-15 0-8 0-8 0-5 0- 5 1- 11 0-5 0-5 0-10 0-5 0-8 4-14 1-11 5-15 5-15 16-26 0-10 11-21 16-26 13-23 5-15 15-25 11-21 19-29 20-30^ 26-36C LVDT 55 0-10 15-25 4-14 1-11 1-11 1-11 5-15 5-15 5-15 4-14 20-30 5-15 7-17 15-25 7-17 1-11 4-14 1-11 13-23 7-17 5-15 15-25 11-21M 18-28 18-28^ LVDT 56 15-25 7-17 9-19 7-17 11-21 7-17 5-15 5-15 11-21 7-17 11-21 5-15 9-19 9-19 13-23 9-19 16-26 5-15 15-25 11-21 9-19 18-28 18-28M 15-25c LVDT 61 9-19 4-14 11-21 0-5 11-21 9-19 11-21 4-14 13-23 5-15 13-23 7-17 13-23 11-21 13-23 1-11 15-25 15-25 15-25^ 11-21 16-26 16-26c LVDT 29 16 14 16 10 18 16 14 14 20 14 18 16 20 16 18 20 18 18 21 16 20 M 21 23 c LVDT 62 23 27 20 23 23 21 21 29 25 20 25 27 25 27 21 23 27 20 18 27 2 7M 23 27 27C Figure 3.47. Microstructure of LVDT 59 on the diametrical axis (line M) shown in Figure 3.41.d, at locations: (a) surface, (b) 2 mm from the surface, x760. Figure 3.48. Same as Figure 3.47, for locations (a) 4 mm from the surface, (b) near the central hole, x760. 121 It is not possible to isolate the contributions of these two effects in short time specimens. If a nickel content of 52.5 wt. % indi-cated by probe analysis, this corresponds either to equilibrium at 1273°C or failure to reach equilibrium at a temperature higher than 1273°C. With the exception of the extreme top and bottom regions, there were no.significant composition gradients in specimens LVDT 29 and LVDT 62 heated for 10 and 21 minutes respectively beyond the start of observed shrinkage. Since a l l specimens were heated selectively from the outside, i t can be inferred not only that the temperature had been relatively uniform in these specimens, but also that constitutional equilibrium had been established. From photomicrographs of the structures (Figures 3.49 and 3.50) at point 'A' in Figures 3.41 and 3.42 the following observations may be made: a) In r e g i o n s where l i q u i d phase had j u s t begun t o form, t h e r e was a p r e f e r e n c e f o r i n t e r g r a n u I a r n u c l e a t i o n o f m e l t i n g ( F i g u r e 3.49.a). b) P a r t i c l e s underwent s i g n i f i c a n t and p r o g r e s s i v e shape change from s p h e r i c a l t o p o l y h e d r a l w i t h i n c r e a s i n g t i m e i n t h e p r e s e n c e of l i q u i d . Some shape change t o o k p l a c e i n r e g i o n s where o n l y s m a l l volume f r a c t i o n s o f l i q u i d (< 5%) were p r e s e n t and i n t i m e s s u b s t a n t i a l l y l e s s t h a n one minute a f t e r l i q u i d had f i r s t been o b s e r v e d a t i n t e r p a r t i c l e b o u n d a r i e s ( F i g u r e s 3.49.d and 3.50). c) With i n c r e a s i n g t i m e a t s u p e r s o l i d u s t e m p e r a t u r e s , s m a l l e r pores became p r o g r e s s i v e l y c l o s e d . How-e v e r , l a r g e pores remained even i n t h e 20 minute specimen (LVDT 62, F i g u r e 3.42.d) which had a t t a i n e d a d e n s i t y of 96 per c e n t o f t h e o r e t i c a l . 122 Figure 3.49. Microstructures at region A in Figure 3.41: (a) LVDT 49, (b) LVDT 59, (c) LVDT 53 (not in Figure 3.41), (d) LVDT 55, x67. 123 (c) (d) Figure 3.50. Microstructures at region A in Figure 3.42; (a) LVDT 56, (b) LVDT 61, (c) LVDT 29, (d) LVDT 62, x67. 124 3.4.5 Effect of Powder Particle Size In Figures 3.51 and 3.52 corrected dilatometric shrinkage curves are compared for specimens made from three particle size fractions of cupronickel powder; 49, 68 and 81 urn. In the early stages of shrinkage, the effect of particle size was apparently insignificant. After about 4 minutes from the start of contraction, however, the rate of shrinkage was high for the finer powders. At this same stage of a run, the pore size was also smaller in the specimens made from finer powders, as shown in Figure 3.42.e. 3.5 Behaviour of Cast Cupronickel 3.5.1 Structure of Cast and Homogenised Specimens Figures 3,53 and 3.54 show the microstructure of cast cupronickel specimens before and after an homogenising anneal. Interdendritic segrega-tion in the cast alloy (Figure 3.53) was reduced by the annealing to a level at which i t could not be detected metallographically. Microprobe analysis (Section 2.4 and Figure 2.4) had shown that composition variations were approximately ±2% of the mean in homogenised specimens. The average planar dendrite spacing was found to be 33 urn. Microporosity was evident in the homogenised alloy (Figure 3.54). The spacing of the pores indicated that they were interdendritic in origin, and their spherical shape suggested that gas evolution as well as shrinkage was involved in their creation. The volume content of porosity, based on density measurements on machined specimens was 2.0 per cent. I Figure 3.52. Linear shrinkage versus time from start of contraction, for runs 30, 31, 35. Figure 3.53. As cast cupronickel alloy, (a) x26, (b) xl20; showing dendritic segregation. 128 The average grain size of the cast cupronickel was ~ 1.2 mm, and was not affected by homogenisation. No annealing twins were observed in any grains in the specimens as shown in Figure 3.54. 3.5.2 Liquid Formation on Heating Above the Solidus Table 3.13 reports data for experiments in which cast and homo-genised specimens were heated in the superkanthal furnace to 1273 ± 2°C for periods ranging from zero to 30 minutes, and then quenched. The heat-ing cycle was described in Section 2.6.2. Metallography and microprobe analyses were conducted on the specimens, with the quantitative results collected in Table 3.13. Typical microstructures are presented in Figures 3.55 to 3.57. Based on the composition of the nickel-rich regions in those specimens which were heated for 15 and 30 minutes at 1273°C, i t was indi-cated that the solidus of the cast cupronickel alloy was lower than that of the cupronickel powder by approximately 8°C. This was not unexpected, since there was 0.23 wt. % silicon in the cast alloy compared with ~ 0.10 wt. % silicon in the powder. From previous experience, i t was assumed that the effect of this additional silicon on the liquidus temperature could be neglected. On this basis, the weight fraction of liquid in equilibrium with solid at 1273°C was estimated as -27 per cent. Data in Table 3.13 thus suggest that equilibrium had probably been established after 15 minutes or less at 1273°C. Microprobe analysis on the "zero-time" specimen revealed that constitutional equilibrium had not been established. From the average composition of the nickel-rich regions, and assuming that there was Table 3.13 Data for Experiments with Cast Cupronickel Spec. No. Treatment Isothermal Heatinq Composition* of Ni rich phase Normalised composition Weight per cent 1iquid (phase diag.) Weight per cent liquid (quant. Metallog. Temp. °C Temp, fluctua-tions Time hours Cu wt. % Ni wt. % Cu wt. % Ni wt. % + - • SPLS-2 H 1000 5 5 288 50.27 50.31 50.0 50.0 - _ SPLS-2 Q 1273 - - 0 48.15 52.42 47.9 52.1 13.9 12.9 SPLS-3 H 1000 5 5 288 49.57 49.92 49.8 50.2 - _ SPLS-3 Q 1273+ 2 1.5 0.25 46.36 54.97 45.8 54.2 24.9 25.-8 SPLS-3 Q 1273+ 2 1.5 0.25 46.04 55.45 45.4 54.6 26.8 SPLS-4 H 1000 5 5 288 51.05 50.87 50.1 .49.9 - _ SPLS-4 Q 1273 + + 1.5 0.5 0.5 46.02 55.69 45.3 54.7 27.1 29.6 H - Homogenised Q - Quenched from temperature indicated * - Composition obtained from probe analyses ** - Composition normalised to 100 per cent + - Took 6 minutes and 36 seconds to reach 1273°C from 1265°C ++ - Took 6 minutes and 38 seconds to reach 1273°C from 1265°C r o t o 130 ft.. [J .,• ; .v i***V-• ."•'•t'i. : I ,.<*. V * . *, . ; m m \ * (a) (b) Figure 3.55. Cast cupronickel specimen SPLS 2, heated at 1273°C for "Zero" minutes in hydrogen and quenched. This reveals liquid pools, discontinuous grain boundary liquid and pool-free zones (as at 'Z'), (a) x26, (b) xl20. 131 (a) (b) Figure 3.56. Cast cupronickel SPLS 3, heated at 1273°C for 15 min. and quenched, revealing elongated liquid pools, (a) x26, (b) xl20. (a) (b) Figure 3.57. Cast cupronickel SPLS 4, heated at 1273°C for 30 min. and quenched; revealing spheroidised liquid pools and concentra-tion of liquid at triple points, (a) x26, (b) x!20. 132 complete mixing in the liquid when 1273°C was attained, the estimated volume fraction of liquid in this specimen was ~14 per cent. Again, this was in good agreement with the results of quantitative metallography. The initiation and progress of melting on heating the cast and homogenised alloy to 1273°C could be followed by examining photomicrographs of the type represented by Figures 3.55 through 3.57. The important observations as follows: a) The ave r a g e g r a i n s i z e o f t h e specimens was n o t a l t e r e d by h e a t i n g f o r up t o 30 mi n u t e s a t I273°C. b) L i q u i d had formed a t many i n t r a g r a n u I a r s i t e s i n the c o u r s e of h e a t i n g between t h e s o l i d u s and I273°C ( z e r o time a t I273°C), F i g u r e 3.55. c) The volume of l i q u i d formed a t i n t r a g r a n u I a r s i t e s ( "pools") was many t i m e s g r e a t e r than t h a t which had formed a t g r a i n b o u n d a r i e s . d) The g r a i n b o u n d a r i e s d i d n o t appear t o be com-p l e t e l y p e n e t r a t e d by l i q u i d . e) Near some g r a i n b o u n d a r i e s t h e r e were " p o o l - f r e e z o n e s " e x t e n d i n g up t o 60 ym from a boundary (as a t Z i n F i g u r e 3.55). f ) The l i q u i d p o o l s i n the z e r o - t i m e specimen were m o s t l y o f r e g u l a r and e q u i a x e d shape, and t h e i r mean p l a n a r s p a c i n g was ~37 ym. T h i s can be compared w i t h t h e ave r a g e d e n d r i t e s p a c i n g o f 33 ym i n the a s - c a s t a l l o y and m i c r o p o r e s p a c i n g of 47 ym i n the homogenised a l l o y . g) With i n c r e a s i n g t i m e a t I273'°C, ( i ) I n t r a p a r t i c I e p o o l s grew i n s i z e , d e c r e a s e d i n number, and i n c r e a s e d i n t o t a l volume. There was, however, l i t t l e change i n t h e t o t a l volume of p o o l s beyond 15 m i n u t e s , c o n s i s t e n t w i t h t h e p r e v i o u s i n d i c a t i o n t h a t c o n s t i t u -t i o n a l e q u i l i b r i u m had been e s t a b l i s h e d i n l e s s t h a n 15 m i n u t e s a t I273°C. 133 ( i i ) The p o o l s changed from r e g u l a r and e q u i a x e d t o i r r e g u l a r s hapes. Between 15 and 30 m i n u t e s t h e r e was a tendency f o r p o o l s t o assume more rounded c o n t o u r s . ( i i i ) More l i q u i d became c o n c e n t r a t e d a t g r a i n b o u n d a r i e s ( p a r t i c u l a r l y a t t r i p l e p o i n t s ) . However, even a f t e r 30 m i n u t e s a t I273°C, the r a t i o o f i n t e r g r a n u I a r t o i n t r a g r a n u I a r l i q u i d had remained v e r y low. Chapter 4 DISCUSSION 4.1 Solid State Sintering Behaviour of Loose Powders 4.1.1 Sintering in Real Systems versus Model Systems In attempting to identify the mechanisms responsible for den-sification during the sintering of powder aggregates, the usual approach has been to compare the experimental time and/or temperature dependence of densitv or dimensional change with that predicted from various mass transport models singly and in combination (see Section 1.2.1). In the case of model experiments this approach has en.ioyed some success. However, real powder aggregates of practical interest di f f e r physically from the models in respect to regularity of packing, uniformity of particle size and shape, and i n i t i a l interparticle contact (which is affected by compaction). To a limited extent, i t is possible to anticipate the effects of particle shape, size distribution and i n i t i a l neck geometry on the progress of sintering and to modify the models appropriately. However i t is also possible, as in the present work, to minimise these effects experimentally by using loose (uncompacted) powders of essentially spherical shape and uniform particle size. In such experiments i t may be possible 134 135 to isolate the effect of the i n i t i a l packing of particles in the powder aggregate. 4.1.2 Observations of Early Sintering Kinetics It is a general observation that loose or lightly compacted powder aggregates undergo more rapid early shrinkage than either heavily compacted powders or model systems when sintered at a given homologous temperature. Typical of this behaviour are the results by Tikkanen and Ylasaari [66] for fine spherical carbonyl nickel powders, reproduced in Figure 4.1. At any given sintering time, the rate of densification (slope of the plots) was higher for specimens of lower i n i t i a l density. Uncom-pacted (loose powder) specimens exhibited the highest rates of shrinkage. Calow and Tottle [67] sintered loose spherical copper powders (20-90 ym particles) with the results plotted in Figure 4.2. A large degree of densification had occurred in specimens after the smallest sintering interval of 30 minutes. Data from the present work with cupronickel powder are plotted with the Calow and Tottle results, and exhibit similar characteristics. As described in Section 1.2.1 most models of mass transport in sintering predict a simple power law time dependence of shrinkage; i.e. (4.1) in which the value of p can be an indicator of the dominant transport mechanism. Few data are available from experiments with loose aggregates of uniform and spherical metal powder particles. Results reported by Figure 4.1. Relative density versus sintering time at 1000°C for fine spherical carbonyl nickel powder, from Tikkanen and Ylasaari [66]. 0-90 i r- 1 1 r r T i m e , hours Relative Density p / p T versus sintering time for solid state sintering. Data of Calow and Tottle [67] for copper, and present data for cupronickel. CO ^1 138 Clark, Cannon and White [68] for 37.5 ym copper powders are plotted as log TT- versus log time in Figure 4.3, together with results from the present »o work for cupronickel powder. Up to a volume shrinkage of roughly 10 per cent the slopes of the plots (p) are in the range of 0.7 to 1. Beyond this degree of sintering the time dependence of shrinkage decreases markedly (p Z 0.2). Short time sintering data from Tikkanen and Makipirtti [69] for copper and nickel powders are plotted in Figure 4.4. The parameter used to describe shrinkage in this case is different, but the slopes of the plots correspond to values of p in the range 0.55 to 0.9. Shumaker and Fulrath [70] followed the early stage of sintering of compacted copper and nickel powders in a scanning microscope. Their results, which exhibit considerable scatter, are qiven in Fiqure 4.5. The average slopes of the log plots are 0.71 for copper powders and 0.73 for nickel powders. 4.1.3 Structural Changes During Sintering That sintering shrinkage in real powder systems is i n i t i a l l y concentrated at the most close-packed or clustered regions in the original agqregate has been amply demonstrated both previously and in the present work. Barrett and Yust [71] described "centres of densification" in three-dimensional aggregates, examples of which are also clearly evident in Figures 3.4, 3.16 and 3.17 (also Figures 3.3 and 3.4 in Part B) from the present work. Eloff and Lenel [72] observed rearrangement of the particles within some regions of planar arrays of powders in the very earlv stages of 139 10 I Cu (37 5 fjLm) V 01 001 T 1—I I I I I I 1 1—I I III 1—I J — I | | I Sinter. Temp. °C 925 O 1020 Cu-Ni (68/i.m) A | 200 01 J 1 I I I I l I 1 I I I I T i m e , Hours 100 Figure 4.3. Volumetric shrinkage versus sintering time for copper (Clark et al. [68]) and for cupronickel (present results). 20 T 1 1 r 10 i 1 1 r V s sintered volume V 8 theoreticol volume T Cu(2-50yLLm), 0-94 Tm,H2 Cu (2-50yu.m),0-90 Tm,H2 Ni(l-20yU.m), 0-86Tin,H2 Cu-Ni (68yU.m),0-93Tm, Vac. • O A A Log t(min) Figure 4.4. Volumetric shrinkage data for copper and nickel (Tikkanen and Makipirtti [69]) and for cupronickel (present results). (plotted as log - v° " -v versus log time). V - V-j-Material Eiin No. Size Urn Temp.° (T ) m Nickel Ni-A -30+20 1200 Nickel (0.85) Ni-B -30+20 1195 Nickel (0.85) Ni-C -30+20 1110 Copper (0 .80) Cu-A -kh+3j 950 Copper (0.90) Cu-B -30+20 ' 810 Copper (0 .80) Cu-C -hh+3J 950 . Copper (0 .90) Cu-D -30+20 810 Copper (0 .80) Cu-E -U+37 950 (0.90) Green Slope C Density log A i / i 0 pth vs. log t k3% (c) 0.69 (c) 0.78 ko% (D) 0.73 h3% (c) 0.36 h3% (D) . 1.08 h2% (c) 0.67 h0% (D) 0.83 28% (c) 0.62 Trme (minutes) Figure 4.5. Linear shrinkage data o f Shumaker and Fulrath [70] for the solid state sintering of Cu and Ni D o w d e r compacts in the S.E.M. (Experimental data in Table, plotted in figure.) o 141 sintering. The local repacking caused a net densification of the array even before interpenetration of particles had occurred at the necks. Exner et al. [73] observed contraction in some areas and expansion in other areas of planar arrays of copper powder particles, and sugqested that a tvpe of rotation was occurring at some necks. Rotations at two-particle necks during sintering have also been observed in scanning micro-scope studies by Gessinger et al. [74], Ha.imrle and Angers [75], and Nil [76]. The observation of annealinq twins in his sintered nickel powder agqreqates was taken by Tikkanen [20] as an indication that plastic flow, followed bv recrystal1isation, occurred at the necks at some early staqe. In a l l sintered cupronickel specimens in the present work, annealing twins were found in almost every grain. However, when individual particles of cupronickel powder were heated at 900°C, twins were also produced in most grains. It must therefore be concluded that solidification shrinkage stresses within as-atomised particles were alone sufficient to induce flow and recrvstallisation. Occasional linear coalescences between powder particles were observed in a l l cupronickel specimens that had been sintered at 1200°C or higher. The incidence of coalescence was distinctly greater in specimens sintered at higher temperatures up to the solidus. By linear coalescence is meant the formation of a coherent interface [77] between two particles. Coalescence-type encounters occur between particles which have closely similar crystallographic orientations at their mating surfaces, or which assume similar orientations as a consequence of annealing twin formation, or which have relative orientations (described by Kronberg and Wilson [78]) that produce a significant density of coincident lattice sites at the 142 interface. In the case of F.C.C. metals, for example, the Kronberq-Wi1 son (K-W) orientations include rotations of 22°, 30°, and 38° about a common [111] pole. Observations of coalescences are important to an interpreta-tion of sintering mechanisms for two reasons: a) t h e y may be an i n d i c a t i o n t h a t r e l a t i v e p a r t i c l e r o t a t i o n s have o c c u r r e d a t necks d u r i n g s i n t e r i n g , and b) t h e growth o f a neck between a c o a l e s c e d p a r t i c l e p a i r must proceed w i t h o u t the a i d of a h i g h a n g l e g r a i n boundary as a vacancy s i n k f o r d i f f u s i o n . (The r o l e o f c o a l e s c e n c e i n s u p e r s o l i d u s s i n t e r -ing i s d i s c u s s e d s e p a r a t e l y below.) If coalescence encounters were purely s t a t i s t i c a l ; i.e. related only to the relative orientations of neighbouring pairs in the oriqinal aggregate, i t would not be expected that an increase in sintering tempera-ture would affect the incidence of coalescence. It therefore appears likely that some of the observed encounters were aided by particle rota-tions, and that the rotations were more prevalent at higher temperatures. No direct metallographic evidence for rotation at necks was found in any of the sintered cupronickel specimens. Such evidence would be hard to find, however, since surface diffusion acts rapidly to influence neck profiles. 4.1.4 Possible Mechanisms of Early Sintering Shrinkage Of the many transport mechanisms which have been suqgested and identified in the sintering of metal powders, i t is recognised that only five types can contribute to shrinkage: 143 a) Volume d i f f u s i o n , d r i v e n by vacancy concen-t r a t i o n g r a d i e n t s b) G r a i n boundary d i f f u s i o n e) D i s l o c a t i o n g l i d e o r c r e e p , under t h e a c t i o n o f e x t e r n a l and/or i n t e r n a l l y -g e n e r a t e d s t r e s s e s d) D i f f u s i o n a l c r e e p ; i . e . volume d i f f u s i o n d r i v e n by e x t e r n a l and/or i n t e r n a l l y g e n e r a t e d s t r e s s e s e) Rearrangement ( r e p a c k i n g ) , i n v o l v i n g p a r t i c l e r o t a t i o n a t necks and p o s s i b l y g r a i n - b o u n d a r y s l i d i n g as a c o o p e r a t i v e p r o c e s s 4.1.4.1 Diffusion Mechanisms There are several models for those transport processes which involve primarily diffusion along vacancy concentration gradients (Section 1.2.1). Of these, only the one due to Kingery and Berg [6] predicts a value of p > 0.5 in the relationship TT- a t^. Both in the present experi-v 0 rnents and in the more reliable of the previous kinetic studies of loose powder sintering, p was found to l i e in the range of 0.6 to 1.1 for the earliest stage of sintering, with most values > 0.7. Kingery and Berg [6] predicted p = 0.8 for one model of transport by volume diffusion with grain boundaries acting as vacancy sinks (see 1.2.1). They argued that this could explain the experimental results obtained by Clark et al. [68] with loose copper powder (Section 4.1.2, Figure 4.3). However, i t has been pointed out by Tikkanen et al. [20] that the model is unsound on fundamental grounds. In the early stage of sintering, the total area of grain boundaries rapidly increases with time (this is both expected and observed metallographically). This cannot be 144 reconciled thermodynamically with annihilation of vacancies at the boundaries during the same time interval. However, the Kingery-Berg model would predict an increase in the rate of shrinkage as more and larger necks became established, which is contrary to observation. The arguments presented above also apply to those models of grain-boundary diffusion which predict shrinkage. While they may be relevant to later stages of sintering, i t is unlikely that they apply to the earlier stage. A quantitative comparison can be attempted between Kingery and Berg's prediction [6] of volume shrinkage, due to volume diffusion with dislocations and grain boundaries as vacancy sinks, and the experimental values for cupronickel. A value of 3.3 contacts per particle (n x) in the density range 53-61% of theoretical density was obtained from plots of De Hoff et al. [79], of the number of contacts per particle versus sintered density. An average value of 1800 ergs/cm2 was assumed for y based on values of 1640 ergs/cm2 [80] for Cu and 1900 ergs/cm2 [80] for Ni. The atomic volume, given by „ _ atomic weight of the alloy m g\ Avogadro's number x theoretical density was found to be 1.13 x 10~ 2 3 cm3. A value of 6.1 x 10" 1 0 cm2/sec was obtained for the diffusion coefficient of 47.8 atom % Cu cupronickel alloy, D v , at 1200°C, by extrapolating the log Dy versus j plot of Brunei et al. [65] and others [43,81], in Figure 4.6. Using these values in the Expression (4.2), a value of w- = 1.4 x 10"3 was obtained for a sintering interval of 30 minutes. The ex-perimental volume shrinkage was 6.5 x 10"2; i.e. 50 times as great. The Figure 4.6. Interdiffusion coefficient versus y for 50-50 weight % cupronickel alloy. 146 necessity for participation of dislocations as sources or sinks has been disputed [15]. Thus, Expression (1.6) reduces to the form of Expression (1.4) which predicts ^- values s t i l l lower, with p = 0.4. Vo Kingery and Berg derived an expression for by a volume d i f -Lo fusion mechanism with the particle surface as a vacancy sink, which yielded p = 0.8. However, Ichinose and Kuczynski [11] predicted = 0 for volume Lo diffusion with particle surface as vacancy sinks. 4.1.4.2 Creep Mechanisms There are some experimental indications that plastic flow occurs, at least during the earliest stages of sintering of metal powders, without the external application of stress. These include observations of inert markers [82,83] and crystallographically oriented particle pairs [84]. Several approaches have been used to estimate the stresses induced by surface tension at a neck during sintering. Probably the most rigorous of these is due to Leary [85], and is based on a virtual work argument. For a two sphere model (Figure 4.7), the compressive stress at the neck is given by a . - ^ . f c ( 4 . where Pi is a dimensionless coefficient related to the geometry of the neck, and h is the centre-to-centre approach of particles (related to AL). Leary states that the analysis applies only for h/a < 0.05; i.e. for r=- < 5%. For the cupronickel powder of the present work a = 3.4 x 10"3 cm and Y = 1800 ergs cm"2, from which the neck stresses given in Table 4.1 have been calculated for different levels of fractional interpenetration. 147 Table 4.1 Compressive Stresses at the Neck for Various Fractional Interpenetration, According to Leary [85], [a = 3.4 x IO"3 cm, y = 1800 erg cm"2] Fractional Interpenetration h. a The Compressive Stress ai MN • m"2 Fractional Interpenetration h a The Compressive Stress MN • m-2 1 x IO-" 535 6 x 10-3 9 2 268 7 8 3 180 8 7 4 135 9 6 5 108 0.01 5 6 91 0.015 4 7 77 0.02 3 8 68 0.025 2 9 60 0.03 1.8 1 x IO"3 55 0.035 1.5 2" 27 0.04 1.3 3 18 0.045 1.2 4 14 0.05 1.0 148 Assuming that the volume of material undergoing deformation in response to the compressive stress is equal to the volume of the neck, then the mean true strain associated with an increment of particle approach, dh, is • 1 dh 2 T The velocity of centre-to-centre approach is th en dh o u de 0, . d t = 2 h dt = 2 h e ' ( 4- 4) where e is the instantaneous strain rate. The stress dependence of the steady-state strain rate of metals at a given high homologous temperature can be described by a power law: e = C a a n (4.5) For stress levels in the range of 10"" to 10"3 G0 (G0 = the shear modulus), a value of n = 4 to 5 has been observed experimentally for a wide range of metals [86]. Weertman [87] predicted n = 4.5 for steady-state creep on the basis of a model in which dislocation climb was the process controlling the rate of deformation. Creep data for many metals, as presented by Sherby [88], are also found to confirm closely to this prediction. Ashby [89] has derived "deformation-mechanism maps" for metals, of which the one for nickel of 32 ym grain size is presented as Figure 4.8. If any two of the variables stress, strain rate and temperature are known, \ 149 i Figure 4.7. Two-sphere model for solid-state sintering with complete penetration (Lenel et al. [85]). the map identifies the dominant deformation process and the level of the unknown variable. Thus for nickel, at stress levels between 10~3 and IO-1* G0, and at high homologous temperatures, dislocation creep is indicated as the dominant deformation mechanism. This prediction is consistent with many experimental observations, as noted above. Reference to Equation 4.3 and Table 4.1 reveals that neck stresses in excess of 10"3 G0 are likely to be encountered in the very early stages of sintering of loose powders (corresponding to ^ < 0.001). Stresses in Lo the range 10 - 3 to 10 _ l tGomight be experienced for a penetration ratio (linear shrinkage) of up to 0.005. In fact, this degree of shrinkage, and corresponding neck development at particle contacts, would occur heating a specimen to the sintering temperature; i.e. a period during which the kinetics of shrinkage could not be followed experimentally. In the present 150 TEMPERATURE °C Figure 4.8. "Deformation-mechanism map" for nickel as derived by Ashby [89]. work with cupronickel powder, specimens underwent 0.008 linear shrinkage when presintered at 900°C. Throughout the rapid " i n i t i a l " stage of sin-tering at 1200°C, therefore, the stresses at necks (other than at those new contacts established as a consequence of shrinkage) were likely to have been substantially below 10_1* G0. At temperatures > 0.9 T m and at stresses < 10_i* G0, Ashby's map predicts that deformation will proceed by Nabarro-Herring Creep, a type of viscous deformation in response to stress-directed diffusion. That such behaviour is exhibited by copper alloys was recently demonstrated by Burton and Bastow [90] in experiments with wires. 151 Theoretical treatment of the viscous creep process [1,2] indicates a linear relationship should exist between applied stress and steady state strain rate. Specifically: 1 v d 2 kT s (4.6) where B is a constant related to grain geometry, 0, is the atomic volume, d $ is the grain [1,2] or sub-grain diameter [2,91], and other quantities were defined previously. In placing constant strain-rate contours on Figure 4.8, Ashby has used a value of 14 for the constant B, and has taken d s to be the grain size. It is possible to predict the rate of linear approach of a particle pair due to the action of Nabarro-Herring creep. From Equations 4.4 and 4.6, dh 2B Q D y H + 2he = 2 = ^— (4 7) On integration this yields 2 B n D y h = Y_ t 4 C d! kT s The constant of integration C would be zero i f h = 0 at t = 0. Thus volume shrinkage is given by 152 This predicts that the rate of shrinkage is independent of stress, and that the fractional amount of shrinkage varies linearly with time (p = 1 in Equation ( 4 . 1 ) ) . This prediction is in good agreement with the observed kinetics of the early shrinkage behaviour of cupronickel powder at 1200°C in the present experiments (p ~ 0.9). For the present experiments, calculations can be made from Equation (4.8), using B ; 10, = 1.13 x 1 0 - 2 3 cm3, Dy = 6.1 x 10" 1 0 cm2/sec [65], Y = 1800 ergs/cm2, k = 1.38 x 10" 1 6 ergs/°K, a = 3.4 x 10"3 cm and T = 1473°K. When values of ~ =0.065 and 0.125 are taken with the corre-Vo sponding sintering times of 0.5 and 1 hour, d g is found to be 1.7 x 10"" and 1.75 x 10"4 cm. This is much smaller than the grain size of cupro-nickel specimens. According to Pines [91] dislocation substructure boundaries within a crystal act as vacancy sources and sinks. Thus the dimension which defines the vacancy concentration gradient should be the size of sub-structure unit (£) rather than the grain size. Mosaic blocks of 2 ym diameter are not unreasonable for cast and annealed metals. Alexander e£ al. [92] stated that the radius of curvature at the "neck" between a wire and a plate is usually < IO - 4 cm while sintering. If viscous flow occurs only in the neck region,, then the effective diffusion distance could be identified with this radius, and the result is again consistent with the above calculations. It is known that transport mechanisms such as surface diffusion and evaporation and condensation can contribute to neck growth and decrease the stresses at the neck. This might account for slopes of less than unity in the experimental plots (Figure 4.3). 153 4.1.4.3 Rearrangement Other processes which could contribute to shrinkage in the sinter-ing of loose powders can be grouped under the t i t l e "Rearrangement." As noted in Section 4.1.3, there is reported experimental evidence that particles can actually rotate [74,75,76] or slide past one another at a neck under the influence of unbalanced stresses [76] (e.g. asymmetric necks). Such motion could not contribute to net shrinkage in a model or close-packed powder array, but might produce at least localised densification in a less regular aggregate. There are two ways in which shrinkage may be augmented by re-arrangement in principle; (a) more efficient packing may be produced, and (b) the relative motion of particles may allow new contacts to be established. It is d i f f i c u t to verify (a) experimentally; the clusters or "centres of densification" observed in the present and in previously reported [73] sintering studies can have their origin in the original localised packing of the loose powder particles. Metallographic observations support the latter suggestion in the present work; i.e. there was no direct evidence that densification of clusters with time at 1200°C occurred by other than . the linear approach of centres of neighbouring particles. The creation of new interparticle contacts can occur as a natural consequence of linear interpenetration at particle necks by mechanisms other than rearrangement. Moreover, there is no experimental evidence that an increase in the number of contacts will result in an instantaneous increase in the rate of bulk shrinkage. To the contrary, shrinkage is commonly found to be faster in aggregates of looser packing. DeHoff et al. [79] used 154 vibration to increase the i n i t i a l number of contacts per particle in loose powder specimens, and found that this decreased the rate of densification. There are other reasons to suggest that rearrangement processes contribute l i t t l e to sintering shrinkage. For example, rotation or grain boundary sliding at a given neck requires cooperative motion at other necks in a three dimensional aggregate. It was noted by Exner et al. [73] that a given rotation or shear is as likely to produce expansion as i t is to produce contraction. A particle which has only one contact could rotate without the restraint of other necks, but its rotation could produce no increase in density, even locally. 4.1.5 Segregation of Solute During Sintering Menon et al. [93] presented a theoretical analysis of d i f f u -sional creep in binary metallic solid solution polycrystals subjected to an uniform uniaxial stress. Equations were derived for the strain rate and 1 the distribution of the components at quasi-steady state for both grain, boundary and volume diffusion paths. Their analysis showed that diffusional creep should cause segregation to occur whenever the di f f u s i v i t i e s of the components were unequal. Following Herring and others they assumed that the behaviour of a uniformly stressed, i n i t i a l l y spherical grain would approximate the behaviour of grains in a uniformly stressed, i n i t i a l l y equiaxed polycrystal1ine material. Diffusion by a vacancy mechanism was assumed in determining the strain rate and the segregation due to diffusion creep. The steady state creep rate due to volume diffusion was derived to be 155 3 kT r | Pi D 2 NJ D2 + N° Di (4.9) which is roughly a factor of 2 smaller than the Nabarro-Herring creep rate from Equation (4.6) with B = 10. The compositions of the components at steady state were given by v i 0 N. = — N • exp i v . i v A. 1?_ r 2 kT (4.10) for 6' = 0 (where 9' is the angle subtended at the centre of the spherical grain between the direction of applied stress and any position on the grain boundary) (-1)72 0-1 fi (1 - N?)(D! - D2) U 3r 2 (< D2 + Hi D:) (4.11) Subscripts 1 and 2 = the component 1 and 2, i = the component 1 or 2, r = any radial distance inside the grain, r c = the grain radius, and v. the activity coefficient for sol id solution with composition N^ °, v . = the activity coefficient for the solid with composition , the original concentration of component i in the alloy. 156 It was shown previously that there exists a compressive stress at the neck. It can also be shown that a tensile stress ch = - = r » p h exists at the neck. Thus the segregation at the neck due to unequal flow of two kinds of atoms could be predicted using Expression (4.10). Multiplying Q the expression for A., by 2, assuming = and r = r g , the values of N C u for various values of h, (ai = ^ ) , were calculated using Expression (4.10). The values of intrinsic diffusion coefficients Dx = and D2 = , at 1200°C, were calculated from reported tracer self diffusion coefficients [94] for Cu and Ni at an alloy composition of 45.4 at % Cu and the interdiffusion coefficient [65] Dy at a composition of 47.8 atom % Cu. The values are given in Table 4.2. Table 4.2 Diffusion Data for Cupronickel Alloy at 1200°C Alloy Composition at % Cu Values DCu £94] 45.4 2 .4 x 10"9 cm2/sec Dji [94] 45.4 1 .9 x 10"9 cm2/sec Dv [65] 47.8 6 .1 x IO" 1 0 cm2/sec (Thermodynamic factor) 45.4-47.8 0 .28 DCu ~ 47.8 6 .7 x 10" 1 0 cm2/sec DNi ~ 47.8 5 .3 x 10"1 0 cm2/sec 157 Values of N C u and (N C u - N C u) were calculated and are plotted h versus ^ values on a log-log scale in Figure 4.9. It is seen that for linear shrinkages of 2.2 x 10"2 and 4.2 x 10 - 2 (after 0.5 and one hour at 1200°C respectively)the excess concentrations of Cu are ]0~h and 4 x 10~5 atomic fractions. This segregation is far too small to be detected by microprobe analysis. For segregation which is at the limit of detection of 6 x 10"3 atomic fraction in the probe, the linear shrinkage would be 3.4 x 10_1* cm, which is achieved at an extremely early stage of sintering. Moreover, the penetration (h) at this stage, which is approximately equal to the neck radius, is only 10"6 cm. This is two orders of magnitude smaller than the beam diameter in the microprobe analyser, and is thus clearly beyond the resolution of the instrument. It is also well below the limits of resolution of optical microscopy. Kuczynski et at. [24] considered two spherical particles of the same radius, a, of a well homogenised binary alloy containing and Ng atom fractions of atoms A and B respectively. If these particles were brought together and heated they would form a neck, which would grow accord-ing to the predictions of a volume diffusion model. If > Dg, where and Dg are the coefficients of self diffusion of atoms A and B respecitvely, the unequal diffusional flow of the two species would cause an excess con-centration 6N^ of atoms A to build up in the neck area. The excess of A atoms over B, AJ, at the neck is given by [24] D - D, AJ = B Vy + kT B VN 'A VN 'A (4.12) where Vy = the gradient of the chemical potential of vacancies at the neck, 159 y A and y g = the chemical potentials of A and B respectively. The second term of the right side of Expression (4.12) represents the flux of atoms A diffusing back into the alloy due to the concentration gradient VN^ produced by the greater flux of A atoms. According to Equation (4.12) 6N^ would increase i n i t i a l l y , reach a maximum corresponding to a certain c r i t i c a l radius of curvature of the neck, .p , and then decrease because of the outflow of atoms A caused by the gradient N^. The value of p c obtained from Expression (4.12) by equating AJ to zero is given by: 2(Dfl - Dn) y a (4.13) But, (4.14) 2(Dfl - D J Y Q N d In Y « (4.15) d In Yi A where 1 + d In N is the thermodynamic factor equal to 'A 160 Using appropriate values in Expression (4.15) and a value of 6 x 10~3 atom-fraction for (the lower limit at which i t can be detected by probe analysis), a value of 5 x 10"6 cm was obtained for p . Again therefore, any segregation which might occur in the cupronickel aggregates would be beyond the capabilities of microprobe analysis or optical metallography to detect. 4.2 Melting Behaviour of Cupronickel 4.2.1 The Partial Melting of Metals and Alloys When a metal or alloy begins to melt at a clean surface, i t is found that the liquid which is formed completely "wets" (covers) the surface of the sol id; i.e. YSV - ^ SL + \\l (contact angle 6 < 0) Thus melting is nucleated at a surface without the need for any superheating above the equilibrium solidus temperature. Indeed, i f > Y<^ + \y» a condition which might prevail locally at a curved solid surface of small radius, melting can be nucleated below the equilibrium solidus. What happens at a grain boundary i s less obvious, and is not as wel1-documented experimentally. In metals and in some alloys, the relation YSL - \ G^B i s s a t l s f i e c l a t n i q n angle grain boundaries, in which case the replacement of a solid boundary by two solid-liquid interfaces is 161 thermodynamically favourable. For Y s l = ^ "Ygg, melting can be nucleated at the boundary without superheat. Again, in principle, i t is also possible for Y S L < ^  Y G B , in which case "grain boundary melting;" i.e. selective melting [95] at high angle grain boundaries in a polycrystal below the equilibrium solidus, will result. Direct experimental evidence for grain boundary melting is somewhat ambiguous. Theoretical predictions have been made by Li [96] for the lowering of the melting point at grain boundaries, but there are insufficient thermodynamic and physical data available to make the predictions quantitative. In experiments with a series of aluminiurn-tin alloys, which were heated above their equilibrium solidus temperatures, Smith [97,98] obtained the dihedral angle data shown in Figure 4.10. Dihedral angles were measured directly from photomicrographs of the alloys after they had been s o l i d i f i e d . It is noted that a value of <J> = 0 was observed at Al - 30 at % Sn. For alloys containing less t i n , t)> > 0; i.e. grain boundary melting would not occur without superheat. For alloys of < 30 at % Sn, extrapolation of Figure 4.11 suggests values of Y S L < j Y R R , and the corresponding possibility 0.56 >: 0.54 I 0 . 5 2 a S 0.50 $ | 0.48 S 1 0.46 0 20 40 60 80 100 Atomic Percentage Al Dissolved tn Liquid Figure 4.10. Relative interfacial energy as a function of composition in the Al-Sn system (Ikeuye et al. [98]). 162 of grain boundary melting. Direct evidence of such behaviour was not obtained from the original experiments. Probably the best experimental indication that grain boundary melting may occur at high angle boundaries was the study of the high temperature fracture behaviour of bicrystals by Weinberg and Teghtsoonian [99]. For a pure metal, not only is melting nucleated at surfaces and grain boundaries without superheat, but melting proceeds to completion without superheat. For a solid solution alloy, melting is initiated at the equilibrium solidus or slightly below, at surfaces and (only i f < l>- Ygg) at grain boundaries. But for melting to continue, the temperature must be increased. Moreover, i f the equilibrium amounts and compositions of phases are to be attained as the temperature is increased, diffusion must occur in both the solid and the liquid. At rapid rates of heating, i t is therefore possible to obtain substantial superheating of a solid solution. This may permit melting to be nucleated at internal locations, either homogeneously or (with less super-heat) at "defects" of many possible types. It can thus be explained why intracrystalline "pools" of liquid can form when a solid solution alloy i s heated above its solidus. The frequency and spacing of such pools would be expected to depend on a) d i f f u s i o n r a t e s i n t h e s o l i d and l i q u i d phase, b) r a t e of h e a t i n g and h i g h e s t t e m p e r a t u r e a t t a i n e d , and c) e f f e c t i v e n e s s and d e n s i t y o f p r e - e x i s t i n g d e f e c t s which might be a c t i v e as n u c l e i f o r m e l t i n g . For most alloy systems, i t can be expected that the liquid which forms above the solidus will occupy substantially more volume than the 163 solid from which i t forms. At surfaces and at grain boundaries when cj> = 0, this expansion meets l i t t l e or no resistance. However, the formation of intragranular pools or discontinuous grain-boundary liquid (<j> > 0) must be accommodated (in the absence of internal holes) by flow of the solid. 4.2.2 The Partial Melting of Cast Cupronickel : When cast cupronickel was heated to 1273°C and held, both intra-granular and grain-boundary melting occurred (Figures 3.55 to 3.57). The majority of the liquid formed as intragranular pools. Although the grain boundaries did not appear to be uniformly and completely penetrated with liquid, the microstructures were consistent with a zero dihedral angle. If <j> were > 0, only grain edges would have been extensively wetted, and few such edges are seen in a metallographic section. The fact that so much liquid formed intragranularly in the presence of wetting grain boundaries reflects the large diffusion distance between grain-boundaries (i.e. very large grain size). In specimens heated for relatively short times at 1273°C, a "pool-free zone" was observed adjacent to the grain boundaries. This is evident in Figure 3.55. This zone can only be satisfactorily explained i f grain boundary melting preceded intra-granular melting. Had melting been simultaneous at both types of site, then the mean planar spacing of nearest neighbour pools should be comparable to the average distance between the grain boundary liquid film and the nearest pools. As noted in the next section, there was other evidence that in sintered specimens grain-boundary liquid formed before intraparticle melting occurred. 164 It seems probable that each of the pools of liquid was nucleated heterogeneously at an intragranular defect. Metallography revealed that the cast alloy specimens contained appreciable interdendritic shrinkage porosity (Figure 3.54) which was not unexpected in the light of the casting practice. Moreover, microsegregation was present in the alloy specimens. Even after homogenisation, composition gradients of as much as ± 1 % Ni were present. The average spacing of secondary dendrites, which was indicated in probe surveys (Figure 2.4), was 33 microns. This is in close agreement with the planar spacing of nearest-neighbour pools in the specimen heated to 1273°C for zero minutes. The observations are consistent with the following: a) i n t r a g r a n u l a r m e l t i n g was n u c l e a t e d a t s h r i n k a g e p o r e s , a d j a c e n t t o c o p p e r - r i c h i n t e r d e n d r i t i c r e g i o n s , b) the s m a l l p o o l s formed i n i t i a l l y by m e l t i n g between se c o n d a r y d e n d r i t i c arms grew as more l i q u i d formed, and t h e n e v e n t u a I Iy u n i t e d t o form l a r g e r and more i r r e g u l a r - s h a p e d p o o l s between p r i m a r y d e n d r i t e arms, c ) once e q u i l i b r i u m was e s t a b l i s h e d , p o o l s no l o n g e r grew but tended t o s p h e r o i d i s e t o reduce t h e i r s u r f a c e area-to-voIume r a t i o , and d) the i n t e r d e n d r i t i c s h r i n k a g e p o r e s , p r o v i d e d space t o accommodate n e t e x p a n s i o n a s s o c i a t e d w i t h t h e m e l t i n g p r o c e s s , as w e l l as p r o v i d i n g s o l i d - v a p o u r i n t e r f a c e s a t which m e l t i n g c o u l d be n u c l e a t e d . 4.2.3 The Partial Melting of Sintered Cupronickel In several respects the melting behaviour of sintered cupronickel powder.was markedly different from that of the cast alloy. Moreover, in the case of powder specimens, rapid and important microstructural changes 165 followed the introduction of liquid into the system, and these changes made i t d i f f i c u l t to describe the process of melting i t s e l f . As in the case of the cast alloy, melting started f i r s t at grain-boundaries (interparticle mecks). Evidence for this was of two types: a) t h e m i c r o s t r u c t u r e s i n t h o s e r e g i o n s o f d i l a t o m e t e r specimens ( e . g . LVDT 54, 49, 59) which had s p e n t v e r y s h o r t t i m e s above t h e s o l i d u s i n d i c a t e d t h a t o n l y i n t e r g r a n u I a r l i q u i d had formed (see r e s u l t , S e c t i o n 3.4.4), and b) i n t r a g r a n u l a r p o o l s were found t o be c l u s t e r e d more d e n s e l y near t h e c e n t r e s o f g r a i n s ( p a r t i c l e s ) than near s u r f a c e s o r g r a i n b o u n d a r i e s , f o l l o w i n g t h e " p o o l - f r e e zone" argument, a p p l i e d t o c a s t c u p r o -n i c k e l i n S e c t i o n 4.2.2 above (see F i g u r e 3.32). Although .it would be expected that melting was nucleated actively at particle surfaces (voids), neither optical microscopy nor microprobe examination revealed that a film of liquid had been present at such surfaces (see results, Section 3.3.3). The liquid film may have been too thin to be resolved. Figure 4.11 shows how the thickness of a uniformly melted layer varies with the volume fraction of a solid sphere of 68 urn diameter that has melted. If 5 per cent of the particle has melted at the surface, the liquid film will be only one micron thick. Moreover, capillary forces tend to hold liquid at an interparticle neck (Figure 3.32). Thus, i f only a small volume fraction of liquid is formed at particle surfaces, i t will tend to be drawn and held in the neck region, leaving an extremely thin layer on the surface remote from the neck. The dendrite spacing, and thus the spacing of shrinkage micropores and copper-rich concentration centres, is roughly 6 times smaller in the sintered powder than in the cast alloy. However, the mean planar spacing of liquid pools was about 3 times smaller in the sintered powder than in 166 Volume Fraction Liquid Figure 4.11. Thickness of the melted shell on a 68 micron spherical particle as a function of the volume fraction melted. 167 the cast cupronickel. This could be explained i f some of the pools coalesced since the interdendritic spacing of 5 um is comparable to the pool radius of 5 um. Following the description of intragranular melting in Section 4.2.2, i t is therefore not surprising that the size and spacing of the pools which formed above the solidus in the powder specimens were also about 3 times less than those of cast cupronickel (compare Figure 3.32.a and 3.55.b). Metallographic examination revealed that in the early stages of supersolidus sintering there was more liquid in intragranular pools than at intergranular sites. Further, the proportion of the liquid inside the grains decreased with time above the solidus. These observations are in contrast to those made for cast cupronickel, which the proportion of intra-granular liquid remained large and essentially constant with time beyond that necessary to achieve alloy equilibrium. The differences in behaviour can be explained as follows: a) Powder specimens had a v e r y l a r g e s p e c i f i c s u r f a c e a r e a a t which m e l t i n g would be a c t i v e l y n u c l e a t e d ( i n t e r n a l p o r e s , w i t h convex s o l i d s u r f a c e s ) . b) Powder specimens had a v e r y s m a l l g r a i n s i z e , and a l a r g e g r a i n boundary a r e a . c ) M e l t i n g was n u c l e a t e d f i r s t (and p r o b a b l y w i t h some u n d e r c o o l i n g ) a t g r a i n b o u n d a r i e s and f r e e s u r f a c e s . S i n c e m e l t i n g i s d i f f u s i o n c o n t r o l l e d i t f o l l o w s from a) and b) t h a t a l a r g e r volume f r a c t i o n o f t h e s o l i d i n a powder specimen c o u l d m e l t a t t h e s e l o c a -t i o n s b e f o r e i n t r a g r a n u l a r m e l t i n g s t a r t e d . d) A t necks i n t h e powder specimens above the s o l i d u s , the s o l i d would be s u b j e c t e d t o c o m p r e s s i v e s t r e s s by t h e l o c a l c o n c e n t r a t i o n of c a p i l l a r y f o r c e s (see K i n g e r y ' s model o f s o l u t i o n - p r e c i p i t a t i o n i n S e c t i o n 1.2). T h i s might tend t o i n c r e a s e l o c a l l y t h e r a t e o f m e l t i n g a t t h e i n t e r p a r t i c l e necks (and p o s s i b l y d e p r e s s t h e s o l i d u s ) . No comparable s i t u a t i o n would e x i s t in the c a s t a l l o y . 168 e) As a r e s u l t o f s o l u t i o n - p r e c i p i t a t i o n e f f e c t s i n the l a t e r s t a g e s o f s u p e r s o l i d u s s i n t e r i n g , d i s -c u s s e d in S e c t i o n 4.3.1, some o f th e g r a i n s i n t h e powder specimens were s e l e c t i v e l y d i s s o l v e d and r e -p r e c i p i t a t e d on o t h e r g r a i n s t o g i v e n e t g r a i n g r o w t h . When a g r a i n was d i s s o l v e d , i t s i n t r a g r a n u l a r l i q u i d was r e l e a s e d t o t h e i n t e r g r a n u I a r l i q u i d n etwork. Thus a d e c r e a s e i n t h e p r o p o r t i o n o f i n t r a g r a n u l a r l i q u i d would be e x p e c t e d t o accompany g r a i n g r o wth. No s i m i l a r p r o c e s s o c c u r r e d a t d e t e c t a b l e r a t e s i n c a s t c u p r o n i c k e l . T h i s i s n o t s u r p r i s i n g , i f o n l y because g r a i n growth would be much s l o w e r i n view o f t h e much l a r g e r i n i t i a l g r a i n s i z e ( s m a l l e r d r i v i n g f o r c e ) o f the c a s t a I Ioy. 4.2.4 Attainment of Solid-Liquid Equilibrium Rough estimates of the time required to reach equilibrium between solid and liquid at 1273°C in both cast and sintered cupronickel can be made using the model of "Diffusion out of a Finite Slab" (Jost [100]). The following assumptions are essential in the calculations: a) L i q u i d n u c l e a t e s a t r e s i d u a l c o p p e r c o n c e n t r a t i o n c e n t r e s ( i n t e r d e n d r i t i c s i t e s ) . b) The mean l i n e a r p l a n a r s p a c i n g between t h e pool edges a t " z e r o " t i m e i s i d e n t i f i a b l e w i t h the t h i c k n e s s , 2%, of t h e s l a b , and i s assumed n o t t o change d u r i n g i s o t h e r m a l h e a t t r e a t m e n t . c) The l i q u i d pool s i z e does not change w i t h t i m e . d) The r a t e - c o n t r o l l i n g s t e p i s d i f f u s i o n i n t h e s o l i d . e) Impingement e f f e c t s a r e n e g l i g i b l e . Interdendritic spacings were estimated from probe analyses (Figures 2.4 and 3.13). The mean planar spacing between pools was calculated using Edelson and Baldwin's [101] relationship 169 (2 d 2-* L = s 3f 0.5 (1 - f) (4. where l _ s = the centre to centre planar spacing f = the volume fraction of the second phase, i.e, 1iquid or pores where is the mean planar edge-to-edge spacing, and d^ is the mean planar diameter of the pools or pores. The values of dendrite spacing, pool spacing, pool diameter and edge-to-edge mean planar spacing of pools for both cast cupronickel and sintered cupronickel are given in Table 4.3. The model for diffusion out of a f i n i t e slab of thickness 21 is shown in Figure 4.12. The fixed composition at the solid/liquid interface is 47.5 wt. % Cu (equilibrium composition, at 1273°C, of the solid). Because the variance of probe analyses is ± 0.6%, equilibrium is assumed to be attained at 47.8 wt. % Cu. Figure 4.13 shows a theoretical plot [102], which is applicable to the present case, of % — = - £ A versus ^ for the car-L i - L o Jo -burisation of a sheet of steel of thickness 21 for various values of -p-; where C 0 is the uniform composition of the solid at t = 0 (50 wt. % Cu in the present case), Ci is the surface composition (interfacial equilibrium composition of the solid: 47.5% Cu), C i s any composition at time t, and xi is the distance given by -I < xx < I. In the present case C is assumed to be 47.8% Cu, at which time equilibrium is attained between solid and liquid. Dt C -C Thus an approximate value of p- = 1 for a-value of ^ — j - ^ - = 0.9 was used to calculate the time interval to reach equilibrium. 170 Table 4.3 Dendrite Spacings, Pool Diameter and Pool Spacings of Cast Cupronickel and Sintered Cupronickel Cast Cupronickel cm Sintered Cupronickel cm Dendrite spacing 3.3 x TO"3 5 x 10-" Homog. pore diameter 8.4 x 10"1* -Homog. pore spacing 4.7 x 10-3 -Vol. fraction porosity 0.02 -Vol. fraction 1iquid 0.13 0.244 Pool diameter, d P 1.9 x 10-3 1.1 x TO"3 Pool diameter, d' P 1.6 x 10- 3 0.9 x lO" 3 Pool spacing, L g (centre-to-centre) 3.7 x 10-3 1.4 x TO"3 Pool spacing, L„ (edge-to-edge) 2.1 x 10"3 5 x lO-1* Using a value of ~ 10~9 cm2/sec for D at 1273°C (obtained from extrapolation in Figure 4.6), and the edge-to-edge pool spacings (L^ = 2i) from Table 4.3, values of 18 min and one minute were calculated as times to reach equilibrium at 1273°C in the case of cast cupronickel and sintered cupronickel respectively. For powder specimens, this estimate is consistent with microprobe analys.es on dilatometer specimens (see Figures3.43 to 3.46, and Section 3.4.4). 171 igur e 4.13. Concentration distributions at various times in the sheet -I < xi < I with i n i t i a l uniform concentration C 0 and surface concentration C i . (Numbers on curves are values of Dt/£ 2). 172 Metallographic observations and estimates of liquid contents also indicated that equilibrium was established within one minute of the attainment of 1273°C at the centre of specimen LVDT 55 (Table 3.12). 4.3 Grain Growth During Supersolidus Sintering 4.3.1 Mechanisms Of Growth The coarsening of solid particles (grains) which are dispersed in a wetting liquid may occur in two ways: a) By t h e l i n e a r c o a l e s c e n c e o f groups o f p a r t i c l e s . b) By s e l e c t i v e d i s s o l u t i o n o f s m a l l e r p a r t i c l e s and growth (by r e p r e c i p i t a t i o n ) o f l a r g e r p a r t i c l e s . According to Ostwald [103] the solubility S at the surface of a particle of radius r is related to the solubility S 0 of the same material at a f l a t surface by c 2 Yci ^ In the present studies, the contribution of coalescence can be considered minor, because i ) l i t t l e o r no g r a i n growth o c c u r r e d a t h i g h tempera-t u r e s i n t h e s o l i d s t a t e ; e.g. 30 minutes a t I262°C ( F i g u r e 3.4). By c o n t r a s t , l a r g e g r a i n s were formed w i t h v e r y l i t t l e l i q u i d p r e s e n t ; e.g. 30 minutes a t I264°C ( F i g u r e 3.5). The f r e q u e n c y o f l i n e a r c o a l e s c e n c e s was n o t much d i f f e r e n t a t I262°C th a n a t I264°C, and i i ) new c o a l e s c e n c e e n c o u n t e r s were n e i t h e r o b s e r v e d nor ex p e c t e d t o c o n t i n u e t o o c c u r beyond t h e e a r l i e s t s t a g e o f s u p e r s o l i d u s s i n t e r i n g ( e . g . the f i r s t 0.6 173 m i n u t e s ) , y e t g r a i n growth was o b s e r v e d t o p r o g r e s s s t e a d i l y w i t h t i m e t o h i g h s i n t e r e d dens i t i e s . Growth of solid particles by solution and precipitation was the subject of an extensive and systematic study by Ostwald [103] in 1900, and has become known as "Ostwald Ripening." The literature of the phenomenon was reviewed by Fischmeister and Grimvall [104]. Two mass-transport models for growth have been analysed previously. In one model, diffusion of atoms between particles is assumed to be the slowest step in the process. The analyses of Wagner [105], Lifshitz and Slyozov [106] and Greenwood [107] a l l yield a prediction of diffusion-con-trolled growth of the form r $ 3 - r 0 3 = kit (4.18) where r 0 and r $ are the i n i t i a l and final mean grain r a d i i , respectively. Slight differences in the analysis yield different values of kj, which according to Wagner [105] is given by 8 Y . ft2 D C 0 ki = 9 RT < 4-19) where Dv is the coefficient of diffusion of solute in the liquid. In the second model, the rate of growth is controlled by solution or deposition of atoms at the particle surfaces; i.e. by a "phase-boundary reaction." Wagner's analysis of this case yields r s 2 - r 0 2 = k 2t (4.20) 174 64 Y s l fi2 k r C 0 where k 2 = ~ — ^ and k r is a rate constant for the phase-boundary reaction involved. It is interesting to compare Equation (4..20) with the law derived by Burke [108] for solid state grain growth. Burke assumes that growth is driven by the curvature of the grain boundary, which is inversely propor-tional to the average grain size, i.e. d r s 1 -jjjr a — . or r s 2 - r 0 2 = k 3t (4 s Exner and Fischmeister [109] used a different assumption than Wagner to describe the original distribution of.particle sizes. For phase boundary reaction-controlled growth, they then predicted ( r s - r 0 ) 2 = kkt (4 Smith and Spencer [110] studied the growth of nickel grains in the presence of intergranular liquid in the Ni-S system, and their data followed the relation r 4 = k 5t ( i n i t i a l grain size was assumed to be negligibly small). This was attributed tentatively to a surface diffusion-controlled mechanism. Exner et al. [ I l l ] found that growth data for VC in liquid nickel and cobalt could be fit t e d with equal statis t i c a l significance to either of Equations (4.18) or (4.20). Comments about the d i f f i c u l t y of obtaining unique f i t s of growth data to one or other relationship were also made by Exner and Fischmeister [109] and by Warren [37]. Where ambiguity was present, attempts have sometimes been made to analyse results in terms of 175 grain size distribution after growth, and in terms of the apparent activa-tion energy of the growth process. The activation energy for diffusion in liquid metals is rarely reported to be above 20 Kcals per mole. However, the value derived by Warren [37] from his growth results with NbC - Co assuming diffusion con-trolled growth, was 95 Kcals per mole. Similarly, Lay [112] found a good graphical f i t with Equation (4.18) for his data from the U02 - A1 20 3 system, but the apparent activation energy was 93 Kcals per mole. Exner and Fischmeister [109], in studies of liquid phase sintering in WC-Co claimed that the growth results fi t t e d Equation (4.22), and were consistent with phase boundary reaction control. The apparent activation energy was reported to be 142 ± 25 K cals/mole, which was in good agree-ment with an estimate by Skolnick [113] for the activation energy of solu-tion of WC in Co. A d i f f i c u l t y with previous analyses of growth is that they do not consider quantitatively the effect of particle interactions when the particles are close together as is the case for small volume fractions of liquid. The kinetics of phase boundary reaction controlled growth should not depend on particle spacing, since a sharp concentration change is expected at the boundary. However, for the diffusion-controlled case, the liquid thickness could markedly affect growth by influencing the interactions between diffusion "fields" around the particles. No solution to this problem is available. 176 4.3.2 Growth Law for the Present Results Table 3.9 and Figure 3.34 present data for the increase of grain size with time at 1273°C for specimens sintered in the superkanthal furnace. Taking do to be74ym, the mean grain diameter of the zero-time specimen, plots have been made of (d - d 0 ) 2 , d 2 - d 0 2 , d 3 - d 0 3 , and d.1* - d0k versus time, and appear as Figures 4.14 to 4.17. The most accurate grain size measurements are on specimens sintered for the longest times, for which corrections for liquid content are minor. Accordingly, lines have been drawn from the origin to the 60-minute points in Figures 4.14 to 4.17, to illustrate that the growth results are best fitted by the relationship in Figure 4.14; i.e. r s 2 - r 0 2 = kt . The results are thus consistent with a phase boundary reaction-controlled process of solution and precipitation. Using the grain growth data for four different sintering tempera-tures compiled in Tables 4.4 and 4.5, i t was possible to evaluate an apparent activation energy for growth. The data were plotted according to K = C exp - ^jr (4.23) an "apparent" rate constant r s n - r 0 n t * 3 and 2 are shown in Figure 4.18. where K = Plots for n = 177 T i m e , m i n . Figure 4.14. Grain size data for 1273°C sintering runs plotted as (d s 2 - d02) versus time. 6 4 | — i r 1 1 1 1 1 r 0 1 0 2 0 3 0 4 0 5 0 6 0 T i m e , m i n . Figure 4.15. Grain size data for 1273°C sintering runs plotted as (d s 3 ~ d)3) versus time. 0 10 20 30 40 50 60 T i m e , m i n . Figure 4.16. Grain size data for 1273°C sintering runs plotted as (d - d 0 ) 2 versus time. T r—~r——i 1—-T 1 " i r T i m e , m i n . Figure 4.17. Grain size data for 1273°C sintering runs plotted as (d s 4 - do1*) versus time. Table 4.4 Grain Size Values for Supersolidus Sintered Specimens at Temperatures Other than 1273°C (From Quantitative Metallography) Spec. No. Total amount of 1iquid wt. % Average planar diameter, ym No. of pools n No. of grains N , , 2 n a P wt. % interparticle 1iquid Grain* size ym Real** Grain size ym pool dP grains dP N < Q18 6 6.5 94 109 30 1.7 4.3 115 113 Q57 32 11.7 87 158 30 9.5 22.5 106 97 Q56 42 13.2 92 222 30 15.0 27.0 113 102 * assuming solid and pore only ** assuming solid, pore and liquid 180 Table 4 . 5 Experimental Data Used In Arrhenius Plots of Figure 4 . 1 8 Spec. :NO. Sintering time min. Temp. °C 1 •T r K ) " 1 x .10* ds ym do ym r s 3 - r 0 3 t um3/sec. t ym2/sec. Q18 30 1268 6 . 4 8 9 113 71 75 1 . 0 7 Q35 30 1273 6 . 4 6 8 140 74 163 1 . 9 6 Q28 30 1273 6 . 4 6 8 139 74 158 1 . 9 2 Q31 5 1273 6 . 4 6 8 92 74 156 2 . 5 0 Q32 5 1273 6 . 4 6 8 83 74 69 1 . 1 8 Q57 5 1280 6 . 4 3 9 97 78 183 2 . 7 7 Q56 5 1285 6 . 4 1 9 102 82 212 3 . 0 7 When the data were plotted according to the assumption of diffusion-controlled growth (n = 3 ) , an apparent activation energy of ~ 270 Kcal per mole was indicated. This is an order of magnitude larger than the activation energy normally associated with diffusion in liquid metals. When surface reaction-control of the growth process was assumed, an apparent activation energy of 280 Kcal mole - 1 was obtained. Unfortunately, no other published data are available with which this result can be compared directly, and no specific phase-interface reaction can be suggested which could be expected to have the large activation energy indicated. The grain growth observed during the supersolidus sintering of cupronickel powder is thus consistent with a model in which material transport o C O n E =1 1000 10 I u to E =1 C M © I 100 10 6-41 T 1 r T 1 1 r 270 Kcal /moie 280 K cal / mole 644 6-47 T °K 6-50 X | 0 4 6-53 Figure 4.18. Arrhenius plots of grain growth data, log K versus reciprocal absolute temperature. Upper plot, Lower plot, K- <rs» - r, 3) t ' 1 r. 2) f 182 occurs from smaller to larger particles by solution and precipitation, with a phase-boundary reaction (possibly dissolution at the solid surfaces) as the rate-controlling step. 4.4 Shrinkage During Supersolidus Sintering Figure 4.19 shows the typical three-stage shrinkage-time behaviour of cupronickel powder specimens heated through the solidus and sintered at a supersolidus temperature. In Stage 1 about 18 per cent volumetric con-traction of a specimen occurred in only half a minute. During the f i r s t part of Stage 1, identified as la in Figure 4.19, the centre of the specimen was increasing to 1273°C; i.e. conditions were far from isothermal. During Stage lb there were substantial temperature gradients in the specimen, and the amount of liquid was steadily increasing in response to solid state diffusion. In Stage 2, specimens typically increased in density from ~ 70% to ~ 90% of solid in 10 minutes, the rate of shrinkage steadily decreasing during the interval. Stage 3 was characterised by slow contraction to f u l l density. Only those specimens which were sintered while suspended provided data which permitted Stage 3 to be defined. In dilatometer experiments, specimens deformed inhomogeneously (sagged) in the late stages of densification (see Section 3.4.1). T — i — i i i i 1 1 | 1 — T — i i i 1111 1 — r i i i i 111 1 — i — i I i i 11 T i m e , min. Figure 4.19. Log plot of linear shrinkage versus time data for 1273°C sintering experiments (time origin is start of contraction). Different "stages" of sintering revealed by slope changes. 00 CO 184 4.4.1 Possible Stage 1 Shrinkage Mechanisms It is suggested that one or more of four transport processes could operate to cause the rapid shrinkage observed in Stage 1. a) Rearrangement b) Accommodation o f i s o t r o p i c m e l t i n g c) Accommodation o f neck m e l t i n g d) S o l u t i o n - p r e c i p i t a t i o n a t c o n t a c t s a) Rearrangement On the assumption that viscous flow was the rate-controlling mechanism in rearrangement, Kingery used the relationship [27] f = k t 1 + y (4.24) Lo where y « 1 (see Section 1.2). Several investigators of liquid phase sintering claim to have found good agreement of their shrinkage-time data with Equation (4.24). Other reported results, however, reveal time exponents of up to 5 for the early stage of sintering (Eremenko [25]). Huppmann and Riegger [114] observed particle repacking in model experiments with planar arrays of copper-coated tungsten particles. Froschauer and Fulrath [115] also reported direct observations of rearrange-ment at the surface of a WC-Co specimen, while i t was being sintered, in a scanning electron microscope. Because there are constraints to particle motion in a three dimensional network which have no counterpart in two-dimensional arrays, these observations can be misleading. 185 In the particular case of supersolidus sintering, i t is here argued that rearrangement is of doubtful importance as a process of densifi-cation, for several reasons: i ) D i r e c t e v i d e n c e o f r e p a c k i n g i s n o t a v a i l a b l e ; i n f a c t , b r i d g e s between c l u s t e r s c l e a r l y do not b r e a k down i n Stage I ( s e e F i g u r e 4.20). i i ) There i s no o b v i o u s r e a s o n why t h e c a p i l l a r y f o r c e s i n a t h r e e - d i m e n s i o n a l s o l i d - l i q u i d network would a c t t o s l i d e s o l i d p a r t i c l e s o v e r one a n o t h e r and i n t o c l o s e r packed a r r a y s . In f a c t , i t seems more r e a s o n a b l e t h a t t h e f o r c e s would r e s i s t such m o t i o n . If unbalanced s t r e s s e s were p r e s e n t a t t h e l i q u i d necks between p a r t i c l e s , t h e y c o u l d e q u a l l y w e l l a c t t o produce movement i n t o a l e s s dense arrangement. A s i m i l a r a r g u -ment was used i n S e c t i o n 4.1.4 t o r u l e o u t a major c o n t r i b u t i o n from rearrangement p r o c e s s e s t o s o l i d s t a t e s i n t e r i n g s h r i n k a g e . i i i ) In t h e p r e s e n t e x p e r i m e n t s , t h e amount o f i n t e r -p a r t i c l e l i q u i d i n c r e a s e d s u b s t a n t i a l l y w i t h t i m e w i t h i n Stage I. T h i s would be e x p e c t e d t o produce a c o r r e s p o n d i n g i n c r e a s e i n t h e r a t e o f s h r i n k a g e by t h e rearrangement p r o c e s s ( d e c r e a s e i n v i s c o s i t y ) , which was not o b s e r v e d . The f i r s t two of the above arguments could also be used to question the role of rearrangement in a l l liquid phase sintering system. It is possible, however, that some particle sliding and repacking might result from the longer-range motion of liquid which can occur when one component of a two-component powder mixture is melted. b) Accommodation of Melting If i t is assumed, as in Figure 4.21, Model A, that (a) surface and grain boundary melting are coincident and isotropic, and (b) solid particles attempt to maintain contact in response to surface tension forces, then'linear shrinkage given by (b) Figure 4.20. Optical micrographs showing the formation of clusters in dilatometer specimens: (a) LVDT 49, (b) LVDT 55; x24. 187 AL , Lo " ' ' f 1/3 (4.25) will occur within a simple cubic array, where f is the volume fraction of alloy melted. Calculations of shrinkage for different amounts of melting are given in Table 4.6. However, in the early stage of melting, most surface liquid will be drawn into the capillaries at particle "contacts." Assumption (b) may not be valid; i.e. there may be a liquid film of fi n i t e thickness at contacts even with <J> = 0. No theoretical treatment of this question is available, and metallographic observations on short-run specimens are inconclusive. However i t is clear from Figure 3.50 that there were stable liquid films of substantial thickness at a l l solid-solid "contacts" in Stage 2. It is therefore not obvious that isotropic melting can produce shrinkage at a l l . Moreover, in view of the small amounts of interparticle liquid present during Stage 1 (Table 4.6), this process can at best account for only a fraction of the shrinkage observed. If there is preferential nucleation of melting at necks, shrinkage will be more positive. In Model B, Figure 4.21, the volume melted is seen to take the form of a spherical segment. Calculations of shrinkage for different amounts of melting and for 81 ym powder are given in Table 4.6. Two cases are treated; one - in which i t is assumed that the solid particles maintain contact, and one - in which a 2-micron thick stable film of liquid is assumed to exist at contacts. Even in the latter case, a relatively small amount of melting can account for a substantial amount of shrinkage. It should be noted that selective melting at necks produces contact-flattening, a phenomenon which was observed after very short times 188 Table 4.6 Shrinkage Produced by Melt-Accommodation Models A and B in Figure 4.21 (Simple cubic packing of solid spheres) Linear shrinkage, ^ Fraction of solid particles which has melted at surfaces and boundaries (f) Model B assuming t^ = 0 AL ~ „ Lo y t Model B assuming t^ = 2 ym 2a = 81 ym Model A assuming t f ' = 0 f = 1 - (1 - f ) 1 / 3 L0 0.0005 0.026 0.001 0.0002 0.001 0.036 0.011 0.0003 0.002 0.052 0.027 0.0007 0.005 0.082 0.057 0.0017 0.010 0.116 0.091 0.0033 0.015 0.141 0.116 0.0050 0.020 0.163 0.138 0.0067 0.030 0.200 0.175 0.0101 0.040 0.231 0.206 0.0135 0.050 0.258 0.233 0.0170 0.060 0.283 0.258 0.0204 0.070 0.306 0.281 0.0239 0.100 0.0345 0.150 0.0527 0.20 0.0717 0.30 0.112 0.40 0.157 0.50 0.206 189 N * 2 a H Accommodation models. Local melting at neck (grain boundary) 0 = <t> = 0 (particle = grain) Isotropic melting at surfaces and neck 8 = <j> = 0 190 above the solidus temperature, and with very small volume fractions of liquid (Figures 4.22). c) Solution-Pveoipitation of Contacts Kingery [27] has suggested that at the contacts between wetted particles as in Figure 4.22 there is a localised stress induced in the solid by capillary forces. This increases the activity, a, of the solid locally according to 1 n A - APR _ 2 k YLV " 1 n a 0 ~ RT - r p RT ( 4- 2 6> where ft is the molecular volume k is a constant relating the maximum contact area pressure to the overall hydrostatic pressure r p is the radius of the pores The increase in activity acts as a driving force for material transport, involving solution of the solid at the contacts, and reprecipitation at less-stressed locations. As shown in Figure 4.22, the operation of this process leads to a flattening of the contacts and an approach of particle centres. If the solution of solid occurs as spherical segments, then the resulting shrinkage is related to the volume fraction of solid transported in the same way that shrinkage is related to the volume fraction of solid melted at necks in the accommodation process, Model B (Figure 4.21). Many previous investigators of liquid phase sintering have accepted that the particle-flattening mechanism accounts for much observed shrinkage. 191 Figure 4.22. Contact flattening and shrinkage by solution-precipitation. (a) Contact after melting and accommodation only. A) Region of high chemical potential where solution is favoured. B) Low-activity surface where reprecipitation occurs. (b) Contact after extensive local solution and reprecipi-tation has occurred to cause contact flattening and shrinkage. 192 However i t was argued by Kingery [27], and has not since been disputed in the literature, that this type of shrinkage occurs only after a rearrange-ment stage is essentially completed. This seems unreasonable, since high stresses at contacts are encountered when the solid-liquid-solid contacts are f i r s t established, and the contact areas are at a minimum. It is there-fore suggested that important shrinkage from this source takes place within Stage 1 and continues into Stage 2. 4.4.2 Role of Coalescence and Bridging More coalescences were observed to have occurred above the solidus temperature than below (Section 3.3.3). Therefore i t is possible that the presence of liquid facilitated coalescence by allowing particles to rotate (at "contacts") into more favourable orientations relative to one another. Coalescences could then be the purely statistical consequence of random rotations of dispersed particles. After coalescence, however, any particle in a coalesced pair or group is not free to rotate. The above process can therefore not lead to the formation of a continuous network of particles. However, i t is possible to visualise the creation of coalesced chains or groupings, the extent of which would be d i f f i c u l t to detect metallographically. The act of coalescence between two particles produces some shrinkage since a liquid film is eliminated. Subsequent growth of the solid neck between the particles is not li k e l y to be able to produce shrinkage at a rate which is any higher than would have prevailed without the coalescence. The higher the frequency of Coalesced contacts, the fewer are the contacts at which shrinkage by accommodation and solution-precipitation must occur to account for any observed bulk contraction. 193 Coalesced groupings of particles would severely restrict re-arrangement, further reducing the likelihood that rearrangement contributes to supersolidus sintering shrinkage. Powder specimens consist of more or less dense clusters. Within clusters, particles group to form stable "bridges" which enclose large pores. The clusters themselves are also bridged. Two-dimensional repre-sentations of these effects are shown in Figures 4.23 and 4.24, in which the large pores A and C are the result of bridging. Three-dimensional equivalents of these groupings can be visualised. It has been argued earlier that packing in the aggregate is not the result of rearrangement processes; rather i t represents the arrangement which loose particles assumed when they were tapped into a crucible. An original tap density of 50 per cent of solid represents the average of more and less dense groupings. Close-packed groupings of particles can, with the aid of l i t t l e interparticle liquid, be f u l l y densified by the operation of the melt accommodation process, Model B (Figure 4.21), or the stress-induced solution-precipitation process. If 10 per cent of the solid melted preferentially at necks in a simple cubic array of spherical particles, complete densifi-cation of the aggregate (~ 20% linear shrinkage) could be accomplished by melt accommodation alone. For the same array with a very small volume fraction of liquid present at capillaries densification could be achieved by the transfer of 10 per cent of the mass of the particles by solution at contacts and reprecipitation nearby. Even smaller amounts of mass transport are required to fu l l y density the closer-packed arrays of particles that occur (and are seen) in some clusters. Pores within clusters (B) and Figure 4.24. at bridges (A). Contribution of grain growth to closure of large pores. Grain 1 smaller than 2 or 3. Grain 1 dissolves and re-precipitates on 2 and 3. Grains 2 and 3 approach. 195 However, bridges between particles and clusters cannot be elimi-nated without the transport of comparatively large amounts of material. Figure 4.25 illustrates in two dimensions the shrinkage of an array of bridged particles which could result due to either of the mechanisms just discussed above. Even when substantial particle approach has occurred, a large void remains. To close this type of void requires either a large amount of liquid to be provided, or a more extensive operation of solution-precipitation effects than was visualised in Stage 1. It must be realised that as the contact areas between the particles in a bridge grow, the forces at the contacts decrease; i.e. the driving force for selective solution precipitation decreases. Stage 1 is seen as a period during which the closest-packed groupings within the original aggregate become fu l l y densified. Once these centres are f i l l e d with liquid, the shrinkage of less-dense groupings and of bridged arrays is necessary to produce macroscopic contraction. Stage 2 involves a steadily declining rate of contraction, during.which progressively larger voids become successively eliminated by mass transport. This is consistent with metallographic observations (Figure 3.50). 4.4.3 Possible Shrinkage Mechanisms in Stages 2 and 3 a) Solut-lon-pveo'Lp'Ltat'ion of contaots There was strong metallographic evidence of continuing contact-flattening (particle shape change) in Stage 2 culminating in the development of obvious polyhedral shapes (see Figure 3.50). 196 Figure 4.25. Shrinkage of bridged array of particles. Dashed lines: Particle positions after solid-state sintering (assume high angle boundaries at a l l necks). Solid lines: Particle positions after supersolidus sintering. Equivalent to ~ 5% by volume of solid transported either by melting at necks alone (accommodation model B) or by solution-precipitation at contacts. 197 b) Particle (Grain) Growth During Stage 2, the average diameter of grains increased by approximately 30% (Tables 3.9 and 3.11) corresponding to more than a doubling of the volume of each particle. Considerable further grain growth occurred in Stage 3. Kingery [27] has argued that particle growth, without shape change at contacts, does not produce contraction in liquid phase sintering. How-ever, i t is believed that there are two ways in which particle growth can independently contribute to densification, the f i r s t of which is unique to supersolidus sintering, but the second of which should apply equally well to liquid phase sintering. i) Release of intraparticle liquid and its subsequent accommoda-tion within capillaries. Experiments with cast cupronickel revealed that intraparticle liquid was stable; i.e. there was no apparent transfer of liquid to or from grain boundaries with increasing time at 1273°C. However, in sintered specimens there was a marked decrease in the number of intra-particle pools with.time at 1273°C. As shown in the sequence of Figures 3.32 and 3.33, pools became concentrated at the centres of particles during Stages 2 and 3. This is clearly what will result from the dissolution of some particles and growth of others. Liquid pools from those particles which dissolved would be released and accommodated in capillaries. The solid which reprecipitated on to larger particles would be free of liquid pools. Thus, the average volume per particle doubles i f slightly more than half the particles dissolve, and the amount of intragranular liquid per particle is reduced by approximately 50 per cent. The metallographic data 198 of Table 3.9, within the limits of experimental accuracy, are reasonably consistent with this explanation. i i ) Breakdown of bridged particle arrays. Figure 4.24 i l l u -strates how the selective dissolution of one particle within a bridged array can allow neighbouring particles in the array to approach. The repetitive operation of this process w i l l , in effect, allow a rearrangement of particles into close packed arrays where bridges once existed. Thus grain growth may contribute significantly in those stages of sintering in which the closing of large pores is necessary to produce appreciable densification. 4.4.4 Transition from Stage 2 to Stage 3 At the start of Stage 3 specimens were found to contain pores which were: a) r e l a t i v e l y l a r g e and few i n number ( F i g u r e 3.7 i n P a r t B). b) e q u i a x e d i n shape (compare F i g u r e s 3.6 and 3.7 i n P a r t B) c) n e a r l y a l l c l o s e d ( S e c t i o n 3.1 and F i g u r e s 3.7 t o 3.9 i n P a r t B) There is abundant metallographic evidence that the solution-precipitation process described in the previous section operated continu-ously through Stages 2 and 3. Thus material transport mechanisms are available in Stage 3 to close pores. However, when pores become isolated from the surface in late Stage 2, the sintering atmosphere is trapped inside them. Closure of the pores, and thus bulk shrinkage of the specimens, could become controlled by the rate of escape of gas by diffusion. Cech 199 [28,25] analysed this problem using Fick's law and assuming that the external gas pressure was small compared to that inside the pores. The gas con-centration gradient was given by jdC_ _ 2y 1 dxi " r 2 X i ( l - 2 r 2 n j ^ 4 > 2 7 ) where n = the number of pores in length x i , r 2 = the pore radius The quantity of gas diffusing from a sphere of radius x x is d p i = -D 4u x i 2 £ x - - ^ _ _ y d t ( 4 . 2 8 ) where D = the diffusion coefficient of gas If V0 is the original volume of gas in a pore, then d p i = | ^ d r 2 (4.29) Performing suitable transformations and integrating from r x to r 2 ( r x was calculated for the case of the closing of pores at the corresponding sintering time t 3 , while r 2 corresponds to time t ) , the following expression was obtained. t, - t = - ^- -11 (r 3 r M t 3 1 O r , 4TT Y ( R 2 " R I } (4.30) 200 where Ni = the number of pores per unit length. If sintering proceeds up to r 2 = 0, then from Equation (4.30) i t follows that f = A L 3 t - t 1/3 (4.31) where A is a constant. 4.4.5 Kinetics of Shrinkage Previous investigators of sintering have used the slopes of different "straight-line" portions of log-log plots such as Figure 4.19 to define kinetics and to deduce sintering mechanisms. This practice can lead to misleading conclusions, particularly i f mechanisms of shrinkage are overlapping in time, and i f i t is impossible to define the dimensional or time origin of each mechanism. Kingery's analysis of liquid-phase sintering data for Fe-Cu [33] and TiC-Ni-Mo [35] was specifically c r i t i c i s e d on these grounds by P r i l l et al. [36]. In the present experiments, Stage la was characterised by non-isothermal conditions, and i t is inappropriate to attempt to analyse the shrinkage-time data quantitatively. However, only about 0.02 linear shrinkage occurred in this stage, the duration of which was only -0.2 minutes. It is not l i k e l y that a large error is introduced, therefore, i f i t is assumed that the mechanisms responsible for shrinkage in later stages did not start within Stage l a . Accordingly, the data have been replotted in Figures 4.26 to 4.28 (upper curves and open symbols only) with the T 1—1 I I I | 1| 1 1—I I ! I I I | 1 1—I I I I I 11 / / / Q.QQ|| ^ • I I I /I I I 1 I 1 1 I I I I I I 1 1 1 1 I I I iJ 001 01 10 10 T i m e , min . , (t-t .^). Figure 4.26. Replots of linear shrinkage data from dilatometer runs: 29, 35, 62. Origin taken as end of stage la. Upper plots (open symbols) are experimental data. Plots through h a l f - f i l l e d symbols are solution-precipitation contribution to shrinkage based on assumptions in text. Plots through f i l l e d symbols are contributions to shrinkage from other than solution-precipita- ° tion processes. T I I I I I I I | 1 1—I I I I I I \ 1 1 I I I I I I j 001 4 01 10 s o T i m e , min ., (t-t_). Figure 4.27. Same as Figure 4.26, for dilatometer runs 30 and 34. r\3 o l\3 Figure 4.28. Same as Figure 4.26, for dilatometer runs 31 and 32. r o o CO 204 origin taken as the start of Stage lb; i.e. where the specimen centre f i r s t reached 1273°C. Slopes of the corrected plots are compiled in Table 4.7. From earlier arguments, the following assumptions can be made in analysing the corrected shrinkage-time data: a) S o i u t i o n - p r e c i p i t a t i o n p r o c e s s o f s h r i n k a g e proceeds t h r o u g h o u t a i l s t a g e s , b) s o l u t i o n - p r e c i p i t a t i o n p r o c e s s e s a r e phase-boundary r e a c t i o n c o n t r o l l e d , c o n s i s t e n t w i t h t h e a n a l y s i s o f g r a i n growth da t a ini 4.3.2, c) rearrangement and m e l t accommodation p r o c e s s e s a r e not p o s s i b l e beyond Stage i b , . d) c l o s e d pores become p r e v a l e n t o n l y a t t h e end o f Stage 2 ( c o n s i s t e n t w i t h p o r o s i m e t r y r e s u l t s i n P a r t B, F i g u r e 3.1), and e) d i f f u s i o n o f gas from c l o s e d pores c o n t r o l s t h e r a t e o f s h r i n k a g e i n Stage 3. Thus the total shrinkage observed in Stages lb and 2 is the sum of two contributions as shown schematically in Figure 4.29. Solution-precipitation gives shrinkage according to curve J and AL LT 1 t - t. 1/2 (4.32) Curve f i t t i n g within Stage 2 allows B to be evaluated, with the results in Table 4.8 for the present experiments. A typical example of such f i t t i n g , for LVDT 35, is shown in Figure 4.30. Curve K in Figure 4.29 represents the sum of other contributions to shrinkage, and can be found by difference. If only solution-precipita-tion processes operate in Stage 2, then j^- in curve K becomes constant LT 205 Table 4.7 Slopes Obtained by the Linear Regression Method for Different Stages of Sintering at 1273°C, Using the Log-Log Plots of Corrected Data in Figures 4.26 to 4.28 Spec. No. Particle size ym Slope Stage lb Slope Stage 2 Slope Stage 3 LVDT (all)' Short Runs - 81 - 0.36 -LVDT 29 81 0.89 0.30 -LVDT 35 81 0.78 0.40 -LVDT 62 81 0.86 0.34 -Q (all) S.K. Runs 68 - 0.54 0.25 LVDT 30 68 0.90 0.36 -LVDT 34 68 0.96 0.42 -LVDT 32 49 0.96 0.43 -LVDT 31 49 0.97 0.41 -F i g u r e 4 . 2 9 . S c h e m a t i c p l o t showing c o n t r i b u t i o n o f components J (due t o s o l u t i o n - p r e c i p i t a t i o n p r o c e s s e s ) and K (due t o o t h e r mass t r a n s p o r t mechan i sms) t o t o t a l l i n e a r s h r i n k a g e o b s e r v e d i n s u p e r s o l i d u s s i n t e r i n g a f t e r s t a g e l a . ro O CD 0 1 2 3 ( t - t T ) 0 ; 9 , m i n . 0 5 Figure 4.30. Experimental data from stage 2 of LVDT run 35 plotted as linear shrinkage versus square root of time, corrected to make origin coincide with end of stage l a . r o o 208 (at a value A) at the end of Stage 1 as indicated. Stage 2 shrinkage is represented by f = A + B LT t - t T 1/2 (4.33) A can also be found by extrapolation of plots of vs (t - t T ) ^ T 1 to t = ty (Figure 4.30). These values of A from the present experiments are compiled in Table 4.8. Expression (4.33) could also be used for Stage lb. In Stage lb A values vary with time as shown in Figure 4.29 (Curve K). The log-log equivalents of curves J and K for the experimental data are superimposed on Figure 4.26 to 4.28 ( f i l l e d and h a l f - f i l l e d symbols) The results are consistent with the assumptions (a) to (d) above. The considerable scatter in values of A probably reflects gradients in tempera-ture and liquid content, plus anisotropy of shrinkage in Stage lb, see Section 3.4.2. An attempt was also made to f i t corrected Stage 2 data to a 1/3 (t - tj) ' relationship; i.e. on the assumption of diffusion-controlled solution-precipitation. Fits as good as Figure 4.30 (LVDT 35) could not be obtained. Moreover, the extrapolation of a l l such plots to t = tj. yielded negative values of A. This result was considered to be excellent further validation of assumption (b) above and of the conclusions regarding grain growth in Section 4.3. Following assumptions (d) and (e) a log-log plot of corrected Stage 3 data has been made (Figure 4.31). The results are described by f - K L 3 ^0.25 t - t (4.34) 209 Table 4.8 Experimental Values of A and B in the Assumed Relation f k = A + B(t - t T ) 0 ' 5 T 1 Spec. No. B, min - 0" 5 A LVDT 29 0.022 0 .023 LVDT 35 0.024 0 .003 LVDT 62 0.023 0 017 LVDT 30 0.024 0 015 LVDT 34 0.029 0 007 LVDT 31 0.031 0 008 LVDT 32 0.036 0. 004 This time-dependence of shrinkage is in reasonable agreement with that predicted by Cech [28,25] and discussed in Section 4.4.4. No other rate-controlling process can be suggested which is consistent with the observed kinetics. Unfortunately, there is a lack of gas diffusion data from which a more quantitative check on the Cech model might be attempted. 4.4.6 Summary The above results and discussion indicate that dimensional changes during supersolidus sintering are dominated by three processes: a) M e l t i n g and m e l t accommodation: A l l o w p a r t i c l e c e n t r e s t o approach w i t h o u t any change i n p a c k i n g mode ( i . e . r earrangement u n n e c e s s a r y ) . A c c o u n t f o r r a p i d l i n e a r 0 1 A L O O I ~~l 1—I I I I I 11 Supersolidus Sintering (68 ftm., 1273 °C) J I 1 » • 1 1 1 ( t - t_ ) , m i n . 1 I I I I I 3 J ' 1 I I 1 0 0 Figure 4.31. Log plot of stage 3 shrinkage data corrected to make origin coincide with slope change between stages 2 and 3. r o o 211 s h r i n k a g e o f between 0.02 and 0.04 d u r i n g Stage I o f t h e p r e s e n t e x p e r i m e n t s . Not o p e r a t i v e beyond Stage I. b) S o l u t i o n - p r e c i p i t a t i o n : S t a r t s i n Stage I , and o v e r l a p s m e l t accommodation as a p r o c e s s of s h r i n k a g e . C o n t i n u e s t h r o u g h o u t s u p e r s o l i d u s s i n t e r i n g t o f u l l d e n s i t y . A c c o u n t s f o r 0.12 t o 0.14 l i n e a r s h r i n k a g e . Dominates Stage 2. c) Gas escape from c l o s e d p o r e s : L i m i t s r a t e o f s h r i n k a g e due t o s o l u t i o n - p r e c i p i t a t i o n when pores become c l o s e d (Stage 3 ) . It is believed that melting is nucleated f i r s t at grain boundaries (necks). The formation of very l i t t l e liquid preferentially at necks allows substantial shrinkage to occur by melt accommodation. However, melting quickly becomes more isotropic; the shrinkage available from accommodation of liquid formed at a l l surfaces is more limited. Solution-precipitation causes shrinkage both by contact-flattening and by grain growth, the former being an important contribution to both Stage 1 and Stage 2 shrinkage. Grain growth is believed to be important in Stages 2 and 3, where it s principal effect on shrinkage derives from the release of intragranular liquid. It is believed that both solution-precipi-tation mechanisms are phase-boundary reaction controlled. 4.5 Comparisons of Supersolidus and Liquid-Phase Sintering Supersolidus sintering has been described as a special case of liquid phase sintering. However, the present work has shown that there are major differences between the two processes, and a comparison is of interest. Not all liquid-phase sintering systems behave identically. How-ever, iron-copper has been selected for the present comparison, because 212 i) i t is of appreciable practical interest, i i ) i t has been the subject of extensive previous study, and i i i ) i t is believed to be typical of several of the more important systems. In the supersolidus sintering of cupronickel powder: a) no p a r t i c l e c o m p l e t e l y m e l t s , b) a l l p a r t i c l e s p a r t i a l l y m e l t , c) a l l s o l i d p a r t i c l e s a r e e x p e c t e d t o d e c r e a s e i n s i z e as a consequence o f p a r t i a l m e l t i n g , d) l i q u i d p r o b a b l y does n o t move o v e r d i s t a n c e s l a r g e r than a p a r t i c l e d i a m e t e r , e) e q u i l i b r i u m i s v e r y r a p i d l y e s t a b l i s h e d between s o l i d and l i q u i d phases; i . e . t he amount and c o m p o s i t i o n o f t h e phases do n o t undergo change beyond t h e f i r s t minute a t t h e s i n t e r i n g tempera-t u r e , and f ) t h e d i h e d r a l a n g l e i s z e r o a t a l l s t a g e s . By contrast, in the liquid-phase sintering of an Fe-Cu powder mixture: a) c o p p e r p a r t i c l e s c o m p l e t e l y m e l t ; c l u s t e r s o f co p p e r p a r t i c l e s a l s o m e l t , b) i r o n p a r t i c l e s do not m e l t a t a l l , c ) s o l i d p a r t i c l e s ( i r o n ) do n o t d e c r e a s e i n s i z e as a d i r e c t r e s u l t o f m e l t i n g (a s m a l l d e c r e a s e i n p a r t i c l e s i z e f o l l o w s soon a f t e r m e l t i n g due t o t h e d i s s o l u t i o n .of some i r o n i n t h e l i q u i d c o p p e r ) , d) i n response t o c a p i l l a r y f o r c e s , l i q u i d c o p p e r may move t h r o u g h t h e a g g r e g a t e o v e r d i s t a n c e s which a r e l a r g e compared t o a p a r t i c l e d i a m e t e r , e) e q u i l i b r i u m between s o l i d and l i q u i d phases i s slow t o be a c h i e v e d . Copper d i f f u s e s i n t o i r o n a t s i n t e r -ing t e m p e r a t u r e s , but f o r t y p i c a l powder p a r t i c l e s i z e s ( e . g . 100 ym d i a m e t e r ) hours may be r e q u i r e d t o reach e q u i l i b r i u m . D u r i n g t h i s p e r i o d t h e amounts o f t h e phases a r e c h a n g i n g , t h e c o m p o s i t i o n o f t h e s o l i d 213 i s c h a n g i n g , and t h e r e i s a c o n t i n u i n g f l u x o f copp e r a c r o s s s o l i d - l i q u i d i n t e r f a c e s , and f ) t h e d i h e d r a l a n g l e may be z e r o i n t h e e a r l y s t a g e s o f s i n t e r i n g D l 6 [ ] , but becomes g r e a t e r t h a n z e r o as e q u i l i b r i u m i s approached o r r e a c h e d . As a result of these differences, the mechanisms responsible for dimensional change in the two processes also dif f e r appreciably throughout the sintering period: a) Rearrangement can c o n t r i b u t e t o e a r l y d e n s i f i c a t i o n i n Fe-Cu, s i n c e s o l i d p a r t i c l e s can be swept i n t o c l o s e r - p a c k e d p o s i t i o n s by t h e l o n g - r a n g e movement o f t h e l i q u i d . T h i s mechanism i s u n l i k e l y t o be o p e r a t i v e a t a l l i n s u p e r s o l i d u s s i n t e r i n g . b) S i n c e a l l p a r t i c l e s d e c r e a s e i n s i z e when m e l t i n g o c c u r s i n s u p e r s o l i d u s s i n t e r i n g , t h e accommodation of l i q u i d between p a r t i c l e s a l l o w s p a r t i c l e c e n t r e s t o a p p r o a c h . There i s no e q u i v a l e n t s h r i n k a g e i n l i q u i d - p h a s e s i n t e r i n g . c) S o l u t i o n - p r e c i p i t a t i o n p r o c e s s e s can o p e r a t e e a r l y and e f f e c t i v e l y t o produce c o n t a c t - f l a t t e n i n g and r a p i d s h r i n k a g e i n t h e c a s e o f s u p e r s o l i d u s s i n t e r -i n g . However, t h e f l u x o f co p p e r a c r o s s s o l id-1 i q u i d i n t e r f a c e s i n t e r f e r e s w i t h s o l u t i o n - p r e c i p i t a t i o n in th e Fe-Cu system d u r i n g t h e e a r l y s t a g e s o f s i n t e r i n g . Moreover, when e q u i l i b r i u m i s approached i n Fe-Cu, s o l u t i o n - p r e c i p i t a t i o n p r o c e s s e s c a n n o t c o n t r i b u t e t o d i m e n s i o n a l change because the d i h e d r a l a n g l e becomes g r e a t e r than z e r o and the system a g g l o m e r a t e s . d) A major s o u r c e o f s h r i n k a g e i n the s i n t e r i n g o f Fe-Cu can be th e approach o f p a r t i c l e c e n t r e s which accompanies a g g l o m e r a t i o n when t h e d i h e d r a l a n g l e becomes g r e a t e r than z e r o D l 6 ] . No e q u i v a l e n t mechansims i s i n v o l v e d i n s u p e r s o l i d u s s i n t e r i n g o f c u p r o n i c k e l . It is probably during only the final stage of sintering that similar mechanisms control the density changes in the two processes; i.e. the escape of gas from closed pores may become the rate controlling process. 214 However, the dominant mass-transport mechanism during the final stage will be solid-state diffusion in the case of Fe-Cu and solution-precipitation in the case of cupronickel. Chapter 5 CONCLUSIONS Solid State Sintering of Loose Cupronickel Powder 1) The i n i t i a l stage of shrinkage (up to 1 hour at 1200°C) is dominated by Nabarro-Herring creep. This conclusion is consistent with observations of sintering kinetics, and with calculations of the stresses at necks due to surface tensions. 2) In contrast to the observations of Kuczynski [24] with several other copper and silver alloys, no detectable segregation of solute at necks occurs during the solid state sintering of cupronickel. 3) Clusters, or centres of densification, do not form during sintering due to relative particle motions, as concluded by previous inves-tigators from observations of surfaces and two-dimensional arrays. Rather, al l such clusters in three-dimensional aggregates have their origin in the i n i t i a l packing of the loose powder particles. 215 216 Melting Behaviour of Sintered Cupronickel Powder when Heated Above  the Solidus 4) Melting is nucleated at necks (high angle grain boundaries) and at particle surfaces; at less than the equilibrium solidus temperature. Subsequent melting occurs intragranularly at interdendritic sites of above-average copper concentration. 5) The dihedral angle in solid-liquid cupronickel is < zero. 6) Constitutional equilibrium is attained within one minute after reaching the supersolidus temperature (for 68 ym powder). Grain Growth During Supersolidus Sintering 7) The growth of solid cupronickel grains during supersolidus sintering proceeds according to the relation r s 2 - r 0 2 = kt. This is consistent with the predictions of an Ostwald Ripening model in which growth is assumed to be due to solution-precipitation with phase boundary reaction control. Shrinkage in Supersolidus Sintering 8) A period of very rapid shrinkage (Stage 1) occurs while a specimen is being heated above the solidus temperature to the final sintering 217 temperature, and prior to the attainment of constitutional equilibrium. This period is dominated i n i t i a l l y by a melting and melt-accommodation sequence of shrinkage, followed by contact-flattening due to localised solution-precipitation. 9) Beyond the attainment of constitutional equilibrium (Stages 2 and 3), a specimen continues to shrink to f u l l density. Solution-precipi-tation processes account for most or a l l of the contraction. Grain growth is important because i t is accompanied by the release of intragranular liquid. 10) When sintered specimens reach approximately 92-93% of solid density, a l l pores are closed. The rate of shrinkage beyond this density (in Stage 3) is controlled by the rate of escape of gas from the pores. 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Magee, B.E., M.A.Sc. Thesis, Department of Metallurgy, The University of British Columbia, 1975. P A R T B MECHANICAL PROPERTIES OF SINTERED CUPRONICKEL Chapter 1 INTRODUCTION 1.1 Review of Previous Work 1.1.1 Elastic Constants for Porous Materials The expressions compiled in Table 1.1 are among many proposed to describe the elastic properties of porous solids as a function of the volume fraction of porosity, P. Most of the relationships in the table are the result of modifications to analyses of the properties of two-phase com-posite materials, in which one phase has been replaced by pores. The analyses are based on the application of linear e l a s t i c i t y theory to different, models of the structure and elastic deformation of composites. Most of the solutions represented by Table 1.1 are "upper bounds." For an isotropic solid, the elastic constants are related by and v 0 = - - 1 (1 -23) 227 Table 1.1 Predictions of Elastic Constants for Porous Materials Author Nature of Expression 1 ; — Proposed Relationship Equation Number Reference Dewey E = E 0 [1 - E 0 ( 9 p i + 4E 0)" 1P] 1.1 1 v = voD - 3E 0 ( 9p i + 4Eo)~ 1P] 1.2 MacKenzie K-1 = L V d - P ) ] " 1 + S P ^ G o d - P ) - 1 + terms of order P 3 1.3 0 G = G 0 [ T - 5P(3K0 + 4 G 0 ) ( 9 K o + S G o ) " 1 + terms of order P 2] 1.4 c MacKenzie I* K"1 = [K-1 (1-P)]" 1 + S P ^ G o d - P ) ] " 1 1.5 0 G = G 0 [ l - 5P(3K0 + 4 G o ) ( 9 K 0 + 8 G 0 ) _ 1 ] 1.6 c MacKenzie K-1 = L V d - P ) ] " 1 + S P ^ G o d - P ) ] " 1 1 .7 II** Analytical G = G 0 [ l - 5P(3K0 + 4Go)(9K 0 + 8 G 0 ) _ 1 - 0.883P2 1.8 2 Kerner "i Hashin Stroppe G = G 0 ( 7 -5v 0)(l-P) [(7 - 5v 0) + (8 - l O v o ^ ] "1 1.9 o 4. 5 Hashin and Shtrikman K = 4 Go Ko (1-P) [4 G P + 3 K0 P]" 1 1.10 6 Gatto E = E 0 ( l - 2.36P) 1.11 7 Weil G = G 0 [ l - 15(1 - vo ) P(7 - 5 V 0 ) " 1 ] 1.12 8 Hashin K = K 0[l - 3(1 - vo) P(2 - 4 v 0 ) _ 1 ] 1.13 9 Skorokhod K = Ko(l-P) [3K0P(4g G 0 ) _ 1 + l ] " 1 1.14 5 G 0 ( 3 G + 2 G 0 ) - 1 e . + (7G + Go) G 0[2(3G + G o j G ] " 1 ^ = 1 c 1.15 10 CONTINUED Table 1.1 (Continued) Author Nature of Expression Proposed Relationship Equation Number Reference hasselman Semi-E = E0{1 + AP[1 - (A + DP]" 1} 1.16 11 Chung Empirical EE"1 = GG;1 = KK"1 = 1 - aP + bP 2 1.17 12 McAdam E = E 0 ( l - P ) 3 - 4 1.18 13 Spriggs Empirical E = E 0 exp(-bP), E = E 0 exp(-b bP b) exp(-b cP c) 1.19, 1.20 14 Hasselman Fryxell and Chandler E = E 0 ( l - bP). 1 — : : 1 1.21 15 16 obtained by dropping the terms of the order of P 2 and P 3 in MacKenzie equations. ** terms of the order of ?* is ignored and terms of the order of P 2 are taken as AP2 A was then evaluated to be -0.883 by setting G/G0 = 0 when P = 1. CONTINUED K 3 K3 Table 1.1 (Continued) where E, G, K, v = the Young's, rig i d i t y and bulk modulus and Poisson's ratio of porous material Eo, G0, K0, v 0 = the Young's, ri g i d i t y and bulk modulus and Poisson's ratio of bulk material Pi = the gas pressure in the pores P = the volume fraction porosity G 9 = Go" 9 S = volume fraction spherical material 0 C = volume fraction cylindrical material A, a, b = the material constants b^, b c = the constants depending on open and closed porosity P^, P c = volume fraction of open and closed porosity Co o 231 where E 0 = Young's modulus Go = Shear modulus K0 = Bulk modulus v 0 = Poisson's ratio Probably the most widely-tested predictions of elastic behaviour are those due to MacKenzie [2] and to Skorokhod [10]. In MacKenzie's model, a relatively small volume of isolated holes is assumed to be distributed through an homogeneous and isotropic solid. The application of MacKenzie's equations should probably be restricted to P < 0.1. Skorokhod depicts the solid part of the porous structure as a mixture of spherical and cylindrical "phases." If the origin of the solid structure is irregular, flake-shaped, or fibre-like particles, then for a given density there will be a higher proportion of the cylindrical phase present than i f the origin was equiaxed particles. Moreover, with increasing density the proportion of the spherical phase increases, regardless of the original shape of the particles. Using a statistical method, Skorokhod calculated the volume fractions of the two phases for different fractional porosity contents with the results shown in Table 1.2. He then applied ela s t i c i t y theory to predict how the bulk and shear moduli should vary with fractional porosity and "phase" distribution with the results shown in Equations (1.14) and (1.15) of Table 1.1. Cal-culated values of the relative shear modulus, G/G0, are also presented in Table 1.2.b. Hashin's analysis [9] reduces to the simple predictions E = E 0 ( l - k'P) (1-24) 232 Table 1.2 Quantities Used in Skorokhod's Model a) Relative Fractions of "Spherical" and "cylindircal" Phases in Porous Bodies Type of body P 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Powder 0s 0.90 0.80 0.69 0.58 0.45 0.32 0.21 0.14 0.085 e c 0 0 0.01 0.02 0.05 0.08 0.09 0.06 0.015 Fibre 9s- 0.67 0.48 0.34 0.23 0.15 0.09 0.05 0.02 0.005 6 c 0.23 0.32 0.36 0.37 0.35 0.31 0.25 0.18 0.095 b) Relative Shear Modul i of Porous Bodies of Various Densities Type of body P 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Powder G 0.83 0.67 0.50 0.35 0.24 0.17 0.11 0.05 0.01 Fibre Go 0.85 0.72 0.60 0.49 0.39 0.30 0.21 0.13 0.06 233 G = GQ(1 - k"P) ( 1 . 2 5 ) Rossi [ 1 7 ] adopted these relationships and identified k' and k" as "stress intensity factors." On the basis of experimental results he then assigned values to these factors for porosity of different degrees of orientation. Hasselman [ 1 1 ] proposed Relationship ( 1 . 1 6 ) in Table 1 . 1 as a result of his attempts to f i t experimental data to Equations ( 1 . 1 4 ) and ( 1 . 1 5 ) derived by Hashin. Chung [ 1 2 ] reported experiments which indicated that Young's modulus varied with the size and shape of pores. He used the form of MacKenzie's Equations ( 1 . 3 ) and ( 1 . 4 ) and proposed the semi-empirical rela-tionship in Equation ( 1 . 1 7 ) . Several purely empirical expressions have been proposed. That due to McAdam [ 1 3 ] in Equation ( 1 . 1 8 ) was based on published experimental data for a wide range of sintered porous alloy products. Spriggs 1 equations [ 1 4 ] , based on studies of the effect of porosity on the elastic modulus of poly-crystalline aluminum oxide [ 1 4 , 1 8 ] have been c r i t i c i s e d since they predict f i n i t e values of E when P = 1 . The other empirical equations are essentially of the form E = E 0 [ l - k'P] i.e. consistent qualitatively with the predictions of one of Hashin's analysis [9]. ! 234 1.1.2 Strength of Porous Materials Porous materials on which attempts have been made to correlate mechanical propoerties with pore content are characteristically b r i t t l e . Accordingly most theoretical and experimental work has been concerned with ultimate tensile strength rather than with any yield or flow property. Theoretical predictions of the tensile strength of porous bodies have been attempted by Eudier [19], Haynes [20,21] and Gallina and Mannone [22] with the results shown in Table 1.3. Eudier [19] treated a sintered body as a solid containing spherical holes. Tensile strength was calculated by considering each cube of material containing a spherical hole. The strength of such a cube is equal to the product of the minimum cross-section times a load (R 0) fa l l i n g between the maximum practicable load and the true breaking load. If the cube is of unit volume containing a spherical hole of radius r 2 , the surface area of minimum section is (1 - TTr 2 2). The volume of the hole, which is numerically equal to the porosity, is P = | Tfr 2 3, from which the relative strength is given by . ^ir = 1 - Trr2 = 1 - IT where a 0 is the strength of pore free material. Haynes [20,21] used Hashin's expression [9] for elastic modulus, which is given by 3_ |4TT| <-/ j p2/3 = 1 kP 2/3 1 - 1.2 P 2/3 (1.26) E = E 0 ( l - KpP) (1.27) Table 1 .3 Empirical Expressions for the Tensile Strength of Porous Materials Authors Expressions for Tensile Strength Equation No. References Balshin Ryshkevitch Duckworth Pines et al. Knudsen Eudier Eudier Hasselman Weil Gallina and Mannone Haynes a = a°(l - P) n a = a o e " b P -bP ' p - p f r r p T a = a°(l - 4 P) o -.-a _-bP a = a u d " e s 2/; a = o° k • P a. = a°(l - 1 . 2 P 2 / 3 ) a = a 0 a = cr AP 1 + (A-l)P T 3 ( l - v 0 ) ( 5 v o + 9)P" 2(7 - 5 v 0 ) (1 - P) 2 / 3 a 0 1 - P 1 1 + BP a 0 = a,b,A,B,k d„ the tensile strength of porous material the tensile strength of bulk material the constants the grain diameter an exponent 1.41 1 . 4 2 , 1 . 43 1.44 1 . 40 1.45 1 .26 1.46 1 .38 1 .34 25 2 6 , 27 23 24 23 19 28 8 22 2 0 , 21 to CO Cn 236 to obtain a stress concentration factor K , which can be given by 1 - E Rel P (1.28) where E R e l = E/E0 and p R e ] = p / p r By analogy with the effect of notches on fatigue properties, the reduction in the tensile strength due to pores was given by a reduction factor IC^, which is defined as K T S ^ - ^ = 1 ^ . (1 T S aTS aRel This is a ratio of the tensile strength of porous material in which pores have no stress-raising effect, to the observed tensile strength of material of the same porosity content. Usually, the effect of the pores is less than that predicted by the use of the theoretical stress concentration factor. Thus, a factor, qp, which defines "pore sensitivity" (or the degree to which the theoretical effect is felt) is used, and defined by: K. TS - 1 K - 1 (1.30) P As a f i r s t approximation i t is assumed that or (1.31) where A is an arbitary constant. 237 From Equations (1.29) and (1.32) K e i 0 T S 1 + A(K p - 1)P 1 + BP Good agreement has been reported between experimental results and the pre-dictions' of both Eudier and Haynes in the case of sintered compacts [19, 21,23], but only for low porosity contents (< 10%). Gallina and Mannone [22] used MacKenzie [2] and Hashin's [9] theories to predict the tensile strength of porous materials. It was assumed that the theory would apply up to 30% porosity. Based on the assumption the following approximate expression was derived: -L - i 3(1 - v 0) (5v 0 + 9)P E 0 ~ 1 2(7 - 5v 0) ( 1- J 5> According to the G r i f f i t h theory of the instability condition for cracking in b r i t t l e materials, 0 ^ = kE where is the fracture stress and k is a proportionality constant depend-ing on the particular material. If and are the stresses required to produce a certain type of fracture in a dense wrought material and in the corresponding sintered one with porosity P, then a f = a f E T ( ]- 3 6) 238 It should be noted that a f is the actual stress applied. The apparent stress, oy; i.e., the applied load divided by the geometrical cross section, could be obtained by a simple introduction of the factor (1 - P ) 2 / 3 in Equation (1.36). Thus a f = a f E7 ( 1 " p ) 2 / 3 ( 1 - 3 7 ) This in turn gives the following relationship (1 - P ) 2 / 3 (1,38) Agreement with experimental results for sintered iron [22] is poor. Knudsen [24] proposed a semi empirical relationship between strength and porosity for sintered materials. He suggested that the load-carrying a b i l i t y was related to the total contact area at particle junc-tions. He calculated the contact areas per unit volume for coalesced arrays of particles with different i n i t i a l packing geometry (Figure 1.1.a). The corresponding relative strength values are plotted in Figure 1.1.b. In the region of 0 to 10 per cent porosity, the calculated strengths fitted the relation a = a 0 exp(-bP) (1.39) aTS °TSI 3(1 - v 0) {5 v0+ 9)± Knudsen further suggested that a 0 should be a function of grain size, d according to a type of Hall-Petch relationship; i.e. 239 RHOMBOHEDRAL (3) O 000 CURVE NUMBER - INDICATES TYPE GRAIN PACKING —O 0 O— CALCULATED VALUES HYPOTHETICAL CURVES ASSUMING LENS SHAPED BOND BETWEEN GRAINS 10 20 30 40 POROSITY (percent) CUBIC PACKING OF GRAINS RHOMUOHEORAL PACKING OF GRAINS • CALCULATED VALUES • HYPOTHETICAL CURVES ASSUMING LENS SHAPED BOND BETWEEN GRAINS 0 10 20 30 40 POROSITY (percent) (a) (b) Figures 1.1. a) Contact area versus porosity plots. b) Relative strength versus porosity plots for ideally packed sintered spheres as claculated by Knudsen [24] a = o° d~ d exp(-bP) (1 Several other strength-porosity relations proposed by previous investigators and included in Table 1.3, have no theoretical basis. 1.2 Scope of the Present Work Most experimental determinations of the elastic properties of porous bodies have been conducted on ceramic materials. Few reliable data appear in the literature which describe the elastic behaviour of porous sintered metals or alloys. With conventional powder processing techniques, i t is d i f f i c u l t to produce bodies which contain uniform distributions of pores, yet which span a wide range of densities. Compacting tends to produce density gradients and directionality in pore geometry, neither of 240 which is effectively eliminated by sintering. If loose powders are used i t is d i f f i c u l t by solid state sintering alone to obtain densities approach-ing theoretical. Good property data in the high density range are thus particularly scarce. In the present work, i t has been possible to produce relatively homogeneous and isotropic metal specimens with zero to 50 per cent porosity (by volume), by employing a combination of: a) l o o s e , s o l i d s o l u t i o n a l l o y powders, b) s p h e r i c a l powders o f narrow p a r t i c l e s i z e d i s t r i b u t i o n , c) s o l i d s t a t e s i n t e r i n g t o produce up t o 90 per c e n t o f t h e o r e t i c a l d e n s i t y , and d) s u p e r s o l i d u s s i n t e r i n g t o produce d e n s i t i e s up t o 100 per c e n t o f t h e o r e t i c a l . The elastic deformation of these specimens could thus be compared, over a wide porosity content range, with that predicted from theoretical analyses. By using compression instead of tension loading, i t was possible to observe plastic stress-strain behaviour up to small total strains without problems of early and unpredictable fracture of specimens. Chapter 2 EXPERIMENTAL PROCEDURE 2.1 Compression Test Specimens and Technique Porous sintered cupronickel specimens were prepared by the solid state sintering and supersolidus sintering procedures described in Part A of the thesis. None of the specimens used in dilatometric studies was employed for mechanical testing. Densities below 58% of theoretical could be obtained by using powder which had been allowed to oxidise slightly after the original hydrogen cleaning (Section 2.3, Part A) but before sintering. Sintered specimens were machined with small cuts to minimise surface deformation, and to produce specimens of 0.33 inch diameter by one inch length. Eight machined specimens at a time.were mounted in a j i g , and surface ground at each f l a t end until the two ends were closely parallel. Densities of the specimens were then determined from weight and dimensions. Compression tests were conducted on an Instron testing machine between adjustable anvils as shown in Figure 2.1. One of the anvils was bolted to the cross-head and the other was fastened to the platform of a compression load cell with a maximum capacity of 10,000 lbs. Teflon tape was used as a lubricant at specimen ends. A strain gauge extensometer of j inch gauge length and 10 per cent elongation was mounted on the specimen (as shown in Figure 2.1). The outputs of the 241 242 Figure 2.1. Apparatus for compression tests on porous sintered cupronickel. Shows specimen, anvils, load cell and extensometer strain gauge mounted directly on the specimen. 243 compression load cell and the extensometer were fed into an X-Y recorder. For each specimen tested, elastic loading-unloading cycles were completed with the extensometer mounted i n i t i a l l y at 0° to a reference position then at 90, 180 and 270°. The strain was measured to 0.0005 accurately with an i n i t i a l strain rate of 0.01 min - 1. Only i f the unloading cycle retraced closely the loading load-strain curve on the X-Y chart was i t assumed that deformation had been purely elastic. Young's modulus, E, was calculated from the elastic load-strain curve for each cycle. If the average E for the 0° and 180° positions was not within 3% of the average for the 90° and 270° positions, the test was rejected and the specimen ends were reground for improved parallelism. In most cases, sets of E values agreed within one per cent. The accuracy of the absolute values of E was checked by carrying out compression tests on hot rolled mild steel and on both annealed and hard drawn commercial purity copper; standard tension tests were performed to establish the modulus values. Close agreement was observed in a l l cases. Upon completion of the elastic test, the specimen was completely unloaded. It was subsequently re-loaded to produce approximately one per cent total strain (elastic plus plastic) to study the yielding and flow behaviour. From the load-strain curve, flow strengths at 0.02, 0.2 and 0.6% offset strain were determined. 2.2 Heat Treatment and Retesting 2.2.1 Homogenisation On the basis that concentration gradients in supersolidus-sintered specimens could affect both elastic and plastic properties, a few of the 244 specimens were homogenised and retested in compression. The composition variation was i n i t i a l l y as shown in Figure 2.2. An estimate of the time required for a given degree of homogenisa-tion was made following the analysis of Singh and Flemings [29] for a binary alloy containing a nonequilibrium eutectic. In this model dendrite arms are assumed plate like, and solute distribution within them is sinusoidal as shown in Figure 2.3. It is also assumed that the interdendritic region is of constant composition. The solution to the diffusion equation is similar to that for homogenisation of a cast structure (Part A, Section 2.4), except for a factor of 4 in the denominator of the exponent as given in the following expression: T T 2 Dt ±=e.W (2. cm For supersolidus sintered specimens, assuming the average composi-tion to be 50 wt. % copper and using values of 4.8 x 10 - 1 1 cm2/sec [30] for D at 1000°C and 0.01 cm for I (Z half the grain size) in Equation (2.1), a time of 45 days was obtained to reduce the concentration gradient to 0.01 of maximum variation in the as-sintered specimen. Accordingly, a few of the supersolidus sintered specimens were homogenised at 1000°C for 45 days in cracked ammonia, machined, remeasured for density determination and retested in compression. 2.2.2 Resintering During homogenisation treatments, i t was observed that low density specimens underwent a substantial increase in density. In order to evaluate 245 2 2. Cu and Ni x-ray intensity lines superimposed on absorbed electron images of supersolidus sintered cupronickel specimen (Q42) showing the variation in composition. The scanning paths were: (a) across the grain boundary, and (b) across the liquid pools, xlOOO. Liquid Solid Liquid V V 7 2 3 Schematic diagram of the composition distribution in super-solidus sintered cupronickel, showing the sinusoidal d i s t r i -bution of composition in the intradendritic region (Ni rich) 246 the possible effect of the "method" of sintering (i.e. solid state versus supersolidus) on mechanical properties, two solid-state sintered specimens were resintered at 1200°C for 115 hours in cracked ammonia to increase their densities into the range usually obtained only by supersolidus sintering. Resintered specimens were machined, their densities were measured and they were retested in compression. 2.3 Estimation of Open and Closed Porosity A Xylene-impregnation technique due to Arthur [31] was applied to a l l the sintered specimens to evaluate the amounts of open (interconnected) and closed pores. The weighed specimens were immersed in xylene and placed in a desiccator. The desiccator was pumped to 10"1 to IO - 2 torr in 30 minutes. A gas trap, immersed in liquid nitrogen, was connected between the desiccator and the fore pump. The function of evacuation was to remove air or gas from the interconnected pores and thus allow xylene enter into the pores. At the end of the treatment air was let into the desiccator. The specimens were removed from the xylene and excess liquid on the surfaces was wiped off using a f i l t e r paper. The specimens were then weighed in air and in water. This procedure was carried out quickly in order to minimise the error from evaporation of the xylene while handling. The amount of total porosity, P, and the open porosity, P , are given by the following expressions: (B - C) - A/pT 247 R - A and P, = j ~ — p j — b (B - C)p x where A = the weight of the original specimen in air B = the weight of the specimen impregnated with xylene, in a i r C = the weight of the specimen impregnated with xylene, in water Pj = the theoretical density of the cupronickel p = the specific gravity of the xylene The specific gravity of the commercial xylene used was determined using a pyknometer to be 0.862 gm/cc. Appropriate corrections were made for the weight of the fine copper wire used to suspend the specimens in water for weighing. The r e l i -a b i l i t y of these tests was checked using highly porous specimens (porosity > 40%) with known porosity obtained from their weight and dimensions. The amount of porosity calculated from the xylene impregnation technique was regularly within ±1% of the known value. The amount of closed porosity was obtained from the difference between the total and the open porosity. Chapter 3 RESULTS AND DISCUSSION 3.1 Microstructure Versus Density r Results of xylene-impregnation tests, showing open and closed porosity as a function of density, are plotted in Figure 3.1 (also refer to Table 3.1). These data may be compared with those of Arthur [31] as reproduced in Figure 3.2. Photomicrographs of unetched sections of typical cupronickel specimens are reproduced in Figures 3.3 to 3.9. Observations from metallo-graphy and impregnation tests may be summarised as follows. a) In specimens c o n t a i n i n g > 13$ p o r e s by volume, th e p o r o s i t y was v i r t u a l l y a l l i n t e r c o n n e c t e d and was h i g h l y i r r e g u l a r i n shape ( F i g u r e s 3.3 t o 3.6). b) In specimens c o n t a i n i n g < 1% p o r o s i t y by volume, n e a r l y a l l t h e pores were c l o s e d , and were m o s t l y e q u i a x e d i n shape ( F i g u r e s 3.8 and 3.9). c) There was a r e l a t i v e l y homogeneous d i s t r i b u t i o n o f pores on a m a c r o s c o p i c s c a l e i n a l l t h e specimens. However, t h e d i s t r i b u t i o n o f f i n e r p o res ( m i c r o p o r o s i t y ) depended on t h e s i n t e r i n g c o n d i t i o n s . d) For s u p e r s o I i d u s - s i n t e r e d s p ecimens, the number of pores d e c r e a s e d markedly w i t h i n c r e a s i n g d e n s i t y in t h e range of about 69 t o 92 per c e n t o f a s o l i d . 248 Table 3.1 Data for Compression and Xylene-Impregnation Experiments Spec. No. Density % theor. Treatment pb % P c % E 10-6 psi Stress at 0.02% offset x 10-3 psi .Stress at 0.2% offset 10-3 psi Stress at 0.6% offset 10-3 psi Stress at 1% strain TO"3 psi R6 51 .1 I 47.7 0.1 1 .9 1.9 3.3 3.7 3.8 R26 52.7 I 44.8 0.8 2.3 2.0 3.0 3.6 3.8 R5 53.6 I - - 2.4 3.2 4.1 4.4 4.5 R22 56.1 •I 43.2 0.1 3.2 4.9 6.1 6.4 6.5 RIO 56.6 I 43.5 0.1 2.8 2.6 3.7 4.4 4.7 R27 57.7 I - - 3.0 3.0 4.1 4.8 5.1 Q70 58.5 IV 39.8 0.3 2.8 2.1 2.9 3.6 3.8 Q71 59.0 IV - - 3.0 2.3 3.2 3.8 4.0 Q72 59.9 IV - - 3.3 2.4 3.5 4.1 4.4 R7 61.0 I 36.9 0.7 4.1 3.3 4.7 5.6 6.0 R9 61.0 I 36.6 0.4 4.0 4.2 5.6 6.7 7.1 R4 61.4 35.7 0.8 4.0 3.3 5.3 6.4 6.8 R24 62.1 I 37.6 0.4 4.0 3.2 5.6 6.9 7.4 R36 63.3 I - - 4.5 3.6 5.4 6.5 7.0 R15 64.0 I - - 5.4 4.9 6.6 8.1 8.5 Rll 65.5 I 33.4 0.5 6.1 4.3 6.6 7.9 8.4 R14 65.5 I 33.7 0.2 5.9 5.1 7.1 8.2 8.6 R17 66.3 1 - 6.6 5.7 7.9 8.3 9.8 CONTINUED Table 3.1 (Continued) Spec. No. Density % theor. Treatment pb % P c % E I0"6 psi Stress at 0.02% Offset x 10"3 psi 1 Stress at 0.2% | offset 10-3 psi Stress at 0.6% offset 10~3 psi Stress at 1% strain 10"3 psi R12 67.0 I 31.8 0.3 7.0 6.7 8.7 10.0 10.7 R16 67.2 I 32.9 0.6 6.6 5.0 7.9 9.2 9.8 Q73 67.5 V 30.9 0.1 7.4 5.0 7.2 8.6 9.2 R59 68.9 II - - 7.1 4.5 7.4 8.8 9.4 Q37 72.8 III 27.6 0.3 9.6 6.5 9.4 11.0 '11.6 Q74 73.4 V 24.9 0.5. 10.8 6.6 9.3 10.9 11.6 Q38 76.4 III 21.9 0.9 11.7 10.6 13.1 14.1 14.7 R65 82.6 II 17.7 0.5 14.6 11.2 13.6 15.2 16.1 Q32 83.7 III 17.2 0.7 14.0 9.3 11.9 13.7 14.5 R54 84.9 II - - 14.9 13.7 16.6 18.7 19.7 R61 85.0 II 13.2 0.9 15.9 10.4 13.3 15.1 16.3 R52 85.2 II 14.4 0.9 16.0 12.6 16.6 18.2 19.2 Q31 86.6 III 12.0 1.4 16.7 9.9 12.9 15.0 15.9 Q33 89.6 III 8.8 2.8 17.9 10.7 13.6 15.6 16.7 Q39 91.8 III - - 19.5 10.4 13.3 15.3 16.5 Q30 92.3 III 0.3 6.5 20.2 8.0 17.9 19.4 20.4 Q34 94.8 III 0.5 4.2 22.3 12.8 16.6 19.0 20.2 Q29 95.5 III 0.5 3.8 22.6 13.6 16.4 18.6 19.8 R57 96.4 II - - 22.0 20.2 21.9 23.7 24.9 R50 96.4 II 0.7 4.3 22.9 20.5 22.4 23.3 24.0 K Q53 96.8 III 0.6 2.7 22.9 i 12.0 — ,—. L 16.2 18.5 o 19.7 CONTINUED Table 3.1 (Continued) Spec. No. Density % theor. Treatment Pb % . P c % E 10-6 psi Stress at 0.02% offset x 10"3 psi Stress at 0.2% offset 10-3 psi Stress at 0.6% offset TO"3 psi Stress at 1% offset 10-3 psi R48 97.2 II 1.2 2.3 22.2 18.6 22.0 24.5 25.8 R49 97.2 II - - 23.1 20.0 22.7 24.6 25.8 . Q27 97.3 III 0.8 1.2 23.4 12.4 15.9 18.2 19.5 Q28 97.4 III 0.6 1.5 23.4 13.2 16.2 18.5 19.8 Q57 97.8 XI 0.6 2.3 23.3 12.1 17.3 19.9 21.1 Q40 98.1 III 0.5 1.2 23.5 12.7 16.1 18.5 19.7 Q36 98.3 III 0.3 1.3 23.5 19.5 23.9 25.1 26.0 Q65 99.1 III 0.2 1.8 23.9 13.2 15.9 18.1 19.3 Q66 100.0 III 0.1 1.2 24.3 12.9 16.4 18.7 19.9 R59 78.7 VI 21.7 0.0 12.7 8.7 9.8 10.7 11.4 R54 85.9 VI 13.7 0.0 16.7 9.1 10.6 12.1 13.0 Q75 86.6 VII 12.9 0.7 16.7 12.6 14.0 14.9 15.6 Q76 94.5 VII 0.9 4.3 22.7 15.6 17.0 17.9 18.6 R49 96.7 VI 0.5 2.7 23.1 10.0 11.9 13.4 14.5 Q77 96.7 VII 0.8 2.6 23.1 10.7 12.6 14.4 15.4 R57 96.9 VI • 0.4 2.5 23.3 10.7 12.1 13.6 14.5 Q71 75.8 VIII 22.8 0.5 11 .2 7.4 10.1 11.8 12.6 R36 85.5 IX 14.5 0.2 16.3 9.1 13.1 15.3 16.2 Q39 92.1 X 2.2 5.9 20.7 9.3 11.8 13.6 14.5 LS7 98.2 XII 0.2 1.6 23.3 10.8 13.7 15.1 15.8 K3 252 Table 3.2 Treatment Numbers and the Symbols Used in the Figures (Figures 3.1, 3.15, 3.17, 3.18, 3.20, 3.21, 3.22 and 3.23) Symbol No. Particle Size ym Treatment O I 68 solid state sintered in vacuum • II 68 supersolidus sintered in vacuum O III 68 supersolidus sintered in hydrogen V IV 81 solid state sintered in hydrogen A V 81 supersolidus sintered in hydrogen H VI 68 supersolidus sintered in vacuum and homogenised VII 81 supersolidus sintered in hydrogen and homogenised • VIII 81 solid state sintered in hydrogen and resintered in hydrogen IX 68 solid state sintered in vacuum and resintered in hydrogen X 68 supersolidus sintered in hydrogen and resintered in hydrogen XI XII 68 supersolidus sintered in hydrogen at 1280°C cast and homogenised cupronickel 100 i 10 O n— i— i—i—r 50 60 i — i — i — i — r i — i — r 70 80 Density, % Theor. 90 100 Amount of open and closed porosity versus density for sintered cupronickel specimens. (Meaninq symbols for plotted points given in Table 3.2.) y 254 Figure 3.2. Amount of open and closed porosity versus total porosity for copper powder (Arthur [31]). a) -300 mesh, loose sintered and b) 240 x 300 mesh, compacted and sintered. 255 Figure 3.3. Specimen sintered in solid state to density of 61.4% of solid (structure typical of specimens with densities less than about 62% of solid) (R4), x73. Figure 3.4. Specimen sintered in solid state to density of 65.5% of solid (R14), x73. 256 Figure 3.5. Specimen sintered in solid state to 85.4% of solid density (sintered twice, once before and once after a f i r s t compression test), (R36), x73. Figure 3.6. Specimen sintered above solidus to 86.6% of solid density (Q31), x73. Figure 3.7. Specimen sintered above solidus to 92.3% of solid density (Q30), x73. Figure 3.8. Specimen sintered above solidus to 97.4% of solid density (Q28), x73. 258 D e n s i f i c a t i o n was a s s o c i a t e d p r i m a r i l y w i t h a r e d u c t i o n i n number o f p o r e s r a t h e r t h a n w i t h a r e d u c t i o n i n t h e i r s i z e . Only i n t h e c l o s e d - p o r e range (0 t o 7 p e r c e n t p o r o s i t y ) d i d t h e pore s i z e d i m i n i s h r a p i d l y w i t h i n c r e a s i n g d e n s i t y . However, i n t h e d e n s i t y range 62 t o 85$ o f s o l i d , s o l i d s t a t e s i n t e r i n g had t h e e f f e c t o f d e c r e a s i n g t h e s i z e o f t h e p o r e s , r a t h e r than t h e number o f p o r e s , and t h u s i n c r e a s i n g t h e d e n s i t y ( F i g u r e s 3.4 and 3.5). T h i s can a l s o be seen by c o m p a r i s o n of t h e m i c r o s t r u c t u r e s o f s u p e r s o l i d u s s i n t e r e d and s o l i d s t a t e s i n t e r e d specimens of comparable d e n s i t y ( F i g u r e s 3.6 and 3.5). e) In t h e range o f 51 t o about 62 per c e n t o f s o l i d d e n s i t y , changes i n pore s t r u c t u r e were not e v i d e n t . The p a r t i c l e c o o r d i n a t i o n appeared t o remain c o n s t a n t . f ) F o r a g i v e n d e n s i t y , pores i n s u p e r s o l i d u s s i n t e r e d specimens were l a r g e r on average t h a n pores i n s o l i d -s t a t e r e s i n t e r e d s p e cimens. However, th e shape o f the p ores d i d not seem t o be a p p r e c i a b l y a f f e c t e d by t h e method of s i n t e r i n g . g) S p h e r o i d i s e d p o r e s were found o n l y i n h i g h d e n s i t y specimens which had been s u b j e c t e d t o long s o l i d - s t a t e homogenising a n n e a l s ( F i g u r e 3.9). Etched microstructures of specimens which were homogenised or re-sintered after a small compressive plastic strain are shown in Figures 3.10 to 3.14. The grain size after these treatments was very large compared to the original powder particle size. Accurate determination of the average grain diameter was not attempted, but would have been d i f f i c u l t since twin boundaries were in many cases d i f f i c u l t to distinguish from grain boundaries in these specimens. 3.2 Young's Modulus 3.2.1 Elastic Modulus Versus Density Results of elastic compression tests on sintered specimens are presented in Table 3.1 and in Figure 3.15 as Young's modulus versus density. Figure 3.10. Supersolidus sintered and homogenised structure (R59), x80. Figure 3.12. Supersolidus sintered and homogenised without prestrain. Reveals large grains (Q77), xl4. Figure 3.13. Same as Figure 3.5, revealing grain shape (R36), x80. Figure 3.14. Supersolidus sintered and resintered after a prestrain. Reveals large grains (Q39), xl4. 262 All experimental stress values are based on the f u l l cross section of the specimens. No consistent effect of grain size or homogenity on the modulus was observed. Reported values [32] are available for the elastic modulus of dense polycrystal1ine pure copper, pure nickel, and for a 55 wt. % copper -45% nickel alloy. It is also possible to calculate the elastic constants for isotropic polycrystal1ine alloys in the copper-nickel system from pub-lished elastic compliance data of the pure metals [33]. A summary of these experimental and calculated constants is given in Table 3.3 and Figure 3.16. The value of Young's modulus thus estimated for the 50 wt. per cent nickel alloy of the present work, from Figure 3.16, is 24.4 x 106 psi (1.69 x 10 s MNm-2). This compares very closely with the value of the modulus, 24.3 x TO6 psi, measured in the present work on specimens which were sintered to f u l l density. Using elastic constants derived from Figure 3.16 i t is also possible to apply the theoretical relationships in Table 1.1 to porous cupronickel. Values of the elastic modulus thus calculated for different theories and for different porosity contents are compiled in Table 3.4 and have been plotted in Figure 3.17.a for comparison with the experimental results. There is excellent agreement between experiment and the predictions of most theories for densities in, excess of about 92 per cent of solid. This agreement has not been well documented previously for sintered metallic specimens, probably because of the experimental d i f f i c u l t y of obtaining suitable high-density metal specimens by sintering. The region of good f i t with theory is one in which only closed pores were found in the specimens; 263 Density, % Theor. Figure 3.15. Young's modulus versus density for porous sintered cupronickel. Experimental data and theoretical "rule of mixtures" line (assuming elastic constants zero at 50% density). Table 3.3 Elastic Constants for Cu-Ni Alloys, at Room Temperature, From Elastic Compliance Data and Reported Experimental Values Composition wt. % P Eo IO"6 psi Go IO"6 psi Ko IO"6 psi V o Ref. Composition wt. % P Eo 10- 6 psi Go 10- 6psi Ko 10 - 6 psi V o Cu J Ni gms/cc Cu Ni gms/cc 100 8.936 18.6 6.9 19.9 0.345 [33] - 100 8.9 32.0 12.3 27.3 0.305 100 - 8.9320 18.6 6.9 19.8 0.344 i - 100 8.9 32.6 12.6 26.9 0.298 100 - 8.9312 18.5 6.9 19.9 0.345 100 8.9 32.4 12.5 26.2 0.294 100 - - 8.9883 18.4 6.9 19.9 0.346 - 100 8.9 30.7 11.7 27.6 0.314 100 - 8.9340 18.7 7.0 20.1 0.345 - 100 8.907 32.5 12.5 26.6 0.297 100 - 8.9320 18.5 6.9 19.9 0.345 - 100 8.910 31.8 12.2 27.0 0.304 97.2 2.8 8.9892 18.8 7.0 20.0 0.343 - 100 8.910 32.7 12.7 25.9 0.290 97.8 2.2 8.9886 18.7 7.0 20.0 0.344 7.8 92.2 8.9183 30.8 11.8 26.3 0.305 95.8 4.2 9.0000 19.0 7.1 20.0 0.342 19.0 81.0 8.9301 29.2 11.2 25.5 0.309 94.4 5.6 8.9894 19.1 7.1 20.1 0.342 21 .3 78.7 8.9330 28.6 10.9 25.6 0.314 90.9 9.1 8.9949 19.4 7.3 20.2 0.340 24.2 75.8 8.9360 28.3 10.8 25.3 0.314 - 100 8.900 27.9 10.5 27.1 0.329 36.3 63.7 8.9495 26.3 9.9 24.6 0.322 - 100 8.900 29.7 11.3 26.8 0.315 48.2 51 .8 8.9620 24.9 9.4 23.9 0.327 - 100 8.900 31 .5 12.1 27.3 0.308 70.6 29.4 8.9586 22.0 8.3 21.9 0.333 - 100 8.900 31.1 12.0 26.2 0.302 55* 45 - 23.6 8.9 22.7 0.327a 100* - - 18.8 7.0 20.0 0.343-4 * 100 - 32.0 12.2 27.2 0.306J Ref. ho F i g u r e 3.16. E l a s t i c c o n s t a n t s f o r Cu-N i a l l o y s ( f r om T a b l e 3.3) to Table 3.4 Predicted Values of E for Sintered Cupronickel, Assuming Elastic Constants are Zero at Zero Density E x "10 psi Porosity Dewey [1] MacKenzie [2] I MacKenzie [2] II Kerner, Hashin and others [3-6] Weil Hashin [8-9] Skorokhod [10] Rule of Mixtures 0.0 24.4 24.4 24.4 24.4 24.4 24.4 24.4 0.025 24.3 23.3 23.3 23.3 23.2 - 23.8 0.05 24.1 22.1 21.9 22.2 21.9 23.2 0.075 23.9 21.0 20.8 21.0 20.7 - 22.6 0.1 23.8 19.8 19.6 20.0 19.6 19.9 22.0 0.2 23.2 (15.8)* (15.1)* (16.3)* (14.3)* 15.8 19.5 0.3 - (12.3) (10.7) (13.0) ( 8.3) 11 .3 17.1 0.4 - (9.3) ( 6.2) (10.5) - 7.8 14.6 0.5 (6.8) (1.6) ( 8.7) - 5.1 12.2 The extension of theoretical analysis to porosity contents > 0.1 is probably uniustified in view of the assumptions in the models. 267 D e n s i t y , % Theor. (0 Figure 3.17. Young's modulus versus density for porous sintered cupronickel. Experimental data and theoretical predictions. a) Theoretical predictions of MacKenzie -2 [2], Skorokhod [10], and Hashin and others [3,6] (assuming elastic constants zero at zero density). b) Predictions from Knudsen's model [24]. c) Hashin's plot [3,6] (assuming elastic constants zero at 50% density) and best-fit-plot. 268 i.e. the internal morphology of the specimens was consistent with most of the models used to treat elastic behaviour analytically. Below about 92 per cent of solid density, a marked discrepancy is observed between experimental values of the moduli and those predicted from any theory. This is typical also of the observations reported in the literature for other porous materials. However, the sharp decrease in modulus (associated with a discontinuity in the E versus density plot) which accompanies a transition from closed to open porosity as shown in Figure 3.18 has not heretofore been reported, and is a particularly inter-esting feature of the present results. Although some of the homogenised and resintered specimens had a very large grain size relative to powder particle size, no effect of grain size on modulus values could be detected. 3.2.2 Interpretation In view of the good agreement between theory and experiment at high densities, several of the analyses discussed in Section 3.2.1 can be said to describe reliably the elastic behaviour of porous sintered cupronickel when the pores are a l l isolated and dispersed. However, no available theory is consistent with the results obtained for specimens with interconnected porosity, and most available theories predict much higher modulus values than were observed. In a sintered powder aggregate, an applied load must be borne at the necks between particles. It is possible to pack uniform spherical particles into a rhombohedral array which f i l l s - 74 per cent of space with Figure 3.18. High density portion of Figure 3.15 and 3.17 270 solid. Until this array of particles sintered, i t has no load carrying capacity at a l l ; i.e. its elastic modulus is zero, yet its porosity content is only 0.26. If the array is even very lightly sintered, necks form and the modulus of the aggregate becomes f i n i t e . To a f i r s t approximation, i t might be assumed that when the array is further sintered, i t s capacity to support a load will increase linearly with increasing density due to neck growth with particle-centre approach. That i s , (P, - P) E = Eo — ^ (3.1) where P.. is the porosity in the loose-powder aggregate (unsintered). Equation (3.1) plotted in Figure 3.15 is a "Rule of Mixtures" which recognises, in marked contrast to most of the theoretical equations collected in Table 1.1, that the elastic modulus of a sintered body can be zero even when the porosity is considerably less than unity. If values of P are replaced by P/P. in the derived equations, a correction is made in effect for the fact that the elastic strength is zero when P = P... Moreover, no assumption about the type of particle packing is required in making this correction. Hashin equations [3,4,5,6] (Table 1.1) have been thus treated to calculate E versus P for cupronickel, with the results shown in Figure 3.17 .C. Agreement with the experimental results is poor, which suggests that Hashin's model (which is similar to that of Kerner and others) cannot apply to systems with interconnected porosity. 271 Clearly the Rule of Mixtures in Equation (3.1) cannot give accurate predictions of modulus variations with porosity i f the load-carrying neck elements do not grow linearly with increasing density during sintering, as was assumed in deriving the equation. As noted in Section 1.1.2, Knudsen [24] has treated quantitatively the growth of contact (neck) areas between coalescing arrays of uniform spherical particles, assuming several different ideal packing arrays. The calculated relation between contact area and porosity is shown in Figure 1.1.a. On the assumption that the elastic stress-bearing capacity is directly related to neck contact area, Young's modulus versus porosity predictions can be made from the results of Figure 1.1.a, as was done for ultimate strength versus porosity by Knudsen [24]. Similar approaches were taken by Spriggs [14,18]. However, i t is necessary to choose an appropriate model for particle packing. In the present work with cupronickel, the i n i t i a l loose-powder porosity was ~ 0.50, which is slightly larger than that calculated for the ideal simple cubic array (0.48) and is widely different from those calculated for any other ideal array of uniform spheres. Metallography has shown (Section 3.2, Part A) that the packing is far from uniform in powder specimens, there being randomly oriented groupings with different types of dense packing joined.by bridges. However, the forms of the curves in Figure 1.1.a for different packing modes are so similar that i t seems reasonable to assume that the average neck growth in the aggregate will vary with density in a manner closely parallel to that predicted for the simple cubic model (Table 3.5). On this basis, the derived plot of E versus P in Figure 3.17.b was made and may be compared with the experimental results. Table 3.5 Contact Area, Density, and Young's Modulus for Ideal Cubic Packing of Spherical Cupronickel Density TTX2 Area of contact without meniscus E x 10" psi 52.36 0 0-0 53.15 0.012 0.3 55.57 0.048 1.2 59.75 0.110 2.7 65.94 0.198 4.8 74.39 0.314 7.7 79.50 0.397 9.7 85.09 0.493 12.0 90.84 0.613 15.0 95.94 0.776 18.9 96.51 0.804 19.6 100.00 1.00.0 24.4 It should be noted that the plot is based on Knudsen's calculation for ideal cubic packing and should therefore have its origin at E = 0,p0 = 52.4 per cent. However, i t has been shifted to P o= 50 per cent in Figure 3.17.b to reflect more accurately the starting density of cupronickel specimens. Discrepancies between the measured modulus values and those dieted from the neck-area argument might be interpreted as follows: a) The model of c o n t a c t - a r e a growth used t o c a l c u l a t e t h e p r e d i c t e d moduli i n F i g u r e 3.1 7.b assumes t h a t when p a r t i c l e c e n t r e s approach t h e p a r t i c l e s adopt t h e shape o f t r u n c a t e d s p h e r e s . E s s e n t i a l l y t h i s t y p e o f c o n t a c t development w i l l a r i s e when s p h e r e s a r e p r e s s e d t o g e t h e r , and m a t e r i a l t r a n s p o r t i s by p l a s t i c f l o w o n l y . However, i f . c o n t a c t development proceeds by d i f f u s i o n a l p r o c e s s e s as i n s i n t e r i n g , a neck w i t h t h e f a m i l i a r rounded meniscus i s formed. T h i s t y p e o f neck has a l a r g e r r e l a t i v e c o n t a c t a r e a f o r a g i v e n approach of p a r t i c l e c e n t r e s t h a n t h a t assumed i n t h e Knudsen C243 model. Thus t h e e f f e c t i v e l o ad b e a r i n g a r e a s and e l a s t i c moduli of s i n t e r e d specimens w i l l be h i g h e r , f o r a g i v e n p o r o s i t y c o n t e n t , t h a n t h e above a n a l y s i s p r e -d i c t s . Knudsen a t t e m p t e d t o make a l l o w a n c e f o r t h e neck meniscus (dashed l i n e s i n F i g u r e I. I . a ) , b u t h i s approach i n v o l v e d a r b i t r a r y a s s u m p t i o n s . b) Neck growth i s a l s o caused by n o n - d e n s i f y i n g mass t r a n s p o r t mechanisms such as e v a p o r a t i o n - c o n d e n s a t i o n and s u r f a c e d i f f u s i o n . In t h e e a r l i e s t s t a g e s o f s i n t e r i n g i t i s p o s s i b l e t h a t more neck growth o c c u r s from t h e s e s o u r c e s t h a n from p r o c e s s e s which c o n t r i b u t e t o a d e c r e a s e i n t h e volume o f p o r o s i t y ( e . g . volume d i f f u s i o n mechanisms). T h i s c o u l d e x p l a i n why, i n the lowest d e n s i t y r e g i o n of t h e p l o t s ( F i g u r e s 3.15 and 3.17) modulus v a l u e s were h i g h e r than t h o s e p r e d i c t e d from c o n t a c t - a r e a growth based on t h e approach of p a r t i c l e c e n t r e s . F o l l o w i n g t h i s argument, t h e slow r i s e o f E w i t h d e n s i t y between 50 and 60 per c e n t of t h e o r e t i c a l s u g g e s t s t h a t a mechanism such as s u r f a c e d i f f u s i o n has e s t a b l i s h e d necks i n v e r y s h o r t s i n t e r i n g t i m e s o r a t low s i n t e r i n g t e m p e r a t u r e , and t h a t s u b s e -quent approach o f p a r t i c l e c e n t r e s ( f o r d e n s i f i c a t i o n ) has somehow proceeded w i t h l i t t l e growth o f t h e o r i g i n a l 274 necks up t o a d e n s i t y of. about 60 p e r c e n t o f s o l i d . I t i s d i f f i c u l t t o v i s u a l i s e how t h i s c o u l d o c c u r , and some doubts a r e t h e r e f o r e c a s t on t h e above argument. An alternate approach to describing the modulus-porosity relation-ship is as follows: a) Use a relationship for the region of closed porosity (high density) from the MacKenzie [2] or similar analyses. Equation (1.35) reuces to E = E 0 ( l - KCP) ( 3 . 2 ) b) As a f i r s t approximation, use a Rule of Mixtures for the open porosity region; i.e. E = Eo P. -P c) To obtain a general equation for the f u l l range of porosity, combine pi us E c - E„(l. - KcP) ^ Eb = E (P,- - P) P, (3.3) (3.4) from which E = E( b b c P " P. P K P c c 275 Using an appropriate value of v 0 for cupronickel, Kc has been evaluated from Equation (1.35) and found to be 2.0. Also, since P. = 0.50 in the present experiments, Equation (3.5) becomes 1 - 2(P b + P c) = E( 1 2P (3.6) with P. = 0.50, the Rule of Mixtures is identical (Figure 3.15). A test has been made of the empirical expressions proposed by Hasselman [15] and by Fryxell and Chandler [16], Table 1.1. When the exponential term in Spriggs 1 [14] relation is replaced by a series expansion, and second order or higher terms are dropped, i t is equivalent to Hasselman's [15]; i.e. E = E 0 ( l - bP) (1.21) This becomes a statement of the simple Rule of Mixtures by b = P T 1 . When the present experimental data are "fitted" to this relationship by linear regression analysis, E 0 is found to be 24.6 x 106 psi with b =2.1 (which is very close to P T 1 ) . The best-fit plot is presented in Figure 3.17 .C. 3.3 Plastic Flow Behaviour Engineering stress-strain curves were derived from X-Y load-elongation plots. Examples are shown in Figure 3.19. From these curves were obtained flow stress values for 0.02, 0.2 and 0.6 per cent offset strain and for 1 per cent total strain (slightly < 1 per cent plastic strain). T 1 1 1 1 1 r 1 Initial Strain Rate 001 min-« i I 1 1 1 1 r 0- 0-2 0-3 0-4 0-5 0-6 Engg. Stra in , % 0-7 0 8 0 9 Figure 3.19. Typical stress-strain curves for sintered cupronickel powder specimens. 277 Results are collected in Table 3.1, and plotted versus porosity in Figures 3.20 to 3.23. The large scatter in the flow stress values can be attributed to the following: a) Variations in shapes and distribution of pores, composition gradients in as-sintered specimens, and differences in neck composition between sintered and homogenised specimens. b) Variations in grain size due to differences in previous history of specimens. These variations are li k e l y to be most evident in the higher density specimens, which is when the greatest experimental scatter was observed. c) Plastic buckling of the compression specimen. Beyond the proportional limit, i f the load applied exceeds a c r i t i c a l , load, W c r i t . , there will be buckling of the specimen in a compression test. The c r i t i c a l load, according to Tangent Modulus theory [34], is given by TT 2 E I W c r i t . = — J J 1 — (3.7) where E T is the tangent modulus at any W, L is the length of the specimen, I is the moment of inertia for the specimen. The moment of inertia, t - 1^1 1 ' 64 for a simple cylinder of diameter d. For porous sintered cupronickel buckling was probably important only in specimens with densities higher than 96% of theoretical and at total strains exceeding 0.9%. 10 D e n s i t y , % T h e o r . F i g u r e 3 .20. 0.02% o f f s e t f l o w s t r e s s i n c o m p r e s s i o n v e r s u s d e n s i t y . L i n e drawn i s l e a s t s qua re s f i t . .00 K> O I I r - 1- 1 1 1 r u_ 0 1 1 1 1 1 1 • 1 i i i I 50 60 70 80 90 100 D e n s i t y , % T h e o r . Figure 3.22. Same as Figure 3.20, but for 0.6% offset flow stress. 282 In view of the large scatter, there was no merit in attempting to describe the results in terms of analytical expression such as those suggested in the literature. The data have been fi t t e d to a Rule of Mixutres; i.e. a = a°(l - b'P) (3.8) Using regression analysis, values of o° and b' for different offset strains were obtained as given in Table 3.6. Table 3.6 Values of o°, and b1 in Equation (3.8) Strain °'° o° Ksi b 1 0.02 plastic 15.1 1 .9 0.2 plastic 18.6 1 .8 0.6 plastic 20.7 1 .8 1.0 (total) 22.0 1 .8 Following the arguments of the previous section, a value of b' =2 would indicate that b' = 1/p.. and the Rule of Mixtures would have the physical meaning already discussed in relation to Young's Modulus. Chapter 4 CONCLUSIONS 1. In porous sintered cupronickel specimens containing only closed porosity (density > 93% of solid), the dependence of elastic modulus on density is adequately described by several of the published analyses based on the application of el a s t i c i t y theory. These analyses approximate to E = Eo(l - K cP c) where Kc is a function of Poisson's Ratio and is equal to 2.0 for cupronickel 2. For lower-density sintered cupronickel specimens (density < 92% of solid), in which interconnected porosity is dominant, modulus-porosity results cannot be closely f i t t e d to any single theoretical or empirical relationship. However, over the whole range of density, an approximate f i t is provided by E = E ( P, 1 " PT- K c P c For the present experiments, Pi = 0.5, and this relationship reduces to 283 284 E = E 0 ( l - 2P), where P = P. + P . D C This dependence is consistent with a model of the powder aggregate in which no strength is available until necks are established by sintering, and the load-carrying neck area after sintering is linearly related to the density. 285 BIBLIOGRAPHY 1. Dewey, J.M., J. Appl. Phys., 1947, V. 18, p. 578. 2. MacKenzie, J.K., Proc. Roy. Soc. (London), 1950, V. 63 B, p. 2. 3. Kerner, E.H., Proc. Phys. Soc, 1956, V. 63 B, p. 808. 4. Hashin, Z., "Mech. of Comp. Materials," Pergamon Press, New York, 1970, p. 201. 5. Pusch, G., Stroppe, H., and Schatt, W., Panseeber. Pulvermet, 1968, Vol. 16, p. 178. 6. Hashin, Z., and Shtrikman, S., J. Mech. Phys. Solids, 1963, V. 11, p. 127. 7. Gatto, F., Alluminio, 1950, V. 19, p. 19. 8. Weil, N.A., International Symposium on High Temperature Technology, London, Butterworths, 1964, p. 189. 9. Hashin, Z., "Non Homogeneity in Elasticity and Plasticity," Edited by W. Ol.szak, Pergamon Press, New York, 1959, p. 463. 10. Skorokhod, V.V., Soviet Powd. Met. and Metal Ceram., 1967, p. 453. 11. Hasselman, D.P.H., J. Am. Ceram. Soc, 1962, V. 45, p. 452. 12. Chung, D.H., Phil. Mag., 1963, V. 8, p. 883. 13. McAdam, G.D., J. Iron and Steel Inst., 1951, V. 168, p. 346. 14. Spriggs, R.M., J. Am Ceram. Soc, 1961, V. 44, p. 628. 59 286 15. Hasselman, D.P.H., and Fulrath, R.M., J . Am Ceram. Soc, 1964, V. 47, p. 52; 16. Fryxell, R.E., and Chandler, B.A., J . Am. Ceram. Soc, 1964, V. 47, p. 283. 17. Rossi, R.C., J . Am. Ceram. Soc, 1968, V. 51, P. 433. 18. Spriggs, R.M., J J Am. Ceram. Soc, 1962, V. 45, p. 454. 19. Eudier, M., Powd. Met., 1962, V. 9, p. 278. 20. Haynes, R., Powd. Met., 1971, V. 14, p. 64. 21. Haynes, R., Powd. Met., 1971, V. 14, p. 71. 22. Gallina, V., and Mannone, G., Powd. Met., 1968, V. 11, p. 73. 23. Salak, A., Miskovic, V., Dudrova, E., and Rudnayova, E., Powd. Met. Inter., 1974, V. 6, p. 128. 24. Knudsen, F.P., J . Am. Ceram. Soc, 1959, V. 42, p. 376. 25. Balshin, M.J., Poroshkovoye Metallovegyeniye Metal 1urgizdat, Moscow, 1948. 26. Ryshkewitch, E., J. Am. Ceram. Soc, 1953, V. 36, p. 65. 27. Duckworth, w.,RJ. Am. Ceram. Soc, 1953, V. 36, p. 68. 28. Hasselman, D.P.H., J . Am. Ceram. Soc, 1963, V. 46, p. 564. 29. Flemings, CM., "Solidification Processing," McGraw-Hill Book Company, 1974, p. 328. 30. Marchukova, I.D., and Miroshkina, I.M., Phys. Met. and Metallogr., 1971, V. 32, p. 133. 31. Arthur, G., J . Inst, of Metals, 1954-55, V. 83, p. 329. 32. Smithells, C.J., Metals Reference Book Vol. 3, 4th Edition, London, Butterworths, 1967, p. 708. 287 33. Simmons, G., and Wang, H., "Single Crystal Elastic Constants and Calculated Aggregate Properties": A Hand Book. Second Edition. The MIT Press, Cambridge, Massachusetts and London, England, 1971. 34. Harris, CO., "Introduction to Stress Analysis," The Macmillan Co., New York, Fourth Printing, 1964, p. 158. 

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