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High velocity impact fragmentation and the energy efficiency of comminution Sadrai, Sepehr 2007

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HIGH VELOCITY IMPACT FRAGMENTATION AND THE ENERGY EFFICIENCY OF COMMINUTION . By SEPEHR S A D R A I B.A.Sc, Tehran Polytechnique (Amir-Kabir University), Tehran, Iran, 1987 M.A.Sc, University of Tehran, Tehran, Iran, 1992 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQULRMENTS FOR THE DEGREE OF D O C T O R OF P H I L O S O P H Y in THE F A C U L T Y OF G R A D U A T E STUDIES (MINING ENGINEERING) THE UNIVERSITY OF BRITISH C O L U M B I A October 2007 © Sepehr Sadrai, 2007 ABSTRACT Comminution processes are essential stages in mining and mineral processing operations to reduce the size of ore and rock, and liberate the valuable mineral for beneficiation. Comminution is energy-intensive and responsible for the majority used during mineral recovery. Energy use is inherently inefficient with almost all being dissipated as heat instead of new surface area (energy). Typical grinding efficiencies in terms of new surface area created range from 1 to 2 percent with crushing efficiencies lying slightly higher at 3 to 4 percent. High-pressure rolls and roller crushers are reported to operate at levels as high as 7 to 8 percent, while blasting has the highest efficiency of all ranging from 13 to 20 percent. This thesis reports on studies conducted into the effect of high strain rate achieved through high velocity impacts to enhance energy efficiency and mineral liberation. The research is focused on understanding the fracture mechanics of comminution at ultra-high strain rates and quantifies the distribution of energy with respect to generating new surface area. In interpreting breakage phenomena, accurate measurement of surface roughness and surface area is essential. A novel approach to determine these parameters based on fractal analysis has been developed. Changes in surface roughness of broken specimens under variable loading rates were studied using a laser probe to generate 3D topographical maps of the fracture surfaces. The results indicate that surface roughness and hence, specific surface area, increases with increasing loading rate by several orders of magnitude as n particle size decreases to ~1 micron. Below this limit, surface.roughness begins to diminish from, particle-particle attrition. The influences of particle shape, porosity, and size have been accounted for in this analysis. A n apparatus to measure the quantitative parameters of high velocity impact on aggregated rock samples has been developed. Experiments have been carried out on three materials at projectile velocities up to 450 ms"1 utilizing a compressed air gas gun. The results, suggest energy efficiency of rock breakage can be improved by as much as 2 to 3 times under high velocity impact for the same energy input level. The effect is subtle and sensitive to the impact zone dimension, the hardness and porosity of the material, and the constraining or not of the sample. Our research aims to develop better understanding of the fundamentals of fragmentation with the purpose to increase efficiency and find ways to reduce the energy required for comminution. in TABLE OF CONTENTS ABSTRACT.... ii TABLE OF CONTENTS .. ..iv TABLE OF FIGURES x LIST OF TABLES xv NOMENCLATURE....... xviii ACKNOWLEDGMENT xxiii CHAPTER 1 INTRODUCTION . 1 1.1 Energy Consumption of Comminution Stages'. 3 1.2 Problem Statement 5 1.2.1 Comminution Efficiency 5 1.2.2 Impact Efficiency 7 1.3 Hypothesis of the Thesis . ............10 1.4 Thesis Objectives ; 11 1.5 Organization of the Thesis . 12 CHAPTER 2 CONVENTIONAL COMMINUTION PROCESSES 14 2.1 Overview 14 2.2 Mineral Liberation.... 15 2.3 Current Comminution Technology 16 2.3.1 Blasting Operation .. 17 2.3.2 Unit Operations ; 18 2.3.3 Crushing Operation .....19 2.3.4 Grinding Operation 20 2.3.5 Special Equipment 21 2.3.5.1 Barmac Crusher 22 iv 2.3.5.2 High Pressure Grinding Rolls..... , 24 2.3.5.3 Jet Mills . 26 2.4 Quality of Comminution Product ^ 27 2.4.1 Particle Size Analysis. 27 2.4.2 Shape of Particles 28 2.4.3 Produced Surface Area 30 2.5 Modeling Approach i ...31 2.5.1 Theories of Comminution 31 2.5.2 Comminution Models 34 CHAPTER 3 MECHANISM OF ROCK BREAKAGE 37 3.1 Overview : ;'. — 37 3.2 Macroscopic Behavior 37 3.2.1 Rock Displacement Effects : , 37 3.2.2 Stress-Strain Response ; 39 3.3 Microscopic Fracture 40 3.3.1 Fracture Propagation 40 3.3.2 Ductile-Brittle Fracture Transition... 42 3.3.3 Fracture Toughness 44 3.3.4 Crack System Energy , 45 3.4 Material Behavior under Impact Loading ; 48 3.4.1 Strength vs Strain Rate 48 3.4.2 Static and Dynamic Loading '.. ....50 3.4.3 Material and Loading Characteristics 52 3.4.4 Rock Breakage under Low Impact ; 56 3.4.4.1 Tensile vs Compression .56 3.4.4.2 Bond Work Index 57 3.4.4.3 Single-particle Breakage Tests 58 3.4.5 Material Breakage under High Impact .....59 3.4.5.1 Split Hopkinson Pressure Bar 62 v 3.4.5.2 Two Stage Light Gas G u n 63 3.4.5.3 Electromagnetic G u n . l 66 3.5 Conclusion ... 67 C H A P T E R 4 D E V E L O P M E N T O F E S T I M A T I O N M E T H O D O N E N E R G Y E F F I C I E N C Y U N D E R S T A T I C R E G I M E F R A G M E N T A T I O N ......69 4.1 Introduction... . , 69 4.2 Energy Efficiency Conceptual Model. . . . 71 4.3 Technical Surface Roughness '. 73 4.4 Fractal Dimension Method •. 75 4.5 Effect of Resolution on Roughness and Surface Area Measurement 79 4.6 Experimental Procedure ." 80 4.6.1 3D Mapping 82 4.6.2 Development of Surface Roughness Technique 86 4.6.3 Development of Surface Area Technique 90 4.6.4 Estimation Method of Energy Efficiency 95 4.6.5 S E M Examinations 97 4.6.6 Discussion 99 C H A P T E R 5 D E S I G N A N D O P E R A T I N G C H A R A C T E R I S T I C S O F T H E H I G H - V E L O C I T Y I M P A C T T E S T F A C I L I T Y .100 5.1 Introduction 100 5.2 Principles of Operating Technique ; 101 5.3 Apparatus M a i n Equipment 102 5.3.1 Machine Design Basis :.. 102 i 5.3.2 General Configuration ....103 5.3.3 Target Chamber and Projectile 104 5.3.4 Reservoir and Launch Tube 107 5.3.5 Multi-task Divider.. 113 5.4 Auxil iary Equipment 114 5.4.1 Selection of Compressor 114 v i 5.4.2 Quick Opening Solenoid Valves 115 5.4.3 Vacuum Pump 117 5.4.4 Laser Intervalometer 118 CHAPTER 6 TESTWORK AND DATA ANALYSIS .120 6.1 Introduction 120 6.2 Selection of Rock Types 121 6.3 Material Sampling 123 6.4 Limestone 125 6.4.1 Particle Size Analysis 125 6.4.2 Material Loss .129 6.4.3 Energy Efficiency 130 6.4.4 Specific Surface Area ....132 6.4.5 Results 136 6.5 Quartz 137 6.5.1 . Particle Size Analysis .137 6.5.2 Material Loss 141 6.5.3 Energy Efficiency.. 142 6.5.4 Specific Surface Area 143 6.5.5 Results 147 6.6 Rock Salt 148 6.6.1 Particle Size Analysis. 148 6.6.2 Material Loss 150 6.6.3 Energy Efficiency 152 6.6.4 Specific Surface Area .< 153 6.6.5 Results ...154 6.7 Comparison of Energy Efficiencies 155 6.8 Comparison to Bond Energy 156 6.8.1 Work Index Correlation ; 156 6.8.2 Bond Work Input and Velocity 157 6.8.3 Bond Work Input and Energy Input 160 CHAPTER 7 RESULTS AND DISCUSSIONS ...161 7.1 Energy Input Model 162 7.2 Impact Velocity Model 165 7.3 Influence of Poisson's Ratio .....168 7.4 Pressure Model of Work Efficiency 169 7.5 Model Adjustment 174 7.6 Efficiency of Bond Energy Formula.. 175 7.7 Measurement of Free Surface Energy 180 7.8 Effect of Material Porosity ..' 183 7.9 Material Loss during Testing . 184 7.10 Assumptions with BET Measurements..... 185 7.11 Direct and Indirect Tensile Stress ; 186 7.12 Particle Size Considerations 186 7.13 Air and Moisture Content 187 7.14 Temperature Measurements ..188 7.15 Electrostatic Charges 189 7.16 Projectile and Target Bed 189 7.17 Actual Energy Consumption : 190 7.18 Future Research '. 191 i CHAPTER 8 CONCLUSIONS AND RECOMMENDATIONS.... ...192 CHAPTER 9 CLAIMS TO ORIGINAL RESEARCH 194 REFERENCES: : 195 APPENDIX A: EXAMPLES OF STRESS-STRAIN CALCULATIONS 206 APPENDIX B: SURFACE AREA MEASUREMENT (COARSEST PIECE) 210 APPENDIX C: SURFACE AREA CALCULATIONS (FINE/COARSE) .214 viii A P P E N D I X D: M O R E S E M E X A M I N A T I O N S 1 ...216 A P P E N D I X E : A P P A R A T U S M A I N E Q U I P M E N T D R A W I N G S „ 220 A P P E N D I X F: R O C K A N D P R O J E C T I L E M A S S A L T E R N A T I V E S 230 A P P E N D I X G : A P P A R A T U S D E S I G N C A L C U L A T I O N S 232 A P P E N D I X H : P A R T I C L E SIZE DISTRIBUTION ( L I M E S T O N E ) ......237 A P P E N D I X I: SPECIFIC S U R F A C E A R E A M E A S U R E . ( L I M E S T O N E ) 241 A P P E N D I X J : P A R T I C L E SIZE D I S T R I B U T I O N ( Q U A R T Z ) '. 242 A P P E N D I X K : SPECIFIC S U R F A C E A R E A M E A S U R E M E N T (QUARTZ) . . . 247 A P P E N D I X L : P A R T I C L E SIZE D I S T R I B U T I O N (SALT) ; 248 A P P E N D I X M : SPECIFIC S U R F A C E A R E A M E A S U R E M E N T (SALT) 250 A P P E N D I X N: B A L L / R O D M I L L G R I N D A B I L I T Y T E S T S 251 ix TABLE OF FIGURES Figure 1.1 Energy distribution during comminution process : 2 Figure 1. 2 Comminution inefficiency ,. 7 Figure 1. 3 Inherent flaws in a particle (Tromans and Meech, 2004) 8 Figure 2.1 Schematic performance of a Barmac crusher 23 Figure 2. 2 Schematic performance of a HPGR 25 Figure 2:3 Relationship between energy input and particle size in . comminution (After Hukki 1961) 32 Figure 2. 4 Mass balance for a single size fraction (Modified after .35 Figure 3.1 Rock displacement effects (Modified after Lowrie, 1997)... 38 Figure 3. 2 Idealized stress-strain responses for a cylindrical rock sample .39 Figure 3. 3 (a) transgranular fracture (b) grain boundary fracture ...41 Figure 3. 4 Various fracture modes: brittle fracture mode I (a, b), mode II (c, d), mode III (e, f) and ductile fracture (g), (Courtney, 1990) 43 Figure 3. 5 Tensile stress adjacent to an elliptical crack. Fracture is possible 46 Figure 3. 6 Total system energy as a function of half crack length 47 Figure 3. 7 Effects of strain rate on strength of Tuff (Olsson, 1991) 49 Figure 3. 8 Typical static and dynamic loading 51 Figure 3. 9 Fragment distribution curves for brittle and ductile fracture under dynamic tensile loading (Grady, 1981) ..........54 Figure 3.10 Specific surface area (SSA) distribution as a function of particle size for brittle and ductile fracture... '. 55 x Figure 3.11 Schematic of a split Hopkinson pressure bar 62 Figure 3.12 Two-stage light gas gun 64 Figure 4.1 Conceptual Model of Energy Efficiency 72 Figure 4. 2 Roughness of technical surfaces (Schey, 1987) 74 Figure 4. 3 Effect of resolution on roughness and surface area measurement. 80 Figure 4. 4 Stress versus strain curves for drill core of rock samples (Tuff) 82 Figure 4. 5 Surface topography of the rock fracture (HV1) 84 Figure 4. 6 Surface topography of the rock fracture (HV2).:. ...84 Figure 4. 7 Surface topography of the rock fracture (HV3) . 85 Figure 4. 8 Surface topography of the rock fracture (HV4) 85 Figure 4. 9 Example of the trace profile in the " X " direction 86 Figure 4.10 Roughness factor measurements along traces 87 Figure 4.11 Comparison of roughness factor along the traces 88 Figure 4.12 Roughness and surface factor vs. loading rate 90 Figure 4.13 Theoretical calculation of specific surface area 91 Figure 4.14 Direct measurement of the specific surface area (coarsest pieces)........ 92 Figure 4.15 Estimation of surface roughness as a function of particle size for a measurement resolution of 4 A .93 Figure 4.16 Energy efficiency of breakage and power efficiency 97 Figure 4.17 SEM examinations of the samples 98 Figure 5.1 Apparatus general configuration 103 Figure 5. 2 UBC-CERM3 high-velocity-impact comminution apparatus 104 xi Figure 5. 3 Target chamber 106 Figure 5. 4 Launch tube length as a function of air pressure 110 Figure 5. 5 Reservoir connection to the compressor and divider 112 Figure 5. 6 Divider multi-task interactions 113 Figure 5. 7 GardnerrDenver compressor 114 Figure 5. 8 Quick opening solenoid valve ...115 Figure 5. 9 Sequence of operation for installed solenoid valves... 116 i' ' Figure 5.10 Vacuum pump in the supply line 117 Figure 5.11 Laser measurement system ....119 Figure 6.1 Particle size analysis before and after breakage at variable impact velocities (Limestone - 75 mm)...... 126 Figure 6. 2 Particle size analysis before and after breakage at variable impact velocities (Limestone - 150 mm) 127 Figure 6. 3 Weight percent of-1 mm vs impact velocity (Limestone) 128 Figure 6. 4 Material loss vs impact velocity (Limestone) 130 Figure 6. 5 Specific surface area vs impact velocity (Limestone) - The minimum & maximum measurements of BET for SSA before breakage are indicated as the range 133 Figure 6. 6 Specific surface area vs particle size (Limestone - zone A) 134 Figure 6. 7 Specific surface area vs particle size (Limestone - zone B) 135 Figure 6. 8 Energy efficiency vs impact velocity (Limestone) 136 x i i Figure 6. 9 Particle size analysis before and after breakage at variable impact velocities (Quartz - 75 mm) ;..138 Figure 6.10 Particle size analysis before and after breakage at variable impact yelocities (Quartz - 150 mm) 139 Figure 6.11 Weight percent of -1 mm vs impact velocity (Quartz) 140 Figure 6.12 Material loss vs impact velocity (Quartz) 142 Figure 6.13 Specific surface area vs impact velocity (Quartz) 144 Figure 6.14 Specific surface area vs particle size (Quartz - zone A).. 145 Figure 6.15 Specific surface area vs particle size (Quartz - zone B) 146 Figure 6.16 Energy efficiency vs impact velocity (Quartz) 147 Figure 6.17 Particle size analysis before and after breakage at variable impact velocities (Rock Salt - 75 mm) 149 Figure 6.18 Weight percent of -1 mm vs impact velocity (Rock Salt) 150 Figure 6.19 Material loss vs impact velocity (Rock Salt) 151 Figure 6. 20 Specific surface area vs impact velocity (Rock Salt) 153 Figure 6. 21 Energy efficiency vs impact velocity (Rock Salt) 154 Figure 6. 22 Comparison of energy efficiencies. 155 Figure 6. 23 Bond work input as a function of impact velocity 159 Figure 6. 24 Bond work input as a function of total energy input 160 Figure 7.1 Energy efficiency vs specific energy input. 163 Figure 7. 2 Energy efficiency vs impact velocity 166 Figure 7. 3 Energy efficiency vs Poisson's ratio (Efficiency® V=200 m/s) 168 xiii Figure 7. 4 Efficiency of Bond formula to predict energy utilization as a function of impact velocity 179 1 ' xiv LIST OF TABLES Table 1.1 Energy consumption by unit operation (After Workman, 2003) ...4 o Table 2.1 Comminution unit operations . 19 Table 4.1 Characteristics of Tuff sample.......... .....81 Table 4. 2 Coefficient of surface and roughness factor 89 Table 4. 3 Estimation of surface area based on theory, measurement and calculation 94 Table 4. 4 Estimation of produced surface area of breakage in an MTS machine. 96 Table 4. 5 Estimation of energy and power efficiency of breakage in an MTS machine. 96 Table 5.1 Chamber and projectile design alternatives 105 Table 5. 2 Launch tube inside diameter versus sabot and projectile mass 108 Table 5. 3 Launch tube length 110 Table 5. 4 Theoretical velocities at different gas pressure I l l Table 6.1 Properties of rock samples as used in this test work 122 Table 6. 2 Characteristics of rock samples 123 Table 6. 3 Sample name designation 124 Table 6. 4 Particle size distribution of representative.sample (Limestone) 125 Table 6. 5 Material loss during experiment (Limestone) 129 Table 6. 6 Calculation of energy efficiency, SE = 1.0 Jrii"2 (Limestone) 132 xv T a b l e 6. 7 S p e c i f i c s u r f a c e a r e a a n d s p l i t s i z e ( L i m e s t o n e - z o n e A ) ( g e o m e t r i c a l m e a n p a r t i c l e s i z e ) 1 3 4 T a b l e 6. 8 S p e c i f i c s u r f a c e a r e a a n d s p l i t s i z e ( L i m e s t o n e - z o n e B ) ( g e o m e t r i c a l m e a n p a r t i c l e s i z e ) 1 3 5 T a b l e 6. 9 P a r t i c l e s i z e d i s t r i b u t i o n o f r e p r e s e n t a t i v e s a m p l e ( Q u a r t z ) . . 1 3 7 T a b l e 6 . 1 0 M a t e r i a l l o s s d u r i n g e x p e r i m e n t ( Q u a r t z ) . . 141 T a b l e 6. l l C a l c u l a t i o n o f e n e r g y e f f i c i e n c y ( Q u a r t z ) . 1 4 3 1 T a b l e 6 . 1 2 S p e c i f i c s u r f a c e a r e a a n d s p l i t s i z e ( Q u a r t z - z o n e A ) ( g e o m e t r i c a l 1 m e a n p a r t i c l e s i z e ) 1 4 5 T a b l e 6 . 1 3 S p e c i f i c s u r f a c e a r e a a n d s p l i t s i z e ( Q u a r t z - z o n e B ) ( g e o m e t r i c a l i m e a n p a r t i c l e s i z e ) : : 1 4 6 T a b l e 6 . 1 4 P a r t i c l e s i z e d i s t r i b u t i o n o f r e p r e s e n t a t i v e s a m p l e ( R o c k S a l t ) 1 4 8 T a b l e 6 . 1 5 M a t e r i a l L o s s d u r i n g e x p e r i m e n t ( R o c k S a l t ) 151 T a b l e 6 . 1 6 C a l c u l a t i o n o f e n e r g y e f f i c i e n c y ( R o c k S a l t ) . . ; 1 5 2 T a b l e 6 . 1 7 B o n d w o r k i n d e x m e a s u r e m e n t s . 1 5 6 T a b l e 6 . 1 8 B o n d w o r k i n p u t c a l c u l a t i o n s ( L i m e s t o n e ) 1 5 7 T a b l e 6 . 1 9 B o n d w o r k i n p u t c a l c u l a t i o n s ( Q u a r t z ) : 1 5 8 T a b l e 6. 2 0 B o n d w o r k i n p u t c a l c u l a t i o n s ( R o c k S a l t ) 1 5 8 T a b l e 1.1 C a l c u l a t i o n o f i m p a c t p r e s s u r e a n d v o l u m e ( z o n e A ) 1 7 0 T a b l e 7. 2 P r e s s u r e m o d e l o f m a x i m u m e n e r g y e f f i c i e n c y ( z o n e A ) 171 T a b l e 7. 3 C a l c u l a t i o n o f i m p a c t p r e s s u r e a n d v o l u m e ( z o n e B ) 1 7 2 T a b l e 7. 4 P r e s s u r e m o d e l o f m a x i m u m w o r k e f f i c i e n c y ( z o n e B ) 1 7 3 xvi Table 7. 5 Efficiency based on Bond work input (Limestone) 176 Table 1. 6 Efficiency based on Bond work input (Quartz) 177 Table 7. 7 Efficiency based on Bond work input (Rock Salt) 178 Table 7. 8 Specific surface energy and energy efficiency @ 150 m/s 182 i i xvii N O M E N C L A T U R E a Flaw size (m) A Launch tube cross section area (m2) A Angstrom (= 10"7 mm) A G Autogenous grinding bij . Breakage function c '' 1 Half of crack length c* Crack of half-length in unstable equilibrium (dU/dc = 0) d Grain size D Fractal dimension D Resolution, dE Incremental energy dX Incremental change in size d50 Particle size (% 50 passing) (um) d80 Particle size (% 80 passing) (jam) E Young's modulus of elasticity (pa) E; ' Specific energy input (J/g) . E M L ' Electromagnetic launcher FoS Factor of safety F80 . Feed size (% 80 passing) (um) g ' Acceleration due to Earth's gravity Gic ' Fracture toughness (Jm") xviii H c Chamber height (cm) HPB Hopkinson Pressure Bar HPGR High Pressure Grinding Rolls i , Feed size fraction ID Inside diameter K B Bond index (kWh/t) Ke Energy input index (% g21 J2) K i Stress intensity factor Kic Critical stress intensity factor Ki Rate of breakage (min"1) K k Kick index (kWh/t) K R Rittinger index (kWh/t) K v Velocity index (s/m) L Total length (fractal) L Launch tube length (m) Lp Projectile length (cm) M Striker mass (kg) Mp Projectile mass (g) M R Rock mass (g) MTS Materials Testing System n Top size N Number of scales (integer) • P Power draw (kW) P Pressure (N/m2) psi Pound per square inches P8.0 Product size (% 80 passing).(pm) r Bolt radius (mm) R Tube outside radius (m) R a Arithmetical average Rc Chamber radius (cm) R O M Run of Mine Rq' Root mean square R t ; Height from maximum peak to deepest trough S Shear strength (Mpa) 1 SA Surface area (m2) S A G Semi-autogenous grinding SD , Standard deviation SE Specific surface energy (Jm"2) S E M Scanning Electron Microscopy S.F . • Safety factor S.G Specific gravity SHPB Split Hopkinson Pressure Bar Sj Breakage matrix Sj Mass of i t h size fraction in the mill 2 S.S.A Specific surface area (m /g) t Minimum thickness (m) T Tensile strength (Mpa). T Throughput (t/h) UCS " Uniaxial Compressive Strength UFLC Ultra-fast Load Cell Y Projectile velocity (ms"1) Vc Chamber volume (cm3) W Work input (kWh/t) W i Work index (kWh/t) . x . Feed size X , Particle size Y Shape factor (crack geometry) Y Size of measurement (scale) Ad Change in displacement (mm) . AP Change in pressure (pa) AV Change in volume (m 3), • ss Specimen strain rate 7 Specific surface energy (Jm"). , • rj Energy efficiency (%) 1 7]e Energy efficiency (based on specific energy input) (%) Tjv . . Energy efficiency (based on impact velocity) (%) /is Microsecond (= 10~6 sec) v Poisson's ratio crc Critical tensile stress (pa) <7S Specimen stress o v Yield point (yield stress) A C K N O W L E D G M E N T To prepare this work, I received advice, support, assistance and encouragement from many people whom I would like to take this opportunity to acknowledge: M y special gratitude and appreciation is extended to my thesis supervisor Professor John Meech who constantly provided me.with invaluable advice, comments and resources for the work. His endless support, encouragement and guidance enabled me to glimmer new ideas and gain significant experience during this study. I would like to express thanks to Professor Desmond Tromahs from materials engineering department for his input, comments and support. I would like to thank Professor Farrokh Sassani from mechanical engineering department and Professor Mory Ghomshei from mining engineering department for their constructive.comments and,suggestions. • I would also like to thank members of the mining department faculty and staff for their assistance throughout my studies. I would like to acknowledge financial support from Canada Foundation • for Innovation. (CFI), Natural Sciences and Engineering Research Council of Canada (NSERC), and Center for Environmental Research in Minerals, Metals and Materials (CERM3) during the course of this research. I am also grateful to my parents, Dr. Seyed-Abbas Sadrai and Mrs. Nasrin Sadrai, for their patience and' support during my doctoral studies. As a result, a copy of this thesis wil l be presented to them to articulate my tremendous appreciation. xxm C H A P T E R 1 I N T R O D U C T I O N . During the last decade, as competition has intensified in the world mining industry, Canadian mines'have continued to pursue lower operating costs. Typical operating costs can be divided between extraction (30-70 %), comminution (30-50 %) and separation (5-20 %). Comminution costs, representing an important contribution to, mining operating costs.! can themselves be divided roughly between energy (50%) and liner/charge wear. (50%) (Radziszewski, 2000). Thus, every aspect of comminution justifies careful consideration1 in order to minimize all elements of cost and associated energy consumption. Crushing and grinding are essential components in most mining and mineral processing operations to reduce the size of ore and rock, and subsequently liberate the valuable mineral for beneficiation. However, comminution is very energy-intensive and consumes a major percentage of the total energy used during mineral recovery. Typically, at least half of the energy (50-70 %) used in a mineral processing plant is expended on size reduction arid the liberation of minerals (Walkiewicz et al, 1996). . The energy efficiency of comminution, which has been a subject of considerable controversy, can be measured as the ratio of the useful output from a machine to the energy input into it. In many cases, the efficiency of comminution has been measured as the ratio of energy "required" to energy used which accounts for the efficiency by which the process runs at near maximum tonnage rate. From a fundamental viewpoint, 1 it is the energy required to create new surfaces that should be considered. By this definition, comminution is found to be of the order of 1% efficient (Whittles et al, 2003; Tromans and Meech, 2002; Fuerstenau and Abouzeid, 2002; Rhodes, 1998; Walkiewicz et al, 1996). Therefore, as shown in Figure 1.1, most of the energy input into comminution processes ends up as heat generated within the material, rock and water, and equipment to eventually be dissipated into the surrounding atmosphere. As an example, in measurements performed on a large ball mill, less than 1 % of the total energy is spent on the fracture process, while 85% is dissipated as heat and 12% corresponds to electro-mechanical losses, with the balance representing other losses such as kinetic energy and noise (Alvarado et al, 1998). 1% 8 5 % • Energy Efficiency • Heat Loss • Electromechanical Loss • Other (Kinetics, Noise) Figure 1.1 Energy distribution during comminution process 2 These facts indicate a need to improve energy efficiency in comminution and justify researching the decrease of energy input for size reduction. Even slight enhancement could result in the saving of considerable amounts of energy and/or improvements in mineral liberation. This provides the possibility of processing lower grade and more complex ore that at present are difficult to treat economically. 1.1 Energy Consumption of Comminution Stages It has been reported that about 3% of the, world's electrical energy was consumed by crushing and grinding in 1976 (Fuerstenau and Abouzeid, 2002). In United States, a survey indicated that 1.3 % of the electrical energy was consumed for comminution in the year 1978 (Schoenert, 1986). The role of microfractures in determining energy consumption is very important, especially during grinding. It is generally considered that fragments become harder to break at each stage of size reduction, because as the feed becomes finer in size, there are fewer and fewer geological and blast-induced fractures present in the fragments. Therefore, grinding has the lowest density of macro fractures and microfractures of any comminution pro.cess that survive to reduce resistance to grinding. For this reason, grinding is the most energy-consuming stage of comminution. Overall reduction, performed in a series of stages may be from an 80% feed size passing 40 cm to a final product size of 80% passing 400 mesh (37 pm). Table 1.1 3 I shows the range of feed and product size, energy input, and energy cost for each unit operation for taconite ore (Workman and Eloranta, 2003). In grinding, size is reduced by a factor of 360, while this factor in primary and secondary crushing is about 4 and 5 respectively. i Operation1 Feed Size (cm). Product Size (cm) Work Input (kWh/ton) Energy Cost ($/ton) (%) Work Index (kWh/ton) Explosives CO 40 ' 0.24 0.087 5.8 15.18 Primary Crushing 40 10.2 0.23 0.016 1.1 14.84 Secondary Crushing 10.2 1.91 0.61 0.043 2.9 14.86 Grinding •1.91 . 0.0053 19.35 1.35 90.2 14.87 Total 20.43 ' 1.496 100 Table 1.1 Energy consumption by unit operation (After Workman, 2003) 4 For ultra-fine grinding as the particle size drops below 50 microns, the absence of microfractures results in a doubling or tripling of the'work index. For sizes below 1 micron, an order of magnitude increase in work index is typical. , This study will determine how different fates of strain affect rock fragmentation . and energy efficiency of crushing and grinding. If a continuum deforms continuously under an applied stress and with small deformation, then the operative phenomenon is velocity, not displacement, and the normalized velocity is indicative of the strain-rate. The development of strain-rate and the strain-rate tensor is exactly analogous to the development of strain and the strain tensor, with velocity replacing displacement. 1.2 Problem Statement 1.2.1 Comminution Efficiency One approach to evaluating comminution efficiency is based on the energy to produce new surface area. In earlier years, comminution efficiency was defined as the ratio of the energy of the new surface created during size reduction (based, on the .i surface free energy of solids) to the mechanical energy supplied to the machine performing. the material size reduction (Fuerstenau and Abouzeid, 2002). The work input is proportional to the new crack tip length produced in particle breakage, and equals the energy represented in the product minus that represented in the feed. :, The, results of previous theoretical work by researchers indicate that the energy efficiency during conventional crushing and grinding of minerals is very low, of the order of 1-2 %. For example, theoretical comminution efficiencies for ionic minerals such as Hematite, Magnetite and Pyrite are 1.76, 1.38 and 0.78 respectively (Tromans and Meech, 2002). Similarly, the estimated energy efficiencies for crushing and grinding of covalent minerals such as Quartzite'and Quartz are very low, of the order of 1 % or less. Consequently, a great deal of energy is lost in operating mill equipment and perhaps in particle deformation especially at very small particle size (Tromans and Meech, 2001). Corrrminution inefficiency can be best described with reference to 'Figure 1.2. The sequence of comminution in mining operation commences with Run of Mine (ROM) resulting from excavation of material via underground and open pit methods. It can be • . i seen that a large amount of input energy in the form of electrical energy is expended for the crushing and grinding operations. Comminution stages are eventually closed by transferring broken rock to the next stage or separation. According to the definition, the output of this system is illustrated as the creation of new surface area. However, the small arrow is indicative of spending only a small portion of input energy on rock fragmentation resulting to inefficient use, of energy. Most of the energy ends up as heat generated in the material, rock and water, and equipment, which eventually dissipates into the atmosphere. 6 INPUT (= Energy) ROM r_) OUTPUT (=? New Surface Area) Crushing Grinding Separation S S Heat • s' s Figure 1. 2 Comminution inefficiency 1.2.2 Impact Efficiency The impact efficiency of particle fracture depends on the loading force, the size and orientation of inherent flaws and other fracture mechanics features (Figure 1.3). In addition:, inefficiency is the result of numerous impacts before one sufficient force causes particle fracture (King and Tavares, 1997), Many impacts may be required'to achieve particle fracture depending on the loading, force, the cyclic nature of loading, and the orientation of particles between consecutive impacts. P Figure 1. 3 Inherent flaws in a particle (Tromans and Meech, 2004) Unsuccessful impacts generate elastic strain energy in the particle as thermal energy without producing any new surface area, thus, contributing to the overall inefficiency of the comminution process (Tromans and Meech, 2004). Fracture energy at a crack tip may be consumed not only in the production of new surfaces but also in plastic deformation in the region of the crack (after Rumpf, 1973), i.e. generation of defects. The actual fracture energy is the energy needed to break chemical bonds within the material when forming new surface area as well as an activation energy at the crack tip, which is converted to heat to some extent, and partially used to alter the atomic structure to a depth of many layers thus transforming the affected material to an "amorphous" state. 1 • When a particle is subjected to opposing impact forces, these forces create a compressive stress along the axis of impact and a tensile stress within the particle that is normal to the impact, axis. Interaction of compressive and tensile forces on the plane of a crack may lead to the failure of the material. Thus, flaw orientation is one of the most important factors that determine impact efficiency. It is assumed that the major mechanisms of breakage in comminution occur, by either impact or attrition (shear) loading. Yet, it is unclear which type of failure is more or less efficient. Traditionally, ball mills and rod mills have been used in comminution circuits in which the values of the loading forces in these machines have a wide distribution, leading to inefficient fracture. The best way to improve control of the load distribution is to use high compression roller mills (Daniel and Morrell, 2004). That is, impact acts only at the contact location on the particle whereas in compression loading, the forces act more generally within the particle in a variety of directions. In addition, the fragments produced in compression may be kept in place while under impact they obtain significant kinetic energy that may be consumed' as elastic waves. In fact, there is a perceptual trend in the use of high-pressure rolls crushing in industry to replace conventional, secondary cone crushing operations because of decreases in energy consumption. 1.3 Hypothesis of the Thesis In view of the large portion of comminution costs represented' by energy, it is clear that crushing and grinding are the most important subjects of interests to the mineral processing industry. Comminution may be regarded as a process of conversion of energy from one form to another. The kinetic energy expended is recovered in the form of potential energy (surface energy), heat and sound. The data indicate that crashing and grinding efficiencies range from a small fraction of 1 percent to a very few percent. It is not known why efficiencies of effective comminution machines should be so low. On the other hand, blasting as the first stage of comminuting materials represents efficiencies of an order of magnitude (e.g. 20%) higher than comminution equipment. The overall efficiency of blasting may be three times more cost effective than that of grinding.; In addition, electrical energy is at least five times' cheaper than powder energy (Eloranta, 1995)1 This, combination suggests that blasting is fifteen times more 10 efficient than grinding, which is consistent with their estimations. In blasting, sudden increases in pressure and rapid deposition of energy in a few milliseconds cause the rock to fracture: Blasting impacts produce shock waves, in all directions which move throughout the rock with velocities of more than 2 kms"1. It is worth mentioning that the amount of energy released from 1 .gram of explosive is less than the amount of energy stored in 1 gram of oil or gas. However, the rate of energy release is about two million times higher (Afrouz, 1985). Thus, the hypotheses herein considered indicate that the application of high velocity impacts and/or high-strain rates on materials and/or rock may enhance the energy efficiency of comminution. Unlike conventional studies in which the goal has been to improve the strength of materials rather than improving the degree of fragmentation, this thesis is focused on, improving comminution practices, hence the degree of fragmentation and energy use. 1.4 Thesis Objectives The aim of this study is to find ways and methods to improve energy efficiency of comminution processes and. equipment with the main purpose of decreasing associated operating cost of energy consumption. In light of this goal, the following objectives have been set: ' 11 ] > To gain a fundamental understanding of the fracture mechanics involved in the process of rock breakage, and the factors that may contribute to energy distribution during crushing and grinding. • . , >, To examine the relationship between energy input and new surface area created within rock fragmentation along with the influence of different rates of strain. > To develop a technique to measure surface roughness as well as study the effect of resolution on surface area and roughness measurements. > To develop a new technique to calculate surface area of broken rock. > To establish a new estimation method for energy efficiency calculations under static regime fragmentation! > To build a new instrument to .measure the effect of high strain rate and high velocity impact on rock samples, and evaluate its proper performance. > To interpret the results of laboratory experiments that examine the effect of velocity impacts on energy efficiency of breaking different rock samples. i . • • • 1.5 Organization of the Thesis This dissertation is. prepared to examine comminution with respect to energy efficiency. The report is divided into nine chapters including the conclusion. The purpose of this study and the scientific rationale for the investigation, the. main objectives and significance of the work are covered in Chapter 1. The state of the art of conventional comminution processes and technology is reviewed in Chapter 2. In ' ' •' ' , . • '12 Chapter 3, fracture mechanics concepts, mechanical behavior of materials arid mechanisms of breakage under high impact loading are discussed. The influence of impact velocity on fragmentation and the energy efficiency of comminution in a static regime1 are described in Chapter 4. The methodology used to analyze the effect of high strain rates on fragmentation and energy efficiency is. presented. The influence of surface roughness and surface area as well as the resolution effect on surface area measurements is discussed in this chapter. Also, two novel techniques developed to measure surface roughness and surface area measurements are presented. Chapter 5 delineates the design and development of a new apparatus to implement high velocity impact on rock fragmentation. A l l features of the machine are also presented in detail. Experimental studies carried out with the device, and the testwork program and analysis are described in Chapter 6. A breakage model to measure the energy efficiency of particulate material is also developed in this section. The overall results and discussions are presented in Chapter 7. Finally, Chapter 8 closes this study by making conclusions and recommendations for future research in this field. And, Chapter 9 explains how this, study opens up a new line of research for future development. 13 CHAPTER 2 CONVENTIONAL COMMINUTION PROCESSES 2.1 Overview The word "comminution" derives from a Latin word meaning "to make smaller". The breaking of rock from large particles to small'ones has a pedigree stretching into human history to build shelters, roads and tools (Napier-Munn et al, 1999). The mining industry has exhausted considerable amounts of money and time in development of new strategies to improve equipment productivity and performance in areas such as drilling, blasting, pulp density, media, speed, etc. Most attempts have been conducted on the design of new equipment, optimization of existing equipment, simulation and computerized control of the process. The development.of A G mill (autogenous/grinding), S A G mill (semi-autogenous grinding), high-pressure grinding rolls and roller crushers are the results of these attempts. Although these efforts have been continued for decades, comminution efficiencies have shown no significant improvements. Earlier studies demonstrate the complexity of breakage of particulate materials and the need to better understand' its fundamental aspects. One approach may take the benefit of latest advancements in other industries like "Impact Engineering" by merging the technology into mining industry. A brief review of the existing literature carried out on the principles of comminution technology and equipment will illustrate the gaps that exist in current knowledge. 1 14 2.2 Mineral Liberation One of the objectives of comminution is to liberate dissimilar minerals from attachment to one other. In fact, this physical objective is the principal goal of 1 i comminution rather than chemical purposes which may be sought in , separation processes. Separation is impracticable, i f liberation has not been successfully accomplished. Therefore, production of a reasonable degree of liberation is prerequisite to making a fair and successful separation of minerals. Ore particles can consist of a single mineral, icalled free particles, or two or more minerals, called locked particles. The degree of liberation of a certain mineral or phase is the percentage of that mineral or phase occurring as free particles in relation to the total of that mineral occurring , in the free and locked forms. Therefore, liberation is increased in comminution by two means, liberation by size reduction and liberation by detachment. Liberation is achieved by means of grain boundary and transgranular fracture. As particle size decreases, the free to locked ratio (F/L) of a material species increases. The size at which 100% liberation occurs is called the liberation size (F/L = 99/1) for valuable mineral. For gangue, this size might give ah area or volume ratio of (F/L = 90/10). So the grade of valuable locked particles would be 3% by weight of mineral content (0.03/0.097 = 3%) taking into account specific gravity differences. The degree of liberation, can be determined by making a large number of separation tests conducted on a product crushed or ground to a different degree. The ' ' , 15 trade-off between increased cprnminution costs and the metallurgical improvement may determine the conditions which is the most advantageous from an economic point of view. Generally, quantitative determination of the degree of liberation is. of practical value to the operator or testing engineer. Also, by using a microscope counting technique, it is possible to calculate the degree of association of minerals that form locked particles and the extent to which each mineral contributes to each particular type of locked particle. 2.3 Current Comminution Technology i Modern industries use Comminution technology over a wide range, from crushing > of mined pre to very fine grinding to produce advanced materials. ,Li mining, rock cutting and blasting can be considered the first stage of comminution, and integrating the comminution stages in a holistic way can produce substantial economic benefits to the industry. Nearly all mining and mineral processing operations are major users of comminution equipment., The grinding process, the most energy-consuming stage, accounts for 90% of the energy used to break rock while crushing uses about 5-7% and explosives 3-5% (Alvarado et al, 1998).. 16 2.3.1 Blasting Operation In most mining operations and construction industries, the extraction of rock mass and subsequent fragmentation generally involves blasting techniques. The detonation of an explosive charge susceptible to impact produces stress waves and an explosive gas which significantly contribute to fragmentation and movement of the material. The stress waves propagate throughout the rock in all directions with velocities of 2 km. s"1 or more. The passage of these waves causes formation of crack patterns that separate as a result of the high pressure of the explosion gas on the crack surfaces. The transmitted energy at the free face produces tensile stresses that move the overburden. The in-situ rock also consists of many discontinuities .such as joints, faults and beddings which help the explosion gas to penetrate through the rock mass as it expands. There are numerous reasons for the high efficiency of blasting with respect to energy. The impact velocity loading during ah explosion is much higher than that produced in conventional equipment which, increases the crack density. Also, the existence, and frequency of joints and discontinuities create weak zones that help break the rock mass more easily. . In rock blasting techniques, the drill holes, consisting of explosives and stemming materials, are created in a unique pattern depending on the strength of the rock mass, the amount Of explosives used and its power, the diameter of the holes, and the fragment size distribution required for further processing of the material. Generally, • 17 the constraint has been on the top size of material required to move the rock to a dump or to,a crusher. More recently, studies have shown that there are benefits to increasing the degree of blasting to higher levels producing a finer top size for the primary crusher and a material with higher crack densities (Dance, 2001). 2.3.2 Unit Operations Comminution is the size reduction of solid materials through the application of energy, usually by means of mechanical forces. The main objectives of comminution processes can be defined as following: l . i . To liberate valuable minerals from waste prior to concentration1. 2. To increase surface area available for chemical reaction. ' 3. To produce mineral particles of required size and shape. Comminution Circuits can be chosen as open or closed circuit: These circuits may include two to three stages of crushing accompanied with screening equipment to separate oversize material and return it to the crusher: Grinding also has several stages that depend on the top size of the material prepared by the previous stage along with classifiers that return coarse ore back to the mill. Comminution includes'the unit operations as shown in Table 1.1. 18 I. MILLS SIZING CRUSHERS Tumbling mills Stirred mills Other PROCESS (Integral Part) Jaw crusher 1 Ball mills Tower mills Jet mills Screens Cone crusher . Rod mills Horizontal pin mills Hydrocyclones Gyratory crusher Autogenous (AG) mills Vertical pin mills Sieve bends Roll crusher Semi-autogenous (SAG) mills . Other classifiers Impact crusher Pebble mills High pressure grinding rolls Table 2.1 Comminution unit operations 2.3.3 Crushing Operation Crushing may be defined as the operation whose object is to reduce large lumps to fragments. Although, the main object of crushing is size reduction, this is occasionally coupled with a requirement for the production of a minimum amount of fines. 19 Crushers have1 been designed to reduce all rock fragments finer than a definite maximum size. But, no crusher has ever been devised to produce only material exceeding a certain minimum size. To compare the performance of different crushing machines, the reduction ratio can be defined as the ratio of particle size %80 passing in the feed and in the product. The crushing action in all machines results from stresses applied to the particles to be crushed by some moving part in the machine, working against a stationary part or against some other moving part. ,The stresses implement strains within the particle to be broken which result, in fracturing whenever they exceed the elastic limit of the material. This explains why crushing machines' are very rugged and massive. Crushers can be used for coarse or primary breakage, intermediate or secondary • crushing, fine crushing and for special uses. Coarse crushing is always conducted on dry material, and the tendency is also.to conduct.intermediate crushing on a dry basis, however, roll crushers are still used to crush wet material. i . 2.3.4 Grinding Operation Grinding is an operation whose objective, similar to that of crushing, is to reduce size, but in this case to a relatively much finer material. It may be said that grinding is the breaking down to the ultimate fineness to which comminution is conducted of the relatively coarse particles made by crushing. In this method of comminution, a heavy •' .20 surface is caused to slide or roll over another, surface, the material to be ground being caught between the two surfaces. In grinding, rupture is affected through development of shearing and impact stresses. In the case of ball milling, the evidence seems to favor the impact fracturing, whether the impact is caused by the blow of falling balls or by the rolling of one layer of balls on another. The reduction ratio in grinding is large compared with ratios obtainable from crushing devices. For example, instead of ranging from 5 to 8 for crushing, the reduction ratio range can be as large as 50 to 100 for a ball mill circuit. Grinding mills are usually employed to grind ore in wet pulp. But for some purposes especially in chemical industries, ball mills are used to grind dry. For example, for coal preparation, dry-grinding ball mills are connected in closed circuit with pneumatic classifiers. Dry7grinding mills are often employed to produce an extremely fine product. 2.3.5 Special Equipment Of all unit operations, the generations of high rates of strain are relevant in certain impact crushers1 such as Barmac crusher, high pressure grinding rolls (HPGR) and roller crusher, and jet mills. These units are reputed to offer improved efficiencies up to as high as 7-8% (Meech, 2004 - Private comminication) for high-pressure grinding rolls but the, mechanisms that produce this increase is not yet fully understood. In i ' .'' 21 recent years, the intention to use this equipment in mining and in the cement'industry has increased due to the high efficiencies of energy use and improvements in wear rates. 2.3.5.1 Barmac Crusher Barmac crushers are mostly used in the cement and aggregate industries for highly abrasive materials. In1 this type of crushing, incoming rocks are distributed in and around the vertical shaft. Figure 2.1 shows schematic performance of a Barmac crusher. 1 i | . ' i . 1 The material that flows into the centre of the unit is accelerated by the centrifugal force of a rotor leading to high impacts with the rock lining (cascading material that drops around the perimeter of the crushing chamber). This rock-on-rock crushing involves several fracture modes such as impact, attrition and abrasion to reduce the size of material. The crushed rock then discharges by gravity from the crusher chamber. Simulation and modeling of pre-crushing of cement clinker using a Barmac crusher showed the overall energy efficiency of the circuit can be improved by about 5-15% (Jankovicet al, 2004; Sedet et al, 2006).'Replacement of a roller crusher circuit with Barmac crushers reduced operating costs and energy consumption of crushing up to 12% (Sandvik et al, 1999). A comparison between Barmac crusher and high 22 pressure grinding rolls (HPGR) indicates that while the cost of Barmac crushing is much lower, the benefits obtained from these two crushing operations are. the same (Sedet et al, 2006). The velocity of impact in Barmac crusher is about 40 m/s. 2.3.5.2 High Pressure Grinding Rolls Compression of particles between two plates has been shown to be the most energy efficient method of comminution (Schoenert, 1979). This was achieved by the invention of high pressure grinding rolls or roller crushers. During the last few years, applications of HPGR have increased significantly since its commercial introduction in 1985.. Various circuit configurations of HPGR have been developed in the mining and cement industry (Kellerwessel, 1996). There are strong signs of increased interest, particularly in copper and, iron ore processing (Lim et al, 1997). This new device offers considerably reduced energy consumption compared to semi-autogenous (SAG) and ball mills (Daniel and Morrell, 2004). Simulation and modeling has shown that use of HPGR technology will be even more attractive in the future (Morrell and Man, 1997). : ' . ' The conceptual performance of HPGR is illustrated in .Figure 2.2. Rock materials fall by gravity from a feeder installed above the machine and are compressed between two counter-rotating rolls. This creates compression forces along the particle bed which result in more efficient breakage than in. a ball mill (Schoenert, 1991). One i • . roller remains stationary while the other is movable, by a hydraulic cylinder in order to optimize the operating conditions. The gap/diameter ratio of the rollers is an important factor to determine throughput and corresponding power draw (Daniel and Morrell, 2004). ! 24 Figure 2 . 2 Schematic performance of a H P G R Tavares has demonstrated that.energy savings in HPGR are the combined1 result of the weakening of the particles and generation of more fines compared to other crushing methods (Tavares, 2005; Fuerstenau et al, 1999). The addition of an HPGR into an existing cement plant has proven successful by increasing the capacity and throughput, and decreasing the specific energy consumption (Aydogan et al, 2006). 25 2.3.5.3 Jet Mills Jet mills are used in industries for grinding of solid materials to ultra-fine sizes. The comminution process has been studied by researchers for the purpose, of understanding the particle breakage in jet milling. In air jet mills, particles fed from a nozzle into the spiral, are accelerated (up to 400 m/s) by the grinding air entering from other nozzles. After breakage in the tube, material is classified.from the center of the mill outlet.'Studies show that the feed rate, angle of feeding nozzle, and air flow rate have great influence on the breakage and chipping of particles in jet milling (Han et al, 2002). High pressure. water jet comminution has shown great potential in coal pulverization with low energy consumption and high comminution efficiency, and low equipment wear. The velocity of a water jet can reach 400 m/s. Particles obtain kinetic energy from the water jet in the mixing chamber and collide with each other and the target and disintegrate: Then, particle grading is done in a hydrocyclone. Energy consumption in a traditional ball mill is about two times more than that' of high pressure water jet mills (Cui et al, 2007) for the same/product size distribution. 26 2.4 Quality of Comminution Product 2.4.1 Particle Size Analysis Particle sizing in comminution is the separation of material after each stage into products characterized by different sizes. There are several methods to size mineral particles including screening, classification, and microscope sizing. It is important to know that in spite of whether the feed to. a crusher or a grinder is sized or not, the product of the unit operation will contain particles of all sizes from the coarsest to the finest. The coarsest size in the product is generally determined by the setting of the comminuting device and by the rate of rock passage. But, there is no way to establish a lower size limit for crushed or ground particles, resulting in the production of finer sizes than desirable. The practical issue is to minimize overgrinding as much as possible. i ' . From an experimental point of view, there are always particles finer than any size at which observation can be made. From a theoretical point of view, on the other hand, a particle finer than a molecule is unthinkable. This molecule produced by grinding will immediately condense oh a neighboring particle to.create the smallest possible solid particle as a unit crystal, i.e., the smallest physical assemblage of atoms or molecules possessing crystalline characteristics. For example, a unit crystal of silica consists of three Si02 molecules. The unit crystal of sodium chloride is a cube 5.6 A on edge while that of quartz is 4.8 A. ' 27 Graphical representation is one way to chart a size analysis. In one type, cumulative passing shows the percentage of the total weight, coarser than a given size. i . . . Normally, the particle size uses the actual screen opening expressed in microns and the graph is plotted on a log-log scale. The geometric sizing scale with a ratio of successive screens of V2has been regarded as a standard scale for some time, hi describing a screen, the. number of openings in microns per square inches of the screen determines the screen size in mesh, i.e. a 200 mesh screen has 200 openings.per inch, each opening being 75 microns square. • In laboratory screening, the material is placed on the coarsest screen on the top with a cover and a bottom. A nest of sieves is shaken in the machine from between 5 to 20 minutes. 2.4.2 Shape of Particles Particles are typically irregular in shape so it is actually' difficult to clearly understand what is meant by particle size. For instance, the size of particles as spheres is the diameter of the sphere. While with cubes, the particle size could be regarded as the edge, the long diagonal or perhaps the diameter of a sphere whose volume is equal to that of the cube. When a particle is measured with a yardstick, the greatest dimension is generally considered. In screening, sieves are made of woven wife having square openings and so the second largest dimension of the particles is the 28 most important. Although angular, the coarsest particles in comminuted products are frequently shaped differently than fine particles. Their shape is more regular in the sense that their three dimensions are more equal. This is considered to be due to the sizing action of most grinding equipment. If all particles in a comminuted product were of one regular shape like cubic, a close measurement of the surface presented by any sized fraction could, be made. Since the shape of the particles is not regular, the only possible way of such a measurement is to use a shape factor to refer the irregularity to a regular shape like cube. A convenient figure for this, factor has been suggested by Gaudin (1967). He indicated [that the shape factor for fine particles in practice for quartz ranges from 1.3 to 2.0 with the average near 1.75! That is, the irregularity shaped particles present 1.75 times as much surface as cubes of the same screen size. This factor can be measured as the ratio of the surface area for an average of each size fraction to the surface of a cube having the same length as the size fraction. Shape factor depends on some parameters such as material, grain size and unit crystal. i Another parameter widely used in determining the shape of particles is aspect ratio. It is the ratio of the greatest dimension of particle to the least one. i 29 2.4.3 , Produced Surface Area The surface area of crushed or ground rock can be estimated from a sizing analysis' together with the shape factor. This method is based on the fact that the surface area of a crushed product is inversely related to the particle size. For fairly-close sized product, average size is the arithmetic mean of that fraction size. But with unsized product, reference has been made to the average size of particulate products. One of most useful measures is the specific surface area (cm2/g) of the particles with the average size equaling the specific surface area of the sample. Therefore, i f all particles of a comminuted product have a regular shape such as a cube, tetrahedral or sphere, a close measurement of the surface area presented by any size fraction can be made. It is1 necessary to mention that much of the surface area in a crushed or ground product is in the finest size fraction. And, any possible error arising from improper surface determination of this size fraction is the greatest source of error. The specific surface energy of liquids can be measured with precision as it is the same as the surface tension. In the case of solids, indirect methods only are available t to determine surface energy since surface tension can not be measured. The surface energy of solids is large compared to that of liquids and divergent values are reported by different chemists. Practically, the surface energy of the common minerals is not yet known. It is obvious that a great difficulty in determining surface area produced by comminution lies in the .uncertainty due to particle shape and the estimation of the finest size fraction. / • ' ' • ' 30 2.5 Modeling Approach 2.5.1 Theories of Comminution Useful models of comminution represent the, application of energy by a breakage machine such as a crusher or ball mill to an ore. Mathematical models of comminution consider incremental energy (dE) required to produce an incremental change (dX) in size. It is clear that more energy is required to achieve a sirnilar degree of size reduction as the product becomes finer. Hence, energy and breakage are related empirically by Equation (2.1). dE = -K — (2.1) X" The expressions of Kick (1885), .von Rittinger (1867) and Bond (1952) are only integration forms of the above formula (Thomas and Filippov, 1999) for different values of the exponent n in the estimated validity range (1 to 104 /xm): n = l ^=> E=KKlog(X,/X2): , . Kick n=2 c = > E = KR( 1 / Xi - 1 / X2) Rittinger n = 1.5 ^=> E = KB (1 /X, 0 J - 1 /X2 05) ,' Bond Hukki (1961) determined the relationship between energy input and particle size in comminution processes, and the regions of applicability (Figure 2.1). 31 10*4 10"2 10° 10 2 10 4 10 6 Size(ujn) • .• •' . • . . i • i • , . . . Figure 2. 3 Relationship between energy'input and particle size in comminution (After Hukki 1961) . Based on experiments and a physical analysis of crack tip propagation, Bond's (1952) third law of comminution determines relationship between work input and particle size, and energy (Equation 2.2 and 2.3). Because this equation is most relevant across' the range of interest in mining and mineral processing (10 mm to 100 microns), ; 1 32' the Bond equation, since its introduction in the late 1950s is recognized by the industry as the .best methodology to design comminution circuits. There are numerous empirical "fudge" factors that are used with the Bond equation to account for certain anomalous behaviors especially as the 80% passing size falls below 100 microns; i.e., into the regime (down to 20 microns) for which Rittinger's law applies, however the Rittinger'equation is rarely used in practice. Generally, at low sizes (<100 microns) Bond is used with suitable correction factors. W= 10 Wj V "^80 V^i 80 '/ W = work input (kWh/t) W i = work index (kWh/t) i Pgo = product size (%80 passing) ((im) F8o = feed size (%80 passing) (pm) (2-2) P=TxW T= throughput of new feed (t/lf> P = power draw (kW) (2.3) 33 2.5.2 Comminution Models Comminution models can be divided into two main classes. • Empirical analysis of industrial equipment with respect to tonnage rates and particle size measured as a size modulus (d50, d80, wt % passing, etc.). • Fundamental analysis - population balance modeling (mass-size balance). A fundamental model considers directly the interactions of ore particles and elements within the machine, largely on the basis of Newtonian mechanics (Napier-Munn et al, 1996). The objective of a fundamental model is to generate a relationship between detailed physical conditions.within a machine and its process outcome. On the other hand, empirical transformation models estimate mill product size distribution as a function of mill feed rate and hardness changes as well as changes in mill operating, conditions. Figure 2.2 shows the transformation model for mass balance of material transforming from a feed size x into a series of smaller size ranges i from 0 to x. The balance is accomplished by using a breakage matrix Si for each size from i to n and then applying this to each of the size ranges in the feed. The major problem with this approach lies in deriving the matrix Si for each feed size i from 0 to n where n is the top size. There does not seem to be a unique matrix that can be determined to calculate this transformation. The suggestion is that population balance modeling is less empirical than analyzing industrial scale data, that it is more mathematical using matrix algebra and therefore "more accurate''. The reality is that the technique is no less empirical and'is simply a,more complicated way to calculate something that is , , 34 inherently simple. The evidence for this is that the, transformation matrix used to model comminution is not unique. At any time we can consider a simple mass balance for a particular size fraction, i , within a mill with transport into. a breakage zone, breakage and transport out as shown. Breakage in Feed Product x Si S p i i=0 Breakage out Figure 2. 4 Mass balance for a single size fraction (Modified after Napier-Munn et al, 1996) 35 At steady state, mass balance shows what goes into a continuous mill equals to what goes out. But, loss of the size fraction can be measured for non steady state mills or batch mills. The population balance model and related models have been widely used in modern process simulation to model many types of comminution devices. The model assumes that the production of ground material per unit time depends on the mass of that size fraction and thus breakage rate in the mill. To derive the model, the balance around a single size fraction can be considered as in Equation 2.4: , Feed in + Breakage in = Product out + Breakage out (2.4) Breakage function, bij, describes the fraction of size range j which reports to size range i after breakage. Thus, the balance equation can be rewritten as: " / i + ftVrM^; • , (2-5) kt•=. Rate of breakage (min _ 1) by = Breakage function s: = mass of i t h size fraction in the mill The more usual format of this equation uses size < distributions for each pulp stream considering the mean solids residence time. 36 CHAPTER 3 MECHANISM OF ROCK BREAKAGE 3.1 Overview Rocks and geological materials are generally classified as brittle1 material. They deform mainly elastically up to the point of fracture. The breakage of rock, depends upon how the, rock material behaves under applied load, which is related to the particular unit process involved. Earlier studies had little contribution to a better understanding of comminution, but demonstrated the complexity of breakage of particulate materials and the need to better comprehend its fundamental aspects. Like other engineering materials, rock will exhibit: • Macro measures of response such as compression and tensile strength and properties that. describe its response to loading. Measures such as Young's Modulus of Elasticity (E) and Poisson's Ratio.(v) are examples of these properties':. • Micro fracture mechanisms: crack initiation arid propagation. ' * • i 3.2 Macroscopic Behavior i i 3.2.1 Rock Displacement Effects . Stress causes bodies to deform, and strain is a measure of the deformation, which is basically called "normalized deformation" i.e., a change in length divided by length. 37 As expected, there is strain associated with normal stress, and a different type of strain associated with shear stress. Deformation from one point to another in a rock body is coupled with displacement. Rock displacement can be viewed as the sum of four effects as shown in Figure 3.1 (Lowrie, 1997). SUM OF 4 EFFECTS No shape change: Translation Shape change = I Shear Rotation Normal (Dilation) • Figure 3.1 Rock displacement effects (Modified after Lowrie, 1997) 38 3.2.2 Stress-Strain Response A stress versus strain curve for the uniaxial compression of cylindrical rock samples is plotted in Figure 3.2 (after Jaeger and Cook, 1979). The region OA is the elastic zone in which the ratio of stress (force per unit area) to strain (relative deformation) in its simplest form gives Young's modulus. At point A , the material is said to yield, (yield point or yield stress O"0). . . ' : o Strain (e) Figure 3. 2 Idealized stress-strain responses for a cylindrical rock sample (Napier-Munn et al, 1996) 39 Between points A and B the rock continues to deform without losing its ability to resist load/ This region is known as the ductile region. Once past point B , the ability, of the material to resist load decreases with increasing deformation and the rock enters the brittle region. Point B therefore denotes the transition from, ductile to brittle behavior.' The stress at this point (Co) defines the1 Uniaxial Compressive Strength (UCS) of the material. Sudden failure of the material wil l then occur somewhere in the BC region of the graph. 3.3 Microscopic Fracture 3.3.1 Fracture Propagation Fractures may propagate in two common ways: transgranular and intergranular (grain boundary) fracture mode.' Transgranular fracture occurs along a randomly oriented plane in polycrystalline materials due to a simple breaking of atomic bonds. During crack propagation in a polycrystalline material, the macroscopic crack plane tends to remain normal to the tensile stress. The result is a stepped fracture surface at the microscopic level that is composed of crystalline facets that depend on the orientation of the crystal grains (Figure 3.3a). 1 ' • , ' . 40 Grain boundary fracture is the most readily recognizable microscopic. fracture mechanism in which the crack prefers to follow grain surfaces where in the.grain boundary regions, atoms are arranged irregularly (Figure 3.3b). This type of fracture can be induced by several factors, for example,: when material is heat-treated. Toughness values or resistance of rock to fracture for transgranular fractures are about 30% higher than that for intergranular fractures (Tromans and Meech, 2002). Figure 3. 3 (a) transgranular fracture (b) grain boundary fracture 41 3.3.2 Ductile-Brittle Fracture Transition Depending on the level of the applied stress, the stress state, the temperature, the material's grain size, the imposed strain rate, etc., a material may exhibit either ductile or brittle fracture. Preceding ductile fracture, plastic deformation will occur and rupture is the extreme case; Moreover, the transition from "brittle" to ."ductile" fracture is a gradual one. Therefore, even brittle fracture may take place with some small degree of plasticity. Depending on the extent of plastic deformation, brittle fracture can be divided into three categories. Various fracture modes are shown in Figure 3.4. Brittle fracture (mode I) occurs without plastic deformation or to a limited degree at the crack tip (a, b). Mode II fracture is preceded by microscopic, but not macroscopic plastic deformation that nucleates.cracks. A limited reduction in area is obtained in a tensile test in, mode III brittle fracture, but propagation takes place prior to necking, which is a reduction in cross-sectional area beyond the ultimate tensile strength. (Van Vlack, 1989). Brittle fractures may propagate by transgranular or intergranular mode whereas ductile tensile fracture propagation preceded by necking takes place by means of plastic deformation. If material becomes stronger as the strain rate increases, this suggests that transgranular fracture becomes more dominant than intragranular fracture. In this case, breakage of normal crystalline bonds becomes more significant than the propagation ; 42 of cracks and microcracks. The idea is that such breakage is more efficient than is plastic deformation within crack voids, wherein, energy is wasted., transgranular, intergranular 1 ductile I 1 ; 1 Figure 3. 4 Various fracture modes: brittle fracture mode I (a, b), mode II (c, d), mode III (e, f) and ductile fracture (g), (Courtney, 1990) .43 3.3.3 F r a c t u r e T o u g h n e s s During comminution, fracture initially. occurs because particles contain pre-existing cracks (flaws), which propagate in response to tensile stresses generated during compressive loading. At the tip of all cracks within a loaded material, the stress is concentrated because the,load cannot be uniformly distributed across the full area. The stress intensity factor (Ki), which is independent of the nature of the material, relates the nominal stress and the depth of a crack to the stress concentration at the tip of the crack. With more intense stresses or with deeper cracks, the stress intensity becomes (sufficient for fracture to progress spontaneously. This threshold stress is a property of the material, which is called the critical stress intensity factor (Kic). Fracture toughness (Gic), resistance of rock to fracture under crack opening (niode I) conditions, is defined as the critical energy release rate per unit area of crack plane (Jm~) that is necessary for crack propagation. Thus, fracture toughness is a,material property of rock that is indicative of how rock behaves under load. For ideal brittle fracture where plastic deformation is negligible, Gic is equivalent to 2% where 7 is the surface energy per unit area (Jm"2). Gic is. related to Kic via Equation 2.4: . \ K l ( ( l - u 2 ) t = ( E G l c)t « K I C Pa. m^ (2.4) E = tensile elastic modulus (Pa) v = Poisson's ratio 44 and Kic is given by Equation 2.5: .K ic = Ya c (a)2 '• Pa.m2 . (2,5) 0"c - critical tensile stress (Pa) a flaw size (m) 1 Y = shape factor (crack geometry) 3.3.4 Crack System Energy The presence of cracks on the surface or within the interior of a material will inhibit plastic deformation, so mode I fracture wil l dominate. A crack at its tip produces a stress concentration the magnitude of which depends on the crack shape and size (Figure 3.5) , , ; As the crack grows, there are two energies associated with the crack and its extension. One is the surface energy, which acts to resist crack advance (retarding force). The other energy is an elastic strain energy that acts to extend the crack (driving force) due to the stress concentration. The stress concentration zone extends a distance ~2c in front of the tip. 45 Figure 3. 5 Tensile stress adjacent to an elliptical crack. Fracture is possible when a max = a th (theoretical strength) (Courtney, 1990) The system energy as a function of crack size at different stress levels is plotted in Figure 3.6. As shown, a crack of half-length C* will not propagate at a low stress (0\) because crack advance is accompanied by an increase in system energy. However, at high stress (03), crack advance takes place with a decrease in system.energy and the crack continues to propagate resulting in fracture. At the critical stress (02), a minuscule increase in either crack length or applied stress leads to spontaneous crack propagation and a decrease in system energy. 46 L'TOT 1 Maximum in this curve at ^ v . ^ ^ 4cy -^ \ i £ c = c* ' \ •~ I 1 1 1 • a = a? > c ; >v 0 I : / a = cr3 > <Jj / V, . O&tC 1. 4 C Y ~ E c* Figure 3. 6 Total system energy as a function of half crack length at three different stress levels (Courtney, 1990) Therefore, i f the stress level is constant, cracks smaller than a certain size (C*) will not advance because the system energy increases,. On the other hand, cracks above this size propagate spontaneously until the system energy is released. The critical stress at this crack length (C*) is associated with the maximum in the curve where the retarding and driving forces are equal. In this situation, the crack is in unstable equilibrium, i.e. dU/dc - 0. 47 3.4 Material Behavior under Impact Loading The behavior of materials and structures under high-speed loading has a number of peculiarities, and its examination is far from complete. This is due to the deficiency of experimental research data on controlled loading in.the micro and nanosecond ranges and by unsuccessful attempts to clarify the results of these experiments on the basis of traditional static mechanics concepts. The mechanical properties of brittle. materials depend strongly on deformation rate and stressing velocity. It has been reported that the dynamic strength of geological materials is significantly greater than their static tensile strength. . 3.4.1 Strength vs Strain Rate Strength and deformation of rock and other brittle materials such as ceramics depend on the applied rates of stress and strain. If a continuum deforms continuously under an applied stress, then the operative phenomenon is velocity, not displacement, and the normalized velocity is the strain-rate. The strength of rock, generally increases ' 2 gradually with an increasing rate in the static regime with strain rates below about TO" sec"1. For greater strain rates, the effect of increased fate on brittle fracture stress is very strong. Fracture strength is a continuous function of strain rate (Li etal, 2000) over many orders of magnitude in strain rate, but the. strength of rock begins, to 48 increase rapidly at high strain rates somewhere in the intermediate range (10"2 to 102 sec"1). Figure 3.7 shows the compressive strength of Tuff (volcanic rock) as a function of strain rate in an experiment. Note that for Tuff, the transition to higher strength-strain rate relationship occurs at 102 (sec"1). Figure 3. 7 Effects of strain rate on strength of Tuff (Olsson, 1991) 49 Obviously, the strength of material increases as a function of strain rate. However, it is not well. understood as to whether the process of rock fragmentation at higher strain rates is less competent than lower rates in terms of energy efficiency. In fact, the evidence with respect to blasting and fragmentation would tend to support the theory that higher efficiencies accompany high strain rates. So despite an increased strength, the efficiency of energy transformed into new surface energy is also increased. 3.4.2 Static and Dynamic Loading Strength characteristics of materials under static and dynamic loading are considerably different. Numerous experiments demonstrate the failure of specimens through fracture under high-intensity pulse loading, when amplitudes of the external effects exceed those forces that would normally cause a fracture under static loading conditions. Traditional parameters of strength and crack growth resistance are constants for a particular material under static conditions. However, these parameters are very complicated under dynamic loading and depend1 on physical and geometrical characteristics of the external action. Rock inhomogeneities also contribute to differences in dynamic and static tensile strengths (Cho.et al,.2003; L i et al, 2,000) In material science and rock mechanics,, it is often considered that strain rate effects are due to crack propagation behavior. At low stressing velocities only the largest or critical flaw is responsible for failure. On the other hand, at high loading 50 velocities, several flaws must propagate simultaneously, given the inability of a single flaw that has a bounded growth velocity to relieve the increasing tensile stresses. The interaction between adjacent flaw propagations may be, responsible for imparting an increased strength to the rock under high loading rates. The range of static and dynamic loading can be extracted from Figure 3.7. As one would expect, comminution process with low energy efficiency occurs at low strain rate while with respect to blasting, high efficiencies take place at high strain rates or high impact velocities (see Figure 3.8). ; • Velocity Ranee (m.s"1) Strain Rate (s 1) 1 blasting •=> 5,000 - 20,000 100-20,000 k • • • this study 10 -103 l - l O 2 dynamic conventional comminution I "=> 10"4-1 10"5 - io:1 static j . •I ' , ! ' .' Figure 3. 8 Typical static and dynamic loading 51 Few studies have been done between these ranges of strain rate. Thus, any attempt to study the breakage function at impact velocities higher than those of comminution 1 equipment and smaller than those of blasting would clarify the behavior of material in this range. 3.4.3 Material and Loading Characteristics One of the main problems in testing the characteristics of resistant materials under dynamic loading is the dependence of dynamic strength on how the external action is applied. This difficulty typically appears under conditions of high-rate loading. In this case, the strength can be interpreted as a critical value of the stress intensity factor that corresponds to microcracking near the crack tip. The strength can also be interpreted as a dynamic local stress leading to rupture of the material. Both are intensity limits of a, local stress field and the fracture occurs when these limits are reached. Basically, higher strain rates generate a large number of microcracks and the interaction of these microcracks can interfere with the formation of the fracture plane. Ultimately, dynamic tensile strength increases at a high strain rate because the crack is arrested by the generation of a large number of microcracks (Cho et al, 2003). On the other hand, violent fragmentation of a body can occur because of dynamic tensile stresses that result from a rapid deposition of energy through contact forces (Grady, 1981). 52 Fragment distribution curves for brittle and ductile fracture under1 dynamic tensile loading are compared in Figure 3.9. The two fragment distribution curves assuming a constant nucleation rate indicate significant differences. The brittle fracture curve is broader and. skewed to the left, or to the finer fragment size. In contrast, the ductile fracture curve is located around the mean fragment size with a scarcity of fine fragments. Therefore, material properties and loading conditions are key elements to determine the fragment distributions resulting from a specific dynamic fracture event. The process of fracture nucleation will depend on both material properties'and the conditions.of loading, and the nucleation rate depends on strain, strain rate or irnpulse duration. So, nucleation rate depends on characteristics of loading such as strain rate and amplitude. ,fri addition, material properties such as the flaw structure in brittle solids and the deformation process leading to shear that precedes fracture in ductile solids plays an important role in determining the locations of fracture nucleation sites. However, experimental work suggests that shock loading is Considerably more catastrophic in terms of producing fine particles than is constant strain rate or ramp wave loading (Grady, 1981). Since the specific surface area ,of fine particles increases inversely with size (approaching an exponential relationship), the brittle fracture distribution for the same dynamic loading should always produce an overall higher specific surface area to that of the ductile fracture distribution. 53 3 % s S 1 i -'. "1 . . . . _ . —r \ / « DUCTILE \ FRACTURE -" / / /-BRITTLE V\S FRACTURE 1 • ••- i •••• '' • -1.0 to LENGTH-1 3.0 Figure 3. 9 Fragment distribution curves for brittle and ductile fracture under dynamic tensile loading (Grady, 1981) Calculations can be done on the distribution in Figure 3.9 to show that the brittle fracture overall specific surface area will be about double that obtained by a ductile fracture of similar energy with about 25% of said specific surface area located in the finest size fractions compared with about 2% for the ductile distribution of surface area (see Figure 3.10). 54 Figure 3.10 Specific surface area (SSA) distribution as a function of particle size for brittle and ductile fracture The implication of high velocity impact technology will assist in the possibility of some control over the process of rock fragmentation in the course of materials selection or stress load optimization within the mineral processing industry. 55 3.4.4 Rock Breakage under Low Impact 3.4.4.1 Tensile vs Compression The amount of strain within a particle under' load is proportional to the applied stress. In brittle materials such as rock, i f the induced tensile stresses exceed the tensile strength, the material will fail. Although compressive loading. behavior is helpful in understanding rock breakage, it is the tensile strength that controls, rock failure. The tensile strength of rock is almost. 10% of the compressive strength (Napier-Munn et al, 1996) control being due to the presence of pre-existing flaws or cracks within the rock. In fact, rocks always break in tension with the high strength achieved being due to very low compression to tensile loading transformation. A maximum efficiency of 7-9% has been theoretically estimated for rock breakage under indirect tension (i.e., comminution equipment) while in blasting where materials are under direct tension towards the free surface, one may achieve a maximum theoretical efficiency as high as 60% (Tromans, 2007). Breakage of rock material depends on the distribution and orientation of flaws and geological structure within the particles. Particle fracture occurs due to the induced tensile stress acting normal to the crack plane. If the plane of the flaw is inclined at an angle with respect,to.the impact axis, the resulting stress will be reduced leading to poor transformations of compression into tensile stresses. As well, tensile stresses induced within particles are influenced by Poisson's ratio, which is very low for rock materials. 56 3.4.4.2 Bond Work Index 1 In comminution, it is important to identify the product size distribution and energy required from a particular breakage function. The complexity of the energy-size reduction relationship has resulted in the development of alternative methods of assessing the energy requirements of size reduction, devices. The .Bond test is a method to determine the energy requirements of comminution in order to properly size the comminution equipment and scale-up from the.bench to the.plant. The Bond-law is the most suitable design criterion across the particle size range of interest in mining and mineral processing. The work index of a material can be directly measured using several laboratory tests such as the Bond crushability test and the Bond ball or rod mill grindability test. The kinetics of a grinding process can be studied with batch grinding of the material within a certain size fraction to determine the breakage rate and breakage function. The test material is classified into a specific size fraction and loaded into the mill. The material is then discharged and sieved. The test is repeated until a desired grinding time or product similar to industrial grinding is achieved. The .breakage function matrix is calculated from the results obtained. Scale-up involves passing the feed distribution through.the matrix until the lab and plant results are obtained. The ratio of the number of "lab" passes to the number of "plant" passes represents the scale-up factor. 57 3 . 4 . 4 . 3 Single-particle Breakage Tests It has, been considered. that the breakage process occurring in'comminution devices is a series of single particle breakage events. A particle is loaded and fractured only under an applied stress. The product is a collection of progeny particles from numerous single particle breakages. The state of stress arising in a particle in comminution depends on the size and distribution of flaws and the deformation behavior of the material. At the very fine sizes, particles are almost flawless and behave inelastically. Therefore, 'a stressed particle will behave differently under a slow and steady compression as opposed to impact compression. The deformation or impact velocity in most comminution processes is between 0.1 and 10 m/s which can be classified as a slow compression. The distinction between impact and slow compression can be determined by the rate of load application, with impact tests being completed in 10"4 to 10"6 seconds depending on strain (Peters Rit et al, 1983). Single-particle tests have been developed to measure standard physical properties of materials. Loading tests,measuring tensile fracture mechanisms correlate well with comminution energy (Marland et al, 2001). For example, the point load test, chevron bend test, and Brazilian test are claimed to be good indicators of comminution energy. In single particle breakage tests by impact, particles are crushed between two hard surfaces and the product size is related to the input energy. The energy required for fracture is determined from load-displacement data collected during testing. The i 58 fragmented .particle distribution is determined from sieve analysis of the tested particles. . . Popular impact tests such as the drop weight, pendulum arid twin pendulum, and falling media have been widely, used in comminution applications in order to achieve higher deformation rates in a dynamic environment. The twin pendulum test relates the specific comminution energy in ball milling to.a single parameter derived from the apparatus (Narayanan, 1987). The drop weight test measures various potential energies as input energies from the falling weight considering initial particle sizes and the product size distribution (Marlahd etal, 2001) Ultrarfast load cell (IIFLC) and Hopkinson pressure bar (HPB) were developed to simulate the loading and energy levels within a very short period of time in comminution such as tumbling mill and cone crushers. Both pieces of equipment utilize the force-time history of the impact to calculate the energy input to the system after measuring product size distribution. HPB is similar to U F L C , but is aligned horizontally. Their limitations are such that they are only capable of testing small particles which are non-representative of the whole material. 1 ' i 3.4.5 , Material Breakage under High Impact Mechanical behavior of materials under high strain rates differ significantly from that observed in static or in the intermediate range. It is well recognized that the 59 mechanical response of all materials is sensitive to the rate of loading. The mechanical properties of rock are also affected by strain rate (Whittles et al, 2006). Experimental results show that the dynamic fracture toughness of the rock as well as' crack branching is increased with increasing loading rate (Zhang et al, 1999). Studies have shown that solid materials subjected to high rate or impulsive loading exhibit dramatically enhanced strength (Grady, 1985). Liu presented a damage model indicating that the dynamic fracture stress of rock material is higher than its static strength dependent on the.strain rate (Liu and Katsabanis, 1997). Dynamic tensile tests at strain rates higher than 10 s"1 for rock are difficult to conduct with existing testing methods (Wang et al, 2006). The International Society for Rock Mechanics (ISRM, 1978) currently suggests the Brazilian disc specimen method to determine static tensile strength for rocks, concrete and other materials. This was extended into dynamic, testing using the split Hopkinson pressure bar (Rodriguez et al, 1994). , Tt has been shown that the strength of material increases with decreasing particle size due to a reduction in inherent flaws within the particle. According to Griffith's theory, fracture occurs when the energy, supplied by an external force, or by the release of stored strain energy, is greater than the energy of new crack surface. At low velocity, (only the largest flaws in a particle initiate to propagate. At high impact loading, several cracks or flaws can simultaneously propagate leading to specific dynamic effects. The corresponding transient wave produced by impact can, cause a tension to arise faster than the stress intensity factor at the crack tips (Morozov and Petroy, 1997). When sufficient, energy is 'available to cause unstable crack , ' ; ' 60 propagation, only a single impact of sufficient level is required to cause fracture (Bwalya.et al, 2001).' Generally, at low fracture velocities, the iritergranular fracture mode dominates while transgranular takes place at higher velocities. Howeyer, stress corrosion may degrade the strength of a grain interior much more than the grain boundary in manganese zinc ferrites (Beauchamp and Monroe, 1.989). Hypervelocity projectile impact has mainly been studied with an interest in the impact of meteorites and debris upon space vehicles. Several methods have been developed to accelerate small projectiles. These include projection by compressed air, explosives, electromagnetic, and one and two stage light gas gun! The limitations in selecting a method include strength of the gun and projectile, the length of the gun, and the attainable velocity.desired (Clark et al, 1969). Currently, a maximum velocity of about 20 km/s for a small projectile.is achievable.utilizing a three-stage,light gas gun (Thornhill et al, 2006). Studies on the projectile impact on soft, porous rock has indicated that the contact geometry of the projectile and not its mass determines the indentation depth for the- same initial bullet energy within the range • of 'impact parameters (Kumano and Goldsmith, 1982). Whether or not this applies tO a target of particulates is still to be determined. 61 3.4.5.1 Split Hopkinson Pressure Bar The split Hopkinson pressure bar (SHPB), also called the Kolsky bar, is a device for measuring the stress-strain relationship in materials at strain rates approximately from 400 to 10000 s"1. This method has been widely used to characterize the dynamic behavior of materials at. high rates of strain, such as metals, ceramics, and composite materials and so on. The method has been developed for compression, tension, torsion and bending tests. Hopkinson tests permit higher strain rates than those achieved by instrumented Charpy impact tests (Lpya et al, 2003). This apparatus allows measuring the forces and displacements applied to both faces of the specimen (Figure 3.9). Specimen Gas gun Strain gauge Figure 3.11 Schematic of a split Hopkinson pressure bar 62 In order to perform a dynamic compression test with a SHPB, a short specimen is inserted between two bars, called the incident (loading) bar and the transmitted bar, with a higher yield stress than the tested material. With the impact of a steel projectile (striker) at the speed of up to 30-40 ms"1 from a gas gun, a longitudinal compressive elastic wave is induced in the incident bar (incident wave). A part of this wave is reflected at the bar-specimen interface (reflected wave) while the other part is transmitted' through the specimen and induces ah elastic wave in the transmitted bar (transmitted wave). The incident, reflected and transmitted pulses are recorded by strain gauges mounted on the surface of the bars. The strain gauges are connected to a digital oscilloscope and a microcomputer is used to analyze the signals. Any measuring technique requires knowing the characteristics of the two elementary waves which propagate in opposite directions (Othniah et al, 2003). The application of one-dimensional wave propagation theory to the SHPB system shows that the engineering, values of the specimen stress (o"s) and strain rate (ss), are proportional to the transmitted and reflected t strain pulses respectively. As well, the velocity of the striker can be measured by using photocells and detectors. i 1 . • 1 3.4.5.2 Two Stage Light Gas Gun Amongst many applications of light gas accelerations, a two-stage light gas gun is the most versatile instrument. In this technique, the propellant in the powder chamber 63 is ignited which pushes the piston down the tube at high velocity (Figure 3.10). The piston movement compresses a light gas such as hydrogen or helium in the pump tube producing a very high pressure until the burst,pressure of the diaphragm is reached. Expansion of the very hot and high-pressure gas into the launch tube accelerates the projectile resting on a sabot (carrier) down the barrel. After leaving the barrel, the projectile, separates from the sabot, passes a velocity measurement system, and eventually hits a target. This happens so fast that the sabot with any defects such as bubbles, cracks or poor cast, can deform. Therefore, it is made of a special plastic material chosen for its strength and rigidity. X-ray equipment and high speed camera are used to record the position of projectile and impact phases (Schneider and Schafer, 2001). Powder Chamber Igniter Light gas (H2 or He) Pump Tube , ^ Piston Diaphragm Figure 3 . 1 2 Two-stage light gas gun 64 With a barrel of 1 meter length and a typical projectile velocity of 6 kms"1,' simple physics dictates that the acceleration is almost 2 million times the acceleration due to Earth's gravity or 2,000,000 g's. In the light gas gun, projectile velocities of up to 10 krn/s have been attained since at a given energy, a light gas with low molecular weight has a high expansion velocity (Seigel, 1965). Most common impact facilities using explosive-driven guns are able to accelerate projectiles up to 9-10 kms"1. In experiments without explosive powder, velocities of 3-4 km/s have been reached using a projectile mass between 100-300 mg (Angrilli et al, 2002). As well, modifications to create a more active piston resulted in accelerating projectile masses of 4 g to speed of 5.5 km/s (Pavarin et al, 2006). In a one-stage light gas gun, the projectile consists of a two stage rocket and cargo. It is propelled by hot, compressed, light gas. Long-term exposure to. hot hydrogen embrittles steel tanks, so helium'is,preferred. The gun replaces the first stage rocket. Maximum velocity is limited to the ..speed of sound at about 2 km/s in hot helium. The maximum velocity can be, increased by additional: heating of the propellant prior to launch,, either with an electric arc pulse or contact with hot particles. . , A three-stage light, gas gun consists of a shock preheating, compression and launch sections. Recent developments in this technique have reached velocities of about 19 km/s at projectile masses of about 0.1 g (Thornhill et al, 2006; Piekutowski and Poormon, 2006). ' ' • 65 3.4.5.3 Electromagnetic Gun A coilgun uses a series of electromagnetic coils to accelerate a magnetic shell to very high velocities , down . a barrel. Although different in operation, coilguns are similar to railguns in general concept since both use electromagnetic effects. A railgun accelerates projectiles down two parallel conducting rails. Recently,, power supplies have been built that can provide currents in excess of 3 M A to railgun barrels. With a small projectile (<1 g), velocities of about 6 km/s are achievable with this gun (McNab, 1999). At present, insufficient knowledge of electromagnetic launchers (EML) prevent us from addressing issues associated with the application. For example, high-speed E M L can not be applied at low-speed situations due to the operating characteristics (Engel et al, 2006). A coilgun consisting of a coil of wire (or solenoid) is a.form Of electric motor with a conducting armature as a projectile. A n induced or driven current generates a strong magnetic field that accelerates the projectile within the coil. By switching each coil on and off, the coils can progressively launch the projectile through the barrel. Coilgun velocities are at supersonic levels but lower than those produced by a railgun. Studies conducted at Sandia National Laboratories show that a muzzle velocity of 2 to 2.5 km/s with a projectile mass of 20 to 60 kg, are basic parameters for a coilgun (Kaye et al, 2002). Several computer models have been developed to simulate and identify the performance and geometries of a coilgun suitable to launch metal plates (Berning et al, 1999). In principle, the force field can be propagated at light speed in • • '', • 66 an E M L . So, this type of gun.can produce higher velocities than can powder guns. (Haugh, 1995). . , . 3.5 Conclusion This chapter reviewed the macroscopic and .microscopic fracture mechanisms. On macro breakage; rock shows ductile behavior prior to entering the brittle zone. The stress at the ductile-brittle transition point is called the UCS (Uniaxial Compressive Strength). On a micro-rlevel, two. fracture. modes occur, in which transgranular represents higher toughness values compared to intergrahular mode. As well, material behavior under low and high impact loading was presented! Testing methods for rock crushing and grinding utilize only single particles.in order to determine the size-energy relationship of material.under impact. In fact, most processes deal with bulk materials with significant interparticle, effects that cannot be observed in single particle tests. Mechanical behaviors of material are highly sensitive to high strain rates. Experimental techniques also exist with single', particles to implement high velocity impacts into a specimen. The ranges of velocity employed in these devices are either, less'than .50 m/s (Hopkinson Bar) or more than 2 km/s (two-stage light-gas gun, electromagnetic launcher). '. 67 In order to examine rock material at higher velocity impacts than take place in conventional comminution equipment, there is a need to design and construct a new apparatus wfach fulfill the following requirements: • 1. Rock bulk samples should be tested instead of a single particle to, simulate the breakage phenomena as close as possible to the real,situation that occurs in conventional comminution equipment. 2. ,' The device should be capable of launching a projectile at velocities from 10 to 500 m/s. This range allows us to study breakage at higher impact velocities than those achievable in conventional comminution equipment that is well below 10 m/s. In addition, the study of HPGR, Barmac crushers and jet mills indicated that the impact velocities in these machine's are an order of magnitude higher than those achieved in other comminution equipment. So, the velocity target of , 500 m/s as the upper limit of the range of interest, will be sufficient for,the purpose of this research. Building an apparatus to apply velocities higher than 500 m/s requires more expensive equipment. Funding for such apparatus is recommended for future studies. ! 68 CHAPTER 4 DEVELOPMENT OF ESTIMATION METHOD ON ENERGY EFFICIENCY UNDER STATIC REGIME FRAGMENTATION To accomplish the objective of the research, it is proposed to examine parameters involved in the process of size reduction under different strain rates and various velocity impacts to facilitate the understanding of the fundamental concepts that underlie fracture physics. Moreover, the energy efficiency of comminution equipment is assumed to be a complex function of diverse variables. Most of the energy in comminution is dissipated as heat instead of generating new surface area. Even a slight enhancement in this • efficiency could result in considerable energy savings, improvements in, mineral liberation, and increased ability to process lower grade and/or complex ores. 4.1 Introduction i \ Crushing and grinding are essential components of all mining and mineral processing operations to reduce the size of ore and rock, and subsequently, liberate the valuable mineral for beneficiation. However, comminution is very energy-intensive 69 and consumes a major percentage of the total energy used during mineral recovery] In many cases, the efficiency of comminution is derived by measuring the ratio of energy "required" to energy used. From a fundamental viewpoint, it is the energy required to create new surfaces that should be considered. Thus, every aspect of comminution justifies careful consideration in order to minimize all elements of cost and associated energy use. What has not been well-accounted for in conventional methods of energy estimation during breakage is the need for accurate measurements of surface area and an understanding of the influence of resolution on such measurementsIn interpreting breakage phenomenon, measurement of surface roughness is indispensable for precise determination of surface area in direct measurements. This chapter reports on studies conducted on high strain rates in a static regime that can enhance energy efficiency and mineral liberation. Novel approaches to measure surface roughness and surface area based on a fractal analysis procedure have been developed. Changes in surface roughness of broken specimens under high loading rates were studied using a laser probe to generate 3D topographical maps of the fracture surfaces. Our study shows that roughness and surface area measurements are highly dependent on the resolution used to, produce these maps. Surface area can be estimated based on theory, measurement and empirical calculation. The results indicate that surface roughness and hence, specific' surface area, increases with increasing loading rate by several orders of magnitude as particle size decreases to ~1 micron. Below this limit, surface roughness begins to diminish from particle-particle attrition. A method now exists to 70 accurately calculate surface area before and after breakage. So, it is now possible to determine the amount of energy expended to create new surface area and thus calculate the efficiency of breakage. It is intended to extend this approach to allow for tighter control of comminution processes and improve overall utilization of energy. The aim of this study was to investigate the influence of different loading rates or strain rates in a static regime on rock fragmentation and then on the energy efficiency of breakage. A coefficient of surface roughness was developed as an index to calculate the true surface area of broken samples. To achieve this goal, a laser probe was used to obtain a digital'data set that represented the fracture surface. 4.2 Energy Efficiency Conceptual Model The main step to evaluate the effectiveness of a size reduction process is to identify parameters involved with that process. Figure 4.1 introduces an approach to model the relationship between the variables and energy efficiency, of breakage under impact loading. Surface area of fractured material is an important measurement to characterize energy use in comminution as well as surface reactions in down-stream processing steps. Conventional approaches to direct measurement of surface area consider the geometry of product and feed particles - both size and shape. What is often ignored in 71 such'work is the influence of fractal geometry factors - surface roughness and the resolution used to measure roughness: Resolution Surface Roughness 1 Surface Area Strain Rate Energy Efficiency Figure 4.1 Conceptual Model of Energy Efficiency 72 Parameters that characterize surface variations include roughness and waviness which are dimensional properties of the material. Roughness is defined as relatively finely-spaced surface irregularities, of which the height, width, and direction establish a definite surface pattern. Waviness refers to a wavelike variation from a perfect surface to one with much wider spacing and higher amplitude changes than surface roughness (Budinski, 1989). ' 4.3 Technical Surface Roughness One way.to analyze the fracture of materials is to determine the topography of a fractured surface. Fracture surfaces have different degrees of roughness and therefore geometrical complexity is a characteristic measure (Zhou and Xie, 2003). In order to distinguish between different surfaces, the roughness can be expressed as a mathematical relation (Schey, 1987). 1 • On a microscopic scale, surface waviness and roughness can be measured and recorded. For ease of visualization, recordings are usually made at a relatively large magnification. This can give a distorted image with sharp peaks and steep slopes (Figure 4.2). In reality, the peaks or asperities of smooth surfaces have gentle slopes of typically -5-20° inclination (Schey, 1987). ' 73 Figure 4. 2 Roughness of technical,surfaces (Schey, 1987) The traces or signal obtained from the profilometer is processed electronically after digitization to derive parameters that quantitatively characterize the surface profile. Of the diverse measures reported, the following are most frequently used: - Maximum roughness height (R t, the height from maximum.peak to deepest trough): This is important when roughness is to be minimized. It is obtained by taking the difference in average height between the 5. highest peaks and 5 deepest valleys within a sampling length (10-point height). . ' , ' 74 - Centerline average ( R a , or arithmetical average): This is the average deviation from the centerline or mean surface. This line is drawn in such a way that the area filled with material equals the area of unfilled portions. . R a = y J ! y | dl • or (4.1) - Root mean square (rms, Rq): This value is frequently preferred in practice and also in contacting surfaces in manufacturing. For technical surfaces. (i:e. turned, ground and lapped surfaces), R . q is. closely related to Ra ( R a = 1.11 R q for a sine wave). Rq=[ y j y 2 d l ] i (4.2) or R , = ( M ! ^ ) 1 2 4.4 Fractal Dimension Method The use, of "fractal dimension" is a way to estimate surface roughness independent of conventional statistical analysis (McWilliams et al, 1993). Fractal analyses of rock 75 surfaces include a variety of one- and two-dimensional techniques. Each method provides a consistent means to generate essential information to designate roughness. As such, fractal parameters Can be a valuable tool, in evaluating rock properties (Chakravarty and Pal, 1996). The word "Fractal" was coined by Benoit/B. Mandelbrot, and derives from the Latin word for "to break". While classical geometry is associated with perfect and well-defined mathematical shapes or objects of integer dimensions, fractal geometry describes the complex natural patterns or objects of non-integer dimensions by a parameter called the "Fractal Dimension". Zero dimensional points, one dimensional lines and curves, two dimensional plane figures like squares and circles, and three dimensional solids such as cubes and spheres make up the world as we generally understand.it using classical geometry. However, most natural phenomena are better described using a dimension that lies between the two whole numbers (1,,2 or 3). So, while a straight line has a dimension of one, a fractal curve has a dimension between one and two depending on how much space it takes up as it twists and curves (Peterson, 1984). The more that a flat fractal fills a plane, the closer it approaches two dimensions. Likewise, a "hilly fractal scene" will reach a dimension somewhere between two and three. So a fractal landscape made up of a large hill covered with tiny bumps would be close to the second dimension, while a rough surface composed of many medium-sized hills would be close to the third dimension. . ' ' ' ' . ' • • ' .• 76 i Generally, the relationship between the total length (X) of a line and the scale (X) used to measure it can be expressed as (Chakravarty and Pal, 1996): L=NYP , where L = total length Y= size of measurement (scale) N = number of scales (integer) D = fractal dimension Thus, on normalization (i.e. L = 1): D = -m ••• • ; , ; ... (4.3) MY) . . • The use of scale invariance of a physical phenomenon gives the ability to project small scale > results onto a very large scale, and thus the same value , of fractal dimension can be employed to estimate the roughness of bigger blocks (after Turcotte, 1993). Fractal dimension as an index can be used to describe the surface topography of a fracture.'Many methods such as divider, box counting, and spectrum have been suggested to estimate the fractal dimensions of a rough profile (Zhou and Xie, 2003). Moreover, new methods such,as the triangular, prism surface area method, the projective covering method, the cubic covering method, and use of the scanning 77 electron microscopy and stereoscopy, have been developed for direct determination of the fractal dimension. However, application of fractals to quantify rock joint roughness has led to controversial findings (Kulatilake and Urn, 1999), in that different fractal parameter values1 are possible for the same roughness profile i f different input parameter ranges with the chosen method are used. In addition, accurate descriptions of surface morphology parameters including surface roughness of rock joints at a large scale is a key for rock mass characterization. Detailed laboratory investigations, indicate that as sample size decreases below a threshold value, the surface roughness of the rock joints is scale-dependent (Fardin et al, 2001). Above this point, fractalparameters remain virtually constant and can1 be considered reliable estimates independent of resolution. Rock properties obtained with sample sizes below this threshold are not representative. Methods to estimate representative1 properties of rock joints in field scale from small samples tested under laboratory conditions still need considerable research. The. US Bureau of Mines (McWilliams et al, 1993) reported,that computing the fractal dimension of profile traces as a measure of roughness is a redundant exercise particularly with regard to the anomalies between the various fractal algorithms. They stated that the profiles were neither self-similar nor self-affine and established that these properties are difficult to estimate especially with empirical data. Furthermore, Piggott (1990) who used statistical, geostatistical, and fractal methods as measures of 78 the roughness of different surface profiles in his work, concluded that statistical and geostatistical analyses are the most appropriate means to quantify fracture surface topography. 4.5 Effect of Resolution on Roughness and Surface Area Measurement This study identifies that the measurement of surface area is highly dependent on the measurement resolution. Different values of surface area result when the resolution is changed. So the meaning of surface area in terms of the objective of a study is an important aspect in choosing the resolution to use in the measurement technique. The less dense the network of the grid, the less, accurate the individual cells are reflected,, and the lower w i l l be the measured surface area. The. surface profile shown in Figure 4.3, indicates the influence of 1 resolution on the roughness measurement and ultimately, on surface area. ' With D as the resolution instead of 4D, the measured surface area increases by about 2.8 times. In order to interpret breakage phenomena, it.is clear that to obtain high accuracy,, measurements at the dimensions of the crystal lattice are necessary since breakage takes place with the breaking of bonds between elements in the crystal lattice. 79 Figure 4.3 Effect of resolution on roughness and surface area measurement. 4.6 Experimental Procedure In order to measure the efficiency of breakage, four drill core samples of volcanic rock (tuff) from Northern Ontario with diameters of about 47 mm and aspect ratios between 2.5 and 3 were prepared and polished flat at the two-end surfaces. The characteristics of the tuff samples are shown in Table 4.1. 8 0 Source Northern Ontario v Type Pyroclastic rock Chemistry Felsic or intermediate Components Augite, plagioclase, olivine with bubbly lava fragments, volcanic ash and sedimentary cementations minerals (zeolite, calcite, glass) Table 4.1 Characteristics of Tuff sample. 'Compressive tests under different loading rates were conducted using a static compressive testing machine (MTS) and stress-versus-strain curves were plotted (Fig. 4:4). Applied loading rates were 10, 20, 30 and 100 K N min"1, respectively. Unlike the general agreement, it was. noticed that the peak stress decreased with increasing loading rate due to the rock sample inhomogeneity and porosity. The data acquisitions and stress-strain calculations are shown in Appendix A . 81 Figure 4. 4 Stress versus strain curves for drill core of rock samples (Tuff). 4.6.1 3D Mapping A laser profilometer (National Research Council of Canada - NRC) was used to study the surface roughness of the broken rock (Budinski, 1989). This is a non-contact device able to produce a data file of x, y, and z coordinates. The profilometer consists of a laser probe mounted on a coordinate measuring machine. The probe automatically 82 moves .over the sample to measure the topography of the.fracture surface. Data are collected and processed using a personal computer. As shown in Fig. 4.5 to 4.8', topographical measurement of the fracture surface was carried out with a 3D imaging program (Mapping - developed by NRC) and an isometric view of the entire scanning field was constructed (Sadrai et al, 2005). The coarsest piece of the broken parts in each test was chosen and sample positions were selected in a direction such that the laser beam scanned parallel to the application of the compressive force. The scanning field was 10 mm x 10 mm. This area constitutes almost between one third and one. fourth of the entire broken surface for all samples tested and hence is considered a representative area. 1 In addition, imaging software enabled us to create cross-section profiles of the entire surface. The distance between profiles in sequence is a constant dependent on the scanning interval (resolution). For our experiments, the probe provided a resolution of either 62.5 um or 30 urn. In this way, a one-dimensional shape of each surface profile was obtained (Fig. 4.9). , i The sample traces are cross-sections perpendicular to the surface plane in the "x" direction, i.e., parallel to the application of the compressive force.. A large number of traces (150 to 350) for each sample were performed. A computer program, EASYDIG, facilitated the digitization and measurement of the surface topography along each trace. . 83 ,, F i l e r i l  M a p p i n g V i e w A n a l y s i s D a t a b a s e O p t i o n s W i n d o w H e l p DlaSlHl o i U I &\m\+\r\blfc.Mn.lBl 0\ +1*1+1 * l B\S\ h i tfl t?l H V 1 5 3 x 5 3 g r * l , c r e a t e d 0 3 / 1 5 ( 0 4 1 2 : 0 8 : 1 4 W r a n g E n g U B C l - D e t r e n d e d Mst-tl ij Si »> | Unite ntmv - [Mwne-Figure 4. 5 Surface topography of the rock fracture (HV1). - H e M a o p n a V i e w A n a r / * i s D a t a b a s e O o o o r s w m d o w H o l e OlsSlBI M-UI « |W | * I « [ blbjltj-lldlgl #| m | - » l » | g | g | - I jg| JjStort| jg 5l 3^ ® : | IBQfiHC Mapping - [Mining,- ^ M n j n o F - n p U B C l - P o i n t CTRL Figure 4. 6 Surface topography of the rock fracture (HV2). 8 4 5 5 x 5 5 g r t a , c r e a t e d 0 3 / 1 5 / 0 4 1 1 : 2 9 : 3 4 0 0 F o r H d p , p r w e P l C T R L Ji5tart| _3 _ _ <£> IWmC MappUg - fining- ^ Q W I n n g e n q L B C - M V Z • P a r t | 8:29 AM Figure 4 . 7 Surface topography of the rock fracture ( H V 3 ) . .' F i e M a p p i n g V i e w A n a l y s i s D a t a b a s e O p t i o n s W i n d o w H e l p - U l * l QlGgiBj L L \ m \ m\w\*-\*\blb.ltolL.llgl 0} m | + l * l g | g | - | |g j*?J 6 0 x 6 0 g r i d , c r e a t e d 03 J15 JD4 1 2 0 9 : 5 1 I—"~ionL — F o r H e l p p f e s t F l JJstart $ ^ (j? jPHJNRC Mapping - [fining- ^ W n l n g E n g U B C - H V a - P a i n t ] (ft) 8:31AM Figure 4 . 8 Surface topography of the rock fracture ( H V 4 ) . 85 Figure 4. 9 Example of the trace profile in the "X" direction. 4.6:2 Development of Surface Roughness Technique Considering,the scale of each plot, the roughness factor can be defined as the ratio of the length of the surface topography to the width of the trace (as a reference) in that cross section. 86 The results of these measurements are graphed for each sample in Fig. 4.10. The ranges of roughness factors are compared in Fig. 4.11, indicating that the sample with the highest loading rate exhibits the roughest surface. R o u g h n e s s vs T r a c e I • HV1 2-20 - i 2.00 --0 1.80 w tl 1.60 • U. CC 1.20 -1.00 • 1.380 1.364 1 -394 1.370 1.410 1 40 T r a c e 120 160 R o u g h n e s s vs T r a c e I H V 3 40 80 120 160 200 240 280 320 333 T r a c e R o u g h n e s s v s T r a c e o H V 2 2,20 2 CO 1.80 0 u m 1.60 LL rr 1.40 1.20 1.00 1.555 1.552 1.558 1.547 1 40 80 120 160 200 240 280 320 326 T r a c e , 160 -a i.4o -R o u g h n e s s vs T r a c e 2 126 2-145 IH V4 Figure 4.10 Roughness factor measurements along traces. 87 Figure 4.11 Comparison of roughness factor along the traces. The mean value is the "roughness factor" in one direction. For surface calculation, the results obtained for one direction can be extended into the second direction since the grid cells have equal length in both directions and the loading force acts in shear along the sample. So, the "surface factor" is found by squaring the roughness factor to provide a 2-D measure (Table 4.2). In fact, the influence of anisotropy makes rock materials behave differently in the two directions of force application (parallel and perpendicular) which may increase or decrease the surface roughness factor and thus 88 the overall calculation of the surface area for this size fraction. The nature of the data collected from these measurements (analog) made it extremely difficult and time-consuming to collect roughness data in the perpendicular direction. So, our approach was to consider equal values of roughness factor in both directions for the coarsest pieces, which is a reasonable approximation and yields lower specific surface area results than might otherwise be present. Obviously, this assumption requires more study in the future. The results indicate that roughness factor increases about 40% in one direction and about 100% in two directions with an order of magnitude increase i n loading rate. . Fig. 4T2 summarizes these results with the trend line showing the enhancement of roughness and surface factor as loading rate increases. As well, note the steady increase in the range (S.D.) of results as a function of loading rate indicating breakage becomes increasingly heuristic at high loading rates. Sample Roughness Factor S.D. Surface Factor HV1 1.384 , • • 0.019 .'; 1.92 HV2 1.557 ' 0.034 2.42 HV3 1 1.504 ' 0.074 ' 2.26 HV4 1.969 0.158 3.88 Table 4. 2 Coefficient of surface and roughness factor. 89 Figure 4 . 1 2 Roughness and surface factor vs. loading rate. 4.6.3 Development of Surface Area Technique Next, it is necessary to find the new surface area created by breakage. Three methods have been developed to obtain the produced surface area based on particle size analysis (Sadrai et a l , 2006). A Quantachrome surface area analyzer (BET) was used to measure the surface area of the finest particles (<400um). For coarse particles between 400um and 9.5mm, surface area was estimated theoretically using the 90 arithmetic mean size of each.fraction (Gaudin, 1967) assuming cubic particles (Fig. 4.13) together with an estimate of the shape factor for each fraction. For the coarsest sizes (>9.5mm), the exact shape of each piece can be readily determined and so, direct measurement of the surface of each piece was done by rolling' on a piece of paper and outlining the extreme boundaries (Fig. 4.14). With this technique, the actual surfaces of each piece of rock can be accurately transferred to a'plane surface. The sum of these surface areas determines the outer surface area for that piece. Digitization and direct measurement of surface.areas are shown in Appendix B. ' So,'it is possible to measure and/or calculate the apparent specific surface area, of the total broken material from each test. In applying shape factors (1.0-1.6), changes in this parameter as a function of particle size was considered to be linear. . ' D Mean size of fraction = D Surface area = 6 D 2 Weight =pD3 Specific surface area = 6 / p b i Figure 4.13 Theoretical calculation of specific surface area. 91 Extremity Digitized Figure 4.14 Direct measurement of the specific surface area (coarsest pieces). Gaudin (1967) recommended that shape factor ranges from 1.3 to 2.0 for finest particles. It is simply reasonable to consider the average of this range' for the finest particles in our tests. A shape factor of 1.0 is assigned to the coarsest pieces, since the shape factor decreases with increasing particle size.. Obviously this assumption requires more detailed study to establish how the parameter size-relationship changes for different materials and/or environments. : For surface roughness as a function of particle; size, it was necessary to combine directly measured surface, roughness of coarse particles (measured at a resolution of 30-60 um) with'the B.E.T..measurements for the finest sizes measured at a resolution 92 of 4 A (i.e., the diameter of nitrogen atoms adsorbed during B.E.T. measurement). So the data for surface roughness of the coarsest sizes shown in Table 4.2 was adjusted to a resolution of 4 A by applying a factor determined from the B.E.T. surface area measurement and the expected surface area based on mean particle size. Detailed calculations of apparent and ultimate specific surface areas can be found in Appendix C. Figure 4.15 depict our anticipated surface roughness-particle size relationship for all samples tested. Figure 4.15 Estimation of surface roughness as a function of particle size for a measurement resolution of 4 A. 93 Note that a decline in surface roughness occurs for the B.E:T. estimates for the finest two sizes (210 and 710 microns). We. believe that this drop is an actual physical occurrence and that surface roughness will continually decline during comminution as particle size decrease below 1 micron. Surface roughness, is reduced as edges and kinks on the surfaces of ultra-fine particles are worn away by attrition as particle size declines to the size of the crystal lattice (Tromans and Meech, 2001). Based on this technique (measurement, calculation and theory), the ultimate specific surface area and total surface area for each fraction was obtained (Table 4.3). HV1 H V 2 H V 3 H V 5 Fraction (mm) Ultimate S.S.A.(cm2/g) Surface Area (%) Ultimate S.S.A.(cm2/g) Surface Area (%) Ultimate S.S.A.(cm2/g) Surface Area (%) Ultimate S.S.A.(cm2/g) Surface Area (%) +9.52 12.58. 27.37' 8.12 10.10 10.79 ' 17.49' 10.03 38.19 +4.76 .59.53' 2.76 49.57 •• 2.51. 48.77 3.62 59.81 2^ 29 +2.38 . 196.71 6.28 192.57' ' 4.43 ' 1 . 187.69 4.64 198.57 3.92 +1.00 , 679.69 8.88 ' 782.18 8.30 ' 755.38 8!94 , 689.33, 9.20 +0^ 42 2624.45 11.46 3550130 13.94 ,3397.29 , , 14.30 2674.21 12.42 ' '+0.00 14293.87 43.25. 22730.44 60.72 21551.71 51.02 14633.50 33.98, Total 43.96 100:00 74.92 100.00 1 57.52 100.00 •25.73 100.00 (S.S.A. '=' Specific Surface Area) Table 4. 3 Estimation of surface area based on theory, measurement and calculation. 94 It can be seen that almost half of the new surface area was produced on the finest particles which make up only -0.2% by weight of the total sample. So, half of the 1 newly-created surface area occurred within less than 1 gram of the total sample. Clearly, material loss during a test can significantly affect the accuracy of measuring new surfaces (recovery of minute dust particles is extremely important to ensure surface areas are determined accurately). Overall accuracy of surface area depends'on several parameters such as shape factor estimation, weight measurement of each size fraction,1 assumptions inherent in a B.E.T. measurement, material porosity, and measurement resolution. , • 4.6.4 Estimation Method of Energy Efficiency; i As shown above, a method exists to calculate the surface area after breakage and the change in surface area can be obtained. So, it was possible to determine how much energy was expended to create new surface area assuming the specific surface energy of the rock is equal to that of quartz, i.e. 2 Jrh"2 (2000 erg.cm"2) (Fuerstenau and Abouzeid, 2002). The amount o f energy input into the rock core during a test can be determined to calculate the efficiency of breakage (Appendix A). Table 4.4 and 4.5, and Fig. 4.16 present the results of this analysis. As expected, the trend in energy efficiency was slightly decreased or almost constant because the tests were performed in a static regime with low strain rate. However, the power efficiency, the rate of energy use, was significantly improved as loading; rate increased. That is, the energy was consumed in shorter times at higher loading rates resulting in better use of power to create new surfaces. Sample Loading Rate (KN/min) Diameter (cm) Length (cm) Initial Surface Area (cm2) !* Modified Initial Surface Area (cm2) ** Determined Final Surface Area (cm2) Produced Surface Area (cm2) HV1 ', 10' ' 4.745' 13.592 237.98 : 290.34 29082.07, 28791.73 HV2 20 4.746 13.591 ' 238.02 290.39 50161.12 49870.73.' IIV 3 30 4.745, . 13.564 237.56 289.83 38019.90- 37730.08 HV4 100 , 4.746 , 13.668 .239.17 ' 291.79 17228.47 16936.68 Outer surface area of core samples before breakage. Projection of initial surface area based on the resolution of measurement at 4A. Table 4. 4 Estimation of produced surface area of breakage in an MTS machine. Sample Surface Energy '• (joule) Maximum Force (KN) Maximum Displacement. (mm) Consumed Energy (joule) Energy Efficiency (%) ' Time \(s) : Power Efficiency • ' (%/s) HV1 5.76 247.31 0.7768 .96.05 . 5.99 1480.83 0.0040 HV2 ' 9.97 ' • 233.53 " 0.7289 85.11 •11.72. 703.78. 0.0167 HV3 ' 7.55. 224.29 • 0.8431 • ', 94.55. •• 7.98 452.88 0.0176 HV4 3.39 172.99 0.6230 .  53.89 , -6.29 116.29 • 0.0541 Table 4. 5 Estimation of energy and power efficiency of breakage in an MTS machine. 96 Figure 4.16 Energy efficiency of breakage and power efficiency. 4.6.5 SEM Examinations Scanning Electron Microscopy (SEM) was used to examine the breakage phenomenon of the ultra-fine particles. It was observed that a considerable amount of fine macro-sized steps or spikes were present on the coarsest particle faces. Also, the 97 existence of numerous surface cracks (fissures) was apparent. HV4 (the highest loading rate) actually revealed this breakage pattern at the dimensions of the crystal structure (Fig. 4.17). It seems that the material in grain boundary regions became more brittle at high loading rates than at lower rates. More S E M examinations are shown in Appendix D. Figure 4.17 S E M examinations of the samples. 98 4.6.6 Discussion In this chapter, the surface roughness of four volcanic rock samples was investigated under different loading conditions in a static regime. A representative area was selected to be measured in each sample. With increasing loading rate, the roughness factor in one direction and surface factor in two directions increase resulting in greater enhancement in surface area production. However, conventional measurement of surface area of broken material is fraught with considerable error due to lack df accounting for surface roughness. As well, surface roughness measurements depend on the resolution used to make the measurement. Volcanic rocks such as tuff are highly porous which can affect the calculation of surface area and estimation of energy efficiency. One reason for high relative efficiencies observed in these tests is porosity. This causes high measurement of the new surface area which is not all created by breakage. Also, relative feed size was infinite (continuum) compared to bulk material. Therefore, outer core surfaces were measured as the initial surface area while open pores exist with high surface area within the core samples that can not be measured or estimated. The aim of this chapter was to develop techniques to enhance the estimation of energy efficiency, through surface area measurements. ; 99 CHAPTER 5 DESIGN AND OPERATING CHARACTERISTICS OF THE HIGH-VELOCITY IMPACT TEST FACILITY Conventional high-strain-rate, high-velocity impact facilities (Grosch and Riegel, 1993) are used to attempt to improve the strength of materials subjected to high energy impact such as spacecraft in outer space. Our research is attempting to use this approach instead to develop better fragmentation and find ways to minimize energy required for comminution: Our high-velocity test facility called "High-Velocity Impact Comminution" includes a one-of-a kind apparatus to.measure the• effect of high-strain-rates on rock breakage at projectile velocities between 10 and 500 m-s"1. 5.1 Introduction Impact velocities in most comminution equipment are about 1 to 10. m-s"1 while in blasting, the impact produces shock waves in all directions that move through the rock with velocities of 2 km-s'1 or more (Chi ;et al, 1996; Liu and Katsabanis, 1997). In order to study comminution in a velocity regime (Cho et al, 2003; Zhang et al, 1999; Grady, 1981), intermediate to these two extremes, an apparatus has been developed to measure the quantitative parameters of impact velocity on aggregated rock samples. The initial design which was considered as a vertical facility was modified to a horizontal one due, to the length of the launch tube and considering the stability of the machine and operating safety issues. In addition, a vertical apparatus would require a • 100 large supporting structure that was difficult to locate in the research building1 because of space limitations. 5.2 Principles of Operating Technique A high-velocity impact comminution apparatus has been designed and used to conduct compression experiments at variable impact velocities up to 500 ms"1 and pressures up to 300 psi. The principle of the method is that a projectile situated in a carrier (sabot) is accelerated down a barrel by compressed air to impact bulk samples. The carrier stops by the end of the barrel but the projectile continues its journey until it strikes the bulk material in the target chamber. In this technique, aggregated rock samples can be fragmented in a confined chamber while subjected to transmission of stress waves produced by impact velocity of the projectile. Part of the stress wave can be reflected and transmitted to the projectile and carrier which can cause permanent deformation. The projectile velocity immediately before impact is measured by two pairs of laser diode detectors. Laser sensors mounted adjacent to the barrel record the time and thus velocity of travel which is used to calculate the dynamic, fragmentation energy imparted into the test materials. The air inside the system and also between particles in the target chamber is evacuated by a vacuum pump. This assists'in launching the projectile without, air resistance. Evacuation also helps eliminate the air cushion I , .. . . '. .• •' . : 101 amongst rock particles and to transfer stress waves to the particles below the point of impact. • | The high-velocity impact apparatus consists of two groups of equipment. The first group.called "main equipment" is the one in which the actual process of acceleration, launching and fragmentation takes place. The second group consisting of auxiliary equipment, is responsible to assist the first, group to achieve their tasks. 5.3 Apparatus Main Equipment 5.3.1 Machine Design Basis In order to design the machine, the first step was tp consider the ,amount of material to be used in each test. The impact forces in comminution equipment apply to bulk material in a bed of particles instead of a single rock specimen which is used in most standard testing machine such as Split Hopkinson Pressure Bar (SHPB). The new device must examine the influence of impact velocities on bulk material to make the breakage phenomenon as close to that of a real operation as possible. Also, by testing bulk material samples rather than single rock particles, the influence of void spaces for expansion of the smaller broken particles can be studied. Therefore, a target chamber should be designed to fulfill these requirements. 102 5.3.2 General Configuration Figure 5.1 and 5.2 illustrate the UBC-CERM3 facility to conduct the impact velocity experiments. The apparatus consists of a reservoir, a launch-tube, a target chamber, a divider, flanges, supports, and structure. Detailed drawings of the apparatus are shown in Appendix E. In this system, a compressor produces compressed air which is cheap, clean, and relatively safe as a generating force. The main components of the apparatus will be described in detail in separate sub-divisions. Reservoir Launch Tube Target Chamber Reservoir Quick opening valve Launch tube J Coupling Vacuum flanges / Vacuum Chamber Projectile velocity measurement F i g u r e 5 . 2 U B C - C E R M 3 h i g h - v e l o c i t y - i m p a c t c o m m i n u t i o n a p p a r a t u s 5 .3 .3 T a r g e t C h a m b e r a n d P r o j e c t i l e Table 5.1 presents the alternatives for the chamber and projectile design. For a given amount of rock material, a chamber with a larger inside diameter or radius (Rc) requires a shorter height (He) and a projectile with higher mass (M P ) for the same unit energy input. 104 ' i Rock Chamber Projectile Lp = R c . Lp = 2R c M R (g) V c (cm3) Re (cm) H c(cm) Mp(g) Mp (g) 25 . 16.67 0.2 132.63 0.2 0.4 16.67 0.4 33.16 1.5 3.0 16.67 0.6 14.74 • 5:1 10.2 16.67 0.8 8.29 1.2.1 24.1 16.67 1.0 5.31 23.6 47.1 50 33.33 0.2 265.26 0.2 0.4 33.33 0.4 66.31 1.5 3.0 33.33 0.6 • 29.47 5.1 1.0.2 33.33 0.8 .. 16.58 .12.1 24.1 33,33 1.0' 10.61 23.6 47.1, 75 . 50.00 0.2 397.89 . 0.2' .0.4 50:00 0.4 99.47 1.5 3.0 ' 50.00 0.6 44.21 5.1 10.2 50.00 0.8 24.87 12.1 24.1 50.00 1.0 15.92 23.6 47.1' 100 66.67 0.2 530.52 0.2 0.4 • 66.67 .0.4 132.63 1.5 3.0 66.67 0.6 58.95 5.1 10.2 66.67 0.8 33.16 12.1 24.1 66.67 1.0 21:22 23.6 47.1 M R .= Rock Mass • • V c = Chamber Volume M P = Projectile Mass , Rc = Chamber Radius L P = Projectile Length H c = Chamber Height Bulk S.G= 1.5 Table 5.1 Chamber and projectile design alternatives 105 However, some restrictions are applied with respect to the size and dimension of the parts and connected sections. Also, a lighter projectile mass is desirable in order to achieve higher velocities in similar circumstances. Detailed calculations can be obtained in Appendix F. Thus, the target chamber has been designed (Appendix E) with a capacity of about 5-50 grams of rock material with a bulk S.G. of 1.5 (Fig. 5.3). Figure 5. 3 Target chamber The steel projectile has been designed as a cylindrical rod with a diameter of 12.5 mm and an S.G. of 7.5. The air gun can launch a projectile of high-strain-rate steel or 106 aluminum-alloy. A cylindrical shape with a flat surface at both ends is considered for all experiments. However, the machine is able to launch different projectile shapes. 5.3.4 Reservoir and Launch Tube The reservoir acts to accumulate a measured quantity of high-pressure air. Before each test, the reservoir is charged to the desired pressure using a compressor. The reservoir, launch tube and striker constitute a unified system able to convert potential energy into kinetic energy. Thus, as shown in Equation .5.1, a relationship among pressure, volume, velocity, and mass can be obtained by equating the potential energy of the gas to the striker's kinetic energy (Bourne, 2003). As a first approximation, it is assumed that the air behaves as a perfect gas with adiabatic expansion. As well, loss in transferring energy from the gas to the striker is assumed to be negligible. In actuality, a small amount of this energy is converted to heat. Different projectile masses and diameters were examined to select a suitable inside diameter (ID) for the tube (see Table 5.2). AP-A-L = 1 / 2 M V 2 (5.1) A P = Maximum change in pressure (Pa) A = Launch tube cross section area (m ) L = Launch tube length (m) M = Striker mass (kg) ' V = Velocity (ms"1) 107 Launch Tube (ID) Diameter (cm) Length (cm) Volume (cm3) Projectile Seat (cm 3) Density (gem-3) Mass (g) 3" 7.62 5.715 260.62 21.72 2.7 645.05 3.81 3.81 43.44 0 7.5 325.78 971 2" ' 5.08 3.81 77.22 6.44, 2.7 191.12 2.54 2.54 12.87 0 7.5 96.53 288 1 y2" 3.81 2.8575 32.58 2.71 2.7 80.63 [ 1.905 , 1.905 5.43 . 0 7.5 40.72 121 Sabot 1" 2.54 1.905 9.65 0.80 •. 2.7 23.89 Projectile 1.27 1.27 1.61 0 7.5 12.07 Total 36 .3/4" 1.905 1.42875 4.07 0.34 2.7 10.08 1. 0.9525 0.9525 0.68 o 7.5 5.09 15 1/2" 1 . 2 7 0.9525 1.21' 0.10 2.7 2.99 0.635 0.635 0.20 0 7.5 1.51 4 Table 5. 2 Launch tube inside diameter versus sabot and projectile mass i As shown above, the mass,of the striker gradually increases as inside diameter of launch tube increases to 1 inch but then increases rapidly at higher diameters. Therefore, an optimum 1 inch ID is selected for launch tube due to the need for a lighter striker and also the availability of a solenoid valve up to this size in the market (Appendix E). The sabot diameter is considered to be twice that of the projectile and is made of aluminum alloy with an S.G. of 2.7 (Table 5.2). Based on these analyses, a maximum pressure of 2 MPa (300 psi) is necessary. This pressure is needed to generate the critical stress for design purposes, although in reality the energy wil l distribute throughout the system at a lower pressure. A l l sections of the machine are made from mild steel with tensile and shear strengths of about 300 and 100 MPa respectively. For overall safety, a material factor of safety of 1.5 was chosen. Based on these considerations, a minimum thickness for each part was calculated. For safety reasons and operating considerations, critical conditions were, considered for all cases in which the selected thickness was calculated to be 42 times the required thickness for the tube, ~3 times for the flange bolts, and 6 times for shear stress failure of the flanges and plates. With these calculations, the thickness of the launch tube has to be at least 12.5 mm and calculations for the flange bolts show a minimum bolt diameter of 12.5 mm as well. For segments subject to possible shear failure such as plates and flanges, the required thickness was 25.4 mm. A novel cylinder and piston design was incorporated in the apparatus compatible with both high pressure and high velocity. Details of apparatus design calculations and stress analysis for all sections can be found in Appendix G. According to Equation 5.1, a 1-inch ID launch tube theoretically requires a 4.29 m (169 inch) length to create sufficient expansion of the pressurized gas to accelerate a 36 g projectile at a velocity of 500 ms"1 towards the ', ' 109 target (Table 5.3). Figure 5.4 presents alternatives of launch tube length as a function of air pressure. . , ' Pressure Pressure Launch Tube (psi) (N/m2) Length (m) 400 2759020 3.22 350 2414142 ' '3.68 300 2069265 4.29 250 • 1724387 ' : 5.15 200 , 1379510 . 6.44 150 1034632 1 8.58 100 689755 12.88 • 50'' '' 344877 . 25.75 Table 5. 3 Launch tube length Pressure vs Length 450 , • — Launch Tube Length (m) Figure 5. 4 , Launch tube length as a function of air pressure. 110 I Table 5.4 presents different projectile velocities that can be obtained at different gas pressures using the pressure regulator in the supply line. The launch tube has been attached to the machine structure using four supports such that it can be slid through i f necessary for maintenance or removal (Appendix. E). Pressure Pressure Launch Tube Area Mass Velocity (psi) (N/m2) Length (m) (m2) (kg) (m/s) 300 , 2069265 4.29 0.000507 0.036 500 250 1724387 4.29 0.000507 0.036 456 200 1379510 4.29 0.000507 0.036 .408 150 1034632 4.29 0.000507 0.036 353 . 100 689755 4.29 , 0.000507 0.036 289 50 344877 4.29 0.000507 . 0.036 204 40 275902 4.29 0.000507 0.036 183 . 30 206926 4.29 . 0.000507 0.036 158 20 137951 4.29 0.000507 0.036' 129 . 10 68975 ' 4.29 0.000507 0.036 . 91 • Table 5. 4 Theoretical velocities at different gas pressure The reservoir is designed with sufficient capacity to accelerate the projectile to a velocity of 500 m-s"1. The reservoir is112 inches long with inside and outside diameter of 4 and 6 inches, respectively; to tolerate, the maximum induced pressure (Appendix 111 E). As show in Figure 5.5, two 6 by 1-inch flanges are bolted on each end of the reservoir, which are connected to the compressor from one end through a quick opening valve and to the launch tube at the other end by a divider and a quick opening valve. The reservoir is attached to the structure by a cubic support. A total of 16 half-inch bolts maintain the reservoir in place in order to prevent any recoil to the system. Figure 5. 5 Reservoir connection to the compressor and divider 112 5.3.5 Multi-task Divider The divider has been designed for multi-task purposes (Appendix E). During experiments, compressed air enters the divider to accelerate the projectile down the barrel. As well, the divider can be used to set-up system to charge the barrel at the beginning of each test and then as an exhaust system to depressurize the system after each test. During evacuation, the divider provides a closed system for the vacuum pump to remove the air (Figure 5.6). Figure 5. 6 Divider multi-task interactions 113 5.4 Auxiliary Equipment 5.4.1 Selection of Compressor A Gardner-Denver compressor capable of producing a nominal pressure of 250 psi with 14 cfm compressed air was selected as the generating force for the system. This unit has an 80-gallon tank on which a 5 hp motor and cylinder are mounted (Figure 5.7). Figure 5. 7 Gardner-Denver compressor 114 5.4.2 Quick Opening Solenoid Valves The quick opening valve is a 1-inch ID, two-way (one inlet and one outlet) through-flow solenoid activated valve designed to operate between 0-300 psi and is in the normally closed position (Figure 5.8). When activated, the valve fully opens in about 50 milliseconds to allow unrestricted flow from compressor to the reservoir and from reservoir to the launch tube. Two more valves, the same as above but 3/ 4 inch in diameter, are connected to the launch tube and reservoir to deplete high pressure air to the atmosphere after each test. Also, a 54 inch valve is used to separate the vacuum pump from the launch tube after it is pressurized. Figure 5. 8 Quick opening solenoid valve 115 Valves are operated in a set sequence in each test in order to complete the operation. Figure 5.9 shows the sequence of operation for all valves installed in the pressure line. A remote electrical panel permits the valves to energize/de-energize in a safe and sound environment. Valve 4 Valve 1 Valve 3 Valve 2 Control Panel Valve 5 1 2 3 4 5 0 0 0 0 0 1. Energize to open valve 1 2. Energize to open valve 2 3. De-energize to close valve 1 4. De-energize to close valve 2 5. Energize to open valve 3 6. Energize to open valve 4 7. De-energize to close valve 3 8. De-energize to close valve 4 9. Energize to open valve 5 10. De-energize to close valve 5 Figure 5. 9 Sequence of operation for installed solenoid valves 116 5.4.3 Vacuum Pump Before each test, a vacuum pump activated by compressed air is used to evacuate the air from the launch tube and the connected sections such as the divider, the laser tube and the target chamber (Fig. 5.10). This is a necessary operation to decrease air resistance in front of the projectile and sabot while traveling. Air removal also prevents shock waves produced at the breach points at the end of the tube from reaching the sample material before actual impact stress causes breakage. Figure 5.10 Vacuum pump in the supply line 117 As shown above, the vacuum pump is installed at the side of the pressure line to evacuate the air from the system. Although these types of pumps offer a high mechanical efficiency of about 95%, the air remaining inside the launch tube still reduces the striker's velocity due to the presence of air molecules. A maximum negative pressure of -29 inHg can be reached with this equipment. Furthermore, the vacuum pump can be used before each test to return the sabot and projectile to the starting position by the pressure differential (atmospheric minus vacuum). At the connection of the vacuum pump to the launch tube, a solenoid valve in closed position avoids flow of pressurized air during operation and in open position allows the vacuum pump to access the tube. A safety, pressure switch is installed to disengage the valve from opening at pressures above 1 atmosphere. 5.4.4 Laser Intervalometer The laser intervalometer shown in Figure 5.11 is a basic laser-interrupt projectile detection system consisting of two lasers with corresponding detection stations and a timer/power supply unit. 1 A n adjustable focus laser is used to illuminate a 1 mm diameter diode in the detector unit that is positioned across the projectile's trajectory from the laser. The. passage of an object is sensed by the reduction of light level at the diode. This reduction of light will cause the detector to generate an output pulse that wil l start or 118 stop the counter. The time interval between the two pulses shown on the counter presents the projectile traveling time. This system is capable of detecting projectiles traveling in a velocity range of 10 to 2500 m/s with 0.1 [is timing resolution for the timer clock. Figure 5.11 Laser measurement system 119 C H A P T E R 6 T E S T W O R K A N D D A T A A N A L Y S I S Understanding the response of rocks under high velocity impact or high strain rates is the main objective of the current research. To achieve this objective, a high velocity test facility was used to examine the influence of impact velocities on rock breakage and energy efficiency in dynamic fragmentation. 6.1 Introduction During rapid loading events, the response of rock and its failure differ from that observed in static load experiments. Also, dynamic laboratory measurements using conventional techniques have shown that rock fracture is strain rate sensitive. But, the main deficiency in studies performed to, date is that the data for compressive behavior of rocks have been obtained for single particle samples. Whilst in reality, aggregated rock materials encounter the impact forces in comminution equipment. Therefore, bulk samples under various impact velocities can clearly present mechanisms of rock breakage similar to that observed in mineral processing equipment. In addition, bulk samples can provide voids for expansion of broken particles after breakage. The overall objective of this testwork program is to characterize compressive behavior of rock samples under high strain rates. The testwork was implemented in the UBC-CERM3 high-velocity impact facility in which a steel projectile was fired at high velocity into sized bulk material. Experiments can be carried out at projectile 120 velocities between 10 and 500 m/s. This range allows comminution to be studied at higher velocities than those of conventional equipment. According to the First Law of Thermodynamics, the energy efficiency of breakage in this work can be defined as the ratio of energy output to energy, input. Before and after each test, the surface area of material was measured. Therefore, the new surface area produced provides a measure of the total energy output from knowledge about the specific surface energy of the solid material. Energy input is calculated with the known mass of projectile and, its velocity of impact. 6.2 Selection of Rock Types Two aspects of rock behavior that are of particular interest include the effect of porosity and Poisson ratio (i>) on the failure of rock and the subsequent post-failure response under high-velocity impacts. Porosity causes material to exhibit high specific surface area after breakage mainly due to the pores within the particles but not due to enhanced fragmentation. On the other hand, intermediate values of the Poisson ratio may help particles to fail with higher transformation of compressive forces to tensile stresses resulting in better fragmentation. For small values of v, the lateral stress induced by a given axial load is relatively'small. In a dynamic experiment, material with low Poisson's ratio is expected to initiate the failure process by axial splitting since the lateral confining pressure is insufficient to completely suppress the tendency 121 for crack initiation and propagation. Therefore, ceramic materials with low Poisson's ratio tend to fail by brittle cracking leading to high fragmentation. On the other hand, a higher Poisson's ratio will induce higher confinement preventing the microcracks from sliding and also resulting in brittle failure. Thus, the failure mode is associated with plastic flow for large values of v (Chen and Ravichandran, 2000). However, the effect of high velocity impact on rock material properties has been suggested, to mask or remove the influence of Poisson ratio, on breakage (Katsabanis et al, 2003). Testwork has been conducted on three materials - highly porous limestone, quartz with low specific surface area (low porosity), and rock salt with the highest Poisson ratio of all material selected. Table 6.1 presents some of the rock properties of these samples. g £ Initial Poisson ^ n ^ ' a * Specific Specific Rock Type , .' V Bulk Density „ ..• Surface Area Surface Energy J r (g/cm) . . 3. v Ratio , 2, ,v -U* V 6 (g/cm3) (m7g) (Jm 2 ) Limestone 2.61 1.36 0.215 ' 0.728 1.0 Quartz 2.64 1.40 0.078 0.005 2.678 Rock Salt 2.1 1.28 0.3 0.02 0.577 * (Tromans and Meech) Table 6.1 Properties of rock samples as used in this test work 122 6.3 Material Sampling A total sample of about 5 kg from each rock type was received from different mines and sources. Characteristics of the rock samples are shown in Table 6.2. Chunk samples (more than 2 inches in diameter) were crushed, ground and sized until passed a 2 mm screen size. Bulk samples (-2 mm + 1 mm) or (-10 mesh +18 mesh) were selected to undergo experiments under high velocity impacts. Sieving time with the shaking machine was set at 10 minutes. Samples were subsequently reduced to the required weight for each target bed using a splitter and random selection technique. Rock Type Source Type/Class Components Limestone Quartz Rock Salt Organogenetic sedimentary rock, (fossiliferous), Calcareous rocks. Rock crystals, a-Sio2 colorless, (silicon oxide), Silica group, hexagonal. Ward's Natural Cubic crystals, NaCl, Science halides, precipitate in sedimentary deposits. Grasberg-Ertsberg Mine, Indonesia Minas Gerais, Brazil Caltite, dolomite, aragonite, some quartz, silicates clay minerals, sand, organic materials. Pure. Occurs in granite, pegmatite, volcanic rocks, alluvial, sandstone. Gypsum, anhydrite, clay, sulfur. Table 6. 2 Characteristics of rock samples 123 The target chamber in which fragmentation takes place is capable of holding about 5-50 g of material. Variable depths for the target bed can be used and two bed zones were established for different experiments. Zone " A " and " B " were designated with a target bed depth of 75 mm (13 g) and 150 mm (25 g), respectively. Samples were designated with the first letter of the rock type, the depth qf target bed (zone) which they are tested for, and the impact velocity in that test. Table 6.3 shows some examples of sample name designations. _ • , _ . ' Target Depth Impact velocity Sample Name Rock Type , . . , , . • J V (mm) (m/s) LB80 ; Limestone 150 80 QA120 Quartz. 75 120 SA50 Salt 75 50 Table 6. 3 Sample name designation 124 6.4 Limestone 6.4J Particle Size Analysis A sample was selected for particle size distribution using a sieving time of 10 minutes. The average weight of each size fraction is shown in Table, 6.4. The representative sample demonstrates the material size before breakage or with zero impact velocity. Sieve (mesh) . . Sieve Size fani) Weight (g) Weight (%) Cumulative Passing (%) + 10' 2000 o . 0.00 100.00 + 12 . 1650 2.795 14.87, 85.13 +.14 1410 4.2 22.35 62.78 + 16 1190 7.88 41.93 20.86 + 18 1000 2.145 11.41 9.44 -.18 0 1.775 9.44 0.00 18.795 100.00 Table 6. 4 Particle size distribution of representative sample (Limestone) 125 Particle size distribution analysis was done for all limestone samples tested at both depths (Appendix H). Particle size analysis of zone " A " is shown in Figure 6.1. It can be seen that significant improvements in breakage (d80) of 75 mm limestone occurs as the impact velocity increases. L imestone (13 g) 0 500 1000 1500 2000 Particle size (micron) Figure 6.1 Particle size analysis before and after breakage at variable impact velocities (Limestone - 75 mm) 126 Also, particle size analysis of zone " B " is shown in Figure 6.2. In this case, breakage (d80) of 150 mm limestone presents less improvement compared to the breakage of 75 mm and reveals unexpected behavior at highest velocity. Limestone (25 g) 0 500 1000 1500 2000 Particle s ize (micron) Figure 6. 2 Particle size analysis before and after breakage at variable impact velocities (Limestone - 150 mm) 127 Figure 6.3 presents weight percentage of -1 mm material before and after the breakage as a function of impact velocity for both zones. For this particle size, more fragmentation in zone A than zone B is indicative of better use of energy in shorter depths particularly at high impact velocities. 100 90 80 70 1 60 X 50 | 40 30 20 H 10 0 . X j j ( A | • LA (75) A LB (150) 0 50 100 150 200 250 300 350 Velocity (m/s) Figure 6. 3 Weight percent of -1 mm vs impact velocity (Limestone) 128 6.4.2 Material Loss In order to determine the material losses after each test, the broken samples extracted from the target chamber were weighed using a small laboratory scale. As shown in Table 6.5 and Figure 6.4, the amounts of losses for both zones are very low, about 2% by weight, and consistent. However, as discussed in chapter 4, material losses generally constitute fine particles which contain most of the surface area produced during a breakage event. Sample Velocity (m-s"1) Weight Loss (g) Weight Loss (%) 75 mm L A 80 82 '.. 0.23 1.79 L A I 10 112 0.25 1.90 L A I 80 180 0.28 2.16 •LA270 ,268 0.48 3.68 150 mm L B 70 73 .. 0.51 2.04 LB 180 , 182 0.61 • 2.43 LB240 236 0.30 1.20 . LB300 302 0.44 1.74 Table 6. 5 Material loss during experiment (Limestone) 129 20 18 16 _ 14 « 12 •3 10 8 6 4 2 0 A LA (13 g) • LB (25 g) 50 100 150 200 250 Velocity (m/s) 300 350 Figure 6. 4 Material loss vs impact velocity (Limestone) 6.4.3 Energy Efficiency Before and after each test, specific surface area of material was measured using a BET surface area analyzer (Appendix I). Total surface area was then calculated considering the retrieved amount of material after each test. According to the First Law of Thermodynamics and also the definition, the energy efficiency of breakage can 1 3 0 be calculated using Equation 6.1 (Sadrai and Meech, 2006) assuming the specific surface energy of limestone (CaCOa) to be equal to 1.0 J/m 2 (Tromans, 2007). 77 = ( ^ 2 - ^ i ) ^ x l Q Q ( 6 J ) —MV2 2 ; rj.— Energy Efficiency (%) ' 2 SSA 2 = Specific surface area after breakage (m /g) SSAi = Specific surface area before breakage (m /g) W = Weight of sample (g) S E = Specific surface energy (Jm") M = Projectile mass (kg) V = Projectile velocity (ms"1) Table 6.6 presents the result of this calculation for the limestone samples. In this table, the average of six BET measurements is used to determine the specific surface area of material before breakage. The specific surface area (SSA) of material after breakage is calculated based on the weighted average of BET measurements for each split size. 131 Velocity S.S.A. Change Energy Projectile Energy Energy (m.s1) (m2/g) (m2/g) Output (J) Mass (g) Input (J) Efficiency (%) 75, mm L A 00 0 , 0.728 LA 80 . 82 0.754 0:026 0.33 11.63 39.19 0.85 LAI 10 112 0^ 882 0.154 2.00 11.65 73.11 2.74 LAI 80 180 . 1.341 .0.613 7.97 11.61 188.10. , 4.24 LA270 268 .1.934 1.206 15.68 11.5.3 414.44 3.78 150 mm LB 00 0 0.728 LB 70 73 0.736 0.008 , 0.21 11.60 30.68 0.68 LB 180 182 1.120 0.392 9.8.1 11.47 190.91 5.14 LB240 236 1.481 0.753 18:84 11.64 324.98 5.80 LB300 302 1.436 ' 0.708 17.71 11.58 527.93 3.35 Table 6. 6 Calculation of energy efficiency, SE = 1.0 Jm 2 (Limestone) i • • . • • 6.4.4 Specific Surface Area Figure 6.5 shows the range of changes in specific surface area of limestone samples as a function of impact velocity. The minimum and maximum measurements of BET for SSA before breakage are indicated as the range on these graphs. It can be seen that the SSA is significantly improved with increasing impact velocities. 132 2.50 CN E, CC <D l_ < CD O 3 CO O id "o Qi a. CO 0.00 50 100 150 200 250 Velocity (m/s) 300 350 Figure 6. 5 Specific surface area vs impact velocity (Limestone) - The rninimum & maximum measurements of B E T for SSA before breakage are indicated as the range. In order to accommodate samples into the measurement cell in the BET apparatus, broken material was divided into different size fraction. Therefore, it is possible to plot the SSA as a function of particle size. Table 6.7 and 6.8 show the specific surface area measured along with the split size for zone A and B, respectively. The particle size is calculated from the geometrical average of upper and lower limit of each split size. Also, Figure 6.6 and 6.7 present the SSA as a function of particle size for zone A and B. It can be seen that the SSA for both zones increases with decreasing particle size. The graphs are generally shifted up with increasing impact velocity indicating that the SSA increases as impact velocity increases. 133 Sample S.S.A (m2/g) Split Size (/im) Particle Size (Jim) S.S.A (m2/g) Split Size (jim) Particle Size (jtxm) LA 80 0.57 +420 917 1.06 -420 20 LAI 10 0.59 +420 917 1.23 -420 20 LAI 80 0.91 +149 546 1.98 -149 12 LA270 1.68 +149 546 2.17 -149 12 Table 6. 7 Specific surface area and split size (Limestone - zone A) (geometrical mean particle size) 2.50 0.50 0.00 • LA80 ALA110 • LA180 LA270 200 400 600 Mean Particle Size (micron) 800 1000 Figure 6. 6 Specific surface area vs particle size (Limestone - zone A) 134 Sample S.S.A (m2/g) Split S. (lim) Particle S. (nm) S.S.A (m2/g) Split S. (lim) Particle S. Oim) S.S.A (m2/g) Split S. (/im) Particle S. (/im) LB 70 0.58 +1000 1414 0.73 +420 648 1.03 -420 20 LB 180 0.74 +1000 1414 0.92 +149 386 1.84 -149 12 LB240 0.96 +420 917 1.56 +74 176 2.16 -74 9 LB300 0.91 +420 917 1.46 +74 176 2.12 -74 9 Table 6. 8 Specific surface area and split size (Limestone - zone B ) (geometrical mean particle size) 2.50 0.50 0.00 • LB70 • LB180 LB240 • LB300 200 400 600 800 1000 1200 1400 1600 Mean Particle S ize (micron) Figure 6. 7 Specific surface area vs particle size (Limestone - zone B ) 135 6.4.5 Results The energy efficiency of limestone as a function of impact velocity is shown in Figure 6.8. It can be seen that the efficiency of breakage for both target depths of 75 and 150 mm increases with increasing impact velocity. However, it seems that the graphs will decline within the velocity range after passing a peak at around 230 m/s. Figure 6. 8 Energy efficiency vs impact velocity (Limestone) 136 6.5 Quartz 6.5.1 Particle Size Analysis The same procedures described in the past section were applied to the quartz samples. Two breakage zones of 75 and 150 mm were also examined for the depth of target bed. Before breakage, samples were selected for particle size distribution. The average weight percentage of each size fraction of the original sample is shown in Table 6.9. Sieve (mesh) Sieve Size (l"n) Weight (g) Weight (%) Cumulative Passing (%) + 10 ' 2000 0.00 0.00 100.00 . • +12 1650 5.39 28.73 71.27 + 14 . 1410 . . 4 : 1 2 . ; 21.95 49.32 1 ' +18 1000 8.34, 44.43 4.89 -18 0 0.92 4.89 0.00. 18.76 100.00 Table 6. 9 Particle size distribution of representative sample (Quartz) 137 Also, particle size distribution has been done for all quartz samples tested in both depths (Appendix J). Particle size analysis of zone " A " is shown in Figure 6.9. It can be seen that significant improvements in breakage (d80) of 75 mm quartz occurs as impact velocity increases. Quartz (13 g) Particle Size (micron) Figure 6. 9 Particle size analysis before and after breakage at variable impact velocities (Quartz - 75 mm) 138 Quartz (25 g) 0 500 1000 1500 2000 Particle Size (micron) Figure 6.10 Particle size analysis before and after breakage at variable impact velocities (Quartz -150 mm) The particle size analysis of zone "B" as a function of breakage velocity is shown in Figure 6.10. Surprisingly, breakage (d80) of 150 mm quartz for all samples presents almost identical behavior with only a small increase in the 80% passing size as velocity increases. Note however that the percentage of -1 mm particles does increase substantially with velocity indicating attrition perhaps. With increasing bed depth, the stress wave from the impact is unable to reach material at the bottom of the chamber 139 with sufficient intensity to break the coarsest particles. This was confirmed as the material extracted after breakage was almost intact at the bottom of the chamber. For both zones, the weight percentage of -1 mm material before and after breakage as a function of impact velocity is graphed in Figure 6.11. It can be seen that more fragmentation for this size fraction occurs in zone A than in zone B. This indicates that the energy of impact in zone A is used for more breakage rather than wasted in zone B. The energy may be wasted as heat or to pack material at the bottom of the target chamber. Therefore, the depth of target bed plays an important role to determine the breakage of material. 100 • Q A (75) A Q B (150) T—1—1—1—|—I—I I I 0 50 100 150 200 250 300 350 Velocity (m/s) Figure 6.11 Weight percent of-1 mm vs impact velocity (Quartz) 140 , 6.5.2 Material Loss For Quartz samples, Table 6.10 and Figure 6.12 present the material loss measured after each test. It can be seen that the losses for both zones are low, about 2.5 % by weight, and consistent. The higher losses for the zone A tests compared to the zone B tests are indicative of ultra-fine material losses. Sample Velocity (m.s1) Weight Loss (g) Weight Loss (%) 75 mm QA 80 82 '• 0.36 . 2.74 QA110 106 0.25 1.90 QA140 145 0.28 2.19 QA160 159 ' 0.51 3.94 QA190 191 0.31 2.38 QA220 216 0.31 2.42 150 mm QB 70 73 0.36 1.44 . QB110 111 ' 0.23 0.93 QB190 190 0.26 1.03 . Table 6.10 Material loss during experiment (Quartz) 141 20 18 16 _ 14 "ST 12 CA o -J 10 •53 8 3 6 4 2 0 • QA (13 g) • QB (25 g) 50 100 150 Velocity (m/s) 200 250 Figure 6.12 Material loss vs impact velocity (Quartz) 6.5.3 Energy Efficiency Before and after each test, specific surface area of material was measured using the BET surface area analyzer (Appendix K). Then, total surface area and the energy efficiency of breakage were calculated using Equation 6.1 allowing for specific surface energy of alpha-quartz (Si02) to be equal to 2.678 J/m 2 (Tromans and Meech, 2004). Table 6.11 presents the results for quartz samples. 142 Velocity S.S.A. Change Energy Projectile Energy Energy (m.s1) (m2/g) (m2/g) Output (J) Mass (g) Input (J) Efficiency (%) 75 mm QA 00 0 0.005 QA 80 82 0.022 0.017 . 0.60 11.55 . 38.41 ; 1 . 5 7 QA110 106 0.049 0.044 1.53 11.56 64.66 2.36 QA140 145 0.102, 0.097 3.38 11.58 121.27 2.79 QA160 159 0.158 0.153 5.34 .11.60 145.80 1 3,66 QA190 191 0.260 0.255 . 8.87 11.55 209.62 . 4.23 QA220 216 0.401 0.396 ' 13.80 11.56 268:72 ; 5.13 150 mm QB 00 '0 0.005 QB 70 73 0.008 ' 0.003 0.21 11.58 30.65 0.70 QB110 111 0.019 0.014 0.92 11.61 71.16 . 1.30 •QB190 190 . 0.052 0.047 3.17 11.65 209.40 , 1.51 Table 6.11 Calculation of energy efficiency (Quartz) 6.5.4 Specific Surface Area Figure 6.13 presents the range of changes in specific surface area of quartz samples as a function of impact velocity for, both zones. The specific surface area 143 before breakage is used as the starting point in these graphs. Like limestone, the SSA of quartz shows significant improvement as impact velocity increases. Table 6.12 and 6.13 show the specific surface area measured along with the split size for zone A and B, respectively. Also, Figure 6.14 and 6.15 present the SSA as a function of particle size for zone A and B. The specific surface area of quartz increases as particle size decreases. Also, the graphs in both zones are shifted up with increasing velocity. 0.45 0 50 100 150 200 250 Velocity (m/s) Figure 6.13 Specific surface area vs impact velocity (Quartz) 144 Sample S.S.A (m2/g) Split Size (/tin) Particle Size (/im) S.S.A (m2/g) Split Size (jim) Particle Size (fim) QA 80 0 +420 917 0.07 -420 20 QA110 0.01 +420 917 0.1 -420 20 QA140 0.01 +420 917 0.16 -420 20 QA160 0.03 +149 546 0.35 -149 12 QA190 0.07 +149 546 0.49 -149 12 QA220 0.21 +149 546 0.58 -149 12 Table 6.12 Specific surface area and split size (Quartz - zone A) (geometrical mean particle size) 0 100 200 300 400 500 600 700 800 900 1000 Mean Particle Size (micron) Figure 6.14 Specific surface area vs particle size (Quartz - zone A) 145 Sample S.S.A Splits. Particle (m2/g) |>m) S. (ftm) S.S.A Splits. Particle (m2/g) (jim) S. (/im) S.S.A Splits. Particle (m2/g) Qim) S. (|im) QB 70 QB110 QB190 0.00 +1410 1679 0.01 +1410 1679 0.01 +1410 1679 0.01 +1000 1187 0.01 +1000 1187 0.01 +1000 1187 0.02 -1000 32 0.04 -1000 32 0.13 -1000 32 Table 6.13 Specific surface area and split size (Quartz - zone B) (geometrical mean particle size) 0.14 0.00 -I 1 I 0 500 1000 1500 2000 Mean Particle Size (micron) Figure 6.15 Specific surface area vs particle size (Quartz - zone B) 146 6.5.5 Results Energy efficiency as a function of impact velocity is shown in Figure 6.16. It can be seen that the energy efficiency of breakage for both 75 mm and 150 mm quartz increases as impact velocity increases. As expected, the slope of the graph for 150 mm shows little improvement in breakage. That is, the stress wave does not have enough intensity to break material at the bottom of the chamber. Similarly, the wave that reflects back from the bottom quickly dies out and is unable to extend itself back to the top of the target bed. The graphs seem to have a peak at around 220 m/s. 6 0 I • • • • I • • • • I • • • • I • • • • I • • • • I 0 50 100 150 200 250 Velocity (m/s) Figure 6.16 Energy efficiency vs impact velocity (Quartz) 147 6.6 Rock Salt 6.6.1 Particle Size Analysis The same procedures described in the previous sections were applied to the rock salt samples. Before the impact tests, two different samples were selected for particle size distribution analysis. The average weight of all size fractions are shown in table. 6.14. ' Sieve (mesh) Sieve Size (pm) Weight (g) Weight (%) Cumulative Passing (%) + 10 2000 0.00 , 0.00 100.00 + 12 1650 2.73 21.06 78.94 .+ 14 1410 • 2.81 21.68 57.26 , + 16 1190 5.91 . 45.63 11.63 + 18 1000 0.82 6.34 5.29 18 o 0.69 5.29 0.00 12.94 100.00 Table 6.14 Particle size distribution of representative sample (Rock Salt) 1.48 For this sample, one breakage zone of 75 mm was only considered for the depth of target bed, since we knew from the earlier tests that zone B tests had too deep a target chamber. Particle size distribution was done for all samples tested (Appendix L). Particle size analysis of zone " A " is shown in Figure 6.17. It can be seen that significant improvements in breakage (d80) of 75 mm rock salt occur as impact velocity increases. Rock Salt (75 mm) Particle Size (micron) Figure 6.17 Particle size analysis before and after breakage at variable impact velocities (Rock Salt - 75 mm) 149 Figure 6.18 presents the weight percentage of -1 mm material before and after breakage as a function of impact velocity. It can be seen that the amount of fine particles increases with increasing impact velocity. Figure 6.18 Weight percent of-1 mm vs impact velocity (Rock Salt) 6.6.2 Material Loss The material loss measured for each rock salt sample is shown in Table 6.15 and Figure 6.19. The weight losses are very low, about 2 % by weight, and consistent. 150 Sample Velocity (m.s_1) Weight Loss (g) Weight Loss (%) 75 mm SA 80 75 0.24 1.82 SAI 10 109 0.12 0.89 SA160 161 0.42 3.23 SA200 204 0.28 2.17 Table 6.15 Material Loss during experiment (Rock Salt) A SA (75 mm) 50 100 150 Velocity (m/s) 200 250 Figure 6.19 Material loss vs impact velocity (Rock Salt) 6.6.3 Energy Efficiency The surface area analyzer (BET) was used to measure the specific surface area of material before and after each test. The.result of these measurements can be found in Appendix M . Equation 6.1 is utilized to calculate the total surface area and the energy efficiency of breakage assuming the specific surface energy of Halite (NaCl) to be equal to 0.577 J/m 2 (Tromans and Meech, 2002). Table 6.16 presents the result of this calculation for rock salt samples. Sample ... Velocity (m.s^ ) S.S.A. (m2/g) Change (m2/g) Energy Output (J) Projectile Mass (g) Energy Energy Input (J) Efficiency (%) SA 00 ' 0 0.020 SA 80 75 0.030 .0.010 0.08 11.57 32.91 0.23 SA110 109 0.080 0.060 0.45 11.56 69.24 0.65 SA160 161 . 0.180 0.160 1.20 . 11.57 149.28 0.80 SA200 204 1 0.229 0.209 • 1.57 • 11.61 242.60 0.65 Table 6.16 Calculation of energy efficiency (Rock Salt) 152 6.6.4 Specific Surface Area Figure 6.20 presents the specific surface area of rock salt samples as a function of impact velocity. The specific surface area before breakage is used as the starting point in the graph. Like other samples, the SSA of Salt shows significant improvement with increasing impact velocity. No measure was made of the influence of particle size on specific surface area for rock salt because of lack of sample. 0.300 T 0.250 A 0.000 -I 1 • , , , __| 0 50 100 150 200 250 Velocity (m/s) Figure 6. 20 Specific surface area vs impact velocity (Rock Salt) 153 6.6.5 Results Energy efficiency as a function of impact velocity is shown in Figure 6.21. It can be seen that the energy efficiency of breakage for 75 mm rock salt increases as impact velocity increases. The graph shows a peak at around 160 m/s. 1.00 Figure 6. 21 Energy efficiency vs impact velocity (Rock Salt) 154 6.7 Comparison of Energy Efficiencies Figure 6.22 presents the influence of impact velocity on the efficiency of rock breakage for all samples tested with 75 and 150 mm as the depth of target bed. As can be seen, the efficiency of all samples has been significantly improved with increasing impact velocities. Therefore, it can be concluded that the energy efficiency is doubled or tripled with increasing velocity of impact on rock breakage. Figure 6. 22 Comparison of energy efficiencies 155 6.8 Comparison to Bond Energy 6.8.1 Work Index Correlation In order to compare the energy efficiency of breakage with the conventional Bond energy, the Bond work index of all material was measured. Ball mill grindability test was used for direct measurement of work index for limestone sample. For quartz and rock salt samples, work index was measured with the reference method utilizing a laboratory rod mill. The procedures of ball/rod mill tests are shown in Appendix N . Table 6.17 presents the result of Bond work index measurements for all sample tested. Sample F80 (urn) P80 (um) Wi (kWh/t) Limestone , (reference) 2700 13.80 Quartz. 2950 285 12.69 Rock Salt 2870 117 7.02 ''. Table 6.17 Bond work index measurements 156 6.8.2 Bond Work Input and Velocity Particle size analysis done before and after breakage can be used to determine the energy requirements based on the Bond equation. Table 6.18 to 6.20.present the results of these calculations for limestone, quartz and rock salt, respectively. It can be seen that the work input increases significantly with increasing velocity for 75 mm target,bed. However, improvement in this parameter is slower or constant for the 150 mm target bed. This proves the idea that most of the work input in longer depth is consumed by packing instead of breaking the rock. Sample Velocity (m/s) d80 (um) Bond Work Input (kWh/t) 75 mm 1.A00 0 1570 0.00 LA80 82 1170 0.55 LAI 10 112 1060 0.76 LAI 80 180 790 1.43 LA270 268 380 3.60, 150 mm LB00 0 1570 . 0.00 . LB70 •73 ' 1290 0.36 LB180 182 • . 1130 0.62 LB240 236 720 : 1.66 LB300 302 720 1.66 Table 6.18 , Bond work input calculations (Limestone) 157 d80 Bond Work Input (um) (kWh/t) 75 mm QAOO •o 1750 0.00 QA80 8 2 ' 1300 0.49 QA110 106 1130 0.74 QA140 • 145 820 1.40 QA160 159 . 710 : ' 1.73 QA19Q •' •'• 191 • 580 2.24 QA220 216 460 2.88 150 mm QB00 0 1750 0.00 QB70 • 73 1640 o.io QB110 111 1650 0.09 . QB190 190 1630 : 0.11 Table 6.19 Bond work input calculations (Quartz) Sample Velocity (m/s) ,d80 (um) Bond Work Input (kWh/t) 75 mm SA00 0 1660 0.0,0 SA80 75 . 1350 0.19 SAI 10 • 109 1240 0.27 SA160 • 161 , 730' 0.88 SA200 204 510 • . 1.39 Table 6. 20 Bond work input calculations (Rock Salt) 158 As shown in Figure 6.23, Bond work energy of all samples has been significantly improved with increasing impact velocities. At the constant velocity in the 75 mm samples, the results are analogous to the energy efficiency of breakage presented in Figure 6.22, particularly at high velocities. For target bed of 150 mm, the intensity of the impact energy is simply not enough to reflect back from the bottom of the target chamber to break more material at the top. As a result, breakage occurs for only a small amount of material and therefore only a small amount of Bond energy is consumed. Bond Energy v s Velocity 4.00 350 Velocity (m/s) Figure 6. 23 Bond work input as a function of impact velocity 159 6.8.3 Bond Work Input and Energy Input Figure 6.24 shows the Bond work input as a function of total energy input for all samples tested. It can be seen that the Bond energy of all samples has been significantly improved as energy input increases. However, this improvement in the target bed of 150 mm is lower than in the 75 mm to eventually become constant at high velocities (high energy input). Figure 6. 24 Bond work input as a function of total energy input 160 C H A P T E R 7 R E S U L T S A N D DISCUSSIONS The research theme in the area of hyper or high-velocity impacts mostly deals with understanding the behavior of material under impact velocities in space applications such as satellites and spaceships. Investigations determine ways to improve the- strength of material used to make the structures and to prevent these bodies from breaking. Instead, our studies have attempted to merge impact engineering as a solution for mining ,and comminution problems in terms of rock breaking. The process of rock fragmentation under high velocity impact has been studied for some time. It is obvious that a high velocity imparts considerable amounts of energy into the rock material. However, it was never known i f an increase in energy efficiency at the,same energy level occurs when strain rates are high. For years, using explosives provided a way to break rock in tension with observed efficiencies about one order of magnitude greater than that of comminution. But, it,,has never been verified until now that high strain rates also provide increased efficiencies in terms of generating new surface area. That is, the percentage of energy used that ,ends up as new surface area increases with the velocity of impact. This effect has never before been demonstrated. 1 This study examined the effect of impact velocity on rock breakage and the energy efficiency of fragmentation in both a static and a dynamic regime. It is now proven that higher strain rates than those achieved by conventional comminution • • 161 equipment provide an opportunity to liberate valuable minerals in a more efficient manner. In material science and rock mechanics, it is considered that strain rates influence the behavior of crack propagation. At low impact velocities, the largest flaw in the particle is responsible for failure, while at high velocities, several flaws propagate simultaneously to relieve the increased tensile stresses. In addition, high strain rates generate a large number of microcracks that reduce the resistance of the rock to post failure breakage. The models herein developed strongly demonstrate that the intensity of energy input into the process is a key variable to enhance the fragmentation of rocks and minerals. The model has been developed based on the energy input and the velocity of impact. , , . 7.1 Energy Input Model In this study, the model of breakage utilizes the energy content of the projectile velocity and mass to measure the efficiency. We found that breakage occurs more efficiently at higher impact velocities than at lower ones. Now, the question remains whether the velocity or the, level of energy input causes this enhancement? These two factors are related via general energy formulae. Figure 7.1 presents the range of energy efficiency as a function of specific energy input for all samples in both zones. Note that the trend line for each data set follows a general logarithmic rule as shown in Equation 7.1 with an exponent value of around 0.5. Had this exponent been close to 1.0, then energy in would be the determining factor. A slope near 0.5 indicates that velocity is likely the key factor since energy input is a function of velocity squared. Thus, it is clear that efficiency of breakage is related directly to the impact which must translate directly into the velocity of the propagation cracks. However, the slope of the trend line is slightly above 0.5 (0.64, 0.64, and 0.52) indicating that the specific energy level does have a small role in overall efficiency. Energy Efficiency vs Specific Energy Input 10 e, = 0.1859x 0.5681 x • Quartz • Limestone • Salt 0.6362 e 0.1 1 10 100 Specific Energy Input (Jig) Figure 7.1 Energy efficiency vs specific energy input 163 (7.1) yje = Energy efficiency (based on energy input) (%) Ei = Specific Energy Input (J/g) . I I Ke = Energy Index (% g1 i f 1 ) This is an empirical equation which is valid . in the range of velocity measurements, i.e. 50 to 250 m/s, or in a dynamic regime. The energy index (Ke) is also an empirical parameter affected by many factors such as type of material, material characteristics, mechanical properties of material, Poisson's ratio, grain size, density, porosity, environment, etc. To determine this factor, a large number of similar tests with different materials and different variations are required. Also, the experiments should be extended to higher and lower velocities than our range in order to. determine the value of Ke in the above equation over an extended dynamic situation. In the static regime, parallel experiments should be performed to establish values for that mode of failure. . 1 , 164 During calculation of energy efficiency, it is assumed that all the kinetic energy of the projectile is transferred to the rock material. In reality, some of this, energy is wasted as heat, sound and vibration generated in the material which eventually dissipates into the surroundings. Also, it is assumed that all input energy is transferred to the sample for breakage of material and rock fragmentation. But, strain energy is partially used to compact voids and spaces among bulk samples which may not transfer to rock fragmentation. Furthermore, there may be deformation of the projectile at the point of impact which may limit some of the strain energy input to the sample. Finally, some of the stress waves produced by the projectile may be transferred to the apparatus structure and not reflected back to the material from the bottom of the target chamber.' This may also reduce; the amount of energy input to the sample. 7.2 Impact Velocity Model The range of energy efficiency as a function of impact velocity has been developed for all samples in both zones. As shown in Figure 7.2, materials with a higher specific surface energy appear to show higher energy efficiency at the same impact velocity. 165 Figure 7. 2 Energy efficiency vs impact velocity The trend line for each data set presents an equation that may be derived to relate efficiency and impact velocity (Equation 7.2). A slope near 1.0 indicates that velocity is the determining factor. But because the exponent lies above 1.0 (1.3, 1.3, and 1.0) means that energy also has an effect. 166 Tjv — Energy efficiency (based on impact velocity) (%) V - Impact velocity (m/s) K v = Velocity Index (% s/m) This equation is empirical with validity over the range of velocity measurements performed in this work, i.e.. 50 to 250 m/s. The velocity index (K v) is an empirical parameter affected by many factors such as type of material, material characteristics, mechanical properties of material, Poisson's ratio, grain size, density, porosity, environment, etc. To determine these relationships, similar tests with different materials and variations,are required. The experiments should be extended to higher and lower velocities than our range in order to measure the value of K v in the above equation, over an extended range. Similar, experiments should be performed to compare K v values for a static mode of failure. From the above considerations, it would appear that' the efficiency of breakage is a function of the velocity of impact which is related to the square root of input energy. Therefore, it can be concluded that impact velocity is the key to enhancing the efficiency of rock fragmentation and has an important effect independent of total energy input. : • ' « . • , • . , ' < , , . 167 7.3 Influence of Poisson's Ratio The effect of Poisson's ratio on the energy efficiency of some rocks and minerals is shown in Figure 7.3. In his theoretical studies, Tromans (2007) predicted that the maximum energy efficiency of brittle materials improves from 5-9 % as Poisson's ratio increases from a low range of 0.05-0.10 to a high range of 0.45-0.50. However, our experimental efficiencies (at a constant velocity of 200 m/s) show a decline with increasing Poisson's ratio of the material tested. 0.1 0.2 0.3 Poisson's Ratio 0.4 0.5 Figure 7.3 Energy efficiency vs Poisson's ratio (Efficiency® V=200 m/s) 168 The reason for this effect is that the theory is based on the material being.a continuum while bulk material was used in our experiments. The voids and spaces among particles create different energy transfer such as higher shear or tensile forces at point contacts between particles. Therefore, the Poisson's ratio for the entire system is different than that of the solid rock. As a result, material with low Poisson's ratio will likely exhibit higher bulk material system values. Arid, material with high Poisson's ratio may exhibit ductility (or plasticity) under high velocities so that the crack propagation and fracture,may decrease. The degree of ductility (or plasticity) for example, is, higher for rock salt than it is for quartz. Indeed, we did Observe some agglomeration of salt particles upon removal of the sample from the target chamber. These agglomerates broke up easily upon preparation of the sample for surface area measurements. 7.4 • Pressure Model of W o r k Efficiency The developed model utilizes a change in surface area of rock material as the output of the fragmentation process caused by the impact energy of the projectile. This work done •oil the sample can also be estimated by direct measurement of pressure and volume change during breakage. It is recommended in the future to install pressure gauges along the target chamber. However the data,in Table 7.1 shows that the impact pressure can be estimated by the projection of force.from the initial reading of the regulator before each test considering the cross section of the tube. The change in ' '. 169 volume can also be calculated by measurement of the compaction level of the material during experiments. Now, the work done to compress the bulk material. can be calculated. Sample (75 mm) Initial Pressure (psi) (N/m2) Force (N). Impact Pressure (N/m2) (psi) Displacement (compaction) (inch) (m) Volume (AV) (m3) QA 80 30 206844 . 105 827376 120 0.3 0.00762 9.65E-07 QA110 50 344740 , 175 1378960 200 0.5 0.0127 1.61E-06 QA140 . 100 689480' 349 2757920• •400 0.8 0.02032 2.57E-06 QA160 150 1034220 524, 4136880 600 0.9 0.02286 2.90E-06 ' QA190 150 1034220 .524 4136880' 600 , • 1 0.0254 3.22E-06 QA220 180 /124L064 629 4964256. 720 1.2 . 0.03048 • 3.86E-06 L A 80 30 , 206844 105' - 827376 120 0,6 0.01524 1.93E-06 LAI 10 50 344740 ' 175 ' .1378960 200 0.8 0.02032 2.57E-06 LAI 80 100 689480 349 2757920 400 1 . 0.0254 3:22E-06 ,,LA270 200 1378960 699 '5515840 800 1.1 0,02794, 3.54E-06 SA 80 • 30 206844 105 ' .827376 120 •0.5 0.0127 1.61E-06 SAI 10 50 344740. 175' 1378960 200 0.75,. 0.01905 2.41E-06 SA160 100 689480 349, 2757920 400. .0.95 0.02413 3.06E-06 SA200 170 1172116 594 4688464 680 1.15 0.02921 3.70E-06 Table 7.1 Calculation of impact pressure and volume (zone A) 170 Table 7.2 presents the work efficiency achievable for each test in zone A . The ratio of this efficiency to that obtained for the surface area measurements indicates what percentage of the work done in compressing the bulk material maybe transferred into breakage and new surface area (or energy). Sample (75 mm) Work Output (P.AV) (Joule) Energy input (=0.5mv2) (Joule) Work Eff.* (maximum) (%) Energy Eff.* (surface area) (%) Ratio •(%) QA 80 ' 0.80 38,41 2.08 .1.57 , 76 QA110 2.22 64.66 ', 3.43 2.36 69 QA140' ' 7,10 ' .. 121.27 . 5.85 . 2.79 • .'48 QA160 11.98" , 145.80 8.22 ; 3.66 . ' 45 QA190 13.31 209.62 6.35 4.23 67 QA220 19.17 268.72 7.13 5.13 72 . , , LA 80 1.60 39.19 4.08' 0.85 21 LAI 10 3.55 . • ' 73.11 4.86 2.74 56 LAI 80 8.87 .188.10 • '4.72 4.24 90 LA270 19.52 ! 414.44 • 4.71 ; 3.78 80 SA 80 1.33' 32.91 . 4.04 . 0.23 , 6 SA110 3.33 '. , 69.24 1 ' 4.81 . 0.65 ' 14'.' SA160 8.43 149.28 5.65 0.80 . 14 SA200 17.35 • 242.60 ' 7.15 0.65 9 * Eff. = Efficiency T a b l e 7. 2 P r e s s u r e m o d e l o f m a x i m u m e n e r g y e f f i c i e n c y ( z o n e A) 171 These calculations were made based on the expansion of compressed air considering the cross section area of the launch tube and projectile. It is assumed that the loss of pressure in the launch tube is negligible. In practice, there is about 5-10 % pressure loss due to friction between moving parts. In addition, there are some small losses at high pressures due to leakage of compressed.air around the o-rings. It is also assumed that the resistance of air. remaining in the launch tube while the projectile.is traveling is insignificant (this is reasonable since the vacuum level is -29 iriHg). Table 7.3 and 7.4 present the estimation Of impact pressure-volume change and the maximum energy efficiency achievable for each test in zone B. Sample (75 mm) Initial Pressure (psi) (N/m2) Force (N) Impact Pressure (N/m2) (psi) Displacement (compaction) (inch) (m) Volume (AV) (m3) QB 70 .f 30 ' 1 206844 105 827376 120 0,3 • 0.00762 9.65E-07 QB110 50 344740 ,175 137,8960 200 0.45 O.OH'43- 1.45E-06 QB190 150 1034220 524 4136880 600 0.7 0.01778 2:25E-06 LB 70 ,30 206844 105 827376 .120 0.5 0.0127 1.61E-06 LB 180 100 689480 349 '2757920 ,400 •1.25 0.03175 4.02E-06 LB240 180 1241064 629 4964256 720 1.4 0.03556 4.50E-06 LB300 200 1378960 699 5515840 800 , 1.6 0.04064 5.15E-06 Table 7. 3 Calculation of impact pressure and volume (zone B ) 172 Sample (75 mm) Work Output (P.AV) (Joule) Energy input Work Eff. Energy; Eff. (=0.5mv2) (Joule) Ratio (maximum) (surface area) (%) (%) (%) QB 70 QB110 QB190 LB 70 LB 180 LB240 LB300 0.80 2.00 9.32 I. 33 II. 09 22.36 28.40 30.65 71.16 209.40 30.68 190.91 324.98 527.93 2.61 2.81 .4.45 4.34 5.81 6.88 5.38 0.70 1.30 1.51 0.68 5.14 5.80 3.35 27 46 34 16 88 84 62 Eff. = Efficiency Table 7. 4 Pressure model of maximum work efficiency (zone B) The total energy input to the projectile in our apparatus is produced as the projectile accelerates along the.barrel. At the point of contact with the material, the projectile has gained its maximum energy according to its velocity. From this moment, free traveling of the projectile is completed as it starts to transfer its.energy to the rock material in the form of some reversible work. This compression (or work) can be measured in the form'of changes in pressure and volume. Therefore, work is equal to APV. During this, process, breakage occurs to cause a change in surface energy. The remaining energy is wasted as heat, light, sound, etc. The work done by the projectile 173 in compressing the target bulk material is of a similar order of magnitude to that of the newly created surface energy. It is not clear i f this work is a parallel energy path or a serial one. Perhaps it is a combination of these two modes of transformation. The fact that the ratio of surface energy out to work done is much lower for the rock salt suggests a lack of correlation between the two modes and hence a parallel path. Whether this work is actually reversible or not, also remains unanswered. A spring when compressed holds potential energy which is released once the compression force is removed. Such is not the case with bulk material although we know that under the right conditions the compressed volume can be recovered. Whether or where the eriergy is recovered is unknown. 7.5 Model Adjustment ' The models for velocity and energy input. developed in the previous sections successfully describe the, behavior of material in accordance with the results of experiments for. the target bed of zone A and B. For both zones, it was shown that the efficiency of breakage is strongly dependent on the velocity of impact. , However, the; data ,for zone B (150 mm) needs some amendment since the majority of breakage occurs in the upper region of zone B (which corresponds to zone ' A with respect to the point of impact). Therefore, the results for limestone, and quartz samples can be adjusted assuming'that the majority,of breakage occurs in the upper !l ' ' ' .• ' .174' region in the zone B tests. Zone B from 75 mm to 150 mm showed little change in terms of producing new surface area, but some of the energy input was consumed to pack material in this section. If the reflected stress wave off the bottom of the target chamber actually has little effect in. our tests, then we can assume that breakage in the zone A tests would be comparable to breakage in the upper region of the zone B tests. To test this hypothesis, all of the breakage in the zone B tests can be assigned to the upper region of the sample. If this attribution results in a specific surface area for the upper zone material less than that achieved in the zone A tests, then the hypothesis fails. This in fact is the case; the change in specific surface area in the zone B tests are less than half that of the zone A tests in virtually all equivalent (same velocity) results which confirms that the reflected stress wave,does play a very important role in the mechanism of breaking bulk material under high velocity impact and the depth of the particles to be broken is limited by the reflection distance of this stress wave. 7.6 Efficiency of Bond Energy Formula Conventional approaches to analyzing energy.use in comminution establish the Bond Work Index to size equipment and calculate process efficiencies. "Bond" is an empirical law but it was based on a theory of crack tip propagation being a square root relationship to tip dimension. ;, 175 Velocity Bond Work Input Energy Output J o ut /Jbond Sample (m/s) (kWh/t) (J) (J) (%) 75 mm LA 00 0 0.00 0.00 - 0.00 LA 80 82 . 0.55 25.82 ' 0.33 . 1.29 LAI 10 ' 112 '• 0.76 35.37 2.00 5.65 LAI80 180 1.43 66.78 7.97 . 11.94 LA270 .. 268 3.60 , 168.31 . .15.68 9.32 150 mm* LB 00 0 0.00 0.00 - , 0.00 LB 70 .. 73 0.45 40.50 0.21 •'• 0.52 LB180 182 0.78 70.20 9.81 , 13.97 LB240 236 2.15 193.59 18.84 9.73 LB300 302 2.15 193.59 17.71 9.15 Corrected size analysis for breakage in the top 75 mm region of the specimen Table 7. 5 Efficiency based on Bond work input (Limestone) The Bond work input can also be used in our work to compare with the efficiency of breakage under high-velocity impact. Energy output is the change in surface energy of material as calculated, in the previous chapter while energy or work input to the sample can be calculated using the Bond energy-size formula. Table 7.5 to 7.7 present the results of these calculations for all samples tested! The results.indicate significant 176 improvement in the efficiency of Bond energy translated into new surface energy for all materials as impact velocity increases. According to the model adjustment described previously, the data for the quartz zone B Bond. work input was .corrected for size analysis assuming breakage only occurred in the top region of the specimen. Sample Velocity Bond Work Input Energy Output Jout/Jbond (m/s) (kWh/t) (J) (J) '(%)' 75mm QA 00 , 0 0.00 0.00 0.00 QA 80 82 0.49 22.75 0.60 2.65 QA110 106 0.74 34.70. ' '' 1.53 4.40 QA140 145 1.40 6543 338 . 5.17 QA160 1 .159 .• 1.73' 80.92 5.34 6.60 QA190 '.191 , 2.24 104.63 8.87 8.48 QA220 216 ' 2.88 . 134.94 13.80 10.22 150 mm* i 1 • ,. QB 00 0 0.00 . 0.00 - 0.00 QB 70 73 0.16 7.16 0.21 2.99 QB110 111 0.24 10.94 0.92 8.46 QB190 190 0.41 18.36 3.17 17.25 Corrected size analysis for breakage in the top 75 mm region of the specimen Table 7. 6 Efficiency based on Bond work input (Quartz) 177 Velocity Bond Work Input Energy Output Jout/Jbond 1 ' ' 1 (m/s) (kWh/t) (J) (J) (%) 75mm i SA 00 0 0.00 0.00 0.00 SA 80 75 0.19 8.78 0.08 0.85 SAI 10 109 0.27 12.66 0.45 3.55 SA160 161 0.88 • 40.96, 1.20 2.93 SA200 204 1.39 64.84 1.57 2.42 Table 7. 7 , Efficiency based on Bond work input (Rock Salt) Figure 7.4 shows the efficiency of the Bond energy formula to predict energy utilization as a function of the velocity of impact. The graph clearly shows that the energy'use for all samples is significantly improved as impact velocity increases. As one would expect the actual energy used in the Bond forrnula at low impact velocity is of the order of 1%. The shaded area is indicative of the range of Bond energy prediction at high-velocity impact with changes in size from finer to coarser. ' • . • .' ' ' • • i •  . - ' • • • As one would expect Bond is a better predictor of energy efficiency for coarser sizes than it is for .finer sizes. Yet in both cases, the efficiency is seen to rise substantially as impact velocity is increased. • One of the reasons for Bond failing to '• ' 1 7 8 predict well for finer sizes relates to the change in d80 size (used in the Bond formula) with respect to change in the amount of very fine particles. At low velocities, the d80 size remains relatively unchanged while the amount of fine material (<0.5 mm) increases with a corresponding increase in overall specific surface energy. Bond does not use this information. 20.00 18.00 16.00 14.00 12.00 10.00 8.00 6.00 4.00 2.00 0.00 • LA O LB • Q A • Q B • S A Coarser • Finer -O-o • o 50 100 150 200 250 300 350 Velocity (m/s) Figure 7. 4 Efficiency of Bond formula to predict energy utilization as a function of impact velocity 179 Since the. feed sample has been scalped (removal of most particles below 1 mm and above 2 mm), the new particles initially created occur inthe ultra-fine regime and as breakage continues, this fraction increases in the distribution until a normally-distributed, particle size distribution is achieved. This can readily be seen in Fig. 6.2 and Fig. 6.10 for the zone B limestone and quartz tests respectively in which significant breakage has taken place (i.e., ultra-fine particles created with little reduction in the d80 size. As a result, the Bond work input is reduced and the predicted efficiency (for a coarser overall size) is enhanced. The Bond formula just cannot handle this type of breakage which may be more attrition-like rather than impact fracturing. The Bond method was never, designed to predict energy use under high velocity impact. . The models developed for energy efficiency calculations can be verified based on several assumptions. .The following sections discuss the alternatives that One may consider while dealing with the issues of high velocity impact. 7.7 Measurement of Free Surface Energy Surface energy quantifies the disruption of chemical bonds that Occurs when a •i surface is created. Cutting a solid body into' pieces disrupts atomic bonds, and therefore consumes energy. Direct measurement of surface energy has mainly been confined to liquids. The popular method for liquids is the contact angle which is a . ' 180-function of the surface energies of the system which can be measured using a du Nouy ring or a Wilhelmy plate. In the case of solid material, the specific surface energy is usually 1 measured with a calorimeter and the adsorption of a particular species (generally a gas) onto the solid surfaces. Free surface energy of solid materials depends on the direction and orientation of the crystal plane. For example, experimental fracture surface energies of quartz have been reported to range from about 0.4 to 11.5 J.m"2 (Parks, 1982). The interfacial energy, twice the surface energy, for silica corresponded to 0.050 J.m" using elastic modulus for sublimation powder assemblies, while theoretical estimations show a value of 1.160 J.m"2 for the, 110 plane of cristobalite (a form of quartz) (Kendal et al, 1987). Different values of surface energy can be determined along different planes of '2 a material and can be quite variable. For example, 5.650 and 9.820 J.m" for 111 and 100 planes respectively, have been reported for diamond (AIP, 1933). The impact of such effects likely becomes very important as the mean size of the bulk material drops below 1 micron. In calculations of energy efficiency in the static regime, an average free specific surface energy of quartz was applied to the tuff material (a silicate rock) used to determine, the energy output of all samples tested. That is, we have no reference to estimate the actual value of specific surface energy for tuff. The method to directly measure specific surface energy was considered to be out of the scope and objectives of this research. As it turns out however, the actual value to be used in Equation 6.1 '• • ' 181 would only decrease or increase the efficiency across the range of loading rates. So, the trend line would exhibit the same relative position at higher or lower values of energy efficiency. So for the tuff material, the lack of an accurate measure of the specific surface energy does not.impact on the trend line. Similarly, the trend lines for, the dynamic tests are also unaffected although their relative position may change for each material. This means that the rock salt results could.be higher i f the specific surface energy is actually higher for the sample used in this work Although a theoretical estimation of free surface energy was used for the samples tested dynamically in this, work, the results suggest that the efficiency of.breakage increases with increasing specific surface energy of material. Table 7.5 shows the correlation between the specific surface energy and the energy efficiency obtained at the velocity of 150 m/s. Sample Initial Specific Surface Area (m2/g) Specific Surface Energy (J/m2)* Energy Efficiency @T50m/s(%) Quartz 0.005 ' 2.7 .' 2.8. Limestone , 0.728 • . ' 1.0. ' 2.7 ' ' Rock Salt 0.020' 0.6 0.65 Assumed values Table 7. 8 Specific surface energy and energy efficiency @ 150 m/s 182 ' Whether or not this relationship of efficiency to specific surface energy is valid will 1 require additional research. The trend, however, for efficiency as a function of impact'velocity,is valid. Increased speed of impact increases the efficiency of energy use for all materials tested. - .' , 7.8 Effect of Material Porosity The existing porosity in rock particles affects the measurement of surface area by allowing the nitrogen gas (other absorbent) to enter the pores. The amount of adsorbed gas on the free surface of particles determines the specific surface area of the material. After breakage of highly porous rock samples, i.e;, tuff, the surface area of pores is . • _ • i .• .', considered as part of the measurement despite the fact that input energy had no effect i • • i • • • , in actually creating these surfaces. In fact, the majority of the increased surface area is due to: porosity and not to fragmentation since the initial measurement prior to breakage did not account for pore surface area. Although pores are likely to decrease the overall strength of the rock, the cellular'structure with highly porous material may actually prevent the propagation of a crack whenever it meets a void which could lead to a strengthening of the material. As such, the effect of high porosity on measurement of energy efficiency of breakage has yet to be fully understood because of its complex nature.! i , . • 183 ! In the case of dynamic testing, i f all the pores are open prior to breakage, then the porosity surfaces are measured both before and after so the effect is cancelled out in terms of measurement error. The vast majority of porosity in rock is open-pores so this is a reasonable assumption. 7.9 Material Loss during Testing Our study shows that almost half of the newly produced surface area occurs within the finest particles. Therefore, material lost during a test is very important to determine the economy of the process with respect to energy utilization. Within our experiments, the retrieved amount of material after breakage was somewhat smaller than the, original material by about 2-3 %. Losses are mainly due to creation of very fine particles that depart the system during the creation of vacuum or the opening of the target chamber at the end of the test. . If all of the measured loss of material was assumed, to have the specific surface area of the finest particles produced during each test, the error in, efficiency values are consistently raised by approximately 50 % in all tests. So there is again, no impact of this discrepancy on the. central issue of how high velocity.impacts affect material breakage efficiency although the measured efficiency is a conservative estimate. 184 7.10 Assumptions with BET Measurements The assumptions inherent with a BET measurement may influence the overall accuracy of surface area. During surface area measurement, nitrogen molecules with an assumed square shape of side'length of 4A are adsorbed on the surface of particles. Particle surfaces have different characteristics such as steps, kinks and edges. The density of, gas molecules on these locations is assumed to be equal during BET measurement which1 may not be correct. Therefore,. there are some errors involved with this type of measurement which may affect the calculation of the average surface area. The impact of such surface phenomena is only significant for ultra-fine particles, although the presence of pores may increase their effect. Depending on the resolution of the adsorbent gas, the accuracy of BET measurements may vary. A gas with higher resolution results in higher accuracy of surface area measurements with, respect to actual bond length conditions. on a material's surface. Krypton gas gives the highest resolution of all - about 4 times that of nitrogen (16 A2/atom vs 4:A2/atdm). A.Krypton adsorption test then might have produced S.S.A. results up to 4 times what we measured for nitrogen gas. So obviously, this plays a major role in estimating the efficiency of breakage. 185 7.11 Direct and Indirect Tensile Stress In fracture mechanics, rocks, break under tension and the transformation of a compression force to tensile loading is very low. Tromans (2007) estimated a maximum efficiency of 7-9 % for fragmentation of materials. under indirect tensile loading during a compression test. On the other hand, the mechanism of rock blasting (direct tension) shows higher efficiencies accompany higher strain rates, which theoretically can be asmuch as 60%. Howeyer, different efficiencies may be obtained during , the, transformation of compression stresses to tensile stresses with bulk materials. Our data clearly shows that efficiencies as high as 5-6 % are achieved with a projectile velocity of 300 m/s which is close to Tromans theoretical.estimate for continuous crack propagation. It is possible that higher efficiencies may be obtained at higher velocities! than this value which is at the limit of our apparatus. 7.12 Particle Size Considerations In this study, a specific size fraction of rock sample was tested in the high-velocity impact experiments. It is recommended that similar experiments for other size ranges smaller than 1 mm and larger than 2 mm should be done. At lower particle sizes, materials require more energy to break than do larger sizes generally due-to grain size effects and the ability to maximize the optimum range of compression forces. , Therefore, exposure to high-velocity impact will determine, the material 186 behavior'at finer sizes and the; overall effect on bulk material with a wide range of particle sizes. The aim of this study was to present evidence that high-velocity impact causes material to break more efficiently than at lower velocities. The developed model to calculate efficiency focused on the change in surface area of material after breakage. Therefore, new surface area produced by impact determines the quantity of breakage regardless of product quality (liberation) or material size. There are numerous issues with respect to processing and separation of ultra-fine: particles in subsequent operations within a concentration plant that restrict product size and output of each comminution stage. Future research should focus on ranges, of product sizes of interest to mineral processing plants that can be achieved by high-velocity technology. The effect of wider size distributions should be determined. 7.13 Air and Moisture Content During experiments, virtually all o f the air is evacuated from the launch tube and target .chamber including the, air in the voids within the rock samples. After completion of the vacuum process, however, there is. still a small amount of air remaining in the confined system. These air molecules act as resistant forces in front of the projectile movement reducing its velocity. Also, the air between rock particles in the chamber act to cushion the forces inhibiting complete transformation of kinetic 187 energy to the rock material, therefore, some input energy is used to compress the remaining air in the system. This amount is likely to be very low. During experiments, dried rock samples were used to undergo the experiments in the target chamber. Neither is it possible to moisturize the material, due to the evacuation1 process which would simply evaporate water molecules. Like air, the water between rock particles may act as a cushion in the target chamber reducing the influence of kinetic energy on the material. In actual grinding equipment, water may or may not decrease the wear on the liner/steel charge and it certainly acts to collect the heat generated in the system. This factor should be a subject of interest in future work. • 7.14 temperature Measurements During our experiments, some of the energy input produced by the impact is changed to. heat. Therefore, the material temperature after breakage wil l rise. The, increase in temperature can be calculated based on thespecific energy input (2-42 J/g) I. . induced into the material and assuming the heat capacity of the rock is equal to 0.2 cal/g °C (value for granite). Based on these numbers, the materials could only gain a temperature of 50°C i f all energy was converted to heat and adsorbed by the sample. Since the sample is enclosed in an, iron chamber, most heat is quickly dissipated meaning the temperature rise is likely much smaller than 50°C. This change in • ' 188 temperature will have no effect on the mechanical properties of material tested, i.e. Poisson's ratio, nor will any phase transformations occur in the rock specimens. In future tests, it is recommended that temperature gauges be installed in the target chamber in order to directly measure this parameter during impact. The gauges should be mounted as close as possible to the center of the chamber where the process of fragmentation takes place. 7.15 Electrostatic Charges During sample breakage, some • electrostatic' charge may be created on rock surfaces. This change can influence the loss of dust due to absorption on chamber surfaces or dispersion into the air upon removal from the chamber. 7.16 Projectile and Target Bed In our experiments, the projectile was a cylindrical rod with a flat surface at both ends. It is/recommended that similar tests be conducted with different types of projectiles such as spherical or cone-shaped ends. As well, the projectile could be made of different materials such as ceramic (magnetite), aluminum, or even from the target rock material: Using magnetite as the projectile would allow the broken target 189 f particles to be separated from: any broken pieces.of the projectile by magnetic separation.. It is suggested that different target lengths be selected to undergo the experiments in order to distinguish the influence of impact velocity oh a variety of target beds. It is also useful i f the target, chamber is equipped with tools to recover portions of the sample at different positions along the chamber in order to determine at what point along the target chamber length, the breakage is maximized. 7.17 Actual Energy Consumption In this study, the contained energy of the projectile traveling at a known velocity is considered to evaluate the efficiency of breakage. But,, the actual energy consumed to launch the projectile is more than its contained energy. Some energy is devoted to accelerating the sabot, to activating the solenoid valves and vacuum pump, and to be wasted as friction between the barrel,and the sabot as it accelerates down the tube. In looking at ways to scale up our work to the design of a new apparatus to exploit high velocity impact comminution, the energy needed to create such, high velocity impacts must be taken into account. ! , • 190 i 7.18 Future Research , Our research indicates that the intensity of energy input into the process: is a key issue to enhance the fragmentation of rocks and minerals. Our data help explain the high efficiencies observed in practice for high-pressure grinding rolls, vertical roller crushers,, Barmac impact crushers, and jet mills. The lossin efficiency in conventional comminution processes is due in the main to impact distributions that generate elastic energy within the mass of the particles without generating new cracks or propagating existing ones. As a result, the elastic energy simply converts to heat produced in the system as the material atoms relax back to their original positions from distortions that are too small to break molecular bonds. Therefore, future research should focus on aspects to increase the impact intensity during comminution, and on methods to decrease the distribution of such impact intensities. 191 C H A P T E R 8 C O N C L U S I O N S A N D R E C O M M E N D A T I O N S This study examined the influence of high-velocity impact on rock fragmentation and the energy efficiency of comminution. The research was carried out by fundamental analysis of the fracture of rocks and minerals in two ways. In the static regime, surface roughness and surface area of four volcanic rock (tuff) samples were investigated under different loading conditions. With increasing loading rate, the surface roughness factor in one direction and in two directions 1 \ 1 , " ' i increase resulting in greater surface area production. Surface roughness measurements depend on the resolution used to make, such measurements. As a result,, new techniques to measure surface roughness and surface area were developed. As well, an estimation of energy efficiency of comminution, under static regime fragmentation was developed. In dynamic fragmentation, a high-velocity impact comminution apparatus was designed and built to directly measure the quantitative parameters of velocity impact on aggregated rock materials. Experiments on three rock materials - porous limestone, quartz, and rock salt, were conducted at projectile velocities from' 50 to 300 m/s. The results suggest energy efficiency of rock breakage is, improved by as much as 2 to 3 times under high velocity impact. • To summarize, the following results can be concluded: . 192 1. The implication of high strain rates and high-velocity impact in comminution provides an opportunity to improve energy efficiency in rock breakage. . 2. ; Regardless of mineralogy, high-velocity impact helps to explain increased efficiency in impact crushing (HPGR, Barmac, roller crushers). 3. Surface area measurement depends on the resolution of measurement. For meaningful results consideration of the utility of the data is important in deciding oh the resolution required. 1 4. The surface roughness factor plays an important role in determining the energy efficiency of breakage. 5. Material porosity may inhibit energy efficiency under high impact velocities but it should not affect surface area measurements. 6. The depth of particle bed is a key variable in determining fragmentation of rocks and minerals by high velocity impact. 7. The finest particles constitute almost half Of the new surface area-produced. So, material loss during a test is an important factor to account for and minimize 8. Estimation of produced surface area is low unless: - particle shape, roughness, and resolution are taken into account high quality dust collection is used 9. Future work should focus on designing new devices to increase impact intensity during comminution. 193 CHAPTER 9 CLAIMS TO ORIGINAL RESEARCH I claim to have discovered: • 1. 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World Scientific, vlO, n5,p751-762. 205 APPENDIX A: EXAMPLES OF STRESS-STRAIN CALCULATIONS HV1 Time (Sec) 30.98584 33.46664 36.14746 39.10336 42.17041 45,35124 48.54004 51.37533 53.757 56.91293 59.90479 63.32487 66.5057 69.4043, 72.28484 75.44857 78.40984 81.35547 84.44109 87.57845 90.17041. 93.309411 96.64404 99.87468 102.4608 104.9518 108.6244 111.5749 114.265 117.8485' 120.8068. 123.6182 126.7137 129.4785 132.5296 135.8265 138.7682 141.5604 144.6636 147.5848 150.8776 153.3875 156.2057 159.6182 Displacement (mm) 2.5267489 2.5291085 2.5320385 2:536412 2.53848 2.5396492, 2.543756 2.5439818 •', 2.5457029 2.5482161 2.55143 2.5549097 2.5567017 '' 2.5578039 2.5613472 2.5622585 2.5658007 2.566277 2.5692904 2.571,1377 2.5737696 2.5743039 2.5777302 2.5788765 2.5809793 2:5828247 2.5837159 2.589674 2,5884824 • 2.5897374 2.5937212 2.5938108 2.596806 2.5983398 2.6013417 2.598732' 2.6054864 2.605371 2.6053298 2.6123302 2.6120996 2.6136529 2.6156595 2.6184888 Axial Force (N) 5545.2915 6052.0566 6552.7012 7053.8267 7556.5 8059.1929. 8559.6992 9062.1904 9563.4316 10064.977 10566.818 11067.129 11568.409 12073.586 12574.957 13077.276 13578.566 14080.629 14582.784 15083.002 15594.722 16098.053 16602.006 17102.225 17603.643. 18104.344 18605.09 19108.234 19612:531 20112:551 20612.877 21114.447 21617.158 22121.096 .22629.477 23134.912 23635.986 24137.451 24638.514 25141.148 25641.297 26142.264 26645.281' 27147.393 (F) (KN). 5.5453 6.0521 , 6.5527 7.0538 7.5565 8.0592 8.5597 9.0622 9.5634 10.065 10.567 11.067 11.568 12.074 12.575 13.077 13.579 14.081 . 14.583 15.083 15.595 16.098 16.602 17.102 17.604 18.104 18.605 . 19.108 19.613 20^113 20.613 . 21.114 21.617 ' 22.121 . 22.629 23.135 123.636 24.137 24.639' 25.141 25.641 26.142 26.645 27.147 Area (A) (m2) 0.001768 0.001768 0:001768 0.00,1768. 0.001768. 0.001768 0.001768 0.001768 0.001768 0.001768 0.001768 0.001768 0.001768 0,001768 0.001768 0.001768 0.001768 0.001768 0.001768 0.001768 0.001768, 0.001768 0.001768 0.001768 0.001768 0.001768 0.001768 0,001768 0.001768 0.001768 0.001768 0.001768 0.001768 0.001768 0.001768 0.001768 0.001768 0.001768 0.001768 0.001768 0.001768 0.001768 0.001768 0.001768 Stress (Mpa) 3.1359 3.4225 3.7056 3.9890 4.2733 4.5575 4.8406 5.1247 5.4082 5.6918 5.9756, ,6.2585 6.5420 6.8277 7.1112 7.3953 7.6788 7.9627 8.2467 8.5295 8.8189 9.1036 9.3885 9.6714 9.9550 10.2381 10.5213 10.8058 ,11.0910. 11.3738 11.6567 11,9404 12.2246 12.5096 1 2 : 7 9 7 1 13.0829 1,3.3663 13.6499 ,13.9332 14.2175 14.5003 1.4.7836 15.0681 15.3520 Ad (mm) 0 0.00236 0.00529 0.009663 0.011731 0.0129 0.017007 0.017233 0.018954 0.021467 0.024681 0.028161 0.029953 0.031055 0.034598 0.03551 0.039052 0.039528 0.042542 0.044389 0.047021 0.047555 0.050981 0.052128 0 :05423 0.056076 0.056967 0.062925 0.061734 0.062989 0.066972 0.067062 0.070057 0^071591 0.074593 0.071983 0.078738 0.078622 0.078581 0.085581 0.085351 0.086904 0.088911 0.09174 , Strain (Ad/d) (mm/mm) , 0.00E+00 1.74E-05 3.89E-05 7.11E-05 8.63E-05 9.49E-05 1:25E-04 1.27E-04 1.39E-04 1.58E-04 1.82E-04 2.07E-Q4 2.20E-04, 2.28E-04 2.55E-04 2.61 E-04 2.87E-04 2.91 E-04 3.13E-04 3.27E-04 3.46E-04 3.50E-04 3.75E-04 3.84E-04 3.99E-04 4.13E-04 4.19E-04 4.63E-04 4.54E-04 4.63E-04 4.93E-04 4.93E-04 5.15E-04' 5.27E-04 5.49E-04 5.30E-04 5.79E-04 5.78E-04 578E-04 6.30E-04 6.28E-04 6.39E-04 6.54E-04 6.75E-04 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 : 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 . 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 1 0 . 0 0 1 0 . 0 0 1 0 . 0 0 1 0 . 0 0 1 ' 0 . 0 0 1 0 . 0 0 1 0 . 0 0 1 0 . 0 0 1 0 . 0 0 1 0 . 0 0 1 0 . 0 0 1 206 HV2 T i m e ( S e c ) 2 0 . 6 4 1 8 2 1 . 7 9 0 5 2 3 . 3 6 1 ; 2 4 . 9 7 0 7 2 6 . 5 3 3 5 2 8 . 1 0 3 2 . 2 9 . 5 9 7 3 1 . 1 0 5 5 3 2 . 7 1 2 6 3 4 . 2 1 0 9 3 5 . 6 7 6 6 3 7 . 1 7 4 6 3 8 . 6 7 0 7 4 0 . 2 9 3 6 41 .8071 43 .1831 4 4 . 6 7 5 3 4 6 . 2 1 3 5 4 7 . 7 4 5 4 9 . 2 6 2 7 5 0 . 8 1 8 4 5 2 . 2 5 3 6 5 3 . 7 7 1 8 5 5 . 2 3 9 7 5 6 . 7 2 8 8 5 8 . 3 2 5 8 5 9 . 4 8 4 2 6 0 . 8 7 6 5 6 2 . 5 4 6 6 6 4 . 1 6 4 9 6 5 . 7 5 5 2 6 7 . 2 8 8 4 6 8 . 7 9 8 7 7 0 . 3 0 5 3 7 1 . 7 8 1 9 7 3 . 3 1 3 8 7 4 . 7 9 6 2 7 6 . 2 7 5 7 7 7 . 8 2 3 2 7 9 . 2 7 1 2 8 0 . 8 3 6 9 82^3757 8 3 . 8 6 2 8 5 . 3 8 6 6 8 6 . 8 4 8 8 . 3 3 3 3 D i s p l a c e m e n t (mm)' 2 . 2 2 2 6 5 6 2 . 2 2 7 9 3 1 3 2 . 2 3 0 2 8 6 8 2 . 2 2 9 0 5 8 7 2 . 2 3 0 9 2 8 9 2 . 2 3 6 5 9 4 2 2 . 2 3 8 3 6 7 8 2 . 2 4 3 3 1 6 9 2 .2440171 '. 2 . 2 4 4 1 9 2 4 2 . 2 4 9 6 4 9 5 2 . 2 5 0 7 5 3 4 2 . 2 5 2 9 6 4 7 2 . 2 5 5 8 8 3 7 2 .2571201 2 . 2 6 1 3 6 9 2 2 . 2 6 2 7 1 1 8 • 2 . 2 6 4 5 6 6 4 2 .2660971 2 . 2 6 7 1 2 4 9 , 2 . 2 7 0 0 6 1 7 2 : 2 7 4 5 5 1 6 2 . 2 7 5 0 7 5 9 . 2 . 2 7 6 7 0 5 3 2 . 2 7 9 7 1 7 4 2 : 2 8 2 5 4 3 2 . 2 . 2858541 2 . 2 8 6 4 5 9 2 2 . 2 8 8 9 3 9 2 .2896121 2 .2926211 2 . 2 9 3 3 5 8 3 ' 2 . 2 9 7 9 6 0 3 2 . 2 9 8 4 8 2 .3004701 2 . 3 0 3 3 7 4 3 2 . 3 0 4 8 5 5 3 2 . 3 0 3 5 2 5 2 . 2 . 3 0 8 5 8 3 5 2 . 3 1 1 5 0 4 4 2 . 3 0 9 7 . 2 . 3 1 3 4 4 4 4 2 . 3 1 5 8 3 0 5 2 . 3 1 8 1 3 3 4 2 . 3 2 0 1 7 4 2 2 . 3 1 9 9 3 7 7 A x i a l F o r c e (N) 5 5 6 3 . 5 6 4 9 ' 6 0 6 6 . 9 3 9 5 6 5 6 7 . 6 5 4 3 7 0 7 0 . 2 9 8 3 7 5 7 3 . 4 6 5 3 8 0 7 5 . 5 8 2 5 8 5 7 6 . 6 9 5 3 9 0 7 7 . 4 8 7 3 9 5 7 7 . 5 8 3 10079 .261 1 0 5 8 0 . 4 2 9 1 1 0 8 1 . 3 1 7 1 1 5 8 3 . 7 9 7 1 2 0 8 4 . 5 2 1 2 5 8 5 . 2 9 2 1 3 0 8 9 . 0 9 8 1 3 5 8 9 . 6 7 9 14091 .761 1 4 5 9 4 . 5 4 3 . 1 5 0 9 5 . 5 3 1 5 5 9 8 . 2 4 1 6 1 0 3 . 8 0 8 1 6 6 0 8 . 8 5 7 1 7 1 1 0 . 2 2 7 1 7 6 1 5 . 2 9 5 1 8 1 1 6 . 4 1 6 1 8 6 1 6 . 4 8 2 1 9 1 1 9 . 5 9 • 1 9 6 2 3 . 3 7 5 20123 .91 2 0 6 2 3 . 9 4 1 2 1 1 3 0 . 5 1 4 2 1 6 3 0 . 7 3 2 2 1 3 1 . 9 7 9 2 2 6 3 2 ! 17 2 3 1 3 3 . 7 0 5 2 3 6 3 6 . 5 4 5 2 4 1 4 0 . 8 8 5 2 4 6 4 5 . 3 7 5 2 5 1 4 6 . 5 9 4 ' 2 5 6 4 9 . 8 1 6 26152 .1 2 6 6 5 2 . 6 2 5 2 7 1 5 2 . 9 8 4 2 7 6 5 3 . 5 2 1 2 8 1 5 3 . 7 3 (F) ( K N ) • 5 .5636 6 . 0 6 6 9 6 .5677 7 . 0 7 0 3 7 . 5 7 3 5 8 .0756 8 . 5 7 6 7 9 . 0 7 7 5 9 .5776 10 .079 10 .58 1 1 . 0 8 1 . 11 :584 1 2 . 0 8 5 1 2 . 5 8 5 ' 1 3 . 0 8 9 ' 1 3 ; 5 9 14 .092 ; 1 4 . 5 9 5 15 .096 15 .598 16 .104 16.609, 17.11 1 7 . 6 1 5 18 .116 18 !616 19 .12 1 9 . 6 2 3 2 0 . 1 2 4 2 0 . 6 2 4 21 .131 , 21 .631 2 2 . 1 3 2 2 2 : 6 3 2 2 3 . 1 3 4 2 3 . 6 3 7 24 :141 2 4 . 6 4 5 2 5 ! 1 4 7 2 5 . 6 5 2 6 . 1 5 2 2 6 . 6 5 3 2 7 . 1 5 3 2 7 . 6 5 4 2 8 . 1 5 4 A r e a (A) (m2) . , 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 , 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 . 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 X J 0 1 7 6 8 3 , 0 .0017683 0 . 0 0 1 7 6 8 3 0:0,017683 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 . 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 . 0 0 1 7 6 8 3 0 : 0 0 1 7 6 8 3 S t r e s s (Mpa) 3 . 1 4 6 2 3 3 3 . 4 3 0 8 9 4 3 . 7 1 4 0 5 2 3 . 9 9 8 3 4 . 2 8 2 8 4 5 4 . 5 6 6 7 9 5 4 . 8 5 0 1 7 8 5 : 1 3 3 3 7 9 5 . 4 1 6 1 8 6 5 . 6 9 9 8 8 9 5 . 9 8 3 3 0 3 6 . 2 6 6 5 5 8 6 . 5 5 0 7 1 4 6 . 8 3 3 8 7 6 7 . 1 1 7 0 6 6 7 .401971 7 . 6 8 5 0 5 3 7 . 9 6 8 9 8 4 , 8 .253311 8 . 5 3 6 6 2 2 8 . 8 2 0 9 0 8 9 .10681 9 . 3 9 2 4 1 8 9 . 6 7 5 9 4 6 9 . 9 6 1 5 6 6 1 0 . 2 4 4 9 5 1 0 . 5 2 7 7 4 . 1 0 . 8 1 2 2 5 1 1 : 0 9 7 1 5 11 .3802 1 1 . 6 6 2 9 7 1 1 . 9 4 9 4 5 1 2 . 2 3 2 3 2 1 2 . 5 1 5 7 8 1 2 . 7 9 8 6 4 1 3 . 0 8 2 2 6 1 3 . 3 6 6 6 2 1 3 . 6 5 1 8 3 1 3 . 9 3 7 1 2 1 4 . 2 2 0 5 7 1 4 . 5 0 5 1 4 1 4 . 7 8 9 1 9 1 5 . 0 7 2 2 4 1 5 . 3 5 5 1 9 1 5 . 6 3 8 2 5 1 5 . 9 2 1 1 2 A d (mm) 0 ' ' : 0 . 0 0 5 2 8 , 0 . 0 0 7 6 3 0 .0064 0 . 0 0 8 2 7 0 . 0 1 3 9 4 0 .01571 0 . 0 2 0 6 6 0 : 0 2 1 3 6 0 . 0 2 1 5 4 0 . 0 2 6 9 9 0 .0281, 0 .03031 0 . 0 3 3 2 3 0 . 0 3 4 4 6 0 .03871 0 . 0 4 0 0 6 0 .04191 0 . 0 4 3 4 4 0 . 0 4 4 4 7 0 .04741 0 . 0 5 1 9 0 . 0 5 2 4 2 0 . 0 5 4 0 5 0 . 0 5 7 0 6 0 . 0 5 9 8 9 , 0 . 0 6 3 2 0 .0638 0 . 0 6 6 2 8 0 . 0 6 6 9 6 0 . 0 6 9 9 7 0 .0707 0 . 0 7 5 3 0 . 0 7 5 8 2 0.0778,1 0 . 0 8 0 7 2 0 . 0 8 2 2 0 . 0 8 0 8 7 0 . 0 8 5 9 3 0 . 0 8 8 8 5 0 . 0 8 7 0 4 0 . 0 9 0 7 9 0 . 0 9 3 1 7 0 . 0 9 5 4 8 0 . 0 9 7 5 2 0 . 0 9 7 2 8 S t ra in (Ad/d) ( m m / m m ) O.OOE+00 3 . 8 8 E - 0 5 5.61 E - 0 5 4.71 E - 0 5 6 . 0 9 E - 0 5 1 .03E-04 1 .16E-04 1 .52E-04 1 .57E-04 1 .58E-04 ' 1 . 99E-04 2 . 0 7 E - 0 4 2 . 2 3 E - 0 4 2 . 4 4 E - 0 4 2 . 5 4 E - 0 4 2 . 8 5 E - 0 4 2 . 9 5 E - 0 4 3 . 0 8 E - 0 4 3 : 2 0 E - 0 4 3 . 2 7 E - 0 4 3 . 4 9 E - 0 4 3 . 8 2 E - 0 4 3 . 8 6 E - 0 4 3 . 9 8 E - 0 4 . 4 . 2 0 E - 0 4 4.41 E-04, 4 . 6 5 E - 0 4 4 . 6 9 E - 0 4 4 . 8 8 E - 0 4 4 . 9 3 E - 0 4 5 . 1 5 E - 0 4 5 . 2 0 E - 0 4 5 . 5 4 E - 0 4 5 . 5 8 E - 0 4 5 : 7 3 E - 0 4 5 . 9 4 E - 0 4 6 . 0 5 E - 0 4 5 . 9 5 E - 0 4 6 . 3 2 E - 0 4 6 . 5 4 E - 0 4 6 . 4 0 E - 0 4 6 . 6 8 E - 0 4 6 . 8 6 E - 0 4 7 . 0 3 E - 0 4 7 . 18E-04 7 . 1 6 E - 0 4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000, 0.000 0.000 0.000 0.000 0.000 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 olool 0.001 0.00,1 0.001 207 HV3 Time , (Sec) 16.258 16.952 17.7 18.522. 19^403 20.361 21.33 22.363 23.352 24.41 25.443 26.485 27.528 28.582 29.654 30.705. 31.778' 32.807 • 33.807 34.819 35.865 36.895i 37.894' 38.905 39.907 40.921 41:966' 421943 43.94 44.915 45.899 46.894 47'.877 48.898 49.929 50.949 51.965 52.905 53.889 54.799 55.787 56788 57.846 58.898 59.964 60.96 Displacement (mm) 2.8382933 2.8424475 2.8447709 2.850842 2.8514848 2.8560627 2.8633246 , 2.8638177 2.8685517 2.8722405 2.8741014 2.8789232 2.8828776 2.8840077 2.8870411 2.8915901 2.8936932 2.8974125 2.9004908 2.9003215 2.9049017 219093621 2.9120057 2.9160924 2.9184804 2.9224362 2.9247661 2.9277322 , 2.9289641 2.9318454 ' 2.9330969 2.9366415 2,9367585 2.9399304 2.9419007 2.9454131 '.. 2.949785 2.953012 2.9538331 2.9574893 2.95790.82 2.9604361 2.9642367 2:9678104 2.9689054 2.9698977 Axial Force (N) 5614.647 6117.718 6618.837 7119.02 7622.931 8131.54 8635.152 9138.23 , 9641.807 10142.41 10644.59 11146 11648.14 12150.14 •12652.24 13154.61 13656.31 14158.4 14660.08 15160.48 15660.71 16163.15 16666.19 17169.87 17672.07 18172.45 18677.72 ' 19178.33 . 19678.92 20180.62 20681.3 21181.82 21683.73 22188.12 22690.02 23191.92 23692.3 24194.97 24696.29 25197.54 25697.9 26199.41 2670,1.29 '27201.6 27704.2 28204.25 (F) (KN) 5.6146 6.1177 6.6188 7:119 7:6229 8.1315 8.6352 9.1382 9.6418 10.142 10.645 11:146 11.648 12.15 . 12.652 13.155 13.656 14.158 14:66 15.16 15.661 16.163 16.666 17.17 17.672 18.172 18.678 19.178 19.679 20.181 20.68,1 21.182 21.684 22:188 22.69 23.192 23.692 24.195 24.696 25.198 25.698 26.199 26.701 27.202 ,27.704 28.204 Area (A) (m2) 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683, 0.0017683, 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 ' 0.0017683. 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 ! 0.0017683. 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683, 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 0.0017683 Stress (Mpa) 3.1751197 3.4596099 3.742996 4.0258529 4.3108177 4.5984394 4.8832357, 5,1677292 5.4525054 5.735601 6.0195866 6.3031389 6.5870979 . 6.8709839 7.1549225 7.4390195 7.7227353 , 8.0066676 8.2903721 8.5733511 8.8562367' 9.1403704 9.42484 9.7096733 9.9936701 10.27664 10.562372 10.845472 11.128557 11.412275 11.69541 11.97846' 12.262293 12.547528 12.831357 13.115183 13.398149 13.682413 13.965917 14.249376 1,4.532332 14.815938 15.099758 15-382682 15.666907 15.949691 Ad (mm) 0 0.0041542 0.0064776 0.0125487 0.0131915 0.0177694 0.0250313 0.0255244 0.0302584 0.0339472 0.0358081 0.0406299 0.0445843 0.0457144 0.0487478 0.0532968 0.0553999 0.0591192 0.0621975 0.0620282 0.0666084 0.0710688 ,0.0737124 0.0777991 0,0801871 0.0841429 0.0864728 0.0894389 0.0906708 0.0935521 0.0948036 0.0983482 0.0984652 0.1016371 0.1036074 0.1,071,198 0.1114917 0.1147187 0.1155398 0.119196 0.1196149 0.1221428 0.1259434 0.1295171 0.1306121 0.1316044 Strain (Ad/d) (mm/mm) 0.00E+00 3.06E-05 4.78E-05 9.25E-05 9:73E-05 1.31 E-04 1.85E-04 i .88E-04 2.23E-04 2.50E-04 2:64E-04 3.00E-04 3.29E-04 3.37E-04 3.59E-04 3.93E-04 4.08E-04 4.36E-04 4.59E-04 4.57E-04 4.91 E-04 5.24E-04 5.43E-04 5.74E-04 5.91 E-04 6:20E-04 6.38E-04 6.59E-04 6.68E-04 6.90E-04 6.99E-04 7.25E-04 7.26E-04 7.49E-04 7.64E-04 7.90E-04 8.22E-04 8.46E-04 8.52E-04 8.79E-04 8.82E-04 9.00E-04 9.29E-04 9:55E-04 9.63E-04 9.70E-04 0.000 0.000 0.000 0.000 o.obo 0.000 0.000 0.000 0.000 0.000 0:000 0.000 0.000 0.000 0.000 0.000 0:000 0.000 o.ooo 0.000 0.000 0.001 0.001 0.001 0.001 0.001 . 0.001 0.001 0.001 0.001 0.001 0.001 . 0.001 0.001, 0.001 0.00,1 0:001 0.001 0.001 0.001 0.001 0,001 0.001 0.001 0.001 0.001 208 HV4 Time (Sec), 15.81104 16.0638 . 1.6.32406 16.59261 16.87533 17.15951 17.44597 17.73796 18.02441 18,33008 . 18.62451 18.92643 19.22656 19.52328 19.82048 20.11979 20.41846 20.72168 21.01839 21.32324 21.62695 21.92773 22.23535 22.53532 22.84294 23.14697 23.44613 23.74821 24.04297 24.34977 24.65316 24.96159 25^26318 25.57064 25.87061 26.17562 26.47754 26.78027 27.08366 27.38412 27.6919 27^98812 28.28825 28.58789 28.8877 29.20003 Displacement (mm) . . 1.8412158 1.8432387 1.8451393 1.8487591. 1.8515079 < 1.8553691 1.8575683 1.8593422 1.8610412 1.8653319 1,8680006 , 1.8713738 1.8727014 118759891 1.8751825 1.8798724 1.8827934 1.8834373 1.8874851 . 1.8920738 .1.8907126 1.8919785 1.8967065 1.8961128 1.9004468 1.9008241 •1.9042988 1.9072928 •1.9103408 '' 1.9091235 ' 1.9122419 1,9141773 1.9151325 1.918178 1.9220022 1:9201454 1.923067 1.9248681 1.9265379 . 1.9294091 1.9318261 1.9315202 1.9357513 1.9347881 1.9373499 1.939777 Axial Force (N) 5598.46 . 6099.127 6599.477 7106.048 7612.865 8114.446 8618.243 9124.022 9628.563 10129.73 10632.03 11132.59 11632.76 12137.61 12640.34 13142.75 13649.67 14151.02 14651.82 15153.19 15654.91 16156.43. 16658.92 17161.68 17662.59 18163.82 18664.92 , 19165.49 .19667,22 20168.84 2067145 21173.73 21676.96 22181.58 22683.34. 23183.78 23686.06 24186.51 ,24688.56 25190.57 25690.7 26191.99 26692.62 27192.84 27695.42 28202.54 (F) (KN) 5.59846 6.09913 6!59948 7.10605 7.61287 8.11445 8^61824 9.12402 9.62856 10.1297 10.632 11.1326 11.6328 12:1376 12.6403 13.1427 13.6497 14.151 14.6518 15.1532 15.6549 16.1564 16.6589 17.1617 17.6626 18.1638 18.6649 19.1655 19.6672 20.1688 20.6714 21.1737 21.677 22.1816 22.6833 23.1838 23.6861 24.1865 24.6886 25.1906 25.6907 26:192 26.6926 27,1928 27.6954 28.2025 Area (A) (m2) ' 0.00176833 0.00176833 0.00176833 0.00.176833 0.00176833 0.00176833 0.00176833. 0.00176833 0.00176833 0.00176833 0.00176833 0.00176833 0.00176833 0.00176833 0.00176833 0,00176833 0.00176833 0.00176833 0.00176833 0.00176833 0.00176833 0.00176833 0.00176833 0.00176833 0.00176833 0.00176833 0.00176833 0.00176833 0.00176833 0.00176833 0.00176833 0.00176833 0.00176833 0.00176833 0:00176833 0.00176833 0.00176833 0.00176833 0:00176833 0.00176833 0.00176833 0.00176833 0.00176833 0.00176833. 0.00176833 0.00176833 Stress (Mpa) 3.1660 3.4491 3.7320 4.0185 4.305.1 4.5888 4.8737 5.1597 5.4450 , 5.7284 6.0125 6.2956 6.5784 .6.8639 7,1482 7.4323 7.7190 8.0025 8.2857 8.5692 . 8,8530 9.1366 9.4207 9.7050 9.9883 10.2718 10.5551 10.8382 11.1219 11.4056 11.6898 11.9739 12.2585 12.5438 12.8276 13.1106 13.3946 13.6776 13.9615 14.2454 14.5283 14.8117, 15.0949 15.3777 15.6619 15.9487 Ad (mm) 0 0.002023 0.003923 0.007543 0.010292 0.014153 0.016353 0.018126 0.019825 0.024116 0.026785 0.030158 0.031486 0.034773 0.033967 0.038657 0.041578 0.042221 0.046269 0.050858 0.049497 0.050763 0.055491 0.054897 0.059231 0.059608 0.063083 0.066077 0.069125 0.067908 0.071026 0.072961 0.073917 0.076962 0.080786 0.07893 0.081851 0.083652 0.085322 0.088193 0.09061 0.090304 0.094535 0.093572 0.096134 0.098561 Strain (Ad/d) (mm/mm), 0.00E+00 148E-05 2.87E-05 5.52E-05 7.53E-05 1.04E-04 1.20E-04' 1.33E-04 1.45E-04 1.76E-04 1.96E-04 2.2.1 E-04 2:30E-04 , 2.54E-04 2.49E-04 2.83E-04 3.04E-04 3!o9E-04 3.39E-04 3.72E-04 3.62E-04 3.71 E-04 4.06E-04 4.02E-04 4.33E-04 4.36E-04 4.62E-04 4.83E-04 5.06E-04 4.97E-04 5.20E-04 5.34E-04 5.41 E-04 5.63E-04 5:91 E-04 5.77E-04 5.99E-04 6.12E-04 6.24E-04 645E-04 6.63E-04 6.61 E-04. 6.92E-04 6.85E-04 7.03E-04 7.21 E-04 0.000 0.000 0.000 0.000 0.000 o:ooo 0,000 0.000 0:000 0.000 0.000 0.000 0.000 0.000 0,000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 o;ooo 0.000 o.poo 0.001 0.000 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 209 APPENDIX B: SURFACE AREA MEASUREMENT (COARSEST PIECE) Piece H V 1 (cm2) H V 2 (cm2) HV3(cm 2 ) HV4(cm 2 ) •Al -. 107.48 96 .. 71.06 . 108,39 , .. A2 61.66 58.43 38.46' . 58.57 ' •' •A3 12.07 ' ' 11.34 15.16 8.69 A4 5.46 6,7' 8:7 0 A5 0 0 2.68 . 0 B l ' 19.43 , ' ' 63.5 • 59.41 97.85 • , B2 23.78 , '36.23 45.56 59.96 B3 23.78 • 4.23 ''4.58 9.02 B4 ' 3.55 ' 2.42' 0 5.27 c i . • 10.17 41.35 30.05 . . 14.05 ' C 2 24.09 2.78 , 24.08 12.68' C3 . 14.66 2.21 ' i .1.16 2.12 . C4 , 4.64 • 0 0.97, . • 0 ' .. '; ' ' cs 7.36 ' ' • 0 ' , ' ' 0 0 DI 18.67 13.3 23.51. 15.57 ' D2 18.68 12.1 • . ' • .19.99 | . 1 3 • D3. . 2.78. .9.18 0' ' 2.97 D4 : '3,57' o. .0 0 • D5 ' 1.28 . , 0 ' 0 , , 0' El • 7.92 ' 1.0.26 1.7.47 13.14 E2 7.48 ,10.4 8.18 13.91 , E3 ' 2.31 ' 5.5 15.91 '. 1.31 E4 2.12 • : 2.37 . 0.74 0.66 E5 1.43 . 2.63 0 0 E6 , . 0.83 0.71 0 , • 0 F l 9.4 . ' 7.91 15.62 • 8.51 F2 8.08, 4.7' 6.18 8.46 F3' 2.68 4.74 12.42 ' 0.61 • ' F4 1.14 5.12 0 0.43' • F5 0.46 \ 1.78 ' 0 ' ' 0 . GI . 1 5.51 " 8.71. 15.97 9.13 • ", G2 3.63 6.62 16.79 ' 7.93 , G3 , 2.56 3.6 1.81 •' . . 1.53 G4 1.74 ' 2.31 ' 0 ' • 0 • ,G5 0 1.63 . o • ' 0 210 HI , 8.81 ; 4:14 13.35. 10.67 112 ' 1.0.64 5.1 '. 13.52 .8.97 H3 0.54 , •3.5 • , 3.71 3.28 H4 0.33- 5.39 0 o -H5 . 0 • 1 . 4 0 0 H6 0 1.'8 •' 0, 0 11 6.51 7.09 14.04' 6.22 . 12 5.82 . 7.04 13.81 5.99 13 2.58 1.31' 1 0.88 . 0.87 .14 ' 0 2.02 . 0.75 0,42 . 15 0 1.56 0' 0 • ' JI 7.63 6.48 . : 9.71 4.56 . J2 ' 9154 7.57', 9.7 4.59 ,' J3 . 0.31 1.7 -. 2.04 •' - 0.74 J4 0 ' 0.56 ' 1.06. .1.36 J5 . 0 0 0.78 : o • KI 6.45 , 4.16 10.68 • 2.9 • K2 ' ,6.3 • • 4.65 10.14 ' 3.36 ,K3 0 , 1:15 2.35 • 0.59 K4 o • 1 1.05 , 0 K5 0 . 0 ' 0.93 . 0 LI- 7.26 6.43 9.98 4 L2 5.44 4.03 9.68 3.88 L3 1.84 0 0.57 0.26 L4 1 0.44 0 . 0.74 0.2 M l . 5.26-. 4.78 . 12.11 3.51 M2 5.19' 5.65 9.96 3.49 M3 1.67 ' • 1.35 1.37 ' 1.17. 1 M4 0 0 0.79 0 • NI '• 4.24 ; 5.5 ' 6.14 • 2.74 • N2 . 4.78 • ' 5.57 • 5.45 - 2.78 -'. N3 • 0:35 0 • , '• .2.98 1.53 '. N4 ' . 0.19. 0 - 2.32- 0.52 ,; 01 5.59 • 2.64 7.87' 2.68 02 8.48 2.84 ;.' • 7.04 2.66 03 '.', 0.25 • 1.04 , . 6.55 0 04 0 0.92 • 0.71 ' '. o 05 0 0.66 o 0 Pl . 4.44 3.06 5.63 1.93 P2 3.92 2.99 4.5 1,98 P3, 0.26 0.65 4:.57 0.62 211 .. P4 ' 0.19 ' 0 , 0 • 0.8. '• Qi '.. .3.57 3'.2 6.77 Q2 3.72 3.35 5.21 Q3 1.14 0 ' 2.04 Q4 0.7 0 1.36 RI 3.33 • 3.34 • 7.01 R2 ' 3.53 • 2.25 . 5.16 1 • ' • ' R3 , 0.43 2.27 ' 1.04 R4 ' . 0.26. ' 0.47 1.09. R5 o •' 0.4.1 0 : SI .. 3.94 2.79 . , 4.53 ,S2 2.67 2.48 • 377 3.52 . 0 2.06 . S4 0.37 0 0.91 • S5 0.15 .' . 0 0 • Tl 4.08 2.49 5.28 T2 : 4.35 3.18 4.87 . T3 0.26 i 0.89 . 1.57 T4 '0 0.29 2.01 U l • 3.5 - ' 2.49 3.73 U2-' 3.9' ' 2.63 3.38 . U3 4.31 0 ;. 1.29 VI 4.23 • • 1:81 3.92 V2 .5.44 1.79 3.06 V3 0 0.41, • : 1.62 V4 0 0.51 ' 0.86 WI 2.96 . 2.11 . • 2.54-W2 2.77 2.53 1.74. ' •, W 3 • • , i •0.39' 0.93 ' . 2.67 '; •W4 0 ' 0.29. ,. 1.15 • ';W5 0 • 0 ' 0.73 •XI 2.77 ' 1.53 3.45 ' X2 3.43 1.64 ' 3.3 X3 , 0 0.57 0 YI • 2.81 . • 1.71 2.75 Y2 3.42 1.4 2.33 ' Y3 ' 0.19 1.05 ! ' ' 1.05 Y4 ', . 0 : 1.14 1/ , 1:21 Y5 q 0.47 1.37 ., ZI 2.42 1.6 . 3.62 Z2 2.77 1.1 2.9 73 0 1.52 •• 2.25 TA 0 0.66 .• 0.87 AA1 2.81 2.48' ; ; •' • • AA2 , 2.33 -2.77 AA3 \ 0.73 .. . 0.29 BB1 '•' 1.86 3.24 BB2 1 2 . '' 3.17 -BB3 0.43 1.49 BB4 0 0.43 CC1 . 2.36 : . 1.34 • . CC2 2.03 . 1.31 CC3 6.26 . 0.93 CC4 ' , 0. "• 0.33 CCS 0 0.57 , DDI 2.57 3.16 , DD2 3.42 - 2.91 DD3 o 0.75 , •"• ' EE1 •' , ' 3 - 5 4 • ' . 2.35 EE2 1.91 2.12 ;.. EE3 0.37 0 • FF1 1.74 1.67. ' " ; FF2 2.93 1.65 . FF3 • 0.69 1.15 FF4 0.48 0:39 GGl 1.63 GG2 2.49 > GG3 . . 0.15 HH1 2.6 HH2 1.89 • •, ' HH3 0.25 HH4 • 0.14 ' JJ1 2.49 , ' JJ2 1:79 • ' . . I l l . 1.72 112 '.' • . 1.6 KK1 •;' 2:6. , -, KK2 2.14 • Total 680.93 611.79 798.89 - 563.03 1 213 APPENDIX C: SURFACE AREA CALCULATIONS (FINE/COARSE) HV1 Fraction (mm) Weight (g) Apparent S.S.A.(cm2/g) Shape factor Surface Roughness Ultimate S.S.A. (cm2/g) @ 4A Surface Area (cm2) ' +9.52 632.8 1.08 1 , 1.92" 12.58 7958.32 +4.76 ,13.47 .3.04 1.125 •' - ' 59.53 801:85 +2.38 9.29 '' 6.09 1.250 - 196.71 - 1827.43 +1.00 3.8 12.86 1.375 679.69 2582.82 +0.42 1.27, 30.62 1.500 - 2624.45 3333.05 +0 . 0.88 103.52 1.625 85 . 14293.87 12578.61 661.51 ' 29082.07 i HV2 Fraction (mm) Weight (9) Apparent • S.S.A.(cm2/g) Shape factor Surface . Roughness Ultimate S.S.A. (cm2/g) @ 4A . Surface Area (cm2) +9.52 624 0.98 ' 1 2.42 8.12 5065.55 +4.76 25.4 3.04 1.125 49.57 1259.20 +2.38 11.54 . 6.09 1.250 • - '• 192.57 2222.27 +1.00 5.32 ' .12.86 1.375 - . 782.18 4161.20 +0.42 1.97 30.62 1.500 '• '- 3550 :30 6994,10 +0 1.34 , 103.52 • 1.625 135 22730.44 30458.80 669.57 ' 50161.12 214 HV3 Fraction (mm) Weight (9) Apparent S,S.A.(cm2/g) Shape factor Surface Roughness Ultimate S.S.A. (cm2/g) @ 4A Surface Area (cm2) +9.52 616.4 1.31 • 1 2.26 10.79 ; .6648.99 +4.76 28.2 3.04 1.125 - ' •• • 48.77 1375!18 +2.38 9.4 6.09 1.250 - 187.69 1764.30 +1.00 4.5 12.86 1.375 , 755.38 3399.23 +0.42 1.6 30.62 1.500 3397.29 . 5435.66 +0 0:9 103.52 „• 1.625 128 21551,71 19396.54 661 38019.90 'i HV4 Fraction1 (mm) Weight ' (9) Apparent S.S.A.(cm2/g) Shape factor Surface Roughness-Ultimate S.S.A. ( cm2 /g )@4A Surface Area (cm2) +9.52 656 . 0.86 ' 1.' 3.88 . 10.03 ' 6580.37 • +4.76 6.6 . 3.04 1.125 : - ' 59.81 . 394.74 +2.38 3.4 6.09 1.250 • - ' ' • 198 :57 . . 675.12 +1.00 • 2.3 12,86 1.375 - 689.33 1585.46 +0.42 0.8 30.62 1.50,0 . 2674.21 2139.37' +0 0.4 103.52 ' 1.625 8 7 14633.50 5853.40 669.5 17228.47 215 A P P E N D I X D: M O R E S E M E X A M I N A T I O N S HV1 HV2 HV4 APPENDIX E: APPARATUS MAIN EQUIPMENT DRAWINGS .220 35 - *"f H — 40 — H 40 230 LEGEND 1 Reservo i r Lid 8 Middle support 2 Reservo i r 9 Project i le Veloc i ty Measuremen t 3 Initial Suppor t 10 C h a m b e r Lid 4 Quick Open ing Va l ve 11 Target C h a m b e r 5 V a c u u m 12 Final support 6 F lange Coup l ings 13 Structure Des ign 7 Launch Tube 14 Connec t ion Des ign Hypervelocity Impact Facility Scale University of British Columbia (CERM3) Mining Engineering Department Design: Sepehr Sadrai Supervisor: Dr. John Meech Date: Map No: Name: 20/8/2004 M-HV0 General dimension 221 12 (Mild Steel or 4340) _T_" L . 0 6 c J (Tap s ize 1/2) Hypervelocity Impact Facility S c a l e Univers i ty of Bri t ish C o l u m b i a ( C E R M 3 ) Min ing Eng inee r ing Depar tment Design: Sepehr Sadrai Superviror: Dr. John Meech 2 1 / 8 / 2 0 0 4 M - H V 2 R e s e r v o i r 223 224 Target Chamber Tap Size 1/2 Hypervelocity Impact Facility Scale 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 ( C E R M 3 ) M i n i n g E n g i n e e r i n g D e p a r t m e n t D e s i g n : S e p e h r S a d r a i S u p e r v i r o r : D r . J o h n M e e c h 2 1 / 8 / 2 0 0 4 M I H V I O T A R 9 E T C H A M B E R 225 6 4 - | . L L •i n-i i L , J 02 ! c b c c 0, Hypervelocity Impact Facility Scale Design: Sepehr Sadrai Superviror: Dr. John Meech University of British Columbia (CERM3) Mining Engineering Department 21/8/2004 M-HV8 Middle Support 226 t 2 (Tap size 1/2") 0 1 (Tap size 1/2") Hypervelocity Impact Facility Scale University of British Columbia (CERM3) Mining Engineering Department Design: Sepehr Sadrai Supervisor: Dr. John Meech 21/8/2004 M-HV15 Divider 227 1 6 5—4 0 -H 1 h-16 (Mild Steel or 4340) 04 Hypervelocity Impact Facility S c a l e University of British Co lumbia ( C E R M 3 ) Mining Engineering Department Design: Sepehr Sadrai Superviror: Dr. John Meech 2 1 / 8 / 2 0 0 4 M - H V 1 R e s e r v o i r Lid 228 Hypervelocity Impact Facility S c a l e University of British Columbia (CERM3) Mining Engineering Department Design: Sepehr Sadrai Superviror: Dr. John Meech 21 /8 /2004 M-HV16 Laser Support APPENDIX F: ROCK AND PROJECTILE MASS ALTERNATIVES Mp •(g) Velocity (m/s) . Energy (kgm 2/s 2) Volume (m3) Pressure . (N/m 2) Pressure (atm) MR = 50 V=1000 5 1000 . 2500 0.00003333 75007500.75 . 740 ;27 .10 1000 5000 0.00003333 150015001.5 1480.53 15 . 1000 7500 0.00003333 225022502.3 2220.80 20 1000 10000 0^00003333 300030003 2961.07, 25 1000 12500 0.00003333 375037503.8 3701.33 30 1000 15000 0.00003333 450045004.5 4441.60 35 1000 17500 0:00003333 525052505.3 5181.87 MR =50 V=500 • 5 500 625 0.00003333 18751875.19 185.07 10 500 1250 0.00003333 37503750.38 370.13 15 500 , 1875 0.00003333 56255625.56 555.20 20 500 2500 0.00003333 .75007500.75 740.27 25 500 3125 0.00003333 93759375.94 925.33 30 500 3750 0.00003333 112511251.1 1110.40 35 500 4375 ' 0.00003333 131263126.3 1295.47 M R = 50 V=300 5 300 225 0.00003333 6750675.068 66.62 10 300 ' 450 ' 0.00003333 13501350.14 133.25 ' 15 300 675 0.00003333 20252025.2 199.87 20 300 900' 0.00003333 27002700.27 266.50 25 300 • 1125 0^00003333 33753375.34 333.12 30 i i 300 1350 " " 0.00003333 40504050.41 399.74 35 300 1575 0.00003333 47254725.47, 466.37 MR = 50 V=100 , • . • , 5 100 25' 0.00003333 750075.0075 7.40 10 100 50 0.00003333 1500150.015, 14.81 15 100 75 0.00003333 2250225.023 22.21 20 100 100 0.00003333 3000300.03 29.61 25 100 125 0.00003333 3750375.038 37:01 30 100 150 0.00003333 4500450.045 44.42 35 100 175 0.00003333 5250525.053 51.82 230 Mp (g) Velocity . (m/s) Energy (kgm 2/s 2) Volume (m3) Pressure / (N/m 2) Pressure (atm) M R = 7 5 V=1000 : 5 1000 2500 0.00005 50000000 493.46 10 1000 5000 0.00005 . 100000000. 986.92 15 1000 7500 • 0.00005 150000000 . . 1480.38 20 1000 10000 0.00005 200000000 1973.85 25 1000 12500 0.00005 250000000 2467.31 30 1000 15000 0.00005 300000000 2960.77 35 1000 17500 0.00005 '350000000 3454.23 , M R = 75 V=500 5 500 625 0.00005 12500000 123:37 10 500 1250 .0.00005 25000000, 246 .73 . 15 500 1875 0.00005. 37500000 370.10 20 500 2500 0.00005 50000000 493.46 25 500 3125 0.00005 62500000 616.83 30 500 3750 ,0.00005 75000000 740.19 , 35 500 4375 0.00005 , 87500000 863.56 M R = 7 5 . V-300 . •5' . 300 225 0.00005 4500000 44.41 10 300 450 0.00005 . ,9000000 88.82 15 300 675 0.00005 .13500000 • 133.23 20 300 900 0.00005. 18000000 177.65 25 300 1125 0.00005 22500000 222.06 30 300 1350 0.00005 ' 27oooood: 266.47 35 300 1575. 0.00005 31500000 310.88 M R = 75 V=100 . 5 . 100 25, 0.00005 500000 4.93 10 100 50 0.00005 1000000 9.87 , 1 5 100 . 7 5 0.00005 , 1500000 14.80 20 100 100 0,00005 2000000 19.74 25 100 125 0.00005 2500000 .24.67 . 3 0 100 150 , 0.00005 ,3000000 29.61 35 100 175 0.00005 • , 3500000 34.54 231 A P P E N D I X G : A P P A R A T U S D E S I G N C A L C U L A T I O N S 1) Potential Energy = Kinetic Energy . To calculate the required length of the tube: A P A L = Vi M V 2 " A P = Maximum change in pressure (Pa) A = Launch tube cross section area (m2) L = Launch tube length (m) M . = Projectile and Sabot mass (kg) V Velocity (ms"1) A P =2.07Mpa A = 3.14159 x.(i.27) 2 x IO"4 M 12 ! 24= 36 g 0.036 kg V - 500 , . , . . (2.07 x 106) (5.07 x IO"4) (L) = (0^5) (0.036) (500)2 L = 4.29 m Selected Length = 4.3 m 232 2) Stress Ana lys is - Tube (longitudinal stress analysis) F 2 = 2F! P' L*D = 2 T ' L ' t PD (Barlow Formula) ,t=> TP t - Minimum thickness (m) P = Maximum pressure (MPa) L = Length (m) D = Outside diameter (m) T • = Tensile strength (MPa) = 200 MPa 2.07x0.0508 0.26xl0" 3 m = ~0.3mm t = 2x200 Selected Thickness = 12.5 mm (FoS=42) D 233 -Tube (cross section stress analysis) V PTTR2 2 ^ - R t T Minimum thickness, (m) Max pressure (MPa) = 2.07 MPa Length (m) . Outside radius (m) = 2.54 x 10~2m Tensile strength (MPa) = 200 MPa ^ PR _ 2.07x0.0254 IT 2x200 t = 0.13 x l O " 3 m = 0.13 mm Selected Thickness = 12.5 mm (FoS=96) t P L R T F 2 P 234 - Bolts (tensile stress analysis) • .' F 2 P TTR2 . IM = T / r r 2 8 F] — F 2 V 8 J r = 2.3 mm; d = 4.6 mm .Minimum diameter (selected) = 12.5 mm (FoS = 2.7) - Flanges and plates (Shear stress analysis) . • PTCR2 t = ' ' 5S . S = Shear strength (MPa) , R = Maximum radius (m) t -4 .1 mm Minimum thickness selected = 25.4 mm (FoS 6.2) 5 • • 1 • , i F , , S F 2 , P 236 APPENDIX H: PARTICLE SIZE DISTRIBUTION (LIMESTONE) 75 mm LA80 Sieve (mesh) Sieve Size (um) Weight (g) Weight (%) Cumulative Passing (%) .+10 2000 0 0 100 + 12 1650 : 0.14 1.10 98.90 + 14 1410 0.75 5.88 93.02 + 18 1000 2.9 22.75 . 70.27 + 40 420 . 4.15 32.55 .37.73 + 100 • 149 ' 2.3 18.04 19.69 + 200 74 1.05 ; 8.24 11.45 -200 0 1.46 11.45 0.00 12.75 100.00. LA110 Sieve (mesh) Sieve Sizie (nm) Weight (g) Weight (%) Cumulative Passing (%) •,'+10 2000 0 o 100 ' + 12' 1650 0.16 1.25 98.75 + 14 1410 0.5 . 3.92 94.83 .+.18 1000 2.34 . 18.34 76.49 . + 40 420 3.92 30.72 45.7.7 . +100 149 2.64 20.69 . 25.08 + 200 • .74 '.' 1.19 : 9:33 " 15.75 - 200 0 . 2.01 15.75 . 0.00 12.76 100.00 237 LA180 Sieve (mesh) Sieve Size (urn) Weight (g) Weight (%) Cumulative Passing (%) . > + 10 2.000 0 0 100 .+ 12 1650 0.08 0.63 99.37 +.14 •• 1410 0.31 . 2.44; 96.93 f. , 1 + 18 1000 • 1.3 '. 10.23 86.70 • 40 420 . 2.64 20.77 65.93 + 100 149 3.23 25.41 . 40.52 + 200 . 74 2.1, 16.52 24.00 -200,. •0." 3.05. 24.00 0.00 . 12.71 100.00 LA270 Sieve (mesh) Sieve Size (urn) Weight (g) Weight (%) Cumulative Passing (%) + 10 2000 .0 . o 1.00 ' : • ' +12 . 1650 ' o 0.00 100.00 . - 14 1410 0.01 0.08 99.92 '• +18 1000 •' .0.37 . 2.98 96.94 + .40 420 . 1.89 15.22 81.72 + 100 149. 3.66 29.47 52.25 + 200: 74 2.71 21.82 . 30.43 . - 200 0 , 3.78 30:43 0.00 12.42 100.00 238 150 mm LB70 Sieve (mesh) Sieve Size (um) Weight (g) Weight (%) Cumulative Passing (%) + 10, 2000 0 0 100 - 14 • '.V ,1410 2.92 • 11.92 88.08 - 18 1,000 8.88 36.26 51.82 : + 40 420 6.27 25.60 26.21 + 100 149 3.19 13.03 13.19 + 200 74 •' . 1.61 6.57 6.61 -200 0 . 1.62 6.61 0.00 • 24.49 . 100.00 LB180 Sieve (mesh) Sieve Size (nm) Weight (g) Weight (%) Cumulative Passing (%) . +10 2000 0 '•• 0' 100 . + 14 1410 1.8.1 7.41 92.59 + 18 1000 4.75 ' 19.44 73.16 + 40 420 6,6 27.00 . •'• 46.15 + 100 149 4:7 19.23 26.92 + 200 74 . ' 2.55 '; ' 10.43 16.49 • - 200 0 ' .- 4.03 , 16.49 0.00 ' 24.44 100.00 i 239 LB240 Sieve (mesh) Sieve Size (urn) Weight (g) Weight (%) Cumulative Passing (%) + 10 2000 0 0 100 ' + 14 1410 0.6 2.42 . 97.58 + 18 ' 1000 .2.07 • 8.35 • ' . . • 89.23 + 40 420 5.54 . • 22.35 : 66.88 + 100 149 6.61 26.66 40.22 1 + 200' 74 , 4.95 19.97 20.25 -200 o 5.02 • 20.25 .0.00 24.79 100.00 LB300 Sieve (mesh) Sieve Size (um) Weight (g) Weight (%). Cumulative Passing (%) ' + 10 . , 2000 •'. 0 0 100 + 14 1410 0.48 1.96 98.04 + 18 1000 2.2 8.96 89.08 + 40 . 420 5.6. 22.81 66.27 + 100 149 ; 6.38 25.99 40.29 + 200 74 ' 3.86 15.72 24.56 -200 0 6.03 24.56 : • • o.oo . 24.55 100.00 240 A P P E N D I X I: SPECIFIC S U R F A C E A R E A M E A S U R E . (L IMESTONE) 75 mm Sample Split 1 Split 2 S.S.A (m2/g) Weight (g) S.S.A (m2/g) Weight (g), L A 00 ' 0.66 6.65 0.81 6.36 . L A 80 0.57 7.98 1.06 4.78 • LAI 10 0.59 6.94 1.23 5.82 L A I 80 ,0.91 7,59 1.98 , 5.13 LA270 1.68 6.02 2.17 6.50 150 mm Sample Split 1 Split 2 Split 3 ' S.S.A (m2/g), Weight (g) S.S.A (m2/g) Weight (g) S.S.A (m2/g) Weight (g) L B 00 0.71 12.50 0.68 12.50 • . L B 70 0.58 11.80 0.73 6.27 1.03 6.42 LB180 0.74 6.51 0.92 11.30 1.84 6.58 LB240 0:96 8,19 1.56 11.56 2.16 4.95 LB300 0.91 8.29 1.46 10.24 2.12 6.03 241 APPENDIX J: PARTICLE SIZE DISTRIBUTION (QUARTZ) 75 mm QA80 Sieve (mesh) Sieve Size (nm) Weight fe) Weight (%) Cumulative Passing (%) + 10 2000 0 0 100 + 12 1650 0.8 6.25 93.75 + 14 1410 1.07 8.35 85.40 .•+ 18 1000 3.01 23.50 ; 61.90 + 40 420 3.82 29.82 . 32.08 + 100 149 2.45 19.13 12.96 , + 200 74 0.84 6.56 6.40 -200 o 0.82 6.40 0.00 12.81 ' 100.00 QA110 Sieve (mesh) Sieve Size (nm) Weight (g) Weight (%) Cumulative Passing '(%) • +1.0 2000 0.00 0 100 • + 1 2 1 ; 1650 0.48 3.75 • 96.25 + 14 1410 0.61 4.77 91.48 ,+ 18 1000 2,25 17.58 73.91 + 40 420 3.91 30.55 43.36 + 100 149 2.98 23.28 20.08 ' + 200 74 1.21 . 9.45 10.63 . ,' ' -200 0 1.36 10.63 0.00 12.80 : 100.00 242 QA140 Sieve (mesh) Sieve Size Weight (g) Weight (%) Cumulative Passing (%) , + 10 2000 0 0 100' + 12 1650 ., 0.06 0.47 99.53 + 14. 1410 0.26 . 2.03 > 97.50 + 18 1000 , •1.39 10.88 86.62 + 40 420 3.2 • 25.04 61.58 + 100 149 3.55 ... 27.78 33.80 + 200 1 '•• 7 4 . 1.78 13.93 19.87 -200 0 2.54 . 19.87 0.00 12.78 100.00 QA160 Sieve (mesh) Sieve Size (^ m) Weight (g) Weight (%) Cumulative Passing (%) 1 +10 2000 0 0 100 + 12 1650 0.1 0.80 99.20 + 14 1410 ; 0.21 1.67 ' 97.53 + 18 1000 1.05 8.36 ' 89.17 + 40 . 420 2.69 21.42 67.75 + 100 . 149 3.43 .27.31 •;. 40.45 + 200 74 2.09 16.64 23.81 -200 o ; 2.99 ' 23.81 o.oo. 12.56 100.00 243 QA190 Sieve , (mesh) Sieve Size (Um) Weight (g) Weight (%) Cumulative Passing (%) + 10 2000 0 0 . 100 + 12 ' 1650 • . 0.04 0.31 99.69 + 14 1410 '. 0.1 0.79 98.90 + 18 1000 •' 0.86 6.76 92.14 + 40 420 2.35 18.47 73.66 + 100 ' '149 3.63 28.54 •' 45.13 + 200; . 7 4 2.16 16.98 . . 28.14 -200 0 3,58 28.14 0.00 . 12.72 100.00 QA220 Sieve (mesh) Sieve Size (lim) Weight (g) Weight (%) Cumulative Passing (%) + i 1 0 , . 2000 .0 0 100 +.12 • 1650 , 0.04 0.31 99.69, + 14 1410 . 0.1 0.79 98.90 + 18 1000 0.66 : .5.19 93.71 + 40 420 2.03 . 15.97 . 77.73 + 100 149 3.3 25.96 ' 51.77, , + 200, 74 2.25 17.70 34.07 , - 200 0 4.33 34.07 0.00 12.71 100.00 244 150 mm QB70 Sieve (mesh) Sieve Size (urn) Weight (g) Weight (%) Cumulative Passing (%) + 10 •'. .2000 .0 0 100 - 12 1650 4.66 18.87 81.13 ,+ 14 1410 4.53 18.34 62.79 + 18 1000 10.72 43.40 • . 19.39 + 40 420 2.74 11.09 8.30 + 100 149 1.3 5.26 .'• 3.04 + 200 74 0.42 / 1.70 1.34 - 200 .0 0.33 1.34 0.00 24.7 .100.00 QB110 Sieve (mesh) Sieve Size (urn) Weight (g) Weight (%) Cumulative Passing (%) - 10 • 2000 0 0 100 + 12 1650 . 5.03 20:22 79.78 + 14 1410 4.04 16.24 63.55 + 18 1000 8.45 33.96 29.58 + 40 420 3.19 12.82 16.76 + 100 149 2.26 9.08 7.68 , +.200 74 0.9 ' 3.62 4.06 -200 ,0 L01 4.06 0.00 24.88 100.00 245 QB190 Sieve (mesh) Sieve Size (urn) Weight (k> Weight •(%) Cumulative Passing (%) + 10 2000 0 0 100 + 12 1650 4.54 . 18.34 '8.1.66 + 14 1410 3.86 15.60 66.06 .+ 18 1000 . 7153-. 30.42 35.64 + 40 . 420 . 2.62 10.59 25.05 + 100 149 2.53 10.22 14.83 + 200 .74 1.44 5.82 9.01 -.200 0 . 2.23. 9.01 '•• 0.00 24.75 100.00 246 APPENDIX K: SPECIFIC SURFACE AREA MEASUREMENT (QUARTZ) 75 mm Sample Split 1 Split 2 ' S.S.A. (m2/g) Weight (g) S.S.A (m2/g) Weight (g) QA 00 ,0.00 6.49 0.01 6.52 , QA 80 0.00 8.61 0.07 4.03 QA110 0.01 7.25 0.1.0 ' 5.50 QA140 0.01 4.90 0.16 7.82 QA160 0.03 7.48 0.35 5.01 QA190 0.07 ' 6.96 0.49 '-5.73 QA220 0.21 6.13 0.58 , 6.56 f 150 mm • Sample Split 1 Split 2 Split 3 ':S.S.A (m2/g) Weight (g) S.S.A (m2/g) Weight (g) S.S.A Weight (m2/g) (g) QB 00 0.00 12.50 0.01 12.5.0 QB 70 0.00 9.18 0.01 10.72 0.02 4.74 QB110 0.01 9.05 0.01 8.45 ., 0.04 . 7.27 QB190 . 0.01 , 8.49 0.01; 7.52 0.13 8.72 247 APPENDIX L: PARTICLE SIZE DISTRIBUTION (SALT) 75 mm SA80 Sieve (mesh) Sieve Size (nm) Weight (g) Weight (%) Cumulative Passing (%) • .+ 10 2000 0,00 0.00 100.00 + 12 1650 0.87 6.82 93.18 • + 14' 1410 1.20 9.41 83.76 + 18 1000 4.29 33.65 50.12 + 40 420 3.60 28.24 21.88 + 100 . 149 ; , 1.70 13.33 8.55 + 200 • 74 '.' 0.59 4.63 3.92. -200 0 0.50 . 3.92 0.00 .' 12.75 . 100.00 SA110 Sieve (mesh) Sieve Size (nm) Weight (g) Weight (%) Cumulative Passing (%) + 10 2000 0.00 0.00 .100.00 ', + 12 ,1650 0.64 5.04 94.96 ; + 14 1410 0.96 7.55 87.41 . +18 • 1000 2.38 ; 18.73 68.69 +40 420 _ 3.22 ; 25.33 43.35 + 100 , 149 2.55 20.06 23.29 + 200 ,74 ' ; 1.31 10.31 12.98 - 200 0 1.65 12.98 0.00 , 12.71 ' 100.00 248 SA160 Sieve (mesh) Sieve Size (nm) Weight (g) Weight (%) Cumulative Passing (%) + 10 2000 0.00 0.00 100.00 + 12 1650 0.24 • 1.92 : 98.08 + 14 1410 0.37 2.96 95.12 • +18 i . 1000 0.83 6.63 88.49 + 40 420 2.66 21.26 67.23 + 100 .149 . 3.01 24.06 43.17 + 200 74 1.90. 15.19 27.98 ' -200 , 0 3.50 , 27.98 .• 0.00 12.51 100.00 SA200 Sieve (mesh) Sieve Size (nm) Weight (g) Weight (%) Cumulative Passing (%) - 10 2000 0.00 1 0.00 100.00 + 12 1650 0.05 .0.40 , 99.60 + 14 . 1410 ; , 0.12 0.96 98.64 + 18 1000 '.' 0.31 248 96.16 + 40 420 ; ' , 2.63 21.06 75.10 + 100 149 '• 3.70 29.62 45.48 . + 200 . 74 - 2.06 16.49 28.98 - 200 . 0 3.62 28.98 . 0.00 12.49 100.00 249 APPENDIX M: SPECIFIC SURFACE AREA MEASUREMENT (SALT) 75 mm Sp l i t ! Split 2 Sample S.S.A (m2/g) Weight (g) S.S.A (m2/g) Weight (g) SA 00 0.01 6.50 0.03 6.50 SA 80 0.03 7.70 0.03 5.06 SAI 10 0.08 6.65 0.08 6.23 SAI 60 0.18 6.60 . 0.18 .. 5.98 SA200 0.22 6.73 0.24 5.99 250 APPENDIX N: BALL/ROD MILL GRIND ABILITY TESTS 1) Bond ball mill work index 251 BOND MILL GRINDABILITY TEST* REPORT Date: 12-Feb-07 Project: Hypervelocity TEST CONDITIONS Cycle Oversize Wt. (grams) Product Wt. (grams) Feed Undersize (grams) Net Product (grams) Product per Rev. (grams/rev.) Required Rev. (rev.) 1 832 196 50 146 1.46 100.00 2 732 296 10 286 1.47 195.24 3 595 433 14 419 2.20 190.35 4 ~ 782 246 21 225 1.81 123.98 5 731 297 12 285 1.84 155.30 6 729 299 14 285 1.87 152.16. 15 149.28 Test: Work Index Sample: Limestone 252 SIZE ANALYSIS TEST RESULTS Sieve Size % Pass ing Tyler mesh pm Feed Product . 6 3360 100.0 Material Charge Wt.-700 mL(g) = 1028 8 2380 73.7 Test Screen (um) = 149 10 2000 61.1 Undersize in Feed (%)= 4.87% 14 1410 41.8 Circulating Load (%) = 246 20 840 25.1 - - Gbp (ave.) = 1.82 30 590 17.8 Product P 8 o (Mm) = 129 " 35 500 17.8 Feed F 8 o (pm) = 2,600 40 420 - 13.4 Wi (kWh/ton) = 12.6 70 210 7.0 Wi (kWh/tonne) = 13.8 100 149 4.9 100.0 140 105 3.3 56.6 200 74 2.2 31.1 270 53 1.0 9.1 325 44 0.6 5.0 400 37 0.2 0.8 • SIZE ANALYSIS Size Feed Product Tyler um Weight Individual Passing Weight Individual Passing mesh (g) (%) (%) (g) (%) (%) 6 3360 0.00 0.0 100.0-8 2380 270.37 26.3 73.7. 10 2000 129.89 12.6 61.1 14 1410 197.97 19.3 41.8 20 840 171.59 16.7 25!1 30 590 74.86 7.3 17.8 -40 420 45.91 4.5 13.4 . 70 210 65.65 . 6.4 7.0 0.00 0.0 100.0 100 149 21.72 2.1 4.9 0.00 0.0 100,0 140 105 15.85 1.5 3.3 . 15.20 43.4 56.6-200 74 12.04 1.2 2.2 8.91 25.5 31.1 270 53 12.10 1.2 1.0 7.70 22.0 9.1 325- 44 4.09 0.4 - 0.6 1.44 4.1 5~0 400 37 4.35 0.4 0.2 1.47 4.2 0.8 -400 0 1.61 0.2 0.0 0.28 - 0.8 0.0 Total 1028.00 100.0 35.00 100.0 F80 = 2600 (from graph) P80= 129 (from graph) 2 ) Reference method Limestone (reference) Size Feed Mesh fjm . . . Individual _ , „ , . Weight (g) ^ Passing (%) + 6 3360 + 7 2830 +10 2000 . +50 297 +100 149 + 140 105 + 200 74 -200 0 0.00 0.00 100.00 30.34 15.17 84.83 62.43 31.22 53.62 93.78 46.89 . 6.72 5.67 2.84 3.89 , 2.31 1.16 2.73 1.62 0.81 1.92 3.85 1.93 0.00 200.00 .100.00 Cumulative % Passing vs Feed Particle Size 1 uu ; on 00 yu fin ou c ' u (A 8 fin ™. ou • d> ou > umul on < • *i n 1 u •d < < )' . 5( )0 10 00 15 1 00 20 'article Si 00 25 ze (micron 00 •' 30 ) , 00 35 00 40 F80 = 2700 257 Size Product Mesh //m Weight (g) Individual (%) Passing (%) + 30 590' . 0 0.00: 100 + 40 420 13.34 6.67 93.33 + 50 297 30.67 15.34 78.00 + 100. 149 57.97 28.99 49.01 + 140 105 23.13 , 11.57 37.45 + 200 . 7 4 20.20 10.10 27.35 + 270 53 28.97 14.49 12.86 -270 0 25.72 12.86 . 0.00 200.00 100.00 Cumulative % Passing vs Product Particle Size on J0 yu 1 OU O ) -rn - - (1 «J ou • 1 ative 3 C umul on ZU • •1 n lU • 0 < ( ) 1( DO 2( )0 3( Part )0 '• ,4( cle Size (mic )0 ' 5( ron) )0 6( )0 7( P80 = 310 258 Quartz Size Feed Mesh fjm Weight (g) Individual (%) Passing (%) + 6 3360 0.00 0.00 100.00 + 7 2830 55.01 27.51 72.50 + 10 2000 106.42 53.21 19:29 + 50 297 37.67 18.84 0.45 + 100 149 0.53 0.27 0.19 + 140 105 0.12 0.06 0.13 + 200 74 0.08 . 0.04 0.09 -200 0 0.17. 0!09 0.00 200.00 • 100.00 Cumulative % Passing vs Feed Particle Size Particle Size (micron) F80 = 2950 259 Size Product Mesh //m Weight (g) Individual (%)• Passing (%) + 30 590 . 0 0.00 100 + 40 420 9.29 4!65 95.36 +. 50 . 297 25.43 12.72 82.64 + 100 ; 149 71.31 ••' 35.66 46.99 + 140 105 29.79 14.90 32.09 + 200 74 19.64 9.82 22.27 +270 53 16.73 8.37 13.91 -270 0 27.81 13.91 . 0.00 200.00 100.00 C u m u l a t i v e % P a s s i n g v s P r o d u c t P a r t i c l e S i z e H r\n i * 1 Qn • DO y u o n OU Ui 7 n '3! IA TO 6 0 lative umul Z> C o n I u 0 i ( D 1( DO 2( DO : 3( P a r t DO 4( i c l e S i z e ( m i c )0 , 5( r o n ) DO 6( DO 7( P80 = 285 260 Rock Salt Size Feed Mesh Weight (g) Individual (%) Passing (%) + 6 . 3360 0.00 0.00 100.00 + 7 2830 43.81 21.91 78.10 * • '•' +.10 2000 . 61.89 30.95 47.15 + 50 297 . 85.28 42.64 4.51 + 100 . 149 5.06 2.53 1.98 + 140 105 1.42 0.71 1.27 + 200 : 74 0.89 0.45 0.82 -200 0 1.65 ,0^83 0.00 200.00 100.00 i C u m u l a t i v e % P a s s i n g v s F e e d P a r t i c l e S i z e 1 u u ; . Qn yu on < ^ / u £ Rn • tO • DU Q. s? • ' lative D C -j t u E on zu i u C\ • U < D 5( DO 10 00 15 00 20 ' a r t i c l e S i : 00 25 e ( m i c r o n 00 . ' 30 00 35 00 4000 F80 = 2870 261 1 Size Product Mesh Weight (g) Individual Passing (%) + 30 590 0 0.00 100 + 40 420 0.3 0.15 99.85 + 50 297 1.14 '• 0.57 99.28 + 100 149 '21.80 ' 10.90 88.38 + 140 105 27.27 13.64 74.75 + 200 74 28.99 14.50 60.25 +270 : 53 35.43 17.72 42.54 : - 270 •' 0 ' ' ' 8507 42.54 '.„• •'. 0.00 200.00 .100.00 C u m u l a t i v e % P a s s i n g v s P r o d u c t P a r t i c l e S i z e •inn : ! . . . ' • ! '. » '. on )0. y u on O U OI 7n c •'0 'K ra. Kn •J Q. b U lative D C umul -> C • A f\ \ U p • '. ( ) • ' K 30 2( 30 3( P a r t 30 4( i c l e S i z e ( m i c 30 5( r o n ) 30 6( 30 7( P80 = 117 262 263 264 

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