Particle Strengths A holistic and straightforward analysis framework for understanding particle strength distributions In Particle Strengths: Extreme Value Distributions in Fracture, distinguished researcher Dr. Robert F. Cook delivers a thorough exploration of the science and related engineering of fracture strength distributions of single particles tested in diametral compression. In the book, the author explains particle strengths in the broader context of material strengths to permit readers to design with particles in systems in which mechanical properties are crucial to application, manufacturing, and handling. Particle Strengths compiles published data on particle strengths into a common format that includes over 140 materials systems and over 270 published strength distributions derived from over 13000 individual particle strength measurements. It offers physically consistent descriptions of strength behavior, including the strength threshold, using simple polynomial distribution functions that can easily be implemented. Readers will also find: A thorough introduction to particles and particle loading, including discussions of particle failure and human activity Comprehensive explorations of stochastic scaling of particle strength distributions, including concave and sigmoidal stochastic distributions Practical discussions of agglomerate particle strengths, including those relevant to pharmaceuticals, foods, and catalysts Detailed treatments of applications and scaling of particle strengths, including particle crushing energy and grinding particle reliability Perfect for materials scientists and engineers, mining and construction engineers, and environmental scientists, Particle Strengths: Extreme Value Distributions in Fracture will also benefit anthropologists, zoologists, pharmaceutical scientists, biomaterials scientists and engineers, and graduate students studying materials science, and chemical, mechanical, and biomedical engineering.

Table of Contents:
Preface xi Abbreviations and Symbols xiii 1 Introduction to Particles and Particle Loading 1 1.1 Particle Failure and Human Activity 1 1.1.1 Particles as Structural Components 1 1.1.2 Particle Loading 4 1.1.3 Particles in Application 12 1.2 Particle Shapes and Sizes 14 1.3 Summary: Particle Loading and Shape 23 References 24 2 Particles in Diametral Compression 29 2.1 Extensive and Intensive Mechanical Properties 29 2.2 Particle Behavior in Diametral Compression 33 2.2.1 Force-Displacement Observations 33 2.2.2 Force-Displacement Models 38 2.3 Stress Analyses of Diametral Compression 48 2.4 Impact Loading 60 2.5 Strength Observations 63 2.6 Strength Empirical Distribution Function 65 2.7 Outline of Particle Strengths 68 2.7.1 Individual Topics 68 2.7.2 Overall Themes 70 References 72 3 Flaw Populations 81 3.1 Flaw Sizes and Strengths 81 3.2 Populations of Flaws and Strengths 84 3.2.1 Population Definitions 84 3.2.2 Population Examples 86 3.3 Samples of Flaws and Strengths 92 3.3.1 Sample Definitions 92 3.3.2 Sample Examples 96 3.4 Heavy-Tailed and Light-Tailed Populations 103 3.5 Discussion and Summary 106 References 110 4 Strength Distributions 113 4.1 Brittle Fracture Strengths 113 4.1.1 Samples of Components 113 4.1.2 Analysis of Sample Strength Distributions 114 4.2 Sample Strength Distributions 116 4.2.1 Sample Analysis Verification 116 4.2.2 Sample Examples 119 4.3 Discussion and Summary 125 References 130 5 Survey of Extended Component Strength Distributions 133 5.1 Introduction 133 5.2 Materials and Loading Survey 134 5.2.1 Glass, Bending and Pressure Loading 134 5.2.2 Alumina, Bending Loading 135 5.2.3 Silicon Nitride, Bending Loading 136 5.2.4 Porcelain, Bending Loading 138 5.2.5 Silicon, Bending and Tension Loading 140 5.2.6 Fibers, Tensile Loading 141 5.2.7 Shells, Flexure Loading 142 5.2.8 Columns, Compressive Loading 144 5.2.9 Materials Survey Summary 144 5.3 Size Effects 148 5.3.1 Stochastic 148 5.3.2 Deterministic 153 5.3.3 Size Effect Summary 159 5.4 Discussion and Summary 159 References 163 6 Survey of Particle Strength Distributions 167 6.1 Introduction 167 6.2 Materials Comparisons 169 6.2.1 Alumina 169 6.2.2 Quartz 171 6.2.3 Limestone 173 6.2.4 Rock 174 6.2.5 Threshold perturbations 175 6.3 Size Comparisons 177 6.3.1 Small Particles 177 6.3.2 Medium Particles 180 6.3.3 Large Particles 181 6.4 Summary and Discussion 182 References 186 7 Stochastic Scaling of Particle Strength Distributions 189 7.1 Introduction 189 7.2 Concave Stochastic Distributions 193 7.2.1 Alumina 193 7.2.2 Limestone 194 7.2.3 Coral 197 7.2.4 Quartz and Quartzite 198 7.2.5 Basalt 201 7.3 Sigmoidal Stochastic Distributions 202 7.3.1 Fertilizer 202 7.3.2 Glass 207 7.4 Summary and Discussion 208 References 213 8 Case Study: Strength Evolution in Ceramic Particles 215 8.1 Introduction 215 8.2 Strength and Flaw Size Observations 217 8.3 Strength and Flaw Size Analysis 220 8.4 Summary and Discussion 222 References 230 9 Deterministic Scaling of Particle Strength Distributions 233 9.1 Introduction 233 9.2 Concave Deterministic Distributions 237 9.2.1 Alumina 237 9.2.2 Quartz 238 9.2.3 Salt 241 9.2.4 Rock 242 9.2.5 Coal 245 9.2.6 Coral 246 9.3 Sigmoidal Deterministic Distributions 248 9.3.1 Glass 248 9.3.2 Rock 252 9.4 Linear Deterministic Distributions 253 9.4.1 Cement 254 9.4.2 Ice 257 9.5 Deterministic Strength and Flaw Size Analyses 258 9.5.1 Linear Strength Distributions 259 9.5.2 Concave Strength Distributions 263 9.6 Summary and Discussion 265 References 270 10 Agglomerate Particle Strengths 273 10.1 Introduction 273 10.2 Pharmaceuticals 276 10.2.1 Porosity 277 10.2.2 Shape 280 10.2.3 Distributions 287 10.3 Foods 290 10.4 Catalysts 292 10.5 Discussion and Summary 294 References 297 11 Compliant Particles 303 11.1 Introduction–Hydrogel Particles 303 11.2 Deformation 308 11.2.1 Axial 308 11.2.2 Transverse 310 11.3 Strength 315 11.4 Summary and Discussion 317 References 322 12 Fracture Mechanics of Particle Strengths 325 12.1 Introduction 325 12.2 Uniform Loading 327 12.2.1 Work and Elastic Energy 327 12.2.2 Mechanical Energy and Surface Energy 328 12.2.3 The Griffith Equation 329 12.2.4 Configurational Forces: G and R 331 12.3 Localized Loading 332 12.3.1 Analysis 332 12.3.2 Examples 334 12.4 Spatially Varying Loading 337 12.4.1 Stress-Intensity Factor and Toughness 337 12.4.2 Crack at a Stressed Pore 339 12.4.3 Crack at a Misfitting Inclusion 341 12.4.4 Crack at an Anisotropic Grain or Sharp Contact 347 12.5 Combined Loading 350 12.5.1 Strength of Post-Threshold Flaws 350 12.5.2 Strength of Sub-Threshold Flaws 353 12.6 Long Cracks in Particles 354 12.6.1 Polymer Discs 354 12.6.2 Microcellulose Tablets 358 12.6.3 Ductile-Brittle Transitions 359 12.6.4 Agglomerate Compaction 361 12.7 Discussion and Summary 363 References 366 13 Applications and Scaling of Particle Strengths 369 13.1 Introduction 369 13.2 Particle Crushing Energy 369 13.3 Grinding Particle Reliability 373 13.4 Mass Effects on Particle Strength 376 13.5 Microstructural Effects on Particle Strength 380 13.6 Discussion 388 References 390 Index 393