Particle Strengths. Extreme Value Distributions in Fracture

Particle Strengths
Contents
Preface
Abbreviations and Symbols
1 Introduction to Particles and Particle Loading
	1.1 Particle Failure and Human Activity
		1.1.1 Particles as Structural Components
		1.1.2 Particle Loading
		1.1.3 Particles in Application
	1.2 Particle Shapes and Sizes
	1.3 Summary: Particle Loading and Shape
	References
2 Particles in Diametral Compression
	2.1 Extensive and Intensive Mechanical Properties
	2.2 Particle Behavior in Diametral Compression
		2.2.1 Force-Displacement Observations
		2.2.2 Force-Displacement Models
	2.3 Stress Analyses of Diametral Compression
	2.4 Impact Loading
	2.5 Strength Observations
	2.6 Strength Empirical Distribution Function
	2.7 Outline of Particle Strengths
		2.7.1 Individual Topics
		2.7.2 Overall Themes
	References
3 Flaw Populations
	3.1 Flaw Sizes and Strengths
	3.2 Populations of Flaws and Strengths
		3.2.1 Population Definitions
		3.2.2 Population Examples
	3.3 Samples of Flaws and Strengths
		3.3.1 Sample Definitions
		3.3.2 Sample Examples
	3.4 Heavy-Tailed and Light-Tailed Populations
	3.5 Discussion and Summary
	References
4 Strength Distributions
	4.1 Brittle Fracture Strengths
		4.1.1 Samples of Components
		4.1.2 Analysis of Sample Strength Distributions
	4.2 Sample Strength Distributions
		4.2.1 Sample Analysis Verification
		4.2.2 Sample Examples
	4.3 Discussion and Summary
	References
5 Survey of Extended Component Strength Distributions
	5.1 Introduction
	5.2 Materials and Loading Survey
		5.2.1 Glass, Bending and Pressure Loading
		5.2.2 Alumina, Bending Loading
		5.2.3 Silicon Nitride, Bending Loading
		5.2.4 Porcelain, Bending Loading
		5.2.5 Silicon, Bending and Tension Loading
		5.2.6 Fibers, Tensile Loading
		5.2.7 Shells, Flexure Loading
		5.2.8 Columns, Compressive Loading
		5.2.9 Materials Survey Summary
	5.3 Size Effects
		5.3.1 Stochastic
		5.3.2 Deterministic
		5.3.3 Size Effect Summary
	5.4 Discussion and Summary
	References
6 Survey of Particle Strength Distributions
	6.1 Introduction
	6.2 Materials Comparisons
		6.2.1 Alumina
		6.2.2 Quartz
		6.2.3 Limestone
		6.2.4 Rock
		6.2.5 Threshold perturbations
	6.3 Size Comparisons
		6.3.1 Small Particles
		6.3.2 Medium Particles
		6.3.3 Large Particles
	6.4 Summary and Discussion
	References
7 Stochastic Scaling of Particle Strength Distributions
	7.1 Introduction
	7.2 Concave Stochastic Distributions
		7.2.1 Alumina
		7.2.2 Limestone
		7.2.3 Coral
		7.2.4 Quartz and Quartzite
		7.2.5 Basalt
	7.3 Sigmoidal Stochastic Distributions
		7.3.1 Fertilizer
		7.3.2 Glass
	7.4 Summary and Discussion
	References
8 Case Study: Strength Evolution in Ceramic Particles
	8.1 Introduction
	8.2 Strength and Flaw Size Observations
	8.3 Strength and Flaw Size Analysis
	8.4 Summary and Discussion
	References
9 Deterministic Scaling of Particle Strength Distributions
	9.1 Introduction
	9.2 Concave Deterministic Distributions
		9.2.1 Alumina
		9.2.2 Quartz
		9.2.3 Salt
		9.2.4 Rock
		9.2.5 Coal
		9.2.6 Coral
	9.3 Sigmoidal Deterministic Distributions
		9.3.1 Glass
		9.3.2 Rock
	9.4 Linear Deterministic Distributions
		9.4.1 Cement
		9.4.2 Ice
	9.5 Deterministic Strength and Flaw Size Analyses
		9.5.1 Linear Strength Distributions
		9.5.2 Concave Strength Distributions
	9.6 Summary and Discussion
	References
10 Agglomerate Particle Strengths
	10.1 Introduction
	10.2 Pharmaceuticals
		10.2.1 Porosity
		10.2.2 Shape
		10.2.3 Distributions
	10.3 Foods
	10.4 Catalysts
	10.5 Discussion and Summary
	References
11 Compliant Particles
	11.1 Introduction–Hydrogel Particles
	11.2 Deformation
		11.2.1 Axial
		11.2.2 Transverse
	11.3 Strength
	11.4 Summary and Discussion
	References
12 Fracture Mechanics of Particle Strengths
	12.1 Introduction
	12.2 Uniform Loading
		12.2.1 Work and Elastic Energy
		12.2.2 Mechanical Energy and Surface Energy
		12.2.3 The Griffith Equation
		12.2.4 Configurational Forces: