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Particle Strengths: Extreme Value Distributions in Fracture

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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.

Author(s): Robert F. Cook
Publisher: Wiley-American Ceramic Society
Year: 2023

Language: English
Pages: 410
City: Columbus

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: ? and ?
12.3 Localized Loading
12.3.1 Analysis
12.3.2 Examples
12.4 Spatially Varying Loading
12.4.1 Stress-Intensity Factor and Toughness
12.4.2 Crack at a Stressed Pore
12.4.3 Crack at a Misfitting Inclusion
12.4.4 Crack at an Anisotropic Grain or Sharp Contact
12.5 Combined Loading
12.5.1 Strength of Post-Threshold Flaws
12.5.2 Strength of Sub-Threshold Flaws
12.6 Long Cracks in Particles
12.6.1 Polymer Discs
12.6.2 Microcellulose Tablets
12.6.3 Ductile-Brittle Transitions
12.6.4 Agglomerate Compaction
12.7 Discussion and Summary
References
13 Applications and Scaling of Particle Strengths
13.1 Introduction
13.2 Particle Crushing Energy
13.3 Grinding Particle Reliability
13.4 Mass Effects on Particle Strength
13.5 Microstructural Effects on Particle Strength
13.6 Discussion
References
Index
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