Brittle Fracture and Damage of Brittle Materials and Composites

Brittle Fracture and Damage of Brittle Materials and Composites

Statistical-Probabilistic Approaches

1st Edition - March 9, 2016

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  • Author: Jacques Lamon
  • Hardcover ISBN: 9781785481215
  • eBook ISBN: 9780081011614

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Flaws are the principal source of fracture in many materials, whether brittle or ductile, whether nearly homogeneous or composite. They are introduced during either fabrication or surface preparation or during exposure to aggressive environments (e. g. oxidation, shocks). The critical flaws act as stress concentrators and initiate cracks that propagate instantaneously to failure in the absence of crack arrest phenomena as encountered in brittle materials. This book explores those brittle materials susceptible to crack arrest and the flaws which initiate crack induced damage. A detailed description of microstructural features covering numerous brittle materials, including ceramics, glass, concrete, metals, polymers and ceramic fibers to help you develop your knowledge of material fracture. Brittle Failure and Damage of Brittle Materials and Composites outlines the technological progress in this field and the need for reliable systems with high performances to help you advance the development of new structural materials, creating advantages of low density, high resistance to elevated temperatures and aggressive environments, and good mechanical properties.

Key Features

  • The effects of flaw populations on fracture strength
  • The main statistical-probabilistic approaches to brittle fracture
  • The use of these methods for predictions of failure and effects induced by flaw populations
  • The application of these methods to component design
  • The methods of estimation of statistical parameters that define flaw strength distributions
  • The extension of these approaches to damage and failure of continuous fiber reinforced ceramic matrix composites


Students, engineers and researchers who are interested in materials science and engineering, most notably fracture and brittle materials.

Table of Contents

    • Dedication
    • Introduction
    • 1: Flaws in Materials
      • Abstract:
      • 1.1 Introduction
      • 1.2 The theoretical strength and the intrinsic strength of materials
      • 1.3 The fracture strength of materials
      • 1.4 The flaws
      • 1.5 Severity of individual flaws
      • 1.6 Influence of flaw populations
      • 1.7 Consequences of failure predictions
    • 2: Statistical-Probabilistic Approaches to Brittle Fracture: The Weibull Model
      • Abstract:
      • 2.1 Introduction
      • 2.2 Weibull statistical model
      • 2.3 Probability of fracture for a uniaxial non-uniform tensile stress field
      • 2.4 Probability of fracture from the surface of specimens
      • 2.5 Weibull multiaxial analysis
      • 2.6 Multiaxial approach based on the principle of independent action of stresses
      • 2.7 Summary on the Weibull statistical model
    • 3: Statistical-Probabilistic Theories Based on Flaw Size Density
      • Abstract:
      • 3.1 Introduction
      • 3.2 Failure probability
      • 3.3 Expressions for flaw size density and distribution
      • 3.4 Introduction of stress state
      • 3.5 Models
      • 3.6 Limits of the flaw size density-based approaches
    • 4: Statistical-Probabilistic Theories Based on Flaw Strength Density
      • Abstract:
      • 4.1 Introduction
      • 4.2 Basic equations of failure probability in the elemental strength approach
      • 4.3 Elemental strength model for a uniform uniaxial stress state: Argon–McClintock development
      • 4.4 The Batdorf model
      • 4.5 The multiaxial elemental strength model [LAM 83]
    • 5: Effective Volume or Surface Area
      • Abstract:
      • 5.1 Introduction
      • 5.2 The Weibull model: the effective volume for a uniaxial stress state
      • 5.3 The multiaxial elemental strength model: the effective volume for a multiaxial stress state
      • 5.4 Analytic expressions for failure probability, effective volume or surface area (Weibull theory)
      • 5.5 Some remarkable exact expressions for failure probability, effective volume or surface area (multiaxial elemental strength theory)
      • 5.5 Conclusion
    • 6: Size and Stress-state Effects on Fracture Strength
      • Abstract:
      • 6.1 Introduction
      • 6.2 Uniform uniaxial stress state
      • 6.3 Non-uniform uniaxial stress state
      • 6.4 Multiaxial stress state: multiaxial elemental strength model
      • 6.5 Applications
      • 6.6 Conclusion
    • 7: Determination of Statistical Parameters
      • Abstract:
      • 7.1 Introduction
      • 7.2 Methods of determination of statistical parameters
      • 7.3 Production of empirical data
      • 7.4 Bias and variability
      • 7.5 Effect of the presence of multimodal flaw populations
      • 7.6 Fractographic analysis and flaw populations
      • 7.7 Examples
    • 8: Computation of Failure Probability: Application to Component Design
      • Abstract:
      • 8.1 Introduction
      • 8.2 Computer programs for failure predictions
      • 8.3 The CERAM computer program
      • 8.4 Validation of the CERAM computer code
      • 8.5 CERAM-based ceramic design
      • 8.6 Relation test specimen/component: identification of allowable material properties
      • 8.7 Determination of statistical parameters using CERAM
      • 8.8 Application to multimaterials and composite materials
      • 8.9 Conclusion
    • 9: Case Studies: Comparison of Failure Predictions Using the Weibull and Multiaxial Elemental Strength Models
      • Abstract:
      • 9.1 Introduction
      • 9.2 Predictions of failure under flexural load
      • 9.3 Prediction of thermal shock failure
      • 9.4 Conclusion
    • 10: Application of Statistical-Probabilistic Approaches to Damage and Fracture of Composite Materials and Structures
      • Abstract:
      • 10.1 Introduction
      • 10.2 Damage mode by successive cracking in continuous fiber reinforced composites
      • 10.3 Flaw populations involved in damage and pertinent flaw strength density functions
      • 10.4 Matrix fragmentation: series system model
      • 10.5 Approach based on Poisson process
      • 10.6 The Monte Carlo simulation method
      • 10.7 The fragment dichotomy-based model (parallel system)
      • 10.8 Evaluation of models: comparison to experimental data
      • 10.9 Ultimate failure of unidirectionnally reinforced composite (Weibull model, uniform tension) in the presence of matrix damage
      • 10.10 Application to composites: unified model
      • 10.11 Conclusion
    • Bibliography
    • Index

Product details

  • No. of pages: 296
  • Language: English
  • Copyright: © ISTE Press - Elsevier 2016
  • Published: March 9, 2016
  • Imprint: ISTE Press - Elsevier
  • Hardcover ISBN: 9781785481215
  • eBook ISBN: 9780081011614

About the Author

Jacques Lamon

Jacques Lamon received an award from the Seymour Cray company in 1990 for his work on failure statistics based predictions of brittle failure. In 2006, he was elected Fellow of the American Ceramic Society. In 2007 he received the First Prize of Best Paper Awards from the American Ceramic Society. He has authored one book on the Mechanics of brittle fracture and damage, authored more than 300 technical articles on ceramics reliability, and the thermomechanical behaviour of fibre-reinforced ceramic matrix composites and contributed to/ edited 13 books; 14 conference proceedings, 3 journal special issues and more than 15 testing method standards (CEN) and presented more than 70 invited lectures. HIs current research interests include Thermomechanical behavior of composite materials, modelling of damage, fracture and durability, effects of the environment, multiscale approaches to behavior, fracture and durability and the probabilistic approaches to fracture and damage.

Affiliations and Expertise

CNRS Research Director (Exceptional Class), ENS Cachan, CNRS, Université Paris Saclay

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