Brittle Fracture and Damage of Brittle Materials and Composites

Statistical-Probabilistic Approaches

Jacques Lamon

• Publisher: ISTE Press - Elsevier
• Year: 2016
• Print ISBN: 9781785481215
• eBook ISBN: 9780081011614
• Topic: Technology & Engineering
• Subtopic: Materials Science
• Index: Technology & Engineering

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.- 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

1

Flaws in Materials

Abstract:

Any material can contain flaws, i.e. materials are never free of flaws. According to dictionaries, a flaw is “an imperfection, often concealed, that impairs soundness”. Here, a flaw is a heterogeneity that disrupts the theoretical order and introduces a discontinuity or a singularity. Flaws impede the working of materials and systems, as well as various optical, magnetic, mechanical, etc. properties. Various words are used for flaws, depending on length scale: dislocation, vacancy, impurity, interstitial (crystal defects), fault (geology), cavity, hole, etc. The flaws of interest in this book are those which are responsible for fractures. The occurrence of flaws is not completely avoidable in the processing, fabrication or service of a material/component. They may appear as cracks, voids, metallurgical inclusions, weld defects, design discontinuities or some combination thereof.

Keywords

Crack extension; Environment; Fracture strength; Machining flaws; Multimodal flaw; Processing flaws; Resistance; Strength; Stress field; Submicrostructure flaws

1.1 Introduction

Any material can contain flaws, i.e. materials are never free of flaws. According to dictionaries, a flaw is “an imperfection, often concealed, that impairs soundness”. Here, a flaw is a heterogeneity that disrupts the theoretical order and introduces a discontinuity or a singularity. Flaws impede the working of materials and systems, as well as various optical, magnetic, mechanical, etc. properties. Various words are used for flaws, depending on length scale: dislocation, vacancy, impurity, interstitial (crystal defects), fault (geology), cavity, hole, etc. The flaws of interest in this book are those which are responsible for fractures. The occurrence of flaws is not completely avoidable in the processing, fabrication or service of a material/component. They may appear as cracks, voids, metallurgical inclusions, weld defects, design discontinuities or some combination thereof.

Flaws are the weakest link of materials. They may have any shape. In certain materials, their size can be as small as a few micrometers (engineering ceramics and glass) or a fraction of a micrometer (fibers of carbon, ceramic or glass). They act as stress concentrators: they cause stress to increase locally, so that the local stress can exceed the intrinsic strength. Intrinsic strength is the strength in the absence of flaws. In single crystals, it is the stress required to break atomic bonds. It is called the theoretical strength or the ideal cohesive strength. It depends essentially on atomic bonding force. In polycrystalline materials, it takes smaller value than the theoretical strength, because of the presence of grain boundaries.

The fracture stress of materials depends on characteristics of flaw populations. As a result, it depends on extrinsic factors that contribute to flaw criticality such as specimen size, loading conditions, etc. Its sensitivity to flaws is significant when flaw extension is instantaneous and causes catastrophic failure. Brittle materials are very sensitive to flaws. The class of brittle materials includes numerous materials such as ceramics, glass, concrete, metals and polymers (at temperature < 0.75 Tg (Tg = glass transition)). By contrast, in ductile materials (like metals) or in damageable materials (like continuous fiber reinforced composites), the effect of flaws on ultimate fracture is less critical because their propagation is hampered by crack arrest phenomena (such as dislocations, slip bands, debonding at interfaces, etc.). However, in ceramic matrix composites, flaws initiate damage.

Flaws must be regarded as fundamental constituents of materials. As a result of their presence, fracture strength exhibits several features that are discussed in this first chapter. These features need to be known and accounted for in order to make sound predictions of in-service failure of components. For convenience in the discussion, we will consider the case of engineering ceramics on which a large amount of research work has been produced. They are a representative class of brittle materials.

1.2 The theoretical strength and the intrinsic strength of materials

Flawless single crystals consist of arrays of atoms that form a regular lattice. Binding of atoms involves interatomic forces, resulting from the energy of crystal. A repulsive energy and a form of attractive energy contribute to total energy. The interatomic forces ensure cohesion. Fractures occur when the links between atoms in a plane are no longer realized, splitting the material apart. The elementary modes of fracture are:

– cleavage or opening mode: the fracture plane is perpendicular to stress direction (Figure 1.1);

Figure 1.1 Interatomic force-intensity curve derivative of the total energy: d is the distance between two atoms, a₀ is the distance for binding energy (0° K): d = a_o + Δa

– slipping or shearing mode: the fracture plane is parallel to the loading direction.

The opening mode governs brittle fracture. The theoretical strength (also termed ideal cohesive strength) is the stress required to break the interatomic links in the fracture plane. An exact calculation of the theoretical strength is possible for simple cases such as ionic crystals. Approximation co...

Table of contents

• Cover image
• Title page
• Table of Contents
• Dedication
• Copyright
• Introduction
• 1: Flaws in Materials
• 2: Statistical-Probabilistic Approaches to Brittle Fracture: The Weibull Model
• 3: Statistical-Probabilistic Theories Based on Flaw Size Density
• 4: Statistical-Probabilistic Theories Based on Flaw Strength Density
• 5: Effective Volume or Surface Area
• 6: Size and Stress-state Effects on Fracture Strength
• 7: Determination of Statistical Parameters
• 8: Computation of Failure Probability: Application to Component Design
• 9: Case Studies: Comparison of Failure Predictions Using the Weibull and Multiaxial Elemental Strength Models
• 10: Application of Statistical-Probabilistic Approaches to Damage and Fracture of Composite Materials and Structures
• Bibliography
• Index