Cover
Preface
CHAPTER 1: Introduction
CHAPTER 2: Fracture Mechanics Background
1. INTRODUCTION
2. EARLY BRITTLE FRACTURE RESEARCH
3. DEVELOPMENT OF FRACTURE MECHANICS
4. CRITICAL FRACTURE TOUGHNESS
5. MIXED‐MODE LOADING
6. SUMMARY
7. QUESTIONS
8. REFERENCES
CHAPTER 3: Environmentally Enhanced Crack Growth
1. INTRODUCTION
2. HISTORICAL BACKGROUND
3. MECHANISMS OF ENVIRONMENTALLY ENHANCED CRACK GROWTH
4. SUMMARY
5. QUESTIONS
6. REFERENCES
CHAPTER 4: Fracture Mechanics Tests
1. INTRODUCTION
2. DOUBLE CANTILEVER BEAM SPECIMENS
3. DOUBLE TORSION TEST
4. FLEXURAL TESTS
5. DOUBLE CLEAVAGE DRILLED COMPRESSION
6. INDENTATION METHODS
7. MIXED‐MODE TESTS
8. SUMMARY
9. QUESTIONS
10. REFERENCES
CHAPTER 5: Strength Testing
1. INTRODUCTION
2. FLEXURE TESTS
3. BIAXIAL FLEXURE TESTS
4. DIRECT TENSILE TESTS
5. OTHER LOADING CONFIGURATIONS
6. COMPRESSIVE LOADING
7. BIOMATERIALS
8. STATISTICAL ANALYSIS OF STRENGTH DATA
9. SUMMARY
10. QUESTIONS
11. APPENDIX 5.A LAMINATE ANALYSIS EXAMPLE
12. REFERENCES
CHAPTER 6: Thermally Induced Fracture
1. BACKGROUND
2. GENERATION OF THERMAL STRESSES
3. THERMAL SHOCK TESTING
4. OTHER PROPOSED THERMAL SHOCK TESTS
5. SUMMARY
6. QUESTIONS
7. REFERENCES
CHAPTER 7: Modeling of Brittle Fracture
1. INTRODUCTION
2. MODELS BASED ON MATERIAL PROPERTIES
3. LATTICE TRAPPING AND ATOMISTICS OF FRACTURE
4. MODELING OF ENVIRONMENTAL INTERACTIONS
5. A NEW APPROACH TO MODELING: APPLICATION OF FRACTAL GEOMETRY
6. QUESTIONS
7. REFERENCES
CHAPTER 8: Quantitative Fractography
1. INTRODUCTION
2. FRACTURE MECHANICS BACKGROUND
3. FRACTURE SURFACE OBSERVATIONS
4. QUANTITATIVE ANALYSIS
5. FRACTOGRAPHIC PROCEDURES
6. FRACTAL GEOMETRY
7. SUMMARY
8. QUESTIONS
9. REFERENCES
CHAPTER 9: Microstructural Effects
1. INTRODUCTION
2. GRAIN SIZE AND ORIENTATION EFFECTS
3. TOUGHENING MECHANISMS
4. SUMMARY
5. QUESTIONS
6. REFERENCES
CHAPTER 10: Reliability and Time‐dependent Fracture
1. BACKGROUND
2. TECHNIQUES FOR ASSURING RELIABILITY
3. SUMMARY
4. QUESTIONS
5. REFERENCES
CHAPTER 11: Concluding Remarks
Subject Index
End User License Agreement

List of Tables

Chapter 05
1. Table 5.1 Comparison of Failure Stresses Calculated from Fracture Mechanics and Laminate Theory
2. Table 5.2 Summary of Advantages and Disadvantages of Useful Strength Tests
Chapter 06
1. Table 6.1 Surface and Center Stresses for Various Shapes
Chapter 07
1. Table 7.1 Data Used in Comparison of Measured and Calculated Values of Fracture Energy
2. Table 7.2 Comparison of Experimental and MD Results for Fractal Dimension Values
Chapter 08
1. Table 8.1 Fracture Properties of Brittle Materials
Chapter 09
1. Table 9.1 Ratio of K_IC/K_IC(SC) as a Function of Misorientation Angle, θ, of Cleavage Plane Segments

List of Illustrations

Chapter 01
1. Figure 1.1 Examples of advanced technical ceramics. From the left to right are an example of a ceramic hip replacement, barium titanate capacitors, various silicon nitride components, and a silicon nitride turbine wheel.
Chapter 02
1. Figure 2.1 Void in a plate in which stresses are concentrated at point A.
2. Figure 2.2 Modes of fracture.
3. Figure 2.3 Schematic of the stress field at a crack tip.
4. Figure 2.4 Surface flaw.
5. Figure 2.5 Schematic of mixed‐mode loading.
Chapter 03
1. Figure 3.1 Schematic of delayed failure.
2. Figure 3.2 Schematic of experimental setup used by Grenet to first investigate delayed failure in glass.
3. Figure 3.3 Crack growth data for soda‐lime‐silica glass.
4. Figure 3.4 Effect of solution pH on crack growth curves for soda‐lime‐silica glass.
5. Figure 3.5 Effect of glass composition on crack growth behavior.
6. Figure 3.6 Low‐level plateaus observed in binary Na₂O–SiO₂ glasses.
7. Figure 3.7 Schematic of stress‐enhanced reaction between water and a strained crack tip bond in silica.
8. Figure 3.8 Crack velocity‐K_I curves in environments that promote crack growth.
9. Figure 3.9 Crack growth in vitreous silica and soda‐lime glass. Environments are (a) water, (b) ammonia, (c) hydrazine, and (d) formamide.
10. Figure 3.10 Environmental effects on crack growth in Al₂O₃.
11. Figure 3.11 Environmental effects on crack growth in MgF₂.
12. Figure 3.12 Proposed mechanism of water reaction in MgF₂.
Chapter 04
1. Figure 4.1 DCB specimen.
2. Figure 4.2 Applied moment DCB specimen.
3. Figure 4.3 AMDCB specimen in loading fixture.
4. Figure 4.4 Contoured or tapered DCB specimen.
5. Figure 4.5 Wedge‐loaded DCB.
6. Figure 4.6 Crack growth data in various polycrystalline aluminum oxide materials taken using the AMDCB technique (Freiman et al. 1974).
7. Figure 4.7 Schematic drawing of the double torsion specimen.
8. Figure 4.8 Crack growth data for a polycrystalline alumina using the load relaxation procedure.
9. Figure 4.9 Plot of stress versus displacement rates for a double torsion specimen in which a crack is growing stably.
10. Figure 4.10 SENB specimen.
11. Figure 4.11 Schematic of CNBT specimen.
12. Figure 4.12 Acceptable (a and b) and (c) unacceptable force time traces.
13. Figure 4.13 So‐called “bridge indentation” device used to introduce a crack into an SEPB specimen.
14. Figure 4.14 Schematic of SCF specimen.
15. Figure 4.15 Typical work of fracture specimen.
16. Figure 4.16 DCDC specimen.
17. Figure 4.17 Crack pattern after indentation.
18. Figure 4.18 Fracture toughness calculated using the indentation‐strength method compared with that determined from more conventional fracture mechanics methods (Chantikul et al. 1981).
19. Figure 4.19 Strength‐indentation load plot for a glass ceramic showing a deviation from the P^⅓ slope expected from Eq. (4.30).
20. Figure 4.20 Schematic of edge chip with dimensions. P is the indent load, h is the distance from the edge, c₀ is the crack depth, and D is the crack width.
21. Figure 4.21 Schematic of the diametral compression test. The maximum tensile stress is at the center of the specimen. This specimen can be used to determine the effect of mixed‐mode loading. When the crack is perpendicular to the loading is pure mode I loading. This specimen is also called the Brazilian disk specimen.
Chapter 05
1. Figure 5.1 Schematic of three‐point flexure test. P is the load, L is the span length, w is width, and t is thickness.
2. Figure 5.2 Schematic of four‐point flexure test. Each arrow represents half the load, i.e. P/2.
3. Figure 5.3 Schematic of different types of loading possible in biaxial flexure. (a) Ball‐on‐ring, (b) ring‐on‐ring, (c) piston‐on‐ring, and (d) piston‐on‐three‐balls.
4. Figure 5.4 Schematic diagram of ring‐on‐ring loading.
5. Figure 5.5 Tensile test specimen shapes. Both rectangular and circular cross sections are shown.
6. Figure 5.6 Schematic of self‐aligning tensile grips.
7. Figure 5.7 Schematic of two‐point flexure apparatus.
8. Figure 5.8 Schematic of C‐ring specimen loaded in compression. Point A is the location of the maximum tensile stress.
9. Figure 5.9 Schematic of C‐ring loaded in tension. B is the location of the maximum tensile stress.
10. Figure 5.10 Schematic of O‐ring loaded in compression. C indicates the location of the maximum tensile stress.
11. Figure 5.11 Schematic of the loading on a tubular component.
12. Figure 5.12 Schematic of the diametral compression test. The maximum tensile stress is at the center of the specimen. This specimen can be used to determine the effect of mixed‐mode loading. When the crack is perpendicular to the loading, it is in pure mode I loading. This specimen is also called the Brazilian Disk Specimen.
13. Figure 5.13 Schematic of theta specimen. Pure tension is generated in the center cross member when the specimen is loaded in compression.
14. Figure 5.14 Microtensile configurations: (a) stick, (b) dumbbell, and (c) hourglass.
15. Figure 5.15 Comparison of load–displacement curves for the 400‐200‐800 laminates compared with monolithic HA.
16. Figure 5.16 SEM image of failure origin located in the middle HA layer. Arrows outline the reinitiated crack in the second HA layer.
17. Figure 5.17 Weibull graph of strength distributions from various loading configurations on SiC specimens.
18. Figure 5.18 Strength distributions for SiC C‐ring specimens loaded in tension and O‐ring specimens loaded in compression. Notice that all the failure origins of the specimens have been identified. This type of analysis helps to understand processing, machining, or other sources of failure and helps obviate these.
19. Figure 5.19 Positions of d₁, d₂, and d₃ boundaries for a normal distribution of strengths.
20. Figure 5.A.1 A schematic representation of a laminate indicating the variables required for calculations.
Chapter 06
1. Figure 6.1 Typical crack pattern produced by thermal stress failure.
2. Figure 6.2 Temperature and stresses in a plate after (a) cooling and (b) heating.
3. Figure 6.3 Evolution of dimensionless stress as a function of dimensionless time at selected locations for (a) β = ∞, (b) β = 10, and (c) β = 1 (Lu and Fleck 1998).
4. Figure 6.4 Crack length and strength as a function of thermal history.
5. Figure 6.5 Room temperature strength of alumina rods subjected to thermal shock by quenching into water.
6. Figure 6.6 Schematic of single‐ and multiple‐cycle thermal shock on retained strength.
7. Figure 6.7 Schematic of thermal stress test apparatus (Faber et al. 1981).
Chapter 07
1. Figure 7.1 Measured fracture energies plotted versus E · d₀ as suggested by Eq. (7.9).
2. Figure 7.2 Calculated fracture energies of single crystals as a function of only elastic constant.
3. Figure 7.3 Schematic of silica fragment used in the MO calculations. The hydrogen atoms are inserted for charge compensation.
4. Figure 7.4 Schematic of bond fracture in silica.
5. Figure 7.5 Experimental determination of a₀ using Eq. (7.10) versus the quantum mechanics calculation of a₀.
Chapter 08
1. Figure 8.1 Fracture surface of a silica glass fiber showing fracture origin, mirror, mist, and hackle regions. The origin is a crack at the surface created by the thermal expansion difference between the fiber and the foreign “dust” particle attached to it while the fiber was still hot during fabrication. The actual fracture origin is a crack on the glass surface at the dust particle.
2. Figure 8.2 Optical fiber fractured in bending. Arrow points to the origin. Notice that the pore or bubble is well away from the origin of failure even though it is much larger. In this particular case, the stress was not great enough in the region of the hole to cause a large enough stress concentration.
3. Figure 8.3 Scanning electron micrograph of the fracture surface of a glass rectangular bar broken in flexure. The white line is drawn just outside the critical crack that led to failure.
4. Figure 8.4 Schematic of fracture surface of material failed in a brittle manner. The critical crack (a_crit, b_crit) is indicated by the dashed line. The solid line (a_i, b_i) indicates the initial crack size. The radii, r_j, indicate the distance from the origin to the respective boundaries between the mirror–mist (j = 1), mist–hackle (j = 2), and macroscopic crack branching (j = 3 or cb). The prime indicates that the values on either side of the crack may be different.
5. Figure 8.5 Graph of the fracture stress for silica‐based glass as a function of the mirror–mist radius (r₁ in Eq. 8.4). The Maurer et al. (1974) data are fibers failed in tension. The ITT‐NRL and Hughes‐NRL data are also fractured in tension. The bulk silica data were rectangular flexure bars (Mecholsky et al. 1974).
6. Figure 8.6 (a) Scanning electron micrograph of a single crystal silicon fracture surface. The features are different from the schematic of Figure 8.2 due to the anisotropic elastic moduli. However, the relationships shown in Eqs. (8.3) and 8.4 are still valid. (b) SEM images of single crystal alumina. (i) Pure sapphire, room temperature; (ii) Cr‐doped sapphire, room temperature; (iii) pure sapphire, high temperature (1400 °C), with surface‐originating defect; and (iv) Cr‐doped sapphire, high temperature (1400 °C) with internal origin.
7. Figure 8.7 SEM image of a ZnSe fracture surface. This is a large‐grain material that failed at a relatively low stress. The features in the image are all in the “mirror” region. However, Eq. (8.3) is applicable. The critical crack is the larger arc shown by the outer (white) arrow. The black arrows show twist hackle (river marks) that fan out from the origin and show direction of local crack propagation. Cleavage steps are shown with the large black arrow.
8. Figure 8.8 (a) SEM image of sintered reaction‐bonded silicon nitride fractured with a crack (arrow) introduced by indenting with a 49 N Knoop diamond. (b) SEM image of a silicon nitride fracture surface showing internal origin (arrow). This fracture is from a turbine rotor fractured in a spin test. Notice the relatively smooth region around the origin that transitions to rougher regions.
9. Figure 8.9 A graph of Eq. (8.5) with r_m = r₁.
10. Figure 8.10 (a) Schematic of fracture surfaces with and without global residual stress. Both fractures occurred in flexure from the same‐size critical crack. The difference in shape is due to residual surface compression in the lower figure. Note that the distance of the mirror boundaries are the same on both surfaces, indicating that they both failed at the same stress level. However, the external loading was different. (b) Fracture origin in tempered glass. Notice mirror–mist boundary (arrows) that mimic the schematic of (a).
11. Figure 8.11 Time to failure as a function of the mirror‐to‐crack size ratio for soda‐lime‐silica glass. The value of ϕ = 1.57 is for a semicircular crack (Eq. 8.1) and of ϕ = 1.42 is for a/b = 0.8. The dot‐dash line is drawn parallel to the ordinate and has a value of r₁/c = 11.6 ± 1.2 for fast fracture.
12. Figure 8.12 SEM image of fracture surface of a soda‐lime‐silica glass after delayed failure. Notice that the mirror boundaries (black arrows in (a)) are over 20 times greater than the initial crack size (white arrow in (a)) [r₁/c ≅ 80]. Initial crack size from machining is shown in (b).
13. Figure 8.13 Schematic of fracture surface showing possible features on the surface to aid in determining origin and crack direction.
14. Figure 8.14 SEM image of a dental crown with zirconia core and a glass veneer. The secondary failure occurred at the interface between the glass and core. The critical crack is shown by the white arrows. The mirror and mist regions are shown but are more difficult to discern in polycrystalline materials.
15. Figure 8.15 SEM images of soda‐lime‐silica glass fractured in flexure from indentation cracks. (a′) and (b′) show greater magnifications of (a) and (b). In (b′), the arrows point to Wallner lines. In (a′) the arrow points to arrest lines at the edge of the critical crack.
16. Figure 8.16 SEM image of a Procera all‐ceramic crown fractured during service. Examples of wake hackle markings are shown by the joined black arrows. The arrow demarked by dcp shows the direction of crack propagation. This demonstrates how to use wake hackle markings to obtain local crack direction.
17. Figure 8.17 Branching angle versus biaxial stress ratios. The macroscopic branching angle is governed by the far‐field stress as indicated by σ_x/σ_y.
18. Figure 8.18 Probability of failure as a function of applied stress at failure for sialon. Fractography is used to identify each failure origin and location on the Weibull graph.
19. Figure 8.19 Representative fracture surfaces. Soda‐lime‐silica glass in (a) mode I failure and (b) mixed‐mode (I/II) failure. Mica glass ceramic in (c) pure mode I loading and (d) mixed‐mode (I/II) loading. For (c) and (d), the inner arrows indicate the critical crack size and the outer arrows indicate the mirror size.
20. Figure 8.20 AFM images at different regions (marked by letters) on the fracture surface of a soda‐lime‐silica glass failed in mixed (I/II) mode. (a) Mirror region. (b) Mirror region. (c) Near twist hackle region. (d) Twist hackle region showing lances. The white specks are debris. The arrows in (a)–(d) indicate the crack propagation direction.
21. Figure 8.21 Scanning electron micrographs of the mist and hackle regions of a glass fracture surface. The region in (b) is similar to the region in (c). However (c) is the same as (a), only magnified.
22. Figure 8.22 Atomic force microscope image of the mirror region of soda‐lime‐silica glass. Notice that it is not smooth as usually appears at greater magnification.
23. Figure 8.23 Schematic summarizing slit‐island analysis (SIA) technique. The Richardson equation (L_A–B = L₀R^–D* where R is the ruler length) is used to determine the fractal dimensional increment, D*. L₀ is a constant.
24. Figure 8.24 Fracture toughness versus the fractal dimensional increment, D*. The results group into classes of materials that behave in a similar manner such as single crystals, glass ceramics, and fine‐grain polycrystalline materials with few toughening mechanisms.
25. Figure 8.25 Mirror‐to‐crack size ratio as a function of 1/D*. Silicon (Si) is single crystalline. The rest of the materials are polycrystalline except for glass that is a silicate‐based glass. This graph shows the relationship between fractography and fractal geometry of the fracture surface.
Chapter 09
1. Figure 9.1 Fracture surface of large‐grained zinc selenide. The two white arrows indicate the edges of the critical crack boundaries. The black arrows indicate the direction of crack propagation indicated by the fracture steps fanning out from the origin.
2. Figure 9.2 Fracture strength of the ZnSe materials as a function of measured flaw sizes. Lines represent values of fracture energy for polycrystalline material (3.4 J m⁻²) and single‐crystal ZnSe (0.8 J m⁻²) used in Eq. (8.3).
3. Figure 9.3 Fracture toughness of ZnSe as a function of the flaw size‐to‐grain size ratio. There is a gradual transition to the polycrystalline value over several grains.
4. Figure 9.4 Transition in fracture energy for a number of materials as a function of flaw size/grain size.
5. Figure 9.5 Schematic showing the relationship between a flaw growing in a large grain under stress and the segments of the growing crack in the adjoining smaller grains.
6. Figure 9.6 Fracture energy as a function of grain size for cubic ceramics.
7. Figure 9.7 Fracture energy as a function of grain size for non‐cubic ceramics.
8. Figure 9.8 Toughening processes leading to a microcracked zone.
9. Figure 9.9 Examples of tractions across crack faces that can lead to toughening.
10. Figure 9.10 Silicon nitride indentation flexure showing R‐curve behavior.
Chapter 10
1. Figure 10.1 Dynamic fatigue data for a borosilicate glass (BK7) tested in water.
2. Figure 10.2 Factors influencing the accuracy of component strengths from laboratory data.

Copyright © 2019 by The American Ceramic Society. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada.

Edition History
John Wiley & Sons, Inc. (1e, 2012)

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Library of Congress Cataloging‐in‐Publication Data

Names: Freiman, S. W., author. | Mecholsky, John J., Jr., author.
Title: The fracture of brittle materials : testing and analysis / Stephen W. Freiman and John J. Mecholsky, Jr.
Description: Second edition. | Hoboken, New Jersey : John Wiley & Sons, Inc., [2018] | Includes bibliographical references and index. |
Identifiers: LCCN 2018036245 (print) | LCCN 2018036557 (ebook) | ISBN 9781118769669 (Adobe PDF) | ISBN 9781118769775 (ePub) | ISBN 9781118769706 (hardcover)
Subjects: LCSH: Fracture mechanics. | Brittleness.
Classification: LCC TA409 (ebook) | LCC TA409 .F765 2018 (print) | DDC 620.1/126–dc23
LC record available at https://lccn.loc.gov/2018036245

Cover design by Wiley
Cover image: Courtesy of Gina and Jason Blume

We want to thank Jason and Gina Blume for the picture of the natural fracture origin on the cover of this book.

Preface

The purpose of this book is to bring together the background, testing procedures, and analysis methods needed to design and use materials that fail in a brittle manner, primarily ceramics. In this context we define ceramics quite broadly as any inorganic nonmetal. Such a definition includes diverse materials such as semiconductors (e.g. Si, GaAs, InP), other single crystals (ZnSe, CaF, etc.), cements and concrete, and of course the oxides, carbides, nitrides, and others that we normally think of as ceramics. Ceramics are also used in composite form, either by dispersing one phase in another or by crystallizing phases from a glassy matrix. Most test procedures designed for monolithic bodies can be used here as well. However, continuous fiber‐reinforced composites behave quite differently and will not be discussed herein. Ceramics are also increasingly used in films and coatings, but determining the mechanical properties of materials in these forms is more complex and will not be addressed in this book.

This book addresses testing and analysis at temperatures for which the material behaves in a brittle manner. At elevated temperatures other modes of failure often are important. These include creep as well as general plastic deformation. Both of these topics are outside the scope of this book.

In this book we provide the reader some of the background needed to understand the brittle fracture process as well as a basis for choosing the proper test procedures. The mathematical development of the expressions used to calculate the various properties will be kept to a minimum; the reader will be referred to fundamental references. We intend to provide examples to allow the reader unfamiliar with the tests to be able to perform the test procedures properly. However, the reader is strongly encouraged to consult formal national and international standards for more extensive test procedures. Questions to test comprehension for self‐evaluation are given at the conclusion of each chapter.

Chapter 1 is a general introduction to the concept of brittle failure. Chapter 2 provides a condensed background into the basic principles of fracture mechanics that underlies most of the test and analysis procedures. Linear elastic fracture mechanics (LEFM) is the basis for measuring the fracture toughness of materials. Chapter 3 gives some background into the theory and mechanisms of environmentally enhanced crack growth, a process that is particularly important for designing components that are intended to survive over long periods of time under stress. Chapter 4 provides extensive details on fracture mechanics tests used to determine both a material’s resistance to fast fracture and the parameters associated with environmentally enhanced crack growth. Chapter 5 addresses the test and analysis methods to determine the strength of ceramics. New in this chapter is a section describing test procedures applicable to biomaterials. Also new is a new procedure for determining the probability of failure within a set of ceramic components based on modern statistical concepts. Chapter 6 is a new addition that provides information on the causes of thermal shock failure, a common occurrence in ceramics. Also included are some of the test procedures that are used to rank the thermal shock resistance of such materials. Chapter 7 is also new; it describes attempts to model the fracture process and to provide predictions of resistance to crack growth. Chapter 8 provides a background and discusses the methods of understanding the fracture process based on quantitative measurements made on the fracture surface. Chapter 9 discusses an important topic with respect to polycrystalline materials, namely, the effect of the microstructure of the specific material. Chapter 10 provides the background, test methods, and analytical procedures needed to confidently predict the safe lifetimes of brittle components under stress. Finally, Chapter 11 summarizes the critical issues with respect to brittle fracture.

STEPHEN W. FREIMAN
JOHN J. MECHOLSKY, JR.

CHAPTER 1
Introduction

The properties of ceramics have made them extremely attractive to society in uses such as electrical and thermal insulators, high temperature crucibles for steel fabrication, elegant dinnerware, etc. More recently, their applications have become even more extensive and sophisticated, ranging from complex electronic devices such as multilayer capacitors and ultrasonic transducers to thermal protection for aircraft engines and applications in the dental and medical fields. However, the brittleness of ceramics, making them subject to sudden failure without prior warning, has at times limited more extensive use. Everyone knows that traditional ceramics, such as dishes and glasses, are brittle: drop a teacup or a plate, break a window, and you experience the brittleness. By brittle we mean that there are no mechanisms to relieve or alter the high stresses at crack tips, such as dislocations in metals or crazing in polymers. The lack of any stress relief mechanism results in cracks growing to failure at stresses that are significantly less than those necessary to initiate and propagate cracks in metals.

Despite their brittleness, advanced technical ceramics form the basis for a wide variety of important products. They are used in applications in which they experience significant stresses imposed by not only mechanical loading but also thermal, magnetic, or electronic conditions. One sees ceramics everywhere: the large electrical insulators on poles, spark plugs, and skyscraper windows that must resist high winds. Some we do not see or are not aware of. Cell phones would not operate without ceramics having special dielectric properties; automobiles contain hundreds of multilayer ceramic capacitors. Aircraft engines depend on ceramic coatings to reduce the temperature of the metal blades. Turbine engines for auxiliary power generation are now being constructed with rotating ceramic blades.

Another use of ceramics that requires complete reliability is aluminum or zirconium oxide hip and knee replacements in the human body. Dental ceramic prosthetic composites are routinely implanted in many patients. The hardness, inertness, and wear resistance of these materials make them ideal candidates to replace metals in such situations. Particularly when the patient is young, the lesser amount of wear debris produced by the ceramic means that the component can be used in the body for a significantly longer time than one made of metal.

The list of ceramic applications is extensive, including materials that we do not normally think of as ceramics, e.g. semiconducting materials, such as silicon, gallium arsenide, etc., and oxide films crucial for the operation of electronic devices. Because of the brittleness of these materials and their similarity in mechanical behavior to conventional ceramics, we refer to each of these materials as ceramics. Figure 1.1 shows some prime examples of advanced technical ceramics.

Image described by caption. — **Figure 1.1** Examples of advanced technical ceramics. From the left to right are an example of a ceramic hip replacement, barium titanate capacitors, various silicon nitride components, and a silicon nitride turbine wheel.

In each of these examples and in the myriad other applications, the brittleness of ceramics necessitates that special care must be taken in determining the mechanical properties of the material and discovering the stresses imposed on the final product during operation. The fact is that unseen, and probably undetectable, defects can lead to catastrophic failure. We will call these defects flaws. By a flaw we do not necessarily mean that errors were made in production. While improper processing can lead to pores or inclusions, component failures caused by these are relatively rare. For the vast majority of the time, brittle failure begins at the surface of a component from small cracks that are produced during the machining, finishing, or handling processes. All ceramics contain such flaws; there is no perfect brittle material. Even the strongest ceramic, pristine glass fibers, contains small flaws in its surface despite the care taken to avoid any surface damage. It is the size and shape of such flaws, i.e. the flaw severity, and their location with respect to the tensile stresses that determine the strength of a component.

Brittle fracture is a statistical process. We usually think of such failure in terms of a “weakest link” model. That is, failure begins from the most severe flaw located in the region of highest tensile stress. Also, the size of flaws in real components, 10–200 μm, means that detection of such defects by some nondestructive means prior to putting the part into service is extremely unlikely.

Another important aspect of most ceramic materials is that even if their strength when placed into service is sufficiently high that failure should not occur, in the presence of certain environments, e.g. water or water vapor, surface cracks will grow under the operational stresses, and failure can occur after a period of days, weeks, or even months. Fortunately, we have sufficient knowledge of this behavior, so that with proper testing and analysis, excellent predictions of the safe operating envelope, stress, and time can be given. Nonetheless, the user of ceramic components should recognize that such analysis only pertains to flaws that existed prior to putting the component in service. Other defects can be created during operation, e.g. from dust or rain, which may limit useful service life.

Knowledge of the brittle fracture process, most of which has been acquired over the past 30–40 years, has played a major part in our ability to design and use these materials, even in situations where the component is subject to significant tensile stresses. Two developments, which at the time were outside the field of materials science, were of major importance in contributing to our ability to safely use these materials. One was the development of the field of linear elastic fracture mechanics. Fracture mechanics provides the framework by which the effect of the stresses imposed on a body can be translated into predictions of the propensity of any cracks or flaws within the body to grow. This has led to the development of test methods and data analysis that permit designers to choose a material, machine it to shape without producing damage that could lead to premature failures, and carry out quality control procedures that provide confidence in the reliability of the part under operating conditions. A second important advancement, allowing us to design with brittle materials, was the development of statistical techniques that account for the uncertainties in the experimental measurements of the various parameters needed to make predictions of reliability.

A third factor that has greatly benefited the use of brittle ceramics in a wide variety of applications is the agreed‐upon use of a common test methodology through national, regional, and international standards. Most of these standards have been developed by consensus by private standards development organizations such as ASTM International and the International Organization for Standardization (ISO). The details of the standards coming out of the deliberation process are based on years of data obtained in laboratories throughout the world.

In this second edition of the book, we summarize the concepts behind the selection of a test procedure for fracture toughness and strength determination and go into some detail in how the statistics of fracture can be used to assure reliability. We explain the importance of the role of microstructure in these determinations and emphasize the use of fractographic analysis as an important tool in understanding why a part failed. We have included a significant quantity of material related to the fracture of biomaterials. We have also included new chapters, one devoted to thermal shock and the other to the modeling of the fracture process. In addition, the portion of the book discussing how to treat the statistics of fracture strength data to ensure reliability has been greatly expanded.

The Fracture of Brittle Materials

Preface

Acknowledgements

CHAPTER 1
Introduction