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Spie Press Book

Strength Properties of Glass and Ceramics
Author(s): John W. Pepi
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Book Description

This text is intended for structural, mechanical, and optical engineers who wish to obtain an understanding of the principles of strength determination for optical components. Those who work with ground-, air-, or space-based systems, as well as with ceramics, semiconductors, and the like, will gain an understanding of fracture mechanics applications. This text expands basic fracture mechanics theory to include residual stress, which is rarely reported on in the literature and can have dramatic effects on lifetime. While complex equations are presented and a basic understanding of engineering principles is necessary, complex knowledge of fracture mechanics and energy principles is not required.

Book Details

Date Published: 30 May 2014
Pages: 186
ISBN: 9780819498366
Volume: PM244

Table of Contents
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Table of Contents

Text Objectives
A Note on Units

1 Crack Basics
1.1 Theoretical Strength
1.2 Crack Terminology
1.3 Failure Modes
1.4 Mode I Failure Description
1.5 Flaw Detection
1.6 Residual Stress
1.7 Learning Outcome

2 Strength Formulations
2.1 Flaws Free of Residual Stress
2.2 Strength Theory
2.3 Stress Intensity
2.4 General Strength Equation
      2.4.1 Finite bodies and free-surface correction
      2.4.2 General point flaws
      2.4.3 The basic fracture mechanics equation
2.5 Example for Consideration
2.6 Learning Outcomes

3 Strength with Residual Stress
3.1 Residual Stress in Point and Line Flaws
3.2 Combined Residual and External Stress
3.3 Crack Stability
3.4 Strength with Residual and Applied Stress
3.5 Measured Strength
3.6 Example for Consideration
3.7 Learning Outcome

4 Stress Corrosion
4.1 Continued Strength Reduction
4.2 Definitions
4.3 A Chemically Active Environment
4.4 Reaction Rates
      4.4.1 I love Paris
4.5 Crack Growth Regions
      4.5.1 Region I relation
4.6 Example for Consideration
4.7 Learning Outcome

5 Residual-Stress-Free Slow Crack Growth
5.1 The Basics
5.2 Residual-Stress-Free Simplification
5.3 The Need for Constants
5.4 Examples for Consideration
5.5 Learning Outcome

6 Slow Crack Growth with Residual Stress
6.1 The Basics Revisited
6.2 A Complex Integration
6.3 Computation of Constants and Resulting Time to Failure
6.4 Examples for Consideration
6.5 Obtaining Constants and Failure Time
6.6 Residual-Stress-Free Conversion
6.7 Learning Outcome

7 Dynamic Fatigue
7.1 Finding Constants
7.2 Enter Dynamic Fatigue
7.3 Stressing Rates
7.4 Example for Consideration
7.5 A Pleasing Result
7.6 Learning Outcome

8 Stress–Time Approximation
8.1 Lack of Data
8.2 Stress–Time Approximation
8.3 Application to Other Materials
8.4 Learning Outcome

9 Intermission
9.1 A Breather
9.2 In a Nutshell

10 Weibull Analysis
10.1 Walloddi Weibull
10.2 Complex and Simplified Formulation
10.3 Reliability and Confidence
10.4 Two- or Three-Parameter Weibull Analysis
10.5 Area Scaling
10.6 Example for Consideration
10.7 Learning Outcome

11 Inert Strength Determination
11.1 Strength Measurement
11.2 Four-Point Bend Equations
11.3 Ring-on-Ring Test
11.4 Sample Dimensional Requirement
11.5 Inert Strength of Scratched or Abraded Surfaces
11.6 Learning Outcome

12 Applied Stress Determination
12.1 Determination of Externally Applied Stress
12.2 Case Examples
      12.2.1 A circular plate under a uniformly distributed load
      12.2.2 A circular plate under a uniformly distributed load: three-point edge support
      12.2.3 A circular plate under a uniformly distributed load: three-point internal support
12.3 Thermal Stress
12.4 Learning Outcome

13 Overload Proof Test
13.1 Proof Test Philosophy
13.2 Application to Ceramics
13.3 Examples for Consideration
13.4 Limited Lifetime Warranty
13.5 Safety Factor Caution
13.6 Subsequent Damage
13.7 Example for Consideration
13.8 Learning Outcome

14 Moist Environments
14.1 Moist-Air Effects
14.2 Moist Strength Reduction
14.3 It's All Relative
14.4 Learning Outcomes

15 Crack Propagation
15.1 How Slow Can You Go?
15.2 Residual Stress Growth and Applied Stress
15.3 Growth Computation and Quantification
15.4 Crack Extension
15.5 Learning Outcome

16 Controlled Grind
16.1 Strength Revisited
16.2 Flaw Source
16.3 Importance of the Grinding Process
16.4 Learning Outcome

17 A Case Study
17.1 Lessons Learned
17.2 Lifetime Requirement
17.3 Lifetime Analysis
17.4 Enter Residual Stress
17.5 Polished and Abraded Strength
17.6 Confidence Limits
17.7 Cyclic Fatigue
17.8 Failsafe Design
17.9 Fragmentation
17.10 Learning Outcome

18 Putting It All Together Again
18.1 Final Example for Consideration

19 In Conclusion
19.1 In Brief
19.2 Final Comment



Poor glass. It has such a bad reputation. Glass is brittle. Glass breaks. Glass shatters.

Many codes use an allowable stress of only 7 MPa (~1000 psi) for glass. NASA codes in the 1970s used 5 MPa (~700 psi). Back in the 1960s, an allowable stress of 3.5 MPa (~500 psi) was used, so at least we can say some progress has been made.

On the other hand, strength of glass fibers has been reported in excess of 7,000 MPa (~1,000,000 psi). Indeed, the theoretical strength, based on strong covalent molecular bonding, lies in excess of 14,000 MPa (~2,000,000 psi). This is true for other amorphous or crystal ceramics as well, such as silicon.

Thus, there appears an apparent disconnect. The enigma is solved, however, when it is realized that a large reduction in strength occurs due to the nature of surface flaws generated during manufacturing and handling processes. This reduction is a function of the initial flaw depth; strength increase is attainable by reduction in flaw size by improving surface finish or otherwise removing such flaws, if practical.

When environmental species are added to the strength-reducing effects of flaws, strength is further reduced with time when subject to externally applied stress, in a process called stress corrosion, or slow crack growth.

As if this were not bad enough, when residual stress, present in most flaws, is added to the mix, strength with time and environment is further reduced. Back in the 1980s, I was involved with a program in which glass failures were being observed to occur several orders of magnitude earlier in time than the usual residual-stress-free theories were predicting. Concurrently, ingenious work at the National Institute of Standards and Technology (NIST) was showing such theoretical time–strength reduction in the presence of such internal residual stress concentrations. The theory had been born and its results realized.

The nature of this strength reduction applies not only to glass but indeed to most ceramics that are brittle in nature; ceramics find their way in many uses for optical lenses in critical visible and infrared applications, in ground, air, and space applications, as well as in the microprocessor and medical industries. Strengths may vary, higher or lower, but the theory is the same. While many ceramics are not amorphous and exhibit grain structure, they nonetheless exhibit similar flaw growth phenomena, with water a prime source for strength degradation, even if "flaws" in such ceramics are limited by their inherent molecular grain structure.

In the chapters to follow, the reader will be guided though the strength-reduction processes. Indeed, if stress levels are kept to below the low allowable level earlier noted, there may be little need for this tutorial, although knowledge is an end in itself. But with weight and envelope being ever more critical, often, stress levels must increase to maximize performance. It is in this case where this book will hopefully be beneficial.

"Forsan et haec olim meminisse iuvabit."*

*From Virgil's The Aeneid.

John W. Pepi
May 2014

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