### Spie Press Book

Strength Properties of Glass and CeramicsFormat | Member Price | Non-Member Price |
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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.

Pages: 186

ISBN: 9780819498366

Volume: PM244

### Table of Contents

*Introduction**Acknowledgments**Text Objectives**A Note on Units**Nomenclature***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
- References
**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
- References
**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
- References
**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
- References
**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
- References
**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
- References
**8 Stress–Time Approximation**- 8.1 Lack of Data
- 8.2 Stress–Time Approximation
- 8.3 Application to Other Materials
- 8.4 Learning Outcome
- References
**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
- References
**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
- References
**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
- References
**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
- References
**14 Moist Environments**- 14.1 Moist-Air Effects
- 14.2 Moist Strength Reduction
- 14.3 It's All Relative
- 14.4 Learning Outcomes
- References
**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
- References
**16 Controlled Grind**- 16.1 Strength Revisited
- 16.2 Flaw Source
- 16.3 Importance of the Grinding Process
- 16.4 Learning Outcome
- References
**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
- References
**18 Putting It All Together Again**- 18.1 Final Example for Consideration
**19 In Conclusion**- 19.1 In Brief
- 19.2 Final Comment
*Index*

## Preface

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.
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*
John W. Pepi
May 2014
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