The Practical Use of Fracture Mechanics

This book is about the use of fracture mechanics for the solution of practical problems; academic rigor is not at issue and dealt with only in as far as it improves insight and understanding; it often concerns secondary errors in engineering. Knowledge of (ignorance of) such basic input as loads and stresses in practical cases may cause errors far overshadowing those introduced by shortcomings of fracture mechanics and necessary approximations; this is amply demonstrated in the text. I have presented more than three dozen 40-hour courses on fracture mechanics and damage tolerance analysis, so that I have probably more experience in teaching the subject than anyone else. I learned more than the students, and became cognizant of difficulties and of the real concerns in applications. In particular I found, how a subject should be explained to appeal to the practicing engineer to demonstrate that his practical problem can indeed be solved with engineering methods. This experience is reflected in the presenta­ tions in this book. Sufficient background is provided for an understanding of the issues, but pragamatism prevails. Mathematics cannot be avoided, but they are presented in a way that appeals to insight and intuition, in lieu of formal derivations which would show but the mathematical skill of the writer.

1. Introduction.- 1.1. Fracture control.- 1.2. The two objectives of damage tolerance analysis.- 1.3. Crack growth and fracture.- 1.4. Damage tolerance and fracture mechanics.- 1.5. The need for analysis: purpose of this book.- 1.6. Exercises.- 2. Effects of Cracks and Notches: Collapse.- 2.1. Scope.- 2.2. An interrupted load path.- 2.3. Stress concentration factor.- 2.4. State of stress at a stress concentration.- 2.5. Yielding at a notch.- 2.6. Plastic collapse at a notch.- 2.7. Fracture at notches: brittle behavior.- 2.8. Measurement of collapse strength.- 2.9. Exercises.- 3. Linear Elastic Fracture Mechanics.- 3.1. Scope.- 3.2. Stress at a crack tip.- 3.3. General form of the stress intensity factor.- 3.4. Toughness.- 3.5. Plastic zone and stresses in plane stress and plane strain.- 3.6. Thickness dependence of toughness.- 3.7. Measurement of toughness.- 3.8. Competition with plastic collapse.- 3.9. The energy criterion.- 3.10. The energy release rate.- 3.11. The meaning of the energy criterion.- 3.12. The rise in fracture resistance: redefinition of toughness.- 3.13. Exercises.- 4. Elastic-Plastic Fracture Mechanics.- 4.1. Scope.- 4.2. The energy criterion for plastic fracture.- 4.3. The fracture criterion.- 4.4. The rising fracture energy.- 4.5. The residual strength diagram in EPFM: collapse.- 4.6. The measurement of the toughness in EPFM.- 4.7. The parameters of the stress-strain curve.- 4.8. The h-functions.- 4.9. Accuracy.- 4.10. Historical development of J.- 4.11. Limitations of EPFM.- 4.12. CTOD measurements.- 4.13. Exercises.- 5. Crack Growth Analysis Concepts.- 5.1. Scope.- 5.2. The concept underlying fatigue crack growth.- 5.3. Measurement of the rate function.- 5.4. Rate equations.- 5.5. Constant amplitude crack growth in a structure.- 5.6. Load interaction: Retardation.- 5.7. Retardation models.- 5.8. Crack growth analysis for variable amplitude loading.- 5.9. Parameters affecting fatigue crack growth rates.- 5.10. Stress corrosion cracking.- 5.11. Exercises.- 6. Load Spectra and Stress Histories.- 6.1. Scope.- 6.2. Types of stress histories.- 6.3. Obtaining load spectra.- 6.4. Exceedance diagram.- 6.5. Stress history generation.- 6.6. Clipping.- 6.7. Truncation.- 6.8. Manipulation of stress history.- 6.9. Environmental effects.- 6.10. Standard spectra.- 6.11. Exercises.- 7. Data Interpretation and Use.- 7.1. Scope.- 7.2. Plane strain fracture toughness.- 7.3. Plane stress and transitional toughness, R-curve.- 7.4. Toughness in terms of J and JR.- 7.5. Estimates of toughness.- 7.6. General remarks on fatigue rate data.- 7.7. Fitting the da/dN data.- 7.8. Dealing with scatter in rate data.- 7.9. Accounting for the environmental effect.- 7.10. Obtaining retardation parameters.- 7.11. Exercises.- 8. Geometry Factors.- 8.1. Scope.- 8.2. The reference stress.- 8.3. Compounding.- 8.4. Superposition.- 8.5. A simple method for asymmetric loading cases.- 8.6. Some easy guesses.- 8.7. Simple solutions for holes and stress concentrations.- 8.8. Simple solutions for irregular stress distributions.- 8.9. Finite element analysis.- 8.10. Simple solutions for crack arresters and multiple elements.- 8.11. Geometry factors for elastic-plastic fracture mechanics.- 8.12. Exercises.- 9. Special Subjects.- 9.1. Scope.- 9.2. Behavior of surface flaws and corner cracks.- 9.3. Break through: leak-before-break.- 9.4. Fracture arrest.- 9.5. Multiple elements, multiple cracks, changing geometry.- 9.6. Stop holes, cold worked holes and interference fasteners.- 9.7. Residual stresses in general.- 9.8. Other loading modes: mixed mode loading.- 9.9. Composites.- 9.10. Exercises.- 10. Analysis Procedures.- 10.1. Scope.- 10.2. Ingredients and critical locations.- 10.3. Critical locations and flaw assumptions.- 10.4. LEFM versus EPFM.- 10.5. Residual strength analysis.- 10.6. Use of R-curve and JR-curve.- 10.7. Crack growth analysis.- 10.8. Exercises.- 11. Fracture Control.- 11.1. Scope.- 11.2. Fracture control options.- 11.3. The probability of missing the crack.- 11.4. The physics and statistics of crack detection.- 11.5. Determining the inspection interval.- 11.6. Fracture control plans.- 11.7. Repairs.- 11.8. Statistical aspects.- 11.9. The cost of fracture and fracture control.- 11.10. Exercises.- 12. Damage Tolerance Substantiation.- 12.1. Scope.- 12.2. Objectives.- 12.3. Analysis and damage tolerance substantiation.- 12.4. Options to improve damage tolerance.- 12.5. Aircraft damage tolerance requirements.- 12.6. Other requirements.- 12.7. Flaw assumptions.- 12.8. Sources of error and safety factors.- 12.9. Misconceptions.- 12.10. Outlook.- 12.11. Exercises.- 13. After the Fact: Fracture Mechanics and Failure Analysis.- 13.1. Scope.- 13.2. The cause of service fractures.- 13.3. Fractography.- 13.4. Features of use in fracture mechanics analysis.- 13.5. Use of fracture mechanics.- 13.6. Possible actions based on failure analysis.- 13.7. Exercises.- 14. Applications.- 14.1. Scope.- 14.2. Storage tank (fictitious example).- 14.3. Fracture arrest in ships.- 14.4. Piping in chemical plant (fictitious example).- 14.5. Fatigue cracks in railroad rails.- 14.6. Underwater pipeline.- 14.7. Closure.- 15. Solutions To Exercises.