Principles of Fracture Mechanics

Prentice Hall
R. J. Sanford  
Total pages
March 2002
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Principles of Fracture Mechanics
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For a first course in the Mechanics of Fracture at the graduate level (or senior undergraduates with a background in engineering mechanics).

The attention of Principles of Fracture Mechanics is on the mathematical principles of linear elastic fracture mechanics and their application to engineering design. The book is a self-contained manual on the mechanics aspects of the theory of brittle fracture and fatigue and is suitable for either self-study or classroom instruction. It includes a guided introduction to the linear theory of elasticity with pivotal results for the circular hole, the elliptical hole and the wedge leading up to the general problem of bodies containing cracks.


  • Extensive original material-Including the mathematical formulation of the stress field around crack tips, the numerical analysis of bodies with finite dimensions and the use of experimental methods to determine the stress intensity factor-based on the author's nearly forty years experience in the field.
  • Typical chapters include problems which extend the mathematical developments presented in the text, applications problems requiring numerical and/or graphic responses, and essay/literature study questions-Additionally, more comprehensive exercises requiring integration of the knowledge throughout the text are included as an appendix.
  • Extensive tables-Listing (a) strength and fracture properties and (b) fatigue data for a wide variety of metallic materials adapted from the NASA/NASGRO database.
  • A unified mathematical treatment throughout-Based on the generalized Westergaard formulation of the elastic problem of stresses in bodies containing cracks.

Table of Contents

Most chapters include an Introduction, Summary, References and Exercises.

 1. Introduction to Fracture Mechanics.

Historical Overview of Brittle Fracture. Elementary Brittle-Fracture Theories. Crack Extension Behavior.

 2. Elements of Solid Mechanics.

Concepts of Stress and Strain. Equations of Elasticity in Cartesian Coordinates. Equations of Elasticity in Polar Coordinates. Solution of the Biharmonic Equation. The Problem of the Elliptical Hole.

 3. Elasticity of Singular Stress Fields.

Overview. The Williams Problems. The Generalized Westergaard Approach. The Central Crack Problem. Single-Ended Crack Problems. The Effect of Finite Boundaries. Determining the Geometric Stress Intensity Factor. The Three-Dimensional Crack Problem.

 4. Numerical Methods for K Determination.

Boundary Collocation. The Finite Element Method.

 5. Experimental Methods for K Determination.

Overview. Classical Photoelesatic Methods. The Method of Caustics. Strain Gages. Multi-Parameter Full-Field Methods: Local Collocation. Interference Patterns. Moire Patterns. Photoelasticity.

 6. A Stress Field Theory of Fracture.

The Critical Stress-State Criterion. Crack-Tip Plasticity. The Effect of Variables on Fracture Toughness. R-Curves.

 7. The Energy of Fracture.

Griffith's Theory of Brittle Fracture. A Unified Theory of Fracture. Compliance.

 8. Fracture Toughness Testing.

Fracture Toughness Standards. Nonstandard Fracture-Toughness Tests.

 9. Fatigue.

Stages of Fatigue Crack Growth. Mathematical Analysis of Stage II Crack Growth. The Effects of Residual Stress on Crack Growth Rates. Life Prediction Computer Programs. Measuring Fatigue Properties: ASTM.

10. Designing against Fracture.

Fracture Mechanics in Conventional Design. The Role of NDE in Design. U.S. Air Force Damage-tolerant Design Methodology. Designing by Hindsight: Case Studies.

11. Elastoplastic Fracture.

Nonlinear Elastic Behavior. Characterizing Elastoplastic Behavior. Comments on the J-Integral in Elastoplastic Fracture Mechanics.

Appendix A: Comprehensive Exercises.

General Comments.

Appendix B: Complex Variable Method in Elasticity.

Complex Numbers. Complex Functions.

Appendix C: An Abbreviated Compendium of Westergaard Stress Functions.

Appendix D: Fracture Properties of Engineering Materials.

Appendix E: NASGRO 3.0 Material Constants for Selected Materials.


Back Cover

Intended for a first course in the mechanics of fracture at the graduate level (or senior undergraduates with a background in engineering mechanics) the focus of the book is on the mathematical principles of linear elastic fracture mechanics and their application to engineering design. The material is presented in a conversational, yet rigorous, manner with the focus on the general formulation of the theory. In this way the origins and limitations of the simplified results presented in other introductory texts is apparent. The selection of topics and order of presentation in the book evolved from a graduate course in fracture mechanics developed by the author over the last two decades.

Key Features of the Book
  • Unified mathematical treatment based on the generalized Westergaard formulation provides a coherent basis for the analytical, numerical, and experimental treatment of crack problems in two dimensions.
  • Introductory chapter on the linear theory of elasticity with pivotal results for the circular hole, elliptical hole, and the wedge leading up to the general problem of bodies with cracks.
  • Thorough treatment of fatigue crack growth behavior including both analytical methods and introductions to the NASGRO 3.0 and AFGROW 4.0 computer programs for lifetime prediction analysis using complex empirical fatigue crack growth models.
  • Extensive tables of fracture properties for a wide variety of metallic materials in both English and S.I. units derived from the NASA database.
  • Broad spectrum of exercises at the end of each chapter ranging from basic analytic derivations to parametric numerical analysis. Also included is a selection of comprehensive open-ended design problems suitable for capstone project assignments or take-home examinations.


Professor Emeritus R.J. Sanford has had two careers involving fracture mechanics. He spent 22 years at the Naval Research Laboratory as a research engineer during a period of intense fracture mechanics discovery at NRL under the direction of George R. Irwin. He left NRL in 1982 to join the faculty at the University of Maryland. At the College Park campus his focus has been on graduate education in solid mechanics and fracture. He is a Fellow in the Society for Experimental Mechanics and has received both their Hetenyi Award (for research) and the Frocht Award (for teaching excellence) and is a member of Committee E08 of the American Society for Materials and Testing (ASTM).

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