Chapter 1
Introductory Information


Fracture studies of structural elements have been revolutionized in the last 50 years by the analysis of their sensitivity to flaws or cracklike defects. Within these studies an essential ingredient is reasonable and proper stress analysis especially with regard to flaws with high local elevations of stresses from which fractures progress through various crack propagation mechanisms, including corrosion and fatigue cracking.

Full studies of fracture behavior cover both the stress analysis aspects and the material behavior in terms of resistance to the stresses imposed. However, the purpose here is limited to the development of significant stress analysis details and relevant parameters, and to the compilation of available stress analysis results with cracks present insofar as they may be foreseeably related to actual fracture studies.

The redistribution of stress in a body caused by introducing a crack or notch may be solved by methods of linear-elastic stress analysis. Of course the greatest attention should be paid to the high elevation of stresses at or surrounding the crack-tip, which will usually be accompanied by at least some plasticity and other nonlinear effects. Nevertheless linear-elastic stress analysis properly forms the basis of most current fracture analysis, at least for “small scale yielding” where all substantial nonlinearity is confined within a linear-elastic field surrounding the crack-tip. Consequently, the character and significant parameters of linear-elastic crack-tip fields are examined first.

  • Introduction
  • Crack-Tip Stress Fields for Linear-Elastic Bodies
  • Alternate Expressions for Crack-Tip Elastic Fields
  • Slender Notches and Stress Concentrations from Stress Intensity Factors
  • Energy Rate Analysis of Crack Extension
  • Relationships between G and K
  • Superposition of G and K Results
  • Meaning of Plane Stress and Plane Strain for Fracture Mechanics Purposes
  • Effects of Small Scale Yielding on Linear-Elastic Fracture Mechanics
  • Introduction to Stress Function Methods
  • Additivity of Crack Stress Fields and K Values
  • Boundary Collocation Method
  • Successive Boundary Stress Correction Method
  • K Estimates from Finite Element Methods
  • Additional Remarks for Part I
  • A. Unified Formulation for In-Plane Two-Dimensional Problems
  • B. On Completeness of Westergaard Single-Function Method for Analysis of Cracks
  • C. Effect of Surface Interference of Partly Closed Cracks

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