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DTD Handbook

Handbook for Damage Tolerant Design

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    • Sections
      • 1. Introduction
      • 2. Fundamentals of Damage Tolerance
      • 3. Damage Size Characterizations
      • 4. Residual Strength
      • 5. Analysis Of Damage Growth
      • 6. Examples of Damage Tolerant Analyses
      • 7. Damage Tolerance Testing
      • 8. Force Management and Sustainment Engineering
      • 9. Structural Repairs
      • 10. Guidelines for Damage Tolerance Design and Fracture Control Planning
      • 11. Summary of Stress Intensity Factor Information
        • 0. Summary of Stress Intensity Factor Information
        • 1. Background of Stress Intensity Factors
        • 2. Methodology For Determining Stress Intensity Factors
          • 0. Methodology For Determining Stress Intensity Factors
          • 1. Principle of Superposition
          • 3. Finite Element Methods
        • 3. Selected Stress Intensity Factor Cases
        • 5. Computer Codes
        • 6. References
    • Examples

Section 11.2.0. Methodology For Determining Stress Intensity Factors

The linear elastic fracture mechanics approach to the analysis of cracked structures depends on the calculation of stress-intensity factors (K) for the typical crack geometries of interest. 

The opening mode stress-intensity factor can always be expressed as

(11.2.1)

where s is the nominal stress remote from the crack and a is the crack size.  The factor b is a function of crack geometry and of structural geometry.  Since the dimension of K is ksiÖin. or equivalent, b must be dimensionless.  For a central crack of length, 2a, in an infinite sheet, the stress-intensity factor may be written

(11.2.2)

Comparison with Equation 11.2.1 shows that for an infinite sheet b is unity.  Thus, b may be considered as a correction factor relating the actual stress-intensity factor to the central crack in an infinite sheet.  The correction factors for various geometrical conditions under a given load condition may be combined in the form of a product to account for the increase or decrease in the stress-intensity factor.

As the linear elastic fracture mechanics approach to engineering problems became a typical design approach, a widespread need for stress-intensity factor solutions for typical geometries arose.  This need was met by a series of handbooks which presented available solutions in a compact format.  Some of these handbooks include

·        Handbook of Stress Intensity Factor (Sih, 1973),

·        The Stress Analysis of Cracks Handbook (Tada, et al., 1973),

·        Compendium of Stress Intensity Factors (Rooke & Cartwright, 1976),

·        Stress Intensity Factors Handbook (Murakami, 1987)

The handbook solutions, which are typically fundamental, may be extended to more complex cases through the principle of superposition or by compound analysis.  The handbook solutions are also quite useful for bounding exact solutions as discussed in Section 11.4.  When the structural geometry and loading system is fairly complicated, engineers normally resort to numerical analysis procedures (e.g., finite element analysis) which have been proven for their accuracy in establishing stress-intensity factors.