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DTD Handbook

Handbook for Damage Tolerant Design

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    • About
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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
        • 0. Structural Repairs
        • 1. Required Analysis
        • 3. Spectrum Analysis for Repair
          • 0. Spectrum Analysis for Repair
          • 1. Definition of Stress Histories
          • 2. Spectra Descriptions
          • 3. Crack Growth Analysis
            • 0. Crack Growth Analysis
            • 1. Generation of Crack Growth Curves
            • 2. Analysis of Observed Behavior
            • 3. Interpertation and Use of Crack Growth Rate Curves
            • 4. Analysis for Multiple Stress Histories
        • 4. Life Sensitivity for Stress Effects
        • 5. Life Sensitivity Analysis for Hole Repair
        • 6. Blend-Out Repairs
        • 7. Residual Strength Parametric Analysis
        • 8. References
      • 10. Guidelines for Damage Tolerance Design and Fracture Control Planning
      • 11. Summary of Stress Intensity Factor Information
    • Examples

Section 9.3.3.0. Crack Growth Analysis

The simplest manner for differentiating a curve is by using the secant method, i.e.

(9.3.5)

where (a1, F1) and (a2, F2) represent two different points on the crack growth life, crack length (a) versus flights (F) curve.  The derivative is considered to be the slope of the curve at the mean crack length of the two points, ie.

(9.3.6)

The mean crack length provides the ability to calculate the stress-intensity factor coefficient (K/s) for the geometry associated with the crack growth life curve.  To describe the crack growth rate as a function of stress-intensity factor, it is necessary to have either a formula or graph that relates stress-intensity factor to crack length for a known external loading condition.  For example, if the stress-intensity factor is related to gross stress conditions (sgross) by the formula

(9.3.7)

Then the stress-intensity factor coefficient is

(9.3.8)

and Equation 9.3.8 is evaluated for a = amean (Equation 9.3.6).  Note that b is typically a function of crack length.