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DTD Handbook

Handbook for Damage Tolerant Design

  • DTDHandbook
    • About
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    • PDF Versions
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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 Generation of Crack Growth Curves

Crack growth life curves were generated for the three transport wing stress histories using a crack growth analysis computer code.  The material chosen for the study was a 7075-T651 aluminum alloy; the associated constant amplitude crack growth rate curve was


with KC = 68 ksi Öin and R = -0.12.  The Willenborg-Chang retardation model embedded within the software was used to account for load-interaction effects.  These modeling choices affect the absolute accuracy of the crack growth predictions but not the implications of the analysis which are presented in a relative sense.

Rather than dealing directly with the actual structural geometries for the three wing locations, it was decided that the crack growth analysis would be applied for a common geometry for all three stress histories.  This choice does not affect the crack growth rate analysis as will be further discussed below.  The choice of common geometry for all three stress histories makes it possible to evaluate the relative effects of per flight and per cycle damage for the analyses.  It was decided also to choose a simple geometry of a four (4) inch wide center cracked panel, giving a stress-intensity factor coefficient of


The initial and final crack length chosen for the configuration were 0.11 and 1.25 inch, respectively.  Figure 9.3.3 summarizes the common configuration employed in this analytical study.





















Figure 9.3.3.  Common Geometry Used to Evaluate Stress History Effect on Crack Growth Behavior

Figure 9.3.4 presents both the crack growth life curve and its crack growth rate counterpart for the center wing stress history.  The crack growth rate curve was generated by forming the secant defined slope for consecutive points on the life curve and relating this slope to the stress-intensity factor calculated using the mean crack length and the RMS maximum stress values (given in Table 9.3.3).  The stress-intensity factor in Figure 9.3.4 is given by


where (smax)RMS = 8.0 ksi, and (K/s) is given by Equation 9.3.10.  The curve through the center of the points in Figure 9.3.4 is the mean trend curve that connects all the points.

Figure 9.3.4.  Crack Growth Behavior for the Center Wing Location

Figure 9.3.5 presents the crack growth life curves generated for the other two wing locations, again using the computer code.  Figure 9.3.6 summarizes the crack growth rate behavior associated with all three stress histories.  The inner and outboard wing crack growth rate data points were also generated by the secant method of analysis.  The RMS maximum stresses used for the stress multiplier in Equation 9.3.11 were 7.24 and 8.01 ksi for the inner wing and the outer wing location, respectively.


Figure 9.3.5.  Flight-by-Flight Crack Growth Life Behavior for Inner Wing (WS-733) and Outboard Wing Stress Histories


Figure 9.3.6.  Flight-by-Flight Fatigue Crack Growth Rate Behavior for Three Transport Wing Histories