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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
        • 0. Structural Repairs
        • 1. Required Analysis
        • 3. Spectrum Analysis for Repair
          • 0. Spectrum Analysis for Repair
          • 1. Definition of Stress Histories
          • 2. Spectra Descriptions
            • 0. Spectra Descriptions
            • 1. Exceedance Curve Descriptions
            • 2. RMS Descriptions
          • 3. Crack Growth Analysis
        • 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 Exceedance Curve Descriptions

One normally generates a stress history for a given mission based upon exceedance information; however, the starting exceedance information is typically based in operational parameters, e.g. nz, airspeed, weight, altitude, etc. for given mission functions.  After a stress history has been generated for a collection of missions, it is recommended that stress exceedance curves be generated for the maximum stress, the minimum stress, and the positive (load-increasing) stress range associated with all stress events.  The exceedance curves for the maximum, minimum, and range of the individual stress events in the three wing stress histories are presented in Figure 9.3.2.


                   (a) Maximum Stress Exceedance                              (b) Minimum Stress Exceedance

(c) Stress Range Exceedance

Figure 9.3.2.  Exceedance Curves for the Three Transport Wing Stress Histories

The exceedance curves for each stress event characteristic are noted (from Figure 9.3.2) to be similar in shape but somewhat displaced relative to number of exceedances.  The behavior observed might have been expected since all three locations are experiencing the same operational history.  Both the minimum stress and stress range exceedance curves indicate a plateau around 8300 exceedances, which is the dividing line between once per flight occurrences and those that occur more frequently.  Thus, because we are dealing with a transport aircraft, it can be noted that the once per flight ground-air-ground (GAG) cycle has a stress range typically larger than 16 ksi, while the gust/maneuver cycles have stress ranges less than 8 ksi.

In anticipating the level of damage that a stress history might generate, the exceedance curve becomes a useful tool.  The highest stresses (all events) are noted to be present in the outboard wing (followed by the inner wing and then center wing).  Also, for a given magnitude of any stress characteristic, the number of exceedances are the highest for the outboard wing location (followed by the inner wing and center wing).  The implication is that, on a per flight basis, more damage is generated at the outer wing location then at the other two locations, all other things being equal (structural geometry, material, crack geometry, etc.).

The shape of the exceedance curve can also be used to determine if the stress history might be expected to introduce major perturbations in the crack growth behavior.  If the exceedance curve associated with the maximum stress characteristic is relatively continuous from the infrequency of the once-per-flight event, then the flight-by-flight crack growth rate curve would also be expected to be relatively continuous.  Except for the outboard wing location curve between 40-60 exceedances, Figure 9.3.2a shows that the maximum stress exceedance curves are relatively continuous.  It is therefore expected that the flight-by-flight crack growth rate curves for the three wing histories will be relatively continuous (not show major effects of retardation).