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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 Analysis for Multiple Stress Histories

Air Logistics Center (ALC) engineers typically need to analyze structural locations within a component for which no stress history is available.  Frequently, a stress analysis of these structural locations must be performed based on a strength of materials approach.  One question asked repeatedly is: What is available that facilitates conducting a simple crack growth life analysis of these structural locations?

One method that has potential for a relatively large component is a wide area crack growth rate equation that describes the rate of damage growth within the area identified.  This section provides an example of how a wide area crack growth rate equation might be generated and then utilized.  The three transport wing stress histories provide the basis for this example.

To develop a wide area crack growth rate equation it is necessary to have crack growth life behavior described at a number of locations within the area of application.  The mission mix and stress sequencing must be the same at all locations considered.  It is anticipated that crack growth lives might be generated for ten or more locations experiencing loading conditions which produce similar contributions of damage.  For the example, only three locations were analyzed for the entire wing; however, the approach and interpretation of results would be similar independent of the component and numbers of location.

As was shown in Figure 9.3.6, the flight-by-flight crack growth rate behavior associated with the three stress histories was different; the rate behavior of each was seen to be relatively continuous and parallel to the others.  To obtain a wide area crack growth rate equation, the analyst must find a method for collapsing the rate curves into one master curve.  This collapsing can only be accomplished (with confidence) if the analyst understands the relationship between the damage generation process and the stress events in the history.  The damage may be generated primarily either by the gust/maneuver cycles or by the GAG cycles.

Figure 9.3.6 shows that the crack growth rates are ordered for the three histories according to the number of gust/maneuver cycles that occur per flight.  The data in Figure 9.3.6 were therefore converted to a crack growth rate per cycle basis and replotted.  Figure 9.3.9 describes the result of this scaling of crack growth rates.  As is shown by Figure 9.3.9, the crack growth rates are found to collapse to tight scatter band with the inner wing location behavior forming the upper curve on the band.

Figure 9.3.9.  Cyclic Crack Growth Rate Behavior for Three Transport Wing Stress Histories

The collapsing of crack growth rate data observed in Figure 9.3.9 does not always occur when the smax(RMS) parameter is used as the stress history characterizing parameters.  If the analyst uses a characterizing parameter that does not describe those events that create damage, one would not expect the crack growth rate data to collapse.  Another good characterizing stress parameter for the three transport wing stress histories is the root mean square (RMS) stress range (DsRMS).  Figure 9.3.10 describes the cycle-by-cycle crack growth rate behavior for the three stress histories where the characterizing stress-intensity factor (K) was calculated using


As Figure 9.3.10 illustrates, the characterizing stress-intensity factor given by Equation 9.3.14 also collapses the rate data.  Additional choices of the characterizing stress maybe necessary when the damage contributions are not dominated by a single loading source.

Once a master crack growth rate curve exists, the curve can be used to integrate the crack growth rate curve at a specific location to produce a crack growth life curve.  Figure 9.3.11 highlights the elements of the analysis.

Figure 9.3.10.  Cyclic Crack Growth Rate Behavior for Three Transport Wing Stress Histories


Figure 9.3.11.  Schematic of Elements Required to Analyze for Crack Growth Life at Specific Locations