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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 9.3.3.2. Analysis of Observed Behavior

A number of observations can be made from the data presented in Figures 9.3.4 through 9.3.6.  First, the life is shortest and the rates are fastest for the outer wing stress history; this stress history is the most damaging from a crack growth point of view.  The next most damaging history is the inner wing stress history; the least damaging history is associated with the center wing location.  Second, the three crack growth rate curves appear to be almost parallel and relatively continuous throughout the range shown.  There are discontinuities in the outer and inner wing curves which tend to locally depress the rate curves.  These discontinuities are not severe and are associated with the exceptionally high but frequently occurring maximum stress events in the stress history.

As a result of the relatively continuous nature of the crack growth rate curves, least square procedures were applied to the data in Figure 9.3.6 in order to generate the constants in Equation 9.3.1.  These constants are presented in Table 9.3.5 along with another set of constants derived using graphical procedures and the assumption that the crack growth rate curves were parallel.  Figure 9.3.7 illustrates the degree of fit achieved by the curve established using least squares procedures for the outer wing data.  The least squares determined power law curve is seen to adequately describe the outer wing data.  The other two least squares power law curves provided similarly adequate descriptions of their respective crack growth rate data.

Table 9.3.5.  Constants C and p for Equation 9.3.1

Stress History

Least Squares Method

Graphical Method

C

p

C

p

Center Wing (BL-70)

2.54x10-7

2.93

3.35x10-7

2.89

Inner Wing (WS-733)

7.29x10-7

2.73

5.10x10-7

2.89

Outer Wing

7.74x10-7

2.86

9.05x10-7

2.89

 

Figure 9.3.7.  Comparison Between Outer Wing Data and the Least Squares Determined Curve

A second crack growth life analysis was conducted using the three transport wing stress histories scaled to a lower stress level; all stress events in the three histories were scaled to 0.903 of their original level (both tensile and compressive levels were scaled equally).  The same computer software was employed for this second analysis, and all geometry and material properties were kept the same.  The stress history mission mix and order (stress sequence) were the same as described in subsection 9.3.1.  As expected, longer crack growth lives were associated with the lower stress magnitude stress histories.  Table 9.3.6 summarizes the life predictions required to grow the crack between the previously defined limits of 2a0 = 0.22 inch and 2af = 1.60 inch.

Table 9.3.6.  Effect of Stress Magnification Factor on Crack Growth Lives (L)

Calculated for a Center Crack (2a) Growing Between 0.22 and 1.60 inch

Stress History

Lives for Two Stress Magnification Factor Values

Life Ratio

L0.903/L1

L1

(Flights)

L0.903

(Flights)

Center Wing (BL-70)

6220

8300

1.33

Inner Wing (WS-733)

4115

5345

1.30

Outer Wing

2385

3117

1.31