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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
        • 0. Analysis Of Damage Growth
        • 2. Variable-Amplitude Loading
        • 3. Small Crack Behavior
        • 4. Stress Sequence Development
        • 5. Crack Growth Prediction
          • 0. Crack Growth Prediction
          • 1. Cycle Definition and Sequencing
          • 2. Clipping
          • 3. Truncation
          • 4. Crack Shape
          • 5. Interaction of Cracks
        • 6. References
      • 6. Examples of Damage Tolerant Analyses
      • 7. Damage Tolerance Testing
      • 8. Force Management and Sustainment Engineering
      • 9. Structural Repairs
      • 10. Guidelines for Damage Tolerance Design and Fracture Control Planning
      • 11. Summary of Stress Intensity Factor Information
    • Examples

Section 5.5.3. Truncation

Truncation of the lower load levels is important for the efficiency of crack growth calculations.  Truncation means that cycles below a certain magnitude are simply omitted.  The argument is that low stress excursions do not contribute much to crack growth, especially in view of the retardation effect.  Since there are so many cycles of low amplitude, their omission would speed up experiments and crack growth calculations.

Figure 5.5.9 shows some experimental data regarding the effect of truncation.  The lowest load levels of a complete stress history were simply omitted, without a correction of the stress history.  These data might be somewhat misleading, because truncation was not carried out properly.  Figure 5.5.10 shows the improper and the correct procedure for truncation.

Figure 5.5.9.  Effect of Lowest Stress Amplitude in Flight-by-Flight Tests Based on Gust Spectrum [Schijve 1970; 1972 ]

The left half of Figure 5.5.10 illustrates the truncation procedure used for the experiments in Figure 5.5.9.  In the example, the 580,000 cycles of level S8 would simply be omitted, thus reducing the total cycle content from 700,000 to 120,000.  Proper truncation requires that the lower spectrum approximation step be reconstructed, as indicated in the right half of Figure 5.5.10.  The hatched areas in the figure should be made equal.  This means that the number of S7 cycles would increase from 80,000 to 260,000, and the total cycle content would be reduced from 700,000 to 300,000.  This increase of 180,000 cycles of S7 would be substituted for 580,000 cycles of S8.  In this way, the effects of lower level truncation are less than suggested by the experimental data in Figure 5.5.9.

Improper Truncation

 

Correct Truncation

Level

Exceedances

Occurrences

 

Level

Exceedances

Occurrences

S1

10

10

 

S1

10

10

S2

100

90

 

S2

100

90

S3

600

500

 

S3

600

500

S4

2,000

1,400

 

S4

2,000

1,400

S5

8,000

6,000

 

S5

8,000

6,000

S6

40,000

32,000

 

S6

40,000

32,000

S7

120,000

80,000

 

S7

300,000

260,000

S8

700,000

580,000

 

 

 

 

 

Figure 5.5.10.  Improper and Correct Truncation

In Section 5.4 it was recommended that the truncation level be selected at 105 - 5x105 exceedances per 1,000 flights, depending upon how steep the exceedance curve is at its extreme point.  That recommendation is reiterated here.