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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
          • 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 9.3.1. Definition of Stress Histories

The transport stress histories utilized for this example were developed during a force management update and represent the expected behavior at three separate locations on the lower wing surface.  The force management update involved a complete durability and damage tolerant analysis of the airframe, as well as reassessment of past and future usage of the aircraft force.  Stress histories were generated for durability and damage tolerant studies at those structural locations identified as potentially critical to the continuing safe operation of the force.

The lower wing stress histories chosen for this example analysis represent locations in the center wing (BL 70), in the inner wing (WS 733) and the outer wing.  All three stress histories were developed assuming the same operation (mission mix) history.  The operational history was considered to be represented by a block of 100 flights with a defined mission order.  Eight (8) separate missions were identified as representative of service operations.  Each mission in the 100-flight block averaged 4.8 hours per flight.

The 100-flight block of ordered missions repeated until the service life of 40,000 flight hours was exceeded; thus, more than 83 applications of the repeating 100-flight blocks were required to define a lifetime of operation.  The mission order for the eight representative missions is defined by Table 9.3.1.  For comparison purposes, Figure 9.3.1 presents the stress histories for mission one at three locations.  The stress histories for the other seven missions could be defined in a similar manner.

Table 9.3.1.  Mission Ordering for Transport Flight-by-Flight Spectrum

Order Per 20 Flight Group

Flights

1-20

Flights

21-40

Flights

 41-60

Flights

61-80

Flights

80-100

1

4

6

7

6

5

2

1

7

7

1

4

3

1

7

 

6

1

6

7

2

3

7

1

5

6

1

6

6

1

6

4

4

2

5

8

7

5

3

6

3

2

8

2

8

7

7

3

9

5

5

3

4

8

10

8

4

8

2

6

11

2

3

8

3

7

12

8

1

7

6

5

13

2

6

3

5

6

14

7

6

1

6

6

15

1

3

8

7

6

16

6

8

5

7

5

17

7

6

7

6

1

18

7

1

6

2

5

19

2

2

2

5

4

20

7

4

4

4

7

 

Figure 9.3.1a.  Center Wing Stress History for Mission 1

Figure 9.3.1b.  Inner Wing Stress History for Mission 1

Figure 9.3.1c.  Outer Wing Stress History for Mission 1

The stress history for each location is now defined except for the infrequently occurring maximum stresses.  The infrequently occurring stresses in each mission were inserted into the history on a periodic basis as a replacement for the first maximum stress in the mission.  The period of occurrence of these replacement load events was during the tenth, the one-hundredth, and the two-hundredth repeat occurrence of any of the individual eight missions.  The replacement maximum stresses for mission 1 for the three locations are listed in Table 9.3.2.  Each mission had a similar set of replacement stresses.

Table 9.3.2.  Replacement Stresses for Mission 1 for the Three Wing Locations

Occurrence
Frequency
(per no. of
mission repeats)

Center Wing
(BL-70) Location (ksi)

Inner Wing
(WS-733)
Location
(ksi)

Outer Wing
Location
(ksi)

1/1

14.64

14.43

16.34

1/10

16.16

16.16

18.36

1/100

17.96

17.96

20.79

1/200

18.6

18.60

21.56