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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
        • 0. Damage Size Characterizations
        • 1. NDI Demonstration of Crack Detection Capability
        • 2. Equivalent Initial Quality
          • 0. Equivalent Initial Quality
          • 1. Description of Equivalent Initial Quality Method
          • 2. Example Application of Equivalent Initial Quality Method
          • 3. Other Applications of Equivalent Flaw Size Distributions
        • 3. Proof Test Determinations
        • 4. References
      • 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
      • 10. Guidelines for Damage Tolerance Design and Fracture Control Planning
      • 11. Summary of Stress Intensity Factor Information
    • Examples

Section 3.2.2. Example Application of Equivalent Initial Quality Method

The purpose of the A-7D quality assessment was to establish the manufacturing quality (ai) of the A-7D aircraft.  This was accomplished using the Equivalent Initial Quality Method.  The method was applied to a sample problem involving an A-7A wing fatigue test failure.  Next, specimens were cut from an A-7D production aircraft and tested to failure under a selected block loading.  The fracture surfaces were then fractographically examined and the equivalent initial quality was established.

A photograph of the failure area of a full-scale fatigue test of an A-7A wing was used as a sample problem to check out the Equivalent Initial Quality Method.  The wing had been subjected to a 10-level, blocked, low-high stress spectrum.  Fractographic measurements were taken from the photograph (Figure 3.2.3), making it possible to generate a large portion of the crack growth curve.  Crack propagation analyses were performed using the computer routine EFFGRO and the Wheeler Retardation Model until the analytical crack growth curve correlated well with the fractographic test data.  This correlation is presented in Figure 3.2.4, which indicates that the manufacturing quality of the test hardware at the failure location was equivalent to an initial crack of length ai = 0.00109 in.  This excellent correlation of the analytical crack growth prediction with the fractographic test supported the validity of the Equivalent Initial Quality Method for this particular problem.

Figure 3.2.3.  A-7A Wing Fatigue Test Fracture Surface [Rudd & Gray, 1978]

 

Figure 3.2.4.  Equivalent Initial Quality Results for A-7A Wing [Rudd & Gray, 1978]

The Equivalent Initial Quality Method was next used to establish the A-7D quality assessment.  This assessment was accomplished using test specimens cut from the lower wing skin of an A-7D production aircraft that had been used as a gunfire target.  Because this particular aircraft had low flight time (691.9 hours), the probability of cracking in the wings was very low.  The location of each specimen in the lower wing skin is illustrated in Figure 3.2.5.  Each specimen was made of 7075-T6 aluminum and contained multiple holes.  The geometric details for each specimen are presented in Table 3.2.1, indicating that the thickness ranged from approximately 3/16 in. to 1/4 in. and the nominal values of the width and hole diameter were 3 in. and 1/4 in., respectively.  The specimens contained two types of holes – countersunk holes (wet-wing region) and straight-shank holes (dry-wing region).

The test specimens were subjected to a fatigue stress spectrum consisting of 5,000 cycles with a maximum stress of 20 ksi and a stress ratio of 0.1 followed by 100 cycles with a maximum stress of 30 ksi and a stress ratio of 0.1.  The block spectrum was chosen because it produced test lives of reasonable length (less than 20 blocks) and fracture surfaces that were readily readable.

Table 3.2.2 contains a summary of the number of fastener holes involved, the number of flaws detected, the number of flaws fractographically examined, the crack length range at the time of specimen failure (af), and the range of the equivalent initial quality (ai).  All but two of the 44 holes contained double flaws.  One of these two holes contained one crack, while no crack was detected in the other hole.  This resulted in a total of 85 flaws, of which 44 were examined fractographically.  The flaws were arbitrarily chosen for fractographic examination at magnifications ranging from 30x to 400x using a universal measuring microscope.  The equivalent initial quality range for all the holes was found to be 0.00015 - 0.0022 in.  A statistical distribution of the A-7D equivalent initial quality was obtained.

Table3.2.1.  Geometric Details of A-7D Quality Assessment Specimens [Rudd & Gray, 1978]

Specimen

Thickness a

Width a

Hole Diameter a

101

0.226

2.93

0.253 b

201

0.226

2.93

0.253 b

301

0.217

3.00

0.253 b

401

0.231

3.00

0.253 b

501

0.183

2.90

0.253 c

502

0.176

3.00

0.253 c

601

0.263

3.00

0.253 c

602

0.264

3.00

0.253 c

                                                              a Dimensions in inches

                                                              b Countersunk hole

                                                              c Straight-shank hole

 

Figure 3.2.5.  A-7D Quality-Assessment Specimen Locations [Rudd & Gray, 1978]

Table 3.2.2.  A-7D Quality Assessment Test Results [Rudd & Gray, 1978]

Specimen

No.
Holes

No.
Flaws

 Range a

Flaws Tracked

ai a Range

101

7

14

0.05-0.75

14

0.0004-0.0022

201

6

12

<0.01-1.10

12

0.0004-0.0012

301

4

8

0.01-0.65

1

0.0003

401

3

6

0.02-0.50

1

0.0002-0.0014

501

8

14

0.00-0.60

1

0.0007

502

8

16

<0.01-0.62

6

0.0006

601

4

8

0.02-0.50

8

0.00015-0.0009

602

4

7

0.00-1.05

1

0.0006

Total

44

85

 

44

 

a Dimensions in in.

 

The fractographic examinations revealed the origins of the flaws for both the straight-shank holes and the countersunk holes as illustrated in Figure 3.2.6.  There is equal possibility of flaw occurrence along the bore of the hole for the straight-shank hole, while the most frequently occurring flaw location for the countersunk hole is at the inside radius of the small-diameter portion of the hole.  Typical flaw origins for each type of hole are shown on the fracture surfaces of Figure 3.2.7.  Also illustrated in Figure 3.2.7 is the readability of the fracture surfaces for the selected stress spectrum, with the dark marking bands resulting from the application of the high-load (maximum stress of 30 ksi) portion of the specimen.

Figure 3.2.6.  A-7D Flaws Origins [Rudd & Gray, 1978]

 

Figure 3.2.7.  Fracture Surfaces for Countersunk (Left) and Straight-Shank (Right) Holes [Rudd & Gray, 1978]

Metallurgical investigations of the A-7D flaw origins revealed that the flaws were the result of two different sources-anodize pitting and mechanical sources.  The majority of the flaws (86.4%) initiated from anodize pits in the following manner.  Insoluble microconstituents were exposed along the bore of the hole during the hole-drilling operation.  The anodizing ate away the microconstituents and caused pitting.  The exposed pits were then filled with aluminum oxide, resulting in flaw initiation.  The remaining flaws (13.6%) were due to the mechanical damage.  Although anodizing provided corrosion protection, it also resulted in the majority of the fatigue cracks.

All but two of the holes contained double flaws, of which none were through-the-thickness flaws.  The selected stress spectrum marked the fracture surfaces extremely well, making it possible to determine the crack length within each loading block.  Hence, it was possible to fractographically determine the equivalent initial quality for each flaw examined.

Figure 3.2.8 presents the probability density of occurrence versus the equivalent initial quality for the A-7D aircraft.  It should be noted that the A-7D equivalent initial quality was determined by fractography alone, since it was possible to measure the crack length during the application of the first block of loading.


 

Figure 3.2.8.  Probability Density of Occurrence of A-7D Equivalent Initial Quality [Rudd & Gray, 1978]

The probability density of occurrence (Figure 3.2.8) was used to determine the cumulative probability of occurrence for the A-7D aircraft.  Figure 3.2.9 presents the cumulative probability of occurrence versus the equivalent initial quality for the A-7D and F-4 C/D aircraft.  Also presented in Figure 3.2.9 is the cumulative probability of occurrence with 95% confidence for each aircraft.  For example, Figure 3.2.9 indicates that with 95% confidence, 99.9% of the A-7D flaws have an equivalent length less than 0.007 in.  This means that one out of a thousand flaws have an equivalent length greater than 0.007 in.

Figure 3.2.9.  Cumulative Probability of Occurrence of A-7D Equivalent Initial Quality [Rudd & Gray, 1978]