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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 5.5.5. Interaction of Cracks

For the initial flaw assumptions, JSSG-2006 paragraph A3.12.1 states: “Only one initial flaw in the most critical hole and one initial flaw at a location other than a hole need be assumed to exist in any structural element.  Interaction between these assumed initial flaws need not be considered.”  Obviously, interaction between these cracks can be disregarded because these cracks are not assumed to occur simultaneously, although each of them may occur separately.  However, more than one initial flaw may occur if due to fabrication and assembly operations two or more adjacent elements can contain the same initial damage at the same location.  Note that each of the adjacent elements has only one flaw. JSSG-2006 paragraph A3.12.1 further states: “For multiple and adjacent elements, the initial flaws need not be situated at the same location, except for structural elements where fabrication and assembly operations are conducted such that flaws in two or more elements can exist at the same location.”

The previous statement that interaction between assumed initial flaws need not be considered is not repeated here because these cracks will interact as they occur simultaneously.  In principle, the damage tolerance calculation should consider this interaction.  However, a rigorous treatment of this problem is prohibitive in most cases.  Consider, e.g., a skin with a reinforcement as in Figure 5.5.12.  Because of assembly drilling, both holes should be assumed flawed (Figure 5.5.12a).  If both elements carry the same stress, there will be hardly any load transfer initially.  Hence, the stress intensities for both flaws will be equal, implying that initially both will grow at the same rate.

If the two cracks continue to grow simultaneously in a dependent manner, their stress-intensity factors (K) will eventually be different (e.g., K of the reinforcement would increase faster if only for the finite size effect).  This means that in a given cycle the rate of growth would be different for the two cracks resulting in different crack sizes.  Since it cannot be foreseen prior how the crack sizes in the two members develop, it would be necessary to develop K-solutions for a range of crack sizes and a range of crack size ratios in the two members.

 

Figure 5.5.12.  Interaction of Cracks

 

EXAMPLE 5.5.1:        Interacting Cracks

Assume the crack size in the skin is as, the crack size in the reinforcement ar.  For a given value of ar, the K for the skin crack would be calculated as a function of as.  This calculation would be repeated for a range of ar sizes.  The same would be done for the reinforcement crack and a range of as values.  For any given combination of ar and as, the two stress-intensity factors then can be found by interpolation.

 

 

Although the consequences of crack interaction should be evaluated, routine calculations may be run without interaction of cracks [Smith, et al., 1975; Smith, 1974].  Obviously, the calculation procedure is much simpler if interaction can be ignored.  However, the procedure may give unconservative results.

If either element remained uncracked, the stress-intensity factor in the cracked element would be much lower because there would be load transferred from the cracked element to the uncracked element.  Obviously, the stress-intensity factor in the cracked skin of Example 5.5.1 would be the lowest.  The cracks could be grown as if the other element was uncracked and crack growth would be slower.

Finally, the reinforcement could be totally cracked.  Interaction must be taken into account, i.e., the crack in the skin would be treated now for the case of a failed reinforced panel (e.g., stringer reinforced structure with middle stringer failed).

This means that two analysis have to be made for a K-determination, one with the reinforcement uncracked, one with the reinforcement failed.  If the two independent crack growth analyses show that the reinforcement has failed, the analysis of the skin is changed appropriately.