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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
        • 0. Residual Strength
        • 1. Introduction
        • 2. Failure Criteria
        • 3. Residual Strength Capability
        • 4. Single Load Path Structure
        • 5. Built-Up Structures
          • 0. Built-Up Structures
          • 1. Edge Stiffened Panel with a Central Crack
          • 2. Centrally and Edge Stiffened Panel with a Central Crack
          • 3. Analytical Methods
          • 4. Stiffener Failure
          • 5. Fastener Failure
          • 6. Methodology Basis for Stiffened Panel Example Problem
          • 7. Tearing Failure Analysis
          • 8. Summary
        • 6. References
      • 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 4.5.2. Centrally and Edge Stiffened Panel with a Central Crack

4.5.2         Centrally and Edge Stiffened Panel with a Central Crack

In the previous subsection, the cases considered pertain to cracks between two stiffeners.  In practice, however, cracks frequently start at a fastener hole and then there will be a stringer across the crack which will have a high load concentration factor.  The problem can be dealt with in a manner similar to a crack between stringers, using either analytical or finite-element procedures.  A schematic residual strength diagram for this case is presented in Figure 4.5.5.  Apart from the residual strength curve g for the edge stiffeners, there will now be an additional residual strength curve k for the central stiffener.

Figure 4.5.5.  Residual Strength Diagram for a Panel with Three Stiffeners and a Central Crack Emanating from a Rivet Hole

For the case where the crack in the skin is small (2a << 2s), the first failure in the structure is noted to occur at point B in Figure 4.5.5 where the skin fails and the crack starts to run.  When the crack reaches a size such that point C is reached, the central stiffener residual strength has dropped to the operating stress level and then the central stringer fails, immediately causing additional loading to be transferred to the edge stiffeners and the skin structure.  The effect of losing the capability of the central stringer is noted in Figure 4.5.5 with a repositioning of the residual strength curves from the edge stiffeners (from curve g to curve g¢) and skin structure (from curve e to curve e¢).  As the crack in the skin structure continues to grow after causing the ultimate tensile strength failure in the central stringer at point C, it reaches a size that causes the ultimate tensile strength failure of the two edge stringers at point D, at which point all potential arrest capability is lost and the structure is lost.

For the case of longer cracks, Figure 4.5.5 shows that skin cracks may start running (line EF), arrest (point F), and tear along curve FL as the stress is increased.  At point L, the crack has reached a length that has resulted in sufficient stress being transferred to the central stringer so that this stiffener now fails.  Again, this failure causes a redistribution of stress in the entire structure so that a new set of residual strength diagrams are required to determine the consequences associated with failing the central stringer.  The new edge stringer and skin structure residual strength curves are presented by curves g¢ and e¢, respectively.

Due to the high load concentration, the middle stringer will usually fail fairly soon by fatigue and, therefore, lines e¢ and g¢, with the middle stringer failed, will have to be used and the residual strength is determined by point H¢.  (Note that e¢, g¢, and H¢ will have different positions in the absence of the middle stringer; a failed central stringer will induce higher stresses in both the skin and the edge stiffeners.)  The foregoing discussion provides the concepts required to establish a complete residual strength diagram.