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DTD Handbook

Handbook for Damage Tolerant Design

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    • About
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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
          • 0. Variable-Amplitude Loading
          • 1. Retardation
            • 0. Retardation
            • 1. Retardation Under Spectrum Loading
            • 2. Retardation Models
          • 2. Integration Routines
          • 3. Cycle-by-Cycle Analysis
        • 3. Small Crack Behavior
        • 4. Stress Sequence Development
        • 5. Crack Growth Prediction
        • 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 Retardation Under Spectrum Loading

An actual service load history contains high- and low- stress amplitudes and positive and negative “overloads” in random order.  Retardation and annihilation of retardation becomes complex, but qualitatively the loading produces behavior that is similar to a constant-amplitude history with incidental overloads.  The higher the maximum stresses in the service load history, the larger the retardation effect during the low-amplitude cycles.  Negative stress excursions reduce the retardation effect and tend to enhance crack-growth.  These effects have been documented in various sources [Schijve, 1972; Schijve, 1970; Wood et al., 1971; Porter, 1972; Potter, et al., 1974; Gallagher et al., 1974; Wood, et al., 1971]; a few examples are now presented.

When the magnitude of the higher loads are reduced (or clipped) without eliminating the cycle, i.e., higher loads are reset to a defined lower level, the cracking rates are observed to speed up as shown in Figure 5.2.4 [Schijve, 1972; Schijve, 1970].  Figure 5.2.4 describes the crack growth life results for a study in which a (random) flight-by-flight stress history was systematically modified by “clipping” the highest load excursions to the three levels shown.


Figure 5.2.4.  Effect of Clipping of Higher Loads in Random Flight-by-Flight Loading on Crack Propagation In 2024-T3 Al Alloy [Schijve, 1972; Schijve, 1970]

In Schijve [1970; 1972], it was also observed that negative stress excursions reduce the retardation effect and omission of the ground-air-ground (G-A-G) cycles (negative loads) in the tests with the highest clipping level resulted in a longer crack growth life for the same amount of crack growth.

Figure 5.2.5 shows the importance of load sequence.  The crack-propagation life for random load cycling is shown at the top.  Ordering the sequences of the loads, low-high, low-high-low, or high-low increases the crack-growth life, the more so for larger block sizes.  Hence, ordering should only be permitted if the block size is small.  Low-high ordering gives more conservative results than high-low ordering.  In the latter case, the retardation effect caused by the highest load is effective during all subsequent cycles.

Figure 5.2.5.  Effect of Block Programming and Block Size On Crack Growth Life All Histories Have Same Cycle Content; Alloy: 2024-T3 Aluminum [Shih & Wei, 1974]