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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
          • 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

A high load occurring in a sequence of low-amplitude cycles significantly reduces the rate of crack-growth during the cycles applied subsequent to the overload.  This phenomenon is called retardation.  Figure 5.2.1 shows a baseline crack-growth curve obtained in a constant-amplitude test [Schijve & Broek, 1962].  In other experiments, the same constant-amplitude loading was interspersed with overload cycles.  After each application of the overload, the crack virtually stopped growing during many cycles, after which the original crack-growth behavior was gradually restored.


Figure 5.2.1.  Retardation Due to Positive Overloads, and Due to Positive-Negative Overload Cycles [Schijve & Broek, 1962]

Retardation results from the plastic deformations that occur as the crack propagates.  During loading, the material at the crack tip is plastically deformed and a tensile plastic zone is formed.  Upon load release, the surrounding material is elastically unloaded and a part of the plastic zone experiences compressive stresses.  The larger the load, the larger the zone of compressive stresses.  If the load is repeated in a constant amplitude sense, there is no observable direct effect of the residual stresses on the crack-growth behavior; in essence, the process of growth is steady state.  Measurements have indicated, however, that the plastic deformations occurring at the crack tip remain as the crack propagates so that the crack surfaces open and close at non zero (positive) load levels.  These observations have given rise to constant amplitude crack-growth models referred to as closure models [Elber, 1971] after the concept that the crack may be closed during part of the load cycle.

When the load history contains a mix of constant amplitude loads and discretely applied higher level loads, the patterns of residual stress and plastic deformation are perturbed.  As the crack propagates through this perturbed zone under the constant amplitude loading cycles, it grows slower (the crack is retarded) than it would have if the perturbation had not occurred.  After the crack has propagated through the perturbed zone, the crack growth rate returns to its typical steady state level. 

Two basic models have been proposed to describe the phenomenon of crack retardation.  The first model is based on the concept of the compressive residual stress perturbation and the second on the concept of plastic deformation with enhanced crack wedging and more closure.

If the tensile overload is followed by a compressive overload, the material at the crack tip may undergo reverse plastic deformation and this reduces the residual stresses.  Thus, a negative overload in whole or in part annihilates the beneficial effect of tensile overloads, as is also shown by curve C in Figure 5.2.1.

Retardation depends upon the ratio between the magnitude of the overload and subsequent cycles.  This is illustrated in Figure 5.2.2.  Sufficiently large overloads may cause total crack arrest.  Hold periods at zero stress can partly alleviate residual stresses and thus reduce the retardation effect [Shih & Wei, 1974; Wei & Shih, 1974], while hold periods at load increase retardation.  Multiple overloads significantly enhance the retardation.  This is shown in Figure 5.2.3.


Figure 5.2.2.  Effect of Magnitude of Overload on Retardation [Shih & Wei, 1974]

Figure 5.2.3.  Retardation in Ti-6V-4Al; Effect of Hold Periods and Multiple Overloads [Wei & Shih, 1974]