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DTD Handbook

Handbook for Damage Tolerant Design

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    • Sections
      • 1. Introduction
      • 2. Fundamentals of Damage Tolerance
        • 0. Fundamentals of Damage Tolerance
        • 1. Introduction to Damage Concepts and Behavior
        • 2. Fracture Mechanics Fundamentals
        • 3. Residual Strength Methodology
        • 4. Life Prediction Methodology
          • 0. Life Prediction Methodology
          • 1. Initial Flaw Distribution
          • 2. Usage
          • 3. Material Properties
          • 4. Crack Tip Stress Intensity Factor Analysis
          • 5. Damage Integration Models
          • 6. Failure Criteria
        • 5. Deterministic Versus Proabilistic Approaches
        • 6. Computer Codes
        • 7. Achieving Confidence in Life Prediction Methodology
        • 8. References
      • 3. Damage Size Characterizations
      • 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 2.4.6. Failure Criteria

The interrelationship between critical crack length, loading, and residual strength of a structure was first discussed in Section 2.2 using Figure 2.2.3.  Based on the information presented in Section 2.3.1, the residual strength (sres), the load-carrying capacity of the cracked structure, can be shown to monotonically* decrease with increasing crack length in the following manner:

sres = Kc/f(a)



Kc = the material resistance to fracture, termed fracture toughness, and

, the structural property, termed the stress intensity factor coefficient.

When the residual strength decays to the level of the maximum stress in the service load history, fracture of the structure occurs.  The crack length associated with fracture (i.e., acr) is normally determined by solving Equation 2.4.5 for crack length, assuming that the residual strength equals the maximum stress in the stress history.  Note that the rate of growth of a crack is directly related to the rate of loss of residual strength through Equation 2.4.5, thus justifying the selection of the crack to quantify structural fatigue damage.

The critical crack length (acr) is thus a function of material, structural geometry, and loading.  As shown in Figure 2.4.12, the relative effect of acr on life is typically small (i.e., when acr/ao ≥ 5).  The primary advantage of designing for a large critical crack length is the increased inspectability it provides.  A large critical crack length increases the probability of locating the crack before it becomes critical, thereby enhancing aircraft safety.

Figure 2.4.12.  Effect of Critical Crack Size on Life

Determination of the critical crack size via Equation 2.4.5 would ordinarily be sufficient for safety limits; however, durability considerations often dictate that the final crack size, af, be chosen smaller than acr to represent rework of repair limits.  A choice of af along these lines is shown in Figure 2.4.13.

Figure 2.4.13.  Economic Final Crack Size

Section 4 provides a summary of available residual strength estimating techniques and procedures that are generally applicable to all different types of structures and materials.  Section 7 presents the experimental methods and procedures used to generate toughness data and residual strength data.


* monotonic implies that the rate of change does not change sign.