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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 2.4.4. Crack Tip Stress Intensity Factor Analysis

The crack tip stress intensity factor (K) interrelates the crack geometry, the structural geometry, and the load on the structure with the local stresses in the region of the crack tip.  The stress intensity factor takes the form



b - geometric term for structural configuration, can be a function of crack length

s - stress applied to the structure

a - crack length

It can be seen that any number of combinations of the parameters b, a, and s can given rise to the same K.  The crack growth analysis rests on the experimentally verified proposition that a given K gives rise to a certain crack growth rate, regardless of the way in which the parameters were combined to generate that K.

A considerable body of data exists which defines experimental and mathematical solutions for stress intensity factors for various structural configurations.  A review of the procedures for obtaining stress intensity factors is covered, and the K solutions for a number of practical structural geometries are presented in Section 11.

Since stress enters Equation 2.4.2 in a linear sense it is appropriate to express the geometrical part of the stress intensity factor by using the stress intensity factor coefficient, K/s.  Figure 2.4.9 illustrates two typical solutions expressed in this manner.  For a through-the-thickness crack in a plate of infinite extent, the value of b is unity and K becomes


Equation 2.4.2a provides one way of normalizing more complex K solutions in terms of the infinite plate solution.  Figure 2.4.10 depicts a typical solution of this type.


Figure 2.4.9.  Stress-Intensity-Factor Coefficients Showing Influence of Hole on K

Figure 2.4.10.  Influence of Hole on Geometric Correction Factor, b

Through-the-thickness cracks are handled quite well analytically.  However, for corner cracks and semi-elliptical part-through cracks, such as illustrated in Figure 2.4.11, K varies from point to point around the crack perimeter.  This variation allows the crack shape to change as it grows, which leads to a complex three-dimensional problem.  The determination of b and K/s for these complex cases have received a substantial amount of attention (see Section 11).

Figure 2.4.11.  Complex Crack Geometries