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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
          • 0. Fracture Mechanics Fundamentals
          • 1. Stress Intensity Factor – What It Is
          • 2. Application to Fracture
          • 3. Fracture Toughness - A Material Property
          • 4. Crack Tip Plastic Zone Size
          • 5. Application to Sub-critical Crack Growth
          • 6. Alternate Fracture Mechanics Analysis Methods
        • 3. Residual Strength Methodology
        • 4. Life Prediction Methodology
        • 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 2.2.2. Application to Fracture

The hypothesis can be stated:

if the level of crack tip stress intensity factor exceeds a critical value, unstable fracture will occur. 

The concept is analogous to the criterion of stress at a point reaching a critical value such as the yield strength.  The value of the stress-intensity factor at which unstable crack propagation occurs is called the fracture toughness and is given the symbol Kc.  In equation form, the hypothesis states:

if K = Kc,


then catastrophic crack extension (fracture) occurs.

To verify the usefulness of the proposed hypothesis, consider the results of a wide plate fracture study given in Figure 2.2.3 [Boeing, 1962].  These data represent values of half crack length and gross section stress at fracture.  The stress-intensity factor for the uniformly-loaded center-cracked finite-width panel is given by:


where W is the panel width.  Application of Equation 2.2.4 given in Figure 2.2.3 followed by averaging the calculated fracture toughness values (except for those at the two smallest crack lengths) gives the average fracture toughness curve shown.  This example illustrates that the fracture toughness concept can be used to adequately describe fractures that initiate at gross sectional stress below 70% of the yield strength.

Figure 2.2.3.  Results of a Wide Plate Fracture Study Compared with a Fracture Toughness Curve Calculated Using the Finite Width Plate Stress Intensity Factor Equation, Equation 2.2.4 (Data from Boeing [1962])

Note that since plastic deformation is assumed negligible in the linear elastic analysis, Equation 2.2.3 is not expected to yield an accurate approximation where the zone of plastic deformation is large compared to the crack length and specimen dimensions.  Figure 2.2.3 shows that the relationship derived on the basis of the Equation 2.2.3 hypothesis does not describe the crack growth behavior for small cracks in plastic stress fields.