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AFGROW | DTD Handbook

Handbook for Damage Tolerant Design

  • DTDHandbook
    • 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
      • 6. Examples of Damage Tolerant Analyses
      • 7. Damage Tolerance Testing
        • 0. Damage Tolerance Testing
        • 1. Introduction
        • 2. Material Tests
          • 0. Material Tests
          • 1. Fracture Toughness Testing Methods
            • 0. Fracture Toughness Testing Methods
            • 1. Plane-Strain Fracture Toughness
            • 2. R-Curve
            • 3. Crack Initiation J-Integral
          • 2. Sub-Critical Crack Growth Testing Methods
        • 3. Quality Control Testing
        • 4. Analysis Verification Testing
        • 5. Structural Hardware Tests
        • 6. References
      • 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 Crack Initiation J-Integral

The JIc can be used as a toughness value at the initiation of crack tearing from a sharp fatigue crack in metallic materials.  This toughness value can serve as a basis for screening tough materials or for evaluating materials utilized in sub-KIc thicknesses.  Requirements for a valid JIc value according to ASTM E1820 are based on the ratio of the JIc to yield strength, i.e.,


where B is thickness and b0 is the initial ligament.  The relationship between the J-integral and the stress-intensity factor was given in Section 11 as,


where E¢ = E, the elastic modulus, for plane stress, and E¢ = E/(1-n2) for plane strain, and n = Poisson’s ratio.  Thus, using Equations 7.2.5 evaluated at the critical condition (J = JIc, K = KJIc) and Equation 7.2.4, the thickness requirement becomes after some algebra


For the typical condition where the ratio of yield strength to elastic modulus (sys/E) is below 0.1, JIc values can be obtained using specimens thinner than that required by the KIc standard (ASTM E399).

The KJIc value in Equation 7.2.6, however, does not normally correspond to the KIc value that would be obtained using the plane-strain fracture toughness standard.  The KJic value based on JIc measurements is typically lower and thus leads to conservative estimates of the ASTM E399 KIc value.  The differences in KJIc and KIc arise as a result of differences in the amount of allowable physical crack growth associated with the two standards; there is less growth allowed for the JIc value than for the KIc value.

While the use of a toughness standard for sub-KIc thickness specimens provides additional opportunities for characterizing material resistance to fracture, the JIc concept appears somewhat limited relative to the design of aerospace structures.  A single test of a JIc type specimen might be similar in cost to a KIc type test; but a number of JIc type specimens must be tested to develop the required crack resistance data prior to estimating the JIc value.  Through unloading compliance testing, it is possible to reduce the number of tests.