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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
        • 0. Residual Strength
        • 1. Introduction
        • 2. Failure Criteria
          • 0. Failure Criteria
          • 1. Ultimate Strength
          • 2. Fracture Toughness - Abrupt Fracture
          • 3. Crack Growth Resistance – Tearing Fracture
            • 0. Crack Growth Resistance – Tearing Fracture
            • 1. The Apparent Fracture Toughness Approach
            • 2. The Resistance Curve Approach
            • 3. The J-Integral Resistance Curve Approach
        • 3. Residual Strength Capability
        • 4. Single Load Path Structure
        • 5. Built-Up Structures
        • 6. References
      • 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 4.2.3.1. The Apparent Fracture Toughness Approach

Due to the complexity of the two parameter fracture criteria for tearing fracture behavior, engineers sometimes obtain preliminary estimates for the residual strength using a single parameter fracture toughness criterion.  Figure 4.2.10 describes the stress-crack length levels associated with the onset of cracking (K = KONSET) and fast fracture (K = Kcr) conditions for a tearing material.  Intermediate between the two curves established from material observations is a third curve referred to as the apparent fracture curve.  The apparent fracture toughness (KAPP) is established from the same data employed to derive KONSET and Kcr.  The calculation procedure uses the onset (or initial) crack length (ai) and the final recorded stress level (scr) for the tests conducted.  Thus, KAPP represents a fracture toughness level bounded by the onset and fast fracture levels.

Figure 4.2.10.  Description of the Three Fracture Toughness Criteria that are Utilized to Estimate Residual Strength Under Tearing Fracture Conditions

For lower bound estimates of the residual strength for fast fracture of a tearing material, one could equate the level of applied stress-intensity factor (K) to the apparent fracture toughness (KAPP), i.e., assume that fracture occurs when

K = KAPP

(4.2.3)

in order to determine the critical level of stress.  Equation 4.2.3 is an abrupt failure criterion for a tearing fracture.