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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
      • 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
        • 0. Summary of Stress Intensity Factor Information
        • 1. Background of Stress Intensity Factors
        • 2. Methodology For Determining Stress Intensity Factors
          • 0. Methodology For Determining Stress Intensity Factors
          • 1. Principle of Superposition
          • 3. Finite Element Methods
            • 0. Finite Element Methods
            • 1. Direct Methods
            • 2. Indirect Methods
            • 3. Cracked Element Methods
        • 3. Selected Stress Intensity Factor Cases
        • 5. Computer Codes
        • 6. References
    • Examples

Section Cracked Element Methods

This approach involves the use of a hybrid-cracked element that is incorporated into a finite-element structural analysis program.  To date, only two dimensional crack problems can be solved with the cracked-element approach.  Elements have been developed [Byskov, 1970; Tracey, 1971; Walsh, 1971; Gallagher, 1978; Jordon, et al., 1973; Atluri, et al., 1974; Hellen, 1979] that allow a stress singularity to occur at the crack tip.

The cracked element consists of boundary nodal points around the geometrical boundary of the element.  The element is either contained within the complete finite-element model or is solved separately using the results of finite-element analysis.  In either case, the crack surface is simulated by unzipping a double-noded line along the line of expected crack extension.  This builds into the structural model the proper stiffness due to the presence of the crack.  The variation of stress-intensity factors (K1 and K2) with crack length is determined by progressively unzipping the sets of coupled nodes.

Studies have been conducted on the variation of stress-intensity factors with cracked-element size and location [Jordon, et al., 1973; Atluri, et al., 1974].  These results define some definite guidelines in using cracked-element models.  First, the distance from the crack tip to the cracked-element nodal points should be as constant as possible.  Secondly, for long edge-cracks or cracks emanating from holes, the cracked element should only contain an area very near the crack tip.