• DTDHandbook
• Contact
• Contributors
• 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 2.2.4. Crack Tip Plastic Zone Size

It is recognized that plastic deformation will occur at the crack tip as a result of the high stresses that are generated by the sharp stress concentration.  To estimate the extent of this plastic deformation, Irwin equated the yield strength to the y-direction stress along the x-axis and solved for the radius.  The radius value determined was the distance along the x-axis where the stress perpendicular to the crack direction would equal the yield strength; thus, Irwin found that the extent of plastic deformation was

 (2.2.5)

Subsequent investigations have shown that the stresses within the crack tip region are lower than the elastic stresses and that the size of the plastic deformation zone in advance of the crack is between ry and 2ry.  Models of an elastic, perfectly plastic material have shown that the material outside the plastic zone is stressed as if the crack were centered in the plastic zone.  Figure 2.2.5 describes a schematic model of the plastic zone and the stresses ahead of the crack tip.  Note that the real crack is blunted as a result of plastic deformation.

Figure 2.2.5.  Small-Scale Yield Model for Restricted Crack Tip Plastic Deformation

If the extent of the plastic zone as estimated by Equation 2.2.5 is small with respect to features of the structural geometry and to the physical length of the crack, linear elastic fracture mechanics analyses apply.  Sometimes, the concept of contained yielding, as illustrated in Figure 2.2.5, is referred to as small scale yielding.  Most structural problems of interest to the aerospace community can be characterized by linear elastic fracture mechanics parameters because the extent of yielding is contained within a small region around the crack tip.