Definition of Crack Tip Opening Displacement |
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There are two common definitions of the crack tip opening displacement (CTOD): 1. The opening displacement of the original crack tip. ![]() 2. The displacement at the intersection of a 90° vertex with the crack flanks. ![]() These two definitions are equivalent if the crack blunts in a semicircle. |
CTOD in Specimen |
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The crack tip opening displacement (CTOD) of a crack at the edge of a three-point bending specimen is shown below: ![]() where CTODm is the measured crack tip opening displacement, usually near the edge of the specimen for ease of access, CTOD is the real crack tip opening displacement, a is the length of the crack, and b is the width of the rest of the specimen. Please note that the figure is for illustration purpose only and not to scale. From simple geometry of two similar triangles: ![]() where For simplicity, let's assume that the center of the hinge locates at the center of b, i.e., ![]() The above hinge model may not be accurate when the displacement is mostly elastic. A more accurate approach is to separate the CTOD into an elastic part and a plastic part: ![]() where |
Relationship between J and CTOD |
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Consider a linear elastic body containing a crack, the J integral and the crack tip opening displacement (CTOD) have the following relationship ![]() where ![]() Shih, C. F., 1981, took a step further and showed that a unique relationship exists between J and CTOD beyond the validity limits of LEFM. He introduced the 90° intercept definition of CTOD, as illustrated below. ![]() The displacement field is ![]() The CTOD is evaluated from ux and uy at r = r* and ![]() Since ![]() The CTOD becomes ![]() |