Formula Home Fracture Mechanics Introduction Ranges of Applicability Linear Elastic Fracture Mechanics Fracture Modes Stress Intensity Fac. Elastic Plastic Fracture Mechanics The J Integral CTOD Resources Bibliography
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 Definition of Crack Tip Opening Displacement 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 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 is a dimensionless rotational factor used to locate the center of the hinge. For simplicity, let's assume that the center of the hinge locates at the center of b, i.e., ~ 1/2. The CTOD then becomes 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 is the small scale yielding stress and m is a dimensionless constant that depends on the material properties and the stress states.
 Relationship between J and CTOD Consider a linear elastic body containing a crack, the J integral and the crack tip opening displacement (CTOD) have the following relationship where and m are defined in the previous section. For plane stress and nonhardening materials, m = 1. Hence, for a through crack in an infinite plate subjected to a remote tensile stress (Mode I), the crack tip opening displacement is 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
Mechanical Engineers Outlook

Guide for those interested in becoming a mechanical engineer. Includes qualifications, pay, and job duties.