Crack tip opening displacement

Crack tip opening displacement (CTOD) or ${\displaystyle \delta _{\text{t}}}$ is the distance between the opposite faces of a crack tip at the 90° intercept position. The position behind the crack tip at which the distance is measured is arbitrary but commonly used is the point where two 45° lines, starting at the crack tip, intersect the crack faces.^[1] The parameter is used in fracture mechanics to characterize the loading on a crack and can be related to other crack tip loading parameters such as the stress intensity factor ${\displaystyle K}$ and the elastic-plastic J-integral.

For plane stress conditions, the CTOD can be written as:^[2][3]

${\displaystyle \delta _{\text{t}}=\left({\frac {8\sigma _{\text{ys}}a}{\pi E}}\right)\ln \left[\sec \left({\frac {\pi \sigma ^{\infty }}{2\sigma _{\text{ys}}}}\right)\right]}$

where ${\displaystyle \sigma _{\text{ys}}}$ is the yield stress, ${\displaystyle a}$ is the crack length, ${\displaystyle E}$ is the Young's modulus, and ${\displaystyle \sigma ^{\infty }}$ is the remote applied stress.

Under fatigue loading, the range of movement of the crack tip during a loading cycle ${\displaystyle \Delta \delta _{\text{t}}}$ can be used for determining the rate of fatigue growth using a crack growth equation. The crack extension for a cycle ${\displaystyle da/dN}$, is typically of the order of ${\displaystyle \Delta \delta _{\text{t}}}$.^[1]