Crack tip opening displacement

Crack tip opening displacement (CTOD) or 
 
 
 
 
 δ
 
 t
 
 
 
 
 {\displaystyle \delta _{\text{t}}}
 
 is the distance between the opposite faces of a <a href="/facts/Fracture/nxDNAj0d">crack</a> 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. The parameter is used in <a href="/facts/Fracture_mechanics/f9QogJzF">fracture mechanics</a> to characterize the loading on a crack and can be related to other crack tip loading parameters such as the <a href="/facts/Stress_intensity_factor/pLrUo683">stress intensity factor</a> 
 
 
 
 K
 
 
 {\displaystyle K}
 
 and the elastic-plastic <a href="/facts/J-integral/d2GUBxo8">J-integral</a>.
For <a href="/facts/Plane_stress/2NXRCwo4">plane stress</a> conditions, the CTOD can be written as:

 
 
 
 
 δ
 
 t
 
 
 =
 
 (
 
 
 
 8
 
 σ
 
 ys
 
 
 a
 
 
 π
 E
 
 
 
 )
 
 ln
 ⁡
 
 [
 
 sec
 ⁡
 
 (
 
 
 
 π
 
 σ
 
 ∞
 
 
 
 
 2
 
 σ
 
 ys
 
 
 
 
 
 )
 
 
 ]
 
 
 
 {\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 
 
 
 
 
 σ
 
 ys
 
 
 
 
 {\displaystyle \sigma _{\text{ys}}}
 
 is the <a href="/facts/Yield_(engineering)/mrSg02gW">yield stress</a>, 
 
 
 
 a
 
 
 {\displaystyle a}
 
 is the crack length, 
 
 
 
 E
 
 
 {\displaystyle E}
 
 is the <a href="/facts/Young%27s_modulus/MV5JMCIM">Young's modulus</a>, and 
 
 
 
 
 σ
 
 ∞
 
 
 
 
 {\displaystyle \sigma ^{\infty }}
 
 is the remote applied stress.
Under <a href="/facts/Fatigue_(material)/zmJY8hMt">fatigue</a> loading, the range of movement of the crack tip during a loading cycle 
 
 
 
 Δ
 
 δ
 
 t
 
 
 
 
 {\displaystyle \Delta \delta _{\text{t}}}
 
 can be used for determining the rate of fatigue growth using a <a href="/facts/Crack_growth_equation/6n78f8Pw">crack growth equation</a>. The crack extension for a cycle 
 
 
 
 d
 a
 
 /
 
 d
 N
 
 
 {\displaystyle da/dN}
 
, is typically of the order of 
 
 
 
 Δ
 
 δ
 
 t
 
 
 
 
 {\displaystyle \Delta \delta _{\text{t}}}
 
.

Crack tip opening displacement open-in-new

Crack tip opening displacement