Crack tip opening displacement

CTOD can be expressed in terms of stress intensity factor ${\displaystyle K}$ as:^[7]

${\displaystyle \delta _{\text{t}}={\frac {4}{\pi }}{\frac {K^{2}}{m\sigma _{\text{y}}E}}}$

where ${\displaystyle \sigma _{\text{y}}}$ is the yield strength, ${\displaystyle E}$ is Young's modulus and ${\displaystyle m=1}$ for plane stress and ${\displaystyle m=2}$ for plane strain.

CTOD can be related to the energy release rate G as:^[7]

${\displaystyle \delta _{t}={\frac {4}{\pi }}{\frac {G}{\sigma _{y}}}}$

The relationship between the CTOD and J is given by:^[1][8]

${\displaystyle \delta _{\text{t}}=d_{n}{\frac {J}{\sigma _{\text{y}}}}}$

where the variable ${\displaystyle d_{n}}$ is typically between 0.3 and 0.8.

A CTOD test is usually done on materials that undergo plastic deformation prior to failure. The testing material more or less resembles the original one, although dimensions can be reduced proportionally. Loading is done to resemble the expected load. More than 3 tests are done to minimize any experimental deviations. The dimensions of the testing material must maintain proportionality. The specimen is placed on the work table and a notch is created exactly at the centre. The crack should be generated such that the defect length is about half the depth. The load applied on the specimen is generally a three-point bending load. A type of strain gauge called a crack-mouth clip gage is used to measure the crack opening.^[3] The crack tip plastically deforms until a critical point after which a cleavage crack is initiated that may lead to either partial or complete failure. The critical load and strain gauge measurements at the load are noted and a graph is plotted. The crack tip opening can be calculated from the length of the crack and opening at the mouth of the notch. According to the material used, the fracture can be brittle or ductile which can be concluded from the graph.

Standards for CTOD testing can be found in the ASTM E1820 - 20a code.^[9]

Early experiments used a flat, paddle-shaped gauge that was inserted into the crack; as the crack opens, the paddle gauge rotates and an electronic signal is sent to an x–y plotter. This method was inaccurate, however, because it was difficult to reach the crack tip with the paddle gauge. Today, the displacement V at the crack mouth is measured and the CTOD is inferred by assuming that the specimen halves are rigid and rotate about a hinge point.^[10]