Calculate the critical crack length:

A wide plate of mild steel is subjected to uniform tensile load causing a stress of 100 MPa. Calculate the critical crack length in the centre of plate which when reached will cause the plate to fracture, if fracture toughness of mild steel is 1340 N / mm²

Solution

The crack will become unstable in the centre of the plate, i.e. the fracture will occur when the crack has attained a critical length (say ac) under given stress ? which remains constant. At this moment K_I → K_IC.

KI for a large plate with central crack of length 2a is by Eq.

and hence

or        

∴          2ac = 114.3 mm

[This example explains how the knowledge of fracture toughness of material and KI of a crack can be used to calculate the length of a crack which must not be permitted to exist. If the cause of crack extension may not be controlled, the only thing left to designer is to calculate critical length in advance. Then the crack length would have to be monitored throughout the life of the structure and as soon as it approaches the critical value, the structure should be discarded to avoid sudden fracture or other measures be taken by which either KI is reduced to KIC is improved.]