A long pressurized pipe with a diameter, $d=5\mathrm{.}5m$ and wall thickness, $t=35mm$ is made of high strength steel and is to operate at an internal pressure, $p=5M\frac{N}{m^2}.$ The design assumes failure will occur by fast fracture from a linear crack, parallel to the longitudinal axis of the pipe, which develops from the inner surface of the pipe. If previous work on steel has estimated an appropriate $K_{\frac{?}{C}}$ c value of $120M\frac{N}{m^{\frac{3}{2}}},$ determine the critical crack length that would cause such failure?

Assume that $=1160$MPa for high strength steel and the stress, $$ that is acting within the wall of the pipe along the hoop direction could be given by:

$=\frac{pr}{t}$

Also, the LEFM validity could be checked with the following equation:

$a,t2\mathrm{.}5(\frac{K_{1c}}{Y}{)}^2$