Example $1$

A long steel plate has a thickness of $3cm$ and a width of $30cm.$ On the basis of the

inspection technique employed, an initial edge crack of length $8\mathrm{.}5mm$ is assumed to

exit. The plate is subjected to a remotely applied tensile force which varies cyclically

between $1\mathrm{.}8MN$ to $2\mathrm{.}7MN.$

A life of $90000$ cycles is required from the component. Does it meet this

requirement?

Discuss critically the options open to the designer in seeking as improved lifetime.

Material properties $K_{IC}=80MN{m}^{-\frac{3}{2}}$

$Kat\frac{{10}^{-9}(m)}{\text{c}\text{y}\text{c}\text{l}\text{e}}=5\mathrm{.}1,MN{m}^{-\frac{3}{2}}$

Paris Law exponent $=3\mathrm{.}3$ assume $Q=1\mathrm{.}121$