A bending member has a rectangular cross$-$section of dimensions, as defined in Fig. $8\mathrm{.}13,$ of depth $b=60$ and thickness

$t=12mm.$ It is made of the AISI $4340$ steel of Table $11\mathrm{.}2$ and is subjected to a cyclic moment between $M_{\text{m}\text{i}\text{n}}=0\mathrm{.}8$ and

$M_{\text{m}\text{a}\text{x}}=4\mathrm{.}0kN*m.$ The failure occurred after $60,000$ cycles of this loading.

a$)$ Estimate the initial crack length present at the beginning of the cyclic loading.

b$)$ Identify the failure mode $($brittle fracture or plastic collapse$).$