PROBLEM $9\mathrm{.}1$

A randomly oriented, short$-$fiber$-$reinforced composite plate having a

central through$-$thickness crack of length $2a$ is subjected to a uniaxial

stress $,$ as shown in Figure $9\mathrm{.}1.$ If the composite has a fracture toughness

$K_{Ic}=50MPa{m}^{\frac{1}{2}}$ and the applied stress $=200$MPa, determine the critical

crack size, $a_c$ for unstable and catastrophic crack growth.

FIGURE $9\mathrm{.}1$

Griffith crack: a through$-$thickness crack in a uniaxially stressed plate of infinite width.