$(10$ points$)$ A structural component in the shape of a flat plate $26\mathrm{.}4$ mm thick is to be fabricated from a metal alloy for which the yield strength and plane strain fracture toughness values are $600$ MPa and $30$MPa$-m\frac{l}{2},$ respectively. For a particular geometry, the value of Y is $1\mathrm{.}3.$ Assuming a design stress of $0\mathrm{.}4$ times the yield strength, calculate the critical length of a surface flaw.