A component in the shape of a large sheet is to be fabricated from $7075-$T$651$ aluminum, which has

fracture toughness K$\_($c$)=24\mathrm{.}2$MPa$-$m$^(0\mathrm{.}5)$ and a tensile yield strength of $490$ MPa $.$

PartA

Determine the number of loading cycles that can be endured if the nominal stress varies from $0$ to $0\mathrm{.}5$ the yield strength and the initial crack had a total length of $2$ mm $.$ The values of the coefficient and exponent for this material are

A$=5*10^(-11)(($mm$)/($cycles$))/[$MPa$^$n $*$ m$^($n$/2)]$ and n$=4.$

Express your answer using three significant figures.

N$\_($c$)=$