Adapted from problem $8\mathrm{.}2(25$ marks$)$ Estimate the theoretical fracture strength of a brittle material if it is known that fracture occurs by the propagation of an elliptically shaped crack of length $0\mathrm{.}25$ mm and width $0\mathrm{.}025$ mm when a stress of $1200$ MPa is applied. The equation of an ellipse is

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

where a and $b$ are the radii in the $x$ and $y$ directions.