Estimate the theoretical fracture strength of a brittle material if it is known that fracture occurs by the propagation of an elliptically shaped surface crack of length 0.25 mm and having a tip radius of curvature of 1.2 x 10\(^{-3}\) mm when a stress of 1200 MPa is applied.
a = 0.25 mm
\(\sigma_t \) 1.2x10\(^{-3}\) mm
\(\sigma \) = 1200 MPa
Theoretical fracture strength
\(\sigma_m\) = theoretical fracture strength for a given crack length and radius of curvature
\( \sigma_m \) = \( 2 \sigma_0 {\left({a \over \rho_t}\right)}^{1 \over 2} \)
\( \sigma_m \) = \(2 (1200 MPa) {\left({0.25 mm \over 1.2x10^{-3} mm}\right)}^{1 \over 2} \)
\( \sigma_m \) = 34.6 GPa