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 0.28 mm and that has a tip radius of curvature of 0.002 mm when a stress of 1430 MPa is applied.

Respuesta :

Answer:

theoretical fracture strength  = 16919.98 MPa

Explanation:

given data

Length (L) = 0.28 mm = 0.28 × 10⁻³ m

radius of curvature (r) = 0.002 mm = 0.002 × 10⁻³ m

Stress (s₀) = 1430 MPa = 1430 × 10⁶ Pa

solution

we get here theoretical fracture strength s that is express as

theoretical fracture strength  =   [tex]s_{0} \times \sqrt{\frac{L}{r} }[/tex]   .............................1

put here value and we get

theoretical fracture strength  =    [tex]1430 \times 10^6\times \sqrt{\frac{0.28\times 10^{-3}}{0.002\times 10^{-3}} }[/tex]  

theoretical fracture strength  =  [tex]16919.98 \times 10^6[/tex]  

theoretical fracture strength  = 16919.98 MPa