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 0.5 mm (0.02 in.) and a tip radius of curvature of 5 × 10–3 mm (2 × 10–4 in.), when a stress of 1035 MPa (150,000 psi) is applied.

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cjmejiab cjmejiab · Answer 1 · 2019-11-06T01:30:57+01:00

Answer:

20700Mpa

Explanation:

We need to find the strenght at the point where can reach a fracture, that is through the equation,

[tex]\sigma_m = 2\sigma_0 (\frac{a}{\rho_1})^(1/2)[/tex]

Where

[tex]\sigma_m[/tex] = Normal stress

a= Either lenght of the internal crack or lenght of surface crack

Substituting the values:

[tex]\sigma_0 = 1035Mpa\\a=0.5mm\\\rho_1 = 5*10^{-3}[/tex]

[tex]\sigma_m = 2(1035)(\frac{0.5}{5*10^{-3}})^(1/2)\\\sigma_m = 20700Mpa[/tex]

That is the fracture strenght of brittle material at crack tip