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8.2 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 (0.01 in.) and having a tip radius of curvature of 1.2 × 10−3 mm (4.7 × 10−5 in.) when a stress of 1200 MPa (174,000 psi) is applied.

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Answer:

34.64Gpa

Explanation:

We can calculate the theoretical fracture strenght by,

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

Here we have,

[tex]\sigma_0 =[/tex] Applied stress

[tex]\rho =[/tex]Tip radius

[tex]\alpha =[/tex] lenght of surface crack or half of the lenght of internal crack

Replacing,

[tex]\sigma_m = 2*1200*(\frac{0.25}{1.2*10^{-3}})^(1/2)[/tex]

[tex]\sigma_m = 34641Mpa = 34.64Gpa[/tex]

Therefore the maximum stress at the crack tip is 34.64Gpa

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