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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 0.54 mm and having a tip radius of curvature of 3.4 × 10−3 mm when a stress of 1050 MPa is applied

Answer :

Answer:

The theoretical fracture strength of a brittle material is 26465.29 MPa.

Explanation:

Given that,

Length = 0.54 mm

Radius curvature [tex]R=3.4\times10^{-3}\ mm[/tex]

Stress = 1050 MPa

We need to calculate the theoretical fracture strength of a brittle material

Using formula of strength

[tex]\sigma_{m}=2\sigma_{0}(\dfrac{l}{\rho_{t}})^{\frac{1}{2}}[/tex]

Where, l = length of the crack

[tex]\rho_{t}[/tex]= tip radius of curvature

Put the value into the formula

[tex]\sigma_{m}=2\times1050\times(\dfrac{0.54}{3.4\times10^{-3}})^{\frac{1}{2}}[/tex]

[tex]\sigma_{m}=26465.29\ MPa[/tex]

Hence, The theoretical fracture strength of a brittle material is 26465.29 MPa.

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