Question

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.

Answer 1

34.64Gpa

Step-by-step explanation:

We can calculate the theoretical fracture strenght by,

`\sigma_m = 2\sigma_0 ((\alpha)/(\rho))^(1/2)`

Here we have,

`\sigma_0 =` Applied stress

`\rho =`Tip radius

`\alpha =` lenght of surface crack or half of the lenght of internal crack

Replacing,

`\sigma_m = 2*1200*((0.25)/(1.2*10^(-3)))^(1/2)`

`\sigma_m = 34641Mpa = 34.64Gpa`

Therefore the maximum stress at the crack tip is 34.64Gpa