Question

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 1

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

Step-by-step explanation:

Given that,

Length = 0.54 mm

Radius curvature
`R=3.4*10^(-3)\ mm`

Stress = 1050 MPa

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

Using formula of strength

`\sigma_(m)=2\sigma_(0)((l)/(\rho_(t)))^{(1)/(2)}`

Where, l = length of the crack

`\rho_(t)`= tip radius of curvature

Put the value into the formula

`\sigma_(m)=2*1050*((0.54)/(3.4*10^(-3)))^{(1)/(2)}`

`\sigma_(m)=26465.29\ MPa`

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