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 0.25 mm (0.01 in) and tip radius of curvature of 1.2 x 10-3 mm (4.7 x 10-5 in.) when a stress of 1200 MPa (174,000 psi) is applied.

Answer 1

the theoretical fracture strength of the brittle material is 5.02 × 10⁶ psi

Step-by-step explanation:

Given the data in the question;

Length of surface crack α = 0.25 mm

tip radius ρ
`_t` = 1.2 × 10⁻³ mm

applied stress σ₀ = 1200 MPa

the theoretical fracture strength of a brittle material = ?

To determine the the theoretical fracture strength or maximum stress at crack tip, we use the following formula;

σ
`_m` = 2σ₀
`(` α / ρ
`_t`
`)^{(1)/(2)`

where α is the Length of surface crack,

ρ
`_t` is the tip radius,

and σ₀ is the applied stress.

so we substitute

σ
`_m` = (2 × 1200 MPa)
`(` 0.25 mm / ( 1.2 × 10⁻³ mm )
`)^{(1)/(2)`

σ
`_m` = 2400 MPa ×
`(` 208.3333
`)^{(1)/(2)`

σ
`_m` = 2400 MPa × 14.43375

σ
`_m` = 34641 MPa

σ
`_m` = ( 34641 × 145 )psi

σ
`_m` = 5.02 × 10⁶ psi

Therefore, the theoretical fracture strength of the brittle material is 5.02 × 10⁶ psi