Question

If the specific surface energy for magnesium oxide is 1.0 J/m2 and its modulus of elasticity is (225 GPa), compute the critical stress required for the propagation of an internal crack of length 0.8 mm.

Answer 1

critical stress required is 18.92 MPa

Step-by-step explanation:

given data

specific surface energy = 1.0 J/m²

modulus of elasticity = 225 GPa

internal crack of length = 0.8 mm

solution

we get here one half length of internal crack that is

2a = 0.8 mm

so a = 0.4 mm = 0.4 ×
`10^(-3)` m

so we get here critical stress that is

`\sigma _c = \sqrt{(2E \gamma )/(\pi a)}` ...............1

put here value we get

`\sigma _c` =
`\sqrt{(2* 225* 10^9 * 1 )/(\pi * 0.4* 10^(-3))}`

`\sigma _c` = 18923493.9151 N/m²

`\sigma _c` = 18.92 MPa