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

Answer:

critical stress required is  18.92 MPa

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

$\sigma _c = \sqrt{\frac{2E \gamma }{\pi a}}$     ...............1

put here value we get

$\sigma _c$ =   $\sqrt{\frac{2\times 225\times 10^9 \times 1 }{\pi \times 0.4\times 10^{-3}}}$

$\sigma _c$ =  18923493.9151 N/m²

$\sigma _c$ =   18.92 MPa