Question

A freshly annealed glass containing flaws of maximum length of 0.1 microns breaks under a tensile stress of 120 MPa. If a sample of this glass is now subjected to stress of 30 MPa, failure is found to occur after 10 days. Assuming that the specific surface energy (or fracture toughness) does not change, the average rate at which the crack has grown during the period of the test is

Answer 1

Answer:

0.16 micron per day

Explanation:

Given:

The initial crack length, a₁ = 0.1 micron = 0.1 × 10⁻⁶ m

Initial tensile stress, σ₁ = 120 MPa

Final stress = 30 MPa

now from Griffith's equation, we have

$\sigma=[\frac{G_cE}{\pi\ a}]^\frac{1}{2}$

where,

Gc and E are the material constants

now,

for the initial stage

$120=[\frac{G_cE}{\pi\ (0.1\times10^{-6}}]^\frac{1}{2}$  ........{1}

and for the final case

$30=[\frac{G_cE}{\pi\ a_2}]^\frac{1}{2}$   ............{2}

on dividing 1 by 2, we get

$\frac{120}{30}=[\frac{a_2}{0.1\times10^{-6}}]^\frac{1}{2}$

or

a₂ = 4² × 0.1 × 10⁻⁶ m

or

a₂ = 1.6 micron

Now,

the change from 0.1 micron to 1.6 micron took place in 10 days

therefore, the rate at which the crack is growing = $\frac{1.6-0.1}{10}$

or

average rate of change of crack = 0.16 micron per day