Question

If S is the applied stress, c is the width of the crack and r the radius of curvature at the tip of the crack, Griffith’s crack theory gives the concentrated stress S_c as
1. 2 S (c/r)^1/2
2. 2 S (c/r)^1/3
3. S (c/r)^1/2
4. 2 S (2c/r)^1/2

Answer 1

Correct Answer - Option 1 : 2 S (c/r)^1/2

Explanation:

According to Griffith’s theory a crack will propagate when the decrease in elastic energy is at least equal to the energy required to create the new crack surface.

According to the Griffith Crack theory

\({{S}_{c}}=2S{{\left( \frac{c}{r} \right)}^{\frac{1}{2}}}\)

Where, S_c is the stress at crack tip, S is the applied stress, r = radius of curvature at crack tip and c is the width of crack.