Question

A sample of glass has a crack of half-length 2 μm. The Young's modulus of glass is 70 GN/m² and specific surface energy is 1 J/m². The fracture strength will be
1. 885 MPa
2. 895 MPa
3. 915 MPa
4. 935 MPa

Answer 1

Correct Answer - Option 4 : 935 MPa

Concept:

According to Orawan theory of brittle fracture,

Fracture stress (σ_f) \( = \frac{1}{2}{\left[ {\frac{{E\gamma }}{C}} \right]^{\frac{1}{2}}}\)

Where, E = young’s modulus, γ = Surface energy, C = semi crack length

Calculation:

Given: E = 70 GN/m², γ = 1 J/m² and C = 2 μm

\({\sigma _f} = \frac{1}{2}{\left[ {\frac{{70 \times {{10}^9} \times 1}}{{2 \times {{10}^{ - 6}}}}} \right]^{1/2}}\)

∴ σ_f = 93.54 MPa.