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A cast iron bed plate for a pump has a crack length of 100. µm. If the Young’s modulus of cast iron is 210 GN/m2 and the specific surface energy is 10 J/m2, the fracture strength required will be nearly (a) 1.0 × 108 N/m2 (b) 1.2 × 108 N/m2 (c) 1.4 × 108 N/m2 (d) 1.6 × 108 N/m2 |
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Answer» Correct option is (d) 1.6 × 108 N/m2 Crack length = 2c = 100 µm E = 210 GN/m2 = 210 × 109 N/m2 Surface energy, γ = 10 J/m2 According to Griffith’s theory of brittle fracture, Fracture strength, σ = \(\left(\cfrac{2Eγ}{\pi c}\right)^{1/2}\) = \(\left[\cfrac{2\times(210\times10^9)\times10}{\pi\times50\times10^{-6}m}\right]^{1/2}\) = 1.6 × 108 N/m2 |
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