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External crack of length of 3.0 mm was detected on the surface of the shaft of wind turbine made from 4340 steel. The diameter of the shaft of wind turbine is equal to 32 mm. Assume the shaft is subjected to a maximum load of 50,000 N during operation and the radius of the curvature of the crack is 3 x 10-2 mm. Determine the Fracture toughness KC of the shaft Express your answer in to four significant figures. Do not include the units.

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Cricetus

Answer:

The correct answer is "[tex]K_c=6.0369 \ MPa\sqrt{m}[/tex]".

Explanation:

Given:

Maximum load,

P = 50,000 N

Crack length,

a = 3mm

or,

  = 3×10⁻³ m

Diameter,

d = 32 mm

As we know,

⇒  Maximum stress, [tex]\sigma=\frac{P}{A}[/tex]

                                      [tex]=\frac{50000}{(\frac{\pi}{4}\times 32^2)}[/tex]

                                      [tex]=62.20 \ N/mm^2[/tex]

Now,

⇒  Fracture tougness, [tex]K_c=Y \sigma\sqrt{\pi a}[/tex]

On substituting the values, we get

                                           [tex]=1\times 62.20\times \sqrt{3.14\times 3\times 10^{-3}}[/tex]

                                           [tex]=6.0369 \ MPa\sqrt{m}[/tex]

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