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A plate of an alloy steel has a plane-strain fracture toughness of 50 MPa-m1/2. If it is known that the largest surface crack is 0.5 mm long, and that the value of Y is 1.1, which of the following can be said about this plate when a tensile stress of 1200 MPa is applied?
a. It is not possible to determine whether or not the plate will fracture.
b. The plate will definitely not fracture.
c. The plate will definitely fracture.

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Answer:

Option C (The plate will definitely fracture) is the correct option.

Explanation:

According to the question,

The critical stress will be:

⇒ [tex]\sigma_c = \frac{K}{Y \sqrt{\pi a} }[/tex]

By putting the values, we get

        [tex]=\frac{50}{1.1\times \sqrt{\pi\times 0.5} }[/tex]

        [tex]=1146.87 \ MPa[/tex]

So,

  • [tex]\sigma_c < \sigma_{apply}[/tex]
  • [tex]1146.87<1200[/tex]

Thus, the above is the correct response.

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