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11Alexandr11 [23.1K]
2 years ago
11

Alarge plate is fabricated from a steel alloy that has a plane strain fracture toughness of 82.4 MPa m1/2. If the plate is expos

ed to a tensile stress of 345 MPa during the service use, determine the minimum length of a surface crack that will lead to fracture. Assume a value of 1.0 for Y.
Physics
1 answer:
Korvikt [17]2 years ago
4 0

Answer:

minimum length of a surface crack is 18.3 mm

Explanation:

Given data

plane strain fracture toughness K = 82.4 MPa m1/2

stress σ = 345 MPa

Y = 1

to find out

the minimum length of a surface crack

solution

we will calculate length by this formula

length = 1/π ( K / σ Y)²

put all value

length = 1/π ( K / σ Y)²

length = 1/π ( 82.4 10^{3/2} / 345× 1)²

length = 18.3 mm

minimum length of a surface crack is 18.3 mm

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Taking into account the rule of three for the change of units, the mass of the book is 45600 miligrams.

First of all, the rule of three is a mathematical tool that helps you quickly solve proportionality problems.

Having three known values ​​and one unknown, a proportional relationship is established between all of them in order to find the fourth term of the proportion.

If the relationship between the magnitudes is direct (when one magnitude increases, so does the other; or when one magnitude decreases, so does the other), the rule of three is applied as follows, where a, b and c are known values ​​and x is the unknown to calculate:

a → b

c → x

So: x=\frac{cxb}{a}

Being 1 kg equivalent to 1000000 milligrams, In this case the rule of three is applied as follows: if 1 kg equals 1000000 milligrams, 4.56×10⁻² kg equals how many milligrams?

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So:

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In summary, the mass of the book is 45600 miligrams.

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