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The lower yield point for an iron that has an average grain diameter of 5 × 10–2 mm is 135 MPa (19,500 psi). At a grain diameter of 8 × 10–3 mm, the yield point increases to 260 MPa (37,500 psi). At what grain diameter will the lower yield point be 205 MPa (30,000 psi)?

Answer :

Answer:

The grain diameter is 0.01477 mm.

Explanation:

Detailed steps are below.

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The grain diameter at which the lower yield point will be 205 MPa is; d = 0.01476 mm

We are given;

Lower yield point for first case; σ_y = 135 MPa

Grain diameter for first case; d = 5 × 10^(-2) mm = 0.05 mm

Lower yield point for second case; σ_y = 260 MPa

Grain diameter for second case; d = 8 × 10^(-3) mm = 0.008 mm

Now, formula for lower yield point is;

σ_y = σ_i + (k_y × d^(-½))

Thus;

For first case, we have;

135 = σ_i + (k_y × 0.05^(-½))

135 = σ_i + 4.472k_y - - - (eq 1)

For second case, we have;

260 = σ_i + (k_y × 0.008^(-½))

260 = σ_i + 11.18k_y - - - (eq 2)

Solving eq 1 and 2 simultaneously gives;

σ_i = 51.67 MPa

σ_i = 51.67 MPak_y = 18.63 MPa/√mm

Now, from the formula σ_y = σ_i + (k_y × d^(-½)) , we can make d the subject to get;

d = (k_y/(σ_y - σ_i))²

Thus, at σ_y = 205 MPa, we have;

d = (18.63/(205 - 51.67))²

d = 0.01476 mm

Read more at; https://brainly.com/question/18883205

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