The GATE Grind

GATE 2022 ME (ME1) – Question 41

Engineering Materials · Phase diagrams and heat treatment · 2 marks · Multiple choice

In Fe-Fe$_3$C phase diagram, the eutectoid composition is 0.8 weight % of carbon at 725 °C. The maximum solubility of carbon in α-ferrite phase is 0.025 weight % of carbon. A steel sample, having no other alloying element except 0.5 weight % of carbon, is slowly cooled from 1000 °C to room temperature. The fraction of pro-eutectoid α-ferrite in the above steel sample at room temperature is

  1. 0.387
  2. 0.864
  3. 0.475
  4. 0.775

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) 0.387

Explanation

A steel with 0.5% C is hypoeutectoid. Just above the eutectoid temperature the fraction of pro-eutectoid ferrite is given by the lever rule with the austenite at 0.8% C: $\frac{0.8 - 0.5}{0.8 - 0.025} = \frac{0.3}{0.775} = 0.387$.