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GATE 2023 ME – Question 52

Engineering Materials · Phase diagrams and heat treatment · 2 marks · Numerical answer

A steel sample with 1.5 wt.% carbon (no other alloying elements present) is slowly cooled from 1100 °C to just below the eutectoid temperature (723 °C). A part of the iron-cementite phase diagram is shown in the figure. The ratio of the pro-eutectoid cementite content to the total cementite content in the microstructure that develops just below the eutectoid temperature is ________. (Rounded off to two decimal places)

a part of the iron-carbon phase diagram. The eutectoid point is at 0.8 wt.% C and 723 °C, the maximum solubility of carbon in ferrite is 0.035 wt.%, the austenite boundary reaches 1.7 wt.%, and cementite is at 6.7 wt.% C. The alloy of 1.5 wt.% C is marked.

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Correct answer: 0.53 to 0.55

Explanation

An alloy with 1.5 wt.% C (hypereutectoid) first forms pro-eutectoid cementite from austenite when cooled below the solvus line. Just above 723 °C, the fraction of pro-eutectoid cementite is, by the lever rule with austenite at 0.8 wt.%, $\frac{1.5 - 0.8}{6.7 - 0.8} = \frac{0.7}{5.9} = 0.1186$. The total cementite just below 723 °C (pro-eutectoid plus the cementite in pearlite), using the ferrite at 0.035 wt.%, is $\frac{1.5 - 0.035}{6.7 - 0.035} = \frac{1.465}{6.665} = 0.2198$. The ratio is $\frac{0.1186}{0.2198} = 0.54$.