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Phase diagrams and the lever rule

A 0.40 wt% C hypoeutectoid steel is cooled under equilibrium to just below 727 °C. Which value is closest to the mass fraction of proeutectoid ferrite? Take the eutectoid composition as 0.76 wt% C, the carbon content of ferrite at 727 °C as 0.022 wt% C, and cementite as 6.70 wt% C.

  1. AAbout 0.51
  2. BAbout 0.94
  3. CAbout 0.49
Show answer and explanation

Answer: C. About 0.49

Proeutectoid ferrite is the ferrite already formed in the α + γ region just above 727 °C, and all the remaining γ becomes pearlite. From the lever rule, W_proeutectoid α = (0.76 − 0.40)/(0.76 − 0.022) = 0.36/0.738 ≈ 0.49. About 0.51 is the fraction of the remaining pearlite, the mistake of taking the opposite distance. About 0.94 is the fraction of all ferrite treating the steel as the two phases α + Fe₃C, (6.70 − 0.40)/(6.70 − 0.022), which includes the ferrite inside the pearlite as well. The area ratio of proeutectoid ferrite to pearlite in a micrograph is a clue for estimating the carbon content of a hypoeutectoid steel.

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