Determine the carbon content of steel:

A hypoeutetoid steel which was cooled slowly from γ-state to room temperature was found to contain 10% eutectoid ferrite. Suppose no change in structure occurred on cooling from just below the eutectoid temperature to room temperature. Determine the carbon content of steel.

Solution

Refer to phase diagram of Figure and let the vertical line xx cross the isotherm at 5 such that 5 is at a distance x′ from temperatures axis. After that by lever rule

% total ferrite = (6.67 - x′   )/ (6.67 - 0.025) = (6.67 - x′)/6.645

% proeutectoid ferrite =  0.80 -  x′ /0.80 - 0.025          =  0.80 -  x′/0.775

            % eutectoid ferrite = % total ferrite - % proeutectoid ferrite

or         10 /100  =  6.67 -  x′ /6.645=  0.80 -  x′/0.775

 0.51, 498 = 5.169 = 0.775 x′ - 5.316 + 6.645 x′

0.51, 645 = 5.87 x′

∴          x′ =  0.51645/3.87  = 0.088%

The steel has 0.088% C.