Calculating percentages of microstructures in equilibrium phase diagrams (engineering)

Question

So I have an equilibrium phase diagram of steel and I am asked to 'Calculate the proportion of pearlite in the microstructure of 0.4 wt% C steel just below the eutectoid temperature (727 °C).'

I have been using the forumlas

$Wa=\frac{Cb-Co}{Cb-Ca}$%

$Wb=100-Wa$%

$Ca=weight$% of (Carbon in this example) at the first intersection point on the eutectoid line.

$Cb=weight$% of (Carbon in this example) at the second intersection point on the eutectoid line or the bottom of the 'V'. I don't know how to explain any better sorry.

So looking at my diagram, I see that $Ca=0.022wt$% Carbon and $Cb=0.76wt$% Carbon, and $Co$ is just 0.4%.

So $Wa=\frac{0.76-0.4}{0.76-0.022}$%

$=0.487805%$%

This is where I am confused. What exactly is Wa? Is that how much ferrite/austenite/cementite that is in the pearlite then? Or how much pearlite is at that point compared to ferrite? And in any case, what does that mean Wb is?

Any help would be much appreciated. Thanks

Answer 1

Assuming you mean this phase diagram, it looks like your calculations are correct.

Based on my understanding of the diagram, at $727\ ^\circ \text{C}$, you have 100% pearlite at $C_b = 0.76\ \%C$ and 0% pearlite at $C_a=0.022\ \%C$. $W_a$ then appears to be how far $C_o$ is between $C_a$ and $C_b$, so $W_a$ should be the amount of pearlite.

The units of $C_a$, $C_b$, and $C_o$ are $\% C\ by\ mass$. That means when you calculate $W_a$ initially, you are calculating the fraction of pearlite and not the percent of pearlite. All of the $\% C\ by\ mass$ units cancel:

$$W_a=\frac{0.76\ \%C-0.4\ \%C}{0.76\ \%C - 0.022\ \%C}=\frac{{\%C}(0.76-0.022)}{{\%C}(0.76-0.022)}=0.487805\implies48.7805\%$$