Question 7 of 7: Question VII: Carbon Equivalent and the Brittleness of Gray Cast Iron

Question VII: Carbon Equivalent and the Brittleness of Gray Cast Iron (15 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

7.1 — (i) Meaning of Carbon Equivalent

Cast irons are, in practice, multi-component Fe–C–Si (plus minor Mn, P, S) alloys, but the binary Fe–Fe₃C/Fe–C(graphite) diagram is drawn for only TWO components. Silicon is itself a strong graphite promoter (Section 7.3), and its effect on where the eutectic point sits is, to a good engineering approximation, equivalent to adding extra carbon — roughly one-third as effective, weight for weight. The Carbon Equivalent folds this Si contribution into a single "effective carbon content," $\text{C.E.}=\%\text{C}+\tfrac{1}{3}\%\text{Si}$, so that a MULTI-component cast iron can still be located on the simple BINARY Fe–C eutectic diagram (true eutectic at C.E.$=4.3$) as if it were a plain binary alloy. This lets a foundry engineer immediately judge, from a single number, whether a given iron composition is hypoeutectic, eutectic or hypereutectic — and hence anticipate its solidification range, fluidity and as-cast graphite morphology — without having to consult a full ternary Fe–C–Si diagram.

7.2 — (ii) Carbon Equivalent for this iron

Given. $\%\text{C}=2.5$, $\%\text{Si}=2.8$.

Find. C.E., and whether the alloy is hypoeutectic or hypereutectic.

1. Apply the C.E. formula. $$\text{C.E.}=\%\text{C}+\frac{1}{3}\%\text{Si}=2.5+\frac{2.8}{3}=\boxed{3.43}$$
2. Compare to the eutectic value. Since $\text{C.E.}=3.43<4.3$ (the eutectic C.E.), this iron's effective carbon content lies BELOW the eutectic point on the binary diagram, so the alloy is hypoeutectic.

7.3 — (iii) Graphitizing vs. carbide-stabilizing elements

Graphite-promoting (graphitizing) elements encourage carbon to precipitate as free graphite rather than remain combined as cementite — the classic example is silicon (the basis of the C.E. formula itself), with nickel, copper and aluminum acting the same way. Carbide-stabilizing (anti-graphitizing) elements do the opposite, promoting or preserving combined carbon as Fe₃C/alloy carbides and suppressing graphite formation — the classic example is chromium, with molybdenum, vanadium and manganese acting the same way.

7.4 — (iv) Why gray cast iron is brittle

Gray cast iron solidifies with a large fraction of its carbon as free graphite flakes — thin, plate-like, essentially strengthless particles distributed through the metallic (ferritic/pearlitic) matrix. Graphite has negligible cohesive strength of its own and does not bond strongly to the surrounding matrix, so each flake behaves mechanically like a pre-existing internal crack. Under tensile or bending load, the SHARP TIPS of these interconnected flakes act as severe stress concentrators, and cracks nucleate there at low applied stress and propagate readily along/between adjacent flakes. The matrix itself may be capable of some plastic flow, but fracture initiates at the flake network long before that ductility can be mobilized, so the bulk material shows very low tensile elongation (typically well under 1%) despite reasonable compressive strength (compression does not open the flake-tip cracks the same way).