Assuming that graphite nuclei originate prior to bulky solidification and don't originate after that time, and that the liquid immediately cools down to the eutectic temperature and maintains the eutectic isotherm once solidification starts, two equations are derived.
N
A1/2⋅r
p = K
RX
t1/3 N
A⋅t = f (X
t) / K
r D
mwhere r
p is the graphite radius; N
A, the number of graphite nodules; t, the time; X
t, the extent of primary reaction; K
R and K
r are constants as a function of various graphite concentrations; and D
m, the diffusion coefficient of carbon in the melt. The numerical calculation for cast irons with certain chemical compositions indicates that the primary graphite grows at an extremely rapid rate compared to the actual and ordinary casting. Cast iron with the composition of 3.5% C and 4.5% Si having N
A 1,000mm
−2 or more, for example, will finish its primary solidification within approximately 0.1 sec.
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