the area below the curve ni ∆T≤ ∆Tm,i
(l) ( Fig. 2a). Although, ∆Tm than for the inoculated melt, ∆Tmi the curve n(l) for lm
From the graphite nucleation potential curves the following arguments on graphite nucleation can be made. Consider two melts (base and inoculated irons). For the base melt, the nucleation potential is given by the curve n(l) which is rela- tively small when compared with that for inoculated iron, ni
≤ l ≤ ∞, (0 ≤ ∆T≤ ∆Tm
). In turn, this indicates that during solidification the inoculated melt contains a higher nuclei density than the base melt.
(l) in the range lm,i
Several factors are known to influence the graphite nu- cleation potential of iron melts. Among these factors are; (a) the chemical composition, (b) the charge materials, (c) the charge sequence, (d) precondition of melts,25
(e) tem-
perature/time ratio, (f) iron handling and (g) inoculation and spheroidization practice. In addition, the presence and amount of various reaction products (i.e., Mn + S = MnS), furnace atmosphere and type of slag, type of furnace, all af- fect the graphite nucleation potential of iron melts. Since each nucleation site gives rise to a single graphite nodule or eutectic cell, the expected nodule, NV,n
Thus, the graphite nucleation potential of iron melts can be directly determined from the nodule or eutectic cell count and indirectly by the nucleation coefficients Ns
be described by the nuclei count (Eqn. 8) Nnuc = NV
count can = NV,n
. , and b.
Discussion Technological Factors
In general, the cell or nodule count depends on the melt graphite nucleation potential (metallurgical quality of liquid iron) and on the cooling rate. The effect of technological fac- tors on the cell or nodule count can be estimated26
using the
following expressions: For flake graphite cast iron:
Equation 11
The cell or nodule counts given by Eqns. (11 and 12) are given per unit volume (cm,-3
mm-3 For ductile cast iron: Equation 12
Where; the Product Log(x) = y is the Lambert function, also known as the Omega function graphically shown in Fig.4. This function can be easily determined following the instruction ProductLog[x] in the Mathematica™ program. Thus, in the above equations:
International Journal of Metalcasting/Summer 10
Equations (1-3) are used for unit conversions. Chemical Composition Effects
foundry practice where they are given per unit area cm-2 mm.-2
), this in contrast with the or
after pouring into the mold, a is the mold material ability to absorb heat, Vc
z = 0.41 + 0.93 B Moreover, Ti
or cell, NV and M is the casting modulus:
Equation 17 Equation 18 Equation 19 Equation 20
Equation 21
the casting, respectively, s is the wall thickness and d is the diameter of the cylindrical casting. The other parameters are defined in Table 1.
is the initial temperature of the cast iron just and Fc
are the volume and surface area of
for the base melt is higher (Fig. 2b) the area below ) is smaller than ≤ l ≤ ∞, (0 ≤
Where; Q and Qn
Equation 13
Equation 14
are the casting cooling rates of flake graph- ite and ductile iron, respectively at the graphite eutectic equilibrium temperature Ts.
Equation 15
Equation 16
The main indicator related to the effect of chemical com- position in cast iron is the carbon equivalent, CE = C + 0.33Si. In general, there is limited information on the rela- tion between the technological factors and the magnitude of the nucleation coefficients, Ns
available data regarding the influence of CE on Ns
and b. Table 2 gives the and b.
39
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