L both increases, the pressure generated during the solidifi- cation of graphite eutectic also increases according to:
Equation 33
Where; η is the viscosity of the liquid in the mushy zone; ε is the contraction coefficient; u is the eutectic cell growth rate and fc
is the fraction of liquid.
Figure 21 schematically shows the formation of shrinkage porosity in a casting. As the cell or nodule count increases the intermixed liquid-solid path narrows down severely re- stricting liquid motion in the mushy zone. In turn this leads to internal pressure generation within the mushy zone as the liquid melt is not able to easily flow into other areas of the casting. The pressure generated in the inter-cell channels acts on the eutectic cell framework and on the solid skin lay- er of the casting causing plastic deformation. Thus, the skin dimensions tend to increase (when the mold lacks sufficient rigidity) and pre-shrinkage expansion occurs.6
The higher
the pressure in the mushy zone, the higher the expansion and the smaller the volume of liquid metal inside the casting that leads to shrinkage porosity.
The solidification pressure depends on the cell or nodule count and of the length of the mushy zone. Hence, the ex- hibited differences in the expansion tendency for the various cast irons at a given CE or Sc
can be given based on Eqn.
33. Accordingly, in flake iron, the shrinkage cavity forma- tion tendency is expected to be the lowest due to the rela- tively small cell count and length of the mushy zone. This is followed by inoculated iron (increasing cell count) and by ductile iron (highest nodule count and largest mushy zone length) in agreement with the experimental outcome.52
An
example of the influence of the cell and nodule count on the size of the shrinkage porosity is given in Figs. 22 and 23. In particular, notice that increasing the cell or nodule count53,54 is not desirable from the viewpoint of shrinkage formation and contraction in castings.
Influence of Cell and Nodule Count on the Type of Graphite
Figure 24 schematically shows the solidification process of a hypoeutectic cast iron and the exhibited correlations between the inter-lamellar graphite distance, λ and the inter-dendritic spacings, d including the type of graphite. The eutectic cells grow around in inter-dendritic spacings. It is known55
that
the inter-lamellar graphite distance, λ (i.e., the distance be- tween branches in the interconnected graphite skeleton in eutectic cells, see Fig. 1b) is related to undercooling, ∆T:
Equation 34 International Journal of Metalcasting/Summer 10 Equation 35 nodule or flake graphite count per unit secant length. Where; fgr is the volume fraction of graphite and NL is the
The λ parameter represents the diffusional distance for alloy- ing elements such as C, Si or Mn, which can lead to modifica- tions in the kinetics of the austenite transformation into ferrite, pearlite or ausferrite. Accordingly, the shorter the distance, λ, the shorter the transformation time in the solid state. For exam- ple57
Where; ξ is a material constant lation) the undercooling decreases from ∆T to ∆Ti
Taking into account Eqns. 24 and 34 it is found that as the eutectic cell count increases from N to Ni
(i.e., due to inocu- and in as a
. In the case of cast iron with similar austenite/dendrite volume fractions (similar carbon equivalent, Fig. 25 Ia,b) the inter-dendritic spacings, d are rather similar. Thus, as the cell count decreases, λ also decreases and since λ∝ d, large graphite branching skeletons are developed inside the inter- dendritic regions giving rise to D type graphite (Fig. 24 Ia). At increasing cell counts the inter-lamellar graphite distance, λ becomes relatively large (λ>>d). In turn this promotes the development of relatively small branching skeletons in the interdendritic spaces (Fig. 24 Ib) resulting in A type graph- ite. In addition, notice that in highly hypoeutectic cast iron when the austenite fraction is very large (Fig. 24Ic) the in- terdendritic distance d is small (d λ) and in consequence interdendritic graphite type E is formed independently of the cell count. Figure 25 shows the ASTM graphite size number and its relationship to cell count and graphite type.
result, the distance between graphite flakes increases from λ to λ1
Influence of Cell and Nodule Count on the Type of Matrix and Microsegregation
The nodule or flake graphite count and graphite fraction can be also related to the inter-graphite distance, λ from the Full- man equation.56
(see Fig. 26a) the starting ferritization time can be clearly correlated with the nodule count (intergraphite distance λ). As the cell count decreases, the distance λ between graphite flakes also decreases (Fig. 24Ia,b). In turn, this is equivalent to reducing the diffusion distance for carbon in austenite during the eutectoid transformation and thus conducive to the forma- tion of a ferrite matrix. In conclusion, when either the nodule or cell count decreases, the probability for the formation of a ferritic matrix increases (see Figs. 26b and 27). Notice from Fig. 27 that for a low cell count (N = 620 cm-2
), the distance
between D type graphite flakes become relatively short (Fig. 27c) and a ferrite matrix is developed in the structure (Fig. 27e). In the case of relatively large cell counts (N = 1659 cm,-2 Fig. 27b), the distances between graphite flakes become sig- nificantly large (Fig. 27d) and a pearlite matrix develops (Fig. 27f) with the corresponding increase in cast iron strength.
51
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