The effect of melt composition on solidification cracking of steel, with particular reference to continuous casting
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I.
INTRODUCTION
CERTAIN features of solidification cracking have been apparent for some time, 1,2,3including the role of the freezing contraction in setting up tensile stresses and the importance of microsegregation in producing solute-enriched liquid of low melting point in the form of interdendritic films. More recent studies 4'5'6 have led to the development of cracking models allowing prediction of the effect of variables such as solute level in binary alloys. Treatment of multi-component systems is more complicated and description of the solute redistribution has been limited to (nonferrous) alloys in which the Scheil equation gives a good approximation. Partly as a result of these factors, the importance of alloy constitution in cracking of steels remains to be explained clearly, despite extensive study7'8'9 and commercial interest. The susceptibility of steels to solidification cracking appears to be quite strongly dependent on the C level, 7'1~ particularly in the range up to about 0.3 C (All solute levels are given in wt pct.) Attributing this to the (0.3 pct) volume contraction associated with 6-3' phase transformation 12 is very unsatisfactory. 3'11 Furthermore, it has long been suspected that back-diffusion of carbon during solidification of steels is sufficiently rapid to eliminate effectively concentration gradients in the solid, so that microsegregation of carbon would be negligible and could not be invoked directly to explain the variations in cracking behavior. Back-diffusion has been described by the Brody and Flemings model, ~3 in which the parameter a is given by
4D ,t/ a =
A2
[1]
where 1 / 2 is a characteristic microsegregation distance. (The value of A should be taken as the secondary dendrite arm spacing, over which diffusional processes control the solute enrichment of interdendritic liquid for a typical cast structure.) The analysis breaks down, however, when solid state diffusion is relatively rapid and a modified model has recently been presented by Clyne and Kurz 14to quantify the effect of back-diffusion over the whole range (a = 0-~ 0% T.W. CLYNE is Lecturer, Department of Metallurgy and Materials Technology, University of Surrey, Guildford, England; M. WOLF is Manager, Process Technology, Concast AG, CH 8027, Ztirich, Switzerland; and W. KURZ is Professor, Department of Materials Engineering, Swiss Federal Institute of Technology, CH 1007, Lausanne, Switzerland. Manuscript submitted June 29, 1981. METALLURGICALTRANSACTIONS B
A new back-diffusion parameter, 12, is in this case calculated from the equation 12 = a ( 1 - e x p ( -
1
l/a)) - ~exp(- I/2a)
[2]
The microsegregation in a binary system (with partition coefficient k) is then characterized by the following expressions C~ = k Co[l - (1 - 212k)f,] (k-')/('-mk)
[3]
An example of the use of Eq. [4] is given in Figure 1, which shows the family o f f , / T curves corresponding to a range of a values for Fe-I.0C. In practice, estimates of for C in steel, while depending on the details of the cooling conditions, would normal
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