4.3. Contribution of MnS to Grain Refinement
Controlling the S content is the key to decreasing the MnS inclusion size and improving their morphology, mitigating the bad influence of sulfide and, indeed, changing MnS into a favorable second phase.
Zener [
22] first gave the basic quantitative principle of the second-phase particles in steel that could prevent the austenite grain coarsening. Gladman [
23] developed a theoretical model of the energy changes accompanying grain boundary movement, which was dependent on the volume fraction and the size of second phase particles.
where
is the average equivalent diameter of grain, and
d and
f are the mean diameter and volume fraction of second phases, respectively. Moreover,
Z is the factor of grain size. Austenite grains are coarse and uniform in the holding process. Hence, the value of Z can be taken as 1.7 [
16].
The volume fraction of MnS can be approximated by the following equations.
where
and
are the atomic weights of Mn and S elements, respectively.
Equation (29) is known as the formula for solving the mass percentage of MnS.
where
and
are the densities of Fe and MnS, respectively.
Mn is the main controlled element during MnS precipitation [
16]. Equations (30) and (31) give the diffusion coefficients of Mn elements in the δ-ferrite and austenite, respectively.
By replacing −1.28994 in Equation (23) with
, the curve of temperature-sedimentation completion time (t0.95) can be obtained. At 70 and 20 ppm sulfur contents, the precipitation temperatures of MnS are much lower than the soaking temperature. Hence, the completion time of MnS transition at 1200 °C must be calculated to estimate the pinning effect of MnS. Referring to
Figure 12, the completion times of MnS transition are estimated to be 250, 150, 40, and 4 s for 380, 150, 70, and 20 ppm S content, respectively.
Equation (32) is the formula for calculating the radius of the precipitate. As the diffusivity of Mn is lower than that of S in δ-ferrite and austenite, diffusion of Mn is assumed to be the controlled element for MnS precipitation.
where
is the rate constant with a typical value of 0.123 [
16]. By combining Equations (30) to (32), the radius of MnS can be deduced. When the S content varied from 20, 70, 150, to 380 ppm, the radius of MnS is 0.01, 0.50, 1.41, and 4.02 μm, respectively. With the decrease of S content, favorable nanoscale MnS can be obtained, as shown in
Figure 10.
Table 6 lists the values of various parameters of MnS at 1150 °C. There seems to be a significant difference between the calculated values of equivalent diameters (especially for 20 and 70 ppm S) and the experimental one shown in
Figure 4. This is because the results in
Figure 4 were measured by an automatic inclusion analysis system that only detects inclusions larger than ca. 1 μm in size, but not the nanoscale MnS, while the equivalent diameters in
Table 6 are calculated theoretically by including both micrometer-scale and nanoscale MnS particles. Since the samples with 20 and 70 ppm S contain a larger number of precipitated nanoscale MnS particles, the measured inclusion equivalent diameter and calculated results appear very different. For the samples with 150 and 380 ppm S, there was nearly no nanoscale MnS precipitating and, thus, the measured results and calculations are in much better agreement.
As mentioned before, the pinning effect is closely correlated with the volume fraction and the equivalent diameter of the second phases.
Table 6 shows that MnS can pin the boundary of austenite effectively and refine the austenite grain. At 20 ppm sulfur content, MnS also has a strong pinning effect, even though its volume fraction is very small. This is because with a reduction of S content, the diameter of MnS is significantly reduced. Clearly, the weak pinning is no longer working when the S content is high.
In Equations (33) through (34), considering the rolling system in
Figure 1, one can calculate the final ferrite grain size after the rolling schedule.
where
,
,
, and
stand for rolling reductions, final ferrite grain size after rolling cooling, austenite grain sizes prior to deformation, and deformation temperature. The values of
a,
b,
c,
A, and
B are taken as 90, 0.7, 0.027, 7.5, and 15, respectively [
24].
can be obtained using Equation (33), and it is the ferrite grain size after the first pass. Substituting this value in Equation (34), one can solve for , which is regarded as the austenite grain size of the second pass. Finally, Equation (33) is used again.
Figure 13 shows the relationship between the final ferrite grain size and different sulfur contents with the same rolling schedule. To better analyze the pinning effect of MnS, the calculation ignores the influence of (Ti, Nb)(C, N) particles. This is the main cause of the difference between the measured and predicted values. With the increase of sulfur content, this difference decreases gradually, which indicates that the pinning effect of MnS also gradually decreases to zero, as shown in
Table 6.