Modeling of manganese sulfide formation during the solidification of steel
Modeling of manganese sulfide formation during the solidification of steel
Dali You 0
Susanne Katharina Michelic 0
Gerhard Wieser 0
Christian Bernhard 0
0 Montanuniversität Leoben , Franz-Josef-Straße 18, 8700 Leoben , Austria
A comprehensive model was developed to simulate manganese sulfide formation during the solidification of steel. This model coupled the formation kinetics of manganese sulfide with a microsegregation model linked to thermodynamic databases. Classical nucleation theory and a diffusion-controlled growth model were applied to describe the formation process. Particle size distribution (PSD) and particle-size-grouping (PSG) methods were used to model the size evolution. An adjustable parameter was introduced to consider collisions and was calibrated using the experimental results. With the determined parameters, the influences of the sulfur content and cooling rate on manganese sulfide formation were well predicted and in line with the experimental results. Combining the calculated and experimental results, it was found that with a decreasing cooling rate, the size distribution shifted entirely to larger values and the total inclusion number clearly decreased; however, with increasing sulfur content, the inclusion size increased, while the total inclusion number remained relatively constant.
-
Non-metallic inclusions formed during solidification
processes can essentially influence the final product
quality. On the one hand, their presence can
negatively affect steel properties [1–3]. On the other hand,
they can contribute to a beneficial microstructure by
acting as heterogeneous nucleation sites. To combine
a preferably high steel cleanness with the creation of
specific inclusion types and sizes for microstructure
evolution, comprehensive knowledge of the inclusion
formation is needed.
A typical inclusion type that is formed in nearly
every steel grade is manganese sulfide (MnS). The
latter can lead to anisotropy of the steel matrix and
act as a possible starting point for crack formation or
corrosion [2, 3]. Apart from these negative effects, in
the field of ‘Oxide Metallurgy’ [4, 5], MnS, whether as
single-phase inclusion or together with titanium
oxides, is known to act as a potential nucleation agent
for the formation of acicular ferrite [6–8]. In addition,
the formation of MnS prevents internal cracks
resulting from the appearance of FeS and reduces hot
tearing segregation [9]. Two factors have a significant
impact on number density, size distribution, and total
amount of formed MnS: the cooling rate and the
sulfur content. Both parameters play an important
role in process control and optimization, especially
during casting, and can therefore directly affect the
final product quality. Thus, it is not surprising that
MnS formation has been extensively studied over the
last several decades.
Mathematical modeling provides a useful tool to
investigate the formation of inclusions during the
solidification of steel. Different researchers [10–13]
developed several models describing MnS formation.
MnS is normally generated from the enrichment of
Mn and S in the residual liquid during the
solidification process. Thus, it is important to consider the
microsegregation of solutes when simulating MnS
formation. Ueshima et al. [10] thermodynamically
evaluated MnS formation based on an analysis of the
interdendritic segregation. Imagumbai [11] applied a
Solidification-Unit-Cell method to calculate the mean
diameter of MnS, which depends on the cell volume,
temperature gradient, and solidification speed.
Valdez et al. [12] coupled Scheil’s model [14] and MnS
growth to predict the size evolution. In their mean
size prediction, Diederichs and Bleck [13] modified
the empirical equation from Schwerdtfeger [15] into a
function of manganese and sulfur contents, cooling
rate, and secondary dendrite arm spacing. In this
model, the concentrations of manganese and sulfur
were calculated using the model of Clyne–Kurz [16].
In total, an enhanced model covering
microsegregation, thermodynamics, and kinetics to describe the
MnS size distribution has not been published thus
far.
The present paper proposes a comprehensive model
of MnS formation during the solidification of steel. A
deeper understanding of the nucleation and growth of
manganese sulfide during the solidification of steels is
desirable to reduce, control, and even benefit from the
formation of MnS. For that purpose, the development
of a comprehensive modeling approach for inclusion
formation is continued. As a first step, a
microsegregation model linked to thermodynamic databases has
been developed [17, 18]. Second, coupled with the
proposed microsegregation model, the
thermodynamics of inclusion formation during the solidification
process has been simulated [19]. In the present case,
the modeling of inclusion formation is conducted by
simultaneously considering the kinetics,
microsegregation, and thermodynamics.
Microsegregation is estimated (...truncated)