1. Introduction
Non-metallic inclusions have a significant influence on the performance of steels [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10]]. The investigation of non-metallic inclusions in steels has been reported since 1905 [11] when the morphology of an inclusion was published. Studies mainly focused on the variation of inclusions in the molten steel during the steelmaking, refining, and continuous casting (CC) processes. Many operation approaches were widely developed to achieve the formation, modification, and removal of inclusions, including deoxidation [[12], [13], [14]], calcium treatment [[15], [16], [17], [18], [19], [20]], slag refining [[21], [22], [23], [24], [25], [26], [27]], vacuum refining [28,29], argon blowing [30], and prevention against reoxidation [[31], [32], [33], [34]], etc. Recent attentions were paid to the transient evolution of inclusions in the steel [[35], [36], [37], [38], [39], [40]], especially for the transformation of inclusions from the molten steel to the solid steel during solidification, cooling or heating [[41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52]]. The transformation of oxide inclusions during the cooling and heating process were mainly caused by the crystallization [47], precipitation [50,51,53,54], and reaction [55,56] of inclusions. It was reported that inclusions were transformed from CaO-Al2O3 to CaS-Al2O3 during the CC of Al-killed Ca-treated steels [41].
Reported mathematical models mainly focused on the prediction of the number and size of inclusions in the liquid steel during nucleation, collision, and removal [[57], [58], [59]]. In the last decade, a few mathematical models were developed to predict the spatial distribution of the size and number of inclusions on the cross-section of CC products, considering turbulent flow, heat transfer and solidification of the molten steel, the transport, removal and entrapment and inclusions [[60], [61], [62]]. Kinetic models were developed to predict the composition evolution of inclusions in the molten steel during refining process considering interaction reactions of steel-slag-inclusion-alloy-refractory-air [[63], [64], [65], [66], [67], [68], [69], [70], [71], [72]]. The distribution of inclusion size and number in the slab was experimentally investigated in several studies [44,73,74]. However, few investigations on the distribution of the composition of inclusions in CC products were reported.
In the current study, the transformation in the composition of inclusions from the molten steel to the solidified steel was investigated through industrial trials and thermodynamic calculations. A model was established to predict the distribution of the composition of inclusions on the entire cross section of a linepipe CC slab, coupling heat transfer of the continuous casting slab, the kinetic mass transfer of the dissolved elements in the steel, and thermodynamic calculation of inclusion transformation at different temperatures.
2. Industrial trials and investigation methodology
The linepipe steel was produced through a route of Basic Oxygen Furnace (BOF)→Ladle Furnace (LF)→ Ruhrstahl-Hereaeus (RH)→Ca treatment→CC. During BOF tapping, aluminum was added for the deoxidation of steel. The high basicity slag was used to enhance the deoxidation and desulfurization during steel refining. After the RH vacuum treatment, the calcium wire was injected to modify rigid Al2O3 inclusions into liquid CaO-Al2O3 ones. Molten steel samples were taken at the CC tundish, and solid steel samples were taken along the thickness of the CC slab with a dimension of 1450 mm × 230 mm. The pouring temperature was 1812 K and the casting speed was 1.3 m/min. The liquidus and solidus of the steel were 1784 K and 1759 K, respectively, and the latent heat of solidification was 271,954 J/kg. The CC mold has an 0.8 m effective length of the CC mold and was water-cooled. The schematic of the entire CC slab cooling process is shown in Fig. 1. The spray zone length was sub-divided into eight regions for the flexibility of the cooling, and dimensions and water flow rates each cooling zone are listed in Table 1. Zones 9 and 10 were under air cooling.
Fig. 1.
Fig. 1.
Dimension of the cooling zones of the entire CC slab.
Table 1 Data of the secondary cooling zones used in the current simulation.
| Spray zone | Length (m) | Water flow rate (L/(m2 min)) |
|---|---|---|
| 1N | 0.7 | 68.0 |
| 1IO | 0.24 | 292.8 |
| 2IO | 0.56 | 432.1 |
| 3IO | 1.11 | 502.6 |
| 4IO | 1.56 | 407.7 |
| 5IO | 1.92 | 294.4 |
| 6I | 3.84 | 180.2 |
| 6O | 270.2 | |
| 7I | 3.84 | 102.8 |
| 7O | 174.8 | |
| 8I | 6.70 | 122.5 |
| 8O | 245.0 | |
| Total | 19.77 | 3093.1 |
Note: N is the narrow face, I is the loose side and O is the fixed side of the wide face of the CC slab.
A certain amount of inclusions in steel samples were detected with an automated SEM/EDS inclusion analysis to achieve statistic data in the number, size, composition, morphology and spatial location of inclusions. Ten samples of S1-S10 from the loose side to the fixed side were machined into 10 mm × 23 mm × 15 mm cuboids, as illustrated in Fig. 2 where inclusions on the shaded surface of each sample were detected. The total aluminum (Alt), the total magnesium (T.Mg), and the total calcium (T.Ca) of the steel were analyzed using inductively coupled plasma emission spectrometry (ICP), the total oxygen (T.O) of the steel was analyzed using a Leco analyzer, and other chemical compositions of the steel were measured using a spark OES.
Fig. 2.
Fig. 2.
Sampling locations along the thickness of the CC slab.
3. Results and discussion
3.1. Inclusions in steel samples
Fig. 3 shows the size, number density and composition of inclusions in the steel of the CC tundish and the CC slab. Isolines of 100 % and 50 % liquid phase in CaO-Al2O3-CaS and CaO-Al2O3-MgO phase diagrams at 1873 K were calculated using FactSage with the database of FToxid and FactPS. The size of circles shows the diameter of inclusions. In Fig. 3(a), inclusions before the solidification and cooling process were mainly CaO-Al2O3 ones close to the target composition of inclusions. In Fig. 3(b), the composition of inclusions on the surface of the slab moved to Al2O3-CaS and Al2O3-MgO lines, and the average composition was near the 50 % liquid line at 1873 K. In Fig. 3(c), the average composition shifted from liquid Al2O3-CaO to solid Al2O3-MgO-CaS. The number density of inclusions increased from the tundish to the slab due to the new precipitated CaS particles.
Fig. 3.
Fig. 3.
Distribution of the composition, size and number of inclusions of (a) the molten steel in tundish, (b) Sample S1 of slab, (c) Sample S5 of slab.
The elemental mapping of inclusions is shown in Fig. 4. The inclusion in the steel of the CC tundish was CaO-Al2O3 with a little MgO and CaS, while the inclusion in the slab was composed of a MgO-Al2O3 core covering with a CaS layer. The average composition of the steel is listed in Table 2. The similar steel composition in the tundish and the slab implied that the transformation in the composition of inclusions was mainly caused by the inclusion/steel reaction.
Fig. 4.
Fig. 4.
Elemental mapping of inclusions in (a) the molten steel of tundish and (b) the CC slab.
Table 2 Chemical compositions of the linepipe steel in the current study.
| Sample | C (%) | Si (%) | Mn (%) | Alt (%) | T.S (ppm) | T.Ca (ppm) | T.Mg (ppm) | T.O (ppm) |
|---|---|---|---|---|---|---|---|---|
| Tundish | 0.069 | 0.204 | 1.65 | 0.042 | 12 | 10 | 3 | 13 |
| Slab | 0.070 | 0.200 | 1.65 | 0.037 | 12 | 8 | 3 | 15 |
The spatial distribution of Al2O3, MgO, CaO, and CaS in inclusions along the thickness of the slab is shown in Fig. 5. Inclusions in the center of the slab were mainly CaS-Al2O3-MgO ones with little CaO while they were Al2O3-CaO-CaS ones within the subsurface of the CC slab. The variation of inclusions along the thickness of the slab stemmed from the varied cooling rate at different locations of the CC slab. The average feature of inclusions in the number density, composition and area fraction in the slab is shown in Fig. 6. The CaS content of inclusions at slab surface was obviously lower than that of the slab center, showing an opposite tendency of the CaO content of inclusions. Contents of MgO and Al2O3 in inclusions was slightly higher at the center of the slab. The number density of >1.5 μm inclusions showed a uniform distribution while >10 μm particles tended to accumulate at the center and the inner radius of the slab. It has been reported that at the initial solidification period, the distance between dendrite arms only provided a space for smaller inclusions while the approaching larger inclusions were pushed to the center of the slab [60], leading to the accumulation of large inclusions in slab center. The area fraction of inclusions in the center of the slab was higher than the surface, the same as the distribution of large inclusions.
Fig. 5.
Fig. 5.
Statistic composition contours of inclusions along the thickness of the CC slab: (a) MgO, (b) Al2O3, (c) CaO, (d) CaS.
Fig. 6.
Fig. 6.
Distribution of inclusions in slab: (a) Al2O3, MgO, CaO, and CaS contents in inclusions, (b) Number density of inclusions, (c) area fraction of inclusions, (d) number density of large inclusions (> 10 μm).
3.2. Thermodynamic calculation for the transformation of inclusions
The transformation in the composition of inclusions in the current linepipe steel with temperature was calculated using the module of Equilib of FactSage with the databases of FactPS, FToxid, and FSstel [75], and is shown in Fig. 7. In the molten steel, inclusions were liquid Al2O3-CaO ones. At the temperature between the liquidus and solidus of the linepipe steel, liquid inclusions were converted to solid CaO·Al2O3, MgO·Al2O3, and CaS ones. With the further decrease of temperature, oxide inclusions transformed from CaO·Al2O3 to CaO·2Al2O3 to CaO·2MgO·8Al2O3 and the amount of CaS gradually increased. The average content of Al2O3, MgO, CaO, and CaS in inclusions is shown in Fig. 7(b). With the temperature decreasing from 1800 K to 1600 K, the CaO in inclusions remarkably decreased and Al2O3, MgO, and CaS in inclusions increased. Inclusions were varied from Al2O3-CaO to CaS-Al2O3-MgO-(CaO), agreeing with the observed result. The transformation of inclusions with temperature was mainly caused by the variation of the reaction equilibrium between the steel and inclusions with temperature. In Fig. 7(c), the calculated and the measured average composition of inclusions in samples S1-S10 were compared. The calculation showed that the content in inclusions remarkably decreased with the decrease of temperature from 1800 K to 1600 K and the contents of Al2O3, MgO, and CaS rose up. The measurement indicated that inclusions in the molten steel of the CC tundish were mainly liquid Al2O3-CaO ones, and after solidification and cooling process of the steel, inclusions in the center of the slab were transformed to Al2O3-MgO-CaS due to the lower cooling rate, showing a similar tendency with calculation. The transformation of inclusions within the subsurface of the slab was less than that in the center due to the larger cooling rate at the slab surface.
Fig. 7.
Fig. 7.
Calculated transformation in the composition of inclusions in the linepipe steel during solidification and cooling process. (a) Phases, (b) Average composition, (c) Comparison between the calculation and the measurement.
3.3. Kinetic prediction of spatial distribution of composition of inclusions in the slab
A model was developed to predict the composition distribution of inclusions on the cross section of the CC slab. The schematic of the model is illustrated in Fig. 8. Industrial parameters, such as casting speed, slab size and cooling conditions were included. The three-dimensional cooling rate of the CC slab was calculated using a heat transfer and solidification model, as described elsewhere [76,77]. The equilibrated composition of the steel and the inclusion with temperatures were calculated using the software FactSage. The mass transfer of the dissolved elements in the steel was calculated using a kinetic model. The temperature of the key parameter that joined the kinetic diffusion, thermodynamic transformation and heat transfer phenomena together.
Fig. 8.
Fig. 8.
Schematic of the scheme of the coupled model to predict the transformation in the composition of inclusions in the steel slab during the CC process.
Fig. 9 shows the thermal history of steel samples S1-S10. Curves for the surface showed a sharp temperature decreased from the mold to the spray cooling zone-3. The temperature slightly increased in subsequent spray cooling zones since the heat supplied from the central portion of the liquid was greater than the heat removed from the surface by the spray water. The temperature at the slab center gradually decreased to the final solidification point due to the slow heat transfer. Simulated temperature curves during the CC process were used in the kinetic and thermodynamic coupling model to simulate the transformation in the composition of inclusions.
Fig. 9.
Fig. 9.
Thermal history of steel slab samples S1-S10 during the CC process.
The main reactions between inclusions and the linepipe steel matrix responsible for the transformation of inclusions from Al2O3-CaO to Al2O3-MgO-(CaO) and CaS during the solidification and cooling process main reactions are proposed in Eqs. (1)-(8). A kinetic model for the transformation was developed and solved using Matlab, as shown in Fig. 10. The transformation of inclusions was divided into the following steps: (1) The temperature at different spatial locations varied during the CC process. (2) Elements of Al, Mg, Ca, S, and O were transferred between the bulk steel and the steel/inclusion interface through diffusion with diffusion rates given by Eq. (9). (3) Elements at the steel/inclusion interface reacted with the inclusion. Local equilibrium between the steel and the inclusion at the interface was recalculated at each time step of 0.15 s. The equilibrium value of the mass percentage of elements in the interface was calculated using FactSage [75].
where [%i] is the mass percentage of element i (Al, Mg, Ca, S, or O) in the steel matrix, D is diffusivity, m2/s; r is the radius of the inclusion, m; and ρsteel is the density of the steel, kg/m3.
Fig. 10.
Fig. 10.
Schematic of the kinetic model of for the composition transformation of inclusions during solidification and cooling processes of the steel.
It was assumed that inclusions were spherical and 2.7 μm in size based on the measured average inclusion diameter and the transformation was controlled by the diffusion of elements between the steel matrix and inclusions with diffusivities listed in Table 3 [[78], [79], [80]]The local equilibrium held at the steel-inclusion interface and each inclusion transformed independently with little overlap diffusion field; The density of Al2O3-CaO inclusions was 2700 kg/m³ and the initial composition of the linepipe steel matrix is given in Table 2.
| Element | Liquid steel | Δ steel | Γ steel |
|---|---|---|---|
| Al | 3.5 × 10-09 | 5.9×exp(-241186/(RT))/10000 | 5.15×exp(-245800/(RT))/10000 |
| Mg | 3.5 × 10-09 | 0.76×exp(-224430/(RT))/10000 | 0.055×exp(-249366(RT))/10000 |
| Ca | 3.5 × 10-09 | 0.76×exp(-224430/(RT))/10000 | 0.055×exp(-249366/(RT))/10000 |
| S | 4.1 × 10-09 | 4.56×exp(-214639/(RT))/10000 | 2.4×exp(-223426/(RT))/10000 |
| O | 2.7 × 10-09 | 0.0371×exp(-96349/(RT))/10000 | 5.75×exp(-168454/(RT))/10000 |
Fig. 11 shows the calculated evolution in the composition of inclusions in samples S1-S10 during the solidification and cooling processes of the CC slab. When the diffusion of elements was ignored, the reaction between the inclusion and the steel was only caused by variation of the reaction thermodynamic equilibrium with temperature, as shown in Fig. 11(a), indicating a wrong uniform composition along the thickness of the slab. The predicted composition of inclusions transformed from Al2O3-CaO to Al2O3-MgO-CaO-CaS and the transformation with slab subsurface was much faster than that in the slab center due to the varied cooling rate. As shown in Fig. 11(b), with the consideration of the element diffusion, Inclusions were transformed from Al2O3-CaO to Al2O3-MgO-CaO and CaS, and the composition with slab subsurface was close to the initial inclusion composition in the molten steel of the CC tundish due to the local higher cooling rate.
Fig. 11.
Fig. 11.
Calculated evolution in the composition of inclusions in steel samples S1-S10 during solidification and cooling processes: (a) without consideration of element diffusion, (b) with consideration of element diffusion.
The transformation fraction of inclusions is given by Eq. (10) which was proposed as the ratio of the CaS percentage in final slab to the equilibrated CaS content at room temperature calculated using FactSage. With the subsurface of the slab, the transformation of inclusions occurred earlier while the transformation fraction of inclusions was lower, showing an opposite tendency with that in the center of slab. Variation in the composition of inclusions at the fixed side and the loose side of the slab was in similar value.
where (CaS) final is the percentage of CaS in inclusion, (CaS)equ with a value 46.7 %is the equilibrated CaS content in inclusion at the room temperature.
Comparing with the calculated temperature curves in Fig. 9, the transformation in the composition of inclusions mainly occurred at the temperature between the liquidus and solidus of the steel. To further validate the accuracy of the current prediction model, the measured and predicted compositions and the transformation fraction of inclusions in the final slab are shown in Fig. 12. Without the consideration of element diffusion implying only thermodynamic phenomena considered, the predicted composition of inclusions was very different from the experimental measurement. With the consideration of element diffusion, the predicted composition of inclusions agreed well with the measured ones. Contents of MgO and Al2O3 in inclusions varied little while the CaS content in inclusions obviously increased up with a consumption of CaO during CC processes. The transformation fraction of inclusions on the fixed side was slightly lower than that for the loose side due to the uneven cooling intensity of the slab during the actual CC process. The predicted transformation fraction of inclusions within the subsurface of the slab was much lower than that of the slab center, which was generally the same as the experimental measurement. The current model can be used to predict the local transformation in the composition of inclusions during the CC process so that the distribution of the composition of inclusions on the cross section of the slab can be predicted.
Fig. 12.
Fig. 12.
Comparison of measured and calculated composition (a) and transformation fraction (b) of inclusions in the CC slab.
To better understand the transformation of inclusions in the steel during the CC process, the evolution of the temperature and the composition of inclusions on an entire cross section of the cc slab were simulated. Fig. 13 shows simulated temperature profiles of the cross section of the slab during the CC process. The temperature distribution at the typical cross section of the mold outlet (0.8 m), zone 4 (4.6 m), zone 6 (10.4 m), and zone 8 (20.9 m) was outputted. The temperature decrease in the center of the slab was much lower than that on the slab surface. On the cross section at 20.9 m from the meniscus, the slab was fully solidified. The corresponding transformation fraction of inclusions in the slab is shown in Fig. 14. The transformation of inclusions in the mold mainly occurred within the subsurface of the CC slab, especially on the wide surface. On the cross section at the outlet of zone 4, the transformation fraction of inclusions on the wide surface of the slab varied little with that of the slab center, implying that the transformation of inclusions was retarded due to the rapid cooling process. During the secondary cooling process, the reaction zone for the transformation of inclusions gradually enlarged from the surface to the center of the slab. In the final slab, the transformation fraction of inclusions was less than 10 % in slab corners while it reached 100 % at 50 mm below slab surface.
Fig. 13.
Fig. 13.
Simulated temperature profiles on the cross section of slab of (a) 0.8 m, (b) 4.639 m, (c) 10.385 m, and (d) 20.929 m from the meniscus during the CC process.
Fig. 14.
Fig. 14.
Simulated composition transformation fraction profiles of inclusions on the cross section of slab of (a) 0.8 m, (b) 4.639 m, (c) 10.385 m, and (d) 20.929 m from the meniscus during the CC process.
The predicted composition profiles of inclusions on the cross section of the slab during the CC process are shown in Fig. 15. The Al2O3 and CaO contents of inclusions were approximately uniform on the cross section at the meniscus. The CaS content in inclusions obviously rose up while the CaO content decreased with the solidification of the steel. The Al2O3 content of inclusions slightly decreased, caused by the increase of CaS and MgO contents. The reaction zone for the transformation of inclusions gradually moved from the surface to the center of the slab. The transformation of inclusions in the slab center was much larger than within slab subsurface due to the longer time at the temperature between the liquidus and solidus of the steel. During the CC process, the composition of inclusions within the subsurface of the slab was close to that in tundish due to the higher cooling rate. In the final slab, the transformation fraction of inclusions was less than 10 % in slab corners while it reached 75 % at 50 mm below the slab surface. The transformation rate of inclusions in the slab center slightly decreased due to the shorter time at the temperature between the liquidus and solidus of the steel.
Fig. 15.
Fig. 15.
Simulated composition profiles of inclusions on the cross section of slab of (a) 0.8 m, (b) 4.639 m, (c) 10.385 m, and (d) 20.929 m from the meniscus during the CC process.
4. Conclusions
(1) During the continuous casting process of linepipe steels, inclusions transformed from Al2O3-CaO to CaS-Al2O3-MgO-(CaO), mainly caused by the variation of thermodynamic equilibrium of the steel and inclusions with temperature. The composition transformation of inclusions mainly occurred at the temperature between the liquidus and solidus of the linepipe steel.
(2) The composition of inclusions on the cross section of the slab varied with locations due to the varied cooling rate. Inclusions in the center of the slab were mainly CaS-Al2O3-MgO with little CaO while they were MgO-Al2O3-CaO-CaS within the subsurface of the slab.
(3) A model was established to predict the composition distribution of inclusions on the cross section of the slab, coupling the solidification and heat transfer of the continuous casting slab, the mass transfer of the dissolved elements in the solid steel, and thermodynamic transformation in the composition of inclusions with temperature.
(4) During the CC process, the transformation of inclusions within the subsurface of the slab hardly occurred due to the higher cooling rate there. In the final slab, the transformation fraction of inclusions was less than 10 % in slab corners while it reached 75 % at 50 mm below the slab surface. The transformation fraction of inclusions at the slab center slightly decreased due to the shorter time at the temperature between the liquidus and solidus of the steel during the CC process.
Acknowledgements
This work was supported financially by the National Science Foundation China (Nos. U1860206 and 51725402), the Fundamental Research Funds for the Central Universities (Nos. FRF-TP-17-001C2 and FRF-TP-19-037A2Z), the High Steel Center (HSC) at Yanshan University, and Beijing International Center of Advanced and Intelligent Manufacturing of High Quality Steel Materials (ICSM) and the High Quality Steel Consortium (HQSC) at University of Science and Technology Beijing (USTB), China.
Reference
This work applied automated particle analysis to study non-metallic inclusions in steel. Compared with traditional methods, the approach has the advantage of capturing the morphology, measuring the size, recording the original positions, and identifying the composition of inclusions on a selected area in a short time. The morphology and composition of typical inclusions were analyzed using partial acid extraction and discussed through thermodynamic calculation. Steel samples were collected from the entire cross section of billets cast during times of steady state and ladle change. The spatial distribution of inclusions agreed well with the measurement of the total oxygen. The spatial distribution of inclusions was plotted to represent the entrapment positions of inclusions on the casting strand and their concentration on the cross section of the billet. Also, regarding the different size and type of inclusions, the spatial distribution of classified inclusions was explored such as the distribution of sulfide, oxide, and high sodium and potassium content inclusions. The sufficient information could be used to identify the source of inclusions and guide the steel refining process. (C) The Minerals, Metals & Materials Society and ASM International 2014
Following a series of laboratory-scale experiments, the mechanism of a chemical reaction between high-alloyed TWIP (TWin-Induced Plasticity) steel containing Mn and Al and molten mold flux composed mainly of CaO-SiO2 during the continuous casting process is discussed in the present article in the context of kinetic analysis, morphological evolution at the reaction interface. By the kinetic analysis using a two-film theory, a rate-controlling step of the chemical reaction at the interface between the molten steel and the molten flux is found to be mass transport of Al in a boundary layer of the molten steel, as long as the molten steel and the molten flux phases are concerned. Mass transfer coefficient of the Al in the boundary layer () is estimated to be 0.9 to 1.2 x 10(-4) m/s at 1773 K (C). By utilizing experimental data at various temperatures, the following equation is obtained for the Activation energy for the mass transfer of Al in the boundary layer is 119 kJ/mol, which is close to a value of activation energy for mass transfer in metal phase. The composition evolution of Al in the molten steel was well explained by the mechanism of Al mass transfer. On the other hand, when the concentration of Al in the steel was high, a significant deviation of the composition evolution of Al in the molten steel was observed. By observing reaction interface between the molten steel and the molten flux, it is thought that the chemical reaction controlled by the mass transfer of Al seemed to be disturbed by formation of a solid product layer of MgAl2O4. A model based on a dynamic mass balance and the reaction mechanism of mass transfer of Al in the boundary layer for the low Al steel was developed to predict (pct Al2O3) accumulation rate in the molten mold flux.
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