The Influence of Mg-Based Inclusions on the Grain Boundary Mobility of Austenite in SS400 Steel

Abstract

In this study, the effects of the addition of Mg to the grain growth of austenite and the magnesium-based inclusions to mobility were investigated in SS400 steel at high temperatures. A high-temperature confocal scanning laser microscope (HT-CSLM) was employed to directly observe, in situ, the grain structure of austenite under 25 torr Ar at high temperatures. The grain size distribution of austenite showed the log-normal distribution. The results of the grain growth curves using 3D surface fitting showed that the n and Q values of the growth equation parameters ranged from 0.2 to 0.26 and from 405 kJ/mole to 752 kJ/mole, respectively, when adding 5.6–22 ppm of Mg. Increasing the temperature from 1150 to 1250 °C for 20 min and increasing the addition of Mg by 5.6, 11, and 22 ppm resulted in increases in the grain boundary velocity. The effects of solute drag and Zener pinning on grain boundary mobility were also calculated in this study.

1. Introduction

Both medium and thick steel plates are used in the building of high-rise buildings, bridges, and in ships. A high-heat-input welding technique with heat input of over 50 kJ/cm has been employed for high-efficiency, low-cost fabrication of these steel plates. Increasing the heat input energy during welding enhances the coarsening of the austenite grains in the heat-affected zone (HAZ). However, coarse grains have detrimental effects on the impact toughness of weldments [1].

TiN inclusions were first applied to improve the toughness of HAZs, which serve as potential nucleation sites for acicular ferrite (AF) formation [2,3,4]. The development of TiN inclusions [5,6,7,8] can be expressed as the zero generation of inclusions for AF formation, before the use of oxide inclusions. However, Nb, V, and Ti nitrides will dissolve into austenite because of the high heat input from welding temperatures above 1300 °C [9]. Thus, Mizoguchi et al. [10] first proposed oxide inclusions to improve the impact toughness of HAZs under high-heat-input welding.

Titanium and magnesium oxides can be called the first and second generations of oxide inclusions for AF formation. In this study, Titanium oxides serve as potent nucleation sites for the formation of intragranular AF [11,12,13,14,15,16,17,18,19]. Magnesium oxide serves as fine dispersed inclusions in steel [20] because Mg has a strong affinity for oxygen and a reasonable amount of Mg is soluble in steel [5]. Kojima et al. [5] first proposed magnesium oxide metallurgy technology, in which MgO, MgS, and Mg(O,S) inclusions were used to pin grain boundaries. According to previous research, Zener pinning was the influence of the dispersion of spherical particles [21], ellipsoidal particles [22] and cylindrical particles [23] on the movement of grain boundaries. The particles acted to prevent the motion of grain boundaries by exerting a pinning force which counteracted the driving force of the grain boundaries. The pinning efficiency against grain growth for grain coarsening was determined by the particle size [21]. This process refined the HAZ microstructure. Suito et al. [24,25,26,27] reported that MgO and soluble Mg can hinder excessive growth of austenite grains. In addition, Zhu et al. found that the addition of 0.005 wt% Mg can effectively inhibit austenite grain growth [28,29] and lead to the formation of AF [30].

The chemical composition of steel, the cooling rate at temperatures ranging from 800 to 500 °C, the size of austenite grains, and the inclusion parameters affect the formation of intragranular AF in metal [31]. In this study, we investigated the effect of the addition of Mg on austenite grain growth in SS400 low-carbon steel using a high-temperature confocal scanning laser microscope (HT-CSLM) in order to observe the high temperature microstructure in situ. In addition, the pinning effect of the magnesium-based inclusions on the mobility of austenite was studied.

2. Materials and Experiments

SS400 low-carbon steels produced by China Steel Corporation were selected as the experimental materials, for which the chemical composition of the steels is listed in

Table 1. Chemical composition of SS400 steel with Mg of 1.5–22 ppm (Unit: wt%).

Mg	C	Si	Mn	P	S	Al	N	O
1.5 ppm	0.120	0.17	1.18	0.0071	0.0006	0.028	0.0053	0.0041
5.6 ppm	0.118	0.17	0.74	0.0102	0.0035	0.033	0.0054	0.0082
11.0 ppm	0.136	0.28	0.94	0.0075	0.0012	0.020	0.0043	0.0027
22.0 ppm	0.127	0.28	0.87	0.0104	0.0021	0.018	0.0052	0.0016

, and Fe-5% Mg alloy wire was used for the addition of Mg during the ladle treatment. The experimental materials obtained from the as-cast slab, 8000 mm long, 1800 mm wide, and 270 mm thick, were cut into specimens 50 mm thick and 200 mm wide. After hot rolling at 1200 °C, the thickness was reduced from 50 mm to 10 mm, and 6 mm × 5 mm × 2 mm specimens were prepared.

The specimens were ground using 1500, 2500, and 4000 SiC paper, polished using 3, 1, and 0.1 µm diamond suspensions, respectively, and finally polished with 0.02 µm SiO₂ suspensions. After the final polish, the austenite grain structure was observed in situ at high temperature under 25 torr Ar using an HT-CSLM (VL2000DX-SVF17SP, Yonekura, Japan). First, the specimen was placed into an Al₂O₃ crucible with a diameter of 8 mm and a height of 3.5 mm. Prior to heating, the chamber was evacuated for 5 min using a diffusion pump backfilled with ultrahigh purity Ar gas (>99.999%), with a discharge rate of 300 mL/min passed through a gas cleaning system to reduce the oxygen content. Then, the specimens were heated to 1000, 1100, 1200, and 1250 °C for 3, 5, 10, and 20 min, respectively. Afterward, the specimens were cooled at a cooling rate of 100 °C/s. After cooling, images of the grain structure were examined with a Leica DM6000 M optical microscope (Leica, Wetzlar, Germany). Microscope Imaging Software (Grain Expert, Leica, Wetzlar, Germany) was used to calculate the average grain size according to the ASTM E112 international standards. Then, the HT-CSLM was employed to investigate the movement of the austenite grains. We used an ASPEX EXplorer system (ASPEX, LLC, Boulder, CO, USA) combining SEM and EDS to automatically classify different types of inclusions and to determine the inclusion size and number within a large measured area.

3. Results and Discussion

3.1. Parameters of Grain Growth Equation

To determine the number of grains, we adopted the Leica analysis Grain Expert software to detect the grains, and Figure 1b shows an image of the detected grains in austenite. The original image is shown in Figure 1a. Then, a representative value of the minimal number of grains was obtained. Figure 2a–d show a histogram of grain size in terms of the number of grains, while Figure 2e shows the effect of the number of grains on the average grain size and standard deviation. The distributions of grain size and the average grain sizes were similar. However, increasing the number of grains decreased the standard deviation. The minimal number of grains was set at 300 for the subsequent analysis.

After measuring the number of grains, a single representative value for the grain sizes should be obtained statistically. Statistical values, including the mean, median, and mode, were considered. Figure 3 illustrates the histogram and cumulative frequency distributions of the grain size of austenite in SS400 with 1.5 ppm Mg. Figure 4 shows the evolution of the austenite grain size using the three statistical values. The mean is found by adding all given data and dividing by the number of data entries. The median is the middle number of all values, while the mode is the number that occurs most often in the data set. Thus, the mean has the highest value, while the mode is the lowest. The median is between the mean and mode (Figure 4). Therefore, in this study, we adapted the mode as the average value to avoid calculating the large grains because large grains lead to abnormal grain growth.

Next, the grain growth equation was derived after the averaging method was determined. The numerous equations that have been proposed to predict the grain growth equation can be divided into three types. First, Beck et al. [32] reported a power law for normal grain growth, while Sellars et al. [33,34,35,36] modified Beck’s equation as follows:

$$d_{}^m-d_o^m=k_0\cdot \exp (-Q/RT)\cdot t$$

(1)

where d is the final grain diameter; d₀ is the initial grain diameter; t is the annealing time, and m and k₀ are constants. Q is the activation energy for grain growth, and T is the temperature in absolute degrees. The simplified Beck’s model was used to predict the initial austenitic grain size as follows [37]:

$$d^m=k_0\cdot \exp (-Q/RT)\cdot t$$

(2)

Moreover, Yoshie et al. [38] and Nishizawa [39] reported a model represented as follows:

$$d_{}^2-d_o^2=k_0\cdot \exp (-Q/RT)\cdot t$$

(3)

In this study, we applied the grain growth formulation in Equations (1) and (2) to predict the grain growth curves for SS400 with 1.5 ppm Mg at 1200 °C as an example. The parameters of the fitting growth equations are summarized in

Table 2. Parameters of the fitting equations of Equations (1) and (2) for SS400 with 1.5 ppm Mg.

Fitting equation	d0 (μm)	m	Q (kJ/mole)	k0 (μm/s)
Equation (1)	4.3	2	232	7.2109
Equation (2)	0	2.9	622	3.21025

. The fitting curves, using Equation (2), agree with the experimental data with an R-value of 0.96, and the results are remarkably better than those using Equation (1) with an R-value of 0.69 [Figure 5a,b]. The values of Q and k₀ using Equation (2) are similar to those of Equation (1). A comparison of the experimental data in Figure 5a,b showed that Equation (2) was the best fitting equation. Thus, Equation (2) was employed for the subsequent investigations.

3.2. Effects of Temperature and Mg-Content on Austenite Grain Growth

Figure 3 illustrates the histogram and cumulative frequency distributions of the grain size of austenite with an Mg content of 1.5–22 ppm at 1150–1250 °C. The average grain size was plotted in terms of the annealing time and temperature with different Mg content, as shown in Figure 6, and the corresponding parameters of the fitting curves are listed in

Table 3. Parameters of the fitting equations for steel with Mg content of 1.5-22.0 ppm using Equation (2).

Mg (ppm)	m	Q (kJ/mole)	k0 (μm/s)
1.5	2.9	622	3.2 × 1025
5.6	4.9	405	2.5 × 1019
11.0	3.8	493	2.8 × 1021
22.0	6	752	1.7 × 1031

. The grain size distributions followed the log-normal distribution, which led to an increase in the average grain size with increases in annealing temperature. The Q and n values are listed in Table 3.

Except for the case of 1.5ppm Mg, the Q value increased from 81 to 150 kJ/mole and the n value was in the range of 0.2–0.26 as Mg content increased from 5.6 to 22ppm. It was noted that the Q value obtained from the references in

Table 4. Parameters of n, Q, and k₀ for the growth equations.

Steels	m	Q (kJ/mol)	k0 (μm/s)	References
Low C-Mn	2	67	4.3 × 1012	[40]
Low C-Mn	5.6	126	9.4 × 1038	[37]
C-Mn	2	64	1.4 × 1012	[41]
C-Mn	1	400 (T>1273)	3.9 × 1032	[36]
C-Mn	1	914 (T<1273)	5.0 × 1053	[36]
C-Mn-V	7	400	1.5 × 1027	[36]
C-Mn-Ti	10	437	2.6 × 1028	[33]
C-Mn-Nb	4.5	435	4.1 × 1023	[33]
High C-Mn	5.3	366	9.1 × 1025	[37]
High C-Mn	0.12	1170	4.1 x 1063	[31]

ranged from 64 to 437 kJ/mole with the exception of 914 kJ/mole. Thus, our Q and n values lie in the range obtained from the references.

We differentiated Equation (2) with respect to time (t) to reveal the grain boundary velocity ($V=\frac{dD}{dt}$) as follows:

$$V=n*k_o\ast \exp (-Q/RT)\ast {\left[t-t_o\right]}^{n-1}$$

(4)

The grain boundary velocity was plotted as a function of annealing time in Figure 7. When 1.5 ppm Mg was added, the grain boundary velocity increased from 0.025 μm/s to 0.1 μm/s after 20 min as the annealing temperature increased from 1150 to 1250 °C. The grain boundary velocity after 20 min increased from 0.005 μm/s to 0.01 μm/s, 0.01 μm/s to 0.02 μm/s, and 0.005 μm/s to 0.07 μm/s when 5.6, 11, and 22 ppm of Mg were added, respectively, as the annealing temperature increased from 1150 to 1250 °C. Considering the annealing time of 20 min, the grain boundary velocity was plotted in terms of Mg content at 1150–1250 °C in Figure 8. However, the grain boundary velocity was reduced with increases in the Mg content, and steels with the addition of 5.6 ppm and 22 ppm of Mg exhibited similar trends. This phenomenon suggests that the grain boundary velocity was significantly decreased by increasing Mg content at 1250 °C. The results in Table 3 show that the increase in Mg content from 1.5 to 22 ppm increased the Q exponent. However, the Q exponent decreased when the Mg content was 5.6 and 11 ppm. In general, the activation energy Q for grain growth was affected by the amount and type of alloying elements. For materials with inclusion pinning and elements of solute drag, grain growth was difficult and activation energy increased. In some mechanisms, the Q exponent decreased. The m exponent depended on the grain growth mechanisms. When the m exponent was 2, the materials had no defects or inclusions. When the m exponent was 3, several phenomena, such as inclusions in the grain, were observed, which indicates the occurrence of the pinning effect. When the m exponent was 4 the alloy element exhibited diffusion in the grain boundaries and produced inclusion, which indicates the occurrence of pinning and solute drag effects [42]. Thus, the effects of the pinning force and solute drag on austenite grain mobility are considered in the subsequent section.

3.3. Zener Pinning Effect of Inclusions on the Austenite Grain Mobility

According to the model [36], the driving force of grain growth is expressed by:

$$F_P=\frac{2{\sigma }_b}{R}$$

(5)

where R is the radius of the curvature of grains, and σ_b is the surface energy of the grain boundary. Moreover, inclusions exert the retarding force (F_R) on the grain boundaries proposed by Zener [43] as:

$$F_R=\frac{3f_v{\sigma }_b}{2r}$$

(6)

where f_v is the volume fraction of inclusions, σ_b is the surface energy of the grain boundary, and r is the radius of the inclusions. Here the surface energy of the grain boundary σ_b is for austenite, the value of which was obtained from Reference [44]. The retarding forces (also called the Zener pinning force) depend on the radius and volume fraction of inclusions, as listed in

Table 5. The retarding force (F_R) of inclusions.

Mg (ppm)	Inclusion	A (m2)	D (m)	fA (10−6 × %)	fV (10−4 × %)	FR (kJ/m3)	FR (kJ/m3)
1.5	MgO-MnS	87.6	1.9	2.5	15.9	2.9	11.7
	MnS	67.9	1.4	2.0	14.0	3.5
	MgAl2O4	693	2.9	19.9	44.6	5.3
5.6	MgO-MnS	26.8	1.9	0.8	8.8	1.6	8.5
	MnS	26.9	2.1	0.8	8.8	1.5
	MgAl2O4	834	3.1	23.9	48.9	5.4
11	MgO	10.4	1.7	0.2	4.7	1.0	20.3
	MgO-MnS	46.6	1.9	1.0	10.0	1.8
	MnS	861	3.4	18.5	43.0	4.3
	MgAl2O4	2030	3.8	43.7	66.1	6.0
	Mg-Al-MnS	2790	3.8	60.0	77.5	7.1
22	MgO	108	2.7	3.1	17.6	2.2	17.1
	MgO-MnS	224	4.4	6.4	25.3	2.0
	MnS	310	2.5	8.9	29.8	4.2
	MgAl2O4	235	2.8	6.7	26.0	3.2
	Mg-Al-MnS	759	3.0	21.8	46.6	5.5

* Note: σ_b is 1.159 J/m² and the measured areas for 1.5, 5.6, 11, 22 ppm Mg are 34.865, 34.865, 46.487 and 34.865 mm², respectively. A—area; D—average diameter; f_A—area fraction; f_V—volume fraction; F_R—retarding force, and F_R—sum of the retarding forces for inclusions.

. Here the radius (r) is equal to half of the average diameter, and f_A is obtained by dividing the number of inclusions (N) by the measured area (A). Next, the equation f_A = 2Nf_V was employed. It has been reported that the addition of 2 ppm Mg led to a change in oxide formation from the Al₂O₃ to MgO·Al₂O₃ phase and a change in inclusion formation from Al₂O₃–MnS to MgO·Al₂O₃–MnS [45].

In the case of 1.5 and 5.6 ppm Mg, the effective inclusion of MgAl₂O₄ exerted the greatest retarding force, and, for 11 and 22 ppm Mg, it was Mg-Al-MnS that exerted the greatest retarding force because the volume fraction of MgAl₂O₄ was the largest phase for 1.5 and 5.6 ppm Mg. The volume fraction of Mg-Al-MnS was the largest phase for 11 and 22 ppm Mg. The average diameter of the inclusions was in the range of 1.4–4.4 μm, and the volume fraction of the inclusions was in the range of 4.7–77.5%. According to Equation (6), the retarding force was mainly determined by the volume fraction because there was no significant difference in the average diameter of inclusions seen in Table 5. Furthermore, there was no a linear relationship found between the addition of Mg and the retarding force.

The mobility of grain growth M is proportional to the net driving force, which is equal to the driving force of grain growth (F_P) subtracted from the Zener pinning force (F_R), which was expressed by Reference [43]:

$$V=M(F_P-F_R)$$

(7)

where V is the grain boundary velocity. Figure 9 shows the grain boundary velocity in terms of the net driving force (F_P – F_R), where the grain boundary velocity was proportional to the net driving force. Here, the ratio of the grain boundary velocity to the net driving force corresponded to the mobility of grains M, that is, the slope, and the corresponding values of mobility are listed in

Table 6. The values of mobility [10⁻⁴ × m⁴/(kJ∙s)] for 1.5–22 ppm Mg at temperatures of 1150, 1200 and 1250 °C.

Mg (ppm)	Temperature (oC)
	1150	1200	1250
1.5	19.8	52.6	105
5.6	8.0	5.9	7.5
11.0	7.7	14.2	21.6
22.0	1.3	1.7	3.7

. It was observed that increasing the temperature resulted in increases in mobility when 1.5–22 ppm of Mg were added because the mobility was dependent on the growth rate V also being proportional to exp($-\frac{Q}{RT}$) in Equation (4). Here, we observed that an increase in Mg content led to a decrease in the mobility at 1150 °C as well as at 1200 and 1250 °C except for 5.6 ppm Mg content, as shown in Table 6. The grain boundary mobility was significantly reduced from 19.8 to 1.3 × 10⁻⁴ × m⁴/(kJ∙s) at 1150 °C, from 52.6 to 1.7 × 10⁻⁴ × m⁴/(kJ∙s) at 1200 °C, and from 105 to 3.7 × 10⁻⁴ × m⁴/(kJ∙s) at 1250 °C, when the Mg content was increased from 1.5 to 22 ppm.

In this study, all measurements of grain size were based on a grooved surface. Grooving has a pinning effect on the migration of grain boundaries, which is therefore slow. The grain boundary mobility measured here was the lower limit of the grain boundary mobility.

3.4. Effect of Solute Drag on the Grain Mobility of Austenite

A lot of studies have reported that solute elements can segregate from the matrix to the grain boundary, and grain boundary migration may be limited by the diffusivity of the dragged solute atoms. The pressure induced by the solute drag is dependent on the boundary velocity [46,47,48,49,50]. According to Cahn et al., the drag effect of mobility (M) is given by [51]:

$$M(X_{\mathrm{Mg}},T)={(\frac{1}{M_{Pure}}+\alpha ·X_{Mg})}^{-1}$$

(8)

and

$$\alpha =\frac{N_v{(kT)}^2\delta }{E_b{D}_{Mg}^{Int}}(sinh(\frac{E_b}{kT})-(\frac{E_b}{kT}))$$

(9)

where M_pure is the mobility of grain boundary in Fe; X_Mg is the concentration of Mg; δ is the width of a grain boundary; N_v is the number of atoms per unit volume; k is the Boltzmann’s constant, and E_b is the binding energy to the Fe grain boundary. The M_pure is according to Kang et al. [52]:

$$M_{pure}=\beta \frac{D_{Fe}^{gb}{V}_m\delta }{b^{2}RT}$$

(10)

where b is the burger vector; R is the gas constant; T is the temperature; $D_{Fe}^{gb}$ is the diffusivity of Fe atoms in ferrite, and V_m is the molar value of ferrite. The values of all the parameters used are listed in

Table 7. Values of parameters used in the calculation.

Parameter	Value	Reference
δ	1 × 10−9 m	[53]
b	2.48 × 10−10 m	[53]
Eb	85 kJ/mol	[54]
β	0.7	[49]
Vm	8.26 x10−5 m3	-
1.8·10−4 m2/s	-
$D_{Fe}^{g.b}$	1.5·10−4 m2/s	[55]

. The mobility calculation result was 1.8 × 10⁻³ × m⁴/(kJ∙s) at 1250 ^°C for 22 ppm Mg. According to the pinning force results, the mobility of grain boundary was 3.4 × 10⁻⁴ × m⁴/(kJ∙s). Comparing the results, the effect of solute drag on grain boundary mobility is an order higher than the effect of Zener pinning. This implies that the effect of Zener pinning is the dominant mechanism for grain boundary migration.

4. Conclusions

In this study, the effect of Mg addition in the range of 1.5–22 ppm on the grain growth behavior of austenite in SS400 steel was investigated at 1150, 1200, and 1250 °C. The grain size distribution exhibited a log-normal distribution. The grain boundary velocity and grain mobility were reduced as Mg was increased from 1.5 ppm to 22 ppm. As the temperature increased from 1150 to 1250 °C, the grain boundary velocity also increased. The inclusion with the most retarding force was MgAl₂O₄, and it was Mg-Al-MnS when 11 and 22 ppm of Mg were added. The mobility of the grain boundary affected by Zener pinning was one order smaller than that affected by solute drag. It was therefore concluded that Zener pinning is a dominant factor by which to effectively retard grain boundary migration.