A Statistical Analysis on the Complex Inclusions in Rare Earth Element Treated Steel

Abstract

In present work the complex inclusions were investigated in the rare earth element treated steels. Based on the results of automated inclusion analysis in the La and Ce added wheel steel a post-processing method was proposed to correct the errors in size distribution, amount and chemical composition introduced by the double-threshold scan. According to the automatic result, the peaks for light-element and heavy-element inclusion were both in range of 0.14–0.53 µm, with the value of 66.5/mm² and 25.9/mm² respectively, and the results were corrected in post-processing to be 27.0/mm² and 15.9/mm² respectively. Meanwhile, the peak of number density for complex inclusion was in range of 0.9–1.3 µm with the value of 10.3/mm². The amount of complex inclusions accounted for about one third of the total. La and Ce dominated in the complex inclusions due to their large size.

1. Introduction

Recent research reveals that the rare earth (RE) elements improve steel properties by affecting inclusions in the steels. The RE elements, such as La and Ce can affine O and S to remove the deleterious types of oxide and sulphide inclusions.^1,2,3,4,5) The size distribution, amount and chemical composition of inclusions related to the RE elements are of great concern. However, these RE elements in most cases are heavier than Fe, and often coexist with the usual non-metallic inclusions, which contain light elements Al, Mg, Si, Mn and so on,⁶⁾ to form complex inclusions. These complex inclusions make the automated inclusion analysis very difficult.^2,7,8,9) It is mainly because that these complex inclusions have several parts with conspicuously different contrast in the back scattered electron (BSE) image and cannot be detected as a whole automatically in the commercial automated inclusion analysis software. This would introduce errors in both size distribution and chemical composition, and thus mislead the valuation on the effect of added RE elements.

In the present work, a post-processing method was proposed to correct the statistic analysis errors on complex inclusions, which can greatly improve the reliability of automated inclusion analysis on the RE elements treated steels. The inclusions in the wheel steel with La and Ce added to refine the inclusions was investigated. In the specimen the main light-element inclusions were MnS and the oxides of Al and Mg.

2. Material and Methods

The specimen was taken from the cross section of full thickness at the 1/4 width of the hot rolled strip. The cross section of the sample was cut into 25 mm in width, and then mechanically grounded and mirror polished using diamond powder. Then it was mounted on the sample holder, and finely adjusted to make the polished sections horizontal.

The scanning electron microscope Hitachi 3400 equipped with Oxford X-Max150 EDS and the automated inclusion analysis software INCA Steel was used to examine the inclusions. The acceleration voltage was 15 kV and the BSE image was used for the inclusions detection. The magnification was 500x, and the resolution was 0.12 μm/pixel. Acquisition time of the EDS for each inclusion was 2 s. The double-threshold scan was applied. One grayscale threshold lower than iron, was set to detect the light-element inclusions. And another grayscale threshold higher than iron, was set to detect the heavy-element inclusions. The thresholds were listed in Table 1. After the automatic analysis procedure, the details of all inclusions in the specimen were exported, including their locations, morphology and the compositions as well as the images of all the scanned fields. A typical complex inclusion was shown in Fig. 1. It can be found that through the automated inclusion analysis this complex inclusion was analyzed as 3 individual inclusions: two MgO inclusions labeled as 1 and 2 and a sulfide of La and Ce labeled as 3. The post-processing was then used to identify the complex inclusions and correct the analysis errors.

Table 1. Settings of the grayscale thresholds.

Iron base	Lower threshold (for light-element inclusions)	Upper threshold (for heavy-element inclusions)
~120	89	148

Fig. 1.

The BSE image and the elements mapping of a complex inclusion in the La and Ce added wheel steel.

3. The Post-processing

3.1. Identify Complex Pairs

The adjacent inclusions in the detected result are considered to be parts of a complex inclusion. So the post-processing examines the heavy-element inclusions in the detected result one by one. If a heavy-element inclusion is very close to its neighboring light-element inclusion, two of them will be identified as a complex pair. The identification includes the following steps.

3.1.1. Determine the Inclusion Shape

In this post-processing the equiaxed inclusion is simplified as a circle and the elongated inclusion is simplified as an ellipse according to the aspect ratio of an inclusion. In the automatic inclusion analysis software INCA Steel, the aspect ratio is defined as the ratio of the maximum Feret diameter over the minimum Feret diameter of an inclusion. It should be noticed that the maximum and minimum Feret diameters are not always perpendicular to each other. Therefore, it is possible for some equiaxed inclusions that would have aspect ratios rather than 1, e.g. the aspect ratio of a one-pixel inclusion is √2 because one pixel is a square. Therefore, in present work, the inclusions with the aspect ratio less than or equal to √2 will be treated as circular, and the others will be treated as elliptical.

3.1.2. Calculate d and rr

All heavy-element inclusions are distinguished from the automatically detected inclusions. Then the ratio d/rr is calculated, where d is the distance between the centers of a heavy-element inclusion and one of its neighboring light-element inclusions, and rr is the sum of their radius in the direction connecting their centers. According to the shapes of the inclusions there are 3 cases to calculate rr: (1) when both of the inclusions are equiaxed, rr is the sum of the radius of the equal-area circles of two inclusions; (2) when one inclusion is equiaxed and the other is elongated, rr is the sum of radius of the equal-area circle of the equiaxed one and the ellipse radius of the elongated one in the direction connecting the two inclusions’ centers; (3) when both of the inclusions are elongated, and rr is the sum of ellipse radius in the direction connecting the two inclusions’ centers. The center locations, the radius of the equal-area circles could be directly found in the automatic result. The ellipse radius in a certain direction can be derived as shown in the Appendices.

3.1.3. Decide the Critical Value

When d/rr is less than a critical value, the heavy-element and the light-element inclusions are recorded as a complex pair. Theoretically the critical value should be 1. However, due to the low magnification in the automatic scan the resolution of the inclusion image is quite low. In order to compensate the pixilation, the critical value of d/rr ratio should be increased a little from the theoretical value of 1. Therefore, the critical value needed to be decided by hypothesis testing of experiment results.

3.2. Merge the Nearby Complex Pairs

It is possible that one inclusion could be repeatedly found in different pairs. As shown in Fig. 1, the heavy-element inclusion 3 was simultaneously in the complex pairs 1&3 and 2&3 and three of them formed a complex inclusion. So those complex pairs, which are connected with each other, compose one complex inclusion. Therefore in the post-processing all the complex pairs, which are connected, are merged into one.

3.3. Export Results

The post-processing outputs a list of complex inclusions, and their member inclusions. Each complex inclusion, no matter how many members it contains, is only counted once. So the amount of the complex inclusions is N_c and the amount of all the members is N_b. For a certain sample, the amount of the valid inclusions detected automatically is N₀, and after merging the amount of all inclusions should be   

$${\mathrm{N}}_{\mathrm{m}}={\mathrm{N}}_0–{\mathrm{N}}_{\mathrm{b}}+{\mathrm{N}}_{\mathrm{c}},$$(1)

Furthermore the size of a complex inclusion can be derived from the sum area of all its members; and the chemical composition of a complex inclusion is the area weighted average value of all its members.

4. Results

In the La and Ce added wheel steel, the major inclusions were the sulfides of La and Ce, and oxides of Al and Mg, as shown in Fig. 1. 330 fields at the magnification of 500x, totally 15.1 mm² were automatically scanned, to find 3395 inclusions in all. By excluding the invalid inclusions like Fe–O and artificial contaminations, 2883 inclusions were validated, including 1618 light-element inclusions and 1265 heavy-element inclusions.

The distribution of the inclusions in this sample was very sparse, about 10 inclusions in one field averagely. For this case, a big tolerance of the critical value was allowed, so a series of critical values for d/rr from 1 to 4 were tried to search the complex inclusions. And the results were compared with the image records to determine the suitable critical value.

Every inclusion automatically detected had an ID, and the complex inclusion could be represented by a collection of all single inclusions it contained in square brackets. As shown in Fig. 2, 4 complex inclusions: [2, 10, 11], [47, 48, 54], [49, 50, 51, 55] and [169, 170, 171, 172, 173, 179], were randomly chosen from the image records to verify the critical values. Nearby the last complex inclusion there was a separate inclusion with ID 168.

Fig. 2.

The details of the complex inclusions randomly chosen in the La and Ce added wheel steel.

The post-processing results of each critical value were listed in Table 2. Only the results of critical value 2 and 3 fitted the image records well, except the complex inclusion [2, 10, 11]. From Fig. 2(a) we knew that the light-element inclusion2 was next to a heavy-element inclusion 10 and another heavy-element inclusion 11 was at the other side of 10, so 2 and 11 were not adjacent. In the post-processing only the nearby light-heavy pairs were examined, while the two nearby heavy-element inclusions were not considered.

Table 2. The post-processing results of a series of critical values of the 4 randomly chosen complex inclusions as shown in Fig. 2.

Critical value	N0	Na*	Nb	Nc	Nm	The complex inclusions and their components
						[2, 10, 11]**	[47, 48, 54]**	[49, 50, 51, 55]**	[169, 170, 171, 172, 173, 179]**
1	2883	321	585	264	2562	Null	[48, 54]	Null	[169, 170, 171, 172, 173, 179]
1.5		767	1286	523	2120	Null	[48, 54]	Null	[169, 170, 171, 172, 173, 179]
2		957	1545	603	1941	[2, 10]	[47, 48, 54]	[49, 50, 51, 55]	[169, 170, 171, 172, 173, 179]
3		1088	1694	634	1823	[2, 10]	[47, 48, 54]	[49, 50, 51, 55]	[169, 170, 171, 172, 173, 179]
3.5		1124	1715	634	1802	[2, 10]	[47, 48, 54]	[49, 50, 51, 55]	[168, 169, 170, 171, 172, 173, 179]
4		1157	1731	633	1785	[2, 10]	[47, 48, 54]	[49, 50, 51, 55]	[168, 169, 170, 171, 172, 173, 179]

^*:  N_a is the amount of the complex pairs.

^**:  Observation from the image records.

Critical value 2 was preferred as it was closer to the theoretical critical value, and the post-proposed result was: 648 heavy-element inclusions and 897 light-element inclusions formed 603 complex inclusions. So the amount of the merged inclusions should be 1941.

5. Discussion

According to the double-threshold scan result, the inclusion size distribution of the La and Ce added wheel steel was drawn in a semi logarithmic coordinate in Fig. 3(a), since the number density of small size was quite larger than that in larger ranges. Rather than the typical bell-shaped curve distribution reported in other literature, it showed a decreasing curve, and the peaks for light-element and heavy-element inclusion were both in range of 0.14–0.53 μm, with the value of 66.5/mm² and 25.9/mm² respectively. That might be because the complex inclusions were divided into smaller parts and repeatedly counted. While as the size increased to 0.91 μm, the density of the heavy-element inclusions exceeded that of the light-element inclusions. After the post-processing the size distribution was shown in Fig. 3(b). It showed a bell-shape curve of the complex inclusions, as reported in other literature.²⁾ The peak of number density for complex inclusion was in range of 0.9–1.3 μm, with the value of 10.3/mm², while for isolated light-element and heavy-element inclusions were still in range of 0.14–0.53 μm, with the value of 27.0/mm² and 15.9/mm² respectively. In the range larger than 0.9 μm, the density of complex inclusions was larger than both heavy and light-element inclusions, it indicated that considerable amount of La and Ce in this sample was consumed in the complex inclusions.

Fig. 3.

The size distribution of all kinds of the inclusions in the La and Ce added wheel steel: (a) result of the double threshold method; (b) post-processed. (Online version in color.)

According to the automatic result the main types in this sample were the light-element oxides such as Al₂O₃, MgO, Magnesia-alumina spinel and CaO, the sulphides such as MnS and the compounds of La and Ce, which might be oxides, the oxysulphides, and the sulphides according to the literature.¹⁾ Ternary diagrams were drawn to visualize the chemical composition of the inclusions. In order to show the effect of adding RE element, RE (La+Ce) was drawn as one corner, and Mn was drawn as another corner and Al+Mg+Ca was the last corner in the diagrams. The ternary phase diagrams obtained from the automatic results (Fig. 4(a)) had already suggested that there were quite a lot inclusions contained both heavy and light elements, and the inclusions concentrated at the corner of RE. There were unusual gaps along the axis RE-(Al+Mg+Ca) and the axis RE-Mn. No gaps were found in the post-processed diagram (Fig. 4(b)) and the inclusions were more concentrated to the corner of RE. The change was caused by merging 1545 inclusions into 603 complex inclusions, and this part of inclusions could be analysed separately, as shown in Figs. 4(c) and 4(d). Since the chemical composition of the complex inclusion was the area weighted average component of all its members, and the concentration to the RE corner confirmed that the compounds of RE dominated in the complex inclusions due to the advantage in size as illustrated in Fig. 3(a). Moreover in the double threshold scan, the chemical composition was taken from a region with uniform contrast by EDS, and it might cover the nearby region but rarely involved a third region far away. So the measured inclusion composition never contained a third corner with very low level, and a gap appeared very close to the axis in the diagram. Actually the composition of a complex inclusion contained all regions it covered, no matter how low the content, it could be reflected in the ternary diagram, so no gap appeared, and that was more reasonable.

Fig. 4.

Ternary diagrams of the inclusions in the La and Ce added wheel steel: (a) the inclusions automatically detected; (b) the post-processed inclusions; (c) the inclusions which forms the complex inclusions; (d) the complex inclusions.

6. Conclusions

In present work the inclusions in the RE element treated steel were investigated. The errors introduced by the double thresholds method in the automatic analysis was corrected by a post-processing method, the result revealed:

(1) In the La and Ce added wheel steel the main types of inclusions were the oxides of Al, Mg, Ca, MnS and the compounds of La and Ce. Considerable amount of La and Ce in this sample was consumed in the complex inclusions.

(2) The number of complex inclusions accounted for about one third of the total. And the RE compounds dominated in the complex inclusions due to their size advantages.

Appendices

The following data provided by the automatic analysis were used to calculate the ellipse radius in a certain direction: take the length (the maximum Feret diameter) of the elongated inclusion as the long axis 2a, and take the inclusion direction θ (the angle from horizontal counter clockwise to the length ranged from 0–π) as the direction of the long axis. The short axis 2b could be derived from 2a dividing the aspect ratio. So the radius in any direction of the ellipse r_e should be   

$$r_e={\displaystyle \frac{\text{b}}{\sqrt{1+\left({\displaystyle \frac{{\text{b}}^2}{{\text{a}}^2}}-1\right){cos}^2\delta }}}$$(A1)

where δ was the angle between r_e and the long axis, and r_e was parallel to the line connecting two centers.

Figure A1 illustrated a neighbourhood of an ellipse and a circle with the centers at point A and point B respectively. r_A was the ellipse radius in the direction connecting A and B, which could be derived from Eq. (A1) and   

$$\delta =\angle \text{BAO}-\theta$$(A2)

Fig. A1.

Schematic illustration for processing a pair containing an elongated inclusion and an equiaxed one.

And r_B was the radius of circle B.   

$$rr=r_A+r_B$$

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