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Digital identification scheme for steel microstructures in low-carbon steel
Materials Characterization 129 (2017) 305–312
Contents lists available at ScienceDirect
Materials Characterization journal homepage: www.elsevier.com/locate/matchar
Digital identification scheme for steel microstructures in low-carbon steel a,⁎
a
b
b
Hidenori Terasaki , Yu Miyahara , Kotaro Hayashi , Koji Moriguchi , Shigekazu Morito a b c
MARK
c
Faculty of Advanced Science and Technology, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan Technical Research & Development Bureau, Nippon Steel & Sumitomo Metal Corporation, 20-1 Shintomi, Futtsu, Chiba 293-8511, Japan Department of Materials Science, Shimane University, 1060 Nishikawatsu, Matsue, Shimane 690-8504, Japan
A R T I C L E I N F O
A B S T R A C T
Keywords: Identification scheme for steel microstructure Kurdjumov–Sachs orientation relationship variants Phase transformation
This study proposes a scheme for digital identification of a steel microstructure based on crystallographic features. A 2D space for classifying mixed microstructures of bainite and martensite formed by seven different thermal cycles is defined using two dimensions related to variants in Kurdjumov–Sachs orientation relationships and dislocations. As a dimension relating to variants, the minor variant pair characterized by a rotation axis of 〈011〉 and a rotation angle of 52° is most useful in classifying the steel microstructure. Furthermore, the kernel average misorientation also served as a suitable dimension for the 2D space. The reasons for using the minor variant pair to classify steel microstructures are discussed from the viewpoint of phase transformation phenomena. The present study demonstrates the possibility for steel microstructures to be digitally identified.
1. Introduction Various microstructures can be designed using different thermal cycling procedures in low-carbon steel as a result of phase transformations, which enables control of a wide range of mechanical properties such as tensile strength. Recent demand for high-strength steel structures has resulted in a tendency toward using mixed microstructures of bainite (upper and lower bainite) and martensite. Therefore, understanding and classifying the mixed microstructures of bainite and martensite formed by various thermal cycling procedures is essential. A bainite classification scheme based on carbide precipitate morphology has been suggested [1]. Another classification scheme is based on bainitic ferrite morphology [2]. In low-carbon steel, martensite has a single morphology known as lath martensite and no carbide is observed. These classification schemes were developed from the perspective of morphology. A classification scheme based on carbide morphology is particularly effective. However, the application of electron backscattering diffraction (EBSD) methods to analyze steel microstructures [3–13] enables a statistical microstructural classification scheme based on crystallographic features and suitable for novices. Takayama et al. [13] investigated the frequency of variant pairs in Kurdjumov–Sachs orientation relationships (KSORs) in the transformation temperature range for bainite and martensite in low-carbon steel. By focusing on four variant pairs in one packet, they noted that the variant-pair frequency varied strongly among bainite formed at high temperatures, bainite formed at low temperatures, and martensite.
⁎
These four variant pairs are referred to as V1–V2, V1–V3/5, V1–V6, and V1–V4 according to the definition proposed by Morito et al. [14] They clarified that the V1–V4 pair with low-angle boundaries dominates in bainite at high temperatures and that the V1–V2 pair with high-angle boundaries increases and V1–V4 decreases with decreasing transformation temperature. In martensite, the V1–V4 pair again increases, reflecting sub-block formation [14]. Morito et al. [15] demonstrated a simpler method for assessing variant-pair frequencies using block boundary profiles. Their method enables the variant frequency to be quantitatively analyzed over a wide area using EBSD data. The aforementioned studies provide a basis for the digital classification of steel microstructures, including mixed microstructures, from a crystallographic perspective. The digital classification scheme has opened doors for the automatic recognition of steel microstructure and/or automatic prediction of mechanical properties of steel based on the recognition of mixed-steel microstructure, using artificial intelligence. In order to achieve the scheme, steel microstructure including mixed microstructure should be evaluated in feature space defined by dimensions (feature vector) that characterize the steel microstructures. In the present study, a 2D space to classify the mixed microstructures comprising bainite and martensite formed during seven thermal cycles using a low-carbon steel were suggested and a method for digital classification in the 2D space is proposed. The results show that the minor variant pair (V1–V6) plays an important role in classifying steel microstructures.
Corresponding author at: 2-39-1 Kurokami, Kumamoto 860-8555, Japan. E-mail addresses: [email protected] (H. Terasaki), [email protected] (Y. Miyahara), [email protected] (K. Hayashi), [email protected] (K. Moriguchi), [email protected] (S. Morito). http://dx.doi.org/10.1016/j.matchar.2017.05.021 Received 17 February 2017; Received in revised form 24 April 2017; Accepted 13 May 2017 Available online 15 May 2017 1044-5803/ © 2017 Elsevier Inc. All rights reserved.
Materials Characterization 129 (2017) 305–312
H. Terasaki et al.
Table 2 Martensite fractions for applied thermal cycles.
Temperature / K
1273 K (1000 °C), 30s 223 K/s Isothermal holding T1-T5 T7
T6
Fig. 1. Diagram of various applied thermal cycles (T1–T7).
2. Experimental Procedures A low-carbon steel with a composition of Fe-0.1 C-0.01 Si-2.0 Mn0.008 P-0.001 S (mass pct) was used. Plate specimens 200 mm in length, 20 mm in width and 2.0 mm thickness were cut from the hotrolled flat bar and heat treated using electrical heating apparatus. It was austenitized at 1273 K (1000 °C) for 30 s and then subjected to seven different thermal cycles. Fig. 1 shows the seven thermal cycles, which are referred to as T1–T7. In cycle T7, the steel was cooled to room temperature at the maximum rate using helium gas. In cycle T6, the steel was cooled to room temperature at a rate of 50 K/s. In cycles T1–T5, the steel was cooled at 50 K/s and then maintained at a given temperature shown in Table 1. The holding time for T1–T5 was 1000 s. The samples were subsequently cooled to room temperature, as shown in Fig. 1. These seven thermal cycles produced seven different steel microstructures to be classified. The martensite fraction (other microstructure was bainite) for each cycle was estimated via dilatation method and it was summarized in Table 2. The microstructures are referred to by the abbreviations for the corresponding thermal cycles (T1–T7) in the present study. After conventional metallographic preparation, polished surface (quarter with reference to the original surface) were etched with 3% nital for subsequent optical microscopy and scanning electron microscopy (SEM). A SEM equipped with a TSL EBSD system was used at an accelerating voltage of 15 kV and a step size of 100 nm. The analyzed area was 12,800 μm, which gave statistical microstructural data corresponding to the applied thermal cycle. No cleanup was performed on the as-acquired dataset. Using EBSD data, the boundaries of six variant pairs in KSORs were visualized. Furthermore, the variant-pair density was quantified by dividing the variant-pair boundary lengths by the observation area with resulting units of μm− 1. The variant-pair names (boundary color), misorientation angles between variant pairs, and rotation axes proposed by Morito et al. [15] are summarized in Table 3. The misorientation angle was defined to consider the shift from the ideal KSOR condition, which is often observed in experiments involving low-carbon steel [14,16]. A kernel average misorientation (KAM) was derived using a third-generation condition and a maximum misorientation of 2° because the mode value of the misorientation angle distribution of lath boundaries measured by TEM Kikuchi pattern analysis was approximately 1.5° [17].
T1 T2 T3 T4 T5
773 K 723 K 673 K 623 K 573 K
T1 T2 T3 T4 T5 T6 T7
0 2.1 63.6 63.9 62.2 70.0 97.8
Variant pair name (in boundary color)
Misorientaion angle between variant pair (Shifted from just KSOR)/degrees
Rotation axis
V1–V2
68
<011>α′
V1–V3/V5
60
<011>α′
V1–V6
52
<011>α′
V1–V4
7
<011>α′
3. Results and Discussion Figs. 2 and 3 show optical microscope and SEM images, respectively, for samples T1–T7. In samples T1 and T2, large blocks and chunks of a second phase were observed. By contrast, fine-scale blocks and second-phase particles were detected in samples T3–T7. Such large changes in block and second-phase size are easy to track qualitatively. However, more experience is needed to classify microstructures between samples T1 and T2 and among samples T3–T7 at this observation scale. Our objective was to find a quantitative method for classifying the steel samples' microstructures. Fig. 4 shows the results of Vickers hardness tests for samples T1–T7. The Vickers hardness is an effective mechanical parameter used to classify steel microstructures. Thus, it can be used to quantitatively classify the microstructures among samples T1, T2, and T3, as shown in Fig. 3; however, its use in classifying microstructures among samples T4–T7 remains difficult. To quantitatively classify the steel microstructures, we propose a classification space with two dimensions. One of the chosen dimensions is the variant-pair density. Fig. 5 shows an inverse pole figure map for samples T1–T7, and Fig. 6 shows variant-pair boundaries superimposed on the image quality map. The variant-pair boundaries for V1–V2, V1–V3/V5, V1–V6, and V1–V4 are visualized using red, green, blue, and yellow lines, respectively. Fig. 5 shows that the block size decreases with decreasing transformation temperature, as expected. This trend is supported by the variant-pair boundary distribution shown in Fig. 6. As shown in Fig. 6(a), the V1–V4 pair (yellow line) with low misorientation angles was the majority pair in sample T1 and the total amount of variant-pair boundaries was less than in the other samples. With decreasing transformation temperature, the V1–V2 pair (red line) with high misorientation angles and the total amount of variant-pair densities both increase. To quantitatively analyze the variant-pair density, Fig. 7 shows the variant-pair density distributions measured from Fig. 6 for samples T1–T7. As shown by Takayama et al. [13], the V1–V2 pair and the V1–V4 pair show large changes with decreasing transformation temperature. The V1–V4 pair is abundant in T1, whereas the V1–V2 pair increases and the V1–V4 pair decreases as the transformation temperature decreases, as shown in the case of sample T2. As transformation temperature decreases further, the V1–V2 pair increases further and the V1–V3/V5 pair increases as shown in the case of sample T3. In the cases of samples T3–T7, the V1–V4 pair again increases, reflecting increasing
Table 1 Isothermal holding temperature for applied thermal cycles. Isothermal holding temperature
Martensite fraction/%
Table 3 KSOR variant-pair names, rotation axes, and misorientation angles proposed by Morito et al. [15].
Time / s
Thermal cycle
Thermal cycle
(500 °C) (450 °C) (400 °C) (350 °C) (300 °C)
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Fig. 2. OM images for samples (a) T1, (b) T2, (c) T3, (d) T4, (e) T5, (f) T6, and (g) T7.
In Fig. 7, the V1–V6 pair does not appear to successfully indicate microstructural changes. To compare the dimension of “variant-pair density” with another dimension (KAM) in suggested 2D space, we carried out normalization by setting the dispersion of each variant pair
numbers of sub-blocks [14]. Therefore, tracking the V1–V2 and the V1–V4 pairs reveals that the aforementioned three-stage change depends on the transformation temperature, as suggested by Takayama et al. [13]. 307
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Fig. 3. SEM images for samples (a) T1, (b) T2, (c) T3, (d) T4, (e) T5, (f) T6, and (g) T7.
stepwise fashion with decreasing transformation temperature. Thus, the V1–V6 pair is a suitable dimension in microstructure classification space. As shown in Fig. 8, distinguishing the V1–V6 pairs between T5 and T6 was difficult. As shown in Table 1 and Fig. 1, in thermal cycle T5, the
to 1. This procedure allows two dimensions with different properties to be used in the same 2D space. Fig. 8 shows the normalized distributions of variant-pair densities. In this case, the V1–V6 pair can clearly be used to effectively classify the microstructures in samples T1–T7. The V1–V6 pair increases in a 308
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sample was cooled at 50 K/s and the phase transformation occurred in the following isothermal stage at 573 K (300 °C). In thermal cycle T6, the sample was cooled at a rate of 50 K/s to room temperature. Thus, nearly identical microstructures appear to have formed in samples T5 and T6. In the present study, another dimension was proposed and a 2D space for microstructure classification was defined using two dimensions. In selecting another dimension, a quantity orthogonal [18] to the first dimension, which is the variant-pair density, is best used. Therefore, the KAM was selected as the other dimension. The KAM value is known to reflect dislocation densities [19]. Fig. 9(a) shows the KAM distributions, and Fig. 9(b) shows normalized distributions of KAM for samples T1–T7 for comparison with other dimensions. Both figures show that a group comprising samples T1 and T2 and another group comprising samples T3–T7 exist in terms of KAM values. Martensite is well known to contain many dislocations because of slip that occurs to minimize the transformation strain. Therefore, the two groups classified by the KAM dimension are compatible with the fact that the martensite start temperature of the present samples is 709 K (436 °C).
Vickers hardness / HV
400
300
200
100
0
T1
T2
T3
T4
T5
T6
T7
Fig. 4. Results of Vickers hardness tests.
(a)
(b)
30um
(c)
30um
(d)
30um
(e)
30um
(f)
30um
30um
(g)
30um
Fig. 5. IPF maps for samples (a) T1, (b) T2, (c) T3, (d) T4, (e) T5, (f) T6, and (g) T7.
309
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H. Terasaki et al.
(a)
(b)
30um
30um
(c)
(d)
30um
30um
(f)
(e)
30um
30um
(g)
V1-V2 V1-V3/V5 V1-V6 V1-V4
30um
Density of variant pair boudaries (Normalized) / NA
Density of variant pair boudaries / μm
-1
Fig. 6. Variant-pair boundaries superimposed on the image quality map for samples (a) T1, (b) T2, (c) T3, (d) T4, (e) T5, (f) T6, and (g) T7. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Fig. 7. Densities of variant-pair boundaries for thermal cycles T1–T7.
Fig. 8. Normalized densities of variant-pair boundaries corresponding to those in Fig. 7.
310
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(b ) Kernel average misorientation (normalized) / NA
Kernel average misorientation / degrees
(a )
Fig. 9. (a) KAM for thermal cycles T1–T7 and (b) normalized KAM for thermal cycles T1–T7.
(a)
(b) T5 T6 T4
T7 T3
T3
T6 T5 T4
T7
T2
T2 T1
T1
KAM (normalized) / NA
(c)
(d)
T7 T6 T2
T6
T5 T4
T5 T4
T3 T1
T3
T2
T7
T1
Fig. 10. Microstructure classification space using dimensions of KAM and variant pairs (a) V1–V2, (b) V1–V3/5, (c) V1–V6, and (d) V1–V4.
observed, thereby allowing the seven microstructures to be classified. However, some rationale should be chosen for selecting the best space. The largest difference in conditions occurred between samples T1 and T7, which is a reasonable basis to use for selecting the microstructural classification space. Therefore, the space wherein the distance between samples T1 and T7 is the largest was selected as the best space. Table 4 shows the distance between samples T1 and T7, which clearly reveals that the 2D space formed by the V1–V6 pair and KAM was the best space to use for classifying the mixed microstructures consisting of bainite and martensite formed in each of the seven different thermal cycles. Three groups can be recognized from the data in Table 2. The first group comprising T1 and T2 has less martensite, whereas the second group comprising T3, T4, T5, and T6 has a considerable amount of martensite (60%–70%). The third group comprising T7 is almost
Table 4 Distances between points for samples T1 and T7 in variant pair–KAM space. Variant pair
Distance between T1 and T7
V1–V2 V1–V3/V5 V1–V6 V1–V4
3.594 3.009 3.922 2.191
Using the aforementioned dimensions, we created a 2D microstructure classification space. Fig. 10 shows the 2D space created using the normalized KAM and normalized variant-pair density values of (a) V1–V2, (b) V1–V3/V5, (c) V1–V6, and (d) V1–V4. Seven microstructures were observed in the 2D space. In each case, no overlap is 311
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density of V1–V6 was sensitive to changes in transformation temperature. Thus, the V1–V6 variant-pair density can be used to effectively classify microstructures, as determined by normalization of the variant-pair density. 2. A 2D space with the V1–V6 variant-pair density and KAM used as dimensions was proposed for microstructure classification. The microstructures produced during seven different thermal cycles were classified in the proposed 2D space. 3. The microstructures (mixed microstructures containing bainite and martensite) formed during the seven thermal cycles were defined using crystallographic properties. This approach provides a method for digital representation of steel microstructures formed under various thermal conditions.
completely composed of martensite. The 2D space formed by the V1–V6 pair and KAM has clearly separated these three groups, as shown in Fig. 10(c). In the 2D space formed by the V1–V6 pair and KAM, T7 was positioned to the left of T4 and T5. This suggested that T7 was tempered during the cooling cycle, and this fact was correlated to the hardness data in Fig. 4. When a 2D space is used to classify the microstructures formed in each thermal cycle, we can define each microstructure using two crystallographic values. For example, the T7 microstructure was described earlier as a mixed microstructure of martensite (dominant) and bainite. However, using a 2D space, we refer to T7 using two crystallographic values: (10.6, 4.4). This approach is an effective method for digitally representing steel microstructures. Our study reveals the importance of the minor variant pair V1–V6 for classifying steel microstructures. The question arises as to why the minor variant important for characterizing steel microstructures is formed in different thermal cycles (for mixed microstructures of bainite and martensite). It originates from accommodation phenomena during phase transformation. As the transformation temperature decreases, the yield strength of the parent austenite increases, which makes accommodation of the phase transformation strain by surrounding austenite difficult. It should be accommodated by a combination of variants including V6 to minimize the shape strain [14]. The minor variant pair V1–V6 increases in a stepwise fashion as the transformation temperature decreases and acts as a dimension in 2D space that is sensitive to the transformation temperature.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
4. Conclusions We developed a new approach to classifying steel microstructures with a crystallographic perspective and applied the developed approach to the classification of mixed microstructures comprising bainite and martensite formed under seven thermal cycling treatments in lowcarbon steel. The following results were obtained:
[16] [17] [18] [19]
1. Densities of variant-pair boundaries for seven thermal cycles were visualized and quantified in low-carbon steel. The variant-pair
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Contents lists available at ScienceDirect
Materials Characterization journal homepage: www.elsevier.com/locate/matchar
Digital identification scheme for steel microstructures in low-carbon steel a,⁎
a
b
b
Hidenori Terasaki , Yu Miyahara , Kotaro Hayashi , Koji Moriguchi , Shigekazu Morito a b c
MARK
c
Faculty of Advanced Science and Technology, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan Technical Research & Development Bureau, Nippon Steel & Sumitomo Metal Corporation, 20-1 Shintomi, Futtsu, Chiba 293-8511, Japan Department of Materials Science, Shimane University, 1060 Nishikawatsu, Matsue, Shimane 690-8504, Japan
A R T I C L E I N F O
A B S T R A C T
Keywords: Identification scheme for steel microstructure Kurdjumov–Sachs orientation relationship variants Phase transformation
This study proposes a scheme for digital identification of a steel microstructure based on crystallographic features. A 2D space for classifying mixed microstructures of bainite and martensite formed by seven different thermal cycles is defined using two dimensions related to variants in Kurdjumov–Sachs orientation relationships and dislocations. As a dimension relating to variants, the minor variant pair characterized by a rotation axis of 〈011〉 and a rotation angle of 52° is most useful in classifying the steel microstructure. Furthermore, the kernel average misorientation also served as a suitable dimension for the 2D space. The reasons for using the minor variant pair to classify steel microstructures are discussed from the viewpoint of phase transformation phenomena. The present study demonstrates the possibility for steel microstructures to be digitally identified.
1. Introduction Various microstructures can be designed using different thermal cycling procedures in low-carbon steel as a result of phase transformations, which enables control of a wide range of mechanical properties such as tensile strength. Recent demand for high-strength steel structures has resulted in a tendency toward using mixed microstructures of bainite (upper and lower bainite) and martensite. Therefore, understanding and classifying the mixed microstructures of bainite and martensite formed by various thermal cycling procedures is essential. A bainite classification scheme based on carbide precipitate morphology has been suggested [1]. Another classification scheme is based on bainitic ferrite morphology [2]. In low-carbon steel, martensite has a single morphology known as lath martensite and no carbide is observed. These classification schemes were developed from the perspective of morphology. A classification scheme based on carbide morphology is particularly effective. However, the application of electron backscattering diffraction (EBSD) methods to analyze steel microstructures [3–13] enables a statistical microstructural classification scheme based on crystallographic features and suitable for novices. Takayama et al. [13] investigated the frequency of variant pairs in Kurdjumov–Sachs orientation relationships (KSORs) in the transformation temperature range for bainite and martensite in low-carbon steel. By focusing on four variant pairs in one packet, they noted that the variant-pair frequency varied strongly among bainite formed at high temperatures, bainite formed at low temperatures, and martensite.
⁎
These four variant pairs are referred to as V1–V2, V1–V3/5, V1–V6, and V1–V4 according to the definition proposed by Morito et al. [14] They clarified that the V1–V4 pair with low-angle boundaries dominates in bainite at high temperatures and that the V1–V2 pair with high-angle boundaries increases and V1–V4 decreases with decreasing transformation temperature. In martensite, the V1–V4 pair again increases, reflecting sub-block formation [14]. Morito et al. [15] demonstrated a simpler method for assessing variant-pair frequencies using block boundary profiles. Their method enables the variant frequency to be quantitatively analyzed over a wide area using EBSD data. The aforementioned studies provide a basis for the digital classification of steel microstructures, including mixed microstructures, from a crystallographic perspective. The digital classification scheme has opened doors for the automatic recognition of steel microstructure and/or automatic prediction of mechanical properties of steel based on the recognition of mixed-steel microstructure, using artificial intelligence. In order to achieve the scheme, steel microstructure including mixed microstructure should be evaluated in feature space defined by dimensions (feature vector) that characterize the steel microstructures. In the present study, a 2D space to classify the mixed microstructures comprising bainite and martensite formed during seven thermal cycles using a low-carbon steel were suggested and a method for digital classification in the 2D space is proposed. The results show that the minor variant pair (V1–V6) plays an important role in classifying steel microstructures.
Corresponding author at: 2-39-1 Kurokami, Kumamoto 860-8555, Japan. E-mail addresses: [email protected] (H. Terasaki), [email protected] (Y. Miyahara), [email protected] (K. Hayashi), [email protected] (K. Moriguchi), [email protected] (S. Morito). http://dx.doi.org/10.1016/j.matchar.2017.05.021 Received 17 February 2017; Received in revised form 24 April 2017; Accepted 13 May 2017 Available online 15 May 2017 1044-5803/ © 2017 Elsevier Inc. All rights reserved.
Materials Characterization 129 (2017) 305–312
H. Terasaki et al.
Table 2 Martensite fractions for applied thermal cycles.
Temperature / K
1273 K (1000 °C), 30s 223 K/s Isothermal holding T1-T5 T7
T6
Fig. 1. Diagram of various applied thermal cycles (T1–T7).
2. Experimental Procedures A low-carbon steel with a composition of Fe-0.1 C-0.01 Si-2.0 Mn0.008 P-0.001 S (mass pct) was used. Plate specimens 200 mm in length, 20 mm in width and 2.0 mm thickness were cut from the hotrolled flat bar and heat treated using electrical heating apparatus. It was austenitized at 1273 K (1000 °C) for 30 s and then subjected to seven different thermal cycles. Fig. 1 shows the seven thermal cycles, which are referred to as T1–T7. In cycle T7, the steel was cooled to room temperature at the maximum rate using helium gas. In cycle T6, the steel was cooled to room temperature at a rate of 50 K/s. In cycles T1–T5, the steel was cooled at 50 K/s and then maintained at a given temperature shown in Table 1. The holding time for T1–T5 was 1000 s. The samples were subsequently cooled to room temperature, as shown in Fig. 1. These seven thermal cycles produced seven different steel microstructures to be classified. The martensite fraction (other microstructure was bainite) for each cycle was estimated via dilatation method and it was summarized in Table 2. The microstructures are referred to by the abbreviations for the corresponding thermal cycles (T1–T7) in the present study. After conventional metallographic preparation, polished surface (quarter with reference to the original surface) were etched with 3% nital for subsequent optical microscopy and scanning electron microscopy (SEM). A SEM equipped with a TSL EBSD system was used at an accelerating voltage of 15 kV and a step size of 100 nm. The analyzed area was 12,800 μm, which gave statistical microstructural data corresponding to the applied thermal cycle. No cleanup was performed on the as-acquired dataset. Using EBSD data, the boundaries of six variant pairs in KSORs were visualized. Furthermore, the variant-pair density was quantified by dividing the variant-pair boundary lengths by the observation area with resulting units of μm− 1. The variant-pair names (boundary color), misorientation angles between variant pairs, and rotation axes proposed by Morito et al. [15] are summarized in Table 3. The misorientation angle was defined to consider the shift from the ideal KSOR condition, which is often observed in experiments involving low-carbon steel [14,16]. A kernel average misorientation (KAM) was derived using a third-generation condition and a maximum misorientation of 2° because the mode value of the misorientation angle distribution of lath boundaries measured by TEM Kikuchi pattern analysis was approximately 1.5° [17].
T1 T2 T3 T4 T5
773 K 723 K 673 K 623 K 573 K
T1 T2 T3 T4 T5 T6 T7
0 2.1 63.6 63.9 62.2 70.0 97.8
Variant pair name (in boundary color)
Misorientaion angle between variant pair (Shifted from just KSOR)/degrees
Rotation axis
V1–V2
68
<011>α′
V1–V3/V5
60
<011>α′
V1–V6
52
<011>α′
V1–V4
7
<011>α′
3. Results and Discussion Figs. 2 and 3 show optical microscope and SEM images, respectively, for samples T1–T7. In samples T1 and T2, large blocks and chunks of a second phase were observed. By contrast, fine-scale blocks and second-phase particles were detected in samples T3–T7. Such large changes in block and second-phase size are easy to track qualitatively. However, more experience is needed to classify microstructures between samples T1 and T2 and among samples T3–T7 at this observation scale. Our objective was to find a quantitative method for classifying the steel samples' microstructures. Fig. 4 shows the results of Vickers hardness tests for samples T1–T7. The Vickers hardness is an effective mechanical parameter used to classify steel microstructures. Thus, it can be used to quantitatively classify the microstructures among samples T1, T2, and T3, as shown in Fig. 3; however, its use in classifying microstructures among samples T4–T7 remains difficult. To quantitatively classify the steel microstructures, we propose a classification space with two dimensions. One of the chosen dimensions is the variant-pair density. Fig. 5 shows an inverse pole figure map for samples T1–T7, and Fig. 6 shows variant-pair boundaries superimposed on the image quality map. The variant-pair boundaries for V1–V2, V1–V3/V5, V1–V6, and V1–V4 are visualized using red, green, blue, and yellow lines, respectively. Fig. 5 shows that the block size decreases with decreasing transformation temperature, as expected. This trend is supported by the variant-pair boundary distribution shown in Fig. 6. As shown in Fig. 6(a), the V1–V4 pair (yellow line) with low misorientation angles was the majority pair in sample T1 and the total amount of variant-pair boundaries was less than in the other samples. With decreasing transformation temperature, the V1–V2 pair (red line) with high misorientation angles and the total amount of variant-pair densities both increase. To quantitatively analyze the variant-pair density, Fig. 7 shows the variant-pair density distributions measured from Fig. 6 for samples T1–T7. As shown by Takayama et al. [13], the V1–V2 pair and the V1–V4 pair show large changes with decreasing transformation temperature. The V1–V4 pair is abundant in T1, whereas the V1–V2 pair increases and the V1–V4 pair decreases as the transformation temperature decreases, as shown in the case of sample T2. As transformation temperature decreases further, the V1–V2 pair increases further and the V1–V3/V5 pair increases as shown in the case of sample T3. In the cases of samples T3–T7, the V1–V4 pair again increases, reflecting increasing
Table 1 Isothermal holding temperature for applied thermal cycles. Isothermal holding temperature
Martensite fraction/%
Table 3 KSOR variant-pair names, rotation axes, and misorientation angles proposed by Morito et al. [15].
Time / s
Thermal cycle
Thermal cycle
(500 °C) (450 °C) (400 °C) (350 °C) (300 °C)
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Fig. 2. OM images for samples (a) T1, (b) T2, (c) T3, (d) T4, (e) T5, (f) T6, and (g) T7.
In Fig. 7, the V1–V6 pair does not appear to successfully indicate microstructural changes. To compare the dimension of “variant-pair density” with another dimension (KAM) in suggested 2D space, we carried out normalization by setting the dispersion of each variant pair
numbers of sub-blocks [14]. Therefore, tracking the V1–V2 and the V1–V4 pairs reveals that the aforementioned three-stage change depends on the transformation temperature, as suggested by Takayama et al. [13]. 307
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Fig. 3. SEM images for samples (a) T1, (b) T2, (c) T3, (d) T4, (e) T5, (f) T6, and (g) T7.
stepwise fashion with decreasing transformation temperature. Thus, the V1–V6 pair is a suitable dimension in microstructure classification space. As shown in Fig. 8, distinguishing the V1–V6 pairs between T5 and T6 was difficult. As shown in Table 1 and Fig. 1, in thermal cycle T5, the
to 1. This procedure allows two dimensions with different properties to be used in the same 2D space. Fig. 8 shows the normalized distributions of variant-pair densities. In this case, the V1–V6 pair can clearly be used to effectively classify the microstructures in samples T1–T7. The V1–V6 pair increases in a 308
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sample was cooled at 50 K/s and the phase transformation occurred in the following isothermal stage at 573 K (300 °C). In thermal cycle T6, the sample was cooled at a rate of 50 K/s to room temperature. Thus, nearly identical microstructures appear to have formed in samples T5 and T6. In the present study, another dimension was proposed and a 2D space for microstructure classification was defined using two dimensions. In selecting another dimension, a quantity orthogonal [18] to the first dimension, which is the variant-pair density, is best used. Therefore, the KAM was selected as the other dimension. The KAM value is known to reflect dislocation densities [19]. Fig. 9(a) shows the KAM distributions, and Fig. 9(b) shows normalized distributions of KAM for samples T1–T7 for comparison with other dimensions. Both figures show that a group comprising samples T1 and T2 and another group comprising samples T3–T7 exist in terms of KAM values. Martensite is well known to contain many dislocations because of slip that occurs to minimize the transformation strain. Therefore, the two groups classified by the KAM dimension are compatible with the fact that the martensite start temperature of the present samples is 709 K (436 °C).
Vickers hardness / HV
400
300
200
100
0
T1
T2
T3
T4
T5
T6
T7
Fig. 4. Results of Vickers hardness tests.
(a)
(b)
30um
(c)
30um
(d)
30um
(e)
30um
(f)
30um
30um
(g)
30um
Fig. 5. IPF maps for samples (a) T1, (b) T2, (c) T3, (d) T4, (e) T5, (f) T6, and (g) T7.
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(a)
(b)
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30um
(c)
(d)
30um
30um
(f)
(e)
30um
30um
(g)
V1-V2 V1-V3/V5 V1-V6 V1-V4
30um
Density of variant pair boudaries (Normalized) / NA
Density of variant pair boudaries / μm
-1
Fig. 6. Variant-pair boundaries superimposed on the image quality map for samples (a) T1, (b) T2, (c) T3, (d) T4, (e) T5, (f) T6, and (g) T7. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Fig. 7. Densities of variant-pair boundaries for thermal cycles T1–T7.
Fig. 8. Normalized densities of variant-pair boundaries corresponding to those in Fig. 7.
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(b ) Kernel average misorientation (normalized) / NA
Kernel average misorientation / degrees
(a )
Fig. 9. (a) KAM for thermal cycles T1–T7 and (b) normalized KAM for thermal cycles T1–T7.
(a)
(b) T5 T6 T4
T7 T3
T3
T6 T5 T4
T7
T2
T2 T1
T1
KAM (normalized) / NA
(c)
(d)
T7 T6 T2
T6
T5 T4
T5 T4
T3 T1
T3
T2
T7
T1
Fig. 10. Microstructure classification space using dimensions of KAM and variant pairs (a) V1–V2, (b) V1–V3/5, (c) V1–V6, and (d) V1–V4.
observed, thereby allowing the seven microstructures to be classified. However, some rationale should be chosen for selecting the best space. The largest difference in conditions occurred between samples T1 and T7, which is a reasonable basis to use for selecting the microstructural classification space. Therefore, the space wherein the distance between samples T1 and T7 is the largest was selected as the best space. Table 4 shows the distance between samples T1 and T7, which clearly reveals that the 2D space formed by the V1–V6 pair and KAM was the best space to use for classifying the mixed microstructures consisting of bainite and martensite formed in each of the seven different thermal cycles. Three groups can be recognized from the data in Table 2. The first group comprising T1 and T2 has less martensite, whereas the second group comprising T3, T4, T5, and T6 has a considerable amount of martensite (60%–70%). The third group comprising T7 is almost
Table 4 Distances between points for samples T1 and T7 in variant pair–KAM space. Variant pair
Distance between T1 and T7
V1–V2 V1–V3/V5 V1–V6 V1–V4
3.594 3.009 3.922 2.191
Using the aforementioned dimensions, we created a 2D microstructure classification space. Fig. 10 shows the 2D space created using the normalized KAM and normalized variant-pair density values of (a) V1–V2, (b) V1–V3/V5, (c) V1–V6, and (d) V1–V4. Seven microstructures were observed in the 2D space. In each case, no overlap is 311
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density of V1–V6 was sensitive to changes in transformation temperature. Thus, the V1–V6 variant-pair density can be used to effectively classify microstructures, as determined by normalization of the variant-pair density. 2. A 2D space with the V1–V6 variant-pair density and KAM used as dimensions was proposed for microstructure classification. The microstructures produced during seven different thermal cycles were classified in the proposed 2D space. 3. The microstructures (mixed microstructures containing bainite and martensite) formed during the seven thermal cycles were defined using crystallographic properties. This approach provides a method for digital representation of steel microstructures formed under various thermal conditions.
completely composed of martensite. The 2D space formed by the V1–V6 pair and KAM has clearly separated these three groups, as shown in Fig. 10(c). In the 2D space formed by the V1–V6 pair and KAM, T7 was positioned to the left of T4 and T5. This suggested that T7 was tempered during the cooling cycle, and this fact was correlated to the hardness data in Fig. 4. When a 2D space is used to classify the microstructures formed in each thermal cycle, we can define each microstructure using two crystallographic values. For example, the T7 microstructure was described earlier as a mixed microstructure of martensite (dominant) and bainite. However, using a 2D space, we refer to T7 using two crystallographic values: (10.6, 4.4). This approach is an effective method for digitally representing steel microstructures. Our study reveals the importance of the minor variant pair V1–V6 for classifying steel microstructures. The question arises as to why the minor variant important for characterizing steel microstructures is formed in different thermal cycles (for mixed microstructures of bainite and martensite). It originates from accommodation phenomena during phase transformation. As the transformation temperature decreases, the yield strength of the parent austenite increases, which makes accommodation of the phase transformation strain by surrounding austenite difficult. It should be accommodated by a combination of variants including V6 to minimize the shape strain [14]. The minor variant pair V1–V6 increases in a stepwise fashion as the transformation temperature decreases and acts as a dimension in 2D space that is sensitive to the transformation temperature.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
4. Conclusions We developed a new approach to classifying steel microstructures with a crystallographic perspective and applied the developed approach to the classification of mixed microstructures comprising bainite and martensite formed under seven thermal cycling treatments in lowcarbon steel. The following results were obtained:
[16] [17] [18] [19]
1. Densities of variant-pair boundaries for seven thermal cycles were visualized and quantified in low-carbon steel. The variant-pair
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