Crystallographic Analysis on the Lower Bainite Formation at the Austenite Grain Boundary in Fe-0.6C-0.8Mn-1.8Si Steel in the Initial Stage of Transformation

Abstract

A crystallographic analysis was conducted on the lower bainite formed at the austenite grain boundary in Fe-0.6C-0.8Mn-1.8Si (in mass%) steel at the initial stage of transformation. The variant selection and the effect of the character of the austenite grain boundary on the formation of lower bainite were investigated from several perspectives: the character of the prior austenite grain boundary (PAGB), the crystal orientation relationship between the bainitic ferrite (BF) and the adjacent prior austenite grain (PAG) across the PAGB, and the geometrical relationship between the BF and PAGB plane. BFs do not form at twin boundaries but form at high-angle grain boundaries. The effect of the orientation of the adjacent PAG across the PAGB is not dominant in the case of lower bainite formation, while the PAGB plane strongly affects the formation and the variant selection of BF. BF tends to form when its habit plane or shape deformation direction is nearly parallel to the PAGB plane. It is suggested that the formation of BF, whose HP is parallel to the PAGB, is favored from the perspectives of the interfacial energy, the elastic strain energy, and the plastic accommodation.

1. Introduction

Bainite is widely used in high-strength steels, such as transformation-induced plasticity (TRIP) steels, and its importance has been increasing. The bainitic transformation proceeds through the nucleation at austenite grain boundaries and the growth by the subsequent autocatalytic nucleation.¹⁾ Therefore, it is crucial to clarify the nucleation behavior of bainitic ferrite (BF) at austenite grain boundaries in order to understand the transformation process. Since BF (bcc, α) holds the Kurdjumov–Sachs orientation relationship (K–S OR) with the austenite grain (fcc, γ) ((111)γ//(011)α, [-101]γ//[-1-11]α),²⁾ 24 equivalent orientations (variants) of BF can be formed in a single austenite grain. The potency for nucleation at austenite grain boundaries varies, resulting in the formation of the specific variant, which is known as variant selection.^{3,4,5,6,7,8,9)} Variant selection rules have been studied for upper bainite,^3,4,5,6) lath martensite,⁷⁾ and lenticular martensite.^8,9) Considering the crystal orientation relationship between the BF and the adjacent austenite across the austenite grain boundary, the BF, which holds near the K–S OR with the adjacent austenite grain, forms preferentially (near K-S rule³⁾). The BF is reported to have a lower interfacial energy with the austenite grain when the BF satisfies the K-S OR.¹⁰⁾ This selection rule implies that BF can form with low interfacial energy with the adjacent austenite grain.³⁾ From the perspective of the geometrical relationship between the BF and the austenite grain boundary plane, the angles between the austenite grain boundary plane and important crystallographic planes and directions, such as close-packed direction (CD, [-1 0 1] γ//[1 -1 -1] α), close-packed plane (CP, (1 1 1) γ//(0 1 1) α), shape deformation direction (SDD), etc., have been investigated. It is reported that the BF whose CD is close to parallel to the prior austenite grain boundary (PAGB) plane is preferentially observed (CD//PAGB rule),³⁾ and the BF whose SDD is close to parallel to the PAGB plane is also preferentially observed (SDD//PAGB rule).⁴⁾

The dominant variant selection rule varies depending on the chemical compositions of steels and the transformation temperatures. With the increase in carbon content or the decrease in the transformation temperature, the fraction of BF that satisfies the near K-S rule decreases, while the fraction of the BF, which satisfies the SDD//PAGB rule and CD//PAGB rule, increases.⁴⁾ This is considered to be due to the difference in the austenite strength. Since the austenite matrix is softer at high temperatures and low carbon contents, the shape strain can be easily accommodated by the plastic accommodation in the austenite grain. While at lower temperatures and higher carbon contents, the austenite matrix is strengthened; thus, the accommodation in the austenite grain is more difficult, and the shape strain is accommodated by the grain boundary sliding.⁴⁾ Although the effects of the chemical compositions of steels and the transformation temperatures on the variant selection of BF have been investigated,⁴⁾ the range of transformation temperatures is higher than 400°C. It is reported that the morphology of BF changes around 400°C from parallel laths (upper bainite, above 400°C) to plate shapes (lower bainite, below 400°C) in the case of Fe-2Si-1Mn-0.6C steel.¹¹⁾ It is noted that the definition of upper or lower bainite is not unified. The upper or lower bainite is classified based on the morphology of the BF^11,12,13) or carbide.¹⁴⁾ In the case of Si-containing steels, the bainite does not contain carbide.^11,15) Therefore, the bainite in this study is classified based on the morphology of BF; when the BFs form in a feather-like shape (parallel laths), they are classified as upper bainite, and when the BFs form in plate shapes, they are classified as lower bainite.^11,12,13) Although the variant selection of upper bainite has been widely studied, the variant selection of lower bainite has not been well studied. In addition, the effect of the character of austenite grain boundary on the formation of BF is still unclear.

This study aimed to clarify the effect of the austenite grain boundary character on the formation of the BF and variant selection of lower bainite in the early stages of transformation. Thus, in this study, the character of austenite grain boundary, such as the misorientation, grain boundary plane, and grain boundary energy, were investigated. In addition, the crystal orientation relationship between the BF and the adjacent austenite grain and the geometrical relationship between the BF and PAGB plane were investigated in detail to consider the variant selection rule and its mechanism.

2. Experimental Procedures

The steel with a chemical composition of Fe-0.61C-0.81Mn-1.79Si-0.027Al (mass%) was used in this study. The M_s of the steel was 260°C (estimated by the dilatation curve measurement). The steel was homogenized at 1200°C for 24 h and cut into 8 mm in diameter and 12 mm in height cylindrical samples. Subsequent heat treatment was conducted using a thermomechanical simulator (Thermecmastor-Z, Fuji Electronic Industrial). Initially, the sample was austenitized at 1200°C for 300 s, followed by quenching to 350°C, and kept for 15 s to proceed with the lower bainite transformation. Based on the dilatation curve, it was estimated that approximately 2% of the bainitic transformation proceeded during this step. Following the isothermal holding, the sample was quenched to room temperature to stop the bainite transformation.

The sample for microstructural characterizations were prepared using the standard metallographic polishing with up to 1 μm of alumina. Microstructural characterizations were conducted using optical microscopy (OM) and scanning electron microscopy (SEM; JSM-7001FA, JEOL) after etching with a 2% Nital solution. Electron backscatter diffraction (EBSD) measurements were performed for the non-etched surface after polishing with 0.04 μm colloidal silica under an SEM equipped with an EBSD system (OIM data collection 7, TSL) at an acceleration voltage of 15 kV and a step size ranging from 0.04 to 0.5 μm.

The character of the grain boundaries comprises the crystal orientation relationship between the grains (misorientation is defined by the misorientation axis and the misorientation angle¹⁶⁾) and the orientation of the grain boundary plane. The crystal orientation of prior austenite grains (PAGs) cannot be obtained directly at room temperature because austenite grains have transformed into martensite. The crystal orientation of PAGs is usually estimated from the crystal orientation of martensite using the K–S OR.³⁾ In this study, the crystal orientation of PAGs was estimated using the TSL–OIM software (OIM analysis 7, TSL) and MATLAB toolbox, MTEX,¹⁷⁾ and PAG GUI.¹⁸⁾ The PAGB plane analysis was conducted following Ref. 6 using Vickers indent. In terms of classical nucleation theory,^19,20) ferrite nucleation may occur at austenite grain boundaries with higher grain boundary energies; therefore, the grain boundary energy was calculated using GB5DOF²¹⁾ following Ref. 6.

The phenomenological theory of martensite crystallography (PTMC)^22,23) was used to calculate the SDD and habit plane (HP) of bainite.^24,25) In the bainitic transformation, the shape deformation matrix F is given by F = RBS₂S₁ = E + md⊗n. Here, R is the rigid body rotation matrix; B is the Bain deformation; S₂ and S₁ are lattice-invariant shears; E is the identity matrix; m is the magnitude of shape strain; d is SDD; n is HP. (The F and n are also called as invariant plane strain and invariant plane, respectively, because n is invariant by the deformation F. Typically, the HP corresponds to the plate surface of BF^22,23)) The HP of the BF differs depending on the transformation temperature.²⁶⁾ As transformation temperature decreases, the HP shifts from (5 7 5) γ, which is reported as the HP of lath martensite,²⁷⁾ to (3 15 10) γ, which is reported as the HP of lenticular martensite.²⁸⁾ In the case that the HP is parallel to (h k h) γ, the HPs of twin-related variants (ex. V1 and V2 in Ref. 27) are parallel. In this study, it was confirmed that is close to (0.33 0.49 0.80) γ from the serial sectioning and the HPs of twin-related variants were not parallel. Therefore, the single shear model,^22,28) which predicts the HP of lenticular martensite, was applied. In the single shear model, the shear system of S₁ is (1 0 1)[-1 0 1] γ, (1 2 1)[-1 -1 1] α (S₂ = E) was applied²²⁾ and the HP was (0.178 0.786 0.591) γ, and SDD was [-0.201 0.707 -0.678] γ.

3. Result

3.1. Morphology of Bainitic Ferrite Formed at Prior Austenite Grain Boundaries

Figure 1(a) shows the OM image of the sample partially transformed to bainite by isothermal holding. Figure 1(b) shows the OM image of BF corresponding to the enclosed region in Fig. 1(a). Figure 1(c) shows the typical SEM image of the BFs formed at PAGB. The BFs are darkly etched in the OM image. The plate-shaped BF formed nearly parallel to the PAGB, so the lower bainite formed in this condition. In the initial stage of transformation, BFs formed mainly on one side of the PAGB and did not cross the PAGB, as shown in Figs. 1(b) and 1(c). In the case of the diffusional transformation, the ferrite grows into both sides of the austenite grains,²⁹⁾ and in the case of the upper bainite transformation, the BF develops into feather shapes on both sides of the PAGB.^3,4,5,6) Therefore, the formation behavior of lower bainite differs from that of the diffusional transformation or the upper bainite transformation.

Fig. 1. (a) Optical image(OM) image of the sample. (b) The typical image of the bainitic ferrite (BF) formed at prior austenite grain boundary (PAGB) corresponding to the area enclosed by the square in (a). (c) Typical image of BF formed at PAGB by SEM. (Online version in color.)

3.2. Effect of the Character of the Prior Austenite Grain Boundary on the Formation of Bainitic Ferrite

In this study, the analysis was mainly conducted in a square with 3000 × 3000 μm². In this area, there were 61 PAGBs (with additional 11 twin boundaries) and BFs formed in 6 out of 61 PAGBs. In addition to this area, the PAGB where BFs were formed was additionally analyzed to investigate the character of the PAGBs. The PAGB plane analyses were conducted on 19 PAGBs where BFs were formed, on 54 PAGBs where BFs were not formed. (One PAGB was difficult to be analyzed because the PAGB plane was almost parallel to the polishing surface. Twins are not included in this count.)

The character of the PAGB plane was analyzed from the perspectives of the misorientation angle between two PAGs across PAGB (Δθ_γ1γ2), tilt- or twist-like grain boundary, grain boundary plane, and grain boundary energy. To evaluate tilt- or twist-like grain boundary, the angle between the misorientation axis and the PAGB plane normal (Δθ_{axis|PAGBnormal}) was investigated, where Δθ_{axis|PAGBnormal} is 0° at the pure twist grain boundary and 90° at the pure tilt grain boundary.

Figure 2 shows the relationship between the character of the PAGBs and the formation of BF. Figure 2(a) shows the distributions of Δθ_γ1γ2 and Δθ_{axis|PAGBnormal}. In Fig. 2(a), the black circles and crosses correspond to the PAGB planes where BFs were formed and the PAGB where BFs were not formed, respectively. It is reported that in the case of upper bainite transformation, the formation of BFs more preferentially observed at the tilt boundaries.³⁾ Table 1 shows the numbers of tilt-like PAGBs (Δθ_{axis|PAGBnormal} > 45°) and twist-like PAGBs (Δθ_{axis|PAGBnormal} < 45°). In Table 1, the number of the tilt-like PAGBs where BFs were formed is bigger than that of the twist-like PAGBs where BFs were formed. The BFs were mainly formed from the tilt-like grain boundary, as previously reported.³⁾ However, the numbers of tilt-like PAGBs and twist-like PAGBs are different. Based on the idea of the solid angle, the solid angle ω is given by ω(S) = ∫_Ssinθdθdϕ. Therefore, if the PAGB planes are randomly distributed, the probability of the tilt-like boundary P (θ_{axis|PAGBnormal} is higher than 45°) is given by $P=\frac{2}{4\pi }{\int }_{\pi /4}^{\pi /2}2\pi \text{sin}\theta d\theta$. Therefore, the fraction of the tilt-like PAGB is expected to be close to 0.7. From Table 1, the fraction of the tilt-like PAGBs where BF formed and the fraction of the tilt-like PAGB where BF did not form are approximately 0.7 in the experiments. Thus, it is suggested that the potency of BFs’ nucleation does not depend on the θ_{axis|PAGBnormal}.

Fig. 2. (a) Distribution of misorientation angles between two PAGs across PAGB (Δθ_γ1γ2) and the misorientation axis and the PAGB plane normal (Δθ_{axis|PAGBnormal}). (b) Distribution of grain boundary energies of the PAGB where BF formed and the PAGB where BF did not form. (c) Inverse pole figure of the PAGB plane normals. The PAGB planes in the coordinate system of PAGs where BFs formed are marked with black circles, the PAGB planes in the coordinate system of the adjacent PAGs where BFs did not form are marked with horizontal bars, and the PAGB plane where BF did not form are marked with crosses. The blue plus corresponds to the HP normal, and the dashed lines correspond to 10° line and 20° line from the HP normal.

Table 1. Numbers of the PAGBs where BFs were formed and the PAGBs where BFs were not formed at twist-like and tilt-like PAGBs and the fraction of tilt-like PAGBs.

	PAGB where BF were formed	PAGB where BF were not formed
Twist-like PAGB	6	18
Tilt-like PAGB	13	36
Fraction of tilt-like PAGB	0.68	0.67

Figure 2(b) shows the distribution of grain boundary energies calculated using GB5DOF. The grain boundary energies of high-angle austenite grain boundaries observed in this study are 0.8–1.3 J/m², and the grain boundary energy of the twin boundary is 0.04 J/m². The formation of BFs at twin boundaries was not observed. It is suggested that one of the reasons for the suppression of BFs at twin boundaries is the lower grain boundary energy. In high-angle austenite grain boundaries, BFs formed at the austenite grain boundaries regardless of the grain boundary energies; thus, the values of Δθ_γ1γ2, θ_{axis|PAGBnormal}, and the grain boundary energy do not affect the formation of the BF.

Figure 2(c) shows the inverse pole figure of the PAGB plane. Since the BF formed on one side of the PAGB plane, the PAGB plane in the coordinate system of PAG where BF formed is marked with a black circle, the PAGB plane in the coordinate system of the adjacent PAG where BF did not form is marked with a horizontal bar, and the PAGB plane where BF did not form is marked with a cross. Figure 2(c) shows that the BFs did not form at the austenite grain boundary planes near {0 0 1}γ or {1 1 1}γ. This result suggests that the orientation of the austenite grain boundary plane may affect the formation of BF.

3.3. Crystal Orientation Relationship between the Bainitic Ferrite and the Adjacent Austenite Grain

Figure 3(a) shows a typical SEM image of BFs formed at the PAGB. The HP of BF is nearly parallel to the PAGB plane. The EBSD orientation map with highlighted BF and martensite, and the corresponding (0 0 1)α pole figure of BFs and martensite are shown in Figs. 3(b) and 3(c), respectively. The BFs are highlighted in red, and the martensite is highlighted based on the PAGs; PAG1: light gray, PAG2: dark gray. From Fig. 3(c), the BF holds the K-S OR with PAG1, while the BF does not hold the K-S OR with PAG2.

Fig. 3. (a) SEM images of BF formed, and the corresponding (b) EBSD orientation map with highlighted BF and PAGs and (c) (0 0 1)α pole figure of BF (red) and the martensite in PAG 1, 2 (light gray, dark gray), and the K-S OR with PAG1 (dark gray rhombus). (Online version in color.)

The crystal orientation relationship between the BF and the adjacent PAG was investigated from the perspective of the near K-S rule. Figure 4 shows the distribution of the misorientation angle of the BF from the K-S OR in the adjacent PAG across the PAGB plane (Δθ_BFγ1|KSγ2). The Δθ_BFγ1|KSγ2 is calculated by the following procedures. First, the crystal orientation of 24 variants in the adjacent PAG is calculated. Then, the misorientation between the BF and the variants in the adjacent PAG (Δθ_BFγ1|V1γ2~Δθ_BFγ1|V24γ2) was calculated. Finally, the minimum value in Δθ_BFγ1|V1γ2 to Δθ_BFγ1|V24γ2 is defined as Δθ_BFγ1|KSγ2. In the previous studies,^3,4) when the Δθ_BFγ1|KSγ2 is smaller than 10°, the BF is considered to satisfy the near K-S rule. In this study, the fraction of the BFs which satisfy the near K-S rule is 53%. In our previous study,⁶⁾ the fraction of the BFs, which satisfy the near K-S rule, is more than 90% at the initial stage of transformation (the transformation rate is about 2%) at 450°C in the steel with the same chemical composition. Thus, the fraction of the BFs, which satisfy the near K-S rule, is less than that of the upper bainite. Therefore, in the case of lower bainite transformation, the near K-S rule is less dominant in the variant selection than the upper bainite transformation.

Fig. 4. Distribution of the misorientation angle of the BF from the Kurdjumov–Sachs orientation relationship in the adjacent PAG (Δθ_BFγ1|KSγ2).

3.4. Geometrical Relationship between the Bainitic Ferrite and the Prior Austenite Grain Boundary

The geometrical relationship between the BF and the PAGB plane was investigated to evaluate the influence of the geometrical orientation of the PAGB plane on the variant selection and the formation of BF in detail. Figure 5(a) is the corresponding pole figure to Fig. 3. In Fig. 5(a), the PAGB plane and the trace of the PAGB plane are plotted in addition to several crystallographic planes and directions of BF, such as CP, HP, CD, SDD, and <0 0 1>α in the sample coordinate system. In Fig. 5(a), the normal of the PAGB plane is close to the normal of the HP, implying that the angle between the HP and PAGB plane is small. Figure 5(b) shows the geometrical orientation relationship of PAGB plane normal and crystallographic planes and directions corresponding to Fig. 5(a) in the BF coordinate system. In Fig. 5(b), the axes of the pole figure are [0 0 1] α, [0 1 0] α, and [1 0 0] α of BF so that CD is [1 -1 -1]α and CP is (0 1 1)α. In Fig. 5(b), the crystal orientations of the BF, such as CP, HP, CD, and SDD, are fixed, and the PAGB plane normal becomes a variable. Figure 5(c) summarizes the geometrical orientation relationship between the BFs and PAGB planes. In Fig. 5(c), the normals of PAGB planes are plotted in the BF coordinate system, as shown in Fig. 5(b). In Fig. 5(c), the crystal orientations of BF, such as HP normal, CP normal, CD, SDD, and aggregates of the directions normal to CD and SDD (CD normal line, SDD normal line), are also plotted. From Fig. 5(c), the normals of PAGB planes are close to the of HP. Therefore, the BFs, whose HPs are close to parallel to the PAGB planes, were more preferentially formed in the case of the lower bainite (HP//PAGB rule). (It should be mentioned that in previous studies that investigated the variant selection of upper bainite,^3,4) the angle between the HP and PAGB plane was also examined; however, the HP was defined as CP since the HP of upper bainite is close to CP.²⁶⁾ In the case of lower bainite, the HP is different from CP; thus, the HP is defined based on the result of PTMC in this study.)

Fig. 5. (a) Pole figure showing the directions and the normal of the planes of BF, the normal of the PAGB plane, and the trace of the PAGB plane corresponding to Fig. 3(a) on the sample coordinate system and (b) on the coordinate system of BF. (c) The geometrical orientation relationship be-tween the BF and PAGB planes on the coordinate system of BF.

4. Discussion

The formation behavior of BF, the effect of the character of the austenite grain boundary on the formation of BF, and the variant selection of BF were investigated. It was shown that the near K-S rule is less dominant in the variant selection thus, the effect of the orientation of the adjacent austenite grain is not dominant. The geometrical orientation relationship between the BF and austenite grain boundary plane affected the variant selection of BF. The BF, whose HP is close to parallel to the PAGB planes, was formed in this study. The formation behavior that the twinned martensite, such as butterfly martensite, forms along the PAGB plane is observed.^30,31) There is a possibility that the formation behavior of lower bainite is similar to that of twinned martensite.

From the perspective of the interfacial energy, the BF whose HP is close to parallel to the austenite grain boundary plane is favored because the BF can eliminate the austenite grain boundary plane effectively. Under the assumption that the BF forms along the austenite grain boundary plane to minimize the increase in the interfacial energy, the shape of BF is considered to be the thin plate whose plate surface is parallel to the austenite grain boundary. From the perspective of the elastic strain energy, it is reported that the elastic strain energy differs by shape strain matrix and the morphology of the product phase (BF in this study).^32,33) Under the condition that the shape strain is the invariant plane strain, the elastic strain energy is minimized when the product phase has a thin plate shape whose plate surface is parallel to the HP.^32,33) In the case that the plate surface and HP are not parallel, the elastic strain energy increases as the deviation angle between the plate surface and HP increases.^32,33) Thus, under the assumption that the BF forms along the PAGB plane, the increase of the elastic strain energy is minimized when the austenite grain boundary plane is parallel to the HP. Therefore, from the perspective of the interfacial energy and the elastic strain energy, the HP//PAGB rule is favored.

Figure 6(a) shows the enlarged pole figure corresponding to Fig. 5(c). Focusing on the geometric relationship between the PAGB normal, the HP normal, and the SDD normal line. From the perspectives of the interfacial energy and elastic strain energy, the PAGB normals are expected to be homogeneously distributed around the HP normal. However, as shown in Fig. 6(a), the PAGB normals are not homogeneously distributed around the HP normal. The PAGB normals are not plotted in the area beyond the SDD normal line from HP. It is noted that PAGBs exist in the area but they do not act as formation sites of BF in the initial stage of transformation. It is reported that the transformation strain of martensite is plastically or elastically accommodated by the surrounding austenite.²⁸⁾ Then, the effect of plastic accommodation is considered from the viewpoint of the geometric relationship between the SDD and PAGB plane. The geometric relationship between the SDD and PAGB varies by the SDD normal line. In the case that the BF forms at the austenite grain boundary on the SDD normal line, the SDD and PAGB are parallel. If the SDD can be towards the inside of the austenite grain, the austenite matrix can accommodate the transformation strain (Fig. 6(b)). On the other hand, if the BF forms at the austenite grain boundary in the area beyond the SDD normal line, the SDD can be towards the adjacent PAG (Fig. 6(c)). In this case, the dislocation movement might be obstructed by the austenite grain boundary plane, and it is not favored for plastic accommodation. Therefore, it was considered that the distribution of PAGB normals is bordered by the SDD normal line. However, this mechanism assumes that the plastic accommodation occurs on one side of the BF lath as observed in the lath martensite²⁸⁾ and that the SDD is towards the inside of austenite grain when the HP//PAGB. It is known that dislocation emission behaviors^34,35) and strain accommodation mechanisms are complicated and differ even in martensite.²⁸⁾ Thus, more precise experiments will be required on the strain accommodation mechanisms near austenite grain boundaries.

Fig. 6. (a)Enlarged pole figure corresponding to Fig. 5(c). (b) The schematic of the BF formation from the PAGB, which is very close to HP indicated by the blue circle in (a). (c) The schematic of the BF formation from the PAGB in the area beyond the SDD normal line indicated by the orange circle in (a).

The reason that the formation of BFs is hardly observed in PAGB planes around {0 0 1}γ and {1 1 1}γ can be explained by the HP//PAGB rule. As shown in Fig. 2(c), the {0 0 1}γ and {1 1 1}γ are quite far from the HP (38° and 26° respectively); therefore, any variants cannot satisfy the HP//PAGB rule when the austenite grain boundary plane is near {0 0 1}γ or {1 1 1}γ. It is considered as another reason for the suppression of BF formation at twin boundaries.

The difference in variant selection between the upper and lower bainite is supposed to be caused by the difference in the transformation temperature, austenite strength, lattice invariant shear systems, and so on. However, since these factors are complicated, more detailed studies are required to understand the formation behavior and the accommodation mechanism of the BFs of lower bainite.

5. Conclusions

The effect of the character of austenite grain boundary on the formation and crystallographic features of BFs in Fe-0.6C-0.8Mn-1.8Si steel was investigated from the perspectives of the character of PAGBs, such as Δθ_γ1γ2, Δθ_{axis|PAGBnormal}, PAGB plane, and grain boundary energy. In addition, the crystal orientation relationship between the BF and adjacent PAG and the geometrical relationship between the BF and PAGB plane were investigated.

BF formation was not observed at the twin boundary but was observed at the high-angle PAGBs. In high-angle austenite grain boundaries, BFs formed at the austenite grain boundaries regardless of the values of Δθ_γ1γ2, Δθ_{axis|PAGBnormal}, and the grain boundary energy, while the PAGB plane affected the formation of BF. The BF was not formed at the austenite grain boundary planes near {0 0 1}γ or {1 1 1}γ.

The effect of the orientation of the adjacent austenite grain across the austenite grain boundary was investigated from the perspective of the near K-S rule. The effect of the near K-S rule is not dominant in the case of lower bainite formation. The BF, whose HP is nearly parallel to the PAGB plane, was formed. It is suggested that the formation of BF whose HP is parallel to the PAGB is favored from the perspectives of the interfacial energy, the elastic strain energy, and the plastic accommodation.

Acknowledgment

This research was conducted as part of a project supported by JSPS KAKENHI (Grant Number 20H02475).

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