Effects of Grain Boundary Geometry and Boron Addition on the Local Mechanical Behavior of Interstitial-Free (IF) Steels

Abstract

Nanoindentation measurements on various grain boundaries were performed to clarify the effects of the geometry of neighboring grains and the addition of boron (B) on plasticity resistance in the vicinity of grain boundaries in interstitial free (IF) steels. We define a parameter, α, which is measured by the slope of a P/h–h curve with load, P, and displacement, h, to estimate the resistance against plastic deformation in the grain interior and at the grain boundaries. The value of α is almost constant with the geometric compatibility factor of the grain boundaries. This result shows that the geometry of the neighboring grains does not affect the plasticity resistance of the grain boundaries. However, the value of α increases by the addition of B due to the segregation of B and Ti to the grain boundaries. It is indicated that the elemental segregation to the grain boundaries enhances the resistance to the plastic deformation in the vicinity of the grain boundaries.

 

This Paper was Originally Published in Japanese in J. Japan Inst. Met. Mater. 85 (2021) 30–39.

1. Introduction

It is well known that the yield stress of polycrystalline metals such as steel is proportional to the square root of the reciprocal of the grain size, which is called the Hall-Petch relationship.^1,2) In addition to grain refinement, control of the constant which indicates the grain size dependence of strength, namely, the Hall-Petch coefficient, is also important for improving strength. The Hall-Petch coefficient is considered to be an index of the resistance of grain boundaries against slip deformation,^3–5) and is evaluated as the average of all grain boundaries included in the specimen in the conventional material tests to evaluate macroscopic mechanical properties, such as the tensile test. However, since geometric factors such as the common rotation axis and misorientation angle are different in each grain boundary, it is anticipated that the plasticity resistance of the individual grain boundaries will also be different, even in the same material. It is expected that a deeper understanding of the mechanism model of the Hall-Petch coefficient can be obtained if the relationship between the grain boundary geometry, microstructure and plasticity resistance can be clarified, and as a result, control of the Hall-Petch coefficient will be possible.

Nanoindentation is a technique for measuring the mechanical response of a material to indentation by a pyramidal or other type of indenter into a local region of a material surface under control with load resolution of µN and displacement resolution of nm.^6,7) Addition of the function of a probe microscope (Scanning Probe Microscope, SPM), which scans the sample surface with an indenter used for indentation, makes it possible to select arbitrary positions such as just above the grain boundary or in the vicinity of the grain boundary with high spatial resolution of about 10 nm, enabling evaluation of the plasticity resistance of individual grain boundaries. It is also possible to obtain crystallographic information for each grain by using electron back scattering diffraction (EBSD) measurement, and to discuss the effect of the dynamic condition and geometric factors under the external force at each grain boundary. Among the reported examples of evaluation of the plasticity resistance of individual grain boundaries by the nanoindentation technique, the local mechanical properties in the vicinity of grain boundaries were measured and the slip systems transferred across grain boundaries were predicted based on the geometric relationship between adjacent grains, and the results were compared with the experimental results.^8–13) For example, Tokuda et al. focused on the pop-in phenomenon, which is the initiation behavior of plastic deformation with the elementary process of generation and propagation of dislocations, and reported that the pop-in stress in the vicinity of the grain boundaries was smaller than that in the grain interior in Al bicrystals with Σ3 symmetric tilt grain boundaries.¹¹⁾ Tsurekawa et al. conducted nanoindentation tests in the vicinity of grain boundaries in Fe–3 mass%Si and estimated the critical stress at which slip deformation propagates through grain boundaries and the Hall-Petch coefficient at each grain boundary, and found that the values differed depending on the misorientation between neighboring grains.¹²⁾ These results suggest that the interaction between dislocations and grain boundaries is related to the grain boundary geometry.

On the other hand, it has been reported that the Hall-Petch coefficient is affected by the grain boundary segregation of light elements such as carbon and nitrogen.^14–17) Takaki et al. quantitatively measured the grain boundary segregation of C and N in ferritic steel by the three-dimensional atom probe (3DAP), and clarified the fact that grain boundary segregation of C increased the Hall-Petch coefficient in comparison with N from the viewpoint of the segregation abilities of the two elements.^14–17) Based on the same viewpoint, the present study focuses on B, which is one of the typical grain boundary segregation elements in steel. The effect of B on the Hall-Petch coefficient in 0.1C–0.5Mo steel was reported by Codd et al., who indicated that the Hall-Petch coefficient increased when 20 ppm of B was added to the steel.¹⁸⁾ However, because of incomplete separation from other factors such as the effect of C segregation and the lack of direct evidence of grain boundary segregation of B, the relationship between B addition and the Hall-Petch coefficient was unclear, and the effect of B on the plasticity resistance of grain boundaries remained to be clarified. In this study, local mechanical properties in the vicinity of grain boundaries were evaluated by nanoindentation tests for grain boundaries in which the misorientation between grains, etc. was measured beforehand using interstitial free (IF) steel, and the controlling factor of the plasticity resistance of the individual grain boundaries was discussed by clarifying the effects of the grain boundary geometry and B addition.

2. Experimental Procedure

Table 1 shows the chemical composition of the steel used in this study. To investigate the effect of the grain boundary geometry on the local mechanical properties in the vicinity of grain boundaries, coarse-grained IF steel (IF-CG steel) was used, as it was necessary to carry out multiple measurements at the same grain boundary. On the other hand, two kinds of IF steels were used to investigate the effect of B segregation: IF steel with B addition and heat treatment to promote grain boundary segregation of B (IF-B steel), and as a comparison material, IF steel without B addition (IF steel) produced by the same process. Figure 1(a) shows the manufacturing process of the IF-CG steel. After melting a 30 kg ingot in a vacuum melting furnace, a slab of the steel with a thickness of 30 mm was produced and hot-rolled to plates with a thickness of 3.5 mm. The hot-rolled plates were then subjected to heat treatment for reducing solute carbon for TiC formation and grain coarsening. Figure 1(b) shows the manufacturing process of the IF steel and IF-B steel. A 20 kg ingot was melted in the vacuum melting furnace and hot-forged, and a slab with a 30 mm thickness, 50 mm width, and 70 mm length was cut from the hot-forged material. The obtained slab was hot-rolled to a thickness of 3 mm, annealed at 900°C, and then annealed at 700°C for 30 min to reduce solute carbon and quenched in water. To enhance B segregation to the grain boundaries, heat treatment was carried out at 700°C for 10 min, followed by furnace cooling. Each specimen was mechanically polished and then electropolished with a solution of 8 vol% perchloric acid, 10 vol% distilled water, 72 vol% ethanol, and 10 vol% butyl cellosolve at 0°C. The crystallographic orientation was analyzed with a scanning electron microscope (SEM; JSM-7000F, JEOL) and an orientation imaging microscopy (OIM) attachment (TSL Solutions Co., Ltd.) with an acceleration voltage of 15 kV. Nanoindentation was carried under load control at room temperature of 27°C. A Berkovich indenter (Hysitron Triboindenter TI 950, Bruker) was employed, and the maximum load was 5000 µN. The tip was indented at the loading/unloading rates of 50 µN/s at a distance of approximately 1.5 µm from the grain boundary on the image obtained by SPM. The holding time at the maximum load was 10 s. When a sample is prepared by electropolishing, the sample surface height after polishing may be different between neighboring grains since the polishing rate depends on the crystallographic orientation on the surface. In this case, if nanoindentation is carried out in the grain on the upper side of the step, the plasticity resistance of the grain boundary may be evaluated incorrectly owing to the effect of the free surface of the step side. Therefore, the nanoindentation test was carried out in the grain on the lower side of the step. The reduced Young’s modulus Er and hardness Hn were determined by the Oliver-Pharr method from the load (P)–displacement (h) curves obtained from the nanoindentation tests. The elemental segregation to grain boundaries was analyzed by 3DAP (LEAP 5000XS, CAMECA). The samples for the 3DAP analyses were prepared by using a focused ion beam (FIB) system (Helios Nanolab Dual Beam G4, FEI) so that the grain boundary was perpendicular to the analysis direction. The 3DAP measurements were performed in laser mode with laser pulse energy of 30 pJ at a base temperature of −243°C. The collected data was reconstructed and analyzed using CAMECA IVAS 3.8.6 software.

Table 1 Chemical compositions of IF steels used in this study (mass%).

Fig. 1

Manufacturing process of (a) IF-CG steel with coarse grain and (b) IF steel and IF-B steel with intergranular segregation of B.

3. Analysis of Grain Boundary Geometry

The geometric factors of grain boundaries in this study were evaluated by considering both the misorientation determined only by the geometric relationship between adjacent grains and the geometry of the slip system activated by external force. Some models of geometric interaction between the grain boundary and slip deformation were investigated,^19–22) and in this study, the geometric compatibility factor (m′ value) proposed by Luster and Morris was adopted as the method for predicting the active slip system in adjacent grains precisely.²²⁾ The m′ value is a parameter which geometrically evaluates the slip system toward the grain boundary and the slip system activated in the adjacent grain, assuming that the slip deformation is transferred across the grain boundary. Figure 2 shows a schematic diagram of the relationship between the grain boundary plane, slip planes and slip directions in adjacent grains. The m′ value can be expressed by the following equation:   

\begin{equation} m' = \cos \phi_{\text{ij}}\times \cos \kappa_{\text{ij}} \end{equation} (1)

Here, ϕ_ij and κ_ij are the angles between the slip plane normals n_i and n_j and the angles between the slip directions g_i and g_j in the slip systems i and j, respectively. The m′ value can be calculated from the orientation relationship between adjacent grains and the slip system of each grain, and increases as the angle between the slip planes and the angle between the slip directions become smaller. The m′ value between adjacent grains changes between 0 and 1. In the case of m′ = 1, both the slip directions and the slip planes are in a parallel relationship, whereas m′ = 0 means that the slip planes or the slip directions have an orthogonal relationship. It has been shown that a slip system with a high m′ value easily becomes active in the tip grain where the slip propagates.²²⁾ In this study, only the {110}⟨111⟩ slip systems, which are the representative slip system of the bcc structure, were considered.

Fig. 2

Schematic illustration of geometrical description for slip systems in grain 1 and adjacent grain 2.

Next, the matrix calculation method of misorientation and the m′ value will be described. The grain on the indentation side (original side of slip propagation) is referred to as Grain 1, and the grain on the tip side where the slip propagates is referred to as Grain 2. The calculation was carried out in the following order.

• ①    Calculation of the common rotation axis and rotation angle
• ②    Determination of the slip system with the highest Schmidt factor of Grain 1 when the tensile axis is horizontal
• ③    Calculation of the m′ values for all slip systems assumed in Grain 2

It is necessary to carry out the calculation in the identical coordinate system in order to consider the geometric factors in Grain 1 and Grain 2, in which the crystal coordinate system differs. Therefore, as a common coordinate system, the calculation in this study is carried out in a sample coordinate system in which the rolling direction is [100], the transverse direction is [010] and the sample surface normal direction is [001], and vector notations such as the rotation axis are shown in the crystal coordinate system of each grain.

When the transform matrices from the crystal coordinate systems of Grain 1 and Grain 2 to the sample coordinate system are S and T, respectively, the rotation matrix R for matching the principal axis orientation of Grain 2 with that of Grain 1 is expressed by the following equation:   

\begin{equation} \boldsymbol{R}_{\text{n}} = \boldsymbol{S T}_{n}^{-1}\ (n = 1{\sim}24) \end{equation} (2)

where, n is the symmetry at a neighboring grain. In this study, there are 24 descriptions of the principal axes for the cubic crystal. The rotation axis and the rotation angle are obtained by solving the eigen equation from the obtained 24 rotation matrices R_n, and the R_n with the smallest rotation angle can be determined. The smallest rotation angle calculated from this R_n is defined as the misorientation. Next, in Grain 1, the Schmidt factors in all 12 kinds of slip systems were calculated for the external force along the [100] direction of the sample coordinate system as the axis of loading, and slip system with the highest Schmidt factor was determined. Then, the slip system with the highest Schmidt factor obtained in Grain 1 and all the slip systems in Grain 2 were expressed in the sample coordinate system by the transformation matrices S and T. Finally, the calculation was performed by eq. (1) using the slip plane normal and the slip direction in the sample coordinate system, and the maximum m′ value was adopted.

4. Results and Discussion

4.1 Relationship between geometry of neighboring grains and local mechanical properties in vicinity of grain boundary

In the IF-CG steel prepared by the heat treatment in Fig. 1(a), coarse grains with a size exceeding 100 µm were confirmed by optical microscopy. Figure 3(a) shows the SPM image after indentation near a grain boundary in the IF-CG steel. The horizontal distance from the grain boundary to the deepest part of the indent is about 1.5 µm, and the length of each side of the triangular indent mark obtained by projecting the dent on the sample surface is about 3.0 µm. It can be confirmed that the size of the plastic deformation zone for evaluating the plasticity resistance at the grain boundary is sufficiently large because part of the indenter reached the grain boundary and the diameter of the plastic deformation zone approximated in the hemisphere is about 1.4 times the length of the side of the triangular indent marks.²³⁾ When the nanoindentation test is carried out with a Berkovich indenter, compressive stress is generated from both the ridge line and indenter surface.²³⁾ Therefore, it can be judged that the indenter shape does not remarkably affect the results of this experiment, since the slip system which is active in the above-mentioned Grain 1 does not change regardless of the orientation of the indenter to the grain boundary. Figure 3(b) shows an optical micrograph of the sample surface after the nanoindentation test. Measurements at the same grain boundary were carried out while ensuring a distance of more than 5 µm between indentations in order to avoid the effect of interaction between the plastic deformation zones. Figure 3(c) to (f) show the Inverse Pole Figure (IPF) maps of the sample surface normal of the reference grains in this study. Here, “reference grain” means a grain surrounded by grain boundaries whose local mechanical properties were measured by the nanoindentation test. The plasticity resistance of the grain boundary was evaluated by comparing the intragranular and intergranular mechanical properties in the reference grain. The reference grains in Fig. 3(c) to (f) are called Grain A, Grain B, Grain C and Grain D, and the sample surface normals were close to ⟨025⟩, ⟨001⟩, ⟨011⟩ and ⟨111⟩. Table 2 shows the Euler angles of the grains surrounding Grain A and the m′ values, misorientation angles and rotation axes obtained from the calculations in eq. (1) and eq. (2). As shown in Fig. 3(c), the grain boundary surrounding Grain A is composed of grain boundary numbers ① to ⑪ (referred to hereinafter as GB1 to GB11). Only the grain boundaries where the height of the surface of the reference grain is lower than that of the adjacent grain were selected, and these grain boundaries are shown in the order of increasing m′ from the top of the table. Comparing the magnitude relationship between the m′ value and the misorientation angle, there is no relation in the order between them.

Fig. 3

(a) Scanning probe microscopy image of indentation near grain boundary, (b) optical microscopy image after nanoindentation. Figures (c) to (f) are inverse pole figure maps of normal direction to surface of grains A in (c), B in (d), C in (e), and D in (f), respectively.

Table 2 Geometrical relationship between grains adjacent to the grain A shown in Fig. 3(d).

Figure 4(a) shows an example of the load (P)–displacement (h) curve obtained in Grain A interior and near GB3 in the IF-CG steel. In Fig. 4(a), the discontinuous strain burst shown by the arrow at the beginning of loading is the phenomenon called pop-in. Comparing the P–h curve of GB3 with the grain interior P–h curve, the pop-in load is almost the same, and there is no significant difference in the P–h curve from the beginning of loading to P = 2000 µN. Therefore, it was concluded that the influence of grain boundaries is not significant in this loading range. In the region over P = 3500 µN, the slope of the P–h curve of GB3 was slightly larger, which means that the depth for the same load was slightly shallower, suggesting the effect of plasticity resistance at the grain boundaries. Nakano et al. suggested that the hardness most commonly used as an index of plasticity resistance at grain boundaries obtained by the nanoindentation test is relatively inaccurate, and proposed an alternative analysis method using the slope α of the P/h–h curve, which is obtained from the P–h curve, as an index of plasticity resistance.²⁴⁾ They exemplified the behavior in which α rose when it reached a certain indentation depth in the nanoindentation test using SUS304, and clarified the fact that this depth was substantially in agreement with the indentation depth at which the plastic zone under the indenter reached the grain boundary. From this result, it is concluded that the increase of α reflected the addition of the plasticity resistance at the grain boundary to the resistance in the grain interior. In the IF-CG steel, the plasticity resistance at the grain boundary is evaluated by the slope α of the P/h–h curve by a similar method, and α is used together with the index of hardness. Figure 4(b) shows the P/h–h curve converted from Fig. 4(a). The slopes α_s and α_e of the P/h–h curve are defined in Fig. 4(b), where α_s and α_e are the slopes of the P/h–h curves corresponding to the load range, 1250 µN ≦ P ≦ 2000 µN and 3500 µN ≦ P ≦ 5000 µN on the P–h curves in Fig. 4(a), respectively. Because the nanoindentation test was carried out under load control, in this study, the calculation intervals of α_s and α_e were set under loading conditions. In order to equalize the measurement accuracy of α, the load range was determined so that the depth range of the P/h–h curve was substantially equivalent in both intervals. The indentation depth corresponding to the upper load limit of α_s is about 220 nm, and the radius of the hemispherical plastic deformation zone estimated from the indentation depth is calculated to be 1.1 µm, which is 5 times the indentation depth, and centers on the contact point between the sample surface and the indenter before deformation.²³⁾ Since the magnitude of the plastic deformation zone in the horizontal direction on the sample surface is largest and the distance from the grain boundary to the indent is smaller than 1.5 µm, this is judged to be a condition which is not affected by the grain boundary at this indentation depth. On the other hand, the minimum indentation depth corresponding to the load range of α_e exceeds 300 nm, and the radius of the hemispherical plastic deformation zone is estimated to exceed 1.5 µm. Therefore, α_e is judged to be affected by the grain boundary. Figure 5(a) and (b) show the relationship between the nanohardness and the misorientation angle and the m′ value, respectively. Here, the value of the misorientation of 0° or m′ = 1 is the nanohardness in each reference grain interior and is shown by an open mark. In order to confirm the existence of crystallographic orientation dependence, the orientations of four kinds of reference grains parallel to the indentation direction are shown separately. The nanohardness in each reference grain was the lowest at 1.1 GPa for Grain B, followed by 1.3 GPa for Grain D and Grain A, and 1.4 GPa for Grain C. The width of the gray band in Fig. 5 corresponds to the range from the maximum value to the minimum value of intragranular hardness. Although the dependence of yield stress on the crystallographic orientation is not always remarkable in bcc metals due to the lack of a clear slip plane, the difference in the nanohardness in each reference grain may reflect crystallographic orientation dependence, because a similar tendency of dependence of yield stress on the crystallographic orientation in compressions test of bcc metals has been reported in previous studies.^25–28) However, no significant tendency was observed in the effect of the misorientation angle or m′ value on the nanohardness near the grain boundary. Moreover, since the distribution of nanohardness of all the grain boundaries is approximately within the distribution of nanohardness in the grain interior, it is judged that the effect of the misorientation angle and m′ value on nanohardness in the vicinity of the grain boundary is small. Next, Fig. 5(c) shows the relationship between the difference Δα between α_e and α_s and the m′ value. Here, Δα is a value that excludes α_s, which is the plasticity resistance in the grain interior, from α_e, which includes both the plasticity resistance in the grain interior and that of the grain boundary. Thus, Δα is an evaluation index of the plasticity resistance of the grain boundary. According to Fig. 5(c), the values of Δα in the grain interior indicated by the open marks spanned a range of about −0.007 to 0.006. Δα is ideally 0, as the effect of the grain boundary is not included in α_e in the nanoindentation test in the grain interior, but it is judged that dispersion of experimental error around 0 occurred here. The tendency of Δα near the grain boundary with respect to the m′ value was not clear, and as in the case of the index of nanohardness, almost no difference larger than the crystallographic orientation difference could be recognized. This result suggests that the influence of geometric factors on the plasticity resistance of grain boundaries is small in IF steels. It should be noted that the grain boundary plane, which is one of the geometric factors describing grain boundaries, is not considered here. Although it is difficult to identify the orientation of the grain boundary plane only by EBSD measurement of the sample surface, the essential conclusion would not change if the orientation of the grain boundary plane were considered because the value of Δα calculated by measuring the curved grain boundary is constant in the range of the conditions in this study.

Fig. 4

(a) Load–displacement (P–h) curves and (b) P/h–h curves obtained from indentations inside Grain A and near GB3 of IF steel. The slopes of α_s and α_e are defined as the slopes of P/h–h curve between 1250 µN and 2000 µN, and between 3500 µN and 5000 µN in (b), respectively.

Fig. 5

(a) Misorientation angle and (b) geometric compatibility factor dependence of nanohardness, Hn of IF-CG steel. (c) Geometric compatibility factor dependence of Δα of IF-CG steel.

When the pile-up model of dislocation is assumed, the plasticity resistance of the grain boundary is understood as the magnitude of the back stress from the dislocation piled up at the grain boundary. Dislocation pile-up at grain boundaries has been experimentally observed in austenitic stainless steels such as SUS304 and SUS310. These fcc steels are characterized by planar dislocation arrays in which the observed dislocation lines are located on the same slip plane.^8,29) This may be because the slip plane of fcc is clearly restricted. On the other hand, in alloys with a bcc structure, such as the IF steel in this study, the screw dislocation, which has lower mobility than the edge dislocation, is dominant for slip deformation, and the slip plane is not always clearly restricted due to the frequent occurrence of cross slip. Regarding dislocation-grain boundary interaction, a phenomenon in which dislocations sink to the grain boundary has been pointed out in a bcc metal,³⁰⁾ and a similar phenomenon was actually observed in in-situ deformation in a TEM.³¹⁾ Although the details of the mechanism of dislocation-grain boundary interaction are unclear, this phenomenon may be related to the high frequency of cross slip.

Thus, in bcc metals, the plasticity resistance of the grain boundary does not appear remarkably, as pile-up at the grain boundary is difficult because the interaction between grain boundaries and dislocations is attributed to the dislocation structure. Moreover, the fact that the plasticity resistance of the grain boundary does not depend on the geometric condition of the grain boundary indicates that a similar interaction occurs in either grain boundary. However, because it is a condition of the present study that external force concentrates in the grain which applies press fit deformation, it is necessary to consider the fact that this is a condition in which the average external force also acts on the adjacent grain in the actual bulk material. For further clarification of the interaction between dislocations and grain boundaries in IF steel, it will be necessary to observe the deformation process in local regions including the grain boundary by TEM and conduct a molecular dynamics simulation considering the dislocations and structure of the grain boundary.

4.2 Effect of B addition on local mechanical properties in vicinity of grain boundary of IF steel

Figure 6(a) and (b) are IPF maps showing the sample surface normal directions of the reference grains in the IF steel and IF-B steel, respectively. The orientation of the sample surface normal of the reference grain indicated by the red arrow was near ⟨111⟩ in both the IF steel and the IF-B steel. As in Fig. 3, the individual grain boundaries surrounding each grain were assigned identification numbers. However, grain boundaries with the reference grain on upper side of the step were no good for the measurement and hence excluded. The grain size of both steels produced by the process shown in Fig. 2(b) was about 50 µm. Figure 7(a) and (b) show SPM images of the sample surfaces of the IF steel and the IF-B steel after the nanoindentation test, respectively. The indent marks in the region surrounded by the dashed lines were formed at locations sufficiently distant from the grain boundaries, i.e., by nanoindentation tests in the grain interior. The identification numbers of the grain boundaries are the same as in Fig. 6. The misorientation angle and m′ values calculated from eq. (1), which are derived from each grain boundary, are given in Table 3 in the order of the identification numbers. The nanoindentation test was carried out for the grain boundaries with these geometric features. Figure 8(a) shows the P–h curves obtained from the nanoindentation tests in the vicinities of GB3 for the IF steel and GB1 for the IF-B steel. The pop-in phenomenon occurred in the early stage of the loading process with or without addition of B, and the pop-in load increased slightly with B addition. This increase in the pop-in load is considered to be due to the interaction between dislocation nucleation and solute B in solution. It has been reported that the pop-in load increases with an increase in solid C, and as the mechanism of this phenomenon, it is suggested that the solute C inhibits the generation and growth of dislocation loops in the elementary process of generation of the pop-in.³²⁾ No significant difference was observed in the P–h curve from pop-up until P = 2000 µN, but the slope of the load became steeper in the IF-B steel than in the IF steel in the high load region over 3500 µN. The P/h–h curve converted from Fig. 8(a) is shown in Fig. 8(b). Here, α_s and α_e are slopes in the same loading range as in Fig. 4. Compared with the IF steel, the IF-B steel showed a clear increase in the value from α_s to α_e in the high load region, suggesting an increase in the plasticity resistance of the grain boundary due to the addition of B. Figure 9 shows the reduced Young’s modulus and nanohardness at each grain boundary of the IF steel and the IF-B steel. Here, GI in Fig. 9 represents the grain interior. Since the reduced Young’s modulus and nanohardness of the IF steel were comparable to those of the IF-CG steel used in Section 3.2, there was no difference in the local mechanical properties in the vicinity of the grain boundary depending on the manufacturing method. From Fig. 9(a) and (b), it is judged that the accuracy of the measurement was within the appropriate level, because Er was almost the same regardless of whether B was added or not and did not depend on the grain boundary. The nanohardness in the grain interior was approximately equal to 1.5 GPa regardless of B addition. The nanohardness at each grain boundary was also similar to the value in the grain interior, and no remarkable effect of B addition could be recognized.

Fig. 6

Inverse pole figure maps showing surface normal direction of (a) IF steel and (b) IF-B steel, respectively. Red arrows in (a) and (b) represent the grains, on which nanoindentation is performed.

Fig. 7

Scanning probe microscope images of the sample surface of (a) IF steel and (b) IF-B steel.

Table 3 Misorientation angle and geometric compatibility factor between neighboring grains related to the grain boundary. Note that each grain boundary number is indicated in Fig. 7.

Fig. 8

Load–displacement (P–h) curves of (a) IF steel and IF-B steel. (b) P/h–h curves obtained from P–h curves of IF steel and IF-B steel for the sites near GB4 and GB1 in Fig. 7.

Fig. 9

Reduced Young’s modulus, Er and nanohardness, Hn obtained from P–h curves of (a) IF steel and (b) IF-B steel, respectively.

Figure 10(a) and (b) show α_s, α_e and Δα at each grain boundary of the IF steel and the IF-B steel, respectively. As in Fig. 5, Δα is the difference between α_e and α_s. The α_s values of the grain interior (GI) regions of the IF steel and the IF-B steel were comparable, being 0.0291 µN/nm² and 0.0265 µN/nm², respectively, and no significant effect of B addition was observed. The α_s of each grain boundary of the IF and IF-B steels were also comparable, being in the ranges of 0.0211 to 0.328 µN/nm² and 0.0222 to 0.0308 µN/nm², respectively. This is consistent with the fact that the nanohardness Hn of the IF steel and the IF-B steel was almost the same in Fig. 9. On the other hand, the values of α_e, in which the plasticity resistance of the grain boundary is taken into account, were calculated to be 0.0266 to 0.0347 µN/nm² and 0.0353 to 0.0425 µN/nm² for the IF steel and the IF-B steel, respectively. Thus, the α_e of the IF-B steel was clearly higher than that of the IF steel. This tendency is also clear in the comparison of Δα expressed in red. The maximum Δα of the IF steel was about 0.005 µN/nm², while that of the IF-B steel was about 0.005 to 0.020 µN/nm², which was higher than that of the IF steel. As shown in Fig. 5, the effect of geometric factors on Δα was not significant, and the result in Fig. 10 shows that the plasticity resistance of the grain boundary is increased by B addition. The following discusses the reason why the difference in the plasticity resistance of the grain boundary due to B addition was detected more sensitively by the index Δα than by the index of nanohardness. The relationship between load P and displacement h in press fit deformation is expressed by the following eq. (3).³³⁾   

\begin{equation} P = \alpha h^{2} + \beta h \end{equation} (3)

Fig. 10

Slopes of P/h–h curves obtained from P/h–h curves of (a) IF steel and (b) IF-B steel, respectively.

As shown in eq. (3), P is given by adding the terms h² and h. Here, the h² term is proportional to the contact area A between the indenter and the sample, which increases with penetration depth of the indenter, and the value obtained by dividing P by A is the definition of hardness itself. Therefore, the coefficient α of the h² term is a quantity with the dimension of the average surface pressure equal to hardness. Since the h term corresponds to the behavior of indentation-induced deformation, in which the contact area does not change, the coefficient β of the h term is considered to reflect the effect of imperfections of the indenter tip and/or the roughness of the sample surface.²⁴⁾ A similar study was also reported by Tsurekawa et al.¹²⁾ Also, in material in which the strain-induced transformation appears, the resistance change by the transition from phase transformation to plastic deformation is quantitatively detected as an increase in α, and it has been shown that the rate of increase depends on the distance from the grain boundary and the strength of the adjacent grain.^33,34) It is considered that the evaluation by α is more sensitive for detecting differences in the plasticity resistance of the grain boundary than the evaluation of hardness because the h² term, which corresponds to the essential plasticity resistance, can be evaluated in the analysis by the P/h–h curve.^24,33,34)

B segregation might be a probable reason for the improved local mechanical properties in the vicinity of the grain boundary. Figure 11(a) and (b) show the 3D atom maps of C, Ti, B, and all elements obtained from the IF and IF-B steels, respectively. Note that the 3DAP analyses were performed for GB3 in the IF steel and GB1 in the IF-B steel, Fig. 10. As shown in Fig. 11(a), only a small amount of Ti was segregated at the grain boundary in the IF steel. In contrast, Ti and B were co-segregated at the GB1 in IF-B steel as shown in Fig. 11(b). The co-segregation of Ti and B occurs at the grain boundary because of the attractive interaction between B and Ti atoms.³⁵⁾ The amount of C segregated to the grain boundary also showed a slight increase by the trace B addition as reported in a previous work.³⁶⁾ However, the co-segregation of B and C was not remarkable in comparison with that of Ti and B, and the details of the interaction between B and C are not yet to be cleared. Figure 11(c) and (d) show the compositional profiles across the grain boundaries analyzed from selected volumes shown in Ti maps for IF and IF-B steels. Note that a ladder diagram was used to calculate the concentration of constituent elements in the grain boundary.³⁷⁾ ∼1.2 mol% of B had segregated at the grain boundary, which was significantly higher than the nominal B content (0.006 mol%). The amount of Ti and C segregated at the grain boundaries was substantially increased by the B addition. These results indicate that the increase in the local mechanical properties in the vicinity of the grain boundaries of IF steels is attributed following two effects. One is that B itself segregates at the grain boundary, and the other is that the addition of B enhances grain boundary segregation of Ti and C. From Fig. 5 and Fig. 10, the effect of geometric factors on the plasticity resistance of the grain boundaries of the IF steel was small. Therefore, we can conclude that the grain boundary segregation of Ti and C as well as B leads to the improvement of the plasticity resistance of the grain boundaries in the IF-B steel. This means that the chemical factors such as grain boundary segregation strongly affects the plasticity resistance of grain boundaries compared with the geometric factors. These findings might be also applicable to general bcc steels. However, because the geometric factors of the grain boundary are closely related to grain boundary energy and grain boundary segregation, the geometric factors may indirectly contribute to strengthening of the grain boundary through grain boundary segregation.³⁸⁾ In this study, the quantitative relationship between Δα and the quantity of grain boundary segregation was not clarified. Therefore, further study will be necessary to improve the measurement accuracy of the mechanical indices, including Δα, and the quantity of grain boundary segregation.

Fig. 11

3D atom maps of all elements, C, Ti, and B analyzed from the specimens including grain boundaries in (a) IF and (b) IF-B steels. 1D compositional profiles obtained from selected volumes in (c) IF and (d) IF-B steels analyzed along the direction indicated by arrows. Note that each data represents GB3 in Fig. 7(a) and GB1 in Fig. 7(b), respectively.

5. Conclusions

In this study, the effects of the grain boundary geometry and B addition on the local mechanical properties in the vicinity of individual grain boundaries were investigated in IF steel with a bcc structure by using a combination of SEM-EBSD measurement, 3DAP analysis and the nanoindentation test. The main conclusions were as follows.

1. (1)    The plasticity resistance of individual grain boundaries in the IF steel was evaluated by the nanoindentation technique. There was no significant difference between the grain boundary values and the grain interior values of either the index of nanohardness or the slope α of the P/h–h curve, and dependence on the crystallographic orientation and m′ value was not detected. This indicates that the effect of geometric factors on the plasticity resistance of grain boundaries is smaller than the detection limit of the method in this study.
2. (2)    As a result of a comparison with and without B addition, the value of α_e in the load range including the effect of the grain boundary tended to rise with B addition. The rise in the plasticity resistance of grain boundaries in the B-added IF steel was remarkable when arranged by Δα (difference between α_e and α_s), which corresponds to the contribution of the grain boundary in isolation from the grain interior.
3. (3)    As a result of a 3DAP analysis of the grain boundary in the B-added IF steel, remarkable grain boundary segregation of B was confirmed. In addition to segregation of B, segregation of Ti and C was also enhanced. Therefore, the increase in the plasticity resistance of grain boundaries by B addition was considered to be due to the effect of grain boundary segregation of these elements.
4. (4)    It was suggested that the effect of chemical factors such as grain boundary segregation of additional elements on the plasticity resistance of grain boundaries was relatively larger than the effect of geometric factors in the case of IF steel with a bcc structure.

REFERENCES

• 1)   E.O.  Hall: Proc. Phys. Soc. B 64 (1951) 747–752.
• 2)   N.J.  Petch: J. Iron Steel Inst. 174 (1953) 25–28.
• 3)   R.W.  Armstrong,  C.S.  Coffey and  W.L.  Elban: Acta Metall. 30 (1982) 2111–2116.
• 4)   J.D.  Eshelby,  F.C.  Frank and  F.R.N.  Nabarro: Philos. Mag. 42 (1951) 351–364.
• 5)   M.D.  Koning,  R.  Miller,  V.  Bulatov and  F.F.  Abraham: Philos. Mag. A 82 (2002) 2511–2527.
• 6)   W.C.  Oliver and  G.M.  Pharr: J. Mater. Res. 19 (2004) 3–20.
• 7)   T.  Ohmura and  K.  Tsuzaki: Materia Japan 46 (2007) 251–258.
• 8)   J.  Kacher,  B.P.  Eftink,  B.  Cui and  I.M.  Robertson: Curr. Opin. Solid State Mater. Sci. 18 (2014) 227–243.
• 9)   E.  Bayerschen,  A.T.  McBride and  T.  Bohkle: J. Mater. Sci. 51 (2016) 2243–2258.
• 10)   F.  Javaid,  Y.  Xu and  K.  Durst: J. Mater. Sci. 55 (2020) 9597–9607.
• 11)   Y.  Tokuda,  S.  Tsurekawa and  D.A.  Molodov: Mater. Sci. Eng. A 716 (2018) 37–41.
• 12)   S.  Tsurekawa,  Y.  Chihara,  K.  Tashima,  S.  Ii and  P.  Lejček: J. Mater. Sci. 49 (2014) 4698–4704.
• 13)   M.G.  Wang and  A.H.W.  Ngan: J. Mater. Res. 19 (2004) 2478–2486.
• 14)   K.  Takeda,  N.  Nakada,  T.  Tsuchiyama and  S.  Takaki: ISIJ Int. 48 (2008) 1122–1125.
• 15)   S.  Araki,  K.  Fujii,  D.  Akama,  T.  Tsuchiyama,  S.  Takaki,  T.  Ohmura and  J.  Takahashi: Tetsu-to-Hagané 103 (2017) 491–497.
• 16)   S.  Takaki: J. Japan Inst. Met. Mater. 83 (2019) 107–118.
• 17)   S.  Araki,  K.  Mashima,  T.  Masumura,  T.  Tsuchiyama,  S.  Takaki and  T.  Ohmura: Scr. Mater. 169 (2019) 38–41.
• 18)   I.  Codd and  N.J.  Petch: Philos. Mag. 5 (1960) 30–42.
• 19)   J.D.  Livingston and  B.  Chalmers: Acta Metall. 5 (1957) 322–327.
• 20)   Z.  Shen,  R.H.  Wagoner and  W.A.T.  Clark: Scr. Metall. 20 (1986) 921–926.
• 21)   Z.  Shen,  R.H.  Wagoner and  W.A.T.  Clark: Acta Metall. 36 (1988) 3231–3242.
• 22)   J.  Luster and  M.A.  Morris: Metall. Mater. Trans. A 26 (1995) 1745–1756.
• 23)   M.  Itokazu and  Y.  Murakami: Trans. Jpn. Soc. Mech. Eng. A 59 (1993) 2560–2568.
• 24)   K.  Nakano,  K.  Takeda,  S.  Ii and  T.  Ohmura: J. Japan Inst. Met. Mater. 85 (2021) 40–48.
• 25)   R.M.  Rose,  D.P.  Ferriss and  J.  Wulff: Trans. Metall. AIME 224 (1962) 981–990.
• 26)   P.  Beardmore and  D.  Hull: J. Less Common Met. 9 (1965) 168–180.
• 27)   A.S.  Argon and  S.R.  Maloof: Acta Metall. 14 (1966) 1449–1462.
• 28)   S.  Takeuchi,  E.  Furubayashi and  T.  Taoka: Acta Metall. 15 (1967) 1179–1191.
• 29)   T.C.  Lee,  I.M.  Robertson and  H.K.  Birnbaum: Metall. Trans. A 21 (1990) 2437–2447.
• 30)   S.  Itoh,  K.  Nakazawa,  T.  Matsunaga,  Y.  Matsukawa,  Y.  Satoh and  H.  Abe: ISIJ Int. 54 (2014) 1729–1734.
• 31)   H.  Li,  S.  Gao,  Y.  Tomota,  S.  Ii,  N.  Tsuji and  T.  Ohmura: Acta Mater. 206 (2021) 116621.
• 32)   K.  Nakano and  T.  Ohmura: Tetsu-to-Hagané 106 (2020) 372–381.
• 33)   K.  Sekido,  T.  Ohmura,  T.  Sawaguchi,  M.  Koyama,  H.W.  Park and  K.  Tsuzaki: Scr. Mater. 65 (2011) 942–945.
• 34)   T.  Man,  T.  Ohmura and  Y.  Tomota: Mater. Today Commun. 23 (2020) 100896.
• 35)   J.  Takahashi,  J.  Haga,  K.  Kawakami and  K.  Ushioda: Ultramicroscopy 159 (2015) 299–307.
• 36)   G.  Miyamoto,  A.  Goto,  N.  Takayama and  T.  Furuhara: Scr. Mater. 154 (2018) 168–171.
• 37)  M.K. Miller: Atom Probe Tomography, (Springer, New York, 2000) pp. 1–423.
• 38)  P. Lejcek: Grain Boundary Segregation in Metals, (Springer-Verlag, Berlin, 2010) pp. 1–239.