Deformation and Fracture Behaviors of Spheroidized Pearlitic Steel under Tensile Loading

Abstract

The deformation and fracture behavior in spheroidized pearlitic steels were investigated using digital image correlation and the replica methods, and the origin of the inhomogeneous strain distribution and its effect on fracture were discussed. The cementite roundness increased while the area fraction within a colony decreased with increasing spheroidization time. Many coarse cementites were observed on the colony and block boundaries, which explains the decrease in the cementite area fraction within a colony. The strength–ductility balance deteriorated with cementite spheroidization. The inhomogeneous strain distribution in a unit of the colony was introduced by the tensile deformation in the spheroidized pearlitic steels. The numerous voids or cracks detected at low- and high-angle boundaries inside the cementite and in ferrite at the ferrite/cementite boundary tended to nucleate from the high-strain region. The deformability of the colony depended on the progress of cementite spheroidization, and the crystallographic orientation relationship between ferrite and cementite could affect the ease of cementite spheroidization in a colony. The strain gradient between the soft ferrite and hard cementite phases induced void or crack nucleation around the coarse cementite at the colony or block boundary; hence, voids or cracks tended to nucleate from the high-strain region. It can be concluded that inhomogeneous cementite spheroidization results in an inhomogeneous strain distribution, which causes the preferential nucleation of voids or cracks in the high-strain colony.

1. Introduction

Pearlite consists of ferrite and cementite lamella structure and a hierarchical substructure of colony and block. The colony and block had been defined as the regions where lamellar alignment and crystallographic orientation of ferrite matrix are identical, respectively,¹⁾ although the continuous crystallographic orientation rotation within a block was recently detected using the electron backscattered diffraction (EBSD) method.^2,3,4) Furthermore, the pearlite structure exhibited defects in the cementite plate. In pearlite structures fabricated by low carbon steel and/or low transformation temperature, discontinuous cementite (namely, spheroidized cementite) was often observed. Such pearlite structures are referred to as degenerated pearlite.^5,6,7) Zhou et al.⁸⁾ reported the curve of the cementite plate and proposed that the steps consisting of several atoms at the ferrite/cementite interfacial boundary compose the curve of the cementite plate. Adachi et al.⁹⁾ visualized the detailed three-dimensional morphology of cementite plates using the serial sectioning method and revealed that the cementite plate had defects such as holes and twists and that the spheroidization of cementite plates progressed as the holes in the plates grew. The increase in spheroidized cementite, namely, holes in the cementite plate in three dimensions, usually reduces the strength. Therefore, in the industry, annealing for cementite spheroidization is performed to improve processing.

The deformation and fracture behaviors of pearlitic steel have been widely investigated. Dislocations have been reported to increase only in the ferrite phase in pearlitic steel subjected to tensile deformation, indicating that the ferrite phase is responsible for the plastic deformation.^10,11) Similar deformation behavior was also confirmed by in-situ neutron diffraction during tensile testing; the ferrite phase was preferentially yielded but the cementite continued the elastic deformation even at a late stage of deformation.^12,13) The characteristic fracture behavior of pearlitic steel, which is referred to as a shear band, was observed.^10,14,15) The cementite plates were continuously broken along the maximum shear direction (45° from the tensile direction), and subsequently, voids nucleated from those cementites. Finally, the growth and coalescence of these voids caused the fracture of pearlitic steel. Many studies have investigated the deformation and fracture behavior of pearlitic steel; however, the role of defects in the pearlite structure on the deformation and fracture behavior has not been thoroughly investigated.

Recently, the digital image correlation (DIC) method which calculates strain from the differences between digital images before and after deformation, has been developed as a strain distribution analysis method.^16,17,18) The DIC method enabled the quantitative analysis of the relationship between the strain distribution and microstructure.^{19,20,21,22,23,24)} In pearlitic steel, the strain distribution introduced by tensile deformation was visualized, which revealed the inhomogeneous distribution of strain in a unit of the colony. This indicated a different deformability for each colony.²⁵⁾ The dependence of lamellar alignment on the deformability of the colony was confirmed; colonies with a lamellar alignment of 0° or 90° from the tensile axis exhibited low strain, while those with a lamellar alignment of 45° exhibited high strain. Furthermore, Yajima et al.²⁶⁾ demonstrated that cementite morphology also affected the deformability of colonies. Colonies with spheroidized cementite exhibited higher deformability than colonies with lamellar cementite. However, the deformability differed even among the colonies with spheroidized cementite, and the factors influencing the deformability of the colony with spheroidized cementite have not yet been clarified.

In this study, the deformation and fracture behaviors of spheroidized pearlitic steels were investigated using the DIC and replica methods, and the origin of the inhomogeneous strain distribution and its effect on fractures were discussed.

2. Experimental Procedure

2.1. Materials

Commercial eutectoid steel (Fe-0.8 mass%C) was used in this study. The specimen was solution-treated at 1203 K for 0.36 ks, then isothermally heat-treated in a salt bath at 873 K for 0.03 ks, and immediately air-cooled. The fabricated specimen had a full pearlite structure and is hereafter referred to as the lamellar specimen. The detailed microstructure has been reported in a previous study.²⁶⁾ The lamellar specimen was annealed at 953 K up to 1.8 ks for spheroidization of the cementite.

2.2. Microstructure Observation

The microstructures of the specimens were studied using a scanning electron microscopy SEM with a field-emission gun. The specimens were mechanically polished using SiC paper and finished by polishing with a colloidal silica suspension. An EBSD apparatus (OXFORD Symmetry) equipped with SEM was employed to analyze the crystal orientation of the ferrite and cementite phases. Data were recorded at an accelerating voltage of 20 kV. Crystal orientation analysis was performed on the data points using a software (OXFORD HKL CHANNEL5 system).

2.3. Tensile Test

Specimens with gage length, width, and thickness of 5 mm, 1.7 mm, and 0.8 mm, respectively, were cut from the plates. They were mechanically polished using SiC papers, finished by polishing with a colloidal silica suspension, and then etched using a 3% nital etchant for DIC analysis. Tensile tests were performed using a universal mechanical testing machine at an initial strain rate of 2.5 × 10⁻⁵ s⁻¹ at 293 K in air.

2.4. Replica Method

The replica film was taken from the specimen surface undergoing tensile test while maintaining the crosshead position at nominal strains (ε_n) of 0.05, 0.07, 0.11, 0.15, 0.18, 0.20, and 0.23. The applied stress was decreased continuously during holding the crosshead. Thus, the replica film was taken after 0.6 ks when the applied stress had almost leveled off. The replica films were immersed in methyl acetate, placed on the surface of the specimen, dried for 60 s, and peeled off. Au was deposited on the replica films using an ion-beam sputtering device (Hitachi E-1030). The deposited replica films were observed by SEM at an accelerating voltage of 7 kV to avoid damage to the replica.

2.5. Digital Image Correlation Analysis

DIC analyses were conducted using VIC-2D for the SEM images of the specimen surface or replica film. The subset and step for the DIC analysis were 41 or 29 pixels and 3 pixels, respectively. The reference image for DIC analysis was an SEM image before deformation or taken from the former strained conditions.

2.6. Measurement of the Cementite Area Fraction and Roundness

The area fraction and roundness of cementites were evaluated from the black and white binary images obtained by thresholding the SEM images. The contours of each cementite in the binary image were extracted using the OpenCV software, and the cementite area and perimeter were measured. Cementites on the colony boundary were excluded from this analysis, as explained later. The cementite area fraction is the ratio of the cementite area to the area of the colony in this study. The roundness (R) was calculated from the average cementite area (S) and perimeter (L) in a colony using the following equation:   

$$R=\frac{4\pi S}{L^2}.$$(1)

In the case of a perfect circle, R is 1.

3. Results

3.1. Microstructure and Tensile Properties

Figure 1 shows the SEM images of the specimens annealed at 953 K for (a) 0.6 ks and (b) 1.8 ks. The number of the colony with lamellar structure continuously decreased with increasing annealing times, and the progress of spheroidization differed among colonies. As shown in Fig. 1(b), most colonies are spheroidized until 1.8 ks. Numerous coarse cementites are detected on colony or block boundaries, as indicated by the black arrows in Fig. 1, and the image analyses revealed that the cementite area fraction within colonies was remarkably lower than that in the lamellar specimen.²⁶⁾ Therefore, cementite spheroidization and Ostwald ripening of cementite,²⁷⁾ namely, the dissolution of fine cementites and growth of coarse cementites, occurred simultaneously on this stage. Figure 2 shows the histograms of cementite (a) roundness and (b) area fraction within colonies measured from the SEM images for the lamellar specimen²⁶⁾ and specimens annealed at 953 K for 0.6 ks and 1.8 ks. Here, to evaluate the cementite within a colony, coarse cementites on the colony boundary were excluded from the analysis. The lamellar specimen exhibited the lowest roundness and highest area fraction among the three, which indicated that the cementite morphology was lamellar and that coarse cementites were absent. It should be noted that, although the area fraction has an error because the observation was conducted on only one cross-section, the remarkably higher average area fraction in the lamellar specimen (0.31) compared to that (0.12) estimated from the Fe–C binary system equilibrium diagram under the assumption that both phases have a complete plate shape. It indicated an overestimation of the cementite area fraction by this method, which should be caused by the edge effect of cementite in the SEM observation. The average values of roundness in the annealed specimen at 953 K for 1.8 ks were slightly higher than that in the annealed specimen at 953 K for 0.6 ks, and both of them were higher than that in the lamellar specimen. While the area fraction of the cementite in the specimen annealed at 953 K for 1.8 ks was significantly lower than that in the specimen annealed at 953 K for 0.6 ks. Some colonies exhibited no cementite and were surrounded by coarse cementites, as indicated by red arrows in Fig. 1(b). Thus, it is suggested that the cementite within a colony decreased with increasing annealing time owing to the Ostwald ripening of coarse cementite at the colony or block boundaries. Considering the decrease in the number of density of cementite within a colony as a part of cementite spheroidization, the annealed specimens at 953 K for 0.6 ks and 1.8 ks are hereafter simply referred to as partially-spheroidized and spheroidized specimens.

Fig. 1.

SEM images of the specimens annealed at 953 K (a) for 0.6 ks and (b) 1.8 ks. (Online version in color.)

Fig. 2.

Histograms of cementite (a) roundness and (b) area fraction within a colony in the as-fabricated (lamellar) specimen and specimens annealed at 953 K for 0.6 ks (partially-spheroidized) and 1.8 ks (spheroidized).

Figure 3 shows the representative nominal stress-strain (SS) curves in the lamellar, partially-spheroidized, and spheroidized specimens. 0.2% proof stress, ultimate tensile stress (σ_UTS), uniform strain (ε_n), total strain (ε_t), and σ_UTS × ε_t measured from tensile tests performed thrice are summarized in Table 1. The lamellar specimen exhibits the typical SS curve of pearlitic steel, exhibiting continuous yielding, high work-hardening, and comparably low total strain. While the strength and work-hardening decreased at cementite spheroidization progressed, ε_t increased slightly. However, σ_UTS × ε_t, namely, the parameter of strength–ductility balance, decreased as shown in Table 1. It indicates that spheroidization did not improve the ductility expected from the decrease of strength, and deteriorated the tensile property of pearlitic steel.

Fig. 3.

Nominal stress – nominal strain curves in the as-fabricated (lamellar) specimen and specimens annealed at 953 K for 0.6 ks (partially-spheroidized) and 1.8 ks (spheroidized).

Table 1. 0.2% proof stress, ultimate tensile stress (σ_UTS), uniform strain (ε_n), total strain (ε_t), and σ_UTS × ε_t measured from tensile tests performed thrice in the as-fabricated (lamellar) specimen and specimens annealed at 953 K for 0.6 ks (partially-spheroidized) and 1.8 ks (spheroidized).

	0.2% proof stress, σ0.2 (MPa)	Ultimate tensile stress, σUTS (MPa)	Uniform strain, εu	Total strain, εt	σUTS × εt
Lamellar	510 ± 20	910 ± 1	0.11 ± 0.01	0.18 ± 0.01	170 ± 10
Partially-spheroidized	360 ± 30	600 ± 50	0.12 ± 0	0.20 ± 0.01	120 ± 10
Spheroidized	300 ± 40	570 ± 20	0.13 ± 0.01	0.23 ± 0.02	130 ± 20

3.2. Strain Distribution Developed by Tensile Deformation

Figure 4 shows (a-1), (b-1) SEM images, (a-2), (b-2) crystallographic orientation along tensile direction in ferrite phase, and (a-3), (b-3) ε_xx strain distributions in the identical regions at ε_n = 0.02 of (a-1)–(a-3) partially-spheroidized and (b-1)–(b-3) spheroidized specimens. (a-1) and (b-1) are the combined images of sixteen SEM images to visualize the high-resolution strain distribution in a wide area. There were several blocks in the analyzed area. The block sizes of partially-spheroidized and spheroidized specimens were identical (approximately 30 μm), which indicated that the blocks were hardly coarsened during the annealing, although the annealing temperature exceeded the recrystallization temperature of the ferrite phase.²⁸⁾ The colony boundaries tended to be low-angle boundaries in pearlitic steel.²⁹⁾ In the spheroidized specimens (Figs. 4(a-2), 4(b-2)), the low-angle boundaries were maintained, and the colony size, which was measured based on the low-angle boundary, was also identical between the partially-spheroidized and spheroidized specimens. Considering that coarse cementites were present along with colony or block boundaries (Figs. 4(a-1), 4(a-2) and 4(b-1), 4(b-2)), it can be reasonably understood that the colonies and blocks hardly grew because of the pinning effect of the coarse cementites. In general, the grain-boundary diffusion is much faster than the lattice diffusion. Thus, the cementites on the colony or block boundaries comprising low- and high-angle boundaries were preferentially spheroidized or grown by annealing, which resulted in coarse cementites in those boundaries (Figs. 4(a-1), 4(b-2)).

Fig. 4.

(a-1), (b-1) SEM images, (a-2), (b-2) crystallographic orientation along tensile direction in ferrite phase, and (a-3), (b-3) ε_xx strain distributions in the identical regions in the specimens annealed at 953 K for (a-1)–(a-3) 0.6 ks (partially-spheroidized) and (b-1)–(b-3) 1.8 ks (spheroidized). (Online version in color.)

In both spheroidized specimens, the strain was inhomogeneously distributed (Figs. 4(a-3), 4(b-3)); the strain in high- and low-strain regions was two times higher than the average strain and almost 0, respectively. The regions along the block boundaries exhibited a high strain, as indicated by arrows in Figs. 4(a-3) and 4(b-3), similar to the lamellar specimen²⁶⁾ or ferrite single-phase steel.³⁰⁾ In a block, the strain was inhomogeneously distributed, and an enlarged strain distribution (Fig. 5) confirms that the strain changes at the colony boundaries. Thus, each colony has different deformability, similar to the lamellar specimen.²⁶⁾ Figure 6 shows the ε_xx strain histograms calculated from Figs. 4(a-3) and 4(b-3) and the ε_xx strain distribution in the lamellar specimen in our previous study.²⁶⁾ The average strain and standard deviation were approximately the same among the specimens. Considering that the standard deviation represents the width of the histogram, i.e., the inhomogeneity of the strain distribution in this analysis, the result suggests that the inhomogeneity of the strain distribution hardly changed with annealing. In the lamellar specimen, the main factors influencing the deformability of the colony were the cementite length, lamellar alignment, and Schmid factor in the slip system where the dislocation glides along the direction parallel to the cementite plate.²⁶⁾ However, in the spheroidized specimens, the lamellar structure was hardly present, and thus, the cementite length, namely, the cementite roundness or area fraction in this analysis, should be important for the deformability of the colony. Notably, the strength was significantly decreased by spheroidization (Fig. 3), but the inhomogeneity of the strain distribution was unchanged by annealing (Fig. 6). Therefore, it is suggested that the inhomogeneity of strain distribution is hardly related to the strength of the specimen.

Fig. 5.

Enlarged ε_xx strain distribution within a block in the specimens annealed at 953 K for (a) 0.6 ks (partially-spheroidized) and (b) 1.8 ks (spheroidized). (Online version in color.)

Fig. 6.

Histograms of ε_xx strain calculated from Fig. 4 and the strain distribution in the as-fabricated (lamellar) specimen in our previous study.²⁶⁾

3.3. Fracture Behavior in Spheroidized Pearlite

3.3.1. Void and Crack Observation on a Specimen Surface

Figure 7 shows SEM images on the specimen surface near the final fracture region in the (a) partially-spheroidized and (b) spheroidized specimens after the tensile test. Numerous voids or cracks were observed, as indicated by the black arrows. In the pearlitic steel, the continuous fracture of cementite plates along the maximum shear stress direction (45°), that is, shear band, was observed. The shear bands grow to micro-cracks, and result in a fracture.^14,15) However, in spheroidized specimens, no clear shear bands formed, and the voids or cracks tended to be randomly distributed because voids preferentially form around the relatively coarse spheroidized cementites as shown later. Coalescence of these voids leads to nucleate micro-cracks, as indicated by red arrows in Fig. 7, which cause fatal fracture of the specimen. Figure 8 shows the fracture surface in the (a) partially-spheroidized and (b) spheroidized specimens. Both fracture surfaces comprise dimples that indicate a ductile fracture. In both spheroidized specimens, the dimples are approximately 1 μm in size, which is smaller than the size of the colony. It implies the nucleation of voids or cracks within a colony. The reduction areas calculated from the area of fracture surfaces in the lamellar, partially-spheroidized and spheroidized specimens were 30%, 44% and 50%, respectively. Although cementite spheroidization improved the reduction area, its value was even low in the spheroidized specimen. Its level was identical to that in the dual phase steel (20%–50%),³¹⁾ which is well known as low area reduction material owing to frequent void nucleation. Considering the low strength-ductility balance in the spheroidized specimens (Table 1), the improvement in ductility by the cementite spheroidization is insignificant.

Fig. 7.

SEM images on the specimen surface near the final fracture region in the specimens annealed at 953 K for (a) 0.6 ks (partially-spheroidized) and (b) 1.8 ks (spheroidized). (Online version in color.)

Fig. 8.

Fracture surface in the specimens annealed at 953 K for (a) 0.6 ks (partially-spheroidized) and (b) 1.8 ks (spheroidized).

Figure 9 shows the (a) enlarged SEM image in the region surrounded by the red square in Fig. 7(b) and (b) orientation map of the cementite phase in an identical region. Three types of void or crack nucleation sites can be seen in Fig. 9(a): in cementite (red arrows), in ferrite at the ferrite/cementite interfacial boundary (black arrows), and inside ferrite grain (blue arrow). Because the crystallographic orientations of the cementite grains around the cracks were different (Fig. 9(b)), several cracks in cementite formed at the high-angle grain boundary. The cementites indicated by the white arrows in Fig. 9(b) possessed similar crystallographic orientations within 15°. The normal of the (010)_Fe3C, which is the cleavage plane of cementite,³²⁾ in these cementites are shown in Fig. 9(c). Furthermore, the red dotted lines denote the two-dimensional traces of cracks in cementite obtained from Fig. 9(a). Figure 9(c) suggests that the fracture plane is not (010)_Fe3C and cleavage fracture did not occur. Thus, these cracks should be nucleated at the low-angle boundary, and it can be concluded that intergranular fracture along the high- and low-angle boundaries is the main fracture mode in cementites.

Fig. 9.

(a) enlarged SEM image in Fig. 7 (b) and (b) orientation map of cementite in identical region with (a). (c) (010)_Fe3C pole figure of the cementites indicated by white arrows. (Online version in color.)

3.3.2. Strain Distribution around Void and Crack Nucleation Region

Figure 10 shows the SS curve during the cyclically interrupted tensile test to take replica films for the spheroidized specimen. Nominal stress dropped while pausing the tensile test owing to stress relaxation; thus, the replica film was taken when the decrease in stress leveled off. Replica films were taken at various values of ε_n. However, some replica films could not transcribe the microstructure on the specimen surface because of the bubbles or wrinkles of the replica film. Thus, the microstructure observation by replica film was performed when ε_n was 0.05, 0.07, 0.11, 0.16, 0.18, 0.20, and 0.23.

Fig. 10.

Nominal stress – nominal strain curve during the cyclically interrupted tensile test for taking a replica film in the specimen annealed at 953 K for 1.8 ks (spheroidized).

Figure 11 shows the SEM images of replica films (a) before deformation, and deformed to (b) ε_n = 0.07 (uniform deformation), (c) 0.18 (necking deformation) and (d) 0.23 (just before fracture), and (e) specimen surface after fracture in the identical regions of the spherodized specimen. The black square region in Fig. 7(b) was observed region in Fig. 11. Numerous voids or cracks were observed on the specimen surface, as indicated by the arrows in Fig. 11(e). Protrusions were detected on the replica film at ε_n = 0.23 (Fig. 11(d)), and the positions of these protrusions agreed well with the positions of voids or cracks on the specimen surface (Fig. 11(e)), which indicates that the replica films successfully transcribed voids or cracks on the specimen surface. These protrusions were hardly detected during uniform deformation (Fig. 11(b)), and those nucleated and grew during the necking deformation (Fig. 11(c)). The voids or cracks tended to nucleate around the coarse cementite on the colony or block boundaries, as indicated by the red arrows in Fig. 11. Figure 12 shows ε_xx strain distribution in the identical region with Fig. 11(b). The reference image was the SEM image at ε_n = 0.05, and the subset size is 29 pixels. Arrows indicate the voids or cracks in Fig. 11. Strain is inhomogeneously distributed and the value of strain in the coarse cementites is almost 0. Furthermore, the stain of the ferrite around the coarse cementites tended to be high. Considering that the cementite is a remarkably harder phase than the ferrite, it suggests that the strain partitioning between ferrite and cementite and the strain concentration at ferrite/cementite interfacial boundary occur. Since the positions of voids and cracks are in accordance well with the high strain regions indicated by the arrows in Fig. 12, it can be concluded that the voids or cracks preferentially nucleate from the high strain regions. In the DIC analysis on the replica films in the martensitic steel, cracks nucleated from the high strain region similarly,³³⁾ and it should be the general tendency in the metal materials.

Fig. 11.

SEM images of replica films (a) before deformation and at ε_n = (b) 0.07 (uniform deformation), (c) 0.18 (necking deformation), and (d) 0.23 (just before fracture) and (e) specimen surface after fracture in the identical regions in the specimen annealed at 953 K for 1.8 ks (spheroidized). (Online version in color.)

Fig. 12.

ε_xx strain distribution in the identical region with Fig. 11(b). The reference image is the SEM image at ε_n = 0.05. Arrows indicate nucleation site of void or crack in Fig. 11. (Online version in color.)

4. Discussion

4.1. Origin of the Inhomogeneous Strain Distribution in the Spheroidized Pearlite Structure

The inhomogeneity of the strain distribution introduced by the tensile test was nearly identical for the lamellar, partially-spheroidized and spheroidized specimens (Fig. 6). Strain was distributed in a unit of the colony in the spherodized specimens (Fig. 5), even though the lamellar structure barely remained. Table 2 shows the cementite roundness and area fraction in the high- and low-strain regions of the partially-spheroidized and spheroidized specimens. The data were obtained from approximately 100 colonies. Here, the high- or low-strain region was defined as the region where the strain within a colony was larger or smaller than the average strain. In Table 2, the value of roundness was approximately the same independent of strain level. This indicates that the morphology of the cementite was quite similar and unrelated to the difference in the strain distribution in spheroidized specimens. The cementite area fraction is the ratio of the cementite and ferrite regions within a colony. As discussed in Section 3.1, assuming a complete plate of ferrite and cementite phases, its value was expected to be 0.12 based on the Fe–C binary system equilibrium diagram. However, although the cementite area fraction tended to be overestimated by this analysis, as shown in Fig. 2(b), all values in Table 2 were lower than 0.12, because the coarse cementites at the colony or block boundaries (see Fig. 1) were excluded from the area fraction analyses. Notably, the cementite area fraction in the high-strain region was remarkably lower than that in the low-strain one; the values in the low-strain one were almost two times larger than that in the high-strain one in both the specimens. This result reasonably explained that high strain was introduced into the region where the cementite volume fraction was low, that is, an almost ferrite single-phase region. Therefore, the inhomogeneous strain distribution in the spheroidized specimens can be attributed to the inhomogeneous progress of the spheroidization among the colonies.

Table 2. Cementite roundness and area fraction in high- and low-strain regions in the specimen annealed at 953 K for 0.6 ks (partially-spheroidized) and 1.8 ks (spheroidized). The high- and low-strain regions were defined as the regions where the strain within a colony is over and under average strain, respectively.

	Partially-spheroidized		Spheroidized
	High-strain	Low-strain	High-strain	Low-strain
Circularity	0.58 ± 0.14	0.51 ± 0.14	0.51 ± 0.18	0.50 ± 0.16
Area fraction (%)	4.1 ± 2.8	11.3 ± 8.5	3.0 ± 3.0	5.8 ± 4.3

The following three crystallographic orientation relationships (OR) between ferrite and cementite have been reported in pearlite structures:

• Isaichev relationship³⁴⁾: (011)_Fe3C//(11-2)_α, [01-1]_Fe3C//[1-10]_α, [100]_Fe3C//[111]_α

• Pitsch-Petch relationship^35,36): (010)_Fe3C//(521)_α, [001]_Fe3C 2.6° from//[-31-1]_α, [100]_Fe3C 2.6° from//[131]_α

• Bagaryatsky relationship³⁷⁾: (010)_Fe3C//(11-2)_α, [011]_Fe3C//[1-10]_α, [100]_Fe3C//[111]_α

Furthermore, a recent study using the EBSD method for spheroidized cementite revealed that each colony had a different OR.³⁸⁾ In this study, various ORs were also detected from the spheroidized specimens, and Table 3 summarizes the cementite roundness and area fraction in the colony with the Pitsch-Petch, Bagaryatsky, and Isaichev ORs in the partially-spheroidized and spheroidized specimens. Although the cementite plate in the lamellar structure was too thin to analyze by the EBSD method, the spheroidized cementite large enough to the EBSD analyses were used. Thus, the results in Table 3 were mainly measured for the spheroidized cementite. Although the values of roundness and area fraction were varied in each OR, in both spheroidized specimens, the colony with the Isaichev OR exhibited the lowest roundness and highest area fraction, indicating the slowest cementite spheroidization. The colony with Pitsch-Petch OR had the highest roundness and lowest area fraction. This suggests that the progress of cementite spheroidization was differed among the ORs, which is one of the factors for inhomogeneous cementite spheroidization. The interfacial energies of these ORs³⁹⁾ are also summarized in Table 3. The Pitsch-Petch and Isaichev ORs possessed the highest and lowest interfacial energies, respectively. It can be said that lower the interfacial energy is more stable the interfacial boundary, and thus, it should inhibits the cementite spheroidization. Therefore, it can be concluded that the different interfacial energies among the ORs provided inhomogeneous cementite spheroidization and inhomogeneous strain distribution in a unit of the colony.

Table 3. Cementite roundness and area fraction in the colony with Pitsch-Petch, Bagaruatsky, and Isaichev orientation relationships in the specimen annealed at 953 K for 0.6 ks (partially-spheroidized) and 1.8 ks (spheroidized). Interfacial energies in these orientation relationships are also shown.

		Pitch-Petsch	Bagaryatsky	Isaichev
Partially-spheroidized	Circularity	0.58 ± 0.14	0.52 ± 0.11	0.48 ± 0.13
	Area fraction (%)	7.0 ± 7.0	7.3 ± 6.8	8.4 ± 7.5
Spheroidized	Circularity	0.56 ± 0.15	0.49 ± 0.19	0.49 ± 0.16
	Area fraction (%)	4.0 ± 3.5	4.5 ± 4.0	4.5 ± 4.0
Interfacial energy (mJ/m2)		66039)	62839)	50039)

It can be pointed out two factors influencing the variation of roundness and area fraction of cementites having each OR (Table 3). They are the OR of the coarse cementite on the colony or block boundaries and the density of hole in the cementite plate before annealing. Figure 13 shows (a) SEM image and (b) orientation map along A₁ axis showing a cementite at block boundary having ORs with adjacent colonies in the spheroidized specimen and (c), (d) stereographic projections of {521}_α, {112}_α, and (010)_Fe3C of the cementite and colonies indicated by the arrows in (a) and (b). The coarse cementite on the block boundary shown in Figs. 13(a) and 13(b) had the Bagaryatsky OR (Fig. 13(c)) with the left-side colony and the Pitsch-Petch OR (Fig. 13(d)) with the right-side colony. It can be note that the coarse cementite seemingly grew into the left-side colony with the Bagaryatsky OR in which interfacial energy is lower than that in the colony having the Pitsch-Petch OR (Table 3). Furthermore, the number density of in-colony cementites is extremely low in the left-side colony compared to the right-side one. Moreover, the cementites in the colony with the Pitsch-Petch OR maintained lamellar structure. Similar preferential growth of precipitate had been reported in the cellular precipitation reaction⁴⁰⁾ or the growth of precipitates on the grain boundary.⁴¹⁾ When a precipitate at grain boundary has an OR with the grain of one side of the precipitate and no OR with the grain of the other side, the precipitate grows into the grain with an OR because the increment of total interfacial energy along with the growth can be lowered. In Fig. 13, it can be reasonably understood that the cementite preferentially grew into the colony having lower interfacial energy between the cementite and ferrite matrix. Thus, the OR of the cementites on the colony or block boundaries should play an important role in the cementite spheroidization. On the other hand, before annealing (lamellar specimen), cementite roundness and area fraction were varied from colony to colony as shown in Fig. 2, and discontinuous cementites or holes of cementite were present as shown in Fig. 14. Wang et al.⁴²⁾ reported that the spheroidization preferentially occurred in the holes of the cementite plate. These holes were formed during the pearlitic transformation owing to the lack of carbon atoms in austenite near the reaction front of the pearlitic transformation,⁴³⁾ and they are expected to be inhomogeneously distributed regardless of the OR. The inhomogeneous distribution of the defects or holes in the cementite lamellae leads to the inhomogeneous cementite spheroidization among colonies even with the identical OR. Therefore, to reveal the origin of the inhomogeneous cementite spheroidization, the OR within the colony and coarse cementite on the colony or block boundaries, and the initial density of holes in the cementite plates must be investigated simultaneously by using such as in-situ heating SEM observation, which is one of the future work.

Fig. 13.

(a) SEM image, (b) orientation map along A₁ axis and (c), (d) {521}_α, {112}_α and (010)_Fe3C pole figures indicated by arrows in (a) and (b). (Online version in color.)

Fig. 14.

SEM image of as-fabricated (lamellar) specimen.

4.2. Relation between the Strain Distribution and Void or Crack Nucleation in Spheroidized Pearlite

The relationship between void or crack nucleation and strain distribution introduced by deformation in a lamellar pearlite structure has been reported,²⁵⁾ and it is schematically illustrated in Figs. 15(a-1)–15(a-3). Each colony has various lamellar alignments, and the colony boundary tends to be low-angle (a-1). During deformation, the strain was inhomogeneously distributed depending on the lamellar alignment of the colony, i.e., colonies with the lamella aligned at 45° from the tensile direction exhibit higher strain than the average, and colonies with the lamella aligned at 0° or 90° exhibit lower strain (a-2). In the colony with a low strain, dislocations pile-up at ferrite/cementite interface, and then, cementites fracture owing to the stress concentration with piled-up dislocations, forming a continuous fracture of cementites, i.e., shear band. Finally, voids are generated along with the shear band (a-3). These voids easily coalesce and form a micro-crack.^14,15,16) Thus, in a lamellar pearlite structure, the nucleation site of voids or cracks is in a low-strain colony.

Fig. 15.

Schematic illustration of deformation and fracture behavior in (a-1)–(a-3) lamellar pearlite and (b-1)–(b-3) spheroidized pearlite structures. (Online version in color.)

In contrast, in the spheroidized pearlite structure, although the strain distribution is identical with that in lamellar pearlite structure (Fig. 6), void or crack nucleation site is different, as schematically illustrated in Figs. 15(b-1)–15(b-3) based on the observation results. Before deformation, each colony has various cementite volume fractions owing to its OR between ferrite and cementite phases within the colony, OR between neighboring coarse cementite and ferrite in the colony, and the density of hole in cementite plate before annealing, as discussed in Section 4.1. Coarse cementite forms at colony boundaries, which are low-angle boundaries (b-1). An inhomogeneous strain distribution was introduced depending on the cementite volume fraction (progress of spheroidization); the strain was preferentially introduced into the colony with a low cementite volume fraction (b-2). Then, voids or cracks formed at low- or high-angle boundaries in the cementite and in ferrite around the cementite (b-3). Therefore, in the spheroidized pearlite structure, voids or cracks nucleate from the high-strain colony, which is different from the lamellar pearlite structure. The fracture mechanism in the spheroidized pearlite structure is expected to resemble that in dual-phase (DP) steel. High strain is introduced into the soft phase, and a large strain gradient occurs at the soft/hard interfacial boundary, which causes void nucleation in the soft phase or fracture of the hard phase.^44,45) In the spheroidized pearlite structure, the cementite phase is remarkably harder than the ferrite phase,⁴⁶⁾ and it can be assumed to be a soft and hard dual-phase structure. In fact, the strain concentration at the ferrite/cementite interfacial boundary was detected as shown in Fig. 12. Thus, the strain gradient at the ferrite/cementite interfacial boundary was large in the high-strain colony, and generated a high-stress concentration in the cementite, leading to intergranular fracture along the high- and low-angle boundaries. While, in the ferrite phase at the ferrite/cementite interface, the stress triaxiality increased owing to the strain gradient, causing void nucleation, as reported in DP steel.⁴⁷⁾ Hence, voids or cracks were preferentially nucleated from the high-strain colonies in the spheroidized specimens.

In the lamellar pearlite structure, the inhomogeneous strain distribution should hardly affect the fracture behavior because the voids nucleated from the low-strain colony. In contrast, the inhomogeneity of the strain distribution is important for the fracture of spheroidized cementite because the voids and cracks were nucleated from the high-strain colony. In DP steel, it was demonstrated that the homogeneous strain distribution provides a high strength-ductility balance by suppressing void nucleation.⁴⁸⁾ Cementite spheroidization inevitably progressed inhomogeneously owing to the existence of various ORs in a unit of the colony or holes of cementite plate, which caused inhomogeneous strain distribution during tensile deformation. Therefore, one of the reasons for the low strength-ductility balance in the spheroidized specimens (Table 1) could be the existence of various ORs and holes of cementite plate, and the control of OR or hole during pearlitic transformation should be crucial for improving the strength-ductility balance of spheroidized pearlitic steels.

5. Conclusion

The deformation and fracture behaviors of spheroidized pearlitic steels were investigated using digital image correlation analyses with utilizing replica methods, and the origin of the inhomogeneous strain distribution and its effect on the fracture were discussed. The main results are summarized as follows.

(1) The cementite roundness increased with annealing, and the cementite area fraction within a colony decreased significantly with increasing annealing time. Coarse cementite presented on the colony and block boundaries.

(2) As cementite spheroidization progressed, the strength decreased whereas the elongation increased. The strength–ductility balance of the spheroidized pearlitic steel was lower than that of the lamellar pearlitic steel.

(3) The strain was inhomogeneously distributed in a unit of the colony in the spheroidized specimens subjected to tensile deformation, and the inhomogeneity of the strain distribution was approximately identical between the lamellar and spheroidized pearlitic steels.

(4) Numerous voids or cracks were detected in spheroidized pearlitic steel after fracture. Voids or cracks were mainly nucleated along low- or high-angle boundaries in cementite and in the ferrite phase at the ferrite/cementite interfacial boundary in high-strain colonies.

(5) High- and low-strain colonies exhibited the low- and high-cementite area fraction, respectively, suggesting that the inhomogeneous strain distribution was attributed to the inhomogeneous progress of cementite spheroidization among colonies.

(6) The crystallographic orientation relationship between ferrite and cementite was different in each colony, and the progress of cementite spheroidization tended to depend on the crystallographic orientation relationship. Furthermore, crystallographic orientation relationship between neighboring coarse cementite and ferrite matrix, and holes of cementite plate formed during pearlitic transformation should also affect the inhomogeneous cementite spheroidization.

(7) The strain gradient between the soft ferrite and hard cementite phases in the spheroidized pearlite are expected to induce void or crack nucleation around the coarse cementite on the colony or block boundaries. Thus, voids or cracks were preferentially nucleated from the high-strain region.

It can be concluded that the inhomogeneous progress of cementite spheroidization results in inhomogeneous strain distribution during deformation, and also causes preferential nucleation of voids or cracks in the high-strain colony. Thus, the low strength-ductility balance of the spheroidized pearlitic steel should be attributed to the inhomogeneous progress of cementite spheroidization, and the control of the crystallographic orientation relationship or holes of cementite plate during pearlitic transformation may be crucial for improving the strength-ductility balance in spheroidized pearlitic steels.

Acknowledgement

This work was supported by JKA and its promotion funds from KEIRIN RACE and the Research Society for heterogeneous deformation structure and its effects on mechanical properties, ISIJ. The authors also acknowledge the financial support of the Grant-in-Aid for Scientific Research (KAKENHI) Grant No. 20K14605.

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