To expand the application of high-strength martensitic steel in automotive body components, improving the bendability and understanding the factors affecting it are essential. In this study, we investigated the formation of shear bands and surface cracks in Fe-0.24C-1.0Mn (mass%) lath martensite during three-point bending tests using scanning electron microscopy and electron backscatter diffraction, with a focus on the effects of tempering up to 400°C. During bending, fine striated steps and elongated notches formed on the surface, which were attributed to block boundary sliding along the {110}_α in-habit-plane slip system and the formation of shear bands, respectively. Boundary sliding dominated subsurface deformation in as-quenched martensite, and shear-band formation was enhanced by tempering at ≥200°C, with a more pronounced effect at higher tempering temperatures. In as-quenched martensite, most surface cracks initiated near less-deformed hard martensite packets, and tempering at ≥200°C retarded the initiation and growth of these cracks. The limiting strain for crack initiation, as evaluated through digital image correlation analysis, increased with an increase in tempering temperature at ≥200°C and was found to correlate with the critical fracture strain determined via tensile tests. These findings suggest that the inhibition of crack initiation and growth by tempering is primarily caused by the improvement in local deformability within shear bands and at crack tips, which is primarily due to the transition from boundary sliding to the enhanced activation of multiple slip systems. The reduction in surface local stress at the bend apex could also be a factor induced by tempering.

High-strength martensitic steel is increasingly used in vehicle body frames and reinforcements to achieve lightweight structures and improved crash performance.¹⁾ During an automotive crash, structural components often undergo folding and bending, resulting in severe tight-radius bending in the folding regions. As crash performance deteriorates when cracks form in these severely bent areas,^2,3,4,5) it is crucial to enhance bendability and understand the relationship between the failure mechanisms and microstructure during bending to extend the use of high-strength martensitic steel in automotive body components.

There are various methods for evaluating the bendability of steel sheets. For automotive applications, the V-block method has traditionally been used, but the three-point bending test based on the VDA238-100 specification⁶⁾ is increasingly favored.¹⁾ A key motivation for using VDA238-100 is the observed correlation between the bend angle at maximum load ( α F max ) and crack initiation within folding regions during crash events in martensitic press-hardened steel (PHS),^2,3) although the validity of α F max as a universal bending failure criterion is not fully established.⁷⁾ Additionally, the post-uniform bending slope (PUBS), which represents the load reduction rate following the maximum load during a bending test, has been reported as an indicator correlated with crash performance.³⁾

Crack initiation during bending tests is closely related to the local formability of the steel sheet. For instance, correlations with bendability have been reported for the hole expansion ratio⁸⁾ and local elongation values estimated for small gauge lengths^9,10) in advanced high-strength steel (AHSS) sheets. As intrinsic measures of local formability in AHSS that can be evaluated via tensile tests, true fracture strain (FS) and critical fracture strain (CFS) have recently attracted attention.^1,11) Hance¹¹⁾ demonstrated an exponential relationship between the limiting bend ratio determined through a 90° V-bend test and the product of true FS and true uniform strain (ε_u) in various 980 MPa-class AHSS sheets. He reasoned that fracture resistance is governed by local formability in the latter stages of deformation, whereas global formability governs strain concentration around the bend apex in the early stages of deformation. In martensitic steels, Nagataki et al.¹²⁾ showed that the limiting bend ratio was independent of ε_u in tensile tests, and Larour et al.²⁾ found a positive correlation between α F max and the CFS in PHS grades. These findings suggest that bendability in martensitic steels strongly depends on local formability criteria. However, the underlying reasons for this dependence are not yet well understood.

The properties of structural components for automotive bodies are finalized in the paint-baking process, which is also known as bake-hardening (BH) treatment. The effect of BH treatment at 170°C on the bendability of martensitic PHS grades has been investigated.^3,10,13) However, inconsistencies have been observed regarding the change in α F max due to BH treatment. Kurz et al.³⁾ found an increase in α F max and a decrease in PUBS in 1.5 GPa-class PHS, while Järvinen et al.¹⁰⁾ and Blesi¹³⁾ could not identify a clear trend in α F max in 2.0-GPa-class and 1.5-GPa-class PHS, respectively. The effect of the microstructure on the bendability of martensitic steels is often discussed in relation to the presence of cementite in the matrix. Nagataki et al.¹²⁾ investigated the effect of tempering in the range of 200–500°C for 0.15–0.4C martensitic steels and found that the limiting bend ratio was correlated with the number density of elongated cementite particles in the tempered martensite. In this context, bendability is expected to deteriorate with BH treatment because transition carbides precipitate at temperatures between 150 and 200°C.¹⁴⁾ However, despite this, crash performance was reported to improve slightly following BH treatment at 170°C,³⁾ which indicates the opposite trend.

The deformation and damage sequence during three-point bending tests has been microscopically analyzed in AHSS,^8,15,16) aluminum alloys,^17,18) and copper alloys.¹⁹⁾ Surface deformation begins with surface roughening, followed by the formation of small notches or grooves along the bend axis, induced by subsurface shear bands. These notches grow alongside the shear bands, eventually evolving into cracks, which propagate in the shear mode, accompanied by a reduction in load. The formation of notches and shear bands in AHSS has been observed in martensitic PHS grades,²⁰⁾ complex-phase grades,^8,15) and dual-phase grades.⁸⁾ However, there is limited information on how tempering affects the formation of shear bands, as well as the initiation and growth of cracks in these steels.

The strength of martensitic steel can be primarily controlled by adjusting the carbon content and tempering temperature, which allows control of its bendability. Microstructural features such as grain size and texture²⁰⁾ also influence bendability. Thus, for developing high-strength martensitic steel with improved bendability, it is essential to quantitatively understand the microstructural factors that affect shear banding and the initiation and growth of cracks. The objective of this study is to investigate the microstructural factors that govern the formation of shear bands and surface cracks during three-point bending tests in low-carbon lath martensitic steel, with a focus on the effect of tempering. The deformation behavior on the outer surface is primarily characterized in situ using scanning electron microscopy (SEM) with a three-point bending apparatus. To examine the dominant factors affecting bendability from a macroscopic perspective, we also quantify the limiting strain for crack formation through a combination of digital image correlation (DIC) analysis in air-bending and in situ SEM observation during bending.

The material used in this study was Fe-0.24C-1.0Mn (mass%). The steel was hot-forged and homogenized at 1280°C, hot-rolled, ground to remove the decarburized surface layer, and then cold-rolled. The cold-rolled sheets (1.2 mm thick) were heated to 1100°C for 30 s for austenitization and then quenched using a high-pressure water jet at a cooling rate exceeding 500°C∙s⁻¹ to 15°C, followed by immediate cooling in liquid nitrogen for sub-zero treatment. Tempering was performed isothermally at 100, 200, 300, and 400°C for 20 min in an oil bath and salt bath. To prevent changes in mechanical properties due to room-temperature aging,²¹⁾ the quenched specimens were kept below −30°C, except during cutting and polishing.

Specimens for uniaxial tensile tests were machined from the sheet into a dogbone shape with a straight-section width of 6.3 mm, length of 15 mm, and thickness of 0.8 mm. The tensile speed was set as 1 mm/min, and the strain was measured using an extensometer with a gauge length of 15 mm. For the bending test, specimens were machined to dimensions of 5 mm × 15 mm with a thickness of 0.44 mm, and the surface was finished via chemical mechanical polishing using a colloidal silica suspension. Three-point bending tests were performed both under the SEM and in air using a bending machine with a fixed support span of 8 mm, a support diameter of 2 mm, and a punch radius of 0.1 mm. The specimen was bent by moving both supports downward at a speed of 132 μm/min, and the height position of the specimen at the bend apex remained unchanged during the test. The bend angle during the test was calculated in accordance with the ISO 7438 standard.²²⁾

In the air-bending test, the change in the strain distribution on the bent surface was analyzed using DIC by capturing top-view images with a CMOS camera positioned directly above the bending surface. The DIC strain analysis was performed using Correlated Solutions Vic-2D software, where the bend and tensile axes were designated as the y- and x-directions, respectively. The subset size and step size for the DIC analysis were set as 0.59 × 0.59 mm² and 0.021 mm, respectively. In this paper, strain is represented as logarithmic (Hencky) strain. It should be noted that single-camera DIC analysis can misinterpret changes in the z-direction position during bending as strain; thus, the strain distribution data should be interpreted with caution. Nevertheless, our bending machine provides an accurate value of the strain at the bend apex, because the punch position remains fixed during bending. The microstructural and surface changes during bending were examined using a field-emission scanning electron microscope (Hitachi SU5000) equipped with an electron backscatter diffraction (EBSD) detector (AMETEC Hikari). The surface roughness distribution was analyzed using backscattered electron (BSE) images taken from split BSE detectors using Hitachi Map 3D software. The cross-sections of the samples obtained from the interrupted bending experiments were investigated using EBSD. For the estimation of dislocation densities and retained austenite (RA) in the martensite, X-ray diffraction (XRD) analysis was conducted using a Rigaku RINT2000 diffractometer in the 2θ range of 10°–130° with a step size of 0.02° with Co-Kα radiation. The specimen for XRD analysis was finished via chemical polishing to remove strain introduced during mechanical polishing. No significant peaks of γ ({111}, {200}, {220}, or {311}) were observed for the as-quenched (AsQ) and tempered martensite, indicating that the amount of RA was below the detection limit. The dislocation density (ρ) was evaluated via the Williamson–Hall method²³⁾ using the microstrain (ε) obtained from the widths of the {110}_α, {211}_α, and {220}_α reflections of martensite according to the relationship ρ=(14.4× ε 2 )/ b v 2 , where b_v denotes the Burgers vector (which has a magnitude of 0.25 nm in this case). Retained tetragonality was not considered in the analysis.

The morphology of the steels exhibited a typical lath martensite structure with a hierarchical microstructure composed of prior austenite grains, packets, blocks, and sub-blocks²⁴⁾ (Fig. 1). The packet size of the lath martensite, which can be identified as a group of blocks elongated in the same direction (Fig. 1(b)), ranged approximately from 10 to 250 μm. The size of the blocks along the major elongation axis varied between 5 and 100 μm (Fig. 1(c)). As observed in secondary-electron (SE) images (Fig. 2), fine carbides formed during water-quenching were present in the blocks of AsQ martensite, and their size increased with the tempering temperature. These carbides, which were identified as transition η-carbides,²⁵⁾ varied in size among the blocks of AsQ martensite, and less-precipitated blocks were observed (Fig. 2(a)). The variation in carbide precipitation among blocks was reduced by tempering (Figs. 2(b) and 2(c)).

Fig. 1. (a) EBSD orientation map; (b) close-packed plane group map showing the distribution of packet grains and (c) Bain group map illustrating the distribution of block grains in AsQ martensite. (Online version in color.)

Fig. 2. SE images of (a) AsQ steel, (b) steel quenched and tempered at 200°C (QT200), and (c) steel quenched and tempered at 400°C (QT400).

The change in dislocation density with tempering is illustrated in Fig. 3. The estimated dislocation density after quenching was approximately 1.2 × 10¹⁵ m⁻²; it remained constant up to tempering at 200°C and then decreased with an increase in the tempering temperature at ≥300°C. This trend closely matches previously reported transmission electron microscopy (TEM) results for Fe-0.2C martensite.²⁶⁾

Fig. 3. Changes in dislocation density with tempering for 20 min, as evaluated using XRD analysis.

Engineering stress–strain curves after quenching and tempering are shown in Fig. 4. Table 1 presents the tensile test results, including the elastic limit (R_e.l), yield strength (R_p0.2), ultimate tensile strength (R_m), uniform elongation (A_gt), and total elongation (A_t). The ultimate tensile strength R_m increased slightly with tempering at 100°C and then decreased with an increase in the tempering temperature at ≥200°C. The increase in R_m at 100°C was likely due to the growth of carbon clusters and transition carbides in the martensite matrix.²⁷⁾ The yield strength R_p0.2 increased slightly with tempering up to 200°C but decreased at temperatures above 200°C. As the 0.2% proof stress reflects the average slip resistance in the material, the decrease in the 0.2% proof stress at temperatures above 200°C suggests a reduction in the critical resolved shear stress (CRSS) due to carbide coarsening (Fig. 2) and matrix recovery (Fig. 3). The elastic limit of AsQ martensite was approximately 400 MPa and increased monotonically with the tempering temperature up to 400°C, which aligns with previous findings for 0.41%C martensite.²⁸⁾ As the elastic limit is related to the onset of micro-yielding, the increase in R_e.l indicates that softer, deformable regions in the microstructure of AsQ martensite are lost or hardened by tempering, as discussed in Section 4.1. With an increase in the tempering temperature, the uniform elongation A_gt decreased slightly, while the total elongation A_t remained largely unchanged. The CFS,^1,29) which corresponds to the estimated true thinning strain at fracture, was calculated using the tensile test results:

where R_f denotes the engineering fracture stress. The CFS increased with the tempering temperature.

Fig. 4. (a) Stress–strain curves for AsQ steel and steels quenched and tempered at 100°C (QT100), 200°C (QT200), 300°C (QT300), and 400°C (QT400); (b) enlarged view of the curves in (a) highlighting the micro-yielding behavior in the tensile test. (Online version in color.)

Figure 5 shows the changes in load and surface during the bending test for AsQ steel. The surface roughness became increasingly apparent from a bend angle (α) of approximately 20°, with small cracks appearing at the bend apex at α = 36° just before α F max (Fig. 5(b-i)). As bending continued, cracks formed within a range of approximately 1 mm at the bend apex, expanding along the bend axis and interconnecting, accompanied by a load reduction (Figs. 5(b-ii)–5(b-iv)). At 80% of the maximum load (F_max), the cracks occupied 80%–90% of the 5-mm specimen width (Fig. 5(b-iii)). Regarding the quenched and tempered (QT) steels, F_max increased slightly for QT100 but decreased with an increase in the tempering temperature above 100°C (Fig. 6). The α F max shifted slightly to a smaller bend angle with the increasing tempering temperature. This trend is contrary to the behavior observed for martensitic PHS evaluated according to the VDA238-100 standard,^2,3) possibly owing to differences in the bending-apparatus settings. The PUBS, which indicates the rate of load decrease after F_max, was largest for the AsQ and QT100 steels and decreased with the increasing tempering temperature. This trend is consistent with previous results for martensitic PHS.^2,3) The changes in F_max and α F max with tempering were similar to the R_m and A_gt variations observed in uniaxial tensile tests.

Fig. 5. (a) Bending load as a function of the bend angle for AsQ steel; (b) SE images at α values of (i) 36°, (ii) 47°, (iii) 63°, and (iv) 75°.

Fig. 6. Effect of tempering on bending curves for lath martensite. (Online version in color.)

Figure 7 shows outer-surface images at α = 41°, slightly above α F max , for the AsQ, QT200, and QT300 steels. The surface roughness is depicted with black and white contrast, revealing two distinct features: the first is a fine striated step with an interval of 5–10 μm, appearing regardless of the bend axis direction (arrow A in Fig. 7(b): type-A), and the second is an elongated notch nearly parallel to the bending axis (arrow B in Fig. 7(b): type-B). In AsQ martensite, surface deformation was primarily characterized by type-A roughness, while the fraction of type-B increased with the tempering temperature. Figure 8 illustrates the growth of type-B notches during bending in QT200 steel. Shallow notches appeared at approximately 20°, expanded in width and depth, and eventually evolved into cracks. These changes in surface morphology are consistent with previous observations in AHSS and other alloys.^{8,15,16,17,18,19)} As shown in Fig. 8, some cracks initiated at the bottom of type-B notches. However, in AsQ, QT100 and QT200 materials, small cracks often originated at the interfaces of less-deformed grains (arrow C in Figs. 7(a) and 7(b)).

Fig. 7. SE images of the bend surface at α = 41° in (a) AsQ, (b) QT200, and (c) QT300 steels. Arrows A, B, and C denote fine striated steps, elongated notches along the bend axis, and cracks appearing on the surface, respectively. (Online version in color.)

Fig. 8. Development of type-B notches into crack on the surface during bending of QT200 steel.

As shown in Fig. 7, crack formation on the bend surface is suppressed by tempering. To quantify this suppression, we evaluated the bend angle for crack formation (α_cr) through in situ SEM observation during the bending test, where crack initiation was defined as the appearance of two microcracks, each 200 μm in length, on the surface. The α_cr in AsQ martensite was approximately 36°, and it increased with the tempering temperature at ≥200°C. Figure 9 presents the effects of tempering on α_cr, α F max , and α 0.8 F max , where α 0.8 F max denotes the angle at 80% of F_max and serves as an indicator of crack-growth or crack-connection behavior accompanying a load reduction. Tempering at ≥200°C effectively suppresses both crack initiation and growth, with the suppression becoming more pronounced at higher tempering temperatures. Additionally, α_cr is not equivalent to α F max . In martensitic PHS, α F max is often used as an indicator of the onset of crack propagation during bending. The present results clearly demonstrate that the assumption of α F max = α cr is invalid, even for martensitic steels.

Fig. 9. Changes in the bend angle α at maximum load ( α F max ), crack initiation (α_cr), and 80% of maximum load ( α 0.8 F max ), with tempering.

To characterize the origin of the two types of surface roughness, a cross-section perpendicular to the bend axis was examined using SEM/EBSD for specimens interrupted at α = 41°. In all the steels, subsurface shear bands oriented approximately 45° to the steel surface were observed below surface notches. These shear bands appeared as dark contrasts in the IQ map and as areas of a large local orientation gradient in the kernel average misorientation (KAM) map (Fig. 10). As shown in the enlarged maps for QT200 steel (Fig. 11), the bands penetrated various boundaries in the martensite, including block boundaries, packet boundaries (blue dotted line), and prior austenite boundaries (black dashed line), demonstrating the non-crystallographic nature of shear-band formation.³⁰⁾ Inside the shear bands, severe plastic deformation and a fine-grained microstructure (with grain sizes of <100 nm) were observed in BSE images (Fig. 11(c)), likely because of the local temperature rise from adiabatic heating.³⁰⁾ As depicted in Fig. 10, the shear bands were more pronounced in specimens tempered at higher temperatures, correlating with a larger fraction of elongated type-B notches along the bend axis on the outer surface (Fig. 10(j)). In AsQ martensite, the shear bands were shorter and less developed.

Fig. 10. (a, d, g) IQ maps, (b, e, h) orientation maps, (c, f, i) KAM maps, and (j) SEM image of the cross-section perpendicular to the bend axis for (a–c) AsQ, (d–f) QT200, and (g–i) QT300 steels. (j) SEM image of the region presented in (g–i) showing that type-B notches accompany shear bands in the subsurface. The development of shear bands is more evident in the steels tempered at higher temperatures. (EBSD analysis step size: 0.3 μm.) (Online version in color.)

Fig. 11. (a) IQ map, (b) orientation map, and (c) enlarged BSE image of shear bands in the region shown in (a) for QT200 steel. The prior austenite grain boundary (PAGB) and packet boundary are indicated by dashed and dotted lines, respectively. Block boundaries are recognized as interfaces between elongated grains of different colors. (EBSD analysis step size: 0.15 μm.) (Online version in color.)

To analyze the fracture mechanism during bending, the fracture surfaces after the bending test were examined via SEM for the AsQ, QT200, and QT400 steels. The fractography revealed a ductile shear failure mode characterized by smooth ductile shear surfaces with terrace-like and shallow extended dimples (Fig. 12). In martensite tempered at higher temperatures, there was an increased fraction of shallow, ellipsoid-shaped dimples elongated in the shear direction. This morphology results from significant plastic deformation due to shear stress. Local shear bands form among void ligaments, propagating in the direction of maximum shear stress. This leads to parabolic void growth and shear linking,³¹⁾ which contributes to the observed fracture surface. The AsQ steel exhibited predominantly shear fracture, with a flat surface and terraces oriented nearly perpendicular to the shear direction and negligible brittle fractures such as cleavage and grain-boundary fractures. The origin of the terraced steps (Fig. 12(d)) is uncertain, but the delamination-like structure may indicate sliding along block or lath boundaries, as the activation of boundary sliding was observed in the subsurface, as discussed in Section 4.1.

Fig. 12. Fracture surfaces after the bending test for the (a) AsQ, (b) QT200, and (c) QT400 steels, along with enlarged images showing (d) the stepped terrace structure observed in AsQ steel and (e) the smooth sheared surface in QT400 steel.

To quantify the effect of tempering on the limiting surface strain for crack formation, the strain evolution at the bend apex was investigated using DIC analysis. As shown in Fig. 13(a), the average equivalent surface strain (ε_eq) in the center region of the bend apex (0.2 mm × 2.5 mm; see inset in Fig. 13(a)) increased during bending. The results revealed that the strain increase was more pronounced with higher tempering temperatures. The higher degree of strain concentration at elevated tempering temperatures is also evident from the line profile of ε_xx across the bend axis (Fig. 13(b)). The diffuse strain profile of the AsQ steel compared with the QT400 steel suggests that the plastic deformation at the bend apex was more restricted in the AsQ steel. The timing of crack initiation α_cr, as determined through in situ bending tests in SEM (Fig. 9), is indicated by stars in Fig. 13(a). The surface strain at crack formation (ε_cr) increased with the tempering temperature: it was 0.138, 0.196, 0.232, and 0.270 for the AsQ, QT200, QT300, and QT400 steels, respectively.

Fig. 13. (a) Evolution of equivalent strain (ε_eq) at the bend apex during bending for the AsQ, QT200, QT300, and QT400 steels. The timing of crack initiation (α_cr) determined via in situ observation of the outer bend surface is indicated by stars. (b) Difference in the strain distribution ε_xx across the bend axis at α = 36° between the AsQ and QT400 steels. The analyzed regions for (a) and (b) are shown in the inset of (a). The inset is the ε_xx map at α = 34° for QT200 steel. In (b), the strain profile is broader for the AsQ steel than for the tempered steels. (Online version in color.)

Through SEM–EBSD observations of both surface and cross-section, two types of deformation features were identified on the bending surfaces. In AsQ martensite, type-A deformation predominated over type-B deformation associated with the formation of shear bands. To clarify this, we characterize type-A deformation in AsQ steels in detail. Figure 14 shows SE images, surface roughness maps, and crystal orientation maps at α = 30°. Comparing the surface roughness map with the crystal orientation map reveals that the direction of striated steps on the surface varies with each martensite packet, and the spacing of these steps is slightly larger than the block spacing within the packets. Furthermore, the direction of the striated steps aligns with the trace lines of the {110}_α habit planes of martensite (black solid lines in Figs. 14(b) and 14(c)) for each packet, where the {110}_α habit plane of each block was determined by finding the corresponding {111} planes of parent austenite estimated using the austenite reconstruction method.³²⁾ This suggests that the striated steps on the surface are formed by block boundary sliding along the habit planes of martensite.

Fig. 14. (a) SE image, (b) surface topography map, and (c) orientation map at α = 30° for AsQ steel. The dotted lines indicate packet boundaries, and the black solid lines represent the trace lines of the {110}_α habit planes in each martensite packet. The {110}_α habit plane of each block was determined by finding the corresponding {111} planes of parent austenite estimated using the austenite reconstruction method.³²⁾ (Online version in color.)

To confirm the relationship between the direction of boundary sliding and the {110}_α habit planes of martensite, we examined the subsurface cross-section of AsQ steel. On the outer surface, several surface steps were visible (Fig. 15(a)). The direction of these steps, indicated by arrows in Fig. 15(a), aligns with the traces of {110}_α habit planes of martensite (white dotted line in Fig. 15(a)). Grain-boundary sliding along habit planes of martensite has been previously observed in tensile tests of low-to-medium-carbon lath martensitic steels^33,34,35,36) and in three-point bending tests.³⁵⁾ Experiments using nanoindentation³⁷⁾ and micromechanical testing³⁸⁾ have indicated that grain-boundary sliding occurs along the interfaces of elongated martensite blocks within packets, as they share the same {110}_α in-habit-plane slip system. Maresca et al.^39,40) proposed an interface sliding mechanism based on RA films present at the lath and block interfaces. However, our XRD analysis did not detect RA peaks in the AsQ steel, suggesting that the RA film mechanism is unlikely. Nonetheless, the possibility of interface sliding due to thin RA films cannot be completely eliminated, as TEM studies have confirmed the presence of such films at lath interfaces in 0.2%C lath martensite.²⁶⁾ The deformation of low-carbon lath martensite is often attributed to the preferential activation of in-lath-plane slip systems rather than the more constrained in-habit-plane slip systems.^33,34,41,42) A detailed analysis of the selection of the preferential slip system on the bend surface is left for future work. In conclusion, although the exact mechanism of interface plasticity remains unclear, the occurrence of type-A deformation is likely due to the preferential activation of the {110} ⟨ 1 ¯ 11⟩ α in-habit-plane slip system along block and lath boundaries, which has a lower CRSS than the out-of-habit-plane {110} ⟨ 1 ¯ 11⟩ α or {211} ⟨ 1 ¯ 11⟩ α slip systems.⁴³⁾

Fig. 15. Cross-section perpendicular to the bend axis showing fine striated steps (type-A deformation) at a bend angle of α = 41° in AsQ steel. (a) IQ map, (b) orientation map, and (c) KAM map. The direction of boundary sliding is indicated by arrows in (a) and (c). The white dotted line represents the plane trace of the {110}_α habit plane (hp). (EBSD analysis step size: 0.15 μm.) (Online version in color.)

The formation and development of shear bands, which are referred to as type-B deformation herein, have long been of interest owing to their role as precursors to material fracture.³⁰⁾ During bending under plane strain conditions, shear bands typically develop with a plate-like geometry influenced primarily by the macroscopic stress state. These bands are observed as notch lines parallel to the bending axis on the surface and as deformation zones inclined approximately 45° to the surface in cross-sectional observations (Fig. 10). As shown in Fig. 11(c), shear bands penetrate martensite blocks regardless of their crystal orientation. These bands consist of heavily deformed and partially recovered structures, with thicknesses ranging from 0.5 to 10 μm. This observation suggests that shear bands form owing to the activation of multiple slip systems,⁴⁴⁾ distinguishing them from microscopic localization phenomena such as slip lines and slip bands. Thus, simultaneous activation of multiple slip systems is essential for the development of shear bands that penetrate randomly oriented grains in martensite. In contrast, the type-A deformation observed in AsQ martensite is constrained to two {110}_α habit planes among the twelve possible {110}_α slip systems. Consequently, the preferential activation of in-habit-plane slip systems likely inhibits the formation of shear bands (type-B) that require the simultaneous activation of multiple slip systems.

The promotion of shear banding in tempered martensite is presumed to result from the suppression of boundary plasticity along the in-habit-plane slip systems with lower CRSS.⁴³⁾ To understand the effect of tempering on the suppression, we refer to changes in the elastic limit observed in tensile tests. As shown in Fig. 4(b), the elastic limit of AsQ martensite is 400 MPa and increases with the tempering temperature up to 400°C. The low elastic limit of AsQ martensite is attributed to early microscopic yielding in “soft” regions.⁴⁵⁾ Boundary sliding along blocks or laths is one of the mechanisms that is activated at low shear stress.⁴⁰⁾ In this case, the increase in the elastic limit due to tempering indicates the inhibition of boundary sliding, which agrees with the observed suppression of type-A deformation.

Another potential origin of the low elastic limit in AsQ martensite is the residual stress introduced during the quenching process.^28,46) Internal shear stress within the blocks constrains the free activity of each slip system, potentially hindering the simultaneous activation of multiple slip systems. Residual stress begins to be released at low tempering temperatures of approximately 200°C,⁴⁷⁾ which aligns with the observed increase in shear-band formation at 200°C in this study. However, because residual stresses initially present in the material are largely relaxed by the significant plastic deformation applied to the bend surface, reaching approximately ε_eq = 0.050 at a bend angle of α = 20° (Fig. 13(a)), it is uncertain whether the relaxation of residual stress is the primary cause of enhanced simultaneous multiple slip activity.

In summary, the promotion of shear banding by tempering in lath martensite is attributed to the suppression of grain-boundary plasticity that impedes the simultaneous activity of multiple slip systems. Additionally, as indicated by the changes in R_p0.2 and R_m, the coarsening of carbides (Fig. 2) and reduction in the dislocation density (Fig. 3) at temperatures above 200°C reduce the average CRSS for all slip systems, including out-of-lath slip systems. The resulting reduction in strength further promotes shear-band formation at temperatures above 200°C.

To understand the crack-initiation inhibition mechanisms of tempering, we begin by examining the cause of crack initiation in AsQ martensite. As mentioned in Section 4.1, the subsurface deformation in AsQ martensite was predominantly governed by the interface sliding mechanism based on the preferential activity of the {110} in-habit-plane slip systems. Morsdolf et al. noted that the degree of interfacial plasticity is influenced by the Schmid factor of the in-lath plane slip system relative to the tensile direction, leading to variability in deformability among martensite packets.³⁵⁾ Figure 16 shows the effect of slip-system constraint on the frequency distribution of the maximum Schmid factor (SF_max) for 106 randomly selected blocks in AsQ martensite. The cases of twelve {110} slip systems and two constrained {110} in-habit-plane slip systems are compared. The slip activation stress for in-habit-plane slip systems, which is estimated via the following equation, is shown in the upper part of the figure:

Here, CRSS^in-hp represents the CRSS of the {110} in-habit-plane slip systems, which is set as 335 MPa.⁴³⁾ Large variation in SF_max is evident under the constrained condition. The variation corresponds to an activation-stress range of approximately 700–10000 MPa. Because the martensite blocks in a packet share the same habit plane, the deformability of each packet varies significantly. The observed variation in the degree of type-A surface roughness among martensite packets (Fig. 7(a)) is attributed to the large variation in packet deformability due to the constrained slip activity in lath martensite.

Fig. 16. Variation in the frequency distribution of the maximum Schmid factor (SF_max) under tensile load or the calculated slip activation stress ( σ y in-hp ) for 106 randomly selected martensite blocks. The activation of twelve {110} slip systems is compared with that of two constrained {110} in-habit-plane slip systems.

During the deformation of polycrystalline metals, microscopic stress and strain partitioning occur within the materials. In general, non-deformable “hard” grains or phases sustain high stress, whereas deformable “soft” grains sustain plastic deformation.^48,49) It can be inferred that the local stress is higher in non-deformed packets compared with their surroundings. Surface SE images of AsQ martensite (Fig. 7(a)) indicate that cracks initiate at the prior γ grain boundaries adjacent to less-deformed packets without type-A roughness and at the shear bands within the less-deformed packets. This suggests that early crack initiation in AsQ martensite is due to local stress concentration in “hard” non-deformed packets.

At tempering temperatures of ≥200°C, the formation of type-B shear bands is promoted at the bend apex with increasing tempering temperature (Figs. 7(b) and 7(c)). We consider that the formation of shear bands is beneficial for the suppression of crack initiation for two reasons. First, the formation of shear bands reduces the number of large non-deformable hard packets enduring high stress. As shown in Fig. 7(c), the shear bands, which are observed as surface notch lines parallel to the bending axis, tend to form regardless of the orientation of packets, reducing the area of non-deformed regions. Second, the formation of shear bands reduces the degree of macroscopic stress concentration at the bend apex. As discussed in this section, the deformation of AsQ martensite relies on the activity of constrained in-habit-plane slip systems, implying that its plastic deformability is inferior to that of materials without such constraints. Consequently, the macroscopic elastic strain at the bend apex becomes large. As shown in Fig. 13(a), the average plastic strain at the bend apex in AsQ martensite was smaller than that in tempered martensite at the same nominal bend angle. This indicates that higher macroscopic elastic strain is applied at the apex region during bending in AsQ martensite, which may enhance the initiation and growth of cracks on the outer surface.

It is noted that shear banding may not be beneficial to surface cracking, as it accompanies surface notches or grooves that function as crack initiation and propagation sites,^8,19) as shown in Fig. 8. However, the positive effect of microscopic and macroscopic stress reduction at the bend apex surpasses the negative effect—particularly for lath martensite.

Finally, we examine the relationship between the bendability and the homogeneity of the microscopic mechanical properties of the materials. Yamazaki et al.⁹⁾ found a correlation between the minimum bending radius and the homogeneity index evaluated from hardness distribution in ultrahigh-strength steel sheets; better bendability was observed with a narrower hardness distribution. In the case of the present 0.24%C lath martensite, the bendability improves with a reduction in the degree of variation of deformability among packets induced by tempering. This result appears to demonstrate that the relationship between bendability and microscopic homogeneity holds true even in martensite.

LTT between 150 and 200°C has long been applied industrially in the manufacturing of low-to-medium carbon martensitic steels for structural and tool applications, as it enhances toughness while maintaining high hardness levels.¹⁴⁾ Kurz et al. demonstrated that paint-baking treatment at 170°C delays fracture initiation in the folding region during crash tests.³⁾ This aligns with our results, indicating that LTT at 200°C inhibits the initiation and growth of cracks at the bend surface (Figs. 9 and 13).

Through surface and cross-sectional observation (Figs. 7 and 10) and fractography of bend crack surfaces (Fig. 12), the main effect of LTT was identified as a slight change in the deformation mode from type-A deformation (interface plasticity along in-habit-plane slip systems) to type-B deformation (shear banding). Regarding type-A deformation, RA films are reported to play a crucial role in sliding at block and lath interfaces along the {110}_α in-habit plane.^39,40) RA typically decomposes into ferrite and iron carbides during tempering, usually within the range of 230–300°C.⁵⁰⁾ Hence, the inhibition of boundary sliding (type-A deformation) at higher tempering temperatures can be attributed to the reduction of RA films at boundaries. However, it is uncertain whether RA decomposition primarily drives the inhibition of grain-boundary sliding under LTT of 200°C in low carbon martensite, because (1) no obvious RA peaks were detected via XRD for our AsQ and QT steels; (2) Morito et al. confirmed via TEM that RA films remain even after tempering at 200°C for 10 min in 0.2%C martensite; and (3) Morsdorf et al.⁵¹⁾ showed via ECCI images that RA films persist in as-quenched 0.225%C martensite after tempering at 230°C for 2 h. An alternative mechanism for the preferential activation of the {110}⟨ 1 ¯ 11⟩ in-habit-plane slip system by LTT could involve the pinning of dislocation migration due to carbon precipitation and segregation along dislocations.⁵²⁾ As interface sliding involves dislocation glide at the interfaces,³⁷⁾ the inhibition of the in-habit-plane slip system by LTT may be explained by the pinning mechanisms. This interpretation is supported by carbide precipitation during tempering at 200°C in less-autotempered blocks of AsQ steels, as shown in the SEM images (Figs. 2(a) and 2(b)). The inhibition mechanism of interfacial plasticity and the effects of LTT remain topics for future research.

This section discusses the influence of iron carbides on bendability. Nagataki et al.¹²⁾ investigated the effect of tempering temperature on the critical bending radius of 0.15–0.4%C martensitic steels through a 180° bending test. They reported that needle-shaped cementite promotes void formation, resulting in degraded bendability at 300°C tempering. However, in the present study, which employed a three-point bending test, the limiting crack initiation strain increased with tempering temperature up to 400°C, and no degradation was observed at 300°C, despite the precipitation of coarse iron carbides. Furthermore, Nagataki et al.¹²⁾ observed a mixture of shear fracture and equiaxed dimple fracture in the fracture surfaces of steel tempered at 400°C. In contrast, the fracture surface of the steel tempered at 400°C in the present study predominantly exhibited a smooth shear fracture with shallow ellipsoid-shaped dimples elongated in the shear direction (Figs. 12(c) and 12(e)), indicating a significant difference in the degree of elongation of the dimples.

The ductile fracture limit of steels containing cementite is influenced by stress triaxiality, which leads to a reduction in the fracture limit as the deformation mode transitions from shear to shear-tensile.⁵³⁾ The deformation mode at the bend apex during bending tests is complex and depends on the type of bending test employed.⁵⁴⁾ This suggests that the sensitivity of carbides to bend cracking is contingent on the bending method and conditions. The smooth fracture surfaces observed in the three-point bending study indicate that the fracture mode had stronger shear-dominated behavior compared with the 180° bending test conducted by Nagataki et al.¹²⁾ Under shear-dominated deformation, the influence of iron carbides on crack formation is relatively small, explaining the minimal effect of carbides observed in the three-point bending test. These findings emphasize the importance of considering the deformation mode at the bend apex when evaluating the impact of iron carbides on bendability.

Fracture during bending of sheet steels is closely related to local formability, as only the outermost surface typically reaches failure criteria.¹⁾ Additionally, the global formability of steels, which influences the strain distribution around the bend apex, affects the bendability of steel sheets.^8,11) As intrinsic measures of local formability and global formability, the CFS (see Eq. (1)) and true uniform strain (ε_u) estimated from tensile tests are often used. Therefore, we investigated the correlation between these measures and the limiting crack initiation strain (ε_cr) evaluated in this study (Section 3.3.4) to better understand the factors controlling crack formation during bending in martensitic steel.

Figure 17 presents ε_u (≈A_gt) and CFS with respect to ε_cr. It is apparent that the inhibition of crack initiation by tempering is primarily due to CFS. While tempering slightly reduces ε_u and promotes strain concentration at the bend apex (Fig. 13), the inhibition of cracking cannot be explained by global formability in terms of tempering in martensite. Conversely, the CFS exhibits a distinct correlation with ε_cr, increasing monotonically with tempering above 200°C. Figure 18 illustrates the correlations between the CFS and α_cr and α 0.8 F max , which are indicators of crack initiation and growth, respectively. The strong correlations of both parameters with the CFS suggest that crack initiation and growth during three-point bending in martensitic steel is dominated by local formability.

Fig. 17. Relationships between the limiting crack initiation strain (ε_cr) evaluated via the bending test and the ε_u and CFS obtained from uniaxial tensile tests. The CFS, as a measure of local formability, exhibits a strong correlation with the crack initiation angle.

Fig. 18. Correlations between the CFS and the angle of crack initiation (α_cr) and crack connection ( α 0.8 F max ). Both crack initiation and crack growth are strongly correlated with the CFS.

In summary, Fig. 19 depicts the effects of tempering on the surface changes, strain distribution, and crack appearance in lath martensite. Shear banding is suppressed in AsQ martensite because of the preferential block boundary sliding along {110} ⟨ 1 ¯ 11⟩ α in-habit-plane slip systems. In AsQ martensite, deformability varies with the orientation of {110}_α in-habit-planes in each packet. Early cracking in AsQ martensite is likely due to the presence of martensite packets with very low deformability, where higher local stress is applied compared with the surrounding regions. Tempering promotes shear banding, probably due to the enhanced activation of multiple slip systems, including out-of-habit-plane slip systems. This promotion retards crack initiation by reducing the macroscopic stress concentration at the bend apex and microscopic stress concentration at less-deformed hard martensite packets. The retardation of crack initiation and growth by tempering is also attributed to increased local formability at shear bands and at crack tips, which is primarily due to the enhanced activation of multiple slip systems.

Fig. 19. Schematic of the effects of tempering on the surface changes, strain distribution, and crack appearance in lath martensite during bending. The color codes represent variations in deformation dominated by interface plasticity along the {110}_α in-habit plane in each martensite packet versus shear banding. Tempering promotes shear banding, likely owing to enhanced simultaneous multiple slips including out-of-habit-plane slip systems. The mechanism underlying the inhibition of crack initiation and growth is also depicted. (Online version in color.)

The effects of tempering up to 400°C on shear-band formation and crack development at the outer surface of Fe-0.24C-1.0Mn lath martensite during three-point bending tests were investigated via SEM/EBSD observations and macroscopic strain measurements based on DIC. The primary findings of this study are as follows:

(1) During bending, fine striated steps and elongated notches formed on the surface, which are attributed to block boundary sliding along the {110}_α in-habit-plane slip systems and the formation of shear bands, respectively. In as-quenched martensite, boundary sliding (boundary plasticity) predominantly governed subsurface deformation, whereas tempering at temperatures ≥200°C enhanced shear-band formation, with the effect becoming more pronounced at higher tempering temperatures. The activation of shear banding in tempered martensite is attributed to the suppression of grain-boundary plasticity, which inhibits the simultaneous activity of multiple slip systems. Additionally, the reduction in the average CRSS across all slip system, including the out-of-lath slip system, due to carbide coarsening and matrix recovery further contributes to the activation of shear banding by tempering.

(2) In AsQ martensite, where deformation is dominated by the {110}_α habit plane orientation, the deformability varied among martensite packets. Surface cracks often initiated near less-deformed hard martensite packets, which are assumed to endure higher stress during bending. Tempering at temperatures of ≥200°C retarded the initiation and growth of surface cracks. This is attributed to the improvement in local deformability within shear bands and at crack tips, which is primarily due to the enhanced activation of multiple slip systems. Additionally, the reduction in microscopic and macroscopic stress at the bend apex could be a factor induced by tempering.

(3) The limiting crack initiation strain, which was evaluated through DIC analysis and in situ SEM observation during the bending test, increased with an increase in the tempering temperature at ≥200°C. It was confirmed that in lath martensite, the limiting strain is correlated with the CFS, which is a measure of local formability.

The authors declare that they have no known competing financial interests or personal relationships that may have influenced the work reported in this paper.

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