Influence of Microstructure Constituents on Ductile to Brittle Transition Behavior in Multi-phase Steel Sheets

Abstract

The influence of martensite-austenite constituents on the two-step ductile to brittle transition (DBT) behavior of low carbon steel sheets was evaluated using Charpy impact tests with sub-size specimens. Four kinds of steel sheets containing 0–38% volume fraction of MA and polygonal ferrite in the matrix were chosen. Small volumes of MA (i.e., 2 and 14%) revealed a slightly higher transition temperature between the middle shelf (MS) and lower shelf, T_ML, compared to sheets with 0% MA. Furthermore, the transition temperature between the upper shelf and MS was not affected. The steel sheet containing 38% MA constituents exhibited a normal one-step DBT curve without MS, and a significantly higher transition temperature than the steel sheets containing 0, 2, and 14% MA. The increase in the austenite volume fraction in MA from 0.6 to 10.2% was not responsible for the DBT behavior, which may depend on the volume fraction of martensite in MA. A model of two-step DBT for multi-phase steel sheets, in which the small volume of MA lowered the fracture stress of the hard structure and elevated T_ML, was proposed. The T_ML depended on the intersection between the fracture stress of the hard structure and the yield stress of the soft structure. In the two-step DBT, the cleavage crack propagation was arrested at ferrite grain boundaries through the MS. A large volume of MA (e.g., all the ferrite grains fully covered) may promote one-step DBT in multi-phase steel sheets, owing to cleavage crack propagation.

1. Introduction

Various types of high strength steel containing multiple phases have been developed.¹⁾ For example, dual phase (DP) steel²⁾ consisting of soft ferrite and hard structures, such as martensite, bainite, and pearlite, combines good formability with high strength. Low alloy transformation induced plasticity (TRIP) steel³⁾ containing a small amount of retained austenite, which creates the TRIP effect, has remarkable balance between high elongation and high strength. Although these high strength steels are widely used especially for automobiles,⁴⁾ there is a limitation for their application due to their fracture properties, which depend on their microstructure.

Toughness is an important fracture property.⁵⁾ Several studies have been performed on the fracture behavior of multi-phase steels. In particular, the effect of martensite austenite constituents (MA)⁶⁾ has gathered attention. MA is hard island surrounded by a soft structure (e.g., ferrite), and consists of martensite and/or metastable austenite containing a large amount of solute carbon.⁷⁾ This hard structure is easy to fracture during impact; thus, the macroscopic brittle fracture often occurs from MA.^8,9,10,11) Moreover, it is easy for brittle clacks to propagate into and along MA.^8,11) Therefore, MA reduces the toughness of high strength steel.

In our previous studies,^12,13,14) we have investigated the ductile to brittle transition (DBT) with decreasing temperature in ferrite + pearlite steel sheets using a Charpy impact test with sub-size specimens. The absorbed energy transition with decreasing temperature showed a clear middle shelf (MS) between upper shelf (US) and lower shelf (LS). Sirithanakorn et al.¹⁵⁾ had called this transition behavior a two-step brittle to ductile transition. In the MS, the absorbed energy remained at the middle level, and the fracture surface was found to be a cleavage-like surface with a few dimples. The fracture mode at the MS was determined to be quasi-cleavage^16,17,18) because the crystallographic orientation on the electron backscatter diffraction (EBSD) patterns indicated that the microstructure absorbed the plastic strain before the fracture. We have already indicated that the volume fraction of hard structure is an important factor in two-step DBT; thus, the transition curve of absorbed energy changes from one- to two-step with the volume fraction of pearlite increasing.¹⁴⁾ Similarly, other microstructural factors seem to affect the DBT behavior of multi-phase steel sheet. This two-step DBT behavior was observed in multi-phase steel sheets containing MA as well as ferrite + pearlite steel sheets.¹⁹⁾ However, the effect of MA on the two-step DBT behavior has not been clear.

In this study, we focused on the effect of MA on the DBT behavior of high strength multi-phase steel sheets. Steel sheets containing ferrite (soft structure) and several hard structures were evaluated.

2. Experimental Procedure

2.1. Material

Four types of laboratory scale multi-phase steel sheets (A, B, C, and D) were prepared. Their chemical compositions were 0.15 C – 1.77 Si – 1.48 Mn – 0.005 P – 0.001 S – 0.001 N in mass%. The ingot melted in a vacuum induction furnace was hot-rolled over 1173 K to a thickness of 2.5 mm and air cooled to room temperature. To produce several types of hard structure with the same ferrite grain size, we reheated the hot-rolled sheets at same temperature, 1033 K, and treated them with several cooling patterns after reheating. Steel sheets A and B were held at 873 K, for 1 h and 10 min, respectively. The steel sheet C was held at 673 K for 5 min and the steel sheet D was water quenched from 1033 K to room temperature.

Figure 1 shows the secondary electron (SE) images of the multiphase steel sheets obtained by field-emission scanning electron microscopy (FE-SEM, JEOL–6500F) at half thickness. The volume fractions of the microstructure constituents in the steel sheets: polygonal ferrite (α), pearlite (P), bainite (B), and MA, are summarized in Table 1. The volume fractions were evaluated using a point counting method on the SE images. The average ferrite grain diameter (d_α) was determined using an intercept method on the SE images. Steel sheet A consists of ferrite and pearlite,^12,13) and steel sheet B consists of ferrite, pearlite, and 2% MA islands. Steel sheets C and D contain MA without pearlite; the total volume fraction of MA in sheet D is higher than in the others. The volume fraction (V_fcc) and the solute carbon content of austenite (C_fcc) shown in Table 1 were evaluated by X-ray diffraction (XRD).

Fig. 1.

Secondary electron images of multi-phase steel sheets, a) A, b) B, c) C, and d) D. α, P, B, and MA represent polygonal ferrite, pearlite, bainite, and martensite austenite constituent, respectively.

Table 1. Volume fractions of microstructure constituents, average ferrite grain diameter, d_α, and austenite detected by XRD. V_fcc and C_fcc indicate the volume fraction and the solute carbon content of austenite.

Steel	Components	Volume fractions (%)				Ferrite	Austenite (XRD)
		α	P	B	MA	dα (μm)	Vfcc (%)	Cfcc (mass%)
A	α +P	85	15	0	0	14	–	–
B	α + P +MA	81	17	0	2	13	0.6	1.31
C	α + B + MA	80	0	6	14	14	10.2	1.29
D	α + MA	62	0	0	38	12	2.5	0.86

2.2. Tensile Test and Charpy Impact Test

The geometry of the tensile test specimen was of type JIS No. 13B with 50 mm gage length, and its longitudinal direction was parallel to the transverse direction (TD) of the steel sheets. The initial strain rate was approximately 2.5 × 10⁻³ s⁻¹.

The DBT behaviors of the prepared sheets were evaluated by the Charpy impact test with sub-size specimens.¹²⁾ The sub-size specimens had a length of 55 mm parallel to TD, a width of 10 mm along the rolling direction (RD), and a thickness of 2.5 mm. A 2 mm V-notch was cut in the center of the specimens. The input energy of this test was 300 J. The specimens were immersed in denatured alcohol, hot water, or hot silicon oil, and maintained at temperatures between 173 and 433 K. For temperatures below 153 K, the specimens were first immersed in liquid nitrogen and removed when sufficiently cooled. The tests were performed when the specimens reached the target temperature.

After the impact tests, we characterized the fracture surfaces of some specimens using FE-SEM. From the SE images, we evaluated the area fraction of the low-energy fracture surface (LEFS)¹²⁾ with respect to the whole fracture surface. The LEFS was flat (macroscopic view), with very few dimples (microscopic view). The LEFS included the cleavage fracture surface and the quasi-cleavage fracture surface.

2.3. Electron Backscatter Diffraction Analysis

We observed the microstructure in the nominal direction (ND) immediately below the fracture surface at half thickness of the specimens via FE-SEM with an EBSD analysis system (OIM Data Collection ver. 7). An observation area in the range of 0.5–1.5 mm was selected far from the tip of the V-notch. In this study, we evaluated the crystallographic orientation of the secondary cracks^20,21) and its surroundings. We compared the crack traces with typical small index plane traces, namely {001}, {011}, and {112} bcc planes.¹³⁾

3. Results

3.1. Tensile Properties

Figure 2 shows stress-strain curves during tensile deformation, and Table 2 lists the tensile properties determined from these curves, namely, yield point, 0.2% proof stress (σ_0.2%), ultimate tensile strength (TS), and total elongation (EL). TS increased with the volume fraction of ferrite decreasing from Steel A to Steel D. EL of Steel C was superior to that of other sheets because it contains 10% austenite. Steel D containing 38% MA had high TS (1 GPa) and low EL (11%).

Fig. 2.

Engineering stress-strain curves (a) and a part of the curves in the initial strain (b) for the multi-phase steel sheets used.

Table 2. Tensile properties of steel sheets used. UYP, σ_0.2%, TS, and EL indicate upper yield point, 0.2% proof stress, ultimate tensile strength, and total elongation, respectively. The yield behavior in Steel D was the roundhouse type; thus, this table shows the elastic limit for UYP of Steel D.

Steel	UYP (MPa)	σ0.2% (MPa)	TS (MPa)	EL (%)
A	405	385	595	31
B	506	448	643	30
C	393	389	705	34
D	(220)	476	1014	11

Figure 2(b) shows the yield behavior in stress-strain curves. Steel A, B, and C had upper yield point (UYP) and yield point elongation. In these steel sheets, the occurrence of plastic deformation in ferrite had a constraint because the dislocations in ferrite were trapped by solute carbon atoms.²²⁾ The yield behavior in Steel D was of the roundhouse type; therefore, the plastic deformation in Steel D started at a smaller stress (220 MPa) than in the other sheets, despite its high TS. Steel D contained a higher amount of MA mainly consisting of martensite, which would introduce mobile dislocations in ferrite.²³⁾

The brittle fracture is depressed by plastic deformation, which renders the stress concentration at the crack tip moderate.²⁴⁾ Thompson reported that the decrease of σ_0.2% at room temperature decreased the DBT temperature in high strength steels.²⁵⁾ From this point of view, the DBT behavior in the steel sheets used in this study would be similar because their σ_0.2% was similar.

3.2. Ductile to Brittle Transition

Figure 3 represents the absorbed energy transition and fracture appearance transition (FAT) as a function of temperature using the Charpy impact test. The absorbed energy of Steel A makes three shelves with two transition temperatures at 297 and 193 K; thus, this curve clearly shows the two-step DBT. The fracture appearance in Steel A transited from a typical ductile fracture surface covered by microvoid coalescence fracture¹⁶⁾ surface consisting of dimples, to an LEFS with temperature decreasing around 297 K, and the fracture appearances between 253 and 197 K were almost covered by LEFS. Therefore, the absorbed energy transition from 193 to 173 K in Steel A did not accompanied with a clear FAT. Figure 4 shows the relationship between absorbed energy and FAT. The absorbed energy in Steel A described clear two steps. It decreased from US with LEFS fraction on fracture surface increasing, and, after the fracture surface was almost covered by LEFS, it decreased obviously with little change of fracture surface. This behavior is a feature of two-step DBT.¹⁴⁾

Fig. 3.

(a) Dependence of absorbed energy on temperature for the multi-phase steel sheets used. (b) Fracture appearance transition with temperature in multi-phase steel sheets used.

Fig. 4.

Relationship between absorbed energy and fracture appearance transitions in multi-phase steel sheets used.

In Fig. 3, the absorbed energy and the FAT curves of Steel B and C were similar to those of Steel A. Steel B and C specimens failed at 253 and 233 K absorbed middle level energy around 600 kJ/m², and showed fracture appearance almost covered by LEFS. Thus, the DBT behaviors of these steel sheets in Charpy impact tests corresponded to the two-step DBT in Fig. 4. In these absorbed energy curves, the US, MS, and LS were detected above 293 K, between 273 and 233 K, and below 213 K, respectively.

The DBT behavior of Steel D was different from the other steel sheets used. In Fig. 3, its absorbed energy at room temperature was significantly small, and its fracture appearance at room temperature was covered by LEFS. The absorbed energy of Steel D increased with LEFS fraction, decreasing from 353 to 433 K, and its transition curve in Figs. 3 and 4 was the usual one-step DBT curve, consisting of LS, US, and transition region without MS.

Figure 5 shows the effect of MA volume fraction on DBT temperatures. Steel A, B, and C show the two-step DBT, each having two transition temperatures, namely, T_UM for the transition from US to MS and T_ML for that from MS to LS. In contrast, Steel D had one transition in its DBT curve. We evaluated the DBT start temperature, T_S, and the finish temperature, T_F, for Steel D because the temperature range of its transition was wider than those in other steel sheets used.

Fig. 5.

Effect of MA volume fraction on DBT temperatures. T_UM: transition temperature from upper shelf to middle shelf. T_ML: transition temperature from middle shelf to upper shelf. T_S, T_F: transition start and finish temperatures during one-step DBT.

Akselsen et al.²⁶⁾ compared the influence of volume fractions of pearlite and MA constituents on the toughness of multiphase steels and reported that their effect was similar. In our previous study,¹⁴⁾ we evaluated the effect of volume fraction of pearlite on ferrite + pearlite microstructure. The increase in the pearlite volume fraction in the ferrite matrix altered the DBT behavior from one-step to two-step, and increased T_UM; however, T_ML remained unaffected.

The influence of MA on DBT behavior in multi-phase steel was clearly different from that of pearlite. In Steel A, B, and C, T_UM was consistent around 293 K, regardless to the volume fraction of MA. T_ML in Steel B and C containing a small amount of MA were higher than that in Steel A containing no MA. The DBT behavior in Steel D containing 38% MA was a one-step transition and brittle. Its T_F was higher than T_UM of other steel sheets, which corresponded to T_S in the one-step transition.

4. Discussion

4.1. Role of Martensite and Austenite in the MA on DBT Behavior

MA in the steel sheets used consisted of martensite and/or austenite. We tried to divide the effects on DBT behavior with the estimated volume fraction of martensite, V_M, which represented the difference between the volume fractions of MA evaluated by SEM and the volume fractions of austenite, V_fcc, evaluated by XRD. Figure 6 shows the variation in the transition temperature with V_M and V_fcc. In Fig. 6(a), the small amount of martensite (1%) made T_ML increase, and the higher amount of martensite (35%) changed the DBT behavior from two-step to one-step. In contrast, in Fig. 6(b), the increase of V_fcc from 0.6 to 10.2% did not increase T_UM or T_ML.

Fig. 6.

a) Effect of martensite volume fraction on DBT temperature. b) Effect of austenite volume fraction on DBT temperatures. T_UM: transition temperature from upper shelf to middle shelf. T_ML: transition temperature from middle shelf to upper shelf. T_S, T_F: transition start and finish temperatures during one-step DBT.

This result suggests that the brittleness caused by the MA depends on V_M. The martensite in high strength multi-phase steel sheets increased the DBT temperature and changed the DBT behavior from a two-step to one-step transition. In addition, the austenite containing a higher amount of carbon did not affect the DBT behavior in this study.

4.2. Influence of Hard Structure on Brittle Fracture

The simple model in Fig. 7(a) proposed by Orowan²⁷⁾ is generally used to understand the DBT behavior. In the previous study,¹²⁾ we proposed a simple model for the two-step DBT behavior in dual-structural steel as illustrated in Fig. 7(b), which was based on the Orowan model. The model suggests that the first transition occurs when the yield stress of the hard structure (σ_Y,B) becomes larger than the brittle fracture stress of the hard structure (σ_F,B) with decreasing temperature. In this case, brittle fracture occurs in the hard structure after plastic deformation in the soft structure. Similarly, the second transition occurs when the yield stress of the soft structure (σ_Y,A) becomes larger than σ_F,B. However, in this case, brittle fracture can occur in the hard structure without plastic deformation. Notably, the fracture mode shifts from microvoid coalescence fracture to quasi-cleavage fracture, and from quasi-cleavage fracture to cleavage fracture during these transitions.

Fig. 7.

Schematic relation among the yield stresses, fracture stress, and ductile to brittle transition temperatures. a) Usual one step DBT.²⁶⁾ b) Two-step DBT in dual-structural steel, containing soft structure (A) and hard structure (B).¹²⁾ σ_f: fracture stress, σ_y: yield stress, T_tr: transition temperature, σ_f,B: fracture stress in hard structure. σ_y,A, σ_y,B: yield stress in soft and hard structures, T_UM: transition temperature from upper shelf to middle shelf, T_ML: transition temperature from middle shelf to upper shelf.

The small amount of MA in the steel sheets used increased T_ML and did not affect T_UM as shown in Fig. 5. Figure 8 shows our understanding of this effect on the proposed model shown in Fig. 7(b). MA was harder than pearlite, and it was rather brittle.^28,29) Particularly, martensite in the MA was more brittle than austenite in the MA;^30,31) thus, σ_F,B in Fig. 8, which corresponds to the fracture stress of martensite, decreased from that of pearlite in Fig. 7 (b). Therefore, T_ML corresponding to the intersection between σ_F,B and σ_Y,A increased.

Fig. 8.

Schematic illustration for the shift of the two-step DBT behavior by MA.

Although martensite is a hard structure, its yield stress is small owing to many mobile dislocations³²⁾ and/or internal stress³³⁾ in its microstructure. In contrast, the yield stress of pearlite would be higher because of its fine lamellar structure.³⁴⁾ Thus, σ_Y,B in Fig. 8, which corresponds to the yield stress of martensite, decreased from that of pearlite in Fig. 7(b). T_UM corresponding to the intersection between σ_F,B and σ_Y,B would not shift, if σ_Y,B decreased as much as σ_F,B.

We could describe the effect of a small amount of MA in this study with the two-step DBT model in Fig. 7(b), as mentioned above. However, it is difficult to understand the effect of a large amount of MA with this model, which changed the DBT behavior of high strength steel sheets from two-step to one-step with high transition temperature. The increase of MA volume fraction decreased σ_Y,A which corresponded to the yield point of the steel sheets shown in Table 2; thus, it would decrease T_ML in our proposed model, if σ_F,B did not change.

4.3. Influence of Hard Structure on Crack Propagation

Figure 9 shows the secondary cracks in Steel C which failed at 193 K, just below T_ML. Figures 9(a) and 9(b) show the SEM images of the secondary cracks in Steel C. Thin lines drawn beside the secondary cracks in these images were {001}, {011}, and {112} plane traces of ferrite grains containing these secondary cracks. Secondary cracks shown in Figs. 9(a) and 9(b) in ferrite grains corresponded to cleavage plane {001} and slip plane {112}, respectively.

Fig. 9.

a), b) SEM images of secondary cracks in Steel C sample which failed at 193 K. White lines drown around secondary cracks (SCs) indicate traces of low index planes, {001}, {011}, and {112}. Numbers written around these traces show the minimum angles between SC trace and each equivalent low index plane. c) Crystallographic orientation misorientation from the standard point (●) in ferrite grain. White arrow corresponds to that in a). The {011} pole figure of 3 points, X, Y, and A were shown in d), and the (011) pole arrowed corresponds to the active slip plane in c). The misorientation chart along black lines, namely AB and XY in c), were shown in e). (Online version in color.)

Figure 9(c) is the magnified image at the secondary crack tip (indicated by arrow) shown in Fig. 9(a), where the crystallographic orientation distribution in the ferrite grain neighboring to secondary crack is demonstrated. Figure 10 shows the schematic for this ferrite grain. The secondary crack corresponding to cleavage plane would propagate from left to right as the fracture surface propagation. The secondary crack, which was arrested at the ferrite grain boundary (indicated by arrow in Fig. 9(a)), induced a certain slip on a slip plane, i.e., the boundary between red and blue layers, in the neighboring ferrite grain. Figure 9(d) shows the {011} pole figure of 3 points, X, Y, and A, picked up from above, below, and on the slip plane in Fig. 9(c), respectively. The slip plane trace corresponds to a (011) pole in Fig. 9(d), which is completely common to X, Y, and Z. Figure 9(e) shows point-to-origin misorientation charts on two lines in Fig. 9(c), namely AB and XY. Although the crystallographic orientation of ferrite did not change on AB along the active slip plane, it jumped around this slip plane on XY across the plane.

Fig. 10.

Schematic illustration for the ferrite (α) grain analyzed in Figs. 9(c), 9(d), and 9(e).

The minimum misorientation between (001) cleavage plane of secondary crack and {001} planes in ferrite grain analyzed in Fig. 9(c) was 13°; thus, it would be difficult for this cleavage clack to propagate over this ferrite grain boundary.²⁰⁾ Figure 11 shows the calculation results for the minimum angle between (001) cleavage plane and low index planes in next ferrite grain over the grain boundary on the grain boundary plane. The crystallographic relationship between two grains and the tilt of the grain boundary plane were random. The grain boundary, in which the angle between cleavage planes were small, was a rare case; i.e., only on 14% of the grain boundaries, the angle was less than or equal to 5°. Therefore, most of cleavage cracks would stop at ferrite grain boundaries, and would make active slip planes in next ferrite grain, as shown in Fig. 9(c).

Fig. 11.

The calculation result for the minimum angle between (001) cleavage plane and low index planes, {001}, {011}, and {112} in ferrite grain neighboring on their grain boundary plane. The crystallographic relationship between two grains and the tilt of grain boundary plane were random.

In the previous study,¹³⁾ we indicated that the fracture at MS propagated on grain boundaries, cleavage planes, and slip planes. The number of slip planes, {011} and {112} is more than that of cleavage planes; therefore, it would be easy for cleavage secondary cracks to find a convenient slip plane for their propagation over the grain boundary. Figure 12 shows the schematic of the fracture propagation model at MS which we propose. At first step shown in Fig. 12(a), a crack occurs with cleavage fracture in the hard structure as Fig. 7(b), and propagates to the neighboring ferrite grain whose crystallographic orientation is similar to that of the hard structure.^35,36,37) This crack stops at the ferrite grain boundary. In next step, Fig. 12(b), this crack activates a certain slip system in the neighboring ferrite grain and induces a slip band. After that, as shown in Fig. 12(c), the crack propagates along the slip band with a slipping-off mechanism,³⁸⁾ and the slip band distributes into the next neighboring ferrite grain. The crack propagates with this consecutive fracture, cleavage fracture, and grain boundary fracture.¹³⁾ The local propagation mode would be selected with various local conditions, e.g., crystallographic orientation, and relationship between ferrite and crack.

Fig. 12.

Schematic illustration for the crack propagation under the middle shelf model.

This fracture propagation model requires cleavage crack stopping at the ferrite grain boundary and slipping-off fracture occurring. When the temperature is low, the cleavage fracture would propagate over the ferrite grain boundary. When the temperature is high, void nucleation and growth would be induced in the next ferrite grain, and microvoid coalescence fracture would occur. In Steel D, there are few ferrite grain boundaries because ferrite grains are separated by MA as shown in Fig. 1(d). Therefore, a cleavage crack crosses the MA island rather than the ferrite grain boundary during its propagation. Figure 13 shows the schematic of the fracture propagation model in Steel D. A cleavage crack, which generates in MA, propagates into the ferrite grain as shown in Fig. 12(a), and reaches to ferrite/MA boundary. MA is a brittle microstructure, and its crystallographic orientation tends to be similar to the neighboring ferrite grains;^35,36,37) thus, it would be easier for a cleavage crack to propagate into the MA. Alternatively, a cleavage crack would propagate along with the MA network,³⁹⁾ not into the ferrite grain. Therefore, the crack propagation in Steel D does not require slipping-off fracture. In this case, the occurrence of cleavage fracture in MA is triggered of macroscopic brittle fracture. The DBT temperature in Steel B would correspond to T_UM in Fig. 7(b). This suggested that the effect of a higher amount of MA in the multi-phase steel sheet on its DBT behavior, namely one-step DBT with high transition temperature, depends on arrangement of MA and not only on its properties.

Fig. 13.

Schematic for the fracture propagation from left to right in multi-phase steel containing much amount of MA. Bold lines in this figure indicate the cleavage fracture cracks.

5. Conclusions

Influence of MA on the DBT behavior of a for multi-phase 0.15%C steel sheet was evaluated using Charpy impact tests with sub-size specimens. The steel sheets consisted of 0–38% MA in volume and a polygonal ferrite matrix. The main conclusions are as follows.

(1) In the steel sheets containing 2 and 14% MA, the transition of the absorbed energy with temperature described the two-step DBT curves, similarly to the ferrite + pearlite dual-phase steel sheet. The small amount of MA slightly increased the transition temperature from MS to LS, and did not affect the transition temperature from US to MS.

(2) In the steel sheet containing 38% MA, the transition of the absorbed energy with temperature described a simple one-step DBT curve without MS. Its transition temperature was much higher than that of other steel sheets containing 0–14% MA.

(3) The influences of martensite and austenite in MA vary. A small amount of martensite (1%) increased T_ML, and a large amount of martensite (35%) changed the DBT behavior from two-step to one-step DBT with high temperature. In contrast, the increase of V_fcc from 0.6 to 10.2% did not affect the DBT behavior.

(4) In the simple model which we proposed for two-step DBT in multi-phase steel sheet, the transition temperature from MS to LS corresponds to the intersection of the yield strength between the fracture stress of the hard structure and the yield stress of the soft structure. This suggested that the decrease in the fracture stress of the hard structure increased the transition temperature from MS to LS.

(5) The cleavage cracks in the multi-phase steel sheet containing 14% MA were constrained by high angle ferrite grain boundaries, and induced slip bands into neighboring ferrite grains, which would propagate the fracture with slipping-off at MS. This suggested that the fracture propagation on the slip plane was not required for macroscopic fracture propagation in multi-phase steel sheets containing a large amount of MA because whole ferrite grains were covered by MA, which propagated cleavage cracks; therefore, the DBT was a one-step without MS.

References

• 1)   N.  Fonstein: Advanced High Strength Sheet Steels, Springer International Publishing, Cham, (2015), 67.
• 2)   T.  Gréday,  H.  Mathy and  P.  Messien: Structure and Properties of Dual-Phase Steels, Proc. TMS-AIME Heat Treatment Committee at the Annual Meeting, (New Orleans, LA), Metallurgical Society of AIME, Warrendale, PA, (1979), 26.
• 3)   Y.  Sakuma,  O.  Matsumura and  H.  Takechi: Metall. Trans. A, 22 (1991), 489.
• 4)   J. N.  Hall and  J. R.  Fekete: Automotive Steels, eds. by R. Rana and S. B. Singh, Elsevier, Amsterdam, (2017), 19.
• 5)   A.  Pineau: Int. J. Fract., 150 (2008), 129.
• 6)   F.  Matsuda,  Y.  Fukada,  H.  Okada,  C.  Shiga,  K.  Ikeuchi,  Y.  Horii,  T.  Shiwaku and  S.  Suzuki: Weld. World, 37 (1996), 134.
• 7)   A.  Lambert,  J.  Drillet,  A. F.  Gourgues,  T.  Sturel and  A.  Pineau: Sci. Technol. Weld. Join., 5 (2000), 168.
• 8)   J. H.  Chen,  Y.  Kikuta,  T.  Araki,  M.  Yoneda and  Y.  Matsuda: Acta Metall., 32 (1984), 1779.
• 9)   C. L.  Davis and  J. E.  King: Metall. Mater. Trans. A, 25 (1994), 563.
• 10)   A.  Lambert-Perlade,  A. F.  Gourgues,  J.  Besson,  T.  Sturel and  A.  Pineau: Metall. Mater. Trans. A, 35 (2004), 1039.
• 11)   L.  Lan,  C.  Qiu,  D.  Zhao,  X.  Gao and  L.  Du: Mater. Sci. Eng. A, 529 (2011), 192.
• 12)   H.  Kawata and  O.  Umezawa: ISIJ Int., 57 (2017), 1282.
• 13)   H.  Kawata and  O.  Umezawa: Mater. Sci. Eng. A, 716 (2018), 252.
• 14)   H.  Kawata and  O.  Umezawa: ISIJ Int., 59 (2019), 1344.
• 15)   T.  Sirithanakorn,  M.  Tanaka and  K.  Higashida: Mater. Sci. Eng. A, 611 (2014), 383.
• 16)   G. R.  Odette: J. Nucl. Mater., 212–215 (1994), 45.
• 17)   K.  Edsinger,  G. R.  Odette,  G. E.  Lucas and  J. W.  Sheckherd: J. Nucl. Mater., 233–237 (1996), 342.
• 18)   J. P.  Naylor and  P. R.  Krahe: Metall. Trans. A, 6 (1975), 594.
• 19)   H.  Kawata and  O.  Umezawa: Mater. Sci. Forum, 941 (2018), 453.
• 20)   J.  Nohava,  P.  Haušild,  M.  Karlík and  P.  Bompard: Mater. Charact., 49 (2002), 211.
• 21)   X.  Li,  X.  Ma,  S. V.  Subramanian and  C.  Shang: Int. J. Fract., 193 (2015), 131.
• 22)   D. V.  Wilson and  B.  Russell: Acta Metall., 8 (1960), 36.
• 23)   T.  Waterschoot,  A. K.  De,  S.  Vandeputte and  B. C.  De Cooman: Metall. Mater. Trans. A, 34 (2003), 781.
• 24)   P. B.  Hirsch and  S. G.  Roberts: Philos. Trans. R. Soc., A, 355 (1997), 1991.
• 25)   S. W.  Thompson: Mater. Sci. Eng. A, 711 (2018), 424.
• 26)   O. M.  Akselsen,  J. K.  Solberg and  Ø.  Grong: Scand. J. Metall., 17 (1988), 194.
• 27)   E.  Orowan: Rep. Prog. Phys., 12 (1949), 185.
• 28)   G.  Lacroix,  T.  Pardoen and  P. J.  Jacques: Acta Mater., 56 (2008), 3900.
• 29)   P.  Mohseni,  J. K.  Solberg,  M.  Karlsen,  O. M.  Akselsen and  E.  Østby: Mater. Sci. Technol., 28 (2012), 1261.
• 30)   P.  Mohseni,  J. K.  Solberg,  M.  Karlsen,  O. M.  Akselsen and  E.  Østby: Metall. Mater. Trans. A, 45 (2014), 384.
• 31)   T.  Tagawa,  N.  Takayama,  S.  Imamura and  S.  Igi: Tetsu-to-Hagané, 102 (2016), 295 (in Japanese).
• 32)   S.  Takaki,  K.-L.  Ngo-Huynh,  N.  Nakada and  T.  Tsuchiyama: ISIJ Int., 52 (2012), 710.
• 33)   S.  Allain,  O.  Bouaziz and  M.  Takahashi: ISIJ Int., 52 (2012), 717.
• 34)   B. M.  Gonzalez,  L. A.  Marchi,  E. J.  da Fonseca,  P. J.  Modenesi and  V. T. L.  Buono: ISIJ Int., 43 (2003), 428.
• 35)   G.  Miyamoto,  Y.  Karube and  T.  Furuhara: Acta Mater., 103 (2016), 370.
• 36)   S.  Zaefferer,  J.  Ohlert and  W.  Bleck: Acta Mater., 52 (2004), 2765.
• 37)   T.  Yamashita,  N.  Koga and  O.  Umezawa: Mater. Trans., 59 (2018), 712.
• 38)   Y.  Tomota,  Y.  Xia and  K.  Inoue: Acta Mater., 46 (1998), 1577.
• 39)   H.  Ikawa,  H.  Oshige and  T.  Tanoue: J. Jpn. Weld. Soc., 49 (1980), 532 (in Japanese).