Effects of Mean Normal Stress on Strain-Hardening, Strain-Induced Martensite Transformation, and Void-Formation Behaviors in High-Strength TRIP-Aided Steels

: To analyze various types of cold formability in TRIP-aided polygonal ferrite (TPF), annealed martensite (TAM), and bainitic ferrite (TBF) steels, the effects of the mean normal stress on the strain-hardening, strain-induced martensite transformation, and void-formation behaviors were investigated. The strain-hardening behavior was influenced by positive mean normal stress and was hardly influenced by zero and negative mean normal stresses in all steels. Positive mean normal stress promoted the strain-induced martensitic transformation behavior, especially in TBF steel due to the high mechanical stability of the retained austenite. The void-formation behavior was also promoted by positive mean normal stress, especially in TPF steel. These behaviors were also related to the microstructural properties, such as the matrix structure, retained austenite characteristics, and second phase.


Introduction
First-, second-, and third-generational advanced high-strength steels (AHSSs) have been applied to automobiles to reduce their weight and improve their crush safety performance [1][2][3][4] because of the various excellent types of cold formability [1][2][3].As these types of formability are evaluated in different stress states or mean normal stress conditions, it is very important to quantify the effects of the mean normal stress on the strain-hardening, strain-induced martensitic transformation, and void-formation behaviors.These three kinds of behavior are also mainly influenced by (1) the microstructural properties, such as the type of matrix structure, grain size, and retained austenite characteristics, (2) microalloying elements, and (3) the deformation temperature and rate [5].Regarding the effect of the microstructure, annealed martensite and bainitic ferrite matrix structures considerably improve the cold formability compared to a polygonal ferrite matrix structure, as shown in Figure 1 [6].Also, a large amount of metastable retained austenite increases the formability by enhancing the strain-hardening rate and suppressing void/crack formation by relaxing the localized stress concentration [5,7].

Materials and Methods
Low-carbon steel with the chemical composition shown in Table 1 was prepared as a 100 kg slab through vacuum melting.The slab was hot-rolled to a 13 mm diameter at a finishing temperature of 850 °C, followed by air cooling.Three kinds of heat treatment (shown in Figure 2) were carried out to produce TPF, TAM, and TBF steels.In this case, an austenitizing temperature of 910 °C, inter-critical annealing temperature of 780 °C (TPF and TAM steels), and isothermal transformation temperature of 375 °C (TPF and TAM steels) or 410 °C (>Ms, TBF steel) were adopted to obtain the maximum retained austenite fraction.This research investigates the effects of the mean normal stress on the strain-hardening, strain-induced martensite transformation, and void-formation behaviors in low-carbon TPF, TAM, and TBF steels.In addition, these behaviors are related to microstructural properties, such as the matrix structure, retained austenite characteristics, and second phase.

Materials and Methods
Low-carbon steel with the chemical composition shown in Table 1 was prepared as a 100 kg slab through vacuum melting.The slab was hot-rolled to a 13 mm diameter at a finishing temperature of 850 • C, followed by air cooling.Three kinds of heat treatment (shown in Figure 2) were carried out to produce TPF, TAM, and TBF steels.In this case, an austenitizing temperature of 910 • C, inter-critical annealing temperature of 780 • C (TPF and TAM steels), and isothermal transformation temperature of 375 • C (TPF and TAM steels) or 410 • C (>M s , TBF steel) were adopted to obtain the maximum retained austenite fraction.hardening, strain-induced martensite transformation, and void-formation behaviors in first-generation AHSSs, such as TPF and TAM steels [5,8], or in third-generation AHSSs, such as TRIP-aided bainitic ferrite (TBF) [6,7,10], carbide-free bainitic (CFB) [15][16][17], quenching and partitioning (Q&P) [10,12,[18][19][20], and medium Mn steels [21][22][23].The research is beneficial in analyzing the various types of cold formability.This research investigates the effects of the mean normal stress on the strainhardening, strain-induced martensite transformation, and void-formation behaviors in low-carbon TPF, TAM, and TBF steels.In addition, these behaviors are related to microstructural properties, such as the matrix structure, retained austenite characteristics, and second phase.

Materials and Methods
Low-carbon steel with the chemical composition shown in Table 1 was prepared as a 100 kg slab through vacuum melting.The slab was hot-rolled to a 13 mm diameter at a finishing temperature of 850 °C, followed by air cooling.Three kinds of heat treatment (shown in Figure 2) were carried out to produce TPF, TAM, and TBF steels.In this case, an austenitizing temperature of 910 °C, inter-critical annealing temperature of 780 °C (TPF and TAM steels), and isothermal transformation temperature of 375 °C (TPF and TAM steels) or 410 °C (>Ms, TBF steel) were adopted to obtain the maximum retained austenite fraction.The microstructure of the steels was observed at a 3/4 radius through field-emission scanning electron microscopy (FE-SEM; JSM-6500F, JEOL Ltd., Akishima, Tokyo, Japan), which was performed using an instrument equipped with an electron backscatter diffraction Metals 2024, 14, 61 3 of 14 system (EBSD; OIM system, TexSEM Laboratories, Inc., Prova, UT, USA).The FE-SEM-EBSD analysis was operated at an acceleration voltage of 25 kV and conducted in an area of 40 × 40 µm 2 with a beam diameter of 1.0 µm and a beam step size of 0.15 µm.The specimens for FE-SEM-EBSD analysis were first ground with alumina powder and colloidal silica, and then ion-thinning was carried out.
The retained austenite characteristics of the steels were evaluated using an X-ray diffractometer (RINT2000, Rigaku Co., Akishima, Tokyo, Japan).The surfaces of the specimens were electropolished after being ground with emery paper (#1200).The volume fraction of the retained austenite phase (f γ, vol.%) was quantified from the integrated intensity of the (200)α, (211)α, (200)γ, (220)γ, and (311)γ peaks obtained through X-ray diffractometry using Mo-Kα radiation [24].The carbon concentration in the retained austenite (Cγ, mass%) was estimated from the empirical equation proposed by Dyson and Holmes [25].To accomplish this, the lattice constant of retained austenite was determined from the (200)γ, (220)γ, and (311)γ peaks of Cu-Kα radiation.The X-ray half-width (HW) of the (211)α peak of Cu-Kα radiation was measured to relate to the equilibrium plastic strain (ε p ) that developed upon press-forming [26].Takebayashi et al. [27] reported that the HW is also able to estimate the dislocation density.
To obtain various mean normal stress states, uniaxial tensile and compressive tests were conducted on a tensile testing machine (AD-10TD, Shimadzu Co., Kyoto, Japan) at 25 • C and a mean strain rate of 2.8 × 10 −3 s −1 (crosshead speed: 10 mm/min).Torsional tests were conducted on a torsional testing machine (AG-300kNXplus, Shimadzu Co., Kyoto, Japan) at 25 • C and a torsional rate of 10 deg./min.Tensile specimens (JIS-14A, 26 mm gauge length, 5 mm diameter), torsional specimens (10 mm gauge length and 5 mm diameter), and compressive specimens (10 mm length and 5 mm diameter) were machined from the hot-rolled bars parallel to the rolling direction (Figure 3), followed by a heat treatment.
conducted in an area of 40 × 40 µm 2 with a beam diameter of 1.0 µm and size of 0.15 µm.The specimens for FE-SEM-EBSD analysis were first alumina powder and colloidal silica, and then ion-thinning was carried out.
To obtain various mean normal stress states, uniaxial tensile and com were conducted on a tensile testing machine (AD-10TD, Shimadzu Co., Ky 25 °C and a mean strain rate of 2.8 × 10 −3 s −1 (crosshead speed: 10 mm/mi tests were conducted on a torsional testing machine (AG-300kNXplus, Sh Kyoto, Japan) at 25 °C and a torsional rate of 10 deg./min.Tensile specimen mm gauge length, 5 mm diameter), torsional specimens (10 mm gauge leng diameter), and compressive specimens (10 mm length and 5 mm dia machined from the hot-rolled bars parallel to the rolling direction (Figure 3) a heat treatment.where σ1, σ2, and σ3 are the principal stresses in directions 1, 2, and 3, resp equivalent stress σ and equivalent strain ε were calculated using th criterion [28] as follows: The mean normal stress was defined by where σ 1 , σ 2 , and σ 3 are the principal stresses in directions 1, 2, and 3, respectively.The equivalent stress σ and equivalent strain ε were calculated using the von Mises criterion [28] as follows: Metals 2024, 14, 61 4 of 14 where σ i , ε i (i = x, y, z), τ ij , and γ ij (i, j = x, y, z) represent the normal stress, normal strain, shear stress, and shear strain in the X-Y-Z coordinate system, respectively.For the tensile tests, σ and ε of the necking region are calculated by where P, d, d 0 , and R are the applied load, the diameter of the neck cross-section, the initial diameter of the specimen, and the radius of the curvature of the neck profile, respectively [29].

Microstructure and Retained Austenite Characteristics
Figure 4 shows the microstructures of the TPF, TAM, and TBF steels analyzed in terms of FE-SEM-EBSD.The microstructure of TPF steel consisted of polygonal ferrite, bainitic ferrite, and retained austenite (γ R ).The volume fraction and carbon concentration of the retained austenite were f γ 0 = 8.0 vol.% and Cγ 0 = 0.51 mass%, respectively (Table 2).Most of the retained austenite existed along the polygonal ferrite (α pf ) grain boundary and in the bainitic ferrite (α bf ) phase (Figure 4g).The carbon concentration of retained austenite in the present TPF steel was very low compared to that in TPF steels reported by other researchers [5][6][7].The reason for this is under consideration.The microstructure of the TAM steel was composed of annealed martensite (α am ) (or tempered martensite) and retained austenite.Many retained austenite phases existed on the annealed martensite lath boundary (Figure 4h).The retained austenite seemed to be in a granular-like phase, differing from that in Ref. [7].The volume fraction and carbon concentration were 12.4 vol.% and 0.84 mass%, respectively.
The microstructure of the TBF steel consisted of bainitic ferrite and retained austenite.Many retained austenite phases existed on the bainitic ferrite lath boundary (Figure 4i).Notably, the retained austenite was finer than that in the TPF and TAM steels (Figure 4g-i).The volume fraction and carbon concentration were 11.4 vol.% and 0.65 mass%, respectively.The volume fraction and carbon concentration were between those of the TPF and TAM steels.The TBF steel also contained a small amount of martensite-austenite (MA) phase (f MA = 2.0 vol.%).
Sugimoto et al. [7,30] reported that the dislocation density of the bainitic ferrite matrix structure was the highest in TBF steel, and the dislocation density of the annealed martensite matrix structure of TAM steel followed it.The dislocation density of the polygonal ferrite matrix structure was the lowest.It was necessary to be careful that the microstructure of the present bars after the heat treatment had a final coarse grain size and strong microstructure gradients compared to the microstructure of industrial cold-rolled sheets.Figure 5 shows the tensile, torsional, and compressive flow curves of TPF, TAM, and TBF steels.The flow stresses in the tension of the TBF steel were higher than those of the TPF and TAM steels.The TAM steel possessed the lowest flow stresses.
Table 3 shows the mechanical properties of the TPF, TAM, and TBF steels.The TAM steel exhibited the lowest yield stress (YS) and tensile strength (TS) in the tension test, as well as the lowest shear yield stress (τ0), maximum shear stress (τmax), and compressive yield stress (σ0).The tensile strength of the TBF steel was the highest, although the yield stress was between those of the TPF and TAM steels.It is noteworthy that the TAM steel had the largest uniform and total elongations (UEl and TEl) and reduction in area (RA).Also, the TBF steel had the second largest UEl, TEl, and RA after the TAM steel.
As shown in Figure 5a, the TAM steel exhibited a high strain-hardening rate in a large strain range.On the other hand, the TBF steel showed a high strain-hardening rate in an early strain range.In torsion and compression, the differences in the strain-hardening rate between the TPF, TAM, and TBF steeled tended to be relatively small compared to those in tension.Table 3 shows the mechanical properties of the TPF, TAM, and TBF steels.The TAM steel exhibited the lowest yield stress (YS) and tensile strength (TS) in the tension test, as well as the lowest shear yield stress (τ 0 ), maximum shear stress (τ max ), and compressive yield stress (σ 0 ).The tensile strength of the TBF steel was the highest, although the yield stress was between those of the TPF and TAM steels.It is noteworthy that the TAM steel had the largest uniform and total elongations (UEl and TEl) and reduction in area (RA).Also, the TBF steel had the second largest UEl, TEl, and RA after the TAM steel.As shown in Figure 5a, the TAM steel exhibited a high strain-hardening rate in a large strain range.On the other hand, the TBF steel showed a high strain-hardening rate in an early strain range.In torsion and compression, the differences in the strain-hardening rate between the TPF, TAM, and TBF steeled tended to be relatively small compared to those in tension.
Figure 6 shows the equivalent stress-plastic strain (σ − ε p ) curves calculated from the flow curves in the tension, torsion, and compression from Figure 5.The equivalent stresses in torsion tended to be higher than those in tension and compression in all steels.The difference in the σ − ε p curves for tension, torsion, and compression was smaller in the TPF steel.On the other hand, a large difference in the curves was shown in the TBF steel, with a large difference in the strain-hardening rate (Figure 6c).
Figure 6 shows the equivalent stress-plastic strain (σ − p ε ) curves calculated from the flow curves in the tension, torsion, and compression from Figure 5.The equivalent stresses in torsion tended to be higher than those in tension and compression in all steels.
The difference in the σ − p ε curves for tension, torsion, and compression was smaller in the TPF steel.On the other hand, a large difference in the curves was shown in the TBF steel, with a large difference in the strain-hardening rate (Figure 6c).

X-Ray Half-Width and Equivalent Plastic Strain Relation
Figure 7 shows the X-ray half-width and equivalent plastic strain (HW − p ε ) relations in the TPF, TAM, and TBF steels plastically deformed in tension, torsion, and compression.The HW linearly increased with increasing equivalent strain in all steels, regardless of the stress state or mean normal stress.When the HW characteristics were quantified with the HW at p ε = 0 (HW0) and the slope of the straight line (n-value), the TBF steel had a high HW0 (0.58 deg.) and a small n-value (0.133, Figure 8).In this case, the n-value of the TBF steel was measured in an equivalent strain range below p ε = 0.7.On the other hand, the TAM steel exhibited the lowest HW0 (0.44 deg.) and the largest n-value (0.187).The HW properties of the TPF steel were between those of the TBF and TAM steels.
The linear relationships shown in Figure 7 were also reported by Polatidis et al. [10].In addition, they agreed with a modified Williamson-Hall equation [27,31].The relationships between the HW0 and n-value and the valuables in the modified Williamson-Hall equation will be investigated in the future.

X-ray Half-Width and Equivalent Plastic Strain Relation
Figure 7 shows the X-ray half-width and equivalent plastic strain (HW − ε p ) relations in the TPF, TAM, and TBF steels plastically deformed in tension, torsion, and compression.The HW linearly increased with increasing equivalent strain in all steels, regardless of the stress state or mean normal stress.When the HW characteristics were quantified with the HW at ε p = 0 (HW0) and the slope of the straight line (n-value), the TBF steel had a high HW0 (0.58 deg.) and a small n-value (0.133, Figure 8).In this case, the n-value of the TBF steel was measured in an equivalent strain range below ε p = 0.7.On the other hand, the TAM steel exhibited the lowest HW0 (0.44 deg.) and the largest n-value (0.187).The HW properties of the TPF steel were between those of the TBF and TAM steels.The linear relationships shown in Figure 7 were also reported by Polatidis et al. [10].In addition, they agreed with a modified Williamson-Hall equation [27,31].The relationships between the HW0 and n-value and the valuables in the modified Williamson-Hall equation will be investigated in the future.
Figure 6 shows the equivalent stress-plastic strain (σ − p ε ) curves calculated from the flow curves in the tension, torsion, and compression from Figure 5.The equivalent stresses in torsion tended to be higher than those in tension and compression in all steels.
The difference in the σ − p ε curves for tension, torsion, and compression was smaller in the TPF steel.On the other hand, a large difference in the curves was shown in the TBF steel, with a large difference in the strain-hardening rate (Figure 6c).

X-Ray Half-Width and Equivalent Plastic Strain Relation
Figure 7 shows the X-ray half-width and equivalent plastic strain (HW − p ε ) relations in the TPF, TAM, and TBF steels plastically deformed in tension, torsion, and compression.The HW linearly increased with increasing equivalent strain in all steels, regardless of the stress state or mean normal stress.When the HW characteristics were quantified with the HW at p ε = 0 (HW0) and the slope of the straight line (n-value), the TBF steel had a high HW0 (0.58 deg.) and a small n-value (0.133, Figure 8).In this case, the n-value of the TBF steel was measured in an equivalent strain range below p ε = 0.7.On the other hand, the TAM steel exhibited the lowest HW0 (0.44 deg.) and the largest n-value (0.187).The HW properties of the TPF steel were between those of the TBF and TAM steels.
The linear relationships shown in Figure 7 were also reported by Polatidis et al. [10].In addition, they agreed with a modified Williamson-Hall equation [27,31].The relationships between the HW0 and n-value and the valuables in the modified Williamson-Hall equation will be investigated in the future.

Strain-Induced Martensite Transformation Behavior
Figure 9 shows the variations in the untransformed retained austenite fraction (fγ) as a function of the equivalent strain in the TPF, TAM, and TBF steels when plastically deformed through tension, torsion, and compression.If the mechanical stability of the retained austenite was defined by the following strain-induced transformation factor (k)

Strain-Induced Martensite Transformation Behavior
Figure 9 shows the variations in the untransformed retained austenite fraction (f γ) as a function of the equivalent strain in the TPF, TAM, and TBF steels when plastically deformed through tension, torsion, and compression.If the mechanical stability of the retained austenite was defined by the following strain-induced transformation factor (k) [5,7], the k-values in compression (a negative mean normal stress state) were the lowest in all steels (Table 2).
(fγ) as a function of the equivalent strain in the TPF, TAM, and TBF steels when plastically deformed through tension, torsion, and compression.If the mechanical stability of the retained austenite was defined by the following strain-induced transformation factor (k) [5,7], the k-values in compression (a negative mean normal stress state) were the lowest in all steels (Table 2). = (ln fγ0 − ln fγ)/ p ε (5) In this case, the k-values were calculated in an equivalent plastic strain range of p ε = 0 and 0.3.A similar result was also reported by Kawata et al. [32].
The lowest k-value (the highest mechanical stability of retained austenite) was obtained in the TBF steel (Table 2).As shown in Figure 10, positive mean normal stress increased the k-value, especially in the TBF steel.The k-values of the TAM steel were slightly higher than those of the TPF steel.
In this case, the k-values were calculated in an equivalent plastic strain range of ε p = 0 and 0.3.A similar result was also reported by Kawata et al. [32].
The lowest k-value (the highest mechanical stability of retained austenite) was obtained in the TBF steel (Table 2).As shown in Figure 10, positive mean normal stress increased the k-value, especially in the TBF steel.The k-values of the TAM steel were slightly higher than those of the TPF steel.

Void-Formation Behavior
Figure 11 shows FE-SEM images of voids initiated on the specimen surface in the TPF, TAM, and TBF steels when plastically deformed to p ε = 0.3 through tension, torsion, and compression.In the TPF steel, most of the voids were initiated at the interface of polygonal ferrite/bainite and polygonal ferrite/retained austenite (or strain-induced martensite).In the TAM steel, many voids seemed to be initiated at the interface of annealed martensite and retained austenite (or strain-induced martensite).Similarly, most of the voids seemed to form at the interface of bainitic ferrite and retained austenite (or strain-induced martensite) in the TBF steel.No voids were observed in any of the steels

Void-Formation Behavior
Figure 11 shows FE-SEM images of voids initiated on the specimen surface in the TPF, TAM, and TBF steels when plastically deformed to ε p = 0.3 through tension, torsion, and compression.In the TPF steel, most of the voids were initiated at the interface of polygonal ferrite/bainite and polygonal ferrite/retained austenite (or strain-induced martensite).In the TAM steel, many voids seemed to be initiated at the interface of annealed martensite and retained austenite (or strain-induced martensite).Similarly, most of the voids seemed to form at the interface of bainitic ferrite and retained austenite (or strain-induced martensite) in the TBF steel.No voids were observed in any of the steels deformed through compression, except for the TAM steel (Figure 11f).These void initiation sites generally agreed with the results reported in Refs.[5,7,30,33].Figure 12 shows the relations of the number of voids with the mean normal stress (N v − σ m ) and of the void size with the mean normal stress (D v − σ m ) in the TPF, TAM, and TBF steels when plastically deformed to ε p = 0.3.Figure 13 shows the relation between the mean number of voids and the mean size of voids in the TPF, TAM, and TBF steels subjected to different equivalent plastic strains.In all steels, positive mean normal stress considerably promoted void formation.A large number and a large size of voids were formed in the TPF steel.On the other hand, the void formation was considerably suppressed in the TBF steel.In the TAM steel, an intermediate void size was observed, although the number of voids was as high as that in the TPF steel.

Effect of Mean Normal Stress on Strain-Hardening Behavior
As shown in Figure 5, the differences in the strain-hardening rate among the TPF, TAM, and TBF steels were large in the positive mean normal stress state and were relatively small in zero and negative mean normal stress states.This implied that the strainhardening behavior was strongly controlled by positive mean normal stress compared to the zero and negative mean normal stress states.In the following, the differences in the strain-hardening behavior in the positive mean normal stress state in the TPF, TAM, and TBF steels are discussed.
In general, the flow stress of TPF, TAM, and TBF steels [5,6] is decided by the following ((i) to (iv)): (i) The flow stress of the matrix structure; (ii) Long-range internal stress hardening, which results from the difference in plastic strain between the matrix structure and the second phase (retained austenite, strain-induced martensite, MA phase, etc.) [34]; (iii) Strain-induced transformation hardening, which results from an increase in the strain-induced martensite fraction.The transformation relaxes the localized stress concentration through an expansion strain [35]; (iv) Forest dislocation hardening, which is estimated with the Ashby equation [36].
Points (ii) to (iv) exhibit the strain-hardening resulting from the second phase.Considering these hardenings, the high strain-hardening rate in an early strain range in TBF steel may reflect the characteristics of the bainitic ferrite matrix structure in point (i),

Effect of Mean Normal Stress on Strain-Hardening Behavior
As shown in Figure 5, the differences in the strain-hardening rate among the TPF, TAM, and TBF steels were large in the positive mean normal stress state and were relatively small in zero and negative mean normal stress states.This implied that the strain-hardening behavior was strongly controlled by positive mean normal stress compared to the zero and negative mean normal stress states.In the following, the differences in the strainhardening behavior in the positive mean normal stress state in the TPF, TAM, and TBF steels are discussed.
In general, the flow stress of TPF, TAM, and TBF steels [5,6] is decided by the following ((i) to (iv)): (i) The flow stress of the matrix structure; (ii) Long-range internal stress hardening, which results from the difference in plastic strain between the matrix structure and the second phase (retained austenite, straininduced martensite, MA phase, etc.) [34]; (iii) Strain-induced transformation hardening, which results from an increase in the straininduced martensite fraction.The transformation relaxes the localized stress concentration through an expansion strain [35]; (iv) Forest dislocation hardening, which is estimated with the Ashby equation [36].
Points (ii) to (iv) exhibit the strain-hardening resulting from the second phase.Considering these hardenings, the high strain-hardening rate in an early strain range in TBF steel may reflect the characteristics of the bainitic ferrite matrix structure in point (i), as well as the strain-induced martensite hardening in point (iii) due to the large amount and high mechanical stability of retained austenite; in addition, the long-range internal stress hardening in point (ii) is reflected by a small amount of the MA phase.On the other hand, the high strain-hardening rate in a large strain range of TAM steel is considered to be mainly associated with the long-range internal stress hardening described in point (ii) and the strain-induced transformation hardening described in point (iii) due to the large amount of retained austenite, as well as the soft annealed martensite matrix structure.
As shown in Figure 6, the equivalent stresses in torsion were higher than those in tension and compression in all steels.This was because the von Mises criterion was applied to calculate σ and ε p .In addition, the differences in the equivalent stress and strainhardening rate for tension, torsion, and compression were larger in TBF steel (Figure 6c).This may have been associated with high flow stress.

Effect of Mean Normal Stress on Strain-Induced Martensite Transformation Behavior
As shown Figures 9 and 10, the k-values increased with increasing mean normal stress in the TPF, TAM, and TBF steels, although the k-values were different for each steel.According to Hiwatashi et al. [8], Takahashi [9], and Polatidis et al. [10], stretchforming (equi-biaxial tension or positive mean normal stress) significantly enhanced the strain-induced martensite transformation in 0.11C-1.18Si-1.55Mn[8,9] and 0.20C-1.46Si-2.48Mn[10] TPF steels.In this case, the strain-induced transformation of the shrink-flanging (compression or negative mean normal stress) was considerably suppressed, and the straininduced transformation of uniaxial tension was slightly suppressed compared to the stretchforming.Sugimoto et al. [5] also reported a similar result in 0.2C-(1.0-2.5)Si-(1.0-2.0)MnTPF and TAM steels subjected to stretch-forming and uniaxial tension.They explained these results as follows: A positive mean normal stress assists the strain-induced martensite transformation because it results in an expansion strain.
As shown in Figures 9 and 10, the lowest k-values were obtained in the TBF steel when they were calculated in an equivalent strain range between 0 and 0.3.This may have been associated with the fine retained austenite because the carbon concentration of the retained austenite was not necessarily high (Table 2).In Figure 10, the k-values in the tension, torsion, and compression of the TAM steel were higher than those of the TPF steel.Sugimoto et al. [5] reported the opposite result.This was because the present TAM steel had a coarser matrix structure and more granular-like retained austenite than the TAM steel in Ref. [5], as shown in Figure 4b,e,h.

Effect of Mean Normal Stress on Void-Formation Behavior
As shown in Figures 11-13, void formation was promoted by a positive mean normal stress in the TPF, TAM, and TBF steels.This was because the positive mean stress easily developed expansion stress/strain, which promoted void/crack initiation and growth.
The mean normal stress dependences of the size and number of voids were prominent in the TPF and TAM steels, although the TAM steel had a smaller void size than that of the TPF steel.On the other hand, in the TBF steel, the void formation was considerably suppressed compared to that in the TPF and TAM steels.According to Azuma et al. [37], Shoji et al. [38], Archie et al. [39], and Kikuzuki et al. [40], void formation was mainly influenced by the strain partitioning between ferrite (matrix structure) and martensite (second phase), strain localization, and the critical strain required for void formation in dual-phase ferritemartensite steel.Reducing the difference in the hardness between martensite and ferrite or in the strength ratio of martensite to ferrite (the strength ratio) slowed the void/crack initiation on the martensite/ferrite interface by decreasing the localized stress concentration.The difference in the hardness was equivalent to the previously mentioned strength ratio.Matsuno et al. [41] suggested that the size and volume fraction of martensite controlled void formation in 0.036/0.067C-0.5Si-1.5Mndual-phase ferrite-martensite steels.On the other hand, in 0.22C-0.27Si-1.89Mn-1.54AlTPF steel, the low k-value or high mechanical stability of retained austenite suppressed void formation through the effective relaxation of localized stress concentration at the matrix structure/second phase interface [6,7,32].Sugimoto et al. [7] showed that many voids were initiated at the matrix/second phase interface in 0.20C-1.5Si-1.5MnTAM and TBF steels.Tang et al. [19] reported that tiny micro-voids were observed in the fine bainite region with a film-like MA phase in 0.20C-1.40Si-1.70Mn-0.045NbCFB steel.
In this research, the TPF steel was characterized by a high strength ratio, a coarse micro-structure, and a small amount of retained austenite, although the k-value was lower than that of the TAM steel (Figure 10).Therefore, the high strength ratio and coarse microstructure may have contributed to the easy void initiation and growth in the TPF steel.A smaller void size in TAM steel may be associated with a lower strength ratio than that of TPF steel.In the TBF steel, the flow stress of the bainitic ferrite matrix structure was nearly the same as that of retained austenite [11].So, the strength ratio was very small.In addition, the TBF steel had a fine lath structure.Although the strain-induced martensite had a high flow stress, the retained austenite had smaller k-values and was much finer than that in the TPF and TAM steels (Figure 4i).Therefore, the low strength ratio, fine microstructure, and mechanically stable fine retained austenite are considered to bring difficulty in void initiation and growth.Alt hough the TBF steel contained a small amount of MA phase, the negative contribution to void initiation/growth behavior was estimated to be small.

Conclusions
The effects of the mean normal stress on the strain-hardening, strain-induced transformation, and void-formation behaviors of the TPF, TAM, and TBF steels were investigated to analyze various types of formability.In addition, these behaviors were related to the microstructural properties, such as the matrix structure, retained austenite characteristics, and second phase.The main results are summarized as follows.
(1) The highest volume fraction of retained austenite was achieved in the TAM steel, although the mechanical stability was the lowest.The TPF steel had the lowest retained austenite fraction.The mechanical stability of retained austenite was between that of the TAM and TBF steels.The TBF steel possessed a high retained austenite fraction second to that of the TAM steel, with high a mechanical stability due to the refined retained austenite.(2) A large difference in the σ − ε p curves for tension, torsion, and compression was shown in the TBF steel, with a large difference in the strain-hardening rate.In the positive mean normal stress state, the TAM and TBF steels had high strain-hardening rates in an early strain range and a large strain range, respectively, which resulted from the large amounts of retained austenite and the matrix structure.The strainhardening behavior was hardly influenced by zero and negative mean normal stresses in all steels.(3) The equivalent plastic strain was linearly related to the X-ray half-width in all mean normal stress states, which enabled the estimation of the equivalent stress in pressformed products.In this case, the TAM steel exhibited the lowest HV 0 and the largest n-value.On the other hand, TBF showed the largest HV 0 .(4) The positive mean normal stress promoted the strain-induced martensitic transformation, especially in the TBF steel, with the high mechanical stability of retained austenite.This was because the positive mean normal stress promoted the expansion strain.(5) The positive mean normal stress considerably promoted void-formation behavior by developing the expansion stress/strain, especially in the TPF steel.The effect of the mean normal stress on the void formation behavior in the TBF steel was smaller than those in the TPF and TAM steels because of the low strength ratio, fine matrix structure, and high mechanical stability of retained austenite.

Figure 2 .
Figure 2. Heat treatment diagrams of (a) TPF (solid lines), TBF (dotted lines), and (b) TAM steels.These heat treatments were carried out in salt and oil baths.O.Q.: Quenching in oil at 50 °C.

Figure 2 .
Figure 2. Heat treatment diagrams of (a) TPF (solid lines), TBF (dotted lines), and (b) TAM steels.These heat treatments were carried out in salt and oil baths.O.Q.: Quenching in oil at 50 °C.Figure 2. Heat treatment diagrams of (a) TPF (solid lines), TBF (dotted lines), and (b) TAM steels.These heat treatments were carried out in salt and oil baths.O.Q.: Quenching in oil at 50 • C.

Figure 2 .
Figure 2. Heat treatment diagrams of (a) TPF (solid lines), TBF (dotted lines), and (b) TAM steels.These heat treatments were carried out in salt and oil baths.O.Q.: Quenching in oil at 50 °C.Figure 2. Heat treatment diagrams of (a) TPF (solid lines), TBF (dotted lines), and (b) TAM steels.These heat treatments were carried out in salt and oil baths.O.Q.: Quenching in oil at 50 • C.

Figure 8 .
Figure 8.Comparison of the HW0 and n-values of TPF, TAM, and TBF steels.

Figure 8 .
Figure 8.Comparison of the HW 0 and n-values of TPF, TAM, and TBF steels.

Figure 9 .
Figure 9. Variations in the volume fraction of untransformed retained austenite (fγ) as a function of equivalent plastic strain ( p ε ) in (a) TPF, (b) TAM, and (c) TBF steels deformed through tension (open marks), torsion (solid black marks), and compression (solid gray marks).

Figure 9 .
Figure 9. Variations in the volume fraction of untransformed retained austenite (f γ) as a function of equivalent plastic strain (ε p ) in (a) TPF, (b) TAM, and (c) TBF steels deformed through tension (open marks), torsion (solid black marks), and compression (solid gray marks). k

Figure 10 .
Figure 10.Relationship between the k-value and mean normal stress (σm) in TPF, TAM, and TBF steels.The k-values are mean values in an equivalent plastic strain range between p ε = 0 and 0.3.

Figure 10 .
Figure 10.Relationship between the k-value and mean normal stress (σ m ) in TPF, TAM, and TBF steels.The k-values are mean values in an equivalent plastic strain range between ε p = 0 and 0.3.

Figure 12 . 15 Figure 12 .
Figure 12.(a) The void size-mean normal stress (D v − σ m ) relation and (b) the number of voids-mean normal stress (N v − σ m ) relation in TPF, TAM, and TBF steels plastically deformed to ε p = 0.3.

Figure 13 .
Figure 13.The relation between the mean number of voids (Nv) and mean size of voids (Dv) in (a) TPF, (b) TAM, and (c) TBF steels subjected to different equivalent plastic strains.Open and solid marks denote the data for tension and torsion, respectively.

Figure 13 .
Figure 13.The relation between the mean number of voids (N v ) and mean size of voids (D v ) in (a) TPF, (b) TAM, and (c) TBF steels subjected to different equivalent plastic strains.Open and solid marks denote the data for tension and torsion, respectively.

Table 1 .
Chemical composition (mass%) and measured martensite starting and finishing temperatures (MS, Mf, °C) of the slab used.

Table 1 .
Chemical composition (mass%) and measured martensite starting and finishing temperatures (M S , M f , • C) of the slab used.

Table 1 .
Chemical composition (mass%) and measured martensite starting and finishing temperatures (MS, Mf, °C) of the slab used.

Table 2 .
Microstructural properties and hardness of the various steels.k-values were calculated in a range of ε p = 0 to 0.3.
f γ 0 : initial retained austenite fraction, Cγ 0 : initial carbon concentration of retained austenite, k: strain-induced transformation factor, f MA : volume fraction of MA phase, HV 0 : original Vickers hardness.k-values are mean values in an equivalent strain range between 0 and 0.3.

Table 3 .
Mechanical properties of the TPF, TAM, and TBF steels.

Table 3 .
Mechanical properties of the TPF, TAM, and TBF steels.