Deformation Twinning Behavior of Twinning-induced ... - J-Stage

ISIJ International, Vol. 55 (2015), No. 8, pp. 1754–1761 ISIJ International, Vol. 55 (2015), No. 8

Deformation Twinning Behavior of Twinning-induced Plasticity Steels with Different Carbon Concentrations – Part 2: Proposal of Dynamic-strain-aging-assisted Deformation Twinning Motomichi KOYAMA,1,2)* Takahiro SAWAGUCHI1) and Kaneaki TSUZAKI1,2) 1) National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki, 305-0047 Japan. 2) Department of Mechanical Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395 Japan. (Received on February 9, 2015; accepted on March 31, 2015; originally published in Tetsu-to-Hagané, Vol. 100, 2014, No. 10, pp. 1253–1260)

In a previous study, the carbon concentration dependence of the deformation twinning behavior in twinning-induced plasticity steels was investigated, which clarified that the deformation twin fraction in the < 144 > tensile orientation did not change with the carbon concentration. In this study, twinning deformation occurred in the Fe–18Mn–1.2C steel at 473 K with a relatively high stacking fault energy of 55 mJ/m2. To explain these experimental results, dynamic strain aging of Shockley partials dislocations was proposed as an additional contributing factor to assist the deformation twinning in high-carbon-added austenitic steels. Most abnormalities concerning deformation twinning such as the high stacking fault energy in Fe–Mn–C austenitic steels were interpreted by considering the effect of dynamic strain aging. KEY WORDS: deformation twinning; dynamic strain aging; austenitic steel; electron backscatter diffraction (EBSD).

1.

In addition to the aforementioned tendency, an addition of carbon has been reported to affect the twinning behavior as follows: 1) The critical strain for the onset of deformation twinning is decreased markedly.8–10) 2) The stacking fault energy range for the occurrence of deformation twinning is extended.11–13) 3) The temperature range for the occurrence of deformation twinning is extended.11,14) A promising approach to interpret the effects of carbon is to consider the dislocation pinning effect due to carbon diffusion/segregation.12,15,16) An important carbon-dislocation interaction in Fe–Mn–C austenitic steels is dynamic strain aging (DSA).17–19) In this study, we attempt to discuss the carbon effect on twinning in terms of dislocation pinning associated with DSA. Phenomena triggering FCC deformation twinning are reported to be the formation of pole and sweep dislocations,20) a pile-up of dislocations against a Lomer-Cottrell (LC) barrier,8,21) dislocation dissociations that form three layers of extended dislocations,22) and infinite separation of dislocations.23,24) Hereafter, the mechanisms triggered by the abovementioned phenomena are called the pole mechanism, LC-lock mechanism, three-layer mechanism, and infinite separation mechanism, respectively. The details of the respective mechanisms are presented in Table 1. In general, low stacking fault energy is necessary for all the twinning mechanisms. Additionally, multiple slip is required for the pole mechanism and LC-lock mechanism to produce a superjog20) and a LC barrier,8,21) respectively. The

Introduction

The main factor affecting FCC deformation twinning is the stacking fault energy. In general, deformation twinning is suppressed with increasing stacking fault energy because the nuclear region of deformation twins consists of stacking faults.1–3) The stacking fault energy has been known to increase with increasing temperature4) and specific solute atom concentration,1) suppressing deformation twinning.1–3) In particular, carbon is an important solute element affecting twinning behavior in high Mn austenitic steels which is a typical low stacking fault energy material. In terms of stacking fault energy, it increases with increasing carbon concentration in high Mn austenitic steels when the concentration exceeds 0.3% wt%.5,6) In a previous study,7) the total amount of deformation twins and local twin fraction in < 111 > tensile orientations decreased with increasing carbon content in Fe–Mn–C austenitic steels. Namely, the carbon concentration dependence of the deformation twinning behavior was confirmed to be the same as the conventional stacking fault energy dependence. However, in < 144 > tensile orientations, the deformation twin fraction did not exhibit an exceptional carbon concentration dependence.7) Namely, the conventional understanding in terms of stacking fault energy does not provide a comprehensive mechanism to explain the carbon concentration dependence of the deformation twinning behavior. * Corresponding author: E-mail: [email protected] DOI: http://dx.doi.org/10.2355/isijinternational.ISIJINT-2015-070

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ISIJ International, Vol. 55 (2015), No. 8 Table 1.

Details of deformation twinning mechanisms.

Twinning mechanism

Twin nuclear

Growth

Activation of multi-slip

Interaction of dislocations

Ref.

Pole mechanism

Super jog

Motion of sweep dislocation

Necessary

Necessary

20)

Cross-slip mechanism

Extrinsic stacking fault

Sequent stacking from the twin nuclear

Necessary

Necessary

8,21)

Three layer mechanism

Intrinsic stacking fault group on successive three layers

Sequent stacking from the twin nuclear

Unnecessary

Necessary

22)

Infinite separation mechanism

Infinitely extended intrinsic stacking fault

Random stacking of infinitely extended dislocations

Unnecessary

Unnecessary

23,24)

three-layer mechanism needs a local stress at an obstacle for rearrangement of dislocation cores among extended dislocations.22) The infinite separation mechanism requires a high resolved shear stress for the screw component of dislocations to achieve a critical strain for the infinite separation of extended dislocations.24) All these factors strongly depend on the crystallographic orientation. Therefore, investigations of the crystallographic orientation dependence would clarify some important aspects of deformation twinning in Fe–Mn–C austenitic steels. In the present study, we discuss the carbon effects based on the twinning behavior at different crystallographic orientations and deformation temperatures in the Fe–Mn–C twinning-induced plasticity (TWIP) steels observed in the previous7) and present studies. Then, we propose a new concept of the necessary conditions for deformation twinning in terms of the dislocation pinning effect (particularly from the viewpoint of DSA), which explains the characteristics of deformation twinning in Fe–Mn–C austenitic steels consisting of a low critical stress and strain for deformation twinning and wide deformation temperature and stacking fault energy ranges for deformation twinning. 2.

Table 2.

Chemical compositions of the steels.

Steel (wt.%)

Mn

Si

C

Fe

Fe–17Mn–0.6C

16.4

0.003

0.57

bal.

Fe–17Mn–0.8C

16.5

0.002

0.81

bal.

Fe–18Mn–1.2C

18.0

0.003

1.15

bal.

electron backscatter diffraction (EBSD) measurements. The specimens for the EBSD analyses were prepared by mechanical polishing for 3.6 ks under a low stress condition. The EBSD analyses were conducted at 20 kV with a beam step size of 300 nm. The stacking fault energies were calculated using the following equation with the same dataset27) as the previous study:7)

γ = 2 ρ (∆G γ →ε + ∆G strain ) + 2σ γ / ε , .............. (1) where ΔGγ →ε is the free energy change by the ε-martensitic transformation from FCC (γ ) to HCP (ε), ρ is the molar surface density along {111}, and σ is the interfacial energy of γ /ε. The interfacial energy was assumed to be 16 mJ/ m2.27) In the previous study, using Eq. (1), the stacking fault energies of the Fe–17Mn–0.6C, Fe–17Mn–0.8C, and Fe–18Mn–1.2C steels were estimated to be 31 mJ/m2, 35 mJ/m2, 43 mJ/m2, respectively.

Experimental Procedure

Fe–17Mn–0.6C, Fe–17Mn–0.8C, and Fe–18Mn–1.2C steels were prepared by vacuum induction melting. The ingots were forged and hot rolled at 1 273 K, solution treated at 1 273 K for 3.6 ks under an argon gas atmosphere, and subsequently water quenched to suppress the formation of carbides. The chemical compositions of the steels are listed in Table 2. Hereafter, the compositions will be described in wt.%. These steels are TWIP steels that exhibit an excellent combination of elongation and ultimate tensile strength (UTS) mainly due to deformation twinning.3,25,26) The solution-treated bars were cut by spark machining to achieve the specimen geometries required for the following experiments. The tensile tests were conducted at ambient temperature for the specimens of the three steels with a gauge dimension of 4.0 mmw × 2.0 mmt × 30 mml with a grip section on both ends. Additionally, the Fe–18Mn–1.2C steel was tensiletested at 223 and 473 K. The deformation temperature was controlled with a thermostatic chamber used in an Instron type machine. The deformation microstructures were examined using

3.

Results

3.1. Stress-strain Response Under Various Conditions Figure 1 presents the engineering stress-strain curves at ambient temperature with an initial strain rate of 1.7 × 10 − 4 s − 1 in the Fe–17Mn–0.6C, Fe–17Mn–0.8C, and Fe–18Mn–1.2C steels. The tensile tests were conducted three times. The three steels exhibited a uniform elongation of more than 60%, and the uniform elongation and UTS increased slightly with increasing carbon concentration. Serrations were observed on all the stress-strain curves. Figures 2 and 3 show the effect of the deformation temperature on the serrated flow behavior. Figure 2 presents a engineering stress-strain curve at 223 K with an initial strain rate of 1.7 × 10 − 4 s − 1 in the Fe–18Mn–1.2C steel. The serrations disappeared for the stress-strain curve at 223 K. Figure 3 presents the engineering stress-strain curves at 473 K with initial strain rates of 1.7 × 10 − 4 and 1.7 × 10 − 2 s − 1 in 1755

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ISIJ International, Vol. 55 (2015), No. 8

the Fe–18Mn–1.2C steel. Both curves exhibited serrations at 473 K. The flow stress shown in Fig. 3 decreased with increasing strain rate. 3.2.

Fig. 1.

Deformation Temperature and Tensile Orientation Dependence of Twinning Behavior As mentioned in the introduction, the stacking fault energy depends on both the chemical composition and deformation temperature, thus affecting the twinning behavior. Figure 4 presents image quality (IQ) and rolling direction-inverse pole figure (RD-IPF: rolling direction // tensile direction) maps for the Fe–18Mn–1.2C steels tensile tested at 223 and 473 K. These images reveal variations of the twinning behavior with changing deformation temperature in the Fe–18Mn–1.2C steel. The tensile deformations were performed up to 10% tensile strains at an initial strain rate of 1.7 × 10 − 4 s − 1. The plate-like products in the IQ images are deformation twins.25,26) Figures. 4(a) and 4(b) reveal that the total number of deformation twins increased by decreasing the deformation temperature from ambient temperature to 223 K. In contrast, Figs. 4(c) and 4(d) show that deformation twins disappeared by increasing the deformation temperature from ambient temperature to 473 K after the 10% tensile deformation, regardless of the crystallographic orientations. However, numerous deformation twins appeared particularly in the grains denoted by A and B after a 20% tensile deformation at 473 K with an initial strain rate of 1.7 × 10 − 4 s − 1 in the Fe–18Mn–1.2C steel, as observed in Fig. 5. The tensile crystal orientations of grains A and B were [ − 9 − 5 − 10] and [1 − 3 3], which are close to < 122 > and < 133 > , respectively. The stacking fault energy at 473 K in the steel was calculated to be 55 mJ/m2 (the stacking fault energy in the same steel at 294 K is 43 mJ/m2). The 200 K temperature increase in high Mn steels is generally reported to increase the stacking fault energy by approximately 10 mJ/m2,4,5,29,30) indicating that the calculated stacking fault energy shows good agreement with that of conventional reports.

Engineering stress-strain curves in the three Fe–Mn–C steels at ambient temperature (294 K).

Fig. 2. Engineering stress-strain curve at 223 K at an initial strain rate of 1.7 × 10 − 4 s −1 in the Fe–18Mn–1.2C steel.

Fig. 4. (a) IQ and (b) RD-IPF maps in the Fe–18Mn–1.2C steels after 10% deformation at 223 K. (c) IQ and (d) RD-IPF maps in the Fe–18Mn–1.2C steels after 10% deformation at 473 K. (Online version in color.)

Fig. 3. Engineering stress-strain curves at 473 K at initial strain rates of 1.7 × 10 − 4 and 1.7 × 10 − 2 s −1 in the Fe–18Mn–1.2C steel.

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from ambient temperature to 223 K (Fig. 2), which promoted deformation twinning, as observed in Figs. 4(a) and 4(b). ε-martensite and α’-martensite were not detected in the Fe–17Mn–0.6, Fe–17Mn–0.8C, and Fe–18Mn–1.2C steels after a 10% tensile deformation at ambient temperature7) despite the appearance of the serrations at less than 10% tensile strain (Fig. 1). In addition, martensitic transformation did not occur at ambient temperature until the 60% tensile strain in the Fe–18Mn–1.2C steel.7) These facts indicate that the serrations are not associated with the martensitic transformation. In Fig. 3, the flow stress clearly decreases with increasing strain rate at 473 K in the Fe–18Mn–1.2C steel, although the flow stress generally increases with increasing strain rate in common metals. The negative strain rate sensitivity of flow stress is widely accepted as strong evidence for the occurrence of DSA.17,35–37) Because strain aging is controlled by carbon motion, DSA is suppressed at low temperature and promoted at high temperature in a specific temperature range. Accordingly, serrations associated with DSA appear and disappear in low and high temperatures, corresponding to the experimental facts obtained in this study. Thus, DSA is the dominant factor for the serrations in this study. 4.2. Deformation Twinning and Stacking Fault Energy As reported in the previous paper,7) the total number of deformation twins and local twin fraction in the near< 111 > tensile orientations decreased with increasing carbon concentration. The increase in temperature was also confirmed to suppress deformation twinning. These experimental results are explained by an increase in stacking fault energy, which increases the critical stress for the onset of deformation twinning.38–41) However, the deformation twin fraction in the < 144 > tensile orientations after the 15% deformation did not change with increasing carbon concentration,7) despite the increase in the stacking fault energy mentioned above. In addition, deformation twinning occurred after the 20% tensile deformation at 473 K in the < 122 > and < 133 > tensile orientations of the Fe–18Mn–1.2C steel, as demonstrated in Fig. 5, although the high stacking fault energy was calculated to be 55 mJ/m2. According to a conventional report, deformation twins do not form when the stacking fault energy is higher than 42 mJ/m2 .11) Even if deformation twinning occurs around the upper limit of the stacking fault energy, deformation twins are observed just before fracture.11) Hence, the present experimental results do not correspond to the reported relationship between the stacking fault energy and twinning behavior. The wider stacking fault energy range is an important characteristic of deformation twinning in the present high-C-alloyed Fe–Mn austenitic steel. The peculiar tendency of the results at a specific tensile crystal orientation and high deformation temperature on twinning is discussed in the next section.

Fig. 5. (a) IQ and (b) RD-IPF maps in the Fe–18Mn–1.2C steel after 20% tensile deformation at 473 K. The stacking fault energy in the Fe–18Mn–1.2C at 473 K is 55 mJ/m 2. The tensile direction is parallel to [− 9 − 5 −10] for grain A and [1 −3 3] for grain B. (Online version in color.)

4.

Discussion

In the previous paper,7) we reported the following facts with respect to the effects of carbon on deformation twinning behavior: 1) The total number of deformation twins decreases with increasing carbon concentration. 2) The carbon addition suppresses deformation twinning in < 111 > tensile orientations. 3) The deformation twinning behavior does not show a carbon concentration dependence in < 144 > tensile orientations. Hereafter, we attempt to discuss the abovementioned and present experimental facts to attain a comprehensive understanding of twinning in Fe–Mn–C austenitic steels. 4.1. Source of Serrations Serrations around ambient temperature can be attributed to α’-martensitic transformation (FCC→BCC or BCT),31) deformation twinning,32) and DSA17) in Fe–Mn–C austenitic steels. Serrations in Fe–Mn–C austenitic steels are widely accepted to arise from DSA.17–19,33,34) Additionally, the circumstantial evidence mentioned below indicates that the deformation twinning and martensitic transformation did not cause the serrations. The serrations in the present steels were not caused by deformation twinning because the serrations disappeared upon decreasing the deformation temperature

4.3. Twinning Mechanism and Crystallographic Orientation Dependence As mentioned in the introduction, deformation twins can be formed by the pole mechanism, LC-lock mechanism, three-layer mechanism, and infinite separation mechanism. Table 3 lists the Schmid factors of leading and trailing 1757

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ISIJ International, Vol. 55 (2015), No. 8 Table 3. Relationship between Schmid factor and occurrence of twinning in high-carbon austenitic steel: Hadfield steels and present steels, the ratio = Schmid factor of leading partial/Schmid factor of trailing partial. Schmid factor

Tensile Orientation

leading

trailing

0.236

0.471

0.50

No

8)

0.314

0.157

2.00

Yes

8, 10)

0.471

0.337

1.40

No

8)

0.471

0.236

2.00

Yes

10)

0.500

0.250

2.00

Yes

7, 10)

0.496

0.248

2.00

Yes

Fig. 5

0.471

0.236

2.00

Yes

Fig. 5

ratio

Reference

where ν is Poisson’s ratio, bp is Burgers vector of partial dislocations, and G is the shear modulus. According to Eq. (2), the separation distance increases with increasing resolved shear stress and increases sharply at a specific stress. The upper limit of the separation distance corresponds to the grain size. Byun regarded the specific stress providing the separation distance ( = grain size) as the critical stress for the infinite separation of dislocations.23) Then, the critical stress for the infinite separation was claimed to be equal to the critical stress for deformation twinning.23) In this context, the critical stress for the infinite separation of a pure screw dislocation in austenitic steels is approximated as23)

partial dislocations and occurrence of deformation twinning in various crystallographic orientations. From the viewpoint of the LC-lock mechanism, deformation twinning cannot occur in the tensile orientations of < 123 > because of the absence of multiple slip because the LC barrier cannot be formed.8) In contrast, deformation twins appear in the < 111 > and < 110 > tensile orientations, which indicate the multiple slip.8) In the same context, deformation twinning associated with the pole mechanism also shows a similar crystallographic orientation dependence, as observed in Table 1. However, deformation twins with a volume fraction of > 20% at a 15% plastic strain were also observed in the near- < 144 > tensile orientations,7) including < 122 > and < 133 > , indicating that deformation twinning acts as a main deformation mode in the tensile orientation. Additionally, deformation twins have been reported to appear at a 1% plastic strain in the < 144 > tensile orientation of a Fe–Mn–C austenitic steel.10) The near- < 144 > tensile orientation has a high primary Schmid factor ≈0.5 and a large difference between the Schmid factors for primary and secondary leading partial dislocation slip despite the absence of a multiple slip at a small strain (although a grain rotation initiates a multiple slip even in the < 144 > tensile orientationi). These facts indicate that the active twinning mechanism in Fe–Mn–C austenitic steels does not require multiple slip, at least in the < 144 > tensile orientation. Hence, considering the underlying twinning mechanism from conventionally reported works, the three-layer mechanism or infinite separation mechanism explains the aforementioned crystallographic orientation dependence. In this paper, we interpret these facts in terms of the infinite separation mechanism. From the viewpoint of the infinite separation of dislocations, a multiple slip is not required; however, a large resolved shear stress is necessary. Therefore, the consideration of infinite separation would describe the twinning behavior along the < 122 > , < 133 > , and < 144 > tensile orientations, which have high Schmid factors. Byun reported the following equation describing the separation distance of screw dislocations under stress:23) d=

Occurrence of twinning

τ = 2γ / bp . ................................. (3) Assuming that bp in Eq. (3) is 145 nm,23) the critical resolved shear stress for the infinite separation is estimated to be 593 MPa at ambient temperature in the Fe–18Mn–1.2C steel (stacking fault energy = 43 mJ/m2). Thus, to activate the infinite separation in the < 144 > tensile orientation, an axial tensile true stress of 1 379 MPa is required. Because most of the plastic strain was provided by deformation twinning along the < 144 > tensile orientation and because deformation twinning has been reported to occur immediately after yielding,8–10) the critical stress for deformation twinning in the Fe–18Mn–1.2C steel must be close to the yield stress. The 0.2%-proof stress of the Fe–18Mn–1.2C steel was 320 MPa, as observed in Fig. 1, which is considerably lower than the estimated critical stress for infinite separation. Hence, the twinning behavior in the < 144 > tensile orientation cannot be explained by considering only the infinite separation. In the next section, we propose a new twinning mechanism to interpret the characteristic twinning behavior in terms of a pinning effect of carbon. 4.4.

Proposal of a Twinning Mechanism in Terms of Dynamic Strain Aging of Extended Dislocations The separation distance during deformation becomes smaller than that in a static condition when the stress applied on the leading partial is larger than that on the trailing partial.8) In addition, the dislocation velocity depends on the experimental conditions and properties of the obstacles against extended dislocation motions. Considering the

(2 − 3ν )Gbp2 , ..................... (2) 8π (1 −ν )(γ − τ bp / 2)

i Since < 144 > is not the stable tensile crystallographic orientation, a multiple slip is activated when the orientation is rotated to < 111 > through a large plastic deformation7).

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effect of obstacles against extended dislocation motions, the dislocation separation would be enhanced if the motion of trailing partials could be suppressed and the leading partials could move about freely. The pinning effect by carbon to prevent the motion of partials has been proposed as a possible method.4,42) Recent works have demonstrated that the motion of trailing partials can be suppressed by DSA associated with the interaction between point defect complexes containing an interstitial carbon and the stacking fault18) or with the interaction between trailing partials and interstitial carbon19,43) in Fe–Mn–C austenitic steels. Then, the DSA broadens the partial dislocation separation anomalously.15) Thus, we introduce the effect of DSA on the dislocation separation to explain the twinning behavior in the < 144 > tensile direction and at high temperature in the present Fe–Mn–C steelsii. The tendency of DSA is described by the following equation:44)

of dynamic strain aging in a Fe–Mn–C austenitic steel, as mentioned below. We previously described a relationship between critical strains for trapping leading and trailing partial dislocations using Eqs. (5) and (6) with the assumption that the constant value of α is equal to 2, which is the same as that with pure Cu48) (see Ref. 19) for further details concerning this assumption). When the tensile crystal orientation is < 144 > , the relationship between the critical strains for leading and trailing partial dislocations is described as follows:19) lnεcL = mlnεcT + m − 1ln4. ........................ (7) For example, the m value of a Fe–17Mn–0.3C austenitic steel was 3.3.19) Equation. (7) indicates a significant difference between the critical strains for trapping leading and trailing partial dislocations. Thus, only leading partial dislocations can move in the strain range from the critical strain for trapping trailing partial dislocations to the critical strain for trapping leading partial dislocations, which causes the two partial dislocations to become infinitely separated as long as the trailing partial is not depinned. The infinite separation of partial dislocations must be regarded as the initiation of deformation twinning. In this case, the critical stress and strain for deformation twinning correspond to the critical stress and the strain for the onset of the serrations associated with DSA, respectively. The serrations were initiated just after yielding in the present steels at ambient temperature, as observed in Fig. 1. Hence, DSA-assisted infinite separation can explain the initiation of twinning at

ε = KC n exp(−QM / RT )ε c m , ................... (4) where ε is the strain rate; K, n, and m are empirical constants; C is the carbon concentration, QM is the activation energy for the thermally activated process responsible for the serration, R is the gas constant, T is the deformation temperature, and εc is the critical strain for the onset of the serration. The activation energy in Eq. (4) was reported to correspond to that for carbon diffusion in Fe–Mn–C austenitic steels.45) In the previous study, we proposed that leading and trailing partial dislocations can be trapped separately by the solute atoms under the assumption that the leading and trailing partial dislocation velocities are significantly different from each other during a transient phase from the static separation distance to the equilibrium separation distance of dislocations under a specific stress.19) The assumption that the leading partial dislocation velocity is different from that of the trailing partial was classically proposed by Copley.46) Based on this consideration and the relationship between the dislocation velocity and stress (Vd = (τ/τ0)α; τ shear stress; α, τ0 = empirical constants47))iii, Eq. (4) was modified as follows:19) 1 1+ (τ L / τ T )

α

 −QM  m ε = K par C n exp   ε cT ......... (5)  RT 

(τ L / τ T )   −QM  m ε = K par C n exp   ε cL , ........ (6) α  RT  1 + (τ L / τ T ) α

where Kpar is an empirical constant for partial dislocations, τL is the resolved shear stress for leading partial dislocations, τT is the resolved shear stress for trailing partial dislocations, εcL is the critical strain for trapping leading partial dislocations, and εcT is the critical strain for trapping trailing partial dislocations. Although the proposed mechanism contains many assumptions and phenomenological laws, this model provided important insights about the behavior

Fig. 6. Width of stacking faults under (a) a static condition, (b) an applied stress, and (c) the effect of dynamic strain aging. In case (c), only the trailing partials are trapped by carbon during the deformation. In the above cases, Wa < W b < Wc.

ii

In this study, the major interaction between trailing partials and carbon is assumed to be DSA at ambient temperature.19) However, an interaction between carbon and point defects in a stacking fault18) also explains the DSA-assisted infinite separation mentioned later because the leading partial can move freely compared to the trailing partial when the interaction acts effectively. This case also requires a high Schmid factor of the leading partial and a large difference in the Schmid factors between the leading and trailing partials for the condition that only the leading partial moves freely. Namely, the interaction between carbon and point defects in a stacking fault assists deformation twinning preferentially in the < 144 > tensile orientation, where the aforementioned required conditions are satisfied (the Schmid factor of the leading partial is 0.50), corresponding to the remarkable deformation twinning observed in the previous study.7) iii Here, the critical strain εc is assumed to depend on the carbon diffusion and dislocation velocity of flight motion to use the Johnston-Gilman relationship.47)

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a rather low stress and plastic strain in the < 144 > tensile orientation. To move only the leading partial dislocations, a specific condition must be satisfied, namely, only the trailing partial dislocations should be trapped by DSA. More specifically, the following three conditions are required: (1) The Schmid factor of the trailing partial dislocation is markedly lower than that of the leading partial dislocation. (2) The dislocation velocity of the trailing partial dislocation is comparable to or slightly higher than the diffusion speed of carbon (dislocations just follow the carbon diffusion when the dislocation velocity is lower than the diffusion speed of carbon). (3) The dislocation velocity of the leading partial dislocation is sufficiently higher than the diffusion speed of carbon (the Schmid factor of the leading partial is high). Under the condition that satisfies (1)–(3), trapping only the trailing partial dislocations triggers the infinite separation of stacking faults. Figure 6(a) shows the width of a stacking fault under a static condition. Figure 6(b) reveals an increase in the width of a stacking fault during deformation in a state where the aforementioned condition is not satisfied, and the width can be calculated using Eq. (2). Figure 6(c) shows a wider or infinite increase in the width of the stacking fault by trapping only the trailing partial dislocation and implies that the critical stress and strain for twinning are remarkably low when the DSA occurs at the specific condition. Here, we discuss the consistency between the proposed twinning mechanism and the obtained results in the previous and present studies. Numerous deformation twins were observed in the < 144 > tensile direction.7) The tensile direction exhibits the highest resolved shear stresses for primary < 112 > twinning shears in the grains and a large difference in Schmid factors between leading (0.50) and trailing partial (0.25) dislocations (see Table 3). The high resolved shear stress provides a high velocity of leading partial dislocations, producing a situation in which the leading partial dislocations leave the solute atoms. In addition, the large difference in the Schmid factors of the leading and trailing partials provides the relatively low velocity of trailing partial dislocations. These conditions are optimal to trap only trailing partial dislocations, promoting deformation twinning as mentioned above. The increase in the carbon concentration enhances the DSA, promoting deformation twining in the specific tensile orientation e.g., < 144 > through the DSAassisted infinite separation. The same discussion explains the formation of the deformation twins in the < 122 > and < 133 > tensile orientations after the 20% deformation at 473 K (Fig. 5) because the tensile orientations also exhibit high Schmid factors for leading partial dislocations and relatively low Schmid factors for trailing partial dislocations, as observed in Table 3. The initiation of deformation twinning at the tensile strain of 10–20% corresponds to the onset of serrations at a tensile strain of approximately 10% at 473 K in the Fe–18Mn–1.2C steel shown in Fig. 3, indicating that deformation twinning can be assisted by the DSA at the specific tensile orientations even at the high stacking fault energy of 55 mJ/m2. In contrast, there is a relatively small difference in the Schmid factors of leading and trailing partial dislocations in the < 123 > and < 001 > tensile orientations, in which deformation twins were not observed in Karaman’s report,8) © 2015 ISIJ

as observed in Table 3. Because the relatively small difference does not satisfy condition (1), deformation twinning is not promoted by the DSA in the tensile directions. Additionally, the < 111 > tensile orientation has a smaller Schmid factor of leading partials compared with the < 144 > tensile orientation, implying that condition (3) is not satisfied. Thus, DSA-assisted infinite separation does not occur in the < 111 > tensile orientation. In the case that DSA does not assist twinning, deformation twinning is suppressed by the carbon addition, as demonstrated in the previous study because carbon increases the stacking fault energy. Accordingly, the total number of deformation twins also decreases with increasing carbon concentration.7) Note that DSA-assisted twinning and conventional twinning mechanisms can coexist. For example, Figs. 4(a) and 4(b) showed deformation twins without any serrations at 223 K. Decreasing the deformation temperature decreases the stacking fault energy, essentially promoting deformation twinning. In addition, the decrease in the deformation temperature suppresses the DSA because of the decrease in the diffusivity of solute atoms. Therefore, the conventional twinning mechanism, e.g., LC-lock mechanism8,21) must be dominant around the < 111 > tensile orientations in a relatively low temperature region. However, DSA-assisted twinning occurs even at high temperature with high stacking fault energy as long as the condition where only trailing partial dislocations are trapped by the DSA is valid. Moreover, the number of active twinning shears increased with increasing plastic strain because of the grain rotation,7) providing higher multiple slips in most of the grains. Because of the increase in flow stress by work hardening and the increase in the number of active slip systems, the DSA-assisted twinning and conventional twinning mechanisms must coexist in the large plastic strain range. The coexistence of the different twinning mechanisms in Fe–Mn–C austenitic steels indicates that the ranges of deformation temperature and stacking fault energy must be wider for deformation twinning to occur than those of other FCC materials. More specifically, it is considered that the conventional twinning mechanism acts in the low-temperature condition and that the DSA-assisted twinning occurs at high temperature. 5.

Conclusion

In this paper, we attempted to comprehensively explain the following experimental facts of the deformation twinning behavior in Fe–Mn–C austenitic steels in terms of carbon effects: (1) The critical strain for the onset of deformation twinning in Fe–Mn–C austenitic steels is markedly smaller than that for other FCC metals. (2) The deformation twin fraction at ambient temperature does not change in the < 144 > tensile orientation, despite an increase in the carbon concentration, which increases stacking fault energy. (3) Deformation twins appeared at the relatively high stacking fault energy of 55 mJ/m2 (Fe–18Mn–1.2C steel at 473 K). The deformation twinning occurred when serrations were observed. These experimental facts cannot be explained by the conventional FCC twinning behavior simply depending on 1760


the stacking fault energy. Instead, we proposed a possible mechanism that dynamic strain aging assists deformation twinning. Dynamic strain aging occurs at high temperature and shows crystallographic orientation dependence. Furthermore, the carbon addition enhances the dynamic strain aging. Therefore, deformation twinning can occur even when the deformation temperature and carbon concentration are increased as long as dynamic strain aging occurs. Because the dynamic strain aging of Fe–Mn–C austenitic steels occurs at a small strain, the effect of dynamic strain aging also explains the small critical strain for the onset of deformation twinning.

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