In situ Observation of the Influence of Al on Deformation-induced Twinning in TWIP Steel

Abstract

The deformation twinning behavior of Fe18Mn0.6C and Fe18Mn0.6C-2.5Al twinning-induced plasticity steels was compared by in-situ electron backscattering diffraction. Al suppressed deformation-induced twinning. A constitutive model considering the effect of Al on the twin formation kinetics was used to show that the work hardening and the ultimate tensile strength were lowered by the suppression of deformation twinning despite the pronounced solution hardening contribution of Al.

1. Introduction

Fe–Mn–C–Al High Mn twinning-induced plasticity (TWIP) steel has been intensively investigated due to its excellent combination of strength and ductility and the suppression of localized deformation by Al addition.^1,2,3) The high strength of TWIP steel is due to a dynamic Hall-Petch effect resulting from the gradual reduction of the effective grain size caused by mechanical twinning and dynamic strain aging (DSA) resulting from the interaction between mobile dislocation and Kim et al.^4,5) reported that the DSA contribution to strength was small. The dynamic Hall-Petch effect associated with mechanical twinning can therefore be considered as the primary strengthening mechanism of TWIP steel. The relationship between mechanical twinning and work hardening has been described in a recently developed constitutive model.^4,5) The occurrence of deformation twinning appears to be limited to alloys with stacking fault energy (SFE) in the range of 12–35 mJ/m² and cross slip is activated when the SFE is higher than 35 mJ/m².⁶⁾ Thermodynamic calculations,^7,8) in-situ neutron diffraction⁹⁾ and transmission electron microscopy (TEM)¹⁰⁾ have shown that the addition of Al leads to an increase of the SFE by approximately 11.3 mJ/m² per mass-% of Al. The direct in situ observation of the effect of Al on the kinetics of deformation twin formation in TWIP steel has not yet been reported, and the aim of the present study was therefore to compare the kinetics of deformation twinning in Fe–Mn–C and Fe–Mn–C–Al TWIP steel using a combination of in-situ tensile deformation and electron backscattering diffraction (EBSD) measurements. In addition, the constitutive model proposed by Kim et al.^4,5) was used to compare the twinning kinetics derived from the stress-strain curve and the experimentally measured twinning kinetics based on EBSD observation.

2. Experimental

Two austenitic TWIP steels with composition Fe-18%Mn-0.6%C and Fe-18%Mn-0.6%C-2.5%Al (in mass-%), which will be referred to as Fe18Mn0.6C and Fe18Mn0.6C-2.5Al in the present contribution, were prepared by vacuum induction melting. Vacuum-cast, hot-rolled materials were cold-rolled to 1.2 mm in thickness and recrystallization annealed. The detailed procedure of the material preparation is described in Ref. 11).

The as-annealed microstructure of both steels was fully austenitic. The average austenite grain size at room temperature was approximately 4 μm. The initial texture was composed of a weak Brass {011}<211> component, the copper {112}<111> component and the Goss {011}<100> component. The intensity of the three texture components was similar in both steels.

In-situ EBSD observations were carried out in a FEI Quanta 3D FEG which combines high resolution field emission source scanning electron microscopy (FE-SEM) and the focused ion beam (FIB) technique used for sample milling. A miniature straining module was used to deform the material in uniaxial tensile tension. The dimension of the miniature tensile specimen for the in-situ observations was 10 mm long, 2 mm wide and 1 mm thick. The tensile stress direction was parallel to the original sample rolling direction (RD). The specimen strain was controlled with by the W75.0 TSL software package. The miniature tensile specimens were mirror polished with colloidal silica after mechanical polishing. The EBSD measurements were carried out on the normal direction (ND) plane for true tensile strains of 0, 0.1, 0.2 and 0.3. No additional polishing was done between the deformation stages. The samples were strained in quasi-static conditions using a constant strain rate of 5 × 10^–3 s^–1. The scanning area was 50 μm × 50 μm, and the step size was 50 nm. Approximately one hundred grains were analyzed at each deformation stage. The confidence index (CI) decreased from a starting value of 0.7 to a value of 0.1 for a strain of 0.3. The decrease of the CI is due to the increase of the surface roughness resulting from differences in the through-thickness deformation.¹²⁾ This deformation-induced surface topology has a negative effect on the CI, because the line of sight configuration gradually deteriorates during straining.¹³⁾ Data points with a CI less than 0.01 were therefore not considered for the data analysis, and these low CI data points appear with a black contrast in the EBSD micrographs.

When analyzing deformed microstructures by means of EBSD, local variations in yielding and plastic flow conditions must be assessed. This was done by computing $\frac{\sum d{\gamma }^l}{d{\epsilon }_M^l}$ , the local Taylor factor, based on the measurement of the local orientation and the information available about the deformation mode. Here $\sum d{\gamma }^l$ is the local micro-mechanical crystal shear increment at the grain level, and $d{\epsilon }_M^l$ is the local von Mises strain increment. If the slip systems, e.g. a/2[110]{111} in fcc metals and alloys, and the deformation mode, e.g. uni-axial strain, are specified, the classical Taylor factor M can be calculated by the Taylor–Bishop–Hill homogenization theory. M is equal to $\frac{\sum d{\gamma }^g}{d{\epsilon }_M^g}$ , the ratio of the global shear strain increment to the global von Mises strain increment. This factor can be averaged for a texture-less polycrystal, and M=3.06 would apply in the present case. In EBSD the local, rather than the macroscopic, Taylor factor is computed. The local Taylor factor is equal to $\frac{\sum d{\gamma }^l}{d{\epsilon }_M^l}$ . Here $\sum d{\gamma }^l$ is the local micro-mechanical crystal shear increment at the grain level, and $d{\epsilon }_M^l$ is the local von Mises strain increment. The calculation of the local Taylor factor is based on the measurement of the local orientation and the information available about the deformation mode. The local Taylor factor provides a means to evaluate the slip response of a grain to specific deformation conditions. As the increment of plastic work is proportional to $\sum d{\gamma }^l$ , a grain with a larger value of M requires a larger amount of plastic work to achieve a specific deformation. The local Taylor factor can therefore also be used as a measure of the influence of orientation on the resistance to deformation: yield resistant or “hard” orientations have a high Taylor factor.¹⁴⁾

Conventional uniaxial tensile tests with the tensile axis aligned along the RD were carried out on a ZWICK universal tensile testing machine using a strain rate of 5 × 10^–3 s^–1. A sub-size ASTM E8 standard specimen was used. Transmission electron microscopy (TEM) of the deformed samples was carried out in a JEOL JEM-2100 operated at 200 kV.

3. Results

Figure 1(a) shows the strain-induced formation of twins in a single <111>//RD-oriented grain in Fe18Mn0.6C. The grain orientation was 13.8° from the exact {112}<111> orientation prior to deformation. At a strain of 0.1, the occurrence of deformation twinning was detected in the inverse pole figure (IPF) map and straight parallel features were observed in the image quality (IQ) map. As the overlap of the diffraction information from narrow twins and the matrix leads to low IQ values, this observation indirectly implies that very narrow deformation twins had developed.¹⁵⁾ At a strain of 0.2, four deformation twins were clearly visible in the IPF map. The twins had a (2 17 11)[-14 1 1] orientation, i.e. they were misoriented by 13.6° from the exact (011)[100] orientation. The twins were 150–200 nm wide. The orientation relationship between the four twins and the matrix corresponded to a Σ3 boundary. At a strain of 0.3, the number of twins in the twinned grain had increased to eight. Comparing the images at a strain of 0.2 and 0.3, it appears that the twins were formed at grain boundaries and propagated across the grain. Figure 1(b) shows the change of orientation of specific grains as a function of the tensile deformation. The matrix gradually developed a <111>//RD fiber orientation with increasing deformation. The <100>//RD fiber orientation was developed in the areas where deformation twinning had occurred.

Fig. 1.

(a) IPF and IQ maps showing the evolution of the deformation-induced twinning for a grain with an orientation close to {211}<111> in Fe18Mn0.6C. The Σ3 twin boundaries are indicated as red lines in the IQ map. (b) IPF along RD (RD//tensile axis) showing the evolution of the orientations within the grain during the in-situ deformation.

Figure 2 compares the microstructure of Fe18Mn0.6C and Fe18Mn0.6C-2.5Al deformed to a strain of 0.2. Several parallel bundles of deformation twins, 200–300 nm wide, can be observed in Fig. 2(a). Figure 2(b) clearly shows that the bundles consist of groups of thin deformation twins, 10–20 nm wide. Beladi et al.¹⁶⁾ observed that a high density of dislocations with widely separated partials and stacking faults were formed prior to reaching the critical strain for twin initiation in a Fe18Mn0.6C-1.5Al alloy. The very thin twins nucleated at grain boundaries and propagated across the grains. The formation of a single deformation twin, when the critical resolved shear stress for twin nucleation is reached, is difficult to detect by EBSD due to the spatial resolution of the technique which is limited by the probe size of about 50 nm. The relatively wide twinned regions observed in the present EBSD analysis are therefore not isolated deformation twins with a thickness of 100 nm but rather groups of thin closely-packed deformation twins. These groups of twins gradually thicken by addition of more thin deformation twins.¹⁶⁾ The gradual thickening of a bundle of deformation twins when the size of the twin bundle exceeds 100 nm appears as the widening of a single wide twin when observed in EBSD, but it actually results from the addition of more twin plates nucleated at the grain boundary. Figure 2(c) shows the dislocation cell structure formed in a twin free grain in Fe18Mn0.6C-2.5Al deformed to a strain of 0.2.

Fig. 2.

(a) TEM micrograph of bundles of deformation twins in a grain in Fe18Mn0.6C deformed to a strain of 0.2. (b) Enlargement the bundle of deformation twins. (c) Dislocation cell structure in a grain which has remained free of deformation twins in Fe18Mn0.6C-2.5Al deformed to a strain of 0.2.

Figure 3 compares the in-situ EBSD results for twinning in Fe18Mn0.6C and Fe18Mn0.6C-2.5Al. Pre-existing annealing twins and deformation twins are easily distinguished by comparing the microstructures before and after deformation. The deformation twins, which have Σ3 twin boundaries with a 60° <111> rotation/axis relationship, are indicated with an asterisk in Fig. 3. Eight of the two hundred grains which were analyzed were found to contain deformation twins in Fe18Mn0.6C. In Fe18Mn0.6C-2.5Al only two of the two hundred analyzed grains contained deformation twins. Several bundles of deformation twins developed within the twinning grains in Fe18Mn0.6. In contrast only a single bundle of deformation twins was observed to form within the twinning grain in Fe18Mn0.6C-2.5Al. The quantitative analysis of the deformation twinning is summarized in Table 1. The actual number of twinned grains is probably slightly larger than the number of twinned grains observed by EBSD because some bundles of deformation twins may not have been large enough to be detected by EBSD. It is however very clear that Al addition results in the suppression of deformation twinning.

Fig. 3.

IPF images illustrating the influence of Al additions on deformation twinning. Grains which undergo deformation twinning are indicated by an asterix.

Table 1. Quantification of deformation twinning Fe18Mn0.6C and Fe18Mn0.6C-2.5Al deformed to a strain of 0.2.

Steel	Volume fraction of grains with twins	Volume fraction of twins in twinned grains	Twinned volume fraction
Fe18Mn0.6C	0.04	0.074	0.0030
Fe18Mn0.6C-2.5Al	0.01	0.020	0.0002

Figure 4 shows rolling direction inverse pole figures (RD IPF) for the initial orientation of all the grains and for the initial orientation of the twinned grains only in Al-free Fe18Mn0.6C and in Fe18Mn0.6C-2.5Al. The blue lines correspond to the Taylor factor for {111}<110> slip. The red line correspond to the grain orientations for which the Schmid factor of the leading partial dislocation and the trailing partial dislocation of a dissociated dislocation is equal in uniaxial tension. In all other orientations the partials are either pushed closer together or pulled further apart. When the partial dislocations are pulled apart by the applied shear stress, it is expected that twinning will be enhanced. The RD IPF reveals that the grains were initially randomly orientated. The RD IPFs for the initial orientation of the twinning grains in both Al-free Fe18Mn0.6C and Fe18Mn0.6C-2.5Al show however that these specific grains had orientations with a Taylor factor of 2.7 or higher and a Schmid factor for the leading partial dislocation which was higher than the Schmid factor for the trailing partial dislocation.

Fig. 4.

RD IPF showing the initial orientations for all grains in Fe18Mn0.6C-xAl and Fe18Mn0.6C-2.5Al (left) and for grains which contain deformation-induced twins (right). The tensile axis was along the RD. The blue lines are iso-Taylor factor lines for {111}<110> slip in grains deformed in uniaxial tension with an orientation within the basic orientation triangle. The dotted red line in the basic orientation triangle indicates the orientations for which the Schmid factor of the leading partial and trailing partial of a dissociated dislocation are equal. Deformation twinning is promoted on the right of this line, and suppressed on the left.

Figure 5 shows the texture evolution of twinning grains in Fe18Mn0.6C and Fe18Mn0.6C-2.5Al examined after in-situ deformation. Most of the grains rotated in such a manner that a <111>//RD fiber texture would develop in both alloys. The <100>//RD fiber texture was a consequence of deformation twinning in Fe18Mn0.6C. A similar texture development due to deformation twinning was not observed for the Fe18Mn0.6C-2.5Al due to the very limited volume fraction of deformation twins resulting from the higher SFE of this alloy, which suppresses twinning.

Fig. 5.

RD IPF for Fe18Mn0.6C and Fe18Mn0.6C-2.5Al deformed to a true strain of 0.2. The evolution of the matrix orientation is indicated in blue. The evolution of the orientation for the deformation twins is indicated in red.

4. Discussion

It is well known that the SFE plays an important role in deformation twinning as, at SFE of approximately 20 mJ/m², the separation of the Shockley partial dislocations allows for the occurrence of deformation-induced twinning.⁶⁾ As an intrinsic stacking fault can be considered to be a two atomic layer thick plate with hcp crystal structure inserted in a matrix with a fcc crystal structure, the SFE can be computed using the thermodynamic properties of the fcc→hcp transformation:^7,8)   

$$SFE=2\cdot \rho \cdot (\mathrm{\Delta }{G}_{\gamma \to \epsilon }^{chem}+\mathrm{\Delta }{G}_{\gamma \to \epsilon }^{mag}+\mathrm{\Delta }{G}_{\gamma \to \epsilon }^{ex})+2\cdot \sigma$$

$\mathrm{\Delta }{G}_{\gamma \to \epsilon }^{chem}$ is the chemical contribution to the free energy change of the fcc→hcp transformation, $\mathrm{\Delta }{G}_{\gamma \to \epsilon }^{mag}$ is the magnetic contribution to the free energy change and $\mathrm{\Delta }{G}_{\gamma \to \epsilon }^{ex}$ is the excess free energy change, which includes the strain energy and the effect of the grain size. ρ is the molar surface density for {111} planes and σ is the {0001}_ε/{111}_γ interfacial energy, which is here considered to be independent of temperature and composition. Figure 6(a) shows the calculated SFE using the thermodynamic model proposed by Akbari et al.,⁸⁾ which was used to calculate the SFE at 25°C for Fe18Mn0.6C (16 mJ/m²) and Fe18Mn0.6C-2.5Al (38 mJ/m²). The increase of the SFE by addition of Al is due to an increase of the chemical contribution to the free energy change for the fcc→hcp transformation as shown in Fig. 6(b). The predicted increase of the SFE by Al addition has been verified experimentally by Jeong et al.⁹⁾ and Kim et al.¹⁰⁾ The increase of the SFE by the addition of Al is therefore the main reason for the suppression of deformation-induced twinning in Fe18Mn0.6C-2.5Al.

Fig. 6.

(a) Stacking fault energy calculation as function of temperature for Fe18Mn0.6C and Fe18Mn0.6C-2.5Al. (b) Chemical and magnetic contributions to the stacking faults energy.

Figure 7 shows a schematic for the evolution of deformation twins formation in a grain based on the present EBSD and TEM observations. Several fundamental mechanisms for deformation twin nucleation and growth in fcc alloys have been discussed in the literature.^17,18) The twin nucleation mechanisms are usually based on the characteristics of the dissociation of perfect a/2<110> glide dislocations into two a/6<112> Shockley partial dislocations on {111} close-packed planes. In their TEM study, Idrissi et al.¹⁹⁾ support the pole mechanism proposed by Cohen and Weertman.²⁰⁾ This mechanism assumes that a perfect dislocation can dissociates into a Frank sessile dislocation and a Shockley partial upon meeting an obstacle. Under the influence of the applied stress twin growth proceeds by the coordinated glide of Shockley partial dislocations on parallel {111} planes. The narrow width of the deformation twins observed in TEM in the present work suggests that twin growth is limited by the shear strains acting on the twinned volume. In addition the present EBSD work also clearly shows an effect of the crystallographic orientation of the grains and the role of grain boundaries as nucleation sites for deformation twins.

Fig. 7.

Schematic of the growth of deformation twins with deformation.

The effect of orientation on deformation twinning can be explained on the basis of Schmid’s law.²¹⁾ Deformation twinning usually requires the buildup of a high local shear stress on the twinning partial dislocations. In the case of a tensile stress, the resolved shear stress acting on a perfect dislocation and the corresponding leading and trailing partial dislocations can easily be computed, and the resulting orientation dependence of the Schmid factor is shown in Fig. 8. When the tensile axis is close to a <100> axis the effective stacking fault energy is increased and the partial dislocation separation is reduced. The dislocation dissociation width increases when the tensile axis is close to a <111> axis, as the stress on the leading partial is higher than the stress on the trailing partial. This reduces the effective stacking fault energy and promotes deformation twinning. This was observed experimentally by Karaman et al.²¹⁾ in their study of deformation twinning, and the present results (Fig. 4) also confirm the clear influence of the grain orientation on deformation twinning.

Fig. 8.

Orientation dependence of the Schmid factor for perfect dislocations, msubscript_{{perfect disl}}, (left) and the corresponding partial dislocations of the dissociated dislocations (right), in uniaxial tension. msubscript_{l.p.disl} and msubscript_{t.p.disl} are the Schmid factors for the leading and the trailing partial dislocation, respectively. The red lines are iso-Schmid factor lines for the leading partial dislocation and the blue lines are for the trailing partial dislocation.

The Taylor analysis, which takes into consideration strain compatibility between neighboring grains, is also appropriate to explain some aspects of the orientation dependence of deformation twinning. The Taylor factor distribution for {111}<110> slip in a fcc alloy with a random grain orientation distribution subjected to uniaxial tension is well known.^22,23) Beladi et al.²⁴⁾ reported that grains with a Taylor factor of 2.6 or higher deformed predominantly by mechanical twinning and that grains with a Taylor factor less than 2.6 deformed by slip. High Taylor factor grains develop a higher dislocation density in order to maintain strain compatibility with the neighboring grains.²⁰⁾ This results in a higher strain hardening, particularly when a wide dislocation dissociation, associated with a low SFE, limits cross slip. The formation of deformation twins is promoted in grains with a large Taylor factor, i.e. grains with a <111> axis oriented along the tensile axis. In contrast grains with an orientation with a small Taylor factor, in particular grains with a <100>-type axis oriented parallel to the tensile axis, do not twin.¹⁵⁾ The results presented in Fig. 4 are consistent with this argument.

In his explanation for the preferred nucleation of deformation twins in grains with a large Taylor factor, Beladi et al.^16,24) argued that whereas in the grain interior most of the slip was achieved by a limited number of active slip systems, multiple slip systems were activated in the vicinity of grain boundaries to satisfy the requirement of strain compatibility between adjacent grains. Alternatively grain boundaries with a pronounced dislocation activity may act as preferred nucleation sites for deformation twins. It is well known that grain boundaries ledges can be sources of dislocations.²⁵⁾ Dislocations emitted from grain boundary ledges or from Frank-Reed dislocation sources can glide across the grains and pile up against grain boundaries as shown in the schematic of Fig. 9. These lattice dislocations can then react with grain boundary dislocations to form twin nuclei. When a critical stress concentration is reached these grain boundary twin nuclei grow into the grain as thin twin plates.

Fig. 9.

Schematic of the mechanism for the nucleation and growth of deformation twins from a grain boundary.

The grain size of the grains which undergo deformation-induced twinning was 1.5–2 times higher than the average grain size as shown in Fig. 3. Ueji et al. has shown that grain refinement (1.8 μm) inhibited deformation twinning.²⁶⁾ Although the mechanism for the inhibition of twinning by grain refinement is still unclear, the grain size effect could be explained by the contribution of the grain size to the excess free energy for the γ→ε phase transformation which increases when the austenite grain size is less than 30 μm.²⁷⁾

In order to explain the deformation texture evolution of TWIP steel, De Cooman et al. calculated the IPF for the tensile axis in uniaxial deformation.²⁸⁾ Assuming {111}<110> slip only, the orientations with <111>//tensile axis and <100>//tensile axis developed a higher intensity after deformation compared to the initially random texture. Assuming both {110}<110> slip and {111}<112> twinning, only the orientation with <100>//tensile axis developed a higher intensity after deformation. This fiber orientation is due to the rotation of the <111> axis to the <511> axis, which is close to <100>, by the twinning shear as shown in Fig. 10. The present results show that the orientation of the matrix of the twinning grains changed to <111>//RD and that no <100>//RD fiber orientation developed after a true strain of 0.2. This is due to the fact that the initial orientation of the twinned grains was never close to <100>//RD. The deformation twinning contributed to a clear <100>//RD fiber orientation but this did not significantly reduce the intensity of the <111>//RD fiber due to the limited volume fraction of deformation twinning as shown in Table 1.

Fig. 10.

Schematic illustrating the local orientation change associated with the formation of a twinned volume by shear deformation.

Figure 11(a) compares the measured and calculated stress-strain curves of Fe18Mn0.6C and Fe18Mn0.6C-2.5Al. The calculated tensile curves are based on the twining kinetics measured by in situ EBSD. An increase of the yield strength of 28 MPa/mass-% Al due to solid solution hardening and a reduction in work hardening and ultimate tensile strength due to the suppression of deformation twinning resulting from the higher SFE were taken into account for the steel containing 2.5 mass% Al.^16,24,25,26) Kim et al.^4,5) proposed a constitutive model for high Mn TWIP steel in which the densities of mobile and forest dislocations are coupled to account for the interaction between the two dislocation populations during deformation. In this model twinning is considered as a process which reduces the dislocation mean free path and increases the dislocation density, thereby increasing the work hardening. In the model the following empirical equation was used for the strain dependence of the deformation twin volume fraction:³⁾   

$$F=F_0{\left(1-exp\left[-\beta \left(\epsilon -{\epsilon }_{ini}\right)\right]\right)}^m$$

ε is the plastic strain, ε_int is the strain required for the initiation of twin formation, F₀ is the saturation deformation twin volume fraction, β and m are kinetic parameters. Figure 11(b) shows the work-hardening rate for Fe18Mn0.6C and Fe18Mn0.6C-2.5Al calculated on the basis of the constitutive model proposed by Kim et al.^4,5) The parameters related to the twinning behavior in Eq. (1) are listed in Table 2. The suppression of the deformation twinning by Al addition results in a higher value for ε_int and a lower value for F₀. The effect of Al on the twinning kinetics is clearly shown in Fig. 12 which compares the calculated and measured twinning volume fraction. The addition of Al also results in a lower work hardening and a reduction of the tensile strength of the Fe18Mn0.6C-2.5Al alloy, despite the considerable solid solution hardening by Al.

Fig. 11.

Comparison of measured and calculated (a) stress-strain and (b) work-hardening curves. The calculated curves incorporate the different deformation twinning kinetics of Fe18Mn0.6C and Fe18Mn0.6C-2.5Al.

Table 2. Parameters of the deformation twinning kinetics.

Steel	F0	εini	β	M
Fe18Mn0.6C	0.25	0.02	4.0	1.0
Fe18Mn0.6C-2.5Al	0.14	0.10	4.0	1.0

Fig. 12.

Comparison of calculated deformation twinning kinetics and measured deformation twinning fraction at 0.2 strain in Fe18Mn0.6C and Fe18Mn0.6C-2.5Al.

4. Summary

The influence of the addition of 2.5 mass% Al on the deformation twinning behavior of Fe18Mn0.6C TWIP steel was investigated by in situ EBSD. Deformation twins were predominantly nucleated at grain boundaries. Deformation twinning occurred preferably in grains with a high Taylor factor (M>2.7) and a higher Schmid factor on the leading partial relative to the training partial in tensile deformation. The kinetics of deformation twinning was suppressed by Al addition, resulting in a lower rate of work hardening. A constitutive model, which takes into account the kinetics of deformation twinning, was used to explain the correlation between the deformation twinning kinetics and the work hardening behavior. A key factor in the model is the dynamic Hall-Petch effect, the progressive reduction of the dislocation mean free path by the deformation twins.

Acknowledgement

The authors sincerely acknowledged the support of the POSCO Technical Research Laboratories. This research was supported by WCU (World Class University) program through the National Research Foundation of Korea, funded by the Ministry of Education, Science and Technology (R32-10147).

References

• 1)   B. C.  De Cooman,  O.  Kwon and  K.-G.  Chin: Mater. Sci. Technol., 28 (2012), No. 5, 513.
• 2)   S.-J.  Lee,  J.  Kim,  S. N.  Kane and  B.C.  De Cooman: Acta Mater., 59 (2011), No. 17, 6809.
• 3)   O.  Bouaziz,  S.  Allain,  C. P.  Scott,  P.  Cugy and  D.  Barbier: Curr. Opin. Solid State Mater. Sci., 15 (2011), No. 4, 141.
• 4)   J.  Kim,  Y.  Estrin,  H.  Beladi,  S.  Kim,  K.-G.  Chin and  B. C.  De Cooman: Mater. Sci. Forum, 654–656 (2010), 270.
• 5)   J.  Kim,  Y.  Estrin,  H.  Beladi,  I.  Timokhina,  K.-G.  Chin,  S.-K.  Kim and  B. C.  De Cooman: Metall. Mater. Trans. A, 43 (2012), No. 2, 479.
• 6)   S.  Allain,  J.-P.  Chateau,  O.  Bouaziz,  S.  Migot and  N.  Guelton: Mater. Sci. Eng. A, 387–389 (2004), 158.
• 7)   S.  Curtze,  V.-T.  Kuokkala, A, Oikari, J. Talonen and H. Hänninen: Acta Mater., 59 (2011), No. 3, 1068.
• 8)   A.  Saeed-Akbari,  J.  Imlau,  U.  Prahl and  W.  Bleck: Metall. Mater. Trans. A, 40 (2009), No. 13, 3076.
• 9)   J. S.  Jeong,  W.  Woo,  K. H.  Oh,  S. K.  Kwon and  Y. M.  Koo: Acta Mater., 60 (2012), No. 5, 2290.
• 10)   J.  Kim,  S.-J.  Lee and  B. C.  De Cooman: Scr. Mater., 65 (2011), No. 4, 363.
• 11)   K.-G.  Chin,  C.-Y.  Kang,  S. Y.  Shin,  S.  Hong,  S.  Lee,  H. S.  Kim,  H.-K.  Kim and  N. J.  Kim: Mater. Sci. Eng. A, 528 (2011), No. 6, 2922.
• 12)   I.  Jung,  J.  Mola,  D.  Chae and  B. C.  De Cooman: Steel Res. Int., 81 (2010), No. 12, 1089.
• 13)   A. J.  Schwartz: Electron Backscattering Diffraction in Materials Science, Springer Science and Business Media, New York, (2009).
• 14)   D.  Raabe,  M.  Sachtleber,  Z.  Zhao,  F.  Roters and  S.  Zaefferer: Acta Mater., 49 (2001), 3433.
• 15)   D.  Barbier,  N.  Gey,  S.  Allain,  N.  Bozzolo and  M.  Humbert: Mater. Sci. Eng. A, 500 (2009), No. 1–2, 196.
• 16)   H.  Beladi,  I. B.  Timokhina,  Y.  Estrin,  J.  Kim,  B. C.  De Cooman and  S. K.  Kim: Acta Mater., 59 (2011), No. 20, 7787.
• 17)   J. A.  Venables: Philos. Mag., 30 (1974), No. 5, 1165.
• 18)   S.  Mahajan and  G. Y.  Chin: Acta Metall., 21 (1973), No. 10, 1353.
• 19)   H.  Idrissi,  K.  Renard,  L.  Ryelandt,  D.  Schryvers and  P. J.  Jacques: Acta Mater., 58 (2010), No. 7, 2464.
• 20)   J. B.  Cohen and  J.  Weertman: Acta Metall., 11 (1963), No. 8, 996.
• 21)   I.  Karaman,  H.  Sehitoglu,  K.  Gall,  Y. I.  Chumlyakov and  H. J.  Maier: Acta Mater., 48 (2000), No. 6, 1345.
• 22)   W. F.  Hosford: The Mechanics of Crystals and Textured Polycrystals, Oxford University Press, Oxford, (1993).
• 23)   J. J.  Jonas and  L. S.  Tóth: Scr. Metall., 27 (1992), No. 11, 1575.
• 24)   H.  Beladi,  P.  Cizek and  P. D.  Hodgson: Acta Mater., 58 (2010), No. 9, 3531.
• 25)   L. E.  Murr: Metall. Trans. A, 6 (1975), No. 3, 505.
• 26)   R.  Ueji,  N.  Tsuchida,  D.  Terada,  N.  Tsuji,  Y.  Tanaka,  A.  Takemura and  K.  Kunishige: Scr. Mater., 59 (2008), No. 9, 963.
• 27)   S.  Takaki,  H.  Nakatsu and  Y.  Tokunaga: Mater. Trans. JIM, 34 (1993), No. 6, 489.
• 28)   B. C.  De Cooman,  J.  Kim and  S.  Lee: Scr. Mater., 66 (2012), No. 12, 986.