Effects of Temperature and Strain Rate on Deformation Twinning in Fe–Si Alloy

Abstract

In this study, the effects of temperature and strain rate on the deformation twinning behavior in Fe–5%Si alloy were investigated. Tensile tests at various temperatures (198–248 K) and strain rates (0.1–0.01 s⁻¹) were carried out up to a strain of 0.8%. The presence of deformation twins was confirmed in all the tensiled specimens. The results of crystal orientation analysis by SEM–EBSP indicated that the {112} plane is the twinning plane for the twins formed in the grains. The area fraction and the width of deformation twin increased with decreasing temperature or with increasing strain rate. This tendency can be explained by the relationship between the resolved shear stress and the dislocation velocity.

1. Introduction

When a tensile stress is applied to a BCC (body–centered cubic) steel at room temperature under static strain-rate conditions, plastic deformation occurs via dislocations. While plastic deformation is maintained only by a dislocation mechanism, deformations in the range from 0.0001 to 1000 s⁻¹ are controlled by a thermally activated process,^1,2,3) where the flow stress depends on temperature and strain rate.^4,5,6)

It is well known that BCC steels have a brittle–ductile transition temperature and that fracture behavior from brittle to ductile changes with increasing temperature.^7,8,9) In pure Fe^10,11) and Fe–Si alloys,^12,13) a low temperature deformation occurs by a combination of deformation twinning and dislocation motion. It is generally accepted that a pile–up dislocation against a barrier provides a suitable stress concentration to initiate twinning.^14,15) Therefore, it is considered that a deformation twinning behavior depends on temperature and strain rate if dislocation motion affects the initiation of deformation twinning.

In this study, the effects of temperature and strain rate on the area fraction and width of the deformation twin in Fe–5%Si alloy were investigated using tensile testing at various temperatures and strain rates.

2. Experimental Procedure

Fe–5%Si alloy samples prepared by an induction melting method were used in this study. The chemical composition of the Fe–5%Si alloy is shown in Table 1. After homogenization at 1473 K for 120 min in an ambient atmosphere, alloy ingots were multi–pass rolled (starting temperature of 1473 K and finishing temperature of 1123 K) followed by air cooling. Next, the samples were heat–treated at 1073 K for 20 min in an ambient atmosphere, and these hot rolled plates were multi–pass rolled at 1073 K to reduce their thickness by 90% followed by water cooling. These sheets were then annealed at 1123 K for 30 min in an Ar atmosphere to obtain the fully recrystallized microstructure with a mean grain size of 180 μm. Simanaka et al.¹⁶⁾ measured the grain size dependence of core loss in Fe–3.2%Si alloys and reported the minimum value at around 150 μm. Furthermore, Shiozaki et al.¹⁷⁾ reported that an optimum grain size was not dependent on the Si content. For these reasons, an optimum grain size was selected. Tensile tests were conducted using conventional testing machines with small tensile test specimens cut from annealed sheets using a wire electrical discharge machine (DWC90C, Mitsubishi Electric Corp.). The gauge length, width, and thickness of the test pieces for tensile tests were 6.0, 2.0, and 1.2 mm, respectively. Temperature and strain-rate dependencies of the flow stress and twinning behavior were investigated. To investigate the temperature dependence, an Instron testing machine (Model 5582) equipped with a thermostat chamber was used. Tensile tests were conducted at various temperatures ranging from 198 K to 248 K at a constant crosshead speed of 0.0006 mms⁻¹ (initial strain rate of 0.0001 s⁻¹) up to a plastic strain of 0.8%. On the other hand, for strain rate dependence measurements, tensile tests were conducted at various crosshead speeds from 0.06 to 0.6 mms⁻¹ (initial strain rates from 0.01 to 0.1 s⁻¹) at a constant temperature of 298 K up to 0.8% plastic strain using an Autograph AGS–10kNX (Shimadzu Corp.). The tensile axis was parallel to the rolling direction (RD). Deformation twinning behavior of as–annealed samples and those after tensile tests were examined using optical microscopy and a JEOL JSM–7001F field emission scanning electron microscope (FE–SEM) equipped with an Oxford Instruments HKL electron backscattering diffraction (EBSD) system and JEOL JEM–3010 transmission electron microscope (TEM). The FE–SEM and TEM samples were observed using accelerating voltages of 15 kV and 300 kV, respectively. The area fraction of the deformation twin and the thickness resulting from each preparation condition were measured from the obtained FE–SEM images.

Table 1. Chemical composition of Fe–5%Si alloy.

C	Si	Mn	P	S	Al	N	Fe
0.0047	4.99	<0.01	0.002	0.0009	0.002	0.0022	Bal.
(in mass%)

3. Results

3.1. Microstructure of As–annealed Samples

Figure 1 shows the optical microstructure (a) and FE–SEM image (b) of the as–annealed Fe–5%Si alloy. The as–annealed alloy had slightly elongated grains along the RD with a mean grain size of 180 μm. TEM observations showed that each grain was a fully recrystallized ferritic grain. No deformation twins were observed in this annealed alloy. In the Fe–Si alloy containing more than 5 mass% Si, Fe₃Si particles, a kind of intermetallic compound, may affect twinning behavior. No Fe₃Si particles were identified by TEM in these samples. Shin et al.¹⁸⁾ investigated the existence of intermetallic compounds in Si steels with various Si contents for specimens with various cooling rates after being annealed at 1123 K for 1 h and reported that Fe₃Si particles did not exist in Si steel samples with a Si content less than 5.4 wt% regardless of the cooling rate. Our observations are in agreement with this report. Because the visual field for TEM observation is limited to ~10 μm², it should be noted that there may be Fe₃Si particles outside this area. However, if any Fe₃Si particles exist, their density in this alloy is low, and it can be assumed that any Fe₃Si particles do not have a large influence on the stress–strain relationship and twinning behavior.

Fig. 1.

Microstructures of annealed Fe–5%Si alloy; Optical micrograph (a) and FE–SEM image (b). ND, RD and TD indicate normal direction, rolling direction and transverse direction, respectively.

3.2. Stress–strain Relationship

Figure 2 shows the nominal stress–nominal plastic strain curves obtained from tensile testing at various temperatures and strain rates. As can be seen from these figures, all tensile tests were successfully undertaken to 0.8% plastic strain. The flow stress at 0.8% plastic strain tended to increase with decreasing temperature and increasing strain rate. However, the dependence of the flow stress on temperature and strain rate were very small. Uenishi and Teodosiu¹⁹⁾ undertook tensile tests at various strain rates and Si contents and found a decrease in the temperature and strain rate dependence on the flow stress at 5% tensile strain with increasing Si content. In Fe–Si alloys, interactions between solute atoms and dislocations form kink pairs. The motion of a screw dislocation with a kink pair affects both sideward motion of a kink and double kink nucleation. It is considered that the increase in Si content affects both of these factors. Sato and Meshii²⁰⁾ reported that the temperature dependence of a stress for sideward motion of a kink overcoming a solute atom is smaller than that for double kink formation. As shown in Fig. 2, the temperature and strain rate dependencies of the flow stress were very small. It is considered that sideward motion of a kink is the rate-controlling process for tensile deformation in a Fe–5%Si alloy.

Fig. 2.

Nominal stress–nominal plastic strain curves obtained from tensile test at various temperatures and strain rates.

3.3. Deformation Twinning Behavior

Figure 3 shows an example of a deformation twin identified from the SEM/EBSD analysis of the sample with 0.8% plastic strain at 0.01 s⁻¹ and 298 K. The SEM image shown in Fig. 3(a) illustrates a typical deformed microstructure. Band–like features with a thickness across the grain were identified. Crystallographic orientations around this feature were analyzed. A typical crystal–orientation map is shown in Fig. 3(b), where the color of each point indicates the crystallographic direction parallel to the tensile axis corresponding to the stereographic triangle shown lower–right of the image. Band–like features appear as approximately parallel strip features that had widths of the order of a micrometer, and their crystal orientation was quite different from that of the grain. The measured orientations for the area in Fig. 3(b) are shown in the <112> pole figure in Fig. 3(c). Blue and red points in this figure indicate the <112> direction obtained from the matrix or band area, respectively. The orientations measured from the band–like area shared the pole with the matrix orientation, indicating that the {112} plane is the twinning plane for the twins formed in this grain. This {112} twin was found in all tensile specimens (all temperatures and strain rates). As shown previously, the existence of deformation twins could be identified by FE–SEM imaging.

Fig. 3.

Typical example of identification of deformation twins based on SEM/EBSD analysis. An SEM image (a) and inverse pole figure map (b) showing the typical deformed microstructure. A {112} pole figure showing the measured orientations of the matrix grain and the deformation twins from IPF map.

Figure 4 shows FE–SEM images obtained from tensile specimens at 0.8% plastic strain. The deformation twins across the grain were found in all tensile specimens (all temperatures and strain rates). The area fractions of the deformation twin were estimated from FE–SEM images of 1200 μm × 900 μm areas using image analysis software. The obtained area fractions of the deformation twins are also shown in the upper–right part of the FE–SEM images. Figure 5 plots the temperature and strain rate dependence of the area fraction of the deformation twin. The area fraction of the deformation twin increased with decreasing temperature, increasing strain rate. Figure 6 shows the temperature and strain rate dependence of the width of the twin. In this figure, the average value and standard deviation of 20–40 twin widths derived from FE–SEM images are shown. The twin width increased with decreasing temperature and increasing strain rate. The deformation twin width varied a lot for each deformation condition. A former study by Mizuguchi et al.²¹⁾ confirmed from FE–SEM/EBSP observation of fractured specimens that the grain orientation of deformation twinning in a polycrystalline Fe–5%Si alloy varies significantly. The angular difference between the sample surface and the twinning plane depends on the crystal orientation. In this study, the grain orientation of deformation twinning was not analyzed. However, it is considered that the twin width variation is predominantly the result of the variation of the crystal orientation by the deformation twins.

Fig. 4.

FE–SEM images obtained from tensiled specimen at the strain of 0.8%.

Fig. 5.

Area fraction of deformation twin as a function of temperature (a) and strain rate (b).

Fig. 6.

Average width of deformation twin as a function of temperature (a) and strain rate (b).

4. Discussion

Our experimental results indicate that the area fraction of deformation twins and twin width increased with increasing strain rate and decreasing temperature, in other words, higher stress conditions. Many researchers have suggested that a pile–up dislocation against a barrier provides a suitable stress concentration for twin initiation. The initiation and propagation mechanisms of deformation twins have been published,^22,23,24) and are briefly summarized here. Figure 7(a) shows the schematic illustration of a tensile test specimen with fully recrystallized microstructure just after starting a tensile test. Perfect dislocations glide on the primary slip plane within the grain, which results in a stress concentration due to dislocation pile–ups at barriers such as grain boundary. This figure shows the dislocations that are directly related to deformation twin formation; therefore, dislocation–dislocation interactions such as dislocation tangle and dislocation cell structures are ignored. After that, a deformation twin initiates from the stress–concentrated area shown in Fig. 7(b). It is considered that the nucleation of a deformation twin is affected by the partial twinning dislocation, $\frac{a}{6}$ 〈111〉, formed from a $\frac{a}{2}$ 〈111〉 dislocation by the dissociative reaction below.   

$$\frac{a}{2}\left[\stackrel{}{1}\stackrel{}{1}\stackrel{}{1}\right]\to \frac{a}{3}\left[\stackrel{}{1}\stackrel{}{1}\stackrel{}{2}\right]+\frac{a}{6}\left[\stackrel{}{1}\stackrel{}{1}\stackrel{-}{1}\right]$$(1)

Around a barrier, the dislocations are piled up in a high energy state. In order to reduce the energy concentration, the dislocation reaction shown below occurs.   

$$\frac{a}{6}\left[\stackrel{}{1}\stackrel{}{1}\stackrel{-}{1}\right]\to -\frac{a}{3}\left[\stackrel{}{1}\stackrel{}{1}\stackrel{-}{1}\right]+\frac{a}{2}\left[\stackrel{}{1}\stackrel{}{1}\stackrel{-}{1}\right]$$(2)

Generated $\frac{a}{2}$ 〈111〉 dislocations are repelled from the twin boundary and move to the grain interior, leaving a $\frac{a}{3}$ 〈111〉 partial dislocation at the twin boundary. As shown by the arrows in Fig. 7, moving of $\frac{a}{3}$ 〈111〉 partial dislocations provides the mechanism for the propagation of deformation twinning in a lengthwise direction by shear stress due to external stresses. At the same time, the partial twinning dislocation $\frac{a}{6}$ 〈111〉 rotates around a $\frac{a}{3}$ 〈112〉 pole dislocation to grow the deformation twin, as shown in Fig. 7(c). In this way, the deformation twin grows in width. As described above, a deformation twin propagates under an action of the motion of $\frac{a}{3}$ 〈111〉 partial dislocation. Next, the temperature and strain rate dependencies of the area fraction of the deformation twin and twin width are discussed from the point of view of the dislocation velocity.

Fig. 7.

Schematic illustration of deformation twinning behavior.

The velocity of dislocation motion in a Fe–Si alloy was measured by Saka and Imura,^25,26) Erickson,²⁷⁾ Stein and Low,²⁸⁾ and Moon and Vreeland.²⁹⁾ They reported that the relationship between velocity, ν, and applied shear stress resolved for the slip plane, τ, is as follows:   

$$\nu =v_0{\left(\frac{\tau }{{\tau }_0}\right)}^m$$(3)

where τ₀ and m are parameters depending on temperature and type of dislocation, and ν₀ is a constant. The Taylor factor, always designated as M, is used in the analysis of the plastic deformation of polycrystalline metals and is often defined by the following equation:   

$${\sigma }_y=M{\tau }_c$$(4)

Where σ_y represents the yield stress of a specific sample and τ_c represents the critical resolved shear stress of the activated slip system. The Taylor factor could convert external tensile stress into shear stress, and the critical resolved shear stress could be calculated by a yield stress in substitution for tensile stress. Former researchers^{25,26,27,28,29)} reported a dislocation velocity under the resolved applied shear stress of 120–200 MPa in Fe–3–3.3%Si increases with increasing shear stress. A dislocation velocity in the Fe–5%Si alloys was not measured in this study; however, it is predicted that this relationship is applicable to the Fe–5%Si alloy.

The results of present study shown in Figs. 5 and 6 indicate that the area fraction of deformation twins and twin width increased with increasing strain rate and decreasing temperature, in other words, sufficiently high stress conditions. As described above, it is widely considered that pile–up dislocation against a barrier (such as a grain boundary), provides a suitable stress concentration to initiate a deformation twin. In the polycrystalline pure Fe, twinning yield stress is independent of the strain rate.¹¹⁾ Therefore, it is considered that the initiation stress for a deformation twin (twinning stress) is also not dependent on the strain rate. This tendency could be predicted for the temperature dependence of the Fe–5%Si alloy. Our experimental results shown in Fig. 5 indicate that the area fraction of deformation twin depends on temperature and strain rate, and increased with the increasing of higher stress condition. These results could be explained by the existence of a deformation twin initiated between the twinning stress and 0.8% stress. Thus, all the deformation twins observed in Fig. 5 did not initiate at the twinning stress. After the tensile tests started, the deformation twin initiates at the twinning stress. As the tensile stress increases, the stress concentration at barriers enhances due to dislocation pile–ups. This stress concentration increases as the velocity of the dislocations increases. Thus, the temperature and strain rate dependence of the area fraction of deformations can be explained. On the other hand, partial twinning dislocation by the dissociative reaction widens a twin by rotating around a pole dislocation influenced by external stress. Therefore, the results of Fig. 6 can be explained from the point of view of dislocation velocity.

Takeuchi and Ikeda³⁰⁾ reported a propagation velocity of a {112} twin tip of 2.5 mmμs⁻¹. It is considered that this velocity corresponds with the velocity of the $\frac{a}{3}$ 〈111〉 partial dislocation. Therefore, the time necessary for a deformation twin to propagate a crystal grain is calculated to be 0.6 ns considering an average grain size of 150 μm. During 0.6 ns, the $\frac{a}{3}$ 〈111〉 partial dislocation can move about 1.5 μm, and this agrees with the twin width. This indicates that the velocity of the dislocation contributing to the growth of the twin width is equal to that of the $\frac{a}{3}$ 〈111〉 partial dislocation.

5. Conclusion

In this study, the effects of temperature and strain rate on the area fraction and width of deformation twins in Fe–5%Si alloys were investigated using tensile testing up to a plastic strain of 0.8%. The results are summarized as follows:

(1) The flow stress at the plastic strain of 0.8% increased with decreasing temperature and increasing strain rate.

(2) The presence of deformation twins with the twinning plane of {112} was confirmed in all tensile specimens by crystal orientation analyses with SEM–EBSP.

(3) The area fraction and the width of the deformation twins increased with decreasing temperature or with increasing strain rate. This tendency can be explained by the relationship between the resolved shear stress and the dislocation velocity.

Acknowledgement

We would like to express our sincere thanks to Prof. Noriyuki Tsuchida (Graduate School of Engineering, University of Hyogo, Japan) for experimental support. This study was financially supported by 22nd Research Promotion Grant from the Iron and Steel Institute of Japan. The author gratefully appreciates all of the support received.

References

• 1)   M.  Kato,  S.  Kumai and  S.  Onaka: Zairyou-kyoudo-gaku, Asakura-syoten, Tokyo, (1999), 81.
• 2)   M.  Kato: Introduction to the Theory of Dislocations, Shokabo, Tokyo, (1999), 103.
• 3)   H.  Conrad and  S.  Frederick: Acta Metall., 10 (1962), 1013.
• 4)   S.  Sakui: Tetsu-to-Hagané, 57 (1971), 2300.
• 5)   S.  Tsuyama,  H.  Tsunoda and  Y.  Hosoda: Tetsu-to-Hagané, 80 (1994), 401.
• 6)   S.  Sakui,  K.  Sato and  T.  Sakai: Tetsu-to-Hagané, 58 (1972), 842.
• 7)   K. F.  Ha,  C.  Yang and  J. S.  Bao: Scr. Metall Mater., 30 (1994), 1065.
• 8)   F.  Sorbello,  P. E. J.  Flewitt,  G.  Smith and  A. G.  Crocker: Acta Mater., 57 (2009), 2646.
• 9)   Y.  Qiao and  A. S.  Argon: Mech. Mater., 35 (2003), 129.
• 10)   T.  Tanaka and  S.  Watanabe: Acta Metall., 19 (1971), 991.
• 11)   S.  Sakui and  T.  Sakai: Tetsu-to-Hagané, 58 (1972), 1438.
• 12)   F.  Sorbello,  P. E. J.  Flewitt,  G.  Smith and  A. G.  Crocker: Acta Mater., 57 (2009), 2646.
• 13)   D.  Hull: Acta Metall., 9 (1961), 191.
• 14)   R.  Priestner and  W. C.  Leslie: Philos. Mag., 11 (1965), 895.
• 15)   W. A.  Biggs and  P. L.  Pratt: Acta Mater, 6 (1958), 694.
• 16)   H.  Shimanaka,  Y.  Ito,  T.  Irie,  K.  Matsumura,  H.  Nakamura and  Y.  Shono: Energy Efficient Electrical Steels, ed. by A. R. Marder and E. T. Stephenson, TMS–AIME, PA, (1981), 193.
• 17)   M.  Shiozaki and  Y.  Kurosaki: J. Mater. Eng., 11 (1989), 37.
• 18)   J. S.  Shin,  J. S.  Bae,  H. J.  Kim,  H. M.  Lee,  T. D.  Lee,  E. J.  Lavernia and  Z. H.  Lee: Mater. Sci. Eng. A, 407 (2005), 282.
• 19)   A.  Uenishi and  C.  Teodosiu: Acta Mater., 51 (2003), 4437.
• 20)   A.  Sato and  M.  Meshii: Acta Metall., 21 (1973), 753.
• 21)   T.  Mizuguchi,  K.  Ikeda,  N.  Karasawa and  Y.  Tanaka: Mater. Sci. Forum, 783–786 (2014), 910.
• 22)   K.  Ogawa: Bull. Jpn. Inst. Met., 5 (1966), 309.
• 23)   A. H.  Cottrell and  B. A.  Bilby: Philos. Mag., 42 (1951), 573.
• 24)   J.  Takamura: Zairyoukyoudo-no-kiso, Kyoto University, Kyoto, (1999), 242.
• 25)   H.  Saka and  T.  Imura: Phys. Stat. Sol.(a), 19 (1973), 653.
• 26)   H.  Saka and  T.  Imura: J. Phys. Soc. Jpn., 32 (1972), 702.
• 27)   J. S.  Erickson: J. Appl. Phys., 33 (1962), 2499.
• 28)   D. F.  Stein and  J. R.  Low: J. Appl. Phys., 31 (1960), 362.
• 29)   D. W.  Moon and  T.  Vreeland, Jr.: J. Appl. Phys., 39 (1968), 1766.
• 30)   T.  Takeuchi and  S.  Ikeda: Aki-no-bunkakai kouenn-yokoushuu, The Physical Society of Japan, Tokyo, (1966), 12.