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Effects of Ni and Mn on brittle-to-ductile transition in ultralow-carbon steels
Materials Science & Engineering A 682 (2017) 370–375
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Effects of Ni and Mn on brittle-to-ductile transition in ultralow-carbon steels
MARK
⁎
Masaki Tanakaa, , Kenta Matsuoa, Nobuyuki Yoshimurab, Genichi Shigesatob, Manabu Hoshinob, Kohsaku Ushiodab, Kenji Higashidaa,c a b c
Department of Materials Science and Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan Technical Research & Development Bureau , Nippon Steel & Sumitomo Metal Corporation, 20-1 Shintomi, Futtsu, Chiba 293-8511, Japan Sasebo College, National Institute of Technology, 1-1 Okishimachi, Sasebo, Nagashiki 857-1193, Japan.
A R T I C L E I N F O
A BS T RAC T
Keywords: Steel Dislocations Fracture Twinning Dislocation shielding DBT
The temperature dependence of the effective stress indicated that both Ni and Mn induce solid solution softening at low temperatures. The activation energy for dislocation glide was obtained from the temperature dependence of the activation volume and effective shear stress. Either Ni or Mn decreases the activation energy for dislocation glide, which suggests that both Ni and Mn decrease the brittle-to-ductile transition (BDT) temperature. However, the temperature dependence of the absorbed energy for fracture showed that the transition temperature decreases with Ni but increases with Mn. Fracture surfaces tested at 100 K indicated transgranular fracture at 2 mass% Ni and intergranular fracture at 2 mass% Mn, which suggests a decrease in energy for grain boundary fracture with Mn. The mechanism behind the opposite effects of Ni and Mn on the transition temperature of ultralow-carbon steels was examined on the basis of dislocation shielding theory.
1. Introduction Manganese (Mn) is an important element added in steel that reduces the grain size and increases the yield stress at room temperature (RT). It also influences the stability of austenite, decreasing a martensite-start temperature. Mechanical properties of transformation-induced plasticity-aided steels are influenced by the Mn, which is mainly due to the change in microstructures with Mn [1–3]. In case of ferrite single phase steels, Mn and nickel (Ni) show similar effects on the mechanical properties. Okazaki, Uenish and Teodosiu [4,5] reported the temperature dependence of the yield stresses for titaniumadded Fe–1 at% Ni and Fe–1 at% Mn, which showed solid solution hardening at RT and solid solution softening at low temperatures or high-strain rates. The solid solution softening suggests that Ni and Mn increase the dislocation velocity at low temperatures. Maeno et al. [6] reported that the decrease in the brittle-to-ductile transition (BDT) temperature with increasing Ni in steel can be explained by the increased dislocation velocity at low temperatures. This suggests that increasing the Mn content decreases the BDT temperature. However, the effect of Mn on toughness is still controversial. For instance, Jolley [7] reported that the BDT temperature of furnace-cooled ferrite with a single phase increases with up to 1.8 mass% Mn, while the BDT temperature of ferrite with cementite decreases with Mn. Yamanaka
⁎
and Kobayashi [8] reported a complex trend for the BDT temperature with Mn. The BDT temperature decreases with increasing Mn to a minimum at 2 mass% Mn and then increases with higher Mn content. They investigated the microstructure and pointed out that the microstructure depends on the Mn content; uniaxial ferrite and massive ferrite are dominant with low Mn content and 3 mass% Mn, respectively. Specimens with a Mn content of 4.8 mass% exhibit lath martensite in massive ferrites. Mn has complicated effects on the microstructure, which include grain refinement, micro-segregation, and changes to the morphology of precipitates. Mn produces many effects, which makes it difficult to understand the specific effect of Mn on the fracture toughness and BDT. In the present study, therefore, the effects of Mn and Ni as solute atoms on BDT were clarified by using single-phase ferrites with different concentrations of Mn and Ni but nearly the same grain sizes. The mechanism behind the changes in the BDT temperature with Mn and Ni was examined on the basis of dislocation shielding theory [9]. 2. Experimental procedure Table 1 presents the chemical compositions of the materials employed in this study. The base material was ultralow-carbon steel with a C concentration of less than 20 ppm. For the specimens, 1 or 2
Corresponding author. E-mail address: [email protected] (M. Tanaka).
http://dx.doi.org/10.1016/j.msea.2016.11.045 Received 30 August 2016; Received in revised form 12 November 2016; Accepted 12 November 2016 Available online 20 November 2016 0921-5093/ © 2016 Elsevier B.V. All rights reserved.
Materials Science & Engineering A 682 (2017) 370–375
M. Tanaka et al.
Table 1 Chemical compositions of the employed materials.
0Mn 1Mn 2Mn 1Ni 2Ni
C
Si
Mn
P
S
Ni
Ti
Al
N
0.0017 0.0018 0.0018 0.0019 0.0019
< 0.01 < 0.01 < 0.01 < 0.01 < 0.01
< 0.01 0.97 1.95 < 0.01 < 0.01
< 0.01 < 0.01 < 0.01 < 0.01 < 0.01
< 0.001 < 0.001 < 0.001 < 0.001 < 0.001
< 0.01 < 0.01 < 0.01 1.01 2.02
< 0.002 < 0.002 < 0.002 < 0.002 < 0.002
0.03 0.03 0.03 0.03 0.03
< 0.001 < 0.001 < 0.001 < 0.001 < 0.001
mass% of Ni or Mn was added to the base material and labelled as 0Mn, 1Mn, 2Mn, 1Ni, and 2Ni. The grain sizes of 0Mn, 1Mn, 2Mn 1Ni and 2Ni were measured to be 147, 91, 59, 86, and 78 µm, respectively. The parallel portion and width of the tensile specimens were 8 and 2 mm, respectively, and they had a thickness of 0.9 mm. Strain gages were attached to the parallel portions of the specimens. The test temperature was varied between 77 and 350 K. The initial strain rate of the tensile tests was set to 4.2×10−4 s−1, and a Shimadzu AG-IS was used for the tests. Strain-rate jump tests were performed in order to obtain the activation volume. The strain rate was jumped by one order of magnitude. The impact fracture energy of the specimens was measured by using an instrumental impact fracture machine (Tanaka MIT-D05KJ). The blade speed of the impact tests was set to be 3.3×10−1 ms−1. 3. Results Fig. 1 shows the nominal stress–strain curves of 1Ni, 2Ni, 0Mn, 1Mn, and 2Mn measured at 77 K and RT. Yield drop was observed at RT for all specimens. At RT, the yield stress of 0 M is the lowest, that of 2Ni was higher than that of 1Ni, and the yield stress of 2Mn was higher than that of 1Mn. These results demonstrate solid solution hardening. On the other hand, at 77 K, the yield stress of 2Ni was lower than that of 1Ni, and the yield stress of 2Mn was lower than that of 1Mn. This indicates that both Ni and Mn induce solid solution softening at 77 K. The temperature dependence of the yield stress was obtained next. Because these materials were low-carbon steels, some specimens showed yield drop, thus, 0.2% proof stress was taken as the yield stress for the specimens that showed continuous yielding while the lower-yield point was taken as the yield stress for those showed the yield drop. Fig. 2 shows the temperature dependence of the yield stress for 1Ni, 2Ni, 0Mn, 1Mn, and 2Mn. The yield stress decreased with increasing temperature; the temperature dependence then a nearly negligible above 300 K. The trend is the same as that typically seen in bcc crystals. It is worth pointing here that slight hump is also seen in between 125 K and 225 K in polycrystalline 0Mn. It is much significant reported in
Fig. 2. Temperature dependence of the yield stress.
single crystalline iron [10]. The normal temperature dependence of the yield stress originates from the process that dislocations overcoming short-range barriers through a thermally activated process. In bcc crystals, the dominant thermally activated process for dislocation glide at low temperatures is overcoming the Peierls barrier. Therefore, temperature dependence of yield stress will be investigated next. The yield stress can be expressed as follows:
σy = σe + σath,
(1)
where σe and σath are the effective stress and athermal stress, respectively. The effective stress and athermal stress are temperaturedependent and temperature-independent, respectively. In the present study, the yield stress at 350 K was defined as the athermal stress. Fig. 3 shows the temperature dependence of the measured effective stresses for 1Ni, 2Ni, 0M, 1Mn, and 2Mn according to Eq. (1). The effective stress decreased with increasing Ni or Mn content, which indicates that the solid solution softening at low temperatures in Fig. 2
Fig. 1. Nominal stress–strain curves from 1Ni, 2Ni, 0Mn, 1Mn, and 2Mn tested at 77 K and RT.
Fig. 3. Temperature dependence of the effective stress.
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originates from the decreased effective stress at low temperatures. Here, the effective stresses of 1Ni and 1Mn were nearly the same. The effective stresses of 2Ni and 2Mn were also nearly the same. This suggests that Ni and Mn have nearly the same effect on the dislocation velocity, especially at low temperatures where the dominant elementary process for dislocation glide is overcoming the Peierls barrier. Dislocations are assumed to overcome the Peierls barrier by forming double-kink pairs because the energy barrier to form double-kink pairs is less than that to overcome the Peierls barrier without forming double-kink pairs. The effective stress at 0 K was estimated by extrapolation in Fig. 3 with parabolic curves expect for 0Mn since it does not fit to a single parabolic curve. It was estimated to be 818, 770, 702, and 684 MPa for 1Mn, 1Ni, 2Mn, and 2Ni, respectively. These values suggest that Ni or Mn decreases the double-kink pair nucleation energy in more than 2 mass%. The dislocation velocity is expressed as follows:
v=
⎛
⎞
⎝
kT ⎠
Fig. 5. Temperature dependence of the absorbed energy in the impact fracture tests.
ΔG v0 τem exp ⎜ − ⎟,
be 0.97, 0.78, 0.8, and 0.6 eV, respectively. The value of 0Mn was not obtained since the values of activation volume with low and high effective stress were not obtainable in this study. Thus, the focus here should be the relative values with Ni or Mn. Both Ni and Mn decrease the activation energy for dislocation glide. That is, the activation energy for dislocation glide decreases with a Ni or Mn component. Maeno et al. [6] reported that the decrease in the BDT temperature with increasing Ni content in interstitial free (IF) steel can be understood by the increased dislocation mobility at low temperatures with increasing Ni content. Therefore, the changes in the BDT temperature with Ni and Mn were investigated. Fig. 5 shows the temperature dependence of the absorbed energy from 1Ni, 2Ni, 0Mn, 1Mn and 2Mn. The BDT temperatures of 0Mn, 1Ni, and1Mn were nearly the same, while adding 2 mass% Ni or Mn clearly affected the BDT temperature. The BDT temperature of 2Ni decreased approximately 50 K from that of 0Mn, while the temperature of 2Mn increased approximately 30 K. The reversed effects of Ni and Mn on the BDT temperatures cannot be explained solely by the change in dislocation velocity with those elements because both Ni and Mn increase the dislocation mobility, as shown in Fig. 4. The reason why Ni and Mn have completely different effects on the BDT temperature even though both elements decrease the dislocation mobility is discussed next.
(2)
whre v0 and m are constants, τe is the effective shear stress, k is the Boltzmann constant, T is the absolute temperature, and ΔG is the activation energy for dislocation glide. The decrease in the effective stress with Ni or Mn, as shown in Fig. 3, suggests that Ni and Mn decrease the value of ΔG in Eq. (2) and that the decreases in value are nearly the same at least up to a concentration of 2 mass%. The activation energy in Eq. (2) can be obtained by integrating the activation volume V* with respect to the effective stress as follows:
V* = −
dΔG , ΔG = − dτe
∫ V *dτe,
with V * ≡ kT
∂ ln γ ̇ ∂ ln ε ̇ ≈ kTM , ∂τe ∂σe (3)
where M is a Taylor factor of 2 for bcc [11] and γ˙ and ε˙ are the shear strain rate and strain rate along the tensile direction in tensile tests, respectively. In order to estimate the change in the activation energy, strain rate jump tests were performed at various temperatures. Fig. 4 shows the shear stress dependence of the activation volume. The activation volume was normalised with b3, where b is the Burgers vector of alpha iron at 0.248×10−9 m. The activation volume decreases with the effective shear stress. The effective shear stress at the activation volume of 0 was expected to be the effective shear stress at 0 K estimated in Fig. 3. Eq. (3) indicates that the area surrounded by the curves in Fig. 4 represents the activation energy for dislocation glide. The values of ΔG for 1Ni, 1Mn, 2Ni, and 2Mn were estimated to
4. Discussion 4.1. Fracture toughness with dislocation activity Fig. 6(a), (b), and (c) show the fracture surfaces of 0Mn, 2Ni, and 2Mn, respectively, at 100 K. The dominant fracture surface was transgranular, which indicates that the main fracture mode in these specimens was cleavage regardless of the element added. The grains where the first crack initiated were determined in each image by tracing river patterns on the fracture surfaces. Fig. 6(d), (e), and (f) show enlarged images that include the grain of the fracture initiated. The origins of the first crack in 0Mn and 2Ni were found to be the crosssection of twins, which is indicated by white arrows in Fig. 6(d) and (e), respectively. It is to be noted here that whereas the origins are in a grain or on a grain boundary, the first crack propagated inside the grain, resulting in cleavage fracture. Plastic deformation was also observed around the origin of the first crack in 2Ni, which is in good agreement with the solid solution softening shown in Fig. 2. In other words, the dislocation velocity of 2Ni was higher than that of 0Mn. Because dislocations moved faster and were more active in 2Ni at 100 K than in 0Mn, plastic deformation took place in 2Ni. Note that the first crack from the origin of fracture in 2Mn seems to propagate along a grain boundary since the fracture surface is smooth without river patterns in some specimens, as indicated by the white arrow in
Fig. 4. Dependence of the activation volume on the effective shear stress. The activation volume was normalised by b3, where b is the Burgers vector of alpha iron at 0.248×10−9 m. The values of the effective stress at V*=0 were obtained by extrapolating the effective stress at 0 K in Fig. 3.
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Fig. 6. SEM images of fracture surfaces tested at 100 K: (a) 0Mn, (b) 2Ni, (c) 2Mn, (d) enlarged image of (a), (e) enlarged image of (b), and (f) enlarged image of (c).
Fig. 6(f); river patterns in surrounding grains flowed from this point. This indicates that the first crack initiated at a grain boundary in 2Mn and propagated inside the grains. The change in the fracture initiation site from inside grains to between grains is discussed next. The fracture toughness depends on the surface energy and relaxation caused by plastic deformation, i.e., dislocation activity [9,12–14]:
2Eγs − kD, 1 − ν2
KIC =
[16], Eq. (5) gives the intergranular surface energy for fracture at the ∑3 {112} tilt coincidence grain boundary as 4.911 J/m2. If the surface energy for the fracture of {100} planes is 2.222 J/m2 [16], the ∑3 {112} tilt coincidence grain boundary does not fracture because the transgranular fracture condition 2γst < 2γsi − γgb is satisfied. The condition for intergranular fracture at the ∑3 {112} tilt coincidence grain boundary is given by Σ3{112} Σ3{112} 2γsiΣ3{112} − (γgb + Δγgb ) < 2γst{100}.
(4)
where E is Young's modulus, ν is Poisson's ratio, γs is the fracture surface energy, and kD is the local stress intensity factor due to dislocations. The first term in Eq. (4) is related to the bonding property, while the second term is related to the ability for stress relaxation due to dislocations at a crack tip. In Eq. (4), 2γs should be different depending on the fracture mode: intergranular or transgranular.
⎧ 2γst … transgranular fracture 2γs = ⎨ . ⎩ 2γsi − (γgb + Δγgb ) … intergranular fracture ⎪
Eq. (7) gives 0.467 < Geng et al. [17] obtained the dependence of the embrittlement potency on solute elements in bcc irons by calculating the heat of dissolution, change in enthalpy compared with the solution and single atom, and changes in the volume of the grain boundaries and bonding energy at grain boundaries. They concluded that the potency of embrittlement of Mn is approximately 0.58 J/m2 while that of Ni is nearly 0 J/m2. Note that ∑{112} are the energy values for the potency of embrittlement and Δγgb close, even though the physics behind them are not exactly the same. It is to be noted that experimental data of the change in the grain boundary energy with Mn or Ni are desired as future works.
(5)
Here, γst is the surface energy for transgranular fracture, γst is the surface energy for intergranular fracture when a grain boundary becomes a free surface, γgb is the grain boundary energy before fracture, and Δγgb is the change in grain boundary energy before fracture when elements are added. Here, the fracture criterion is given as follows:
⎧ 2γst < 2γsi − (γgb + Δγgb ) … transgranular fracture ⎨ . ⎩ 2γsi − (γgb + Δγgb ) < 2γst … intergranular fracture
4.2. Effects of Ni and Mn on deformation twinning Another important factor for fracture at low temperatures is deformation twinning, which also affects the BDT in steels. Therefore, the effects of Ni and Mn on deformation twinning were also investigated. Fig. 7(a) and (b) show an orientation map and image quality map, respectively, of the 2Mn specimen that was deformed up to a maximum stress of 570 MPa and unloaded at 77 K. The horizontal and vertical lines in Fig. 7(b) are scratches made during polishing. Fig. 7(c) shows an inverse pole figure from grains in Fig. 7(a) facing the tensile direction (horizontal direction in the figure). The circle size in the standard triangle represents the relative grain size. The orientation was nearly random with a maximum intensity of 1.4, where grains facing < 100 > or < 110 > had slightly higher intensities. The ∑3 tilt boundaries are drawn as black lines in Fig. 7(a), which indicate deformation twins. Those twins were also detected as lines with low image quality, as shown in Fig. 7(b). The number of grains that
⎪ ⎪
(7)
Σ3{112} . Δγgb
(6)
Note that Δγgb does not depend only on the atomic bonding at grain boundaries. In this study, Δγgb was defined as the total change in the grain boundary energy with the addition of elements. The first crack in 2Ni and 2Mn originated inside a grain and at a grain boundary, respectively, as shown in Fig. 6. This suggests that Mn increases Δγgb sufficiently to change the first crack propagating transgranular to intergranular while Ni does not. Here, the change in Δγgb with Mn was estimated using calculated values since there is no experimental data of grain boundary energy with Mn. Because the ∑3 tilt coincidence grain boundary energy of αiron is 0.267 J/m2 [15], and the {112} surface energy is 2.589 J/m2 373
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grams of the ratio of grains with twins to grains with a Schmidt factor of 0.3–0.5 for < 111 > {112} twinning. The value is shown on the left vertical axis. Nearly 70% of grains with a Schmidt factor of 0.3–0.5 had twins in 1Ni while around 40% of such grains had twins in 2Ni. This indicates that deformation twinning is suppressed by the addition of Ni. The same tendency was found when Mn was added. In other words, deformation twinning is also suppressed by the addition of Mn, although the effect is slightly weaker than that of adding Ni. The difference in the effect between Ni and Mn may be due to the grain sizes; reducing the grain size suppresses deformation twinning. The grain size of 2Ni was slightly smaller than that of 1Ni, while the grain sizes of 1Mn and 2Mn were nearly the same. The square plots indicate the average number of twins in a grain counted only from grains with twins. They show that the average number of twins in a grain is not strongly affected by Ni or Mn. Those results indicate that the increase in the BDT temperature with Mn cannot be explained by the promotion of deformation twinning because deformation twinning is suppressed by the addition of Mn. Therefore, the dominant factor for the increase in the BDT temperature of ultralow-carbon steels with increasing Mn was concluded to be the decreased fracture energy at grain boundaries as expected in Eq. (4). 5. Conclusion The effects of Ni and Mn on the BTD were investigated in ultralowcarbon steel. The following results were obtained.
Fig. 7. (a) Orientation map of the normal direction to the tensile direction (horizontal in the figure) from 2 Ma after a tensile test at 77 K. The tensile stress was terminated at a stress of 570 MPa. (b) Image quality map of the same area shown in (a). (c) Inverse pole figure from all grains in (a) of the grains facing the tensile direction. Circle size indicates the grain size. (d) Inverse pole figure of the normal direction from grains with twins. The orientation of the grains is facing the tensile direction. The colour key is shown to the right of the inverse pole figures.
(1) The effective stress at low temperature decreases in 2 mass% Ni and 2 mass% Mn, showing solid solution softening. The temperature dependences of the activation volume and effective stress indicate that the dislocation mobility was higher in 2Ni and 2Mn than in 1Ni and 1Mn. (2) The BDT temperature decreased with 2 mass% Ni and increased with 2 mass %Mn. The fractures of 2Ni and 2Mn at 100 K in fracture tests were transgranular and intergranular, respectively, in origin. (3) Both Ni and Mn suppress the deformation twinning at low temperatures. (4) The inverse effects of Ni and Mn on the BDT temperature in ultralow-carbon steel, even though both Ni and Mn induce solid solution softening at low temperatures, can be explained by the decreased energy for grain boundary fracture with increasing Mn. References [1] Y. Zou, Y.B. Xu, Z.P. Hu, X.L. Gu, F. Peng, X.D. Tan, S.Q. Chen, D.T. Han, R.D.K. Misra, G.D. Wang, Austenite stability and its effect on the toughness of a high strength ultra-low carbon medium manganese steel plate, Mater. Sci. Eng. A 675 (2016) 153–163. [2] J. Hu, L.X. Du, G.S. Sun, H. Xie, R.D.K. Misra, The determining role of reversed austenite in enhancing toughness of a novel ultra-low carbon medium manganese high strength steel, Scr. Mater. 104 (2015) 87–90. [3] K. Sugimoto, H. Tanino, J. Kobayashi, Impact toughness of medium-Mn transformation-induced plasticity-aided steels, Steel Res. Int. 86 (2015) 1151–1160. [4] K. Okazaki, Solid-solution hardening and softening in binary iron alloys, J. Mater. Sci. 31 (1996) 1087–1099. [5] A. Uenishi, C. Teodosiu, Solid solution softening at high strain rates in Si- and/or Mn-added interstitial free steels, Acta Mater. 51 (2003) 4437–4446. [6] K. Maeno, M. Tanaka, N. Yoshimura, H. Shirahata, K. Ushioda, K. Higashida, Change in dislocation mobility with Ni content in ferritic steels and its effect on brittle-to-ductile transition, Tetsu-to-Hagané 98 (2012) 667–674. [7] W. Jolley, Effect of Mn and Ni on impact properties of Fe and Fe-C alloys, J. Iron Steel Inst. 206 (1968) 170–173. [8] K. Yamanaka, M. Kobayashi, Mechanical properties and fracture behavior of Fe-Mn alloys, J. Jpn. Inst. Met. 43 (1979) 1151–1157. [9] R. Thomson, Physics of fracture, in: F. Seitz, D. Turnbull (Eds.), Solid State Physics, Academic Press, INC., Orlando, San Diego, New York, Austin, Boston, London, Sydney, Tokyo, Toronto, 1986, pp. 1–129. [10] Y. Aono, K. Kitajima, E. Kuramoto, Thermall actived slip deformation of Fe-Ni alloy single-crsytals in the temperature-range of 4.2 K to 300 K, Scr. Metall. 15 (1981) 275–279. [11] M.J. Marcinkowski, H.A. Lipsitt, The plastic deformation of chromium at low
Fig. 8. Histogram of the ratio of grains with twins to grains with a Schmidt factor of 0.3– 0.5 (left vertical axis). Square plots indicate the average number of twins in a grain counted only from grains with twins (right vertical axis).
contained deformation twins was counted in Fig. 7(a) and (b). Fig. 7(d) indicates an inverse pole figure from grains with twins, which indicates that grains of nearly < 001 > facing the tensile direction tended to have more deformation twins. This tendency is the same as that reported for single crystals [18], where tensile deformation along < 001 > directions induces deformation twins and fracture in single crystalline Fe–Si alloys. In order to investigate the effects of Ni and Mn on deformation twinning, 1Ni, 2Ni, 1Mn, and 2Mn were deformed in tensile tests at 77 K until a tensile stress of 600 MPa and then unloaded. The number of grains with twins were measured. Because the crystallographic orientation against the tensile direction strongly affects the onset of deformation twinning, the grains with a Schmidt factor of 0.3–0.5 for < 111 > {112} twinning were taken into account. Fig. 8 shows histo374
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symmetric tile boundary, Tetsu-to-Hagané 86 (2009) 357–362. [16] L. Vitos, A.V. Ruban, H.L. Skriver, J. Kollár, The surface energy of metals, Surf. Sci. 411 (1998) 186–202. [17] W. Geng, A. Freeman, G. Olson, Influence of alloying additions on grain boundary cohesion of transition metals: first-principles determination and its phenomenological extension, Phys. Rev. B 63 (2001) 165415. [18] R. Honda, Cleavage fracture in single crystals of silicon iron, J. Phys. Soc. Jpn. 16 (1961) 1309–1321.
temperatures, Acta Metall. 10 (1962) 95–111. [12] A.A. Griffith, The phenomena of rupture and flow in solids, Trans. R. Soc. Lond. Ser. A 221 (1921) 582–593. [13] R. Thomson, Brittle fracture in a ductile material with application to hydrogen embrittlement, J. Mater. Sci. 13 (1978) 128–142. [14] K. Higashida, N. Narita, Crack tip plasticity and its role in the brittle-to-ductile transition, JJAP Ser.2, Lattice Defects in Ceramics, 1989, pp. 39–43. [15] H. Nakashima, M. Takeuchi, Grain boundary energy and structure of α-Fe < 110 >
375
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Effects of Ni and Mn on brittle-to-ductile transition in ultralow-carbon steels
MARK
⁎
Masaki Tanakaa, , Kenta Matsuoa, Nobuyuki Yoshimurab, Genichi Shigesatob, Manabu Hoshinob, Kohsaku Ushiodab, Kenji Higashidaa,c a b c
Department of Materials Science and Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan Technical Research & Development Bureau , Nippon Steel & Sumitomo Metal Corporation, 20-1 Shintomi, Futtsu, Chiba 293-8511, Japan Sasebo College, National Institute of Technology, 1-1 Okishimachi, Sasebo, Nagashiki 857-1193, Japan.
A R T I C L E I N F O
A BS T RAC T
Keywords: Steel Dislocations Fracture Twinning Dislocation shielding DBT
The temperature dependence of the effective stress indicated that both Ni and Mn induce solid solution softening at low temperatures. The activation energy for dislocation glide was obtained from the temperature dependence of the activation volume and effective shear stress. Either Ni or Mn decreases the activation energy for dislocation glide, which suggests that both Ni and Mn decrease the brittle-to-ductile transition (BDT) temperature. However, the temperature dependence of the absorbed energy for fracture showed that the transition temperature decreases with Ni but increases with Mn. Fracture surfaces tested at 100 K indicated transgranular fracture at 2 mass% Ni and intergranular fracture at 2 mass% Mn, which suggests a decrease in energy for grain boundary fracture with Mn. The mechanism behind the opposite effects of Ni and Mn on the transition temperature of ultralow-carbon steels was examined on the basis of dislocation shielding theory.
1. Introduction Manganese (Mn) is an important element added in steel that reduces the grain size and increases the yield stress at room temperature (RT). It also influences the stability of austenite, decreasing a martensite-start temperature. Mechanical properties of transformation-induced plasticity-aided steels are influenced by the Mn, which is mainly due to the change in microstructures with Mn [1–3]. In case of ferrite single phase steels, Mn and nickel (Ni) show similar effects on the mechanical properties. Okazaki, Uenish and Teodosiu [4,5] reported the temperature dependence of the yield stresses for titaniumadded Fe–1 at% Ni and Fe–1 at% Mn, which showed solid solution hardening at RT and solid solution softening at low temperatures or high-strain rates. The solid solution softening suggests that Ni and Mn increase the dislocation velocity at low temperatures. Maeno et al. [6] reported that the decrease in the brittle-to-ductile transition (BDT) temperature with increasing Ni in steel can be explained by the increased dislocation velocity at low temperatures. This suggests that increasing the Mn content decreases the BDT temperature. However, the effect of Mn on toughness is still controversial. For instance, Jolley [7] reported that the BDT temperature of furnace-cooled ferrite with a single phase increases with up to 1.8 mass% Mn, while the BDT temperature of ferrite with cementite decreases with Mn. Yamanaka
⁎
and Kobayashi [8] reported a complex trend for the BDT temperature with Mn. The BDT temperature decreases with increasing Mn to a minimum at 2 mass% Mn and then increases with higher Mn content. They investigated the microstructure and pointed out that the microstructure depends on the Mn content; uniaxial ferrite and massive ferrite are dominant with low Mn content and 3 mass% Mn, respectively. Specimens with a Mn content of 4.8 mass% exhibit lath martensite in massive ferrites. Mn has complicated effects on the microstructure, which include grain refinement, micro-segregation, and changes to the morphology of precipitates. Mn produces many effects, which makes it difficult to understand the specific effect of Mn on the fracture toughness and BDT. In the present study, therefore, the effects of Mn and Ni as solute atoms on BDT were clarified by using single-phase ferrites with different concentrations of Mn and Ni but nearly the same grain sizes. The mechanism behind the changes in the BDT temperature with Mn and Ni was examined on the basis of dislocation shielding theory [9]. 2. Experimental procedure Table 1 presents the chemical compositions of the materials employed in this study. The base material was ultralow-carbon steel with a C concentration of less than 20 ppm. For the specimens, 1 or 2
Corresponding author. E-mail address: [email protected] (M. Tanaka).
http://dx.doi.org/10.1016/j.msea.2016.11.045 Received 30 August 2016; Received in revised form 12 November 2016; Accepted 12 November 2016 Available online 20 November 2016 0921-5093/ © 2016 Elsevier B.V. All rights reserved.
Materials Science & Engineering A 682 (2017) 370–375
M. Tanaka et al.
Table 1 Chemical compositions of the employed materials.
0Mn 1Mn 2Mn 1Ni 2Ni
C
Si
Mn
P
S
Ni
Ti
Al
N
0.0017 0.0018 0.0018 0.0019 0.0019
< 0.01 < 0.01 < 0.01 < 0.01 < 0.01
< 0.01 0.97 1.95 < 0.01 < 0.01
< 0.01 < 0.01 < 0.01 < 0.01 < 0.01
< 0.001 < 0.001 < 0.001 < 0.001 < 0.001
< 0.01 < 0.01 < 0.01 1.01 2.02
< 0.002 < 0.002 < 0.002 < 0.002 < 0.002
0.03 0.03 0.03 0.03 0.03
< 0.001 < 0.001 < 0.001 < 0.001 < 0.001
mass% of Ni or Mn was added to the base material and labelled as 0Mn, 1Mn, 2Mn, 1Ni, and 2Ni. The grain sizes of 0Mn, 1Mn, 2Mn 1Ni and 2Ni were measured to be 147, 91, 59, 86, and 78 µm, respectively. The parallel portion and width of the tensile specimens were 8 and 2 mm, respectively, and they had a thickness of 0.9 mm. Strain gages were attached to the parallel portions of the specimens. The test temperature was varied between 77 and 350 K. The initial strain rate of the tensile tests was set to 4.2×10−4 s−1, and a Shimadzu AG-IS was used for the tests. Strain-rate jump tests were performed in order to obtain the activation volume. The strain rate was jumped by one order of magnitude. The impact fracture energy of the specimens was measured by using an instrumental impact fracture machine (Tanaka MIT-D05KJ). The blade speed of the impact tests was set to be 3.3×10−1 ms−1. 3. Results Fig. 1 shows the nominal stress–strain curves of 1Ni, 2Ni, 0Mn, 1Mn, and 2Mn measured at 77 K and RT. Yield drop was observed at RT for all specimens. At RT, the yield stress of 0 M is the lowest, that of 2Ni was higher than that of 1Ni, and the yield stress of 2Mn was higher than that of 1Mn. These results demonstrate solid solution hardening. On the other hand, at 77 K, the yield stress of 2Ni was lower than that of 1Ni, and the yield stress of 2Mn was lower than that of 1Mn. This indicates that both Ni and Mn induce solid solution softening at 77 K. The temperature dependence of the yield stress was obtained next. Because these materials were low-carbon steels, some specimens showed yield drop, thus, 0.2% proof stress was taken as the yield stress for the specimens that showed continuous yielding while the lower-yield point was taken as the yield stress for those showed the yield drop. Fig. 2 shows the temperature dependence of the yield stress for 1Ni, 2Ni, 0Mn, 1Mn, and 2Mn. The yield stress decreased with increasing temperature; the temperature dependence then a nearly negligible above 300 K. The trend is the same as that typically seen in bcc crystals. It is worth pointing here that slight hump is also seen in between 125 K and 225 K in polycrystalline 0Mn. It is much significant reported in
Fig. 2. Temperature dependence of the yield stress.
single crystalline iron [10]. The normal temperature dependence of the yield stress originates from the process that dislocations overcoming short-range barriers through a thermally activated process. In bcc crystals, the dominant thermally activated process for dislocation glide at low temperatures is overcoming the Peierls barrier. Therefore, temperature dependence of yield stress will be investigated next. The yield stress can be expressed as follows:
σy = σe + σath,
(1)
where σe and σath are the effective stress and athermal stress, respectively. The effective stress and athermal stress are temperaturedependent and temperature-independent, respectively. In the present study, the yield stress at 350 K was defined as the athermal stress. Fig. 3 shows the temperature dependence of the measured effective stresses for 1Ni, 2Ni, 0M, 1Mn, and 2Mn according to Eq. (1). The effective stress decreased with increasing Ni or Mn content, which indicates that the solid solution softening at low temperatures in Fig. 2
Fig. 1. Nominal stress–strain curves from 1Ni, 2Ni, 0Mn, 1Mn, and 2Mn tested at 77 K and RT.
Fig. 3. Temperature dependence of the effective stress.
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originates from the decreased effective stress at low temperatures. Here, the effective stresses of 1Ni and 1Mn were nearly the same. The effective stresses of 2Ni and 2Mn were also nearly the same. This suggests that Ni and Mn have nearly the same effect on the dislocation velocity, especially at low temperatures where the dominant elementary process for dislocation glide is overcoming the Peierls barrier. Dislocations are assumed to overcome the Peierls barrier by forming double-kink pairs because the energy barrier to form double-kink pairs is less than that to overcome the Peierls barrier without forming double-kink pairs. The effective stress at 0 K was estimated by extrapolation in Fig. 3 with parabolic curves expect for 0Mn since it does not fit to a single parabolic curve. It was estimated to be 818, 770, 702, and 684 MPa for 1Mn, 1Ni, 2Mn, and 2Ni, respectively. These values suggest that Ni or Mn decreases the double-kink pair nucleation energy in more than 2 mass%. The dislocation velocity is expressed as follows:
v=
⎛
⎞
⎝
kT ⎠
Fig. 5. Temperature dependence of the absorbed energy in the impact fracture tests.
ΔG v0 τem exp ⎜ − ⎟,
be 0.97, 0.78, 0.8, and 0.6 eV, respectively. The value of 0Mn was not obtained since the values of activation volume with low and high effective stress were not obtainable in this study. Thus, the focus here should be the relative values with Ni or Mn. Both Ni and Mn decrease the activation energy for dislocation glide. That is, the activation energy for dislocation glide decreases with a Ni or Mn component. Maeno et al. [6] reported that the decrease in the BDT temperature with increasing Ni content in interstitial free (IF) steel can be understood by the increased dislocation mobility at low temperatures with increasing Ni content. Therefore, the changes in the BDT temperature with Ni and Mn were investigated. Fig. 5 shows the temperature dependence of the absorbed energy from 1Ni, 2Ni, 0Mn, 1Mn and 2Mn. The BDT temperatures of 0Mn, 1Ni, and1Mn were nearly the same, while adding 2 mass% Ni or Mn clearly affected the BDT temperature. The BDT temperature of 2Ni decreased approximately 50 K from that of 0Mn, while the temperature of 2Mn increased approximately 30 K. The reversed effects of Ni and Mn on the BDT temperatures cannot be explained solely by the change in dislocation velocity with those elements because both Ni and Mn increase the dislocation mobility, as shown in Fig. 4. The reason why Ni and Mn have completely different effects on the BDT temperature even though both elements decrease the dislocation mobility is discussed next.
(2)
whre v0 and m are constants, τe is the effective shear stress, k is the Boltzmann constant, T is the absolute temperature, and ΔG is the activation energy for dislocation glide. The decrease in the effective stress with Ni or Mn, as shown in Fig. 3, suggests that Ni and Mn decrease the value of ΔG in Eq. (2) and that the decreases in value are nearly the same at least up to a concentration of 2 mass%. The activation energy in Eq. (2) can be obtained by integrating the activation volume V* with respect to the effective stress as follows:
V* = −
dΔG , ΔG = − dτe
∫ V *dτe,
with V * ≡ kT
∂ ln γ ̇ ∂ ln ε ̇ ≈ kTM , ∂τe ∂σe (3)
where M is a Taylor factor of 2 for bcc [11] and γ˙ and ε˙ are the shear strain rate and strain rate along the tensile direction in tensile tests, respectively. In order to estimate the change in the activation energy, strain rate jump tests were performed at various temperatures. Fig. 4 shows the shear stress dependence of the activation volume. The activation volume was normalised with b3, where b is the Burgers vector of alpha iron at 0.248×10−9 m. The activation volume decreases with the effective shear stress. The effective shear stress at the activation volume of 0 was expected to be the effective shear stress at 0 K estimated in Fig. 3. Eq. (3) indicates that the area surrounded by the curves in Fig. 4 represents the activation energy for dislocation glide. The values of ΔG for 1Ni, 1Mn, 2Ni, and 2Mn were estimated to
4. Discussion 4.1. Fracture toughness with dislocation activity Fig. 6(a), (b), and (c) show the fracture surfaces of 0Mn, 2Ni, and 2Mn, respectively, at 100 K. The dominant fracture surface was transgranular, which indicates that the main fracture mode in these specimens was cleavage regardless of the element added. The grains where the first crack initiated were determined in each image by tracing river patterns on the fracture surfaces. Fig. 6(d), (e), and (f) show enlarged images that include the grain of the fracture initiated. The origins of the first crack in 0Mn and 2Ni were found to be the crosssection of twins, which is indicated by white arrows in Fig. 6(d) and (e), respectively. It is to be noted here that whereas the origins are in a grain or on a grain boundary, the first crack propagated inside the grain, resulting in cleavage fracture. Plastic deformation was also observed around the origin of the first crack in 2Ni, which is in good agreement with the solid solution softening shown in Fig. 2. In other words, the dislocation velocity of 2Ni was higher than that of 0Mn. Because dislocations moved faster and were more active in 2Ni at 100 K than in 0Mn, plastic deformation took place in 2Ni. Note that the first crack from the origin of fracture in 2Mn seems to propagate along a grain boundary since the fracture surface is smooth without river patterns in some specimens, as indicated by the white arrow in
Fig. 4. Dependence of the activation volume on the effective shear stress. The activation volume was normalised by b3, where b is the Burgers vector of alpha iron at 0.248×10−9 m. The values of the effective stress at V*=0 were obtained by extrapolating the effective stress at 0 K in Fig. 3.
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Fig. 6. SEM images of fracture surfaces tested at 100 K: (a) 0Mn, (b) 2Ni, (c) 2Mn, (d) enlarged image of (a), (e) enlarged image of (b), and (f) enlarged image of (c).
Fig. 6(f); river patterns in surrounding grains flowed from this point. This indicates that the first crack initiated at a grain boundary in 2Mn and propagated inside the grains. The change in the fracture initiation site from inside grains to between grains is discussed next. The fracture toughness depends on the surface energy and relaxation caused by plastic deformation, i.e., dislocation activity [9,12–14]:
2Eγs − kD, 1 − ν2
KIC =
[16], Eq. (5) gives the intergranular surface energy for fracture at the ∑3 {112} tilt coincidence grain boundary as 4.911 J/m2. If the surface energy for the fracture of {100} planes is 2.222 J/m2 [16], the ∑3 {112} tilt coincidence grain boundary does not fracture because the transgranular fracture condition 2γst < 2γsi − γgb is satisfied. The condition for intergranular fracture at the ∑3 {112} tilt coincidence grain boundary is given by Σ3{112} Σ3{112} 2γsiΣ3{112} − (γgb + Δγgb ) < 2γst{100}.
(4)
where E is Young's modulus, ν is Poisson's ratio, γs is the fracture surface energy, and kD is the local stress intensity factor due to dislocations. The first term in Eq. (4) is related to the bonding property, while the second term is related to the ability for stress relaxation due to dislocations at a crack tip. In Eq. (4), 2γs should be different depending on the fracture mode: intergranular or transgranular.
⎧ 2γst … transgranular fracture 2γs = ⎨ . ⎩ 2γsi − (γgb + Δγgb ) … intergranular fracture ⎪
Eq. (7) gives 0.467 < Geng et al. [17] obtained the dependence of the embrittlement potency on solute elements in bcc irons by calculating the heat of dissolution, change in enthalpy compared with the solution and single atom, and changes in the volume of the grain boundaries and bonding energy at grain boundaries. They concluded that the potency of embrittlement of Mn is approximately 0.58 J/m2 while that of Ni is nearly 0 J/m2. Note that ∑{112} are the energy values for the potency of embrittlement and Δγgb close, even though the physics behind them are not exactly the same. It is to be noted that experimental data of the change in the grain boundary energy with Mn or Ni are desired as future works.
(5)
Here, γst is the surface energy for transgranular fracture, γst is the surface energy for intergranular fracture when a grain boundary becomes a free surface, γgb is the grain boundary energy before fracture, and Δγgb is the change in grain boundary energy before fracture when elements are added. Here, the fracture criterion is given as follows:
⎧ 2γst < 2γsi − (γgb + Δγgb ) … transgranular fracture ⎨ . ⎩ 2γsi − (γgb + Δγgb ) < 2γst … intergranular fracture
4.2. Effects of Ni and Mn on deformation twinning Another important factor for fracture at low temperatures is deformation twinning, which also affects the BDT in steels. Therefore, the effects of Ni and Mn on deformation twinning were also investigated. Fig. 7(a) and (b) show an orientation map and image quality map, respectively, of the 2Mn specimen that was deformed up to a maximum stress of 570 MPa and unloaded at 77 K. The horizontal and vertical lines in Fig. 7(b) are scratches made during polishing. Fig. 7(c) shows an inverse pole figure from grains in Fig. 7(a) facing the tensile direction (horizontal direction in the figure). The circle size in the standard triangle represents the relative grain size. The orientation was nearly random with a maximum intensity of 1.4, where grains facing < 100 > or < 110 > had slightly higher intensities. The ∑3 tilt boundaries are drawn as black lines in Fig. 7(a), which indicate deformation twins. Those twins were also detected as lines with low image quality, as shown in Fig. 7(b). The number of grains that
⎪ ⎪
(7)
Σ3{112} . Δγgb
(6)
Note that Δγgb does not depend only on the atomic bonding at grain boundaries. In this study, Δγgb was defined as the total change in the grain boundary energy with the addition of elements. The first crack in 2Ni and 2Mn originated inside a grain and at a grain boundary, respectively, as shown in Fig. 6. This suggests that Mn increases Δγgb sufficiently to change the first crack propagating transgranular to intergranular while Ni does not. Here, the change in Δγgb with Mn was estimated using calculated values since there is no experimental data of grain boundary energy with Mn. Because the ∑3 tilt coincidence grain boundary energy of αiron is 0.267 J/m2 [15], and the {112} surface energy is 2.589 J/m2 373
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grams of the ratio of grains with twins to grains with a Schmidt factor of 0.3–0.5 for < 111 > {112} twinning. The value is shown on the left vertical axis. Nearly 70% of grains with a Schmidt factor of 0.3–0.5 had twins in 1Ni while around 40% of such grains had twins in 2Ni. This indicates that deformation twinning is suppressed by the addition of Ni. The same tendency was found when Mn was added. In other words, deformation twinning is also suppressed by the addition of Mn, although the effect is slightly weaker than that of adding Ni. The difference in the effect between Ni and Mn may be due to the grain sizes; reducing the grain size suppresses deformation twinning. The grain size of 2Ni was slightly smaller than that of 1Ni, while the grain sizes of 1Mn and 2Mn were nearly the same. The square plots indicate the average number of twins in a grain counted only from grains with twins. They show that the average number of twins in a grain is not strongly affected by Ni or Mn. Those results indicate that the increase in the BDT temperature with Mn cannot be explained by the promotion of deformation twinning because deformation twinning is suppressed by the addition of Mn. Therefore, the dominant factor for the increase in the BDT temperature of ultralow-carbon steels with increasing Mn was concluded to be the decreased fracture energy at grain boundaries as expected in Eq. (4). 5. Conclusion The effects of Ni and Mn on the BTD were investigated in ultralowcarbon steel. The following results were obtained.
Fig. 7. (a) Orientation map of the normal direction to the tensile direction (horizontal in the figure) from 2 Ma after a tensile test at 77 K. The tensile stress was terminated at a stress of 570 MPa. (b) Image quality map of the same area shown in (a). (c) Inverse pole figure from all grains in (a) of the grains facing the tensile direction. Circle size indicates the grain size. (d) Inverse pole figure of the normal direction from grains with twins. The orientation of the grains is facing the tensile direction. The colour key is shown to the right of the inverse pole figures.
(1) The effective stress at low temperature decreases in 2 mass% Ni and 2 mass% Mn, showing solid solution softening. The temperature dependences of the activation volume and effective stress indicate that the dislocation mobility was higher in 2Ni and 2Mn than in 1Ni and 1Mn. (2) The BDT temperature decreased with 2 mass% Ni and increased with 2 mass %Mn. The fractures of 2Ni and 2Mn at 100 K in fracture tests were transgranular and intergranular, respectively, in origin. (3) Both Ni and Mn suppress the deformation twinning at low temperatures. (4) The inverse effects of Ni and Mn on the BDT temperature in ultralow-carbon steel, even though both Ni and Mn induce solid solution softening at low temperatures, can be explained by the decreased energy for grain boundary fracture with increasing Mn. References [1] Y. Zou, Y.B. Xu, Z.P. Hu, X.L. Gu, F. Peng, X.D. Tan, S.Q. Chen, D.T. Han, R.D.K. Misra, G.D. Wang, Austenite stability and its effect on the toughness of a high strength ultra-low carbon medium manganese steel plate, Mater. Sci. Eng. A 675 (2016) 153–163. [2] J. Hu, L.X. Du, G.S. Sun, H. Xie, R.D.K. Misra, The determining role of reversed austenite in enhancing toughness of a novel ultra-low carbon medium manganese high strength steel, Scr. Mater. 104 (2015) 87–90. [3] K. Sugimoto, H. Tanino, J. Kobayashi, Impact toughness of medium-Mn transformation-induced plasticity-aided steels, Steel Res. Int. 86 (2015) 1151–1160. [4] K. Okazaki, Solid-solution hardening and softening in binary iron alloys, J. Mater. Sci. 31 (1996) 1087–1099. [5] A. Uenishi, C. Teodosiu, Solid solution softening at high strain rates in Si- and/or Mn-added interstitial free steels, Acta Mater. 51 (2003) 4437–4446. [6] K. Maeno, M. Tanaka, N. Yoshimura, H. Shirahata, K. Ushioda, K. Higashida, Change in dislocation mobility with Ni content in ferritic steels and its effect on brittle-to-ductile transition, Tetsu-to-Hagané 98 (2012) 667–674. [7] W. Jolley, Effect of Mn and Ni on impact properties of Fe and Fe-C alloys, J. Iron Steel Inst. 206 (1968) 170–173. [8] K. Yamanaka, M. Kobayashi, Mechanical properties and fracture behavior of Fe-Mn alloys, J. Jpn. Inst. Met. 43 (1979) 1151–1157. [9] R. Thomson, Physics of fracture, in: F. Seitz, D. Turnbull (Eds.), Solid State Physics, Academic Press, INC., Orlando, San Diego, New York, Austin, Boston, London, Sydney, Tokyo, Toronto, 1986, pp. 1–129. [10] Y. Aono, K. Kitajima, E. Kuramoto, Thermall actived slip deformation of Fe-Ni alloy single-crsytals in the temperature-range of 4.2 K to 300 K, Scr. Metall. 15 (1981) 275–279. [11] M.J. Marcinkowski, H.A. Lipsitt, The plastic deformation of chromium at low
Fig. 8. Histogram of the ratio of grains with twins to grains with a Schmidt factor of 0.3– 0.5 (left vertical axis). Square plots indicate the average number of twins in a grain counted only from grains with twins (right vertical axis).
contained deformation twins was counted in Fig. 7(a) and (b). Fig. 7(d) indicates an inverse pole figure from grains with twins, which indicates that grains of nearly < 001 > facing the tensile direction tended to have more deformation twins. This tendency is the same as that reported for single crystals [18], where tensile deformation along < 001 > directions induces deformation twins and fracture in single crystalline Fe–Si alloys. In order to investigate the effects of Ni and Mn on deformation twinning, 1Ni, 2Ni, 1Mn, and 2Mn were deformed in tensile tests at 77 K until a tensile stress of 600 MPa and then unloaded. The number of grains with twins were measured. Because the crystallographic orientation against the tensile direction strongly affects the onset of deformation twinning, the grains with a Schmidt factor of 0.3–0.5 for < 111 > {112} twinning were taken into account. Fig. 8 shows histo374
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symmetric tile boundary, Tetsu-to-Hagané 86 (2009) 357–362. [16] L. Vitos, A.V. Ruban, H.L. Skriver, J. Kollár, The surface energy of metals, Surf. Sci. 411 (1998) 186–202. [17] W. Geng, A. Freeman, G. Olson, Influence of alloying additions on grain boundary cohesion of transition metals: first-principles determination and its phenomenological extension, Phys. Rev. B 63 (2001) 165415. [18] R. Honda, Cleavage fracture in single crystals of silicon iron, J. Phys. Soc. Jpn. 16 (1961) 1309–1321.
temperatures, Acta Metall. 10 (1962) 95–111. [12] A.A. Griffith, The phenomena of rupture and flow in solids, Trans. R. Soc. Lond. Ser. A 221 (1921) 582–593. [13] R. Thomson, Brittle fracture in a ductile material with application to hydrogen embrittlement, J. Mater. Sci. 13 (1978) 128–142. [14] K. Higashida, N. Narita, Crack tip plasticity and its role in the brittle-to-ductile transition, JJAP Ser.2, Lattice Defects in Ceramics, 1989, pp. 39–43. [15] H. Nakashima, M. Takeuchi, Grain boundary energy and structure of α-Fe < 110 >
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