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Compressive behavior of a Fe–Mn–Al–C lightweight steel at different strain rates
Materials Science & Engineering A xxx (xxxx) xxx
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Compressive behavior of a Fe–Mn–Al–C lightweight steel at different strain rates Zhuang Li a, Yingchun Wang a, b, *, Xingwang Cheng a, b, Jiaxin Liang a, Shukui Li a, b a b
School of Materials Science and Engineering, Beijing Institute of Technology, Beijing, 100081, China National Key Laboratory of Science and Technology on Materials under Shock and Impact, Beijing, 100081, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Fe-Mn-Al-C austenite-based steel Strain-rate sensitivity κ-carbide Compression properties Slip band
Experiments were conducted to evaluate the compression behavior at strain rates in the range 10 3–103 s 1 of a Fe–Mn–Al–C lightweight steel micro-alloyed with Mo and Nb after aging at different temperatures. The results show that the microstructures of the steels after aging at temperatures from 400 to 600 � C are composed of austenite grains and two types of nano-sized precipitates, (Nb,Mo)C and κ-carbides, distributed uniformly in the matrix. Increasing the aging temperature results in the growth of the κ-carbides but has no effect on the sizes and distribution of the (Nb,Mo)C particles. The aged steel exhibits a significant strain-rate strengthening effect resulting from the enhancement of the interactions between dislocations and the carbides in the matrix at higher strain rates. With increasing strain rate, the strain hardening rate decreases because more κ-carbides are sheared by dislocations during deformation at higher strain rates, which causes a reduction in the hindrance to dislo cation slip. Increasing the aging temperature leads to an increase in the strength for the same strain rate, and an enhancement in the strain-rate sensitivity of the yield strength at strain rates of 10 3–100 s 1 due to the increasing precipitation of κ-carbides. In addition, the effect of dynamic strain aging during deformation on the strain hardening rate was discussed as well.
1. Introduction Fe–Mn–Al–C austenite-based lightweight steels have potential ap plications in the automotive industry due to their low densities and superior combination of high strength and good ductility, which allows them to meet the strict requirements for vehicle safety and low fuel consumption [1–7]. The steels usually contain a high content of Mn (12–30 wt%), Al (<12 wt%), and C (0.6–2.0 wt%) [1–13]. The addition of Al to the steels has two important effects besides reducing the density: increasing the stacking fault energy (SFE) and producing κ-carbide [(Fe, Mn)3AlC] precipitates, which affect the mechanical properties and deformation behavior [10,11,14]. The sizes, morphologies, and distribution of κ-carbide precipitates in the steels are influenced by heat treatments and their compositions. Aging Fe–Mn–Al–C steels containing 5–10 wt% Al at temperatures be tween 450 and 625 � C for several hours after solid-solution treatment results in the formation and growth of nano-sized κ-carbides in the matrix, which is beneficial for improving the strength [3,8,15,16]. With increasing aging time or temperature, the mean size of the κ-carbides increases, generally from 2 to 30 nm [3,8,15–18]. The formation of
inter-granular κ-carbides and β-Mn precipitates along the grain bound aries after over-aging deteriorates the strength and ductility synchro nously [8,19]. In addition, alloying elements, such as Cu and Si in Fe–Mn–Al–C steels, produce other phases or affect the precipitation of κ-carbides [5,20–22]. For example, adding Cu in Fe-0.5C–12Mn–7Al steel causes the formation of Cu-rich B2 particles [5]. The addition of Si facilitates the coarseness of κ-carbides, while the addition of Mo inhibits their formation [21,22]. Furthermore, micro-alloying elements, such as Ti, Nb, Mo, and V, can improve the strengths of the steels through further precipitation strengthening [23–25]. However, to date, no re ports have been published on the effect of multiple additions of Mo and Nb on the microstructures and precipitation of κ-carbides in these lightweight steels. The deformation of austenite-based lightweight steels is mainly dominated by planar glide due to the high SFE, over 70 mJ/m2, and dislocations cutting the κ-carbides [26–30]. Organized substructures, e. g., Taylor lattices, microbands, and slip bands, can form during defor mation, and the spacing of the bands decreases with strain, resulting in excellent ductility [28,31–35]. Additionally, the increase in the volume fraction and sizes of the κ-carbide precipitates decreases the density of
* Corresponding author. School of Materials Science and Engineering, Beijing Institute of Technology, Beijing, 100081, China. E-mail address: [email protected] (Y. Wang). https://doi.org/10.1016/j.msea.2019.138700 Received 24 September 2019; Received in revised form 15 November 2019; Accepted 17 November 2019 Available online 19 November 2019 0921-5093/© 2019 Elsevier B.V. All rights reserved.
Please cite this article as: Zhuang Li, Materials Science & Engineering A, https://doi.org/10.1016/j.msea.2019.138700
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slip bands by restricting dislocation activities in the limited slip systems [10,21]. Although the deformation mechanism has been widely studied, most of the studies involved quasi-static tensile loading, and few papers have documented the deformation behavior of these steels under different strain rates. Moreover, the effect of strain rate on the in teractions between dislocations and κ-carbides is not clear. A review of the published data shows that the microstructures and quasi-static tensile properties of the Fe–Mn–Al–C steels have been extensively investigated. Nevertheless, no reports are available in which the compressive behavior of Fe–Mn–Al–C austenitic lightweight steels micro-alloyed with Mo and Nb at different strain rates are evaluated, even though this behavior is crucial for future industrial applications. For example, as parts of vehicles, these steels may be subjected to im pacts at different strain rates during service or in automotive crashes. Accordingly, the present research was conducted to address this deficiency by studying the microstructure and compressive behavior at strain rates ranging from 10 3 to 103 s 1 of a Fe–Mn–Al–C lightweight steel micro-alloyed by Mo and Nb after solid-solution treatment and aging at temperatures from 400 to 600 � C.
microscopy (TEM, Tecnai F20) were used to observe the microstructures before and after compression testing. The samples for TEM testing were prepared by electro-polishing in an electrolyte of 90% methanol and 10% perchloric acid (vol%) using a voltage of 20 V at 30 � C. After electro-polishing, the samples were further thinned by ion-milling (Leica RES 101) at 3 kV using a current of 1 mA for 30 min to remove any possible contamination caused by electro-polishing. 3. Results 3.1. Microstructures characterization after aging Fig. 1 shows XRD patterns of the steel after aging at temperatures of 400–600 � C, which reveals the presence of austenite and κ phases in the aged samples. The (111) and (200) peaks of the austenite in the A60 are significantly broader, as indicated by the arrows, than those of the samples aged at lower temperatures. The full widths at half maximum of the (200) peaks are broadened from 0.595� to 0.684� with increasing aging temperature, indicating an increase in volume fraction of the κ-carbides [36]. Fig. 2 shows the microstructures of the steel after aging. The left-hand column of Fig. 2 shows the OM micrographs with equiaxial austenite grains within annealing twins. The SEM images displayed in the middle column at high magnification show the distribution of an unknown larger second phase in the matrix. The right-hand column shows the TEM images illustrating the morphology and distribution of a kind of nanoscale precipitate in the matrix with the corresponding selected-area electron-diffraction (SAED) patterns inserted, which verify the presence of the κ-carbides. To examine the compositions of the white particles in Fig. 2(b), (e), and (h), energy-dispersive X-ray-spectroscopy (EDX) tests were conducted, and Fig. 3(a) shows that the particles are composed of elemental carbon, niobium, and molybdenum. The SAED pattern shown in Fig. 3(b) suggests that the particles possess face-centered-cubic (fcc) crystal structure with a lattice parameter of ~4.59 Å. Therefore, these particles are determined to be (Nb,Mo)C. Overall, the microstructures of the steel after aging at different tem peratures consist of equiaxial austenite grains within annealing twins and two types of precipitates, namely, κ-carbide with smaller sizes and (Nb,Mo)C carbide with larger sizes, and both are distributed uniformly in the matrix. Upon increasing the aging temperature from 400 to 600 � C, the austenite grains coarsen slightly, with mean sizes increasing from ~14 to ~16 μm, as shown in Fig. 2(b), (e), and (f). This is ascribed to the presence of a large number of precipitates in the matrix that hinder
2. Experimental material and procedures A steel having a chemical composition (wt.%) of Fe–27Mn–8Al-1.6C0.1Nb-0.3Mo was fabricated by a vacuum induction melting furnace under an Ar atmosphere. The density was measured to be 6.78 g/cm3 by the Archimedes method, which is 13% lighter than traditional com mercial steels. An ingot was hot-forged into rods with ~12 mm in diameter at 1100–900 � C followed by air cooling. Next, short bars cut from the forged rods were solution-treated at 950 � C for 1 h followed by water quenching and subsequent aging at temperatures ranging from 400 to 600 � C for 2 h, after which they were air cooled to room tem perature. For convenience, the samples aged at 400, 450, 500, 550, and 600 � C are henceforth designated A40, A45, A50, A55, and A60, respectively. Compressive testing was carried out at room temperature using an INSTRON5985 testing machine with a strain rate of 10 3 s 1, a Gleeble 3500 thermal simulator with strain rates of 10 1 and 100 s 1, and a split Hopkinson pressure bar with a strain rate of 103 s 1. The compressive specimens were cut from the aged bars with diameters of 5 mm and heights of 5 mm. Four samples for each condition were tested to verify repeatability. The phase constitution was analyzed by X-ray diffraction (XRD, Bruker D8 Advance). Optical microscopy (OM), scanning electron microscopy (SEM, HITACHI-S4800), and transmission electron
Fig. 1. XRD patterns of the Fe–Mn–Al–C steel after aging at 400–600 � C. 2
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Fig. 2. Microstructures of the steel after aging at (a–c) 400 � C, (d–f) 500 � C, and (g–i) 600 � C. The left-hand column (a,d,f) shows OM images, the middle column (b,e, h) shows SEM images, and the right-hand column (c,f,i) shows TEM images.
Fig. 3. (a) EDX results of the (Nb,Mo)C particles in the Fe–Mn–Al–C steel and (b) SAED of the (Nb,Mo)C particles.
grain-boundary migration during aging. Fig. 2(b), (e), and (f) show that the (Nb,Mo)C precipitates possess mean size of ~57 nm. Furthermore, the sizes and distribution remain unchanged with increasing aging temperature. This is because the (Nb,Mo)C particles form during hotforging and could not dissolve during the solution treatment at 950 � C. Thus, no more Nb and Mo solutes exist in the matrix to provide nucleation sites for new (Nb,Mo)C particles or coarseness during aging. Fig. 2(c) and (f) show that the spherical κ-carbides with average sizes of ~1.6 and ~2.5 nm are distributed in the matrix of the A40 and A50 steels, respectively. After aging at 600 � C, the κ-carbides became cu boids, and the average size of the κ-carbides increases to ~5.4 nm, as shown in Fig. 2(i). Based on the literature, larger sized κ-carbides were present in Fe–Mn–Al–C lightweight austenitic steels with similar pro portions of Al, Mn, and C but without Nb and Mo after aging at lower temperatures or solution treatment. For example, κ-carbides in Fe30.5Mn-8.0Al-1.2C steel after aging at 450 � C for 1 h were 2–5 nm in size. In Fe-25.7Mn-10.6Al-1.16C steel after solution treatment at 1050 � C followed by water cooling, the sizes were ~7.7 nm [3,35]. This demonstrates that multiple additions of the micro-alloying elements Nb
and Mo to the steels suppress the growth of κ-carbides during aging. 3.2. Compressive properties Fig. 4 displays the true stress–true strain curves of the steel after aging at different temperatures tested at strain rates of 10 3–103 s 1. It is obvious that the strength and flow stress are influenced by the aging temperature and strain rate. Upon increasing the aging temperature from 400 to 600 � C, the yield and flow stresses increase significantly at the same strain rates. Table 1 shows the yield strengths of the steels at different strain rates, illustrating that, with the strain rate increasing from 10 3 to 103 s 1, the yield strength increases by ~430–530 MPa for these aged steels, showing a strain-rate strengthening effect. Further more, it shows a stronger strain-rate strengthening effect when strain rate is increased from 100 to 103 s 1 than from 10 3 to 100 s 1. For example, the increases in yield strength are 99, 106, and 174 MPa for the A40, A50, and A60 steels, respectively, upon increasing the strain rate from 10 3 to 100 s 1, and they are 366, 361, and 362 MPa when the strain rate is increased from 100 to 103 s 1 3
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Fig. 4. True stress–true strain curves of Fe–Mn–Al–C steel after aging at 400–600 � C at different strain rates: (a) 10 Table 1 Yield strengths (MPa) values at strain rates from 10 Fe–Mn–Al–C steel after aging at 400 � C–600 � C. Strain rate
3
–103 s
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3
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, (b) 10
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, and (d) 103 s
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.
of the
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450 � C
500 � C
550 � C
600 � C
1017 � 15.6 1067 � 14.8 1116 � 26.2 1482 � 21.0
1031 � 19.9 1075 � 14.6 1140 � 20.5 1509 � 1.7
1177 � 30.9 1203 � 22.3 1283 � 10.5 1644 � 32.6
1383 � 41.3 1472 � 4.9
1597 � 12.4 1691 � 2.3
1560 � 24
1771 � 12.6 2133 � 13.1
1915 � 26.2
The flow stresses at strain rates of 10 3–100 s 1 increase continu ously with strain until unloading, as shown in Fig. 4(a–c), indicating that strain hardening dominates the plastic deformation. At 103 s 1, A40, A45, and A50 still exhibit a strain-hardening effect, whereas A55 and A60 exhibit a strain-softening effect, showing a gradual decrease in the flow stress with further straining, as shown in Fig. 4(d). 3.3. Microstructures characterization after compression To examine the strain-rate dependence of the deformation mecha nism, Fig. 5 presents the deformation microstructures of A55 after compression at different strain rates. It shows the appearance of slip bands, indicated by dotted lines, which consist of a high density of curved dislocations [37,38]. Two sets of slip bands on different slip planes that intersected after compression at a strain rate of 10 3 s 1 are visible in Fig. 5(a), showing a planar glide characteristics [28,35]. At 10 1 s 1, two sets of slip bands with smaller spacings than that observed at 10 3 s 1 are evident in Fig. 5(b). At 100 s 1, three non-coplanar slip bands appear with the presence of high density of dislocations, as shown in Fig. 5(c). Fig. 5(d) displays a similar slip-band configuration at 103 s 1
Fig. 5. Slip-band configurations of the Fe–Mn–Al–C steel aged at 550 � C after compression at different strain rates: (a) 10 3 s 1, (b) 10 1 s 1, (c) 100 s 1, and (d) 103 s 1.
as shown in Fig. 5(c), but with a smaller spacing. Similar results have been previously reported [39]. This indicates that more dislocations are involved in the deformation at higher strain rates. Meanwhile, limited cross-slip traces are evident after compression at 103 s 1, as shown in Fig. 6. 4
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To evaluate the influence of aging temperature on deformation, Fig. 7 shows the deformed microstructures of A40 and A60 after compression at 10 3 s 1. Two non-coplanar slip bands are shown in Fig. 7(a) and (b) in the aged steels after compression at a strain rate of 10 3 s 1. Inspection of Figs. 5(a), 7(a) and (b) shows that the mean spacings of the two non-coplanar slip bands are ~120 and ~42 nm for A40, ~144 and ~63 nm for A55, and ~262 and ~74 nm for A60. Thus, the spacings of the slip bands increase with increasing aging temperature. Fig. 8 shows a TEM dark-field image of the κ-carbides in A60 after compression at 10 3 s 1. The enlarged area in Fig. 8 shows the κ-car bides being sheared by dislocations, proving the shearability of the κ-carbides [37]. Fig. 9 shows high-resolution TEM (HRTEM) images of the (Nb,Mo)C particles in A55 and the corresponding inverse-Fourier-transform (IFT) images of the {111} planes after compression at 10 3 and 103 s 1. The interfaces of the (Nb,Mo)C/γ are indicated by white spots in Fig. 9(b) and (d). At 10 3 and 103 s 1, a high density of dislocations in the matrix around the particles is evident. This demonstrates that the (Nb,Mo)C particles have a considerable effect on hindering the dislocation motion. The densities of the piled-up dislocations around the (Nb,Mo)C particles in the matrix shown in Fig. 9(b) and (d) are calculated by the number of dislocations per unit area. They are 0.120 and 0.141 nm 2 after compression at 10 3 and 103 s 1, respectively. A higher dislocation density is presented at 103 s 1, indicating that the dislocation slip ac tivity is more intensive at 103 s 1 than at 10 3 s 1.
Fig. 7. Slip-band configurations of the Fe–Mn–Al–C steel aged at (a) 400 � C and (b) 600 � C after compression at strain rate of 10 3 s 1.
4. Discussion 4.1. Effect of strain rate on compression behavior Fig. 4 and Table 1 show that the yield strengths of the aged steel increase with increasing strain rate, exhibiting a significant strain-rate strengthening effect. Because the dislocation motion is accelerated by increasing strain rate [40], the interactions between dislocations and κ-carbides are enhanced, which improves the precipitation strength ening. In addition, the larger number of dislocations in front of the (Nb, Mo)C particles after compressive testing at 103 s 1 than that at 10 3 s 1, as shown in Fig. 9(b) and (d) indicates that more dislocations interact with the (Nb,Mo)C precipitates as well at higher strain rates. This also contributes to the strain-rate strengthening effect for the aged steel. To evaluate the influence of the aging temperature on strain-rate strengthening effect, the sensitivity of the yield stress to the strain rate was quantitatively analyzed using the following equation [41]: ln_ε ¼ ðσ
σμ ÞV * =MkT þ ln_ε0
Fig. 8. Morphologies of the κ-carbides in the Fe–Mn–Al–C steel aged at 600 � C after compression at 10 3 s 1.
where σ is the total yield stress, σμ is athermal component of σ, V * is the activation volume of moving dislocations, M ¼ 3.06 is the average Taylor factor for untextured polycrystalline materials, k is the Boltz mann constant, T is the absolute temperature, ε_ 0 is the pre-exponential factor, and ΔG0 is the Helmholtz free energy of activation, which is the total energy required to overcome short-range obstacles without the aid of an applied shear stress [42]. Eq. (1) can be simplified as follows:
(1)
ΔG0 =kT;
ln_ε ¼ K σ þ B;
Fig. 6. Cross-slip lines in A55 after compression at 103 s
1
(2)
and thus, K ¼ V*/MkT, which reflects the strain-rate sensitivity (SRS). A smaller K value corresponds to a higher sensitivity of strength to strain rate. The parameter B ¼ ln_ε0 ðΔG0 V * σμ Þ=kT, and B can be regarded as a constant for a material at fixed testing temperature. Fig. 10 shows plots of ln_ε versus the yield stress (σ). The experimental data for the steel after different aging treatments were linearly fitted in the strain-rate range of 10 3–100 s 1 and 100–103 s 1. Based on Eq. (2), the values of K were obtained from the slopes of the fitting lines and are shown in Fig. 10. It shows with aging temperature increasing K (K1) decreases from ~0.070 to ~0.040 which indicates that the SRS increase in the strain-rate range of 10 3–100 s 1, whereas the K values (K2) remained at ~0.019 in the strain-rate range of 100–103 s 1. It is also apparent that the K values (K1) for strain rates below 100 s 1 are larger than those (K2) for strain rates above 100 s 1 for the five as-aged steels. It is attributed to the dislocation motion having different driving
. 5
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e., SRS), the activation volume V * can be written as follows [44]: V * ¼ b � ξ � l* :
(3)
Thus, K ¼ b � ξ � l* =MkT;
(4)
where b is the Burgers vector of the dislocations, ξ is the distance swept out by the mobile dislocation during one activation event, which can be regarded as a constant, and l* is the length, which scales with the average contact distance between two obstacles. Owing to the increase in the volume fraction and slight coarseness of the κ precipitates with increasing aging temperature, as shown in Figs. 1 and 2, the spacing between κ-carbides decreases, leading to a decrease in l*. Thus, the value of K decreases according to Eq. (4), which indicates the increase in the strain-rate sensitivity of the yield stress. 4.2. Effect of aging temperature on compressive behavior The yield strength of the steel is enhanced with increasing aging temperature at a fixed strain rate, as shown in Fig. 4. The grain refine ment strengthening can be ignored because the sizes of the austenitic grains are only coarsened slightly after aging at temperatures from 400 to 600 � C. Thus, the enhancement in the strength is mainly due to pre cipitation strengthening. Fig. 8 reveals that the κ-carbide precipitates are sheared by the dislocations, and the strength can be calculated using the Friedel statistics equation [45]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 1 3k2 M μ pffiffi ðfv RÞ2 ; σp ¼ (5) 4πβ b
Fig. 9. HRTEM images showing the (Nb,Mo)C particles in the Fe–Mn–Al–C steel aged at 550 � C after compression at (a) 10 3 s 1 and (c) 103 s 1 and the corresponding IFT images of the {111} planes at (b) 10 3 s 1 and (d) 103 s 1.
where σp is the yield strength increment, β is a constant, M is the Taylor factor, μ is the matrix shear modulus, b is the Burgers vector, fv is the volume fraction, and R is the mean radius of the precipitates. As the aging temperature increases from 400 to 600 � C, the volume fraction and the sizes of the κ-carbides increase, as shown in Figs. 1 and 2, leading to an increase in the yield strength according to Eq. (5). Addi tionally, the piled-up dislocations around the (Nb,Mo)C particle in Fig. 9 indicate that the (Nb,Mo)C particles distributed in the matrix are effective for improving the strength as well. However, the contribution to the strengthening for the sample aged at different temperatures is almost the same, because the distribution and sizes of the (Nb,Mo)C particles in the matrix remain basically unchanged. The pronounced planar glide characteristics expressed by the noncoplanar slip bands are observed in the aged steel after compression at strain rates from 10 3 to 103 s 1, as shown in Figs. 5 and 7. Therefore, the planar glide mechanism dominates the plastic deformation during the compression at different strain rates. The SFE of the aged steel was calculated to be ~77 mJ/m2. This plays an important role in the planar glide appearance during deformation because a high SFE, i.e., over 70 mJ/m2, can suppress the effect of Transformation-Induced Plasticity (TRIP) and Twinning-Induced Plasticity (TWIP) in high-Mn and high-Al Fe–Mn–Al–C steels [11,29,30,46]. Moreover, the κ-carbides in the austenite matrix facilitate the planar glide mechanism [13,16]. After the κ-carbides are sheared by the leading dislocations, the blocking forces for the dislocation motion are significantly weakened. As a result, the subsequent dislocations could glide easily on the same glide plane, causing glide plane softening [28,33]. In addition, the solute interstitial C atoms in the matrix were found to hinder dislocation cross-slip [38] and this may offset the promotion to cross-slip by high SFE in the steels. Fig. 7 reveals that there was a larger spacing between the slip bands in A60 than in A40 after deformation at the same strain rate. This is ascribed to the increase in the volume fraction and the coarseness of the κ-carbides in the matrix with increasing aging temperature, as shown in Figs. 1 and 2. In the steel aged at 600 � C, the κ-carbide was more difficult to be sheared by the mobile dislocations due to their larger sizes relative
Fig. 10. Plots of ln_ε as a function of yield stress σ obtained from the compression experiments shown in Fig. 4 at room temperature (298 K). The solid and dotted lines are linear fits between ln_ε and σ of the as-aged steel below and above 100 s 1, respectively. The values of K are equal to the slopes of the lines.
mechanism below and above strain rate of 100 s 1 [43]. At strain rates below 100 s 1 the dislocation motion is thermally activated so that the precipitates in the matrix control the glide resistance of dislocation, thus, with increasing aging temperature the increased number of κ-carbides further hinder the dislocation motion. As a result, the strain-rate strengthening effect increases, yielding a decrease in the K values (K1). However, at strain rates above 100 s 1, the dislocation motion is drag-dependent and only weakly depends on the precipitates. Thus, the strain rate sensitivity is almost independent of the variation of the κ-carbides after different aging treatments and K values (K2) above 100 s 1 in Fig. 10 are the same for the five different aging treated steels. To further understand the effect of κ on the K values below 100 s 1 (i. 6
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to the precipitates in A40, so that the critical stress required to cut the κ-carbides is increased. Thus, dislocations in A60 would slip more likely along the as-activated planes (softened planes) rather than activate new glide planes than that in A40. This created a larger spacing between the slip bands [26].
temperatures, as shown in Fig. 2, which reduced the density of slip bands, as shown in Figs. 5(a) and 7. The boundaries of the slip bands can block the dislocation motion with further straining [8,10,16,38]. Consequently, the reduction in the density of the slip bands with increasing aging temperature decreases the impediment to the disloca tion motion and thereby weakened the effect of strain hardening. Second, as the aging temperature increases, the reduction in the θ value is also related to the dynamic strain aging (DSA), which results from the interaction between the diffusing solute atoms (mainly carbon atoms in this work) and mobile dislocations [48]. The serrated curves of the strain hardening rate versus true strain in the 10 3–100 s 1 range shown in Fig. 11 verifies that the Portevin–Le Chatelier (PLC) effect is induced by the DSA [49]. As the aging temperature increases from 400 to 600 � C, the formation of more κ-carbides decreases the number of interstitial carbon atoms in the matrix, which reduces the contribution of the DSA strengthening to strain hardening. Consequently, the strain hardening rates of the steel after aging at 400 and 450 � C are higher than that after aging at 500–600 � C shown by Fig. 4 (a–c) and Fig. 11. However, it is considered that the DSA is either insignificant or does not occur at 103 s 1. Because the flow stress increases with the aging tem perature increasing during the whole deformation at 103 s 1, which is different from the behavior at strain rates in the 10 3–100 s 1 range, as shown in Fig. 4. For example, the flow stress of A40 is higher than that of A45 from a certain true strain at the strain-rate range of 10 3–100 s 1. This indicates a little or no contribution of DSA to the strain hardening rate at 103 s 1 as comparison to that at 10 3–100 s 1. In addition, the fluctuation on the strain hardening rate curves at 103 s 1 shown by Fig. 11 could be induced by the load fluctuation of split Hopkinson pressure bar test. As a result, DSA is not evident at 103 s 1. It is obvious in Fig. 11(a–e) that the value of θ for the A40 and A45 remains positive and for the A50, it is below zero from the yield point to the true strain of ~0.09, after which it is positive again. However, for the A55 and A60 steels, it is negative after yield, showing that flow softening is dominant during plastic deformation. This is caused by the reduction in the density of slip bands mentioned before as well as the adiabatic temperature rise during dynamic testing at 103 s 1. The temperature rise can be calculated as follows [47]: Z εf β ΔT ¼ σ dε; (6) ρC p 0
4.3. Strain hardening rates The curves of the strain hardening rate (θ) (θ ¼ dσ /dε, where σ is the true stress and ε is the true strain) versus the true strain for various strain rates are plotted in Fig. 11. Under all of the experimental conditions, the values of θ are initially very large and subsequently decrease rapidly. This stage can be regarded as the transition from elastic to plastic deformation. Next, the values of θ change slowly with further straining, indicating that plastic deformation is in progress. In Fig. 11(a), the values of θ for A40 tested at strain rates from 10 3 to 103 s 1 remain positive. This demonstrates that strain hardening plays a dominant role throughout the plastic deformation. Additionally, the strain hardening rate decreases with increasing strain rate, and it de creases more significantly when the strain rates increase from 100 to 103 s 1 than when they increase from 10 3 to 100 s 1, because the adiabatic temperature rise assists the thermal softening at high strain rates [47]. The continuously decreasing trend of the strain hardening rate with increasing strain rate is ascribed to the difference in the initial amount of activated dislocations at various strain rates. With increasing strain rate, the increased yield strength leads to an enhancement in the initial driving force for dislocation motion, which produces more dislocations involved in the slip at higher strain rates, as shown in Fig. 5. Conse quently, more κ-carbides are cut by dislocations at higher strain rates, so that the hindrance to the dislocation slip is reduced, resulting in a decrease in the strain hardening rate. It is noted that the increase of strain rate promotes the formation of slip bands which reduces spacing between slip bands, as shown in Fig. 5. The boundaries of slip bands are obstacles for dislocation movement so that finer spacing between slip bands can increase strain hardening rate [10]. In this case, increasing strain rate has both adverse and beneficial effects on strain hardening, but it is clear that the adverse effect is dominant. A comparison of Fig. 11(a–e) shows that the θ values decrease as the aging temperatures increase from 400 to 600 � C at the same strain rate. First, more and larger precipitates form in the steels after aging at higher
Fig. 11. Strain-hardening rate–true strain curves of the Fe–Mn–Al–C steel after aging at (a) 400 � C, (b) 450 � C, (c) 500 � C, (d) 550 � C, and (e) 600 � C after compression at strain rates ranging from 10 3 to 103 s 1. 7
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References
where β ¼ 0.9 is the fraction of energy conversion, ρ ¼ 6.78 g/cm3 is the density of the sample, Cp ¼ 460 J/(kg⋅K) is the specific heat capacity, σ is the flow stress, and εf is the final true strain. Flow stresses of the aged samples increase with increasing aging temperature at 103 s 1, as shown in Fig. 4(d). For example, at a true strain of 0.15, the ΔT increases from 56.2 to 76.2 � C after the aging temperature increases from 400 to 600 � C. Hence, the difference in the adiabatic temperature rise is small for the five age-treated steels. The main reason for the reduction of the SHR with the aging temperature at 103 s 1 is the reduction in the density of the slip bands. In addition, the adiabatic temperature rise also causes the SFE to increase. The maximum SFE increase of the as-aged steel, obtained for the A55 steel, is calculated to be ~10 mJ/m2. As a result, cross-slip is observed after compression at 103 s 1 due to this effect, as shown in Fig. 6.
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5. Conclusions Experiments were conducted to examine the effect of the aging temperature between 400 to 600 � C and in the strain-rate range of 10 3–103 s 1 on the microstructural evolution and compressive behavior of a Fe–Mn–Al–C-lightweight steel micro-alloyed with Mo and Nb. The following conclusions were drawn. 1. After aging at temperatures from 400 to 600 � C, the microstructure of the steel is composed of equiaxial austenite grains within annealing twins, and two types of nano-sized precipitates (Nb,Mo)C and κ-carbides, distributed uniformly in the matrix. With increasing aging temperature, the austenite grains coarsen slightly with the volume fraction and sizes of the κ-carbides increasing, whereas the sizes and distribution of the (Nb,Mo)C particles remain unchanged. 2. The aged steel exhibits a significant strain-rate strengthening effect resulting from the enhancement of the interactions between dislo cations and the carbides in the matrix at higher strain rates. With increasing strain rate, the strain hardening rate decreases because the number of κ-carbides cut by dislocations increases during deformation, which reduce the hindrance to dislocation slip. 3. Increasing aging temperature leads to an increase in the strength at the same strain rate and an enhancement in the strain-rate sensitivity of the strength at strain rates from 10 3–100 s 1 due to the increased precipitation strengthening of the κ-carbides. The strain-rate sensi tivity of the strength above 100 s 1 is independent of the aging temperature. Insufficient aging up to 450 � C causes dynamic strain aging during compression at stain rates from 10 3–100 s 1, which also contribute to the strain hardening rate. Author contributions section Zhuang Li: Conceptualization, Validation, Formal analysis, Investi gation, Writing-Original Draft, Writing-Review & Editing. Yingchun Wang: Conceptualization, Writing-Review & Editing, Supervision. Xingwang Cheng: Project administration, Funding acquisition, Super vision, Jiaxin Liang: Investigation. Shukui Li: Supervision. Declaration of competing interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work was supported by the National Natural Science Foundation of China under Grant no. 51671030. 8
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[29] C. Haase, C. Zehnder, T. Ingendahl, A. Bikar, F. Tang, B. Hallstedt, W. Hu, W. Bleck, D.A. Molodov, On the deformation behavior of κ-carbide-free and κ-carbide containing high-Mn light-weight steel, Acta Mater. 122 (2017) 332–343. [30] H. Ding, D. Han, J. Zhang, Z.H. Cai, Z.Q. Wu, M.H. Cai, Tensile deformation behavior analysis of low density Fe-18Mn-10Al-xC steels, Mater. Sci. Eng. A 652 (2016) 69–76. [31] E. Welsch, D. Ponge, S.M.H. Haghighat, S. Sandlobes, P. Choi, M. Herbig, S. Zaefferer, D. Raabe, Strain hardening by dynamic slip band refinement in a highMn lightweight steel, Acta Mater. 116 (2016) 188–199. [32] S.S. Sohn, H. Song, B.C. Suh, J.H. Kwak, B.J. Lee, N.J. Kim, S. Lee, Novel ultrahighstrength (ferrite þ austenite) duplex lightweight steels achieved by fine dislocation substructures (Taylor lattices), grain refinement, and partial recrystallization, Acta Mater. 96 (2015) 301–310. [33] V. Gerold, H.P. Karnthaler, On the origin of planar slip in f.c.c. alloys, Acta Metall. 37 (1989) 2177. [34] E. Nembach, K. Suzuki, M. Ichihara, S. Takeuchi, In situ deformation of the γ’ hardened superalloy Nimonic PE16 in high-voltage electron microscopes, Philos. Mag. A 51 (1985) 607. [35] I. Gutierrez-Urrutia, D. Raabe, Influence of Al content and precipitation state on the mechanical behavior of austenitic high-Mn low-density steels, Scr. Mater. 68 (2013) 343–347. [36] W.K. Choo, J.H. Kim, J.C. Yoon, Microstructural change in austenitic Fe-30.0wt% Mn-7.8wt%Al-1.3wt%C initiated by spinodal decomposition and its influence on mechanical properties, Acta Mater. 45 (1997) 4877–4885. [37] M.J. Yao, E. Welsch, D. Ponge, S.M.H. Haghighat, S. Sandl€ obes, P. Choi, M. Herbig, I. Bleskov, T. Hickel, M.L. Chwalek, P. Shanthraj, C. Scheu, S. Zaefferer, B. Gault, D. Raabe, Strengthening and strain hardening mechanisms in a precipitationhardened high-Mn lightweight steel, Acta Mater. 140 (2017) 258–273.
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Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: http://www.elsevier.com/locate/msea
Compressive behavior of a Fe–Mn–Al–C lightweight steel at different strain rates Zhuang Li a, Yingchun Wang a, b, *, Xingwang Cheng a, b, Jiaxin Liang a, Shukui Li a, b a b
School of Materials Science and Engineering, Beijing Institute of Technology, Beijing, 100081, China National Key Laboratory of Science and Technology on Materials under Shock and Impact, Beijing, 100081, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Fe-Mn-Al-C austenite-based steel Strain-rate sensitivity κ-carbide Compression properties Slip band
Experiments were conducted to evaluate the compression behavior at strain rates in the range 10 3–103 s 1 of a Fe–Mn–Al–C lightweight steel micro-alloyed with Mo and Nb after aging at different temperatures. The results show that the microstructures of the steels after aging at temperatures from 400 to 600 � C are composed of austenite grains and two types of nano-sized precipitates, (Nb,Mo)C and κ-carbides, distributed uniformly in the matrix. Increasing the aging temperature results in the growth of the κ-carbides but has no effect on the sizes and distribution of the (Nb,Mo)C particles. The aged steel exhibits a significant strain-rate strengthening effect resulting from the enhancement of the interactions between dislocations and the carbides in the matrix at higher strain rates. With increasing strain rate, the strain hardening rate decreases because more κ-carbides are sheared by dislocations during deformation at higher strain rates, which causes a reduction in the hindrance to dislo cation slip. Increasing the aging temperature leads to an increase in the strength for the same strain rate, and an enhancement in the strain-rate sensitivity of the yield strength at strain rates of 10 3–100 s 1 due to the increasing precipitation of κ-carbides. In addition, the effect of dynamic strain aging during deformation on the strain hardening rate was discussed as well.
1. Introduction Fe–Mn–Al–C austenite-based lightweight steels have potential ap plications in the automotive industry due to their low densities and superior combination of high strength and good ductility, which allows them to meet the strict requirements for vehicle safety and low fuel consumption [1–7]. The steels usually contain a high content of Mn (12–30 wt%), Al (<12 wt%), and C (0.6–2.0 wt%) [1–13]. The addition of Al to the steels has two important effects besides reducing the density: increasing the stacking fault energy (SFE) and producing κ-carbide [(Fe, Mn)3AlC] precipitates, which affect the mechanical properties and deformation behavior [10,11,14]. The sizes, morphologies, and distribution of κ-carbide precipitates in the steels are influenced by heat treatments and their compositions. Aging Fe–Mn–Al–C steels containing 5–10 wt% Al at temperatures be tween 450 and 625 � C for several hours after solid-solution treatment results in the formation and growth of nano-sized κ-carbides in the matrix, which is beneficial for improving the strength [3,8,15,16]. With increasing aging time or temperature, the mean size of the κ-carbides increases, generally from 2 to 30 nm [3,8,15–18]. The formation of
inter-granular κ-carbides and β-Mn precipitates along the grain bound aries after over-aging deteriorates the strength and ductility synchro nously [8,19]. In addition, alloying elements, such as Cu and Si in Fe–Mn–Al–C steels, produce other phases or affect the precipitation of κ-carbides [5,20–22]. For example, adding Cu in Fe-0.5C–12Mn–7Al steel causes the formation of Cu-rich B2 particles [5]. The addition of Si facilitates the coarseness of κ-carbides, while the addition of Mo inhibits their formation [21,22]. Furthermore, micro-alloying elements, such as Ti, Nb, Mo, and V, can improve the strengths of the steels through further precipitation strengthening [23–25]. However, to date, no re ports have been published on the effect of multiple additions of Mo and Nb on the microstructures and precipitation of κ-carbides in these lightweight steels. The deformation of austenite-based lightweight steels is mainly dominated by planar glide due to the high SFE, over 70 mJ/m2, and dislocations cutting the κ-carbides [26–30]. Organized substructures, e. g., Taylor lattices, microbands, and slip bands, can form during defor mation, and the spacing of the bands decreases with strain, resulting in excellent ductility [28,31–35]. Additionally, the increase in the volume fraction and sizes of the κ-carbide precipitates decreases the density of
* Corresponding author. School of Materials Science and Engineering, Beijing Institute of Technology, Beijing, 100081, China. E-mail address: [email protected] (Y. Wang). https://doi.org/10.1016/j.msea.2019.138700 Received 24 September 2019; Received in revised form 15 November 2019; Accepted 17 November 2019 Available online 19 November 2019 0921-5093/© 2019 Elsevier B.V. All rights reserved.
Please cite this article as: Zhuang Li, Materials Science & Engineering A, https://doi.org/10.1016/j.msea.2019.138700
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slip bands by restricting dislocation activities in the limited slip systems [10,21]. Although the deformation mechanism has been widely studied, most of the studies involved quasi-static tensile loading, and few papers have documented the deformation behavior of these steels under different strain rates. Moreover, the effect of strain rate on the in teractions between dislocations and κ-carbides is not clear. A review of the published data shows that the microstructures and quasi-static tensile properties of the Fe–Mn–Al–C steels have been extensively investigated. Nevertheless, no reports are available in which the compressive behavior of Fe–Mn–Al–C austenitic lightweight steels micro-alloyed with Mo and Nb at different strain rates are evaluated, even though this behavior is crucial for future industrial applications. For example, as parts of vehicles, these steels may be subjected to im pacts at different strain rates during service or in automotive crashes. Accordingly, the present research was conducted to address this deficiency by studying the microstructure and compressive behavior at strain rates ranging from 10 3 to 103 s 1 of a Fe–Mn–Al–C lightweight steel micro-alloyed by Mo and Nb after solid-solution treatment and aging at temperatures from 400 to 600 � C.
microscopy (TEM, Tecnai F20) were used to observe the microstructures before and after compression testing. The samples for TEM testing were prepared by electro-polishing in an electrolyte of 90% methanol and 10% perchloric acid (vol%) using a voltage of 20 V at 30 � C. After electro-polishing, the samples were further thinned by ion-milling (Leica RES 101) at 3 kV using a current of 1 mA for 30 min to remove any possible contamination caused by electro-polishing. 3. Results 3.1. Microstructures characterization after aging Fig. 1 shows XRD patterns of the steel after aging at temperatures of 400–600 � C, which reveals the presence of austenite and κ phases in the aged samples. The (111) and (200) peaks of the austenite in the A60 are significantly broader, as indicated by the arrows, than those of the samples aged at lower temperatures. The full widths at half maximum of the (200) peaks are broadened from 0.595� to 0.684� with increasing aging temperature, indicating an increase in volume fraction of the κ-carbides [36]. Fig. 2 shows the microstructures of the steel after aging. The left-hand column of Fig. 2 shows the OM micrographs with equiaxial austenite grains within annealing twins. The SEM images displayed in the middle column at high magnification show the distribution of an unknown larger second phase in the matrix. The right-hand column shows the TEM images illustrating the morphology and distribution of a kind of nanoscale precipitate in the matrix with the corresponding selected-area electron-diffraction (SAED) patterns inserted, which verify the presence of the κ-carbides. To examine the compositions of the white particles in Fig. 2(b), (e), and (h), energy-dispersive X-ray-spectroscopy (EDX) tests were conducted, and Fig. 3(a) shows that the particles are composed of elemental carbon, niobium, and molybdenum. The SAED pattern shown in Fig. 3(b) suggests that the particles possess face-centered-cubic (fcc) crystal structure with a lattice parameter of ~4.59 Å. Therefore, these particles are determined to be (Nb,Mo)C. Overall, the microstructures of the steel after aging at different tem peratures consist of equiaxial austenite grains within annealing twins and two types of precipitates, namely, κ-carbide with smaller sizes and (Nb,Mo)C carbide with larger sizes, and both are distributed uniformly in the matrix. Upon increasing the aging temperature from 400 to 600 � C, the austenite grains coarsen slightly, with mean sizes increasing from ~14 to ~16 μm, as shown in Fig. 2(b), (e), and (f). This is ascribed to the presence of a large number of precipitates in the matrix that hinder
2. Experimental material and procedures A steel having a chemical composition (wt.%) of Fe–27Mn–8Al-1.6C0.1Nb-0.3Mo was fabricated by a vacuum induction melting furnace under an Ar atmosphere. The density was measured to be 6.78 g/cm3 by the Archimedes method, which is 13% lighter than traditional com mercial steels. An ingot was hot-forged into rods with ~12 mm in diameter at 1100–900 � C followed by air cooling. Next, short bars cut from the forged rods were solution-treated at 950 � C for 1 h followed by water quenching and subsequent aging at temperatures ranging from 400 to 600 � C for 2 h, after which they were air cooled to room tem perature. For convenience, the samples aged at 400, 450, 500, 550, and 600 � C are henceforth designated A40, A45, A50, A55, and A60, respectively. Compressive testing was carried out at room temperature using an INSTRON5985 testing machine with a strain rate of 10 3 s 1, a Gleeble 3500 thermal simulator with strain rates of 10 1 and 100 s 1, and a split Hopkinson pressure bar with a strain rate of 103 s 1. The compressive specimens were cut from the aged bars with diameters of 5 mm and heights of 5 mm. Four samples for each condition were tested to verify repeatability. The phase constitution was analyzed by X-ray diffraction (XRD, Bruker D8 Advance). Optical microscopy (OM), scanning electron microscopy (SEM, HITACHI-S4800), and transmission electron
Fig. 1. XRD patterns of the Fe–Mn–Al–C steel after aging at 400–600 � C. 2
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Fig. 2. Microstructures of the steel after aging at (a–c) 400 � C, (d–f) 500 � C, and (g–i) 600 � C. The left-hand column (a,d,f) shows OM images, the middle column (b,e, h) shows SEM images, and the right-hand column (c,f,i) shows TEM images.
Fig. 3. (a) EDX results of the (Nb,Mo)C particles in the Fe–Mn–Al–C steel and (b) SAED of the (Nb,Mo)C particles.
grain-boundary migration during aging. Fig. 2(b), (e), and (f) show that the (Nb,Mo)C precipitates possess mean size of ~57 nm. Furthermore, the sizes and distribution remain unchanged with increasing aging temperature. This is because the (Nb,Mo)C particles form during hotforging and could not dissolve during the solution treatment at 950 � C. Thus, no more Nb and Mo solutes exist in the matrix to provide nucleation sites for new (Nb,Mo)C particles or coarseness during aging. Fig. 2(c) and (f) show that the spherical κ-carbides with average sizes of ~1.6 and ~2.5 nm are distributed in the matrix of the A40 and A50 steels, respectively. After aging at 600 � C, the κ-carbides became cu boids, and the average size of the κ-carbides increases to ~5.4 nm, as shown in Fig. 2(i). Based on the literature, larger sized κ-carbides were present in Fe–Mn–Al–C lightweight austenitic steels with similar pro portions of Al, Mn, and C but without Nb and Mo after aging at lower temperatures or solution treatment. For example, κ-carbides in Fe30.5Mn-8.0Al-1.2C steel after aging at 450 � C for 1 h were 2–5 nm in size. In Fe-25.7Mn-10.6Al-1.16C steel after solution treatment at 1050 � C followed by water cooling, the sizes were ~7.7 nm [3,35]. This demonstrates that multiple additions of the micro-alloying elements Nb
and Mo to the steels suppress the growth of κ-carbides during aging. 3.2. Compressive properties Fig. 4 displays the true stress–true strain curves of the steel after aging at different temperatures tested at strain rates of 10 3–103 s 1. It is obvious that the strength and flow stress are influenced by the aging temperature and strain rate. Upon increasing the aging temperature from 400 to 600 � C, the yield and flow stresses increase significantly at the same strain rates. Table 1 shows the yield strengths of the steels at different strain rates, illustrating that, with the strain rate increasing from 10 3 to 103 s 1, the yield strength increases by ~430–530 MPa for these aged steels, showing a strain-rate strengthening effect. Further more, it shows a stronger strain-rate strengthening effect when strain rate is increased from 100 to 103 s 1 than from 10 3 to 100 s 1. For example, the increases in yield strength are 99, 106, and 174 MPa for the A40, A50, and A60 steels, respectively, upon increasing the strain rate from 10 3 to 100 s 1, and they are 366, 361, and 362 MPa when the strain rate is increased from 100 to 103 s 1 3
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Fig. 4. True stress–true strain curves of Fe–Mn–Al–C steel after aging at 400–600 � C at different strain rates: (a) 10 Table 1 Yield strengths (MPa) values at strain rates from 10 Fe–Mn–Al–C steel after aging at 400 � C–600 � C. Strain rate
3
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1
3
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, (b) 10
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1017 � 15.6 1067 � 14.8 1116 � 26.2 1482 � 21.0
1031 � 19.9 1075 � 14.6 1140 � 20.5 1509 � 1.7
1177 � 30.9 1203 � 22.3 1283 � 10.5 1644 � 32.6
1383 � 41.3 1472 � 4.9
1597 � 12.4 1691 � 2.3
1560 � 24
1771 � 12.6 2133 � 13.1
1915 � 26.2
The flow stresses at strain rates of 10 3–100 s 1 increase continu ously with strain until unloading, as shown in Fig. 4(a–c), indicating that strain hardening dominates the plastic deformation. At 103 s 1, A40, A45, and A50 still exhibit a strain-hardening effect, whereas A55 and A60 exhibit a strain-softening effect, showing a gradual decrease in the flow stress with further straining, as shown in Fig. 4(d). 3.3. Microstructures characterization after compression To examine the strain-rate dependence of the deformation mecha nism, Fig. 5 presents the deformation microstructures of A55 after compression at different strain rates. It shows the appearance of slip bands, indicated by dotted lines, which consist of a high density of curved dislocations [37,38]. Two sets of slip bands on different slip planes that intersected after compression at a strain rate of 10 3 s 1 are visible in Fig. 5(a), showing a planar glide characteristics [28,35]. At 10 1 s 1, two sets of slip bands with smaller spacings than that observed at 10 3 s 1 are evident in Fig. 5(b). At 100 s 1, three non-coplanar slip bands appear with the presence of high density of dislocations, as shown in Fig. 5(c). Fig. 5(d) displays a similar slip-band configuration at 103 s 1
Fig. 5. Slip-band configurations of the Fe–Mn–Al–C steel aged at 550 � C after compression at different strain rates: (a) 10 3 s 1, (b) 10 1 s 1, (c) 100 s 1, and (d) 103 s 1.
as shown in Fig. 5(c), but with a smaller spacing. Similar results have been previously reported [39]. This indicates that more dislocations are involved in the deformation at higher strain rates. Meanwhile, limited cross-slip traces are evident after compression at 103 s 1, as shown in Fig. 6. 4
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To evaluate the influence of aging temperature on deformation, Fig. 7 shows the deformed microstructures of A40 and A60 after compression at 10 3 s 1. Two non-coplanar slip bands are shown in Fig. 7(a) and (b) in the aged steels after compression at a strain rate of 10 3 s 1. Inspection of Figs. 5(a), 7(a) and (b) shows that the mean spacings of the two non-coplanar slip bands are ~120 and ~42 nm for A40, ~144 and ~63 nm for A55, and ~262 and ~74 nm for A60. Thus, the spacings of the slip bands increase with increasing aging temperature. Fig. 8 shows a TEM dark-field image of the κ-carbides in A60 after compression at 10 3 s 1. The enlarged area in Fig. 8 shows the κ-car bides being sheared by dislocations, proving the shearability of the κ-carbides [37]. Fig. 9 shows high-resolution TEM (HRTEM) images of the (Nb,Mo)C particles in A55 and the corresponding inverse-Fourier-transform (IFT) images of the {111} planes after compression at 10 3 and 103 s 1. The interfaces of the (Nb,Mo)C/γ are indicated by white spots in Fig. 9(b) and (d). At 10 3 and 103 s 1, a high density of dislocations in the matrix around the particles is evident. This demonstrates that the (Nb,Mo)C particles have a considerable effect on hindering the dislocation motion. The densities of the piled-up dislocations around the (Nb,Mo)C particles in the matrix shown in Fig. 9(b) and (d) are calculated by the number of dislocations per unit area. They are 0.120 and 0.141 nm 2 after compression at 10 3 and 103 s 1, respectively. A higher dislocation density is presented at 103 s 1, indicating that the dislocation slip ac tivity is more intensive at 103 s 1 than at 10 3 s 1.
Fig. 7. Slip-band configurations of the Fe–Mn–Al–C steel aged at (a) 400 � C and (b) 600 � C after compression at strain rate of 10 3 s 1.
4. Discussion 4.1. Effect of strain rate on compression behavior Fig. 4 and Table 1 show that the yield strengths of the aged steel increase with increasing strain rate, exhibiting a significant strain-rate strengthening effect. Because the dislocation motion is accelerated by increasing strain rate [40], the interactions between dislocations and κ-carbides are enhanced, which improves the precipitation strength ening. In addition, the larger number of dislocations in front of the (Nb, Mo)C particles after compressive testing at 103 s 1 than that at 10 3 s 1, as shown in Fig. 9(b) and (d) indicates that more dislocations interact with the (Nb,Mo)C precipitates as well at higher strain rates. This also contributes to the strain-rate strengthening effect for the aged steel. To evaluate the influence of the aging temperature on strain-rate strengthening effect, the sensitivity of the yield stress to the strain rate was quantitatively analyzed using the following equation [41]: ln_ε ¼ ðσ
σμ ÞV * =MkT þ ln_ε0
Fig. 8. Morphologies of the κ-carbides in the Fe–Mn–Al–C steel aged at 600 � C after compression at 10 3 s 1.
where σ is the total yield stress, σμ is athermal component of σ, V * is the activation volume of moving dislocations, M ¼ 3.06 is the average Taylor factor for untextured polycrystalline materials, k is the Boltz mann constant, T is the absolute temperature, ε_ 0 is the pre-exponential factor, and ΔG0 is the Helmholtz free energy of activation, which is the total energy required to overcome short-range obstacles without the aid of an applied shear stress [42]. Eq. (1) can be simplified as follows:
(1)
ΔG0 =kT;
ln_ε ¼ K σ þ B;
Fig. 6. Cross-slip lines in A55 after compression at 103 s
1
(2)
and thus, K ¼ V*/MkT, which reflects the strain-rate sensitivity (SRS). A smaller K value corresponds to a higher sensitivity of strength to strain rate. The parameter B ¼ ln_ε0 ðΔG0 V * σμ Þ=kT, and B can be regarded as a constant for a material at fixed testing temperature. Fig. 10 shows plots of ln_ε versus the yield stress (σ). The experimental data for the steel after different aging treatments were linearly fitted in the strain-rate range of 10 3–100 s 1 and 100–103 s 1. Based on Eq. (2), the values of K were obtained from the slopes of the fitting lines and are shown in Fig. 10. It shows with aging temperature increasing K (K1) decreases from ~0.070 to ~0.040 which indicates that the SRS increase in the strain-rate range of 10 3–100 s 1, whereas the K values (K2) remained at ~0.019 in the strain-rate range of 100–103 s 1. It is also apparent that the K values (K1) for strain rates below 100 s 1 are larger than those (K2) for strain rates above 100 s 1 for the five as-aged steels. It is attributed to the dislocation motion having different driving
. 5
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e., SRS), the activation volume V * can be written as follows [44]: V * ¼ b � ξ � l* :
(3)
Thus, K ¼ b � ξ � l* =MkT;
(4)
where b is the Burgers vector of the dislocations, ξ is the distance swept out by the mobile dislocation during one activation event, which can be regarded as a constant, and l* is the length, which scales with the average contact distance between two obstacles. Owing to the increase in the volume fraction and slight coarseness of the κ precipitates with increasing aging temperature, as shown in Figs. 1 and 2, the spacing between κ-carbides decreases, leading to a decrease in l*. Thus, the value of K decreases according to Eq. (4), which indicates the increase in the strain-rate sensitivity of the yield stress. 4.2. Effect of aging temperature on compressive behavior The yield strength of the steel is enhanced with increasing aging temperature at a fixed strain rate, as shown in Fig. 4. The grain refine ment strengthening can be ignored because the sizes of the austenitic grains are only coarsened slightly after aging at temperatures from 400 to 600 � C. Thus, the enhancement in the strength is mainly due to pre cipitation strengthening. Fig. 8 reveals that the κ-carbide precipitates are sheared by the dislocations, and the strength can be calculated using the Friedel statistics equation [45]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 1 3k2 M μ pffiffi ðfv RÞ2 ; σp ¼ (5) 4πβ b
Fig. 9. HRTEM images showing the (Nb,Mo)C particles in the Fe–Mn–Al–C steel aged at 550 � C after compression at (a) 10 3 s 1 and (c) 103 s 1 and the corresponding IFT images of the {111} planes at (b) 10 3 s 1 and (d) 103 s 1.
where σp is the yield strength increment, β is a constant, M is the Taylor factor, μ is the matrix shear modulus, b is the Burgers vector, fv is the volume fraction, and R is the mean radius of the precipitates. As the aging temperature increases from 400 to 600 � C, the volume fraction and the sizes of the κ-carbides increase, as shown in Figs. 1 and 2, leading to an increase in the yield strength according to Eq. (5). Addi tionally, the piled-up dislocations around the (Nb,Mo)C particle in Fig. 9 indicate that the (Nb,Mo)C particles distributed in the matrix are effective for improving the strength as well. However, the contribution to the strengthening for the sample aged at different temperatures is almost the same, because the distribution and sizes of the (Nb,Mo)C particles in the matrix remain basically unchanged. The pronounced planar glide characteristics expressed by the noncoplanar slip bands are observed in the aged steel after compression at strain rates from 10 3 to 103 s 1, as shown in Figs. 5 and 7. Therefore, the planar glide mechanism dominates the plastic deformation during the compression at different strain rates. The SFE of the aged steel was calculated to be ~77 mJ/m2. This plays an important role in the planar glide appearance during deformation because a high SFE, i.e., over 70 mJ/m2, can suppress the effect of Transformation-Induced Plasticity (TRIP) and Twinning-Induced Plasticity (TWIP) in high-Mn and high-Al Fe–Mn–Al–C steels [11,29,30,46]. Moreover, the κ-carbides in the austenite matrix facilitate the planar glide mechanism [13,16]. After the κ-carbides are sheared by the leading dislocations, the blocking forces for the dislocation motion are significantly weakened. As a result, the subsequent dislocations could glide easily on the same glide plane, causing glide plane softening [28,33]. In addition, the solute interstitial C atoms in the matrix were found to hinder dislocation cross-slip [38] and this may offset the promotion to cross-slip by high SFE in the steels. Fig. 7 reveals that there was a larger spacing between the slip bands in A60 than in A40 after deformation at the same strain rate. This is ascribed to the increase in the volume fraction and the coarseness of the κ-carbides in the matrix with increasing aging temperature, as shown in Figs. 1 and 2. In the steel aged at 600 � C, the κ-carbide was more difficult to be sheared by the mobile dislocations due to their larger sizes relative
Fig. 10. Plots of ln_ε as a function of yield stress σ obtained from the compression experiments shown in Fig. 4 at room temperature (298 K). The solid and dotted lines are linear fits between ln_ε and σ of the as-aged steel below and above 100 s 1, respectively. The values of K are equal to the slopes of the lines.
mechanism below and above strain rate of 100 s 1 [43]. At strain rates below 100 s 1 the dislocation motion is thermally activated so that the precipitates in the matrix control the glide resistance of dislocation, thus, with increasing aging temperature the increased number of κ-carbides further hinder the dislocation motion. As a result, the strain-rate strengthening effect increases, yielding a decrease in the K values (K1). However, at strain rates above 100 s 1, the dislocation motion is drag-dependent and only weakly depends on the precipitates. Thus, the strain rate sensitivity is almost independent of the variation of the κ-carbides after different aging treatments and K values (K2) above 100 s 1 in Fig. 10 are the same for the five different aging treated steels. To further understand the effect of κ on the K values below 100 s 1 (i. 6
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to the precipitates in A40, so that the critical stress required to cut the κ-carbides is increased. Thus, dislocations in A60 would slip more likely along the as-activated planes (softened planes) rather than activate new glide planes than that in A40. This created a larger spacing between the slip bands [26].
temperatures, as shown in Fig. 2, which reduced the density of slip bands, as shown in Figs. 5(a) and 7. The boundaries of the slip bands can block the dislocation motion with further straining [8,10,16,38]. Consequently, the reduction in the density of the slip bands with increasing aging temperature decreases the impediment to the disloca tion motion and thereby weakened the effect of strain hardening. Second, as the aging temperature increases, the reduction in the θ value is also related to the dynamic strain aging (DSA), which results from the interaction between the diffusing solute atoms (mainly carbon atoms in this work) and mobile dislocations [48]. The serrated curves of the strain hardening rate versus true strain in the 10 3–100 s 1 range shown in Fig. 11 verifies that the Portevin–Le Chatelier (PLC) effect is induced by the DSA [49]. As the aging temperature increases from 400 to 600 � C, the formation of more κ-carbides decreases the number of interstitial carbon atoms in the matrix, which reduces the contribution of the DSA strengthening to strain hardening. Consequently, the strain hardening rates of the steel after aging at 400 and 450 � C are higher than that after aging at 500–600 � C shown by Fig. 4 (a–c) and Fig. 11. However, it is considered that the DSA is either insignificant or does not occur at 103 s 1. Because the flow stress increases with the aging tem perature increasing during the whole deformation at 103 s 1, which is different from the behavior at strain rates in the 10 3–100 s 1 range, as shown in Fig. 4. For example, the flow stress of A40 is higher than that of A45 from a certain true strain at the strain-rate range of 10 3–100 s 1. This indicates a little or no contribution of DSA to the strain hardening rate at 103 s 1 as comparison to that at 10 3–100 s 1. In addition, the fluctuation on the strain hardening rate curves at 103 s 1 shown by Fig. 11 could be induced by the load fluctuation of split Hopkinson pressure bar test. As a result, DSA is not evident at 103 s 1. It is obvious in Fig. 11(a–e) that the value of θ for the A40 and A45 remains positive and for the A50, it is below zero from the yield point to the true strain of ~0.09, after which it is positive again. However, for the A55 and A60 steels, it is negative after yield, showing that flow softening is dominant during plastic deformation. This is caused by the reduction in the density of slip bands mentioned before as well as the adiabatic temperature rise during dynamic testing at 103 s 1. The temperature rise can be calculated as follows [47]: Z εf β ΔT ¼ σ dε; (6) ρC p 0
4.3. Strain hardening rates The curves of the strain hardening rate (θ) (θ ¼ dσ /dε, where σ is the true stress and ε is the true strain) versus the true strain for various strain rates are plotted in Fig. 11. Under all of the experimental conditions, the values of θ are initially very large and subsequently decrease rapidly. This stage can be regarded as the transition from elastic to plastic deformation. Next, the values of θ change slowly with further straining, indicating that plastic deformation is in progress. In Fig. 11(a), the values of θ for A40 tested at strain rates from 10 3 to 103 s 1 remain positive. This demonstrates that strain hardening plays a dominant role throughout the plastic deformation. Additionally, the strain hardening rate decreases with increasing strain rate, and it de creases more significantly when the strain rates increase from 100 to 103 s 1 than when they increase from 10 3 to 100 s 1, because the adiabatic temperature rise assists the thermal softening at high strain rates [47]. The continuously decreasing trend of the strain hardening rate with increasing strain rate is ascribed to the difference in the initial amount of activated dislocations at various strain rates. With increasing strain rate, the increased yield strength leads to an enhancement in the initial driving force for dislocation motion, which produces more dislocations involved in the slip at higher strain rates, as shown in Fig. 5. Conse quently, more κ-carbides are cut by dislocations at higher strain rates, so that the hindrance to the dislocation slip is reduced, resulting in a decrease in the strain hardening rate. It is noted that the increase of strain rate promotes the formation of slip bands which reduces spacing between slip bands, as shown in Fig. 5. The boundaries of slip bands are obstacles for dislocation movement so that finer spacing between slip bands can increase strain hardening rate [10]. In this case, increasing strain rate has both adverse and beneficial effects on strain hardening, but it is clear that the adverse effect is dominant. A comparison of Fig. 11(a–e) shows that the θ values decrease as the aging temperatures increase from 400 to 600 � C at the same strain rate. First, more and larger precipitates form in the steels after aging at higher
Fig. 11. Strain-hardening rate–true strain curves of the Fe–Mn–Al–C steel after aging at (a) 400 � C, (b) 450 � C, (c) 500 � C, (d) 550 � C, and (e) 600 � C after compression at strain rates ranging from 10 3 to 103 s 1. 7
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References
where β ¼ 0.9 is the fraction of energy conversion, ρ ¼ 6.78 g/cm3 is the density of the sample, Cp ¼ 460 J/(kg⋅K) is the specific heat capacity, σ is the flow stress, and εf is the final true strain. Flow stresses of the aged samples increase with increasing aging temperature at 103 s 1, as shown in Fig. 4(d). For example, at a true strain of 0.15, the ΔT increases from 56.2 to 76.2 � C after the aging temperature increases from 400 to 600 � C. Hence, the difference in the adiabatic temperature rise is small for the five age-treated steels. The main reason for the reduction of the SHR with the aging temperature at 103 s 1 is the reduction in the density of the slip bands. In addition, the adiabatic temperature rise also causes the SFE to increase. The maximum SFE increase of the as-aged steel, obtained for the A55 steel, is calculated to be ~10 mJ/m2. As a result, cross-slip is observed after compression at 103 s 1 due to this effect, as shown in Fig. 6.
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5. Conclusions Experiments were conducted to examine the effect of the aging temperature between 400 to 600 � C and in the strain-rate range of 10 3–103 s 1 on the microstructural evolution and compressive behavior of a Fe–Mn–Al–C-lightweight steel micro-alloyed with Mo and Nb. The following conclusions were drawn. 1. After aging at temperatures from 400 to 600 � C, the microstructure of the steel is composed of equiaxial austenite grains within annealing twins, and two types of nano-sized precipitates (Nb,Mo)C and κ-carbides, distributed uniformly in the matrix. With increasing aging temperature, the austenite grains coarsen slightly with the volume fraction and sizes of the κ-carbides increasing, whereas the sizes and distribution of the (Nb,Mo)C particles remain unchanged. 2. The aged steel exhibits a significant strain-rate strengthening effect resulting from the enhancement of the interactions between dislo cations and the carbides in the matrix at higher strain rates. With increasing strain rate, the strain hardening rate decreases because the number of κ-carbides cut by dislocations increases during deformation, which reduce the hindrance to dislocation slip. 3. Increasing aging temperature leads to an increase in the strength at the same strain rate and an enhancement in the strain-rate sensitivity of the strength at strain rates from 10 3–100 s 1 due to the increased precipitation strengthening of the κ-carbides. The strain-rate sensi tivity of the strength above 100 s 1 is independent of the aging temperature. Insufficient aging up to 450 � C causes dynamic strain aging during compression at stain rates from 10 3–100 s 1, which also contribute to the strain hardening rate. Author contributions section Zhuang Li: Conceptualization, Validation, Formal analysis, Investi gation, Writing-Original Draft, Writing-Review & Editing. Yingchun Wang: Conceptualization, Writing-Review & Editing, Supervision. Xingwang Cheng: Project administration, Funding acquisition, Super vision, Jiaxin Liang: Investigation. Shukui Li: Supervision. Declaration of competing interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work was supported by the National Natural Science Foundation of China under Grant no. 51671030. 8
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