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Inverse grain size effect on twinning in nanocrystalline TWIP steel
Author’s Accepted Manuscript Inverse grain size effect on twinning in nanocrystalline TWIP steel Roghayeh Mohammadzadeh, Mohammadzadeh
Mina
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S0921-5093(18)31610-1 https://doi.org/10.1016/j.msea.2018.11.085 MSA37205
To appear in: Materials Science & Engineering A Received date: 21 August 2018 Revised date: 17 November 2018 Accepted date: 17 November 2018 Cite this article as: Roghayeh Mohammadzadeh and Mina Mohammadzadeh, Inverse grain size effect on twinning in nanocrystalline TWIP steel, Materials Science & Engineering A, https://doi.org/10.1016/j.msea.2018.11.085 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Inverse grain size effect on twinning in nanocrystalline TWIP steel
Roghayeh Mohammadzadeh1, Mina Mohammadzadeh2*
1 2
Department of Materials Engineering, Azarbaijan Shahid Madani University, Tabriz, Iran
Department of Mechanical Engineering, University of California, Merced, CA 95340, USA,
[email protected] [email protected]
Abstract Mechanical twinning plays a significant role in the plastic deformation of Twinning Induced Plasticity steel (TWIP). The effect of grain size on the twinning nucleation stress, yield stress, twin morphology and deformation mechanisms of Fe-22 wt. % Mn steel have been studied using molecular dynamics simulations. The nanostructure materials with mean grain sizes of 11.1, 14.3, 17.7 and 32 nm are constructed using the Voronoi tessellation method, and the plastic deformation behavior is studied by molecular dynamics simulation. A meta-atom potential is applied to represent the atomic interactions. The result of tensile test showed that the yield strength and twin nucleation stress increase by grain size decreasing. Structural analysis of the samples deformed to 10 and 20 % total strain disclosed thicker primary twins in 1
the coarse-grained material in comparison with the fine-grained one. Moreover, a high volume fraction of twins was formed in the coarse-grained sample. Dislocation analysis exhibited that the dislocation structure influenced by the initial grain size. The density of nucleation sites for twins and subsequently the developing twin substructure is affected by the dislocation substructure. It is concluded that with decreasing grain size, deformation of nanocrystalline TWIP steel by mechanical twinning can become difficult.
Keywords: TWIP steel, Grain size, Deformation twinning, Molecular dynamics, morphology.
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1. Introduction The high formability and excellent ultimate tensile strength of Twinning Induced Plasticity (TWIP) steels have been draw attention over the past few years [1–4]. The superior tensile properties of TWIP steels result from formation of deformation twins continuously during plastic deformation, which enhances the work hardening capacity of these steels. Plastic deformation by TWIP mechanism is observed in steels which possesses medium stacking fault energy (SFE), usually in the range of 18–45 mJ.m-2 [5] and is characterized by the formation of straight and parallel lines inside grains. The excellent strengthductility combination makes the TWIP steels most suitable material for high strain rate energy absorption demands such as military vehicle armor plates and automotive crash safety [6]. The remarkable strain hardening of TWIP steels is mainly related to dynamic Hall–Petch effect [7, 8]. As twins nucleated during plastic deformation of TWIP steels, they can act as barriers for dislocation glide and resulting in a continuously dynamic grain refinement. Therefore, dislocation mean free path reduces as a consequence of twin boundaries formation which leads to high strain-hardening rate [9]. Various mechanisms have been suggested for the deformation twinning formation via gliding of dislocations for example; pole mechanism and nucleation of twin across the stacking faults [10]. However, the low yield stress of TWIP steels (200-450 MPa) in comparison to advanced high strength steels (AHSS) limits the
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extensive use of these steels in industrial applications (specially automotive) [11]. The yield strength of materials can be modified using different strengthening mechanisms such as grain size reduction, solid solution and precipitation hardening [12]. Although yield and ultimate tensile strengths increase by solid solution and precipitation hardening process but elongation and toughness decrease [13,14]. The grain refinement is the most effective method for improving both strength and ductility simultaneously without any change in the chemical composition of the alloy [15]. It has been reported by K.M. Rahman et al. [16] that deformation twinning of TWIP steels is greatly dependent on the initial grain size of material. K.M. Rahman et al. [16] have shown that with decreasing grain size of Fe-15Mn-2Al2Si-0.7C TWIP steel from 84 to 0.7 µm, the yield stress increased from 350 to 720 MPa without substantially change in the ductility. G. Dini et al. [17] have obtained a yield stress of 572 MPa in an Fe–31Mn–3Al–3Si TWIP steel plate with a mean grain size of 2.1 µm. Y.Z. Tian et al. [18] have obtained an ultrafine-grained Fe-22-Mn-0.6 C (wt .%) TWIP steel with a fully recrystallized structure and average grain size of 550 nm through a repeating cold working and annealing heat treatment with good strength-ductility balance (the yield stress of 793 MPa, ultimate tensile strength of 1247 MPa, and uniform elongation of 47%). Similarly, R. Ueji et al. [19] have shown that the grain refinement of Fe-31Mn–3Al–3Si (wt. %) TWIP steel until 1.8 µm gives high
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yield stress (525 Mpa) with great ductility (uniform elongation of 48%). S. Kang et al. [20] have investigate the influence of grain refinement (with initial grain sizes of 2, 10, and 50μm) on yield strength of Fe–18Mn–0.6C–1.5Al TWIP steel and have concluded that steel sample with grain size of 2 μm exhibited higher yield strength of 500 MPa in comparison to coarse grained specimens. Although there are more studies on the influence of grain size on the yield strength of microcrystalline TWIP steels, there are a few studies which investigate the effect of initial grain size on the behavior of deformation twinning in TWIP steels [16, 19, 21]. I. Gutierrez-Urrutia et al. [21] have investigated the effect of initial grain size (3 and 50 µm) on deformation behavior of Fe-22Mn-0.6C (wt. %) TWIP steel at room temperature by microstructure observation of tensile deformed samples using electron channeling contrast imaging (ECCI). The authors achieved that by decreasing the grins size from 50 µm to 3 µm, the area fraction of deformation twinning at 0.3 logarithmic strain decreases from 0.2 to 0.1. Also, Ueji et al. [19] observed by TEM studies many deformation twinning (13 grains of total 26 grains) in a Fe-31Mn–3Al–3Si (wt. %) TWIP steel with a coarse grain size of 49.6 µm. On the other hand, they [19] observed a few deformation twinning in a fine grain size sample (1.8 µm, 5 grains of 30 grains). However, K.M. Rahman et al. [16] have studied the effect of grain size on stress required for the growth of
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deformation twins in the Fe-15Mn-2Al-2Si-0.7C (wt. %) TWIP steel and have observed that the ductility of steel samples was not influenced by grain refinement. They [16] have shown by TEM studies that the initial grain size, influence the morphology of twins, and a smaller grain size promotes the formation of thinner twins. The contradictory results from the two studies [19, 21] can be due to different stacking fault energy values of the investigated steels. Gutierrez-Urrutia et al. [21] and Ueji et al. [19] used a TWIP steel with a stacking fault energy of 24 and 42 mJ.m-2, respectively, whereas K.M. Rahman et al. [16] investigated steel samples with SFE of 30 mJ.m-2. These reports emphasize the influence of both the sample preparation and the measurement method on the experimental results. Beside the accuracy of experimental values, the measurement itself is quite complicated and difficult, since many parameters including sample quality (grain size, homogeneity, impurity, etc.) and picture quality must be well controlled in order to get reliable results. It is significantly important to increase the fraction of deformation twins in TWIP steel because twinning can cause both high ductility and strength. To develop alloys with innovative mechanical properties, it is important to investigate deeply the deformation mechanism of TWIP steels. Because of the controversies among published results and these difficulties, a theoretical approach for evaluating the influence of initial grain size on the dynamics behavior of deformation twinning is highly motivated. A systematic
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study based on theoretical methods would lead to a fundamental understanding of the topic, which is of great importance for designing new materials. Molecular Dynamics (MD) simulations have shown to be an effective approach for atomistic study of deformation mechanisms in nanocrystalline metals and alloys with precisely simulation boxes in which the dynamics behavior of the microstructures can be investigated [22]. Also, atomistic simulations by MD approach have shown a change in the plastic deformation mechanism at the critical grain size, i.e., from the classical Hall-Petch relationship to inverse HallPetch effect [23]. In the present study, the influence of initial grain size on the atomic-level deformation mechanism of a TWIP steel has been studied by performing a series of large scale MD simulations, that will help to achieve innovative ways for obtaining superior mechanical properties in TWIP steels. 2. Simulation Details The
MD
simulations
have
been
carried
out
by
the
Large-scale
Atomic/Molecular Massively Parallel Simulator (LAMMPS) [24] and a Metaatom potential developed by P. Wang et al. [25] for Fe-22Mn-0.6C (wt. %) TWIP steel. P. Wang et al. [26, 27] developed a novel interaction potential that enables them to perform molecular dynamics simulations of complex alloy systems. The central idea is that there is a set of finite material parameters that governs the mechanical properties of an alloy system. Using this set of material constants for TWIP steel, they developed the so-called meta-atom potential for 7
Fe-22Mn-0.6C (wt. %) TWIP steel based on the embedded-atom method. They further performed extensive simulations to validate their potential/approach against experimental data. The meta-atom potential for Fe-22Mn-0.6C (wt. %) steel was calibrated in accordance with lattice constants, elastic moduli (C11, C12 and C44), SFE, unstable SFE and single vacancy formation energy (Evac) which were obtained by experimental results and the ab initio calculations [25]. Their detailed simulations reveal various competing mechanisms that govern twinning-induced plasticity in steels. Interestingly, their observation that twin boundaries in steel serve as effective barriers for dislocation motion as well as accommodate plasticity thereby offering high strength and ductility is consistent with studies on nano-twinned fcc metals. As among different types of TWIP steels, a Fe-22Mn-0.6C (wt. %) steel exhibits a very large work hardening capacity in comparison to Fe-31Mn-3Al3Si (wt. %) steels [26], the authors used Fe-22Mn (wt. %) as a model alloy. The nanocrystalline samples with mean grain size of 11.1, 14.3, 17.7 and 32 nm were constructed using the Voronoi tessellation method [27]. Periodic boundary conditions were applied for x, y and z directions. Figure 1 shows the initial configuration of a nanocrystalline sample, in which the atoms at the perfect FCC sites are shown in grey, and the grain boundary (GB) atoms are shown by blue colored atoms. Details of simulation box size and number of atoms for each sample are listed in Table 1.
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Before straining, as-created sample models firstly were exposed to energy minimization using the conjugate gradient procedure and finally relaxed under the pressure of 0 bar and the temperature of 300 K by the Nose/Hoover isobaricisothermal ensemble (NPT) for 200 ps with time step of 1 fs. The pressure variable in thermal relaxation was controlled by the Parrinello–Rahman method [28] with a damp time of 1000 steps. The Nose–Hoover method [29] with a damp time of 100 steps was applied to maintain a stable temperature. After energy and thermal relaxations, the simulation boxes were strained along y-axis with strain rate of 0.001 ps−1 up to a total strain of 50 %. The pressure in the x and z directions were set to be zero during the tensile loading to retain the uniaxial loading state in the samples. In order to visualize deformation structure, the authors alter the coloring scheme of common neighbor analysis (CNA) [30]. The CNA is a well known computational analysis technique that identifies the crystalline order of atoms locally and as a result of that characterizes regions with a disordered arrangement of neighboring atoms. However, different types of crystal defects such as stacking faults and coherent twin boundaries cannot be recognized by CNA alone. Therefore, it can work only for visualization aims. To overwhelm these restrictions, we have implemented a second analysis method to determine coherent twin boundaries (TBs) from intrinsic stacking faults (ISFs). In usual visualization tools such as common neighbor analysis method, these planar
9
defects were generally identified by detecting atoms having a local hcp crystal structure, which is typical for both coherent twin boundaries and intrinsic stacking faults in fcc metals. To determine coherent twin boundaries and stacking faults, it is necessary to do a further topological and crystal orientation analysis of the neighboring atoms. In order to calculate the numbers of atoms present in the coherent TBs and ISFs, the authors have implemented an additional structural analysis algorithm into the MD simulation code. This improved analysis allows to make ISFs and coherent TBs readily recognizable in the visualization images and to quantify the exact densities of ISFs and TBs in the simulation box as a function of strain. In the following figures, ISFs are colored green and coherent TBs red, respectively. Post-processing and visualization of simulation snapshots were carried out with the scientific software package “Open Visualization Tool OVITO” [31]. 3. Results and discussion 3.1. Microstructure characterization before tensile deformation Figure 2 shows the cross-sectional views of the nanocrystal TWIP steel with different grain sizes of 32, 17.7, 14.3 and 11.1 nm, in which atoms are characterized in accordance with CNA method [31]. This coloring pattern clarifies the crystal structure of atoms locally according to its neighbor atoms. The calculated CNA values define an atom as simple cubic, face centered cubic (fcc), body centered cubic (bcc) and hexagonal close-packed (hcp) or others. It 10
can be observed that as-constructed nanocrystal steel samples consisted of small grains with different crystal orientation, which are surrounded by disordered boundaries (GBs). In atomic structure of the studied samples two types of atoms can be seen; crystal atoms with ordered arrangement corresponding to the lattice and boundary atoms with different inter-atomic spacing. In Figure 2, atoms with fcc structure are colored gray and atoms without certain crystal structure (GBs) are colored blue. 3.2. Effect of grain size on the flow behavior Figure 3 displays the simulated tensile stress-strain curves of studied TWIP steel samples with different grain sizes. It can be seen that tensile stresses in all investigated samples firstly increase with strain linearly to a maximum value, then decreasing to a steady-state value with some fluctuations. As can be shown later, the maximum stress was corresponding with the onset of plastic deformation (yielding point), which is known to be caused by the higher strain rates typically applied in MD simulations [32]. After reaching maximum stress, the flow stress abruptly reduced to a steady-state level in all studied samples due to; i) relaxation of stress owing to high strain rate applied in the current simulation [33], or ii) formation of cracks during tensile deformation [34]. A remarkable characteristic of the stress-strain curve of the sample with grain size of 11.2 nm is that flow stress drop to 0.02 GPa. This difference in flow behavior
11
is due to nucleation and propagation of cracks significantly in the sample having a grain size of 11.1 nm (as confirmed visually in section 3.3). As the deformation twinning nucleation and growth in TWIP steels is determined by the glide of Shockley partial dislocations, it is physically more important to compare the effect of grain size on the yield stress. In order to elucidate the influence of grain size on the yield strength of nanocrystalline samples by MD simulations it is essential to calculate the average of flow stress over a specific strain interval [35] due to significant influence of strain rate on the maximum stress of tensile curves. In the present nanocrystalline TWIP steel with mean grain size of 11.2 nm, the critical strain for inter-granular crack initiation was found to be 5% of total strain. On the other hand, the samples with larger grain sizes of 14.4, 17.7 and 32 nm did not show any appreciable crack formation up to total strain of 40%, suggesting that nucleation of intergranular crack could be retarded by increasing the initial grain size. To remove any possible crack formation effect, average flow stress in the plastic strain range of 0.1-3 % was selected for obtaining the yield stress in this study, since inter-granular cracks were not detected in any of samples within this plastic strain range. Beyond this plastic strain range, inter-granular cracks were found to nucleate first in the sample with the smallest grain size of 11.2 nm, which decreasing the flow stress with further straining. Variation in yield versus the mean grain size is plotted in Figure 4. It can be observed that the yield stress
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increases to a maximum value of 4.97 GPa down to a grain size of 11.2 nm. The usual Hall-Petch relation (the strength increasing as the grain size is reduced) can be observed for nanocrystalline TWIP steel with grain sizes larger than 11.2 nm. 3.3. Deformation substructure In order to comprehend the effect of initial grain size on the deformation mechanism of nanocrystalline TWIP steel, the analysis of deformation substructure at the atomistic level was conducted. Figures 5 and 6 illustrate cross-section views of deformation substructure in the deformed samples with the grain sizes of 32, 17.7, 14.3 and 11.1 nm after 10 and 20 % total strain, respectively. In Figures 5 and 6, the atoms with perfect fcc structure are colored gray, while atoms in grain boundaries, incoherent twin boundaries and dislocations are colored blue. Stacking faults and coherent twin boundaries appear as green and red atoms within grain interiors, respectively. At large strain of 10 and 20 % three deformation defects types can be distinguished as follow: (i)
Stacking faults leaving behind the leading partial dislocations which were emitted from the grain boundaries (as indicated by number 1 in Figure 5(b)) or stacking fault between the leading and trailing partials of dissociated dislocations or extended partial dislocations (as shown by number 2 in Figure 5(b)). In figures 5 and 6, the leading partial 13
dislocations are found to have a Burgers vector of a /6 [112] and the corresponding stacking faults are intrinsic. (ii)
Coherent deformation twins (as indicated by number 3 in Figure 5(d)).
(iii)
Incoherent deformation twins (as shown by number 4 in Figure 5(d)).
As can be observed in Figures 5 and 6, grain boundaries and triple junctions are the main sites for the nucleation of twins. By comparing deformation substructure of nanocrystalline TWIP steel in this study with experimental ones [36, 37] obtained by TEM observations on deformed TWIP steels (see Figure 7), it can be seen that they share many deformation substructures similarities like stacking faults and deformation twining. The consistency of the deformation substructure between experimental reports and MD simulation results verifies the validation of EAM inter-atomic potential which was used in this study. Detailed analysis of deformation substructure images at total strain of 10 and 20% (Figure 5 and 6) reveals that the twin substructure in the all investigated nanocrystalline samples mostly occurs as single variant twining system. It can be seen from figures 5 and 6 that, after the critical stress for nucleation of twins is achieved, any additional stress seems to thicken the nucleated twins. By increasing the strain from 10 to 20%, the lamellar twin substructure formed by the accumulation of the twin boundaries. Further analysis of deformation substructure shows that the coarse-grain sample dose indeed consists of thicker 14
deformation twins in comparison with those of fine grain sizes, despite the fact that all samples have been deformed to the same strain. Therefore, the initial grain size effects the morphology of twins, a large grain size encourages the development of thicker twins, because; the twins need to grow over a large distance. Hence, it can be expected that the coarse-grained sample can be able to exhibit considerable plastic strain upon tensile loading, because the thickness of deformation twins is greater. Further investigation of deformation substructure of the fine and coarse grain size samples show that the area fraction of deformation twins (coherent and incoherent) in the coarse-grained sample (32 nm) is higher than that observed in the fine-grained specimens. Figure 8 shows the histograms of volume fraction of deformation twins and stacking faults in samples deformed under tension up to a total strain of 10 and 20 %. As it can be seen in Figures 8 (a) and (b), with decreasing grain size the volume fraction of deformation twins obviously reduces for the studied TWIP steel with grain size of smaller than 32 nm whilst, the volume fraction of stacking faults increases. This demonstrates that mechanical twins tend to develop in coarse-grained samples, while stacking faults tend to form in fine-grained samples. The reduction of twining tendency with decreasing grain size is called the inverse grain size effect [38]. One of the important characteristic of the data in Figure 8 is that inverse grain size effect occurs for deformation twins, while no inverse grain size effect revealed for stacking faults. The obtained results in this study is consistent with a previous analytical model [39] and experimental observation 15
on the electrodeposited nanocrystalline nickel foil with grains in the range of 10-75 nm [38]. The inverse grain size effect on the mechanical twins can be described by the combined effects of general planar fault energy and grain size [38, 40]. The prerequisite for the deformation twin nucleation is to create a stacking fault firstly. That is a stacking fault was formed initially by a leading partial dislocation, and afterwards a twinning partial dislocation transformed the stacking fault region to a twin nucleus (as shown in Figures 6 and 7). Also, it has been reported that [41] the required stress for emission of twinning partial dislocation increases with decreasing grain size. Therefore, as the stress required to emit twinning partial dislocation is higher than leading partial dislocation, one can conclude that the stress needed to emit a twinning partial dislocation gets greater than the applied stress below a critical grain size, which prevents deformation twinning although still lets the emission of the leading partial dislocations to form extended stacking faults. This will lead to a statistical reduction in deformation twining density by decreasing grain size, (the inverse grain size effect on deformation twining). Therefore, it can be say that leading partial dislocations can be activated in all grains with different sizes to generate stacking faults, but if the inverse grain size effect is governing, nucleation and growth of twinning partial dislocations get more difficult by decreasing grain size. Therefore, the higher applied stress is required to emit a twinning partial dislocation than a leading partial dislocation below a critical grin size. The higher stress requirement for nucleation of twinning partials was 16
observed experimentally in reference [38]. X. L. Wu et al. [38] have shown that the area fraction of twinned grains increased from 28% under tension to 38% under rolling and to 44% under split Hopkinson pressure bar (SHPB) test. They reported that flow stress under tension was 1.5 GPa, which was increased to 2.0 GPa under SHPB test. 3.4. Twin nucleation and growth mechanism To reveal the dislocation processes involved in the formation of deformation twins, a small part of the simulation cells is considered for further analysis. Figure 9 shows snapshots of an in-situ tensile straining of the investigated TWIP steel with mean grain size of 17.7 nm. In the initial stage of deformation (total strain of 9%), six planar defects are designated in the investigated grain as shown in Fig. 9 (a). These six planar defects are parallel which indicates that the planar defects have the identical habit plane. The green planar defects are stacking faults, while the red planar defects are deformation twins. Hereinafter, the stacking fault is indicated to as SF while, twinning dislocation is specified to as TD. It can be seen from Figures 9 (a) and 9 (b) that by increasing strain from 9 to 9.5 %, twin dislocations nucleated from grain boundaries moves rapidly toward the stacking fault position and changes the stacking fault area to a twin one. Deformation twin growth is controlled by gradual glide of the twinning dislocations. Also it can be seen that by more straining, the whole of stacking fault 1 (SF1) transformed to twin area. As can be shown in Figure 10, the initial 17
stacking fault with thickness of one atomic layer changes to a twin with the thickness of two atomic layers by the movement of single twinning partial dislocation. The current observation confirms the nucleation of a thin twin at grain boundary by the emission of specific partial dislocation from grain boundary. In order to analyze the type of dislocation in the twin area, a dislocation analysis using Ovito was carried out. The dislocation analysis was conducted on two regions, i.e (1) the region where the dislocation twinning exists and (2) the grain boundary region where dislocations are piled up. Based on the dislocation analysis shown in Figure 10 (c), the twin dislocations are Shockely partial dislocations with Burgers vector of a/6<112>. Also, it can be seen that the dislocations at the grain boundaries are consisted of perfect and some Shockely partial dislocations. The emission of Partial dislocations from grain boundaries has been observed in nano-crystalline metals by molecular dynamics (MD) simulations [42, 43] and experimental studies [44]. In nanocrystalline nickel samples with mean grain size of 12 and 20, H. Van Swygenhoven et al. [43] shown by MD simulation that grain boundaries could emit partial dislocations during plastic deformation by local atomic shuffling and stress-assisted free volume migration. It has been reported that dissociated dislocations [44], ledges [45] in the grain boundaries and triple junctions [46] could be the sources of partial dislocations at grain boundaries. X. L. Wu et al. [44] have observed experimentally by high resolution transmission electron microscopy the glide of leading partial dislocation from grain boundaries with a 18
high density of extrinsic dislocations into the grain interior. This is also consistent with the work of Gutierrez-Urrutia and Raabe Jin-Kyung Kim et al. [47] who studied the deformation twinning mechanism in Fe-17Mn-0.45C1.5Al-1Si TWIP steel by means of in-situ TEM deformation tests and observed formation of a thin twin by Shockley partial dislocations generated in a grain boundary. 3.5. Dislocation substructure Dislocation analysis also reveals a difference in the dislocation substructure between the coarse and fine-grained nanocrystalline samples. Figure 11 illustrates dislocation substructure at total strain of 5% in studied samples. It can be seen that the dislocation substructure is different in the coarse-grained sample (32 nm) from that observed in the fine-grained samples. In the coarsegrained sample (Fig. 11 (a)), well-developed cell structures can be observed in deformed grains. On the other hand, the cell structure is rarely distinguished in fine-grained samples (Fig. 11 (b,c,d)), and most of dislocations were arranged on the primary slip plane. Also, it can be seen that the dislocation configuration in the fine-grained samples shows an approximately loose arrangement and lower volume fraction in comparing with the coarse-grained sample. This morphology has a close similarity to planar dislocation pattern often detected by bright field TEM with low to medium stacking fault energy [48-50]. The dislocation substructure shown in Figure 11 (a) is similar to wavy dislocation 19
substructure observed in alloys and metals with medium to high stacking fault energy [51]. Wavy dislocation substructure is developed in grains when a large number of slip planes are activated and cross-slip of dislocations is facilitated [52]. The influence of grain size on the dislocation substructure developed at the initial deformation stage (total strain of 5%) can be comprehended by the Hall– Petch relationship. To accomplish the tensile stress associated to total strain of 5%, the coarse-grained sample needs a larger strain, owing to the low yield stress. At the initial plastic deformation step, dislocation glide mostly control plasticity and, correspondingly, the density of dislocation ascends with strain. Due to high density of dislocations in the coarse-grained sample, the dislocations are predominately piled up as the cell blocks (Fig. 11 (a)). However, the fine-grained samples keep a less dislocation density prior to the total strain of 5%, due to the high yield stress. Therefore, fine-grained sample exhibits loose dislocation substructure (Fig. 11 (d)). If we take into account that twin nucleated as a result of some certain dislocation reactions, the relatively homogeneous distribution of dislocations in the coarse-grained sample (Fig. 11 (a)) supplies a large number of nucleation sites for deformation twins. However, the fine-grained sample (Fig. 11(d)) contains a low overall dislocation density which will create a less number of sites for nucleation of twins. 20
3.6. Effect of grain size on the twining nucleation stress Twining involves two processes, nucleation and subsequent twin growth. The stress needed to create twinning can be regarded to be a combination of two different processes; (i) a required stress for twin nucleation and (ii) an additional stress for growth of twin. But, experimental determination of the required stress for nucleation of twin is very hard [53, 54]. As the twins nuclei (for example stacking faults), normally present inside the alloys, the experimental measurements of twinning stress actually is the required stress for growth of twins. Atomistic simulations have shown to be strong tools for study of the dynamic behavior of plastic deformation substructures. It is normally considered that deformation twins in metals and alloys are nucleated by preexisting dislocations that dissociated into partial dislocations which creates multi-layered stacking faults. Various models based on specific dislocation reactions have been suggested for nucleation of deformation twins in the literature [55, 56]. All require the glide of partial dislocations with Burgers vector of a/6 [112] on success {111} planes. As the snapshots of structure evolution in the MD simulations at different times can be readily acquired, the deformed structures in investigated samples were visualized at different time steps. Visualization of samples substructure at the maximum stress of tensile curves (Figure 12) shows that the peak stress is connected with the nucleation of partial dislocation from grain boundaries or 21
triple junctions. According to the Figure 12, the maximum stress in the stressstrain curves is the critical stress to detach leading partial dislocations from trailing one. Therefore, the peak stress in the tensile curves can be considered to be the stress for deformation twin nucleation. The influence of initial grain size on the maximal tensile stress of nanocrystalline TWIP steel is presented in Figure 13. The results show that the stress for nucleation of deformation twins in the investigated nanocrystalline TWIP steel increases by decreasing the initial grain size. Furthermore, less initial strain for twinning in the coarse-grained sample compared to fine-grained sample (see Figure 3) indicates that refinement of grains suppresses formation and thickening of twins. Therefore, large grain size promotes twining more easily because the slip length according to figures 5 and 6 is greater. Also K. M. Rahman et al. [16] have measured the twin stress in the Fe-15Mn-2Al-2Si-0.7C TWIP steel with grain sizes of 0.7, 4.3, 10, 45 and 84 µm by cyclic tensile testing at sub-yield stress. They have found that the stress required for deformation twinning growth increased with decreasing grain size. Additionally, G. Urne et al. [57] have shown that twinning stress is significantly influenced by the yield strength of material which is in turn influenced by grain size. Hence, G. Urne et al. [57] proposed a Hall-Petch type relation for the effect of grain size on the twinning stress in Fe-22Mn-0.6C (wt. 5) TWIP steel with average grain sizes of 3 µm and 50 µm. However, the present study is not consistent with the results of Bouaziae et al. [58]. They have reported that the twin stress in Fe-22Mn-0.6C (wt. 5) TWIP steel is not 22
influenced by the initial grain size of samples and lies constant at the level of 550-600 MPa for grain sizes in the range between 25 and 1.3 µm. Conversely, As the twining stress is unified with the yield stress in reference [58], this confusion probably causes the controversy between the present study and the results of Bouaziae et al. [58].
Conclusions The effect of initial grain size on deformation twining behavior of Fe-22Mn (wt. %) TWIP steel has been investigated using a series of large-scale molecular dynamics simulations. The following conclusions can be drawn from this study: 1) A considerable fraction of deformation twins was detected in the coarsegrained steel sample which indicates the relative easy formation of deformation twin in coarse-grained sample in comparison to fine-grained one. 2) Deformation substructure analysis of samples deformed to 10 and 20% total strain revealed the presence of thicker deformation twins in the coarse-grained steel sample in comparison to fine-grained one. 3) The applied stress required for nucleation of deformation twin was found to increase with decreasing grain size from 32 nm to 11.1 nm . 4) Dislocation analysis also showed that dislocation substructure is affected by the initial grain size. 23
5) The formation of deformation twin exhibits the following features: (i) the primary stacking faults and deformation twin structures are formed in grains with only a single dominant slip system, (ii) the dislocations involved in the deformation twin nucleation process are Shockley partial dislocations and (iii) The deformation twinning growth is controlled by succeeding emission of Shockley partial dislocations from grain boundaries.
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[57] Gutierrez-Urrutia I, Zaefferer S, Raabe D. The effect of grain size and grain orientation on deformation twinning in a Fe–22 wt.% Mn–0.6 wt.% C TWIP steel. Materials Science and Engineering: A. 2010 Jun 15;527(15):355260. [58] Bouaziz O, Allain S, Scott C. Effect of grain and twin boundaries on the hardening mechanisms of twinning-induced plasticity steels. Scripta Materialia. 2008 Mar 1;58(6):484-7.
Fig 1. MD simulation model of nanocrystalline TWIP steel. Gray atoms are in a perfect fcc structure, while blue atoms are in grain boundaries.
32
(a)
(b)
(c)
(d)
Fig 2. Grain structure of simulated nanocrystal TWIP steel with mean grain size of (a) 32 nm, (b) 17.7 nm, (c) 14.3 nm and (d) 11.1 nm. Atoms are colored according to common neighbor analysis. Colors denote the local crystal structure. Gray color: fcc structure and blue color: grain boundaries.
33
8
d=32 nm d=17.7 nm d=14.3 nm d=11.1 nm
7
Stress (GPa)
6 5 4 3 2 1 0
0.0
0.1
0.2
0.3
0.4
0.5
Strain
Fig 3. The tensile curves of nanocrystalline TWIP steel with different grain sizes.
34
7
Yeild Stress (GPa)
6 5 4 3 2 1 10
15
20
25
30
35
Grain size (nm)
Fig 4. Variation in yield stress as a function of mean grain size.
35
(a)
(b)
(c)
(d)
Fig 5. Cross-sectional views of nanocrystalline TWIP steel with grain size of (a) 32 nm, (b) 17.7 nm, (c) 14.3 nm and (d) 11.1 nm deformed to 10% total strain. Atoms colored according to CNA values. Gray atoms are in a perfect fcc structure, while blue atoms are in grain boundaries, incoherent twin boundaries and dislocations. Stacking faults and coherent twin boundaries appear as green and red atoms within grain interiors, respectively. Dislocations appear as blue dots within grain interiors.
36
(a)
(b)
(c)
(d)
Fig 6. Cross-sectional views of nanocrystalline TWIP steel with grain size of (a) 32 nm, (b) 17.7 nm, (c) 14.3 nm and (d) 11.1 nm deformed to 20% total strain. Atoms colored according to CNA values. Gray atoms are in a perfect fcc structure, while blue atoms are in grain boundaries, incoherent twin boundaries and dislocations. Stacking faults and coherent twin boundaries appear as green and red atoms within grain interiors, respectively. Dislocations appear as blue dots within grain interiors.
37
(a)
(b)
(c)
(d)
Fig 7. Comparison of deformation substructure in the present MD simulation with experimental observations by TEM studies. Formation of (a, b) stacking faults, (c, d) deformation twins within grain interior. (Fig. 7(b) from D.T. Pierce et al. [36], Fig. 5, p. 244 and Fig. 7(d) from H.K. Yang et al. [37], Fig. 2, p. 253).
38
14
Stacking Faults Deformation Twins
14
12
Volume Fraction (%)
12
Volume Fraction (%)
Stacking Faults Deformation Twins
10 8 6 4 2
10 8 6 4 2
0 12
16
20
24
28
0
32
12
Grain size (nm)
16
20
24
28
32
Grain Size (nm)
(a)
(b)
Fig 8. Grain size effect on the volume fraction of stacking faults and deformation twins in nanocrystalline TWIP steel deformed under tension to total strain of (a) 10 % and (b) 20 %.
39
Fig 9. Snapshot of deformation structure of the Fe-22 Mn nanocrystalline TWIP steel at strain of (a) 9% and (b) 9.5%, (c, d) in-situ straining TEM test of the Fe-17Mn-0.45C-1.5Al-1Si TWIP steel taken from J. Kim et al. [36], a twinning dislocation (TD) generated on the right hand side of the image (c) approaches dislocation D, replacing the stacking fault fringes contrast by a homogeneous white contrast.
40
(a)
(b)
(c) Fig 10. (a) Gliding of Shockley partial dislocations along twin boundary, (b) twin lamella formed by repetitive emission of twinning partials from grain boundaries onto successive (111) stacking planes, (c) Dislocation analysis of the grain analyzed in Figure 9. The analysis focuses on two regions, i.e. (1) the region where the twinning dislocations (TD) are present, and (2) the grain boundary region, where some dislocations are localized.
41
(a)
(b)
(d)
(e)
Fig 11. Effect of grain size on the dislocation substructure at the early deformation stage in studied samples deformed to a total strain of 5%. (a) 32 nm, (b) 17.7 nm, (c) 14.3 nm and (d) 11.1 nm.
42
(a)
(b)
(c)
(d)
Fig 12. Nucleation and growth of partial dislocations from grain boundaries or triple junctions in nanocrystalline TWIP steel with an average grain size of (a) 32 nm, (b) 17.7 nm, (c) 14.3 nm and (d) 11.1 nm at the peak stress according to the tensile curves.
43
Twinning nucleation Stress (GPa)
7
6
5
4
3 10
15
20
25
30
35
Grain size (nm)
Fig 13. Effect of initial grain size on the twinning nucleation stress
Table 1. Simulation cell dimensions (LX,LY, LZ), number of atoms and the mean grain size of samples investigated in this study. Grain size (nm) LX(nm) LY(nm) LZ(nm) Number of atoms 32
80
80
10
5418912
17.7
80
80
10
5418935
14.3
80
80
10
5621438
11.1
80
80
10
5419208
44
Mina
www.elsevier.com/locate/msea
PII: DOI: Reference:
S0921-5093(18)31610-1 https://doi.org/10.1016/j.msea.2018.11.085 MSA37205
To appear in: Materials Science & Engineering A Received date: 21 August 2018 Revised date: 17 November 2018 Accepted date: 17 November 2018 Cite this article as: Roghayeh Mohammadzadeh and Mina Mohammadzadeh, Inverse grain size effect on twinning in nanocrystalline TWIP steel, Materials Science & Engineering A, https://doi.org/10.1016/j.msea.2018.11.085 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Inverse grain size effect on twinning in nanocrystalline TWIP steel
Roghayeh Mohammadzadeh1, Mina Mohammadzadeh2*
1 2
Department of Materials Engineering, Azarbaijan Shahid Madani University, Tabriz, Iran
Department of Mechanical Engineering, University of California, Merced, CA 95340, USA,
[email protected] [email protected]
Abstract Mechanical twinning plays a significant role in the plastic deformation of Twinning Induced Plasticity steel (TWIP). The effect of grain size on the twinning nucleation stress, yield stress, twin morphology and deformation mechanisms of Fe-22 wt. % Mn steel have been studied using molecular dynamics simulations. The nanostructure materials with mean grain sizes of 11.1, 14.3, 17.7 and 32 nm are constructed using the Voronoi tessellation method, and the plastic deformation behavior is studied by molecular dynamics simulation. A meta-atom potential is applied to represent the atomic interactions. The result of tensile test showed that the yield strength and twin nucleation stress increase by grain size decreasing. Structural analysis of the samples deformed to 10 and 20 % total strain disclosed thicker primary twins in 1
the coarse-grained material in comparison with the fine-grained one. Moreover, a high volume fraction of twins was formed in the coarse-grained sample. Dislocation analysis exhibited that the dislocation structure influenced by the initial grain size. The density of nucleation sites for twins and subsequently the developing twin substructure is affected by the dislocation substructure. It is concluded that with decreasing grain size, deformation of nanocrystalline TWIP steel by mechanical twinning can become difficult.
Keywords: TWIP steel, Grain size, Deformation twinning, Molecular dynamics, morphology.
2
1. Introduction The high formability and excellent ultimate tensile strength of Twinning Induced Plasticity (TWIP) steels have been draw attention over the past few years [1–4]. The superior tensile properties of TWIP steels result from formation of deformation twins continuously during plastic deformation, which enhances the work hardening capacity of these steels. Plastic deformation by TWIP mechanism is observed in steels which possesses medium stacking fault energy (SFE), usually in the range of 18–45 mJ.m-2 [5] and is characterized by the formation of straight and parallel lines inside grains. The excellent strengthductility combination makes the TWIP steels most suitable material for high strain rate energy absorption demands such as military vehicle armor plates and automotive crash safety [6]. The remarkable strain hardening of TWIP steels is mainly related to dynamic Hall–Petch effect [7, 8]. As twins nucleated during plastic deformation of TWIP steels, they can act as barriers for dislocation glide and resulting in a continuously dynamic grain refinement. Therefore, dislocation mean free path reduces as a consequence of twin boundaries formation which leads to high strain-hardening rate [9]. Various mechanisms have been suggested for the deformation twinning formation via gliding of dislocations for example; pole mechanism and nucleation of twin across the stacking faults [10]. However, the low yield stress of TWIP steels (200-450 MPa) in comparison to advanced high strength steels (AHSS) limits the
3
extensive use of these steels in industrial applications (specially automotive) [11]. The yield strength of materials can be modified using different strengthening mechanisms such as grain size reduction, solid solution and precipitation hardening [12]. Although yield and ultimate tensile strengths increase by solid solution and precipitation hardening process but elongation and toughness decrease [13,14]. The grain refinement is the most effective method for improving both strength and ductility simultaneously without any change in the chemical composition of the alloy [15]. It has been reported by K.M. Rahman et al. [16] that deformation twinning of TWIP steels is greatly dependent on the initial grain size of material. K.M. Rahman et al. [16] have shown that with decreasing grain size of Fe-15Mn-2Al2Si-0.7C TWIP steel from 84 to 0.7 µm, the yield stress increased from 350 to 720 MPa without substantially change in the ductility. G. Dini et al. [17] have obtained a yield stress of 572 MPa in an Fe–31Mn–3Al–3Si TWIP steel plate with a mean grain size of 2.1 µm. Y.Z. Tian et al. [18] have obtained an ultrafine-grained Fe-22-Mn-0.6 C (wt .%) TWIP steel with a fully recrystallized structure and average grain size of 550 nm through a repeating cold working and annealing heat treatment with good strength-ductility balance (the yield stress of 793 MPa, ultimate tensile strength of 1247 MPa, and uniform elongation of 47%). Similarly, R. Ueji et al. [19] have shown that the grain refinement of Fe-31Mn–3Al–3Si (wt. %) TWIP steel until 1.8 µm gives high
4
yield stress (525 Mpa) with great ductility (uniform elongation of 48%). S. Kang et al. [20] have investigate the influence of grain refinement (with initial grain sizes of 2, 10, and 50μm) on yield strength of Fe–18Mn–0.6C–1.5Al TWIP steel and have concluded that steel sample with grain size of 2 μm exhibited higher yield strength of 500 MPa in comparison to coarse grained specimens. Although there are more studies on the influence of grain size on the yield strength of microcrystalline TWIP steels, there are a few studies which investigate the effect of initial grain size on the behavior of deformation twinning in TWIP steels [16, 19, 21]. I. Gutierrez-Urrutia et al. [21] have investigated the effect of initial grain size (3 and 50 µm) on deformation behavior of Fe-22Mn-0.6C (wt. %) TWIP steel at room temperature by microstructure observation of tensile deformed samples using electron channeling contrast imaging (ECCI). The authors achieved that by decreasing the grins size from 50 µm to 3 µm, the area fraction of deformation twinning at 0.3 logarithmic strain decreases from 0.2 to 0.1. Also, Ueji et al. [19] observed by TEM studies many deformation twinning (13 grains of total 26 grains) in a Fe-31Mn–3Al–3Si (wt. %) TWIP steel with a coarse grain size of 49.6 µm. On the other hand, they [19] observed a few deformation twinning in a fine grain size sample (1.8 µm, 5 grains of 30 grains). However, K.M. Rahman et al. [16] have studied the effect of grain size on stress required for the growth of
5
deformation twins in the Fe-15Mn-2Al-2Si-0.7C (wt. %) TWIP steel and have observed that the ductility of steel samples was not influenced by grain refinement. They [16] have shown by TEM studies that the initial grain size, influence the morphology of twins, and a smaller grain size promotes the formation of thinner twins. The contradictory results from the two studies [19, 21] can be due to different stacking fault energy values of the investigated steels. Gutierrez-Urrutia et al. [21] and Ueji et al. [19] used a TWIP steel with a stacking fault energy of 24 and 42 mJ.m-2, respectively, whereas K.M. Rahman et al. [16] investigated steel samples with SFE of 30 mJ.m-2. These reports emphasize the influence of both the sample preparation and the measurement method on the experimental results. Beside the accuracy of experimental values, the measurement itself is quite complicated and difficult, since many parameters including sample quality (grain size, homogeneity, impurity, etc.) and picture quality must be well controlled in order to get reliable results. It is significantly important to increase the fraction of deformation twins in TWIP steel because twinning can cause both high ductility and strength. To develop alloys with innovative mechanical properties, it is important to investigate deeply the deformation mechanism of TWIP steels. Because of the controversies among published results and these difficulties, a theoretical approach for evaluating the influence of initial grain size on the dynamics behavior of deformation twinning is highly motivated. A systematic
6
study based on theoretical methods would lead to a fundamental understanding of the topic, which is of great importance for designing new materials. Molecular Dynamics (MD) simulations have shown to be an effective approach for atomistic study of deformation mechanisms in nanocrystalline metals and alloys with precisely simulation boxes in which the dynamics behavior of the microstructures can be investigated [22]. Also, atomistic simulations by MD approach have shown a change in the plastic deformation mechanism at the critical grain size, i.e., from the classical Hall-Petch relationship to inverse HallPetch effect [23]. In the present study, the influence of initial grain size on the atomic-level deformation mechanism of a TWIP steel has been studied by performing a series of large scale MD simulations, that will help to achieve innovative ways for obtaining superior mechanical properties in TWIP steels. 2. Simulation Details The
MD
simulations
have
been
carried
out
by
the
Large-scale
Atomic/Molecular Massively Parallel Simulator (LAMMPS) [24] and a Metaatom potential developed by P. Wang et al. [25] for Fe-22Mn-0.6C (wt. %) TWIP steel. P. Wang et al. [26, 27] developed a novel interaction potential that enables them to perform molecular dynamics simulations of complex alloy systems. The central idea is that there is a set of finite material parameters that governs the mechanical properties of an alloy system. Using this set of material constants for TWIP steel, they developed the so-called meta-atom potential for 7
Fe-22Mn-0.6C (wt. %) TWIP steel based on the embedded-atom method. They further performed extensive simulations to validate their potential/approach against experimental data. The meta-atom potential for Fe-22Mn-0.6C (wt. %) steel was calibrated in accordance with lattice constants, elastic moduli (C11, C12 and C44), SFE, unstable SFE and single vacancy formation energy (Evac) which were obtained by experimental results and the ab initio calculations [25]. Their detailed simulations reveal various competing mechanisms that govern twinning-induced plasticity in steels. Interestingly, their observation that twin boundaries in steel serve as effective barriers for dislocation motion as well as accommodate plasticity thereby offering high strength and ductility is consistent with studies on nano-twinned fcc metals. As among different types of TWIP steels, a Fe-22Mn-0.6C (wt. %) steel exhibits a very large work hardening capacity in comparison to Fe-31Mn-3Al3Si (wt. %) steels [26], the authors used Fe-22Mn (wt. %) as a model alloy. The nanocrystalline samples with mean grain size of 11.1, 14.3, 17.7 and 32 nm were constructed using the Voronoi tessellation method [27]. Periodic boundary conditions were applied for x, y and z directions. Figure 1 shows the initial configuration of a nanocrystalline sample, in which the atoms at the perfect FCC sites are shown in grey, and the grain boundary (GB) atoms are shown by blue colored atoms. Details of simulation box size and number of atoms for each sample are listed in Table 1.
8
Before straining, as-created sample models firstly were exposed to energy minimization using the conjugate gradient procedure and finally relaxed under the pressure of 0 bar and the temperature of 300 K by the Nose/Hoover isobaricisothermal ensemble (NPT) for 200 ps with time step of 1 fs. The pressure variable in thermal relaxation was controlled by the Parrinello–Rahman method [28] with a damp time of 1000 steps. The Nose–Hoover method [29] with a damp time of 100 steps was applied to maintain a stable temperature. After energy and thermal relaxations, the simulation boxes were strained along y-axis with strain rate of 0.001 ps−1 up to a total strain of 50 %. The pressure in the x and z directions were set to be zero during the tensile loading to retain the uniaxial loading state in the samples. In order to visualize deformation structure, the authors alter the coloring scheme of common neighbor analysis (CNA) [30]. The CNA is a well known computational analysis technique that identifies the crystalline order of atoms locally and as a result of that characterizes regions with a disordered arrangement of neighboring atoms. However, different types of crystal defects such as stacking faults and coherent twin boundaries cannot be recognized by CNA alone. Therefore, it can work only for visualization aims. To overwhelm these restrictions, we have implemented a second analysis method to determine coherent twin boundaries (TBs) from intrinsic stacking faults (ISFs). In usual visualization tools such as common neighbor analysis method, these planar
9
defects were generally identified by detecting atoms having a local hcp crystal structure, which is typical for both coherent twin boundaries and intrinsic stacking faults in fcc metals. To determine coherent twin boundaries and stacking faults, it is necessary to do a further topological and crystal orientation analysis of the neighboring atoms. In order to calculate the numbers of atoms present in the coherent TBs and ISFs, the authors have implemented an additional structural analysis algorithm into the MD simulation code. This improved analysis allows to make ISFs and coherent TBs readily recognizable in the visualization images and to quantify the exact densities of ISFs and TBs in the simulation box as a function of strain. In the following figures, ISFs are colored green and coherent TBs red, respectively. Post-processing and visualization of simulation snapshots were carried out with the scientific software package “Open Visualization Tool OVITO” [31]. 3. Results and discussion 3.1. Microstructure characterization before tensile deformation Figure 2 shows the cross-sectional views of the nanocrystal TWIP steel with different grain sizes of 32, 17.7, 14.3 and 11.1 nm, in which atoms are characterized in accordance with CNA method [31]. This coloring pattern clarifies the crystal structure of atoms locally according to its neighbor atoms. The calculated CNA values define an atom as simple cubic, face centered cubic (fcc), body centered cubic (bcc) and hexagonal close-packed (hcp) or others. It 10
can be observed that as-constructed nanocrystal steel samples consisted of small grains with different crystal orientation, which are surrounded by disordered boundaries (GBs). In atomic structure of the studied samples two types of atoms can be seen; crystal atoms with ordered arrangement corresponding to the lattice and boundary atoms with different inter-atomic spacing. In Figure 2, atoms with fcc structure are colored gray and atoms without certain crystal structure (GBs) are colored blue. 3.2. Effect of grain size on the flow behavior Figure 3 displays the simulated tensile stress-strain curves of studied TWIP steel samples with different grain sizes. It can be seen that tensile stresses in all investigated samples firstly increase with strain linearly to a maximum value, then decreasing to a steady-state value with some fluctuations. As can be shown later, the maximum stress was corresponding with the onset of plastic deformation (yielding point), which is known to be caused by the higher strain rates typically applied in MD simulations [32]. After reaching maximum stress, the flow stress abruptly reduced to a steady-state level in all studied samples due to; i) relaxation of stress owing to high strain rate applied in the current simulation [33], or ii) formation of cracks during tensile deformation [34]. A remarkable characteristic of the stress-strain curve of the sample with grain size of 11.2 nm is that flow stress drop to 0.02 GPa. This difference in flow behavior
11
is due to nucleation and propagation of cracks significantly in the sample having a grain size of 11.1 nm (as confirmed visually in section 3.3). As the deformation twinning nucleation and growth in TWIP steels is determined by the glide of Shockley partial dislocations, it is physically more important to compare the effect of grain size on the yield stress. In order to elucidate the influence of grain size on the yield strength of nanocrystalline samples by MD simulations it is essential to calculate the average of flow stress over a specific strain interval [35] due to significant influence of strain rate on the maximum stress of tensile curves. In the present nanocrystalline TWIP steel with mean grain size of 11.2 nm, the critical strain for inter-granular crack initiation was found to be 5% of total strain. On the other hand, the samples with larger grain sizes of 14.4, 17.7 and 32 nm did not show any appreciable crack formation up to total strain of 40%, suggesting that nucleation of intergranular crack could be retarded by increasing the initial grain size. To remove any possible crack formation effect, average flow stress in the plastic strain range of 0.1-3 % was selected for obtaining the yield stress in this study, since inter-granular cracks were not detected in any of samples within this plastic strain range. Beyond this plastic strain range, inter-granular cracks were found to nucleate first in the sample with the smallest grain size of 11.2 nm, which decreasing the flow stress with further straining. Variation in yield versus the mean grain size is plotted in Figure 4. It can be observed that the yield stress
12
increases to a maximum value of 4.97 GPa down to a grain size of 11.2 nm. The usual Hall-Petch relation (the strength increasing as the grain size is reduced) can be observed for nanocrystalline TWIP steel with grain sizes larger than 11.2 nm. 3.3. Deformation substructure In order to comprehend the effect of initial grain size on the deformation mechanism of nanocrystalline TWIP steel, the analysis of deformation substructure at the atomistic level was conducted. Figures 5 and 6 illustrate cross-section views of deformation substructure in the deformed samples with the grain sizes of 32, 17.7, 14.3 and 11.1 nm after 10 and 20 % total strain, respectively. In Figures 5 and 6, the atoms with perfect fcc structure are colored gray, while atoms in grain boundaries, incoherent twin boundaries and dislocations are colored blue. Stacking faults and coherent twin boundaries appear as green and red atoms within grain interiors, respectively. At large strain of 10 and 20 % three deformation defects types can be distinguished as follow: (i)
Stacking faults leaving behind the leading partial dislocations which were emitted from the grain boundaries (as indicated by number 1 in Figure 5(b)) or stacking fault between the leading and trailing partials of dissociated dislocations or extended partial dislocations (as shown by number 2 in Figure 5(b)). In figures 5 and 6, the leading partial 13
dislocations are found to have a Burgers vector of a /6 [112] and the corresponding stacking faults are intrinsic. (ii)
Coherent deformation twins (as indicated by number 3 in Figure 5(d)).
(iii)
Incoherent deformation twins (as shown by number 4 in Figure 5(d)).
As can be observed in Figures 5 and 6, grain boundaries and triple junctions are the main sites for the nucleation of twins. By comparing deformation substructure of nanocrystalline TWIP steel in this study with experimental ones [36, 37] obtained by TEM observations on deformed TWIP steels (see Figure 7), it can be seen that they share many deformation substructures similarities like stacking faults and deformation twining. The consistency of the deformation substructure between experimental reports and MD simulation results verifies the validation of EAM inter-atomic potential which was used in this study. Detailed analysis of deformation substructure images at total strain of 10 and 20% (Figure 5 and 6) reveals that the twin substructure in the all investigated nanocrystalline samples mostly occurs as single variant twining system. It can be seen from figures 5 and 6 that, after the critical stress for nucleation of twins is achieved, any additional stress seems to thicken the nucleated twins. By increasing the strain from 10 to 20%, the lamellar twin substructure formed by the accumulation of the twin boundaries. Further analysis of deformation substructure shows that the coarse-grain sample dose indeed consists of thicker 14
deformation twins in comparison with those of fine grain sizes, despite the fact that all samples have been deformed to the same strain. Therefore, the initial grain size effects the morphology of twins, a large grain size encourages the development of thicker twins, because; the twins need to grow over a large distance. Hence, it can be expected that the coarse-grained sample can be able to exhibit considerable plastic strain upon tensile loading, because the thickness of deformation twins is greater. Further investigation of deformation substructure of the fine and coarse grain size samples show that the area fraction of deformation twins (coherent and incoherent) in the coarse-grained sample (32 nm) is higher than that observed in the fine-grained specimens. Figure 8 shows the histograms of volume fraction of deformation twins and stacking faults in samples deformed under tension up to a total strain of 10 and 20 %. As it can be seen in Figures 8 (a) and (b), with decreasing grain size the volume fraction of deformation twins obviously reduces for the studied TWIP steel with grain size of smaller than 32 nm whilst, the volume fraction of stacking faults increases. This demonstrates that mechanical twins tend to develop in coarse-grained samples, while stacking faults tend to form in fine-grained samples. The reduction of twining tendency with decreasing grain size is called the inverse grain size effect [38]. One of the important characteristic of the data in Figure 8 is that inverse grain size effect occurs for deformation twins, while no inverse grain size effect revealed for stacking faults. The obtained results in this study is consistent with a previous analytical model [39] and experimental observation 15
on the electrodeposited nanocrystalline nickel foil with grains in the range of 10-75 nm [38]. The inverse grain size effect on the mechanical twins can be described by the combined effects of general planar fault energy and grain size [38, 40]. The prerequisite for the deformation twin nucleation is to create a stacking fault firstly. That is a stacking fault was formed initially by a leading partial dislocation, and afterwards a twinning partial dislocation transformed the stacking fault region to a twin nucleus (as shown in Figures 6 and 7). Also, it has been reported that [41] the required stress for emission of twinning partial dislocation increases with decreasing grain size. Therefore, as the stress required to emit twinning partial dislocation is higher than leading partial dislocation, one can conclude that the stress needed to emit a twinning partial dislocation gets greater than the applied stress below a critical grain size, which prevents deformation twinning although still lets the emission of the leading partial dislocations to form extended stacking faults. This will lead to a statistical reduction in deformation twining density by decreasing grain size, (the inverse grain size effect on deformation twining). Therefore, it can be say that leading partial dislocations can be activated in all grains with different sizes to generate stacking faults, but if the inverse grain size effect is governing, nucleation and growth of twinning partial dislocations get more difficult by decreasing grain size. Therefore, the higher applied stress is required to emit a twinning partial dislocation than a leading partial dislocation below a critical grin size. The higher stress requirement for nucleation of twinning partials was 16
observed experimentally in reference [38]. X. L. Wu et al. [38] have shown that the area fraction of twinned grains increased from 28% under tension to 38% under rolling and to 44% under split Hopkinson pressure bar (SHPB) test. They reported that flow stress under tension was 1.5 GPa, which was increased to 2.0 GPa under SHPB test. 3.4. Twin nucleation and growth mechanism To reveal the dislocation processes involved in the formation of deformation twins, a small part of the simulation cells is considered for further analysis. Figure 9 shows snapshots of an in-situ tensile straining of the investigated TWIP steel with mean grain size of 17.7 nm. In the initial stage of deformation (total strain of 9%), six planar defects are designated in the investigated grain as shown in Fig. 9 (a). These six planar defects are parallel which indicates that the planar defects have the identical habit plane. The green planar defects are stacking faults, while the red planar defects are deformation twins. Hereinafter, the stacking fault is indicated to as SF while, twinning dislocation is specified to as TD. It can be seen from Figures 9 (a) and 9 (b) that by increasing strain from 9 to 9.5 %, twin dislocations nucleated from grain boundaries moves rapidly toward the stacking fault position and changes the stacking fault area to a twin one. Deformation twin growth is controlled by gradual glide of the twinning dislocations. Also it can be seen that by more straining, the whole of stacking fault 1 (SF1) transformed to twin area. As can be shown in Figure 10, the initial 17
stacking fault with thickness of one atomic layer changes to a twin with the thickness of two atomic layers by the movement of single twinning partial dislocation. The current observation confirms the nucleation of a thin twin at grain boundary by the emission of specific partial dislocation from grain boundary. In order to analyze the type of dislocation in the twin area, a dislocation analysis using Ovito was carried out. The dislocation analysis was conducted on two regions, i.e (1) the region where the dislocation twinning exists and (2) the grain boundary region where dislocations are piled up. Based on the dislocation analysis shown in Figure 10 (c), the twin dislocations are Shockely partial dislocations with Burgers vector of a/6<112>. Also, it can be seen that the dislocations at the grain boundaries are consisted of perfect and some Shockely partial dislocations. The emission of Partial dislocations from grain boundaries has been observed in nano-crystalline metals by molecular dynamics (MD) simulations [42, 43] and experimental studies [44]. In nanocrystalline nickel samples with mean grain size of 12 and 20, H. Van Swygenhoven et al. [43] shown by MD simulation that grain boundaries could emit partial dislocations during plastic deformation by local atomic shuffling and stress-assisted free volume migration. It has been reported that dissociated dislocations [44], ledges [45] in the grain boundaries and triple junctions [46] could be the sources of partial dislocations at grain boundaries. X. L. Wu et al. [44] have observed experimentally by high resolution transmission electron microscopy the glide of leading partial dislocation from grain boundaries with a 18
high density of extrinsic dislocations into the grain interior. This is also consistent with the work of Gutierrez-Urrutia and Raabe Jin-Kyung Kim et al. [47] who studied the deformation twinning mechanism in Fe-17Mn-0.45C1.5Al-1Si TWIP steel by means of in-situ TEM deformation tests and observed formation of a thin twin by Shockley partial dislocations generated in a grain boundary. 3.5. Dislocation substructure Dislocation analysis also reveals a difference in the dislocation substructure between the coarse and fine-grained nanocrystalline samples. Figure 11 illustrates dislocation substructure at total strain of 5% in studied samples. It can be seen that the dislocation substructure is different in the coarse-grained sample (32 nm) from that observed in the fine-grained samples. In the coarsegrained sample (Fig. 11 (a)), well-developed cell structures can be observed in deformed grains. On the other hand, the cell structure is rarely distinguished in fine-grained samples (Fig. 11 (b,c,d)), and most of dislocations were arranged on the primary slip plane. Also, it can be seen that the dislocation configuration in the fine-grained samples shows an approximately loose arrangement and lower volume fraction in comparing with the coarse-grained sample. This morphology has a close similarity to planar dislocation pattern often detected by bright field TEM with low to medium stacking fault energy [48-50]. The dislocation substructure shown in Figure 11 (a) is similar to wavy dislocation 19
substructure observed in alloys and metals with medium to high stacking fault energy [51]. Wavy dislocation substructure is developed in grains when a large number of slip planes are activated and cross-slip of dislocations is facilitated [52]. The influence of grain size on the dislocation substructure developed at the initial deformation stage (total strain of 5%) can be comprehended by the Hall– Petch relationship. To accomplish the tensile stress associated to total strain of 5%, the coarse-grained sample needs a larger strain, owing to the low yield stress. At the initial plastic deformation step, dislocation glide mostly control plasticity and, correspondingly, the density of dislocation ascends with strain. Due to high density of dislocations in the coarse-grained sample, the dislocations are predominately piled up as the cell blocks (Fig. 11 (a)). However, the fine-grained samples keep a less dislocation density prior to the total strain of 5%, due to the high yield stress. Therefore, fine-grained sample exhibits loose dislocation substructure (Fig. 11 (d)). If we take into account that twin nucleated as a result of some certain dislocation reactions, the relatively homogeneous distribution of dislocations in the coarse-grained sample (Fig. 11 (a)) supplies a large number of nucleation sites for deformation twins. However, the fine-grained sample (Fig. 11(d)) contains a low overall dislocation density which will create a less number of sites for nucleation of twins. 20
3.6. Effect of grain size on the twining nucleation stress Twining involves two processes, nucleation and subsequent twin growth. The stress needed to create twinning can be regarded to be a combination of two different processes; (i) a required stress for twin nucleation and (ii) an additional stress for growth of twin. But, experimental determination of the required stress for nucleation of twin is very hard [53, 54]. As the twins nuclei (for example stacking faults), normally present inside the alloys, the experimental measurements of twinning stress actually is the required stress for growth of twins. Atomistic simulations have shown to be strong tools for study of the dynamic behavior of plastic deformation substructures. It is normally considered that deformation twins in metals and alloys are nucleated by preexisting dislocations that dissociated into partial dislocations which creates multi-layered stacking faults. Various models based on specific dislocation reactions have been suggested for nucleation of deformation twins in the literature [55, 56]. All require the glide of partial dislocations with Burgers vector of a/6 [112] on success {111} planes. As the snapshots of structure evolution in the MD simulations at different times can be readily acquired, the deformed structures in investigated samples were visualized at different time steps. Visualization of samples substructure at the maximum stress of tensile curves (Figure 12) shows that the peak stress is connected with the nucleation of partial dislocation from grain boundaries or 21
triple junctions. According to the Figure 12, the maximum stress in the stressstrain curves is the critical stress to detach leading partial dislocations from trailing one. Therefore, the peak stress in the tensile curves can be considered to be the stress for deformation twin nucleation. The influence of initial grain size on the maximal tensile stress of nanocrystalline TWIP steel is presented in Figure 13. The results show that the stress for nucleation of deformation twins in the investigated nanocrystalline TWIP steel increases by decreasing the initial grain size. Furthermore, less initial strain for twinning in the coarse-grained sample compared to fine-grained sample (see Figure 3) indicates that refinement of grains suppresses formation and thickening of twins. Therefore, large grain size promotes twining more easily because the slip length according to figures 5 and 6 is greater. Also K. M. Rahman et al. [16] have measured the twin stress in the Fe-15Mn-2Al-2Si-0.7C TWIP steel with grain sizes of 0.7, 4.3, 10, 45 and 84 µm by cyclic tensile testing at sub-yield stress. They have found that the stress required for deformation twinning growth increased with decreasing grain size. Additionally, G. Urne et al. [57] have shown that twinning stress is significantly influenced by the yield strength of material which is in turn influenced by grain size. Hence, G. Urne et al. [57] proposed a Hall-Petch type relation for the effect of grain size on the twinning stress in Fe-22Mn-0.6C (wt. 5) TWIP steel with average grain sizes of 3 µm and 50 µm. However, the present study is not consistent with the results of Bouaziae et al. [58]. They have reported that the twin stress in Fe-22Mn-0.6C (wt. 5) TWIP steel is not 22
influenced by the initial grain size of samples and lies constant at the level of 550-600 MPa for grain sizes in the range between 25 and 1.3 µm. Conversely, As the twining stress is unified with the yield stress in reference [58], this confusion probably causes the controversy between the present study and the results of Bouaziae et al. [58].
Conclusions The effect of initial grain size on deformation twining behavior of Fe-22Mn (wt. %) TWIP steel has been investigated using a series of large-scale molecular dynamics simulations. The following conclusions can be drawn from this study: 1) A considerable fraction of deformation twins was detected in the coarsegrained steel sample which indicates the relative easy formation of deformation twin in coarse-grained sample in comparison to fine-grained one. 2) Deformation substructure analysis of samples deformed to 10 and 20% total strain revealed the presence of thicker deformation twins in the coarse-grained steel sample in comparison to fine-grained one. 3) The applied stress required for nucleation of deformation twin was found to increase with decreasing grain size from 32 nm to 11.1 nm . 4) Dislocation analysis also showed that dislocation substructure is affected by the initial grain size. 23
5) The formation of deformation twin exhibits the following features: (i) the primary stacking faults and deformation twin structures are formed in grains with only a single dominant slip system, (ii) the dislocations involved in the deformation twin nucleation process are Shockley partial dislocations and (iii) The deformation twinning growth is controlled by succeeding emission of Shockley partial dislocations from grain boundaries.
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Fig 1. MD simulation model of nanocrystalline TWIP steel. Gray atoms are in a perfect fcc structure, while blue atoms are in grain boundaries.
32
(a)
(b)
(c)
(d)
Fig 2. Grain structure of simulated nanocrystal TWIP steel with mean grain size of (a) 32 nm, (b) 17.7 nm, (c) 14.3 nm and (d) 11.1 nm. Atoms are colored according to common neighbor analysis. Colors denote the local crystal structure. Gray color: fcc structure and blue color: grain boundaries.
33
8
d=32 nm d=17.7 nm d=14.3 nm d=11.1 nm
7
Stress (GPa)
6 5 4 3 2 1 0
0.0
0.1
0.2
0.3
0.4
0.5
Strain
Fig 3. The tensile curves of nanocrystalline TWIP steel with different grain sizes.
34
7
Yeild Stress (GPa)
6 5 4 3 2 1 10
15
20
25
30
35
Grain size (nm)
Fig 4. Variation in yield stress as a function of mean grain size.
35
(a)
(b)
(c)
(d)
Fig 5. Cross-sectional views of nanocrystalline TWIP steel with grain size of (a) 32 nm, (b) 17.7 nm, (c) 14.3 nm and (d) 11.1 nm deformed to 10% total strain. Atoms colored according to CNA values. Gray atoms are in a perfect fcc structure, while blue atoms are in grain boundaries, incoherent twin boundaries and dislocations. Stacking faults and coherent twin boundaries appear as green and red atoms within grain interiors, respectively. Dislocations appear as blue dots within grain interiors.
36
(a)
(b)
(c)
(d)
Fig 6. Cross-sectional views of nanocrystalline TWIP steel with grain size of (a) 32 nm, (b) 17.7 nm, (c) 14.3 nm and (d) 11.1 nm deformed to 20% total strain. Atoms colored according to CNA values. Gray atoms are in a perfect fcc structure, while blue atoms are in grain boundaries, incoherent twin boundaries and dislocations. Stacking faults and coherent twin boundaries appear as green and red atoms within grain interiors, respectively. Dislocations appear as blue dots within grain interiors.
37
(a)
(b)
(c)
(d)
Fig 7. Comparison of deformation substructure in the present MD simulation with experimental observations by TEM studies. Formation of (a, b) stacking faults, (c, d) deformation twins within grain interior. (Fig. 7(b) from D.T. Pierce et al. [36], Fig. 5, p. 244 and Fig. 7(d) from H.K. Yang et al. [37], Fig. 2, p. 253).
38
14
Stacking Faults Deformation Twins
14
12
Volume Fraction (%)
12
Volume Fraction (%)
Stacking Faults Deformation Twins
10 8 6 4 2
10 8 6 4 2
0 12
16
20
24
28
0
32
12
Grain size (nm)
16
20
24
28
32
Grain Size (nm)
(a)
(b)
Fig 8. Grain size effect on the volume fraction of stacking faults and deformation twins in nanocrystalline TWIP steel deformed under tension to total strain of (a) 10 % and (b) 20 %.
39
Fig 9. Snapshot of deformation structure of the Fe-22 Mn nanocrystalline TWIP steel at strain of (a) 9% and (b) 9.5%, (c, d) in-situ straining TEM test of the Fe-17Mn-0.45C-1.5Al-1Si TWIP steel taken from J. Kim et al. [36], a twinning dislocation (TD) generated on the right hand side of the image (c) approaches dislocation D, replacing the stacking fault fringes contrast by a homogeneous white contrast.
40
(a)
(b)
(c) Fig 10. (a) Gliding of Shockley partial dislocations along twin boundary, (b) twin lamella formed by repetitive emission of twinning partials from grain boundaries onto successive (111) stacking planes, (c) Dislocation analysis of the grain analyzed in Figure 9. The analysis focuses on two regions, i.e. (1) the region where the twinning dislocations (TD) are present, and (2) the grain boundary region, where some dislocations are localized.
41
(a)
(b)
(d)
(e)
Fig 11. Effect of grain size on the dislocation substructure at the early deformation stage in studied samples deformed to a total strain of 5%. (a) 32 nm, (b) 17.7 nm, (c) 14.3 nm and (d) 11.1 nm.
42
(a)
(b)
(c)
(d)
Fig 12. Nucleation and growth of partial dislocations from grain boundaries or triple junctions in nanocrystalline TWIP steel with an average grain size of (a) 32 nm, (b) 17.7 nm, (c) 14.3 nm and (d) 11.1 nm at the peak stress according to the tensile curves.
43
Twinning nucleation Stress (GPa)
7
6
5
4
3 10
15
20
25
30
35
Grain size (nm)
Fig 13. Effect of initial grain size on the twinning nucleation stress
Table 1. Simulation cell dimensions (LX,LY, LZ), number of atoms and the mean grain size of samples investigated in this study. Grain size (nm) LX(nm) LY(nm) LZ(nm) Number of atoms 32
80
80
10
5418912
17.7
80
80
10
5418935
14.3
80
80
10
5621438
11.1
80
80
10
5419208
44