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Molecular dynamics simulation of nanostructure formation in copper foil under laser shock forming
Computational Materials Science 172 (2020) 109352
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Molecular dynamics simulation of nanostructure formation in copper foil under laser shock forming
T
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Huixia Liu , Yunfeng Zhang, Youjuan Ma, Jiankun Cui, Maowen Li, Jinxi Gong, Xiao Wang School of Mechanical Engineering, Jiangsu University, Zhenjiang 212013, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Molecular dynamics Dislocation Grain refinement Deformation twinning Laser shock forming
The microstructure evolution of polycrystal copper under high strain rate loading is studied via the molecular dynamics simulation, and the formation of nanostructures in copper foil under laser shock forming is revealed. Deformation is dominated by dislocations in the early stage. Partial dislocations are emitted from grain boundaries. Then, they pass through grains and are absorbed by the opposite grain boundaries. When stress is concentrated, second slip, cross slip, and slip system alternation occur. Different dislocation motions form subgrain boundaries, and sub-grains transform into refined grains via dynamic recrystallization. In our previous experiment, the effect of dislocations on grain refinement was neglected. Deformation twinning, including the nano-twin bundles observed in the experiment, appears in the late stages of deformation. Twins are formed by a series of dislocation motions. Twins and dislocations collectively dominate plastic deformation and form a competing relationship, increasing the toughness and the strength of the material. High strain rate and large strain are vital to the formation of these nanostructures.
1. Introduction As electronics and precision manufacturing industries continue to develop, micro-machining technology is rapidly increasing its presence as a method for understanding and interacting with the micro-world. Micro-machining, characterized by small operating and tool size, has become especially popular in the fields of communication, electronics, and electromechanical systems. Applying conventional metal forming techniques in the field of micro-forming, however, has many limitations [1]. For example, micro-punches are difficult to fabricate and often exhibit undesirable forming precision, or formability. Although traditional forming methods are continuously improving, they must meet the requirements of micro-forming to remain practical as new micro-forming methods continue to be developed [2–5]. In recent years, laser shock forming (LSF) methods have shown rapid improvements, providing new ways of solving problems associated with micro-forming. LSF techniques evolved from laser-driven flyer forming [5–7] of soft molds—as intermediate media for forming [8]—and laser shock micro hydraulic bulging [9]. LSF eliminates the necessity for imprecise micropunching. Moreover, LSF does not require direct contact between the punch tool and the workpiece, greatly improving surface quality. Given the high strain rate while loading LSF, the working material has relatively high fluidity and can process small local features. ⁎
LSF combines the advantages of high strain rate forming and laser shock processing (LSP). The LSF method improves the formability of materials and refines the microstructure of workpieces. Thus, fatigue, corrosion, and wear resistance can be significantly improved, thereby extending the service life of workpieces [9]. The refinement of material microstructure is a particularly useful phenomenon associated with LSF. Its significance is not only with regard to material strengthening, but also in developing a new method for obtaining nanocrystalline (NC) metals. In an LSP experiment of A202 aluminum alloy, Lu et al. [10] found refined grains of 100–200 nm in size. They emphasized that strain and strain rate significantly influence grain refinement. Lu et al. also proposed a dislocation-based grain refinement technique as follows: (i) the formation of dislocation lines; (ii) the formation of dislocation tangles (DTs) and dense dislocation walls (DDWs); (iii) the transformation of DTs and DDWs into sub-grain boundaries; and (iv) the evolution of continuous dynamic recrystallization (DRX) in sub-grain boundaries to refined grain boundaries. The group presenting this paper has also studied this phenomenon [6,7]. In the LSP experiment of copper foil, Hu et al. [7] found small grains (20–30 nm) in the center region of LSF, with many deformation twins inside. These researchers also observed a nano-twin bundle structure. In the region farther from the center, only dislocations were observed. Hu et al. [7] discovered that nano-grains are formed via the
Corresponding author. E-mail address: [email protected] (H. Liu).
https://doi.org/10.1016/j.commatsci.2019.109352 Received 14 July 2019; Received in revised form 10 October 2019; Accepted 12 October 2019 0927-0256/ © 2019 Published by Elsevier B.V.
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following mechanisms: DRX of elongated grains and deformation twinning (twin–twin intersections and twin/matrix lamellae fragmentation). The high strain rate of LSP (107–108/s) and its short duration (ns order) have made the observation of deformation difficult under current experimental conditions. Previous studies have proposed relevant hypotheses, but they were based on samples after shocking, and the cause of deformation remains unclear. Because of these drawbacks, it is necessary to adopt molecular dynamics (MD) methods to analyze the deformation process. MD simulations can present the properties of samples on nanometer order scale and in nanosecond order time, similar to LSP. This precision validates comparisons of experimental results through simulation. The first MD simulations related to shock were conducted by Mogilevsky [11,12]. This early work revealed the generation of dislocations with an associated decrease in deviatory stresses during compression. Holian [13–15] considered the cases in which shock travels along the [1 0 0], [1 1 0], and [1 1 1] directions. Germann et al. [16] demonstrated that the configuration of dislocations predicted by MD depends significantly on the crystal orientation. Ma et al. [17] revealed three stages of the shock wave front and microstructure evolution in NC copper and aluminum under shock loading. Recently, Xiong et al. [18] improved the loading method. They proposed laser shock compression and studied the differences between laser shock compression and direct mechanical shock compression. The evolution of dislocations and the formation of sub-grain boundaries are presented and analyzed. Although their simulations reveal undiscovered phenomena, Xiong et al. only focused their research on single crystal, and the effect of grain boundaries is not taken into account. The samples were cuboids under shock loading, which makes it difficult to clearly observe microstructures. Yamakov [19,21] et al. adopted another loading method. They replaced shock loading with uniaxial deformation, so the sample could be a textured or columnar microstructure containing several grains. This type of sample is more suitable for a detailed study of dislocations and twins. Their research indicates that twins play an important role during the deformation of nano-material. In this paper, sample construction and loading method refer to Yamakov et al. The microstructure evolution of polycrystal copper under high strain rate loading will be discussed. This discussion will include dislocation motion, the formation of a sub-grain boundary, dynamic rotational crystallization and deformation twinning. Details of sub-grain boundary and nano-twin bundle formation will be presented.
Fig. 1. Copper sample.
Ei = Fα
⎛ ⎞ 1 ρ r )+ ⎜ ∑ α ij ⎟ 2 ⎝ j!=i ⎠
∑ ∅αβ (rij) j!=i
(1)
where F is the embedding energy as a function of the electron density ρ, and φ is a pair potential as a function of distance rij between atoms i and j. In this study, the EAM potential developed by Mishin et al. [23] is used. 2.2. Relaxation Given the small atomic density of grain boundaries (GBs) and different orientations between grains, the initial energy of the sample is high and the internal stress is large; therefore, the sample must be relaxed to reach a stable state. The LAMMPS MD simulation software monitors the average atomic energy to judge sufficient relaxation. Energy minimization through the conjugate gradient (CG) method is performed, and the model is relaxed under constant pressure and temperature. The pressure is set to 0 Pa, and the temperature is set to 300 K. The periodic boundary is used, and the time step is 1 fs. The energy profile (Fig. 2) demonstrates that the
2. Simulation approach and background 2.1. Sample modeling A 3D model has a complex spatial structure, which may complicate the deformation analysis. To combat this complexity, a quasi-3D model is used for observation. This model is constructed via the Voronoi construction method [20] on the Atomsk software. The model used in this simulation refers to the model proposed by Yamakov et al. [19,21] with idealized 〈1 1 0〉 textured microstructures consisting of four grains. The overall size is 50 nm × 50 nm × 2.169 nm. X-, y-, and z-axes correspond to the [1 0 0], [0 1 0], and [0 0 1] orientations of Grain I, respectively, and the three other grains are sequentially rotated by 50°, 20°, and 30° around the z-axis, as illustrated in Fig. 1. A periodic boundary is used in all directions to form a columnar structure along the z-axis, thereby ensuring that dislocations can slip on the (1 1 1) or (1 1 −1) planes without restriction. The embedded-atom method (EAM) potential developed by Daw and Baskes et al. [22] is applied. The total atomic energy produced by the embedded atomic potential is
Fig. 2. Average atomic energy. 2
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average atomic energy remains stable, indicating full relaxation after 5 ps. 2.3. Loading and analysis Under laser shock loading, copper foil experiences high strain rate deformation at a nanosecond level. Most plastic works generated by deformation are converted into heat, which must be exhausted through often difficult means. Thus, the forming process is typically considered adiabatic, and loading is performed under the micro-canonical ensemble by which no heat exchange occurs with the outside environment. The periodic boundary condition is still used for all directions, and the time step is still set as 5 fs. A constant strain of 1 × 109/s is loaded along the negative direction of the Y-axis, and the resulting total strain is 0.4. The visualization software Ovito is used for defect analysis. Common neighbor analysis and dislocation extraction algorithm (DXA) methods are used to identify crystal defects, such as dislocations and stacking faults (SFs). There are four types of atoms: normal or slightly compressed facecentered cubic (FCC) atoms (green atoms), hexagonal close-packed (HCP) atoms (red atoms), body-centered cubic atoms (blue atoms), and amorphous structural atoms (white atoms). In the copper sample, HCP atoms represent twin boundaries (TBs) or SFs, and amorphous structural atoms represent GBs or dislocation cores.
Fig. 4. Initial dislocations (blue circles) and discontinuous GBs (black circles).
Grain III and IV are slightly fused at the GBs after relaxation. AB segment: Slip systems in grains gradually start, and numerous partial dislocations are emitted from GBs while SFs expand. The crossslip phenomenon is observed in Grains I and II (Fig. 5a). The cross-slip zone in Grain Ⅰ then disappears, and the cross-slip zone in Grain II meets the SFs of the original slip system to form the Hirth lock, where they interface (Fig. 5a). Two slip systems are activated in Grain I. Fig. 5b displays two sets of SFs that belong to different slip planes. The activation of slip systems releases stress, thereby causing a stress decrease in the AB segment. CD segment: A slip system alternation occurs in Grain III. Under the effect of shear stress [24], the SFs split and disappear (Fig. 6a). Then, a new slip system is activated (Fig. 6b). Moreover, stress concentration results in a second slip in Grains I and III (Fig. 6b). The start of the new slip system and second slip releases stress, thereby decreasing stress in the CD segment. The intrinsic SFs (i.e., ISF, two layers of HCP atoms) in Grains I, II, and IV are transformed into extrinsic SFs (i.e., ESF, HCP–FCC–HCP layer). As shown in Fig. 6b, these structures then form nano-twin bundles in Grains II and IV (Fig. 7). Additional details are discussed in Section 3.4.1. DE segment: Grain III is divided into two parts via the sub-grain boundary. One side is subjected to second slip, and the other side continuously alternates slip systems. Simultaneously, a few sub-grain boundaries have appeared with the presence of TBs, blocking dislocation motion. Several dislocations slip, thus increasing stress. More TBs appear beyond Point E, and the grains are divided and refined under the joint action of TBs and sub-grain boundaries, as illustrated in Fig. 8. These grains are essential for material strengthening. According to the stress–strain curve, stress shows an upward trend.
3. Analysis and discussion of molecular dynamics simulation 3.1. Stress–strain profile and microstructural evolution Fig. 3 exhibits the stress–strain profile of von Mises flow stress during deformation. This profile is expressed as
σVM =
[(σxx − σyy )2 + (σxx − σzz )2 + (σzz − σyy )2] 2
(2)
where σxx , σyy, andσzz are the normal stresses along the x, y, and z directions, correspondingly. Stress continuously fluctuates between 2 and 6 GPa during loading, and multiple local peak and valley points appear. The stress, however, typically increases. OA segment: At the beginning, the material is at the elastic deformation stage, and only a few initial dislocations are found in the grains (Fig. 4). Given that the difference in grain orientation is small,
3.2. Dislocation motion Dislocation is important for plastic deformation. According to Schmidt’s law, the resolved shear stress τr on the slip plane is
τr = σ cosψcosλ
(3)
where σ is the normal stress, ψ is the angle between the slip surface and the normal stress, and λ is the angle between the slip direction and the normal stress. The slip system is activated when the shear stress τr on the slip plane exceeds the critical shear stress τc . In accordance with this formula, the Schmidt factor of the {1 1 1} 〈1 1 0〉 slip system is approximately 0.41, and the critical shear stress of single crystal copper is
Fig. 3. Stress-strain profile. 3
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Fig. 5. (a) Cross-slip (black circles); (b) two sets of SFs (yellow line indicates the junction).
to the stress concentration at GBs. Hirth sessile dislocations are formed at the intersection of cross-slip, and they cannot move along the original slip plane but are pinned inside the grain (Fig. 9). When stress is concentrated, the second slip occurs in the slipped area (Fig. 6b). After the first slip, the atomic position of the slipped region is distorted, and the second slip occurs between the two layers of atoms near the distorted position. The critical shear stress of the second slip is higher than that of the first. The generation of the second slip can release the concentrated stress and facilitate plastic deformation. As mentioned in Section 3.1, the alternation of slip systems occurs in Grain III (Fig. 6a). Two Shockley partial dislocations with opposite Burgers vectors are generated in the SFs, and they slide along the SFs, causing them to split (Fig. 10). This phenomenon is driven by shear stress, and Bulatov et al. [24] estimated that a shear stress of 930 MPa is required to split an SF, after which new dislocations are emitted from the top side of the GB.
between 10 and 10.5 GPa [25]. Correspondingly, the normal stress is 24.5–25.7 GPa [18]. However, the case of polycrystal copper is complicated. Slip systems of each grain do not start simultaneously but in a certain order. When grains are oriented differently, their Schmidt factors are different. Thus, the critical shearing stress that produces slip also varies. In addition, the stress concentration in grains may be an influential factor. Limited by the sample size, partial dislocations are mostly observed, whereas perfect dislocations are scarce. By summarizing previous studies [26–28], Yamakov et al. [21] concluded that when the grain size is smaller than the dislocation splitting distance, i.e. the size of the SF, which connects the partial dislocations, the SF size is larger than the grain size. They also concluded that trailing partial dislocations are not emitted. Only partial dislocations can nucleate from GBs, passing through the grains and becoming adsorbed after reaching the GBs on the other side. Whether a trailing partial dislocation can be emitted depends on the ratio between the stable SF energy and the unstable SF energy [29]. If the ratio is approximately 1, a perfect dislocation, or twins, can be observed. Asaro and Suresh [30] predict that perfect dislocations can be found in copper with grain sizes greater than 40 nm. Therefore, dislocation propagation can only be performed in the initial stage of deformation, which is significantly different from the slip mechanism observed in coarse-grained materials. Despite this limitation, a few dislocation motions are observed. In the early stage of deformation, cross-slip appears in Grains I and II (Fig. 5a). The cross-slip in both grains occurs near the GBs, due in part
3.3. Grain refinement 3.3.1. Formation of sub-grain boundary Sub-grain boundaries are present in low-angle grain boundaries with a phase difference of less than 10°, usually less than 2°. They are products in which two grains rotate at a certain angle around a rotating axis and consist of a series of edge dislocations, screw dislocations, or dislocation networks. Therefore, the formation of the sub-grain boundary is closely connected with dislocation motion. Fig. 11 depicts the formation of the
Fig. 6. Different dislocation motions: (a) SFs splitting; (b) second slip (black circles) and ISFs to ESFs (blue circles). 4
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Fig. 7. Nano-twin bundles: (a) nano-twin bundles in grain II and IV; (b) nano -twins observed in the experiment [7].
Fig. 10. Splitting of SFs in grain III. Fig. 8. Sub-grain boundaries (blue lines) and TBs (black circles).
With the expansion of the ISFs, Shockley partial dislocations on the (1 1 1) and (1 1 −1) planes meet in the grain and form an initial subgrain boundary (Fig. 11a and b). With the increase in stress, dislocations are continuously emitted. They move along the ISFs, transform ISFs into ESFs, and meet at the junction, where a dislocation wall is formed (Fig. 11c and d). Then, dislocations move along the neighboring slip plane of ESFs and form mixed ESF and ISF structures (Fig. 11e). Finally, the sub-grain boundary in Grain I is formed after multiple dislocation motions (Fig. 11f). Grain III, however, appears different. After the initial sub-grain boundary is formed, Grain III divides into two parts (Fig. 12a and b). The left side initially undergoes a second slip (Fig. 12c and d). Then, the ISF–ESF transition occurs at the ISFs produced by the second slip, and mixed structures of ISFs and ESFs are formed (Fig. 12e and f). The splitting of ISFs and the emission of new dislocations accumulate dislocations on the sub-grain boundary. Fig. 12c displays an image of the sub-grain boundary processed by DXA method. The sub-grain boundary is wrapped in the defect mesh. In the DXA method, this defect mesh marks the “bad” region – a complex defect region that is difficult to identify, thus, resulting in the sub-grain boundary in Grain III having a complicated structure. Only a few dislocation reactions are observed owing to the limited sample size. Two typical dislocation reaction products—stair-rod sessile dislocation (Lomer–Cottrell lock) and Hirth sessile dislocation (Hirth lock)—are displayed in Fig. 13. They are pinned inside the grains, and they hinder dislocation movement. When sufficient dislocations are stacked at the junction, it turns into a sub-grain boundary [18].
Fig. 9. Hirth sessile dislocations at intersection of cross-slip.
sub-grain boundary in Grain I. The process is divided into three stages: (i) formation of ISFs, (ii) formation of ESFs, and (iii) formation of mixed structures of ESFs and ISFs.
3.3.2. Sub-grains to refined grains When strain and strain rate are sufficiently high, the plastic strain is 5
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Fig. 11. Formation of sub-grain boundary in grain I: snapshots of (a), (c), (e) show different dislocation motions in the grain, analyzed by CNA method (FCC atoms not shown); snapshots (b), (d), (f) show the sub-grain boundary, analyzed by DXA method (only dislocation lines shown).
only a slight difference in orientation between the two sides. Then, the grain orientation changes gradually (Fig. 14b and c). This change can be seen after new slip systems sweep through the grains. It can be speculated that this is because of grain orientation that promotes the initiation of a new slip system. Finally, with the increase of the orientation difference, the sub-grain boundary becomes a high angle boundary (Fig. 14d). Refining by sub-grain boundary is consistent with the proposal by
accommodated by the DRX [31] that occurs in this process [7]. The orientation difference of grains on both sides of the sub-grain boundary is increased. Finally, when the orientation difference is sufficiently large, the sub-grain boundary becomes a high-angle grain boundary. The sub-grain boundary in Grain II is taken as an example to show this process (the sub-grain boundaries in Grain I and Grain III never turn into high angle boundaries). Fig. 14a presents the initial state of the sub-grain boundary. There is
Fig. 12. Formation of sub-grain boundary in grain III: snapshots of (a), (c), (e) show different dislocation motions in the grain, analyzed by CNA method (FCC atoms not shown); snapshots (b), (d), (f) show the sub-grain boundary, analyzed by DXA method (only dislocation lines shown). 6
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Fig. 13. Two sessile dislocations: (a) stair-rod sessile dislocation; (b) Hirth sessile dislocation.
Lu et al. [10]. After finding refined grains of 100–200 nm in size in LY2 aluminum alloy in the LSP experiment, they set forth the following grain refinement mechanism: (i) the formation of dislocation lines, (ii) the formations of DTs and of DDWs; (iii) the transformation of DTs and DDWs into sub-grain boundaries; and (iv) the evolution of continuous DRX in sub-grain boundaries to refined grain boundaries (Fig. 15).
of strain, dislocation density increases with strain rate, and at a certain strain rate, an increase in strain leads to a high density of dislocations and, eventually, to finer grains [10]. Hu et al. proposed that nano-grains are formed via two mechanisms, namely, DRX of elongated grains and deformation twinning (twin–twin intersections and twin/matrix lamellae fragmentation) [27]. They suggested that the dislocations under such a high strain rate do not have sufficient time to form sub-grain boundaries. There are mostly SFs but not dislocations in the refined grains. Fig. 17 illustrates that the grains are elongated, broken, and rotated, forming nano-grains under shock loading. This process is called DRX. The twinning refinement mechanism is demonstrated in Fig. 18. By combining the theory of Lu [10] with the content of the
3.3.3. Comparison with the previous experiment The research group, which prepared this paper, previously conducted an experiment – on LSF copper foil [7] – in which numerous nano-grains (20–30 nm) were found at the center of the workpiece with deformation twins inside (Fig. 16). The grains found during LSP are smaller because the strain is considerably higher in LSF. At a given level
Fig. 14. High angle grain boundaries from sub-grain boundaries (black lines indicate original orientations, yellow lines indicate sub-grain boundaries, blue lines indicate new orientations). 7
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Fig. 15. Grain refinement process [10].
deformation twins. The simulation discussed in this paper, however, shows that many dislocations appear during deformation. They are absorbed by GBs or turn into sub-grain boundaries. The TEM image (Fig. 19b) shows that nearly no dislocations are present. Given the lack of deformation analysis, the experiment only considers the effect of DRX and TBs, and the contribution of dislocations was disregarded. 3.4. Deformation twinning Twins are common in metals that lack sufficient slip systems, such as HCP metals. Deformation twins rarely appear in FCC metals under normal conditions because FCC metals have enough slip systems to accommodate for plastic deformation. Furthermore, the stress required is higher for deformation twinning than slip. Thus, deformation twinning in FCC metals occurs only after sufficient strain hardening, thereby creating high stress concentrations. This phenomenon requires a low temperature or high strain rate loading environment in which material recovery is suppressed. Given the high strain rate loading and the large plastic deformation of LSF, many deformation twins are observed in the experiment. Unique structures called nano-twin bundles are also found. Such nano-twin bundles also appear in Grains II and III (Fig. 7).
Fig. 16. Deformation twins at the center region of workpiece.
3.4.1. Nano-twin bundles Yamakov et al. [21] analyzed deformation twinning in Al. They proposed two formation mechanisms: heterogeneous and homogeneous nucleation. During Heterogeneous nucleation, TBs are formed by successively transmitting 1/6 [1 1 2] edge partial dislocations of adjacent (1 1 1) planes from GBs. These partial dislocations are twinning dislocations. The process is divided into five parts: (i) perfect FCC crystal, (ii) ISF, (iii) ESF, (iv) two coherent TBs separated by two layers of FCC atoms, and (v) widely separated twins. Nano-twin bundles in Grain II are formed through heterogeneous nucleation. Grain II is divided into two parts by the sub-grain boundary, and the twin bundles are formed in the left part as follows: (i) partial dislocations from the sub-grain boundary slip along the ISFs, and one layer of HCP atom in the ISFs migrates to form ESFs (Fig. 20a); (ii) partial dislocations continuously emit and extend ESFs into microtwins (Fig. 20b). For the nano-twin bundles present in Grain III, formation is similar to that of heterogeneous nucleation but with a slight difference: The dislocations that extend ISFs to ESFs are not from grain boundaries but are generated in SFs (Fig. 21). This situation is similar to the splitting of
Fig. 17. Dynamic recrystallization [31].
simulation recounted in this paper, however, it is found that dislocations also play a role in the refining process. Sections 3.2 and 3.3 indicate that dislocation motion remains active under high strain rate loading. These dislocations can form sub-grain boundaries, which may turn into refined grains via DRX. As mentioned in Section 3.2, the dislocation density is significantly lower in nano-grains than in coarse-grained materials. Nano-sized grains are too small to form perfect dislocations, and GBs absorb dislocations. As shown in Fig. 19a, the refined grains have already formed, but few dislocations appear. The structures are mostly SFs and
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Fig. 18. Four refinement mechanisms of nano-TBs [32].
conversion of the slip systems. Both reactions produce dislocations on TBs and expend twins. When the TBs in Grains II and III are restored to ISFs, new TBs form in other grains. Dislocation and deformation twins form competing deformation mechanisms. In summary, twins have a twofold effect on the mechanical properties of a material. On one hand, TBs hinder dislocation motion, thus causing dislocation accumulation and resulting in strain hardening of the material; on the other hand, the dislocation–twin reactions promote the transfer between existing slip systems to facilitate deformation.
SFs. Two Shockley partial dislocations with opposite Burgers vectors move in opposite directions on SFs, thereby transforming ISFs to ESFs. The dislocations emitted from the grain boundary then expand the ESFs to twins. Xiong et al. [18] analyzed the mechanism of TB nucleation. These researchers found that the overlapping regions produce a pair of partial dislocations with opposite Burgers vectors, which turn SFs to twins after the overlap of the two ISFs. Xiong et al. [18] considered that this phenomenon is driven by stress and concluded that this mechanism can be applied to other cases. Therefore, in this paper, it is speculated that the partial dislocations on the SFs in Grain III are also driven by stress.
4. Conclusions 3.4.2. Twinning and untwining processes Similar to how dislocations annihilate and reorganize twins, twinning and untwinning processes occur during deformation. Dislocation motion can not only produce new twins but also cause them to disappear. When dislocations slip on the TBs, they migrate and expend the twins. If the migration direction is reversed, however, twins eventually return to ISFs (Fig. 22.). There are also reactions between dislocations and TBs [21]. These reactions produce stair-rod sessile dislocations on TBs that hinder dislocation motion or lead to cross slip, which is conducive to the
The MD simulation of a highly idealized columnar sample shows microstructure evolution of grains under high strain rate loading, revealing the formation process of nanostructures in copper foil under LSF. In the early stages of loading, plastic deformation is mediated by dislocations, and slip systems in grains are gradually activated. When the stress is concentrated, second slip, cross slip, and alternation of slip systems occur. Only a few dislocation reactions, which are limited by sample size, are observed. Dislocation motion forms sub-grain boundaries, and sub-grains
Fig. 19. SFs in the grains: (a) Snapshot with strain at 0.4, very few dislocations; (b) TEM image of refined grains with SFs inside. 9
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Fig. 20. Formation of TBs: (a) ISFs to ESFs; (b) ESFs to microtwins.
twins, including nano-twin bundles, appear and are formed by a series of dislocation motions. Twins and dislocations form a competing deformation relationship. Twins have a twofold effect: They expand material toughness and cause strain hardening. High strain rate and large strain are vital to the formation of these nanostructures. CRediT authorship contribution statement Huixia Liu: Conceptualization, Investigation. Yunfeng Zhang: Writing - original draft, Software, Visualization. Youjuan Ma: Formal analysis. Jiankun Cui: Investigation. Maowen Li: Data curation. Jinxi Gong: Writing - review & editing. Xiao Wang: Supervision, Resources, Project administration. Declaration of Competing Interest
Fig. 21. Two sets Shockley partials expend ISFs to ESFs, green lines indicate Shockley partials.
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.
transform into refined grains via DRX. Given that previous experiments have relied on samples after shocking to reverse the deformation mechanism, the effect of dislocations was ignored. The experimental and simulation results suggest that in addition to DRX of elongated grains and deformation twinning, dislocation motion is important for grain refinement. In the middle and late stages of deformation, numerous deformation
Acknowledgements This work is supported by the National Natural Science Foundation of China (Grant No. 51675243) and the 2018 Innovation Practice Fund of Jiangsu University Industrial Centre (Grant No. ZXJG2018008).
Fig. 22. TBs to ISFs. 10
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References [17]
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Molecular dynamics simulation of nanostructure formation in copper foil under laser shock forming
T
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Huixia Liu , Yunfeng Zhang, Youjuan Ma, Jiankun Cui, Maowen Li, Jinxi Gong, Xiao Wang School of Mechanical Engineering, Jiangsu University, Zhenjiang 212013, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Molecular dynamics Dislocation Grain refinement Deformation twinning Laser shock forming
The microstructure evolution of polycrystal copper under high strain rate loading is studied via the molecular dynamics simulation, and the formation of nanostructures in copper foil under laser shock forming is revealed. Deformation is dominated by dislocations in the early stage. Partial dislocations are emitted from grain boundaries. Then, they pass through grains and are absorbed by the opposite grain boundaries. When stress is concentrated, second slip, cross slip, and slip system alternation occur. Different dislocation motions form subgrain boundaries, and sub-grains transform into refined grains via dynamic recrystallization. In our previous experiment, the effect of dislocations on grain refinement was neglected. Deformation twinning, including the nano-twin bundles observed in the experiment, appears in the late stages of deformation. Twins are formed by a series of dislocation motions. Twins and dislocations collectively dominate plastic deformation and form a competing relationship, increasing the toughness and the strength of the material. High strain rate and large strain are vital to the formation of these nanostructures.
1. Introduction As electronics and precision manufacturing industries continue to develop, micro-machining technology is rapidly increasing its presence as a method for understanding and interacting with the micro-world. Micro-machining, characterized by small operating and tool size, has become especially popular in the fields of communication, electronics, and electromechanical systems. Applying conventional metal forming techniques in the field of micro-forming, however, has many limitations [1]. For example, micro-punches are difficult to fabricate and often exhibit undesirable forming precision, or formability. Although traditional forming methods are continuously improving, they must meet the requirements of micro-forming to remain practical as new micro-forming methods continue to be developed [2–5]. In recent years, laser shock forming (LSF) methods have shown rapid improvements, providing new ways of solving problems associated with micro-forming. LSF techniques evolved from laser-driven flyer forming [5–7] of soft molds—as intermediate media for forming [8]—and laser shock micro hydraulic bulging [9]. LSF eliminates the necessity for imprecise micropunching. Moreover, LSF does not require direct contact between the punch tool and the workpiece, greatly improving surface quality. Given the high strain rate while loading LSF, the working material has relatively high fluidity and can process small local features. ⁎
LSF combines the advantages of high strain rate forming and laser shock processing (LSP). The LSF method improves the formability of materials and refines the microstructure of workpieces. Thus, fatigue, corrosion, and wear resistance can be significantly improved, thereby extending the service life of workpieces [9]. The refinement of material microstructure is a particularly useful phenomenon associated with LSF. Its significance is not only with regard to material strengthening, but also in developing a new method for obtaining nanocrystalline (NC) metals. In an LSP experiment of A202 aluminum alloy, Lu et al. [10] found refined grains of 100–200 nm in size. They emphasized that strain and strain rate significantly influence grain refinement. Lu et al. also proposed a dislocation-based grain refinement technique as follows: (i) the formation of dislocation lines; (ii) the formation of dislocation tangles (DTs) and dense dislocation walls (DDWs); (iii) the transformation of DTs and DDWs into sub-grain boundaries; and (iv) the evolution of continuous dynamic recrystallization (DRX) in sub-grain boundaries to refined grain boundaries. The group presenting this paper has also studied this phenomenon [6,7]. In the LSP experiment of copper foil, Hu et al. [7] found small grains (20–30 nm) in the center region of LSF, with many deformation twins inside. These researchers also observed a nano-twin bundle structure. In the region farther from the center, only dislocations were observed. Hu et al. [7] discovered that nano-grains are formed via the
Corresponding author. E-mail address: [email protected] (H. Liu).
https://doi.org/10.1016/j.commatsci.2019.109352 Received 14 July 2019; Received in revised form 10 October 2019; Accepted 12 October 2019 0927-0256/ © 2019 Published by Elsevier B.V.
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following mechanisms: DRX of elongated grains and deformation twinning (twin–twin intersections and twin/matrix lamellae fragmentation). The high strain rate of LSP (107–108/s) and its short duration (ns order) have made the observation of deformation difficult under current experimental conditions. Previous studies have proposed relevant hypotheses, but they were based on samples after shocking, and the cause of deformation remains unclear. Because of these drawbacks, it is necessary to adopt molecular dynamics (MD) methods to analyze the deformation process. MD simulations can present the properties of samples on nanometer order scale and in nanosecond order time, similar to LSP. This precision validates comparisons of experimental results through simulation. The first MD simulations related to shock were conducted by Mogilevsky [11,12]. This early work revealed the generation of dislocations with an associated decrease in deviatory stresses during compression. Holian [13–15] considered the cases in which shock travels along the [1 0 0], [1 1 0], and [1 1 1] directions. Germann et al. [16] demonstrated that the configuration of dislocations predicted by MD depends significantly on the crystal orientation. Ma et al. [17] revealed three stages of the shock wave front and microstructure evolution in NC copper and aluminum under shock loading. Recently, Xiong et al. [18] improved the loading method. They proposed laser shock compression and studied the differences between laser shock compression and direct mechanical shock compression. The evolution of dislocations and the formation of sub-grain boundaries are presented and analyzed. Although their simulations reveal undiscovered phenomena, Xiong et al. only focused their research on single crystal, and the effect of grain boundaries is not taken into account. The samples were cuboids under shock loading, which makes it difficult to clearly observe microstructures. Yamakov [19,21] et al. adopted another loading method. They replaced shock loading with uniaxial deformation, so the sample could be a textured or columnar microstructure containing several grains. This type of sample is more suitable for a detailed study of dislocations and twins. Their research indicates that twins play an important role during the deformation of nano-material. In this paper, sample construction and loading method refer to Yamakov et al. The microstructure evolution of polycrystal copper under high strain rate loading will be discussed. This discussion will include dislocation motion, the formation of a sub-grain boundary, dynamic rotational crystallization and deformation twinning. Details of sub-grain boundary and nano-twin bundle formation will be presented.
Fig. 1. Copper sample.
Ei = Fα
⎛ ⎞ 1 ρ r )+ ⎜ ∑ α ij ⎟ 2 ⎝ j!=i ⎠
∑ ∅αβ (rij) j!=i
(1)
where F is the embedding energy as a function of the electron density ρ, and φ is a pair potential as a function of distance rij between atoms i and j. In this study, the EAM potential developed by Mishin et al. [23] is used. 2.2. Relaxation Given the small atomic density of grain boundaries (GBs) and different orientations between grains, the initial energy of the sample is high and the internal stress is large; therefore, the sample must be relaxed to reach a stable state. The LAMMPS MD simulation software monitors the average atomic energy to judge sufficient relaxation. Energy minimization through the conjugate gradient (CG) method is performed, and the model is relaxed under constant pressure and temperature. The pressure is set to 0 Pa, and the temperature is set to 300 K. The periodic boundary is used, and the time step is 1 fs. The energy profile (Fig. 2) demonstrates that the
2. Simulation approach and background 2.1. Sample modeling A 3D model has a complex spatial structure, which may complicate the deformation analysis. To combat this complexity, a quasi-3D model is used for observation. This model is constructed via the Voronoi construction method [20] on the Atomsk software. The model used in this simulation refers to the model proposed by Yamakov et al. [19,21] with idealized 〈1 1 0〉 textured microstructures consisting of four grains. The overall size is 50 nm × 50 nm × 2.169 nm. X-, y-, and z-axes correspond to the [1 0 0], [0 1 0], and [0 0 1] orientations of Grain I, respectively, and the three other grains are sequentially rotated by 50°, 20°, and 30° around the z-axis, as illustrated in Fig. 1. A periodic boundary is used in all directions to form a columnar structure along the z-axis, thereby ensuring that dislocations can slip on the (1 1 1) or (1 1 −1) planes without restriction. The embedded-atom method (EAM) potential developed by Daw and Baskes et al. [22] is applied. The total atomic energy produced by the embedded atomic potential is
Fig. 2. Average atomic energy. 2
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average atomic energy remains stable, indicating full relaxation after 5 ps. 2.3. Loading and analysis Under laser shock loading, copper foil experiences high strain rate deformation at a nanosecond level. Most plastic works generated by deformation are converted into heat, which must be exhausted through often difficult means. Thus, the forming process is typically considered adiabatic, and loading is performed under the micro-canonical ensemble by which no heat exchange occurs with the outside environment. The periodic boundary condition is still used for all directions, and the time step is still set as 5 fs. A constant strain of 1 × 109/s is loaded along the negative direction of the Y-axis, and the resulting total strain is 0.4. The visualization software Ovito is used for defect analysis. Common neighbor analysis and dislocation extraction algorithm (DXA) methods are used to identify crystal defects, such as dislocations and stacking faults (SFs). There are four types of atoms: normal or slightly compressed facecentered cubic (FCC) atoms (green atoms), hexagonal close-packed (HCP) atoms (red atoms), body-centered cubic atoms (blue atoms), and amorphous structural atoms (white atoms). In the copper sample, HCP atoms represent twin boundaries (TBs) or SFs, and amorphous structural atoms represent GBs or dislocation cores.
Fig. 4. Initial dislocations (blue circles) and discontinuous GBs (black circles).
Grain III and IV are slightly fused at the GBs after relaxation. AB segment: Slip systems in grains gradually start, and numerous partial dislocations are emitted from GBs while SFs expand. The crossslip phenomenon is observed in Grains I and II (Fig. 5a). The cross-slip zone in Grain Ⅰ then disappears, and the cross-slip zone in Grain II meets the SFs of the original slip system to form the Hirth lock, where they interface (Fig. 5a). Two slip systems are activated in Grain I. Fig. 5b displays two sets of SFs that belong to different slip planes. The activation of slip systems releases stress, thereby causing a stress decrease in the AB segment. CD segment: A slip system alternation occurs in Grain III. Under the effect of shear stress [24], the SFs split and disappear (Fig. 6a). Then, a new slip system is activated (Fig. 6b). Moreover, stress concentration results in a second slip in Grains I and III (Fig. 6b). The start of the new slip system and second slip releases stress, thereby decreasing stress in the CD segment. The intrinsic SFs (i.e., ISF, two layers of HCP atoms) in Grains I, II, and IV are transformed into extrinsic SFs (i.e., ESF, HCP–FCC–HCP layer). As shown in Fig. 6b, these structures then form nano-twin bundles in Grains II and IV (Fig. 7). Additional details are discussed in Section 3.4.1. DE segment: Grain III is divided into two parts via the sub-grain boundary. One side is subjected to second slip, and the other side continuously alternates slip systems. Simultaneously, a few sub-grain boundaries have appeared with the presence of TBs, blocking dislocation motion. Several dislocations slip, thus increasing stress. More TBs appear beyond Point E, and the grains are divided and refined under the joint action of TBs and sub-grain boundaries, as illustrated in Fig. 8. These grains are essential for material strengthening. According to the stress–strain curve, stress shows an upward trend.
3. Analysis and discussion of molecular dynamics simulation 3.1. Stress–strain profile and microstructural evolution Fig. 3 exhibits the stress–strain profile of von Mises flow stress during deformation. This profile is expressed as
σVM =
[(σxx − σyy )2 + (σxx − σzz )2 + (σzz − σyy )2] 2
(2)
where σxx , σyy, andσzz are the normal stresses along the x, y, and z directions, correspondingly. Stress continuously fluctuates between 2 and 6 GPa during loading, and multiple local peak and valley points appear. The stress, however, typically increases. OA segment: At the beginning, the material is at the elastic deformation stage, and only a few initial dislocations are found in the grains (Fig. 4). Given that the difference in grain orientation is small,
3.2. Dislocation motion Dislocation is important for plastic deformation. According to Schmidt’s law, the resolved shear stress τr on the slip plane is
τr = σ cosψcosλ
(3)
where σ is the normal stress, ψ is the angle between the slip surface and the normal stress, and λ is the angle between the slip direction and the normal stress. The slip system is activated when the shear stress τr on the slip plane exceeds the critical shear stress τc . In accordance with this formula, the Schmidt factor of the {1 1 1} 〈1 1 0〉 slip system is approximately 0.41, and the critical shear stress of single crystal copper is
Fig. 3. Stress-strain profile. 3
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Fig. 5. (a) Cross-slip (black circles); (b) two sets of SFs (yellow line indicates the junction).
to the stress concentration at GBs. Hirth sessile dislocations are formed at the intersection of cross-slip, and they cannot move along the original slip plane but are pinned inside the grain (Fig. 9). When stress is concentrated, the second slip occurs in the slipped area (Fig. 6b). After the first slip, the atomic position of the slipped region is distorted, and the second slip occurs between the two layers of atoms near the distorted position. The critical shear stress of the second slip is higher than that of the first. The generation of the second slip can release the concentrated stress and facilitate plastic deformation. As mentioned in Section 3.1, the alternation of slip systems occurs in Grain III (Fig. 6a). Two Shockley partial dislocations with opposite Burgers vectors are generated in the SFs, and they slide along the SFs, causing them to split (Fig. 10). This phenomenon is driven by shear stress, and Bulatov et al. [24] estimated that a shear stress of 930 MPa is required to split an SF, after which new dislocations are emitted from the top side of the GB.
between 10 and 10.5 GPa [25]. Correspondingly, the normal stress is 24.5–25.7 GPa [18]. However, the case of polycrystal copper is complicated. Slip systems of each grain do not start simultaneously but in a certain order. When grains are oriented differently, their Schmidt factors are different. Thus, the critical shearing stress that produces slip also varies. In addition, the stress concentration in grains may be an influential factor. Limited by the sample size, partial dislocations are mostly observed, whereas perfect dislocations are scarce. By summarizing previous studies [26–28], Yamakov et al. [21] concluded that when the grain size is smaller than the dislocation splitting distance, i.e. the size of the SF, which connects the partial dislocations, the SF size is larger than the grain size. They also concluded that trailing partial dislocations are not emitted. Only partial dislocations can nucleate from GBs, passing through the grains and becoming adsorbed after reaching the GBs on the other side. Whether a trailing partial dislocation can be emitted depends on the ratio between the stable SF energy and the unstable SF energy [29]. If the ratio is approximately 1, a perfect dislocation, or twins, can be observed. Asaro and Suresh [30] predict that perfect dislocations can be found in copper with grain sizes greater than 40 nm. Therefore, dislocation propagation can only be performed in the initial stage of deformation, which is significantly different from the slip mechanism observed in coarse-grained materials. Despite this limitation, a few dislocation motions are observed. In the early stage of deformation, cross-slip appears in Grains I and II (Fig. 5a). The cross-slip in both grains occurs near the GBs, due in part
3.3. Grain refinement 3.3.1. Formation of sub-grain boundary Sub-grain boundaries are present in low-angle grain boundaries with a phase difference of less than 10°, usually less than 2°. They are products in which two grains rotate at a certain angle around a rotating axis and consist of a series of edge dislocations, screw dislocations, or dislocation networks. Therefore, the formation of the sub-grain boundary is closely connected with dislocation motion. Fig. 11 depicts the formation of the
Fig. 6. Different dislocation motions: (a) SFs splitting; (b) second slip (black circles) and ISFs to ESFs (blue circles). 4
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Fig. 7. Nano-twin bundles: (a) nano-twin bundles in grain II and IV; (b) nano -twins observed in the experiment [7].
Fig. 10. Splitting of SFs in grain III. Fig. 8. Sub-grain boundaries (blue lines) and TBs (black circles).
With the expansion of the ISFs, Shockley partial dislocations on the (1 1 1) and (1 1 −1) planes meet in the grain and form an initial subgrain boundary (Fig. 11a and b). With the increase in stress, dislocations are continuously emitted. They move along the ISFs, transform ISFs into ESFs, and meet at the junction, where a dislocation wall is formed (Fig. 11c and d). Then, dislocations move along the neighboring slip plane of ESFs and form mixed ESF and ISF structures (Fig. 11e). Finally, the sub-grain boundary in Grain I is formed after multiple dislocation motions (Fig. 11f). Grain III, however, appears different. After the initial sub-grain boundary is formed, Grain III divides into two parts (Fig. 12a and b). The left side initially undergoes a second slip (Fig. 12c and d). Then, the ISF–ESF transition occurs at the ISFs produced by the second slip, and mixed structures of ISFs and ESFs are formed (Fig. 12e and f). The splitting of ISFs and the emission of new dislocations accumulate dislocations on the sub-grain boundary. Fig. 12c displays an image of the sub-grain boundary processed by DXA method. The sub-grain boundary is wrapped in the defect mesh. In the DXA method, this defect mesh marks the “bad” region – a complex defect region that is difficult to identify, thus, resulting in the sub-grain boundary in Grain III having a complicated structure. Only a few dislocation reactions are observed owing to the limited sample size. Two typical dislocation reaction products—stair-rod sessile dislocation (Lomer–Cottrell lock) and Hirth sessile dislocation (Hirth lock)—are displayed in Fig. 13. They are pinned inside the grains, and they hinder dislocation movement. When sufficient dislocations are stacked at the junction, it turns into a sub-grain boundary [18].
Fig. 9. Hirth sessile dislocations at intersection of cross-slip.
sub-grain boundary in Grain I. The process is divided into three stages: (i) formation of ISFs, (ii) formation of ESFs, and (iii) formation of mixed structures of ESFs and ISFs.
3.3.2. Sub-grains to refined grains When strain and strain rate are sufficiently high, the plastic strain is 5
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Fig. 11. Formation of sub-grain boundary in grain I: snapshots of (a), (c), (e) show different dislocation motions in the grain, analyzed by CNA method (FCC atoms not shown); snapshots (b), (d), (f) show the sub-grain boundary, analyzed by DXA method (only dislocation lines shown).
only a slight difference in orientation between the two sides. Then, the grain orientation changes gradually (Fig. 14b and c). This change can be seen after new slip systems sweep through the grains. It can be speculated that this is because of grain orientation that promotes the initiation of a new slip system. Finally, with the increase of the orientation difference, the sub-grain boundary becomes a high angle boundary (Fig. 14d). Refining by sub-grain boundary is consistent with the proposal by
accommodated by the DRX [31] that occurs in this process [7]. The orientation difference of grains on both sides of the sub-grain boundary is increased. Finally, when the orientation difference is sufficiently large, the sub-grain boundary becomes a high-angle grain boundary. The sub-grain boundary in Grain II is taken as an example to show this process (the sub-grain boundaries in Grain I and Grain III never turn into high angle boundaries). Fig. 14a presents the initial state of the sub-grain boundary. There is
Fig. 12. Formation of sub-grain boundary in grain III: snapshots of (a), (c), (e) show different dislocation motions in the grain, analyzed by CNA method (FCC atoms not shown); snapshots (b), (d), (f) show the sub-grain boundary, analyzed by DXA method (only dislocation lines shown). 6
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Fig. 13. Two sessile dislocations: (a) stair-rod sessile dislocation; (b) Hirth sessile dislocation.
Lu et al. [10]. After finding refined grains of 100–200 nm in size in LY2 aluminum alloy in the LSP experiment, they set forth the following grain refinement mechanism: (i) the formation of dislocation lines, (ii) the formations of DTs and of DDWs; (iii) the transformation of DTs and DDWs into sub-grain boundaries; and (iv) the evolution of continuous DRX in sub-grain boundaries to refined grain boundaries (Fig. 15).
of strain, dislocation density increases with strain rate, and at a certain strain rate, an increase in strain leads to a high density of dislocations and, eventually, to finer grains [10]. Hu et al. proposed that nano-grains are formed via two mechanisms, namely, DRX of elongated grains and deformation twinning (twin–twin intersections and twin/matrix lamellae fragmentation) [27]. They suggested that the dislocations under such a high strain rate do not have sufficient time to form sub-grain boundaries. There are mostly SFs but not dislocations in the refined grains. Fig. 17 illustrates that the grains are elongated, broken, and rotated, forming nano-grains under shock loading. This process is called DRX. The twinning refinement mechanism is demonstrated in Fig. 18. By combining the theory of Lu [10] with the content of the
3.3.3. Comparison with the previous experiment The research group, which prepared this paper, previously conducted an experiment – on LSF copper foil [7] – in which numerous nano-grains (20–30 nm) were found at the center of the workpiece with deformation twins inside (Fig. 16). The grains found during LSP are smaller because the strain is considerably higher in LSF. At a given level
Fig. 14. High angle grain boundaries from sub-grain boundaries (black lines indicate original orientations, yellow lines indicate sub-grain boundaries, blue lines indicate new orientations). 7
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Fig. 15. Grain refinement process [10].
deformation twins. The simulation discussed in this paper, however, shows that many dislocations appear during deformation. They are absorbed by GBs or turn into sub-grain boundaries. The TEM image (Fig. 19b) shows that nearly no dislocations are present. Given the lack of deformation analysis, the experiment only considers the effect of DRX and TBs, and the contribution of dislocations was disregarded. 3.4. Deformation twinning Twins are common in metals that lack sufficient slip systems, such as HCP metals. Deformation twins rarely appear in FCC metals under normal conditions because FCC metals have enough slip systems to accommodate for plastic deformation. Furthermore, the stress required is higher for deformation twinning than slip. Thus, deformation twinning in FCC metals occurs only after sufficient strain hardening, thereby creating high stress concentrations. This phenomenon requires a low temperature or high strain rate loading environment in which material recovery is suppressed. Given the high strain rate loading and the large plastic deformation of LSF, many deformation twins are observed in the experiment. Unique structures called nano-twin bundles are also found. Such nano-twin bundles also appear in Grains II and III (Fig. 7).
Fig. 16. Deformation twins at the center region of workpiece.
3.4.1. Nano-twin bundles Yamakov et al. [21] analyzed deformation twinning in Al. They proposed two formation mechanisms: heterogeneous and homogeneous nucleation. During Heterogeneous nucleation, TBs are formed by successively transmitting 1/6 [1 1 2] edge partial dislocations of adjacent (1 1 1) planes from GBs. These partial dislocations are twinning dislocations. The process is divided into five parts: (i) perfect FCC crystal, (ii) ISF, (iii) ESF, (iv) two coherent TBs separated by two layers of FCC atoms, and (v) widely separated twins. Nano-twin bundles in Grain II are formed through heterogeneous nucleation. Grain II is divided into two parts by the sub-grain boundary, and the twin bundles are formed in the left part as follows: (i) partial dislocations from the sub-grain boundary slip along the ISFs, and one layer of HCP atom in the ISFs migrates to form ESFs (Fig. 20a); (ii) partial dislocations continuously emit and extend ESFs into microtwins (Fig. 20b). For the nano-twin bundles present in Grain III, formation is similar to that of heterogeneous nucleation but with a slight difference: The dislocations that extend ISFs to ESFs are not from grain boundaries but are generated in SFs (Fig. 21). This situation is similar to the splitting of
Fig. 17. Dynamic recrystallization [31].
simulation recounted in this paper, however, it is found that dislocations also play a role in the refining process. Sections 3.2 and 3.3 indicate that dislocation motion remains active under high strain rate loading. These dislocations can form sub-grain boundaries, which may turn into refined grains via DRX. As mentioned in Section 3.2, the dislocation density is significantly lower in nano-grains than in coarse-grained materials. Nano-sized grains are too small to form perfect dislocations, and GBs absorb dislocations. As shown in Fig. 19a, the refined grains have already formed, but few dislocations appear. The structures are mostly SFs and
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Fig. 18. Four refinement mechanisms of nano-TBs [32].
conversion of the slip systems. Both reactions produce dislocations on TBs and expend twins. When the TBs in Grains II and III are restored to ISFs, new TBs form in other grains. Dislocation and deformation twins form competing deformation mechanisms. In summary, twins have a twofold effect on the mechanical properties of a material. On one hand, TBs hinder dislocation motion, thus causing dislocation accumulation and resulting in strain hardening of the material; on the other hand, the dislocation–twin reactions promote the transfer between existing slip systems to facilitate deformation.
SFs. Two Shockley partial dislocations with opposite Burgers vectors move in opposite directions on SFs, thereby transforming ISFs to ESFs. The dislocations emitted from the grain boundary then expand the ESFs to twins. Xiong et al. [18] analyzed the mechanism of TB nucleation. These researchers found that the overlapping regions produce a pair of partial dislocations with opposite Burgers vectors, which turn SFs to twins after the overlap of the two ISFs. Xiong et al. [18] considered that this phenomenon is driven by stress and concluded that this mechanism can be applied to other cases. Therefore, in this paper, it is speculated that the partial dislocations on the SFs in Grain III are also driven by stress.
4. Conclusions 3.4.2. Twinning and untwining processes Similar to how dislocations annihilate and reorganize twins, twinning and untwinning processes occur during deformation. Dislocation motion can not only produce new twins but also cause them to disappear. When dislocations slip on the TBs, they migrate and expend the twins. If the migration direction is reversed, however, twins eventually return to ISFs (Fig. 22.). There are also reactions between dislocations and TBs [21]. These reactions produce stair-rod sessile dislocations on TBs that hinder dislocation motion or lead to cross slip, which is conducive to the
The MD simulation of a highly idealized columnar sample shows microstructure evolution of grains under high strain rate loading, revealing the formation process of nanostructures in copper foil under LSF. In the early stages of loading, plastic deformation is mediated by dislocations, and slip systems in grains are gradually activated. When the stress is concentrated, second slip, cross slip, and alternation of slip systems occur. Only a few dislocation reactions, which are limited by sample size, are observed. Dislocation motion forms sub-grain boundaries, and sub-grains
Fig. 19. SFs in the grains: (a) Snapshot with strain at 0.4, very few dislocations; (b) TEM image of refined grains with SFs inside. 9
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Fig. 20. Formation of TBs: (a) ISFs to ESFs; (b) ESFs to microtwins.
twins, including nano-twin bundles, appear and are formed by a series of dislocation motions. Twins and dislocations form a competing deformation relationship. Twins have a twofold effect: They expand material toughness and cause strain hardening. High strain rate and large strain are vital to the formation of these nanostructures. CRediT authorship contribution statement Huixia Liu: Conceptualization, Investigation. Yunfeng Zhang: Writing - original draft, Software, Visualization. Youjuan Ma: Formal analysis. Jiankun Cui: Investigation. Maowen Li: Data curation. Jinxi Gong: Writing - review & editing. Xiao Wang: Supervision, Resources, Project administration. Declaration of Competing Interest
Fig. 21. Two sets Shockley partials expend ISFs to ESFs, green lines indicate Shockley partials.
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.
transform into refined grains via DRX. Given that previous experiments have relied on samples after shocking to reverse the deformation mechanism, the effect of dislocations was ignored. The experimental and simulation results suggest that in addition to DRX of elongated grains and deformation twinning, dislocation motion is important for grain refinement. In the middle and late stages of deformation, numerous deformation
Acknowledgements This work is supported by the National Natural Science Foundation of China (Grant No. 51675243) and the 2018 Innovation Practice Fund of Jiangsu University Industrial Centre (Grant No. ZXJG2018008).
Fig. 22. TBs to ISFs. 10
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