Nanocrystalline and nanotwinned metals exhibit ultrahigh strength but suffer from low ductility due to the absence of the strain hardening effect. Here, we report sustained strong strain hardening up to 20% compressive strain in a melt-quenched nanocrystalline Cu structure, which contains numerous fivefold twins, stacking faults, and twin boundaries. Our molecular dynamics simulations reveal that the strong strain hardening results from the synergistic effect of constant nucleation and impedance of dislocations, restricted twin boundary migration, and abundant dislocation reactions in fivefold twin networks. Specifically, we find that fivefold twins both nucleate and impede dislocations, and the migration of fivefold twin boundary is restricted by the core of fivefold twins. Moreover, we observe a new migration mechanism, in which fivefold twin boundary migrates by two atomic planes directly, enabled by the gliding of two different Shockley partial dislocations in the opposite directions. Finally, dislocation transmission, which is adverse to strain hardening, occurs very scarcely in fivefold twins. This is caused by the large misfit strains in fivefold twins and abundant immobile dislocations generated by frequent dislocation reactions in fivefold twin networks. This work reveals the advantage of fivefold twins over nanotwins to overcome the strength-ductility trade-off.

Twinning in nanocrystalline (nc) materials has drawn extensive research interest because it can enhance both strength and ductility without deteriorating the electric conductivity.1,2 The underlying twinning mechanisms in nc face-centered-cubic (fcc) metals have been extensively studied through both experiments3–10 and molecular dynamics (MD) simulations.11–23 The tendency of a material to form twins is largely determined by its stacking fault (SF) energy.12,13,23 Consequently, earlier observations of nanotwins were limited to metals with a low to medium SF energy such as Cu. Later on, nanotwins were also found in high SF energy metals such as Al, facilitated by the low-temperature and high-strain-rate conditions applied in the experiment.24 One important twin that has been less observed and understood is fivefold twin, in which five {111} coherent twin boundaries (TBs) join together at a common 110 axis. The formation of fivefold twin follows the sequential twinning mechanism that requires a high stress level and a rapid change in stress orientation.25 Therefore, the abundant observation of fivefold twins was very scarce and mainly limited to metals with a low SF energy in the form of nanowires,26–28 nanoparticles,29 and thin films.29 More recently, nc Cu was found to contain fivefold twins, which is attributed to the high stress level and rapid change in stress orientation during ball milling and high-pressure torsion.30,31

The majority of previous studies focused on elucidating the formation mechanism of fivefold twins experimentally25,30,32 or computationally.33–39 Besides the interest in the formation mechanism of fivefold twins, a few recent studies focused on the mechanical properties of fivefold twinned nanowires. Cao and Wei40 performed MD simulations of fivefold twinned Cu nanowires and observed an increase in the strength while a decrease in the ductility compared to single crystalline nanowires. A similar strengthening phenomenon was also found in MD simulations of fivefold twinned Ag nanowires.41,42 In another combined experimental-computational study of fivefold twinned Ag nanowire, Filleter et al.43 observed size effect in the strength and strain hardening, which were attributed to surface-controlled nucleation of SF decahedrons. Narayanan et al.44 reported high yield strength and strain hardening in fivefold twinned Ag nanowires from both experiment and MD simulation. In addition, Wu et al.45 simulated fivefold twined fcc Fe nanowires with various diameters and temperatures and found that the fivefold twin prohibits dislocation activities and causes an increase in the yield strength and Young’s modulus. Finally, Niekiel et al.46 compared the deformation and failure in fivefold twinned nanowires among several fcc metals. They reported an increased yield strength in Ag nanowires while a decreased yield stress in Al nanowires. Specifically, the Ag nanowire was found to fail by formation and growth of pores, whereas the Al nanowire fails by necking.

While the aforementioned studies on nanowires confirmed the great potential of fivefold twins for enhancing strength and strain hardening, the impact of fivefold twin on nc materials has never been studied yet, to the best of the authors’ knowledge. In this work, we report the detailed deformation mechanism involving fivefold twins in nc Cu, which initially contains considerable amount of dislocations and numerous fivefold twin networks. Such a complex microstructure of nc Cu cannot be constructed manually and is obtained through a melt-quenching process in our MD simulations. Previously, fivefold twins have been observed in thin films and particles processed by rapid solidification,47,48 which is similar to the melt-quenching process adopted in our MD simulations. Starting with this unique initial structure, we observe complex interactions between dislocations, grain boundaries (GBs), and fivefold twins, which have never been reported before. Such deformation mechanisms were not observed in previous studies of fivefold twinned nanowires due to the scarcity of dislocations, absence of GBs, and strong surface effect in nanowires. Moreover, our MD simulations reveal a sustained strain hardening in the stress-strain curve, which is attributed to the interactions between fivefold twins and dislocations, and the restricted migration of fivefold TBs. We observe five different deformation mechanisms involving fivefold twins: (1) the core of fivefold twins both nucleates and impedes Shockley partial dislocations; (2) fivefold TBs serve as barriers to dislocation motion; (3) fivefold TB migrates by two atomic planes directly through the gliding of two Shockley partial dislocations in the opposite directions; (4) fivefold TB migrates by one plane through the gliding of a twinning dislocation; and (5) a dislocation transmits across three TBs between two connected fivefold twins.

This paper is organized as follows. Section II describes the setup of our MD simulations. In Sec. III, we present our simulation results on the deformation mechanisms around fivefold twins. In Sec. IV, we discuss the contribution of fivefold twins to the strong strain hardening effect and the difference between fivefold twins and nanotwins. Finally, we conclude this paper in Sec. V.

The MD simulations in this work are performed using the LAMMPS Molecular Dynamics Simulator.49 The interactions between Cu atoms are described by the embedded-atom model (EAM) potential.50 The integration time step size is 1 fs and the periodic boundary conditions are applied in all three dimensions. The simulation domain contains approximately 950000 fcc Cu atoms with a dimension of 34.5 (x axis)×18.1×18.1 nm3. Initially, each atom is assigned a random velocity corresponding to a temperature of 300 K following the Gaussian distribution. Then, the system temperature is gradually increased to 1650 K, which is well above the melting temperature (1320 K) of Cu for the EAM potential adopted in this work. The entire simulation domain is then relaxed in the isothermal-isobaric51 ensemble at 1650 K for 100 ps to ensure that the Cu melts completely. Subsequently, the Cu melt is quenched back to room temperature. Several cooling rates have been used and the corresponding crystallinity of the structures are examined. It is noted that large cooling rates result in large amorphous areas in the melt-quenched structure. A slow cooling rate of 0.225 K/ps is chosen to obtain a nc Cu with atomically thin GBs at the end of the quenching process. The obtained structure [inset of Fig. 1(a)] after the melt-quenching process is referred to as the melt-quenched structure in this paper and serves as the initial structure in the compression simulation. The average grain size of the melt-quenched structure is 10.6 nm.

FIG. 1.

Stress-strain curves of the melt-quenched structure [shown in the inset of (a)] and the Voronoi polycrystal [shown in the inset of (b)] under compression at a strain rate of 108 s1. The melt-quench structure exhibits strong strain hardening. In comparison, the stress-strain curves for nc Cu with various amount of nanotwins18,23 are also plotted in (a). The melt-quenched structure contains considerable fivefold twins, SFs, and TBs. Fcc atoms are shown in cyan, hcp atoms are shown in red, and noncrystalline atoms are shown in gray.

FIG. 1.

Stress-strain curves of the melt-quenched structure [shown in the inset of (a)] and the Voronoi polycrystal [shown in the inset of (b)] under compression at a strain rate of 108 s1. The melt-quench structure exhibits strong strain hardening. In comparison, the stress-strain curves for nc Cu with various amount of nanotwins18,23 are also plotted in (a). The melt-quenched structure contains considerable fivefold twins, SFs, and TBs. Fcc atoms are shown in cyan, hcp atoms are shown in red, and noncrystalline atoms are shown in gray.

Close modal

At the beginning of the MD simulation, two consecutive energy minimizations are conducted, of which the first one optimizes only the internal coordinates of the atoms and the second one optimizes both the internal atomic locations and the volume of simulation box simultaneously. This ensures a thorough relaxation of the stress and forces in the melt-quenched structure. Then, the system is relaxed at a temperature of 10 K for 100 ps. Subsequently, the melt-quenched structure is subjected to uniaxial compression in the x direction under a strain rate of 108 s1 and at a temperature of 10 K to avoid thermal fluctuation. Constant stress is maintained in the lateral dimensions with a barostat. The software OVITO52 is used to visualize the microstructure evolution during the compression process. Fcc atoms are shown in cyan, hexagonal closest packed (hcp) atoms are shown in red, and noncrystalline atoms are shown in gray. Under this coloring scheme, TBs are represented by one plane of red atoms, stacking faults (SFs) are represented by two consecutive planes of red atoms, and GBs are indicated by gray atoms.

The deformation mechanisms of nc metals have been extensively studied using MD simulations over the last two decades.53–58 The polycrystals used were commonly created by Voronoi tessellation,59 of which the grain interior is free from defects. As displayed in the inset of Fig. 1(a), the melt-quenching process presented here generates a large amount of SFs, TBs, and fivefold twin networks. Therefore, the melt-quenched structure contains a high percentage (20.4%) of hcp atoms. This is in distinct contrast to the Voronoi polycrystals commonly used in previous MD simulations.

Figure 1(a) shows the stress-strain curve of the melt-quenched structure under compression up to an applied strain of 20%. After initial yielding, the melt-quenched structure undergoes strong strain hardening. The stress-strain curve between the yield point and 6% strain is the stage II strain hardening regime60 and is, thus, used to calculate the strain hardening exponent. Specifically, the yield point (at 2.43% strain) is followed by a stress drop at the end of the elastic regime in the stress-strain curve. The strain hardening exponent, n, follows the Hollomons equation,61σ=Kϵn. To obtain more statistically accurate and reliable results, we calculate the strain hardening exponent based on three independent simulations, in which atoms are initialized with different velocities, but all are statistically equivalent to 10 K. We obtain an average strain hardening exponent of 0.26. In comparison, stress-strain curves from MD simulations18,23 of nc Cu with various amount of nanotwins under tensile loading are plotted in Fig. 1(a), which exhibit a softening effect. Two recent studies on nanotwinned19 and fivefold twinned44 nanowires reported a strain hardening effect, which is limited to a few percent strain and followed by a sharp stress drop. In contrast, the melt-quenched structure in our work shows a sustained strain hardening up to 20% strain and a continuous increase in the average flow stress, which has not been reported in previous MD simulations of nc metals, to the best of our knowledge. In addition, the stress-strain curve in this work also shows frequent stress drops as commonly observed in MD simulations under strain loading conditions,18,43–46 which are caused by the large plastic deformation from the fast gliding of dislocations in the small simulation domain.62,63

To understand the observed strong strain hardening effect, the melt-quenched structure is compared with a nc Cu with similar size but without fivefold twins, SFs, and TBs [as shown in the inset of Fig. 1(b)]. We construct a Voronoi polycrystal64 with box size and grain size (10.6 nm) similar to the melt-quenched structure. The Voronoi polycrystal is subjected to compression in the same way as the melt-quenched structure, and the predicted stress-strain curve is shown in Fig. 1(b). As one can see, the flow stress is always lower than the yield stress/peak stress, which indicates a softening effect. The comparison in the stress-strain curves between melt-quenched structure and Voronoi polycrystal clearly reveals that the unique strain hardening behavior is attributed to the fivefold twin networks, SFs, and TBs, of which the deformation mechanisms will be discussed later.

It is well understood that the plastic deformation in nc Cu is accommodated by Shockley partial dislocations and mechanical twinning due to its low SF energy and twin fault energy.12 To visualize the evolution of dislocations and TBs during compression, the dislocation analysis function in OVITO is applied in the melt-quenched structure. Different types of dislocations are represented by colored cylindrical wires in all the subsequent figures: green is Shockley partial dislocation, blue is perfect lattice dislocation, pink is stair-rod dislocation, and yellow is Hirth dislocation. Fcc atoms are removed to clearly show dislocation activities.

The unique finding of the current work is the plastic deformation involving fivefold twins, which is the underlying mechanism of the strong strain hardening of the melt-quenched structure. It is observed that the plastic deformation is mainly carried by the interactions of Shockley partial dislocations with fivefold twins and the migration of fivefold TBs. Dislocation gliding impeded by fivefold TBs and the core of fivefold twins are reported in Secs. III A and III B, respectively. Sections III C and III D describe two different mechanisms for the migration of fivefold TBs. Lastly, Sec. III E shows the less frequently observed dislocation transmission across two connected fivefold twins.

The microstructure evolution in the melt-quenched Cu during the compression process is carefully inspected. It is found that the gliding of partial dislocations is often impeded by fivefold TBs. A representative process is shown in Fig. 2. Initially, a Shockley partial dislocation, which is nucleated from the GB, glides toward one of the fivefold TBs (denoted as TB1). Afterward, this Shockley partial dislocation remains pinned by TB1 for the rest of loading process [Fig. 2(b)]. The angles between fivefold TBs are measured manually and marked in Fig. 2(a). It is worth noting that the angle ranges from 69° to 74°. In fcc metals, the theoretical angle between different {111} slip planes is 70.53°. In order to cover 360° by fivefold twins, the angle between each TBs should be 72°, which is larger than 70.53° and, thus, leaves a gap of 7.33°. Evidently, all the five angles marked in Fig. 2(a) are different from the theoretical value of 70.53°. After a careful inspection of many other fivefold twins in our MD simulations, this conclusion holds for all the cases. Despite the uncertainty in the measurement of the angles, our results univocally show that the 7.33° gap is distributed between all five twinned regions. Accordingly, all five twinned regions are elastically strained.

FIG. 2.

A Shockley partial dislocation (a) glides upward (ϵ=10.84%) and (b) is impeded by TB1 (ϵ=10.92%). The angles between fivefold TBs are marked in (a). Different types of dislocations are represented by colored cylindrical wires in all subsequent figures: green is Shockley partial dislocation, blue is perfect lattice dislocation, pink is stair-rod dislocation, and yellow is Hirth dislocation. An “L” is used to mark the location of the Shockley partial dislocation.

FIG. 2.

A Shockley partial dislocation (a) glides upward (ϵ=10.84%) and (b) is impeded by TB1 (ϵ=10.92%). The angles between fivefold TBs are marked in (a). Different types of dislocations are represented by colored cylindrical wires in all subsequent figures: green is Shockley partial dislocation, blue is perfect lattice dislocation, pink is stair-rod dislocation, and yellow is Hirth dislocation. An “L” is used to mark the location of the Shockley partial dislocation.

Close modal

Besides the restriction by fivefold TBs, our simulations reveal that the gliding of lattice dislocations is frequently impeded by the core of fivefold twins. This will result in an SF pinned between two connected fivefold twins when the dislocation is nucleated from the core of a fivefold twin. Figure 3(a) shows a fivefold twin network containing three fivefold twins connected by three common TBs. Initially, a Shockley partial dislocation is nucleated from the core of the lower right fivefold twin. Subsequently, it glides toward the core of the upper fivefold twin [Fig. 3(a)], leaving behind an SF next to the common TB. Finally, it reaches and reacts with the core of the upper fivefold twin [Fig. 3(b)], forming a sessile dislocation in the upper fivefold twin. It is noted that the extended SF is on the adjacent plane of the common TB, resulting in three consecutive atomic planes of hcp atoms.

FIG. 3.

(a) A partial dislocation is nucleated from the core of the lower right fivefold twin and glides next to the common TB between the upper and lower fivefold twins (ϵ=5.88%). (b) The resulting SF is pinned between the cores of the two fivefold twins (ϵ=5.92%).

FIG. 3.

(a) A partial dislocation is nucleated from the core of the lower right fivefold twin and glides next to the common TB between the upper and lower fivefold twins (ϵ=5.88%). (b) The resulting SF is pinned between the cores of the two fivefold twins (ϵ=5.92%).

Close modal

Based on Sec. III A and this section, it can be concluded that the role of fivefold twins in the plastic deformation of nc materials is similar to that of GBs, as both dislocation sources and barriers.58 The decrease in grain size (increase in GB regions) leads to an increase in material strength,53,56,65 which is commonly known as the Hall-Petch effect.66,67 Similarly, it is expected that the increase in the number of fivefold twins will enhance material strength due to the impedance of dislocation motions. Moreover, fivefold twins also cause strong strain hardening, which was rarely observed in nc metals.

Besides dislocation interactions with fivefold twins, the migration of fivefold TBs occurs equally frequently in the melt-quenched structure. Figure 4 shows a unique migration process of fivefold TB by two {111} planes directly, which involves the gliding of two different Shockley partial dislocations in the opposite directions. Initially, the first Shockley partial dislocation is nucleated from the intersection of a fivefold TB with a GB [Fig. 4(a)]. Then, it glides adjacent to the fivefold TB [Fig. 4(b)] and, subsequently, it reaches and is stopped by the core of the fivefold twin [Fig. 4(c)]. Finally, the second Shockley partial dislocation, which is nucleated from the core of the fivefold twin, glides back to the lower GB as shown in Fig. 4(d). Note that the two partial dislocations are parallel but on two different {111} planes. Through this process, the fivefold TB migrates to the left by two {111} planes directly, in contrast to the conventional migration of coherent TBs: a TB migrates by only one atomic plane through the gliding of twinning dislocation.15,16,18,22 In addition, with the migration of the fivefold TB, its core is distorted and expanded. There are many noncrystalline atoms in the core as shown in Fig. 4(d). Numerous dislocation activities are observed in this distorted fivefold twin with increasing strain. In contrast, fivefold twins with a perfect core of only one layer of noncrystalline atoms carry fewer plastic activities.

FIG. 4.

A fivefold TB moves to the left by two {111} planes directly through the gliding of two Shockley partial dislocations in the opposite directions. A Shockley partial dislocation [(a) and (b)] glides toward and (c) arrives at the core of a fivefold twin. (d) A new Shockley partial dislocation nucleated from the core of the fivefold twin glides back to the GB. The dashed and solid lines represent the original and final positions of the TB, respectively. The corresponding strains are (a) ϵ=4.16%, (b) ϵ=4.20%, (c) ϵ=4.24%, and (d) ϵ=5.28%.

FIG. 4.

A fivefold TB moves to the left by two {111} planes directly through the gliding of two Shockley partial dislocations in the opposite directions. A Shockley partial dislocation [(a) and (b)] glides toward and (c) arrives at the core of a fivefold twin. (d) A new Shockley partial dislocation nucleated from the core of the fivefold twin glides back to the GB. The dashed and solid lines represent the original and final positions of the TB, respectively. The corresponding strains are (a) ϵ=4.16%, (b) ϵ=4.20%, (c) ϵ=4.24%, and (d) ϵ=5.28%.

Close modal

In addition to the new mechanism discussed in Sec. III C, i.e., a TB migrates by two planes directly, our MD simulations also reveal the migration of fivefold TBs via the gliding of twinning dislocations, which is the same as the case in nanotwins.15,16,18,22 As depicted in Fig. 5(a), a twinning dislocation, of which the Burgers vector corresponds to Shockley partial dislocations,68 is nucleated from the intersection of fivefold TB with another TB. The gliding of this twinning dislocation forms a step in the originally straight TB [Fig. 5(b)]. Finally, when it is absorbed by the core of the fivefold twin, the fivefold TB migrates by one atomic plane [Fig. 5(c)].

FIG. 5.

The migration of a fivefold TB by one {111} plane through the gliding of a twinning dislocation. The twinning dislocation (a) glides toward the core of the fivefold twin and (b) results in a step in the fivefold TB. (c) After the twinning dislocation is absorbed by the core of the fivefold twin, the fivefold TB is one atomic plane from its original position, which is represented by the dashed line. An “L” is used to mark the location of the twinning dislocation. The corresponding strains are (a) ϵ=1.12%, (b) ϵ=1.32%, and (c) ϵ=1.64%.

FIG. 5.

The migration of a fivefold TB by one {111} plane through the gliding of a twinning dislocation. The twinning dislocation (a) glides toward the core of the fivefold twin and (b) results in a step in the fivefold TB. (c) After the twinning dislocation is absorbed by the core of the fivefold twin, the fivefold TB is one atomic plane from its original position, which is represented by the dashed line. An “L” is used to mark the location of the twinning dislocation. The corresponding strains are (a) ϵ=1.12%, (b) ϵ=1.32%, and (c) ϵ=1.64%.

Close modal

Our simulations frequently reveal that a coherent TB is pinned between two fivefold TBs. As shown in Fig. 6(a), the coherent TB (denoted as TB0) extends between two fivefold TBs (denoted as TB1 and TB2). Later on, a twinning dislocation glides on TB0 and approaches TB2 [Fig. 6(b)]. Finally, when the twinning dislocation arrives at TB2, TB0 migrate upward by one {111} plane [Fig. 6(c)]. It should be noted that, unlike other TBs that are perpendicular to the paper and, thus, appear as lines of hcp atoms, TB0 is inclined to the paper and, therefore, manifests itself as a plane of atoms.

FIG. 6.

The migration of a coherent TB by one {111} plane through the gliding of a twinning dislocation. (b) The twinning dislocation glides toward TB2 and results in a step in TB0. (c) After the twinning dislocation reaches TB2, TB0 migrate up one atomic plane from its original position (the dashed line). An “L” is used to mark the location of the twinning dislocation. The corresponding strains are (a) ϵ=15.20%, (b) ϵ=15.28%, and (c) ϵ=15.44%. It should be noted that, unlike other TBs that are perpendicular to the paper and, thus, appear as lines of hcp atoms, TB0 is inclined to the paper and, therefore, manifests itself as a plane of atoms.

FIG. 6.

The migration of a coherent TB by one {111} plane through the gliding of a twinning dislocation. (b) The twinning dislocation glides toward TB2 and results in a step in TB0. (c) After the twinning dislocation reaches TB2, TB0 migrate up one atomic plane from its original position (the dashed line). An “L” is used to mark the location of the twinning dislocation. The corresponding strains are (a) ϵ=15.20%, (b) ϵ=15.28%, and (c) ϵ=15.44%. It should be noted that, unlike other TBs that are perpendicular to the paper and, thus, appear as lines of hcp atoms, TB0 is inclined to the paper and, therefore, manifests itself as a plane of atoms.

Close modal

It is worth noting that TB migrations described in this section and in nanotwins are both through twinning dislocations. However, they demonstrate distinctly different mobility. The TB migration in fivefold twins is usually restricted by the core and other joining TBs, which is in contrast to the fast twinning and detwinning in nanotwins.16 Indeed, our simulations reveal that the majority of fivefold TBs moves back and forth around their original locations throughout the entire compression simulation (up to a strain of 20%). Such restricted TB migration is expected to contribute to the sustained strain hardening in the melt-quenched structure.

Figure 7 shows a dislocation transmission process across three TBs (denoted as TB1, TB2, and TB3) of two connected fivefold twins. The twinned regions next to the three TBs are denoted as twinned regions 1, 2, and 3. Initially, a leading Shockley partial dislocation reaches TB1 [Fig. 7(a)]. Then, it transmits across TB1, traverses twinned region 1, and arrives at TB2. As shown in Fig. 7(b), an SF extends between TB1 and TB2 after the trailing partial dislocation reacts with another dislocation and forms a Hirth dislocation on TB1. Afterward, the leading partial transmits across TB2 and TB3 and continues gliding in twinned region 3 [Fig. 7(c)]. Meanwhile, the trailing dislocation is still lagging behind in twinned region 1. Subsequently, the SF in twinned region 2 reacts with dislocations beneath the sample surface, which removes the SF and leaves some noncrystalline atoms in twinned region 2 [Fig. 7(c)]. Finally, the SF in twinned region 2 completely disappears and additional dislocation reactions generate a Hirth dislocation on TB3 [Fig. 7(d)]. Due to the change in orientations of each twinned region, the dislocation exhibits a zigzag slip path, which is marked by the dashed lines in Fig. 7.

FIG. 7.

Dislocation transmission across two connected fivefold twins. The slip path of the dislocation is indicated by the dashed lines. The dislocation (a) arrives at TB1, (b) traverses twinned region 1 and reaches TB2, and (c) traverses twinned region 2 and glides in twinned region 3. (d) Dislocation reactions have removed the SF lagging behind and the leading partial dislocation glides further in twinned region 3. The corresponding strains are (a) ϵ=13.92%, (b) ϵ=13.96%, (c) ϵ=16.96%, and (d) ϵ=17.04%. The pink and yellow dislocations are stair-rod dislocation and Hirth dislocation, respectively.

FIG. 7.

Dislocation transmission across two connected fivefold twins. The slip path of the dislocation is indicated by the dashed lines. The dislocation (a) arrives at TB1, (b) traverses twinned region 1 and reaches TB2, and (c) traverses twinned region 2 and glides in twinned region 3. (d) Dislocation reactions have removed the SF lagging behind and the leading partial dislocation glides further in twinned region 3. The corresponding strains are (a) ϵ=13.92%, (b) ϵ=13.96%, (c) ϵ=16.96%, and (d) ϵ=17.04%. The pink and yellow dislocations are stair-rod dislocation and Hirth dislocation, respectively.

Close modal

In contrast to the aforementioned frequently observed fivefold TB migrations, only one dislocation transmission across the fivefold TBs is observed in this work. The scarcity of the dislocation transmission is attributed to the misfit strain and abundant dislocation reactions in fivefold twins. Firstly, we observe that the gap of 7.33° for fivefold twin to cover 360° is divided between all the five TBs. This misfit strain will induce considerable stress field in fivefold twins, which effectively hinders the transmission process. Secondly, dislocations that impinge on fivefold twins often react with other dislocations on the fivefold TB, forming immobile dislocations (e.g., Hirth dislocation) and prohibiting the transmission process. Shabib and Miller18 observed a peak stress followed by softening in nanotwinned Cu, which is attributed to the activation of abundant dislocation transmissions across TBs. In our simulations, the difficulty in slip transmission in fivefold twin and the back stress caused by immobile dislocations69 are expected to contribute to the sustained strain hardening.

We attribute the sustained strong strain hardening to the synergistic effect of constant nucleation and impedance of dislocations (Figs. 2–4), restricted TB migration (Figs. 4 and 5), and abundant dislocation reactions (Fig. 7) in fivefold twin networks. Specifically, the fivefold TBs are observed to block the lattice partial dislocations (Fig. 2), which remains sessile and hard to transmit due to the large misfit strain (to close the 7.33° gap) in fivefold twins. This is verified by the scarcity in the dislocation transmission process in fivefold twins. In addition, lattice dislocations are often impeded by the core of fivefold twins (Figs. 3 and 4). Therefore, dislocations accumulate in fivefold twins, leading to the strain hardening effect. Secondly, fivefold twins are stable during the entire deformation process because its migration is restricted by its core and fivefold TB only oscillates around its original location (Figs. 4 and 5). In contrast, nanotwins can migrate more freely and often undergo fast detwinning process and lost their high density. Therefore, fivefold twin can provide more sustained strain hardening than nanotwins. Moreover, along with the TB migration, the core of fivefold twin becomes distorted and expands over several atomic planes [Figs. 4(d) and 5(c)], which is expected to resist further migration of TB and cause strain hardening. Thirdly, the distorted cores of fivefold twins are observed to nucleate many twinning dislocations, which react with lattice dislocations and form sessile dislocations such as stair-rod and Hirth dislocations (pink and yellow dislocations in Fig. 7). The dislocation reaction and resulting sessile dislocations further contribute to the strain hardening effect.

Our simulations show that fivefold twins have several advantages over nanotwins in terms of the strain hardening effect. Firstly, dislocations are confined by nanotwins only in the thickness direction of twin lamellae while a sufficient free path for dislocation slip is maintained along twin boundary directions. In contrast, dislocations are confined by the cage of fivefold twin boundaries. Secondly, besides the restriction by fivefold TBs, our simulations reveal that the gliding of lattice dislocations is frequently impeded by the core of fivefold twins. Thirdly, we observe abundant twinning dislocation nucleation from distorted cores of fivefold twins and the resulting dislocation reactions and formation of sessile dislocations. Lastly, the aforementioned 7.33° angle gap induces elastic distortion inside all fivefold twin regions, which can render dislocation gliding more difficult than nanotwins. In summary, the more significant impedance provided by fivefold twins leads to more accumulation of dislocations and thereby a stronger strain hardening effect than nanotwins.

In this work, MD simulations have been performed to investigate the compression response of a melt-quenched nc Cu structure, which initially contains extensive SFs, TBs, and fivefold twin networks. The key deformation mechanisms observed are interactions between dislocations and fivefold twins, as well as the migration of fivefold TBs. Specifically, five deformation mechanisms are observed: (1) the core of fivefold twins both nucleates dislocations and impedes dislocation motion; (2) fivefold TBs impede dislocation motion; (3) fivefold TB migrates by two atomic planes directly through the gliding of two Shockley partial dislocations in opposite directions; (4) fivefold TB migrates by one atomic plane through the gliding of a twinning dislocation; and (5) a dislocation transmits across three TBs between two connected fivefold twins.

Our simulations have revealed that the role of fivefold twin in the deformation process of nc materials is similar to that of GBs, both nucleating and impeding dislocations (Figs. 2–4). In contrast to the small core area in fivefold twinned nanowires, the core of fivefold twin in our melt-quenched structure is usually distorted and expanded [Figs. 4(d) and 5(c)], which serves as a preferred nucleation site for lattice dislocations and twinning dislocations. In addition, we have also observed the migration of fivefold TB by two planes directly, which was never observed in nanotwins, to the best of our knowledge. It involves two Shockley partial dislocations: the first one glides on one side of the TB toward the core of the fivefold twin, while the second one glides on other side of the TB in the opposite direction (Fig. 4). It is noted that fivefold TBs are restricted by the core and other TBs in the fivefold twin and, therefore, cannot migrate as freely as nanotwins. Indeed, our simulations have revealed that fivefold TBs move back and forth around their original locations, and, thus, fivefold twin networks are stable throughout the compression process. Moreover, the 7.33° gap is found to be accommodated in all five twinned regions, resulting in large misfit strain and stress fields. Furthermore, dislocation transmission across fivefold twin is rarely observed, which is attributed to the misfit strain and abundant dislocation reactions in fivefold twins. In summary, the complex fivefold twin networks lead to constant nucleation, gliding, and impedance of dislocations (Figs. 2–4), the restricted TB migration (Figs. 4 and 5), and the abundant dislocation reactions (Fig. 7). These mechanisms result in the sustained strong strain hardening during the entire compression process up to a strain of 20%, which is unique in the melt-quenched nc Cu structure.

The authors are supported by the faculty startup funds from the University of Nevada, Reno. A.Z., P.C., and L.C. are partially supported by the NSF-CMMI Mechanics of Materials and Structures Program under Grant No. 1727428. All authors acknowledge the financial support from NASA Space Grant (No. NNX15AK48A).

1.
L.
Lu
,
Y.
Shen
,
X.
Chen
,
L.
Qian
, and
K.
Lu
, “
Ultrahigh strength and high electrical conductivity in copper
,”
Science
304
,
422
426
(
2004
).
2.
Y.
Zhao
,
Y.
Zhu
,
X.
Liao
,
Z.
Horita
, and
T.
Langdon
, “
Tailoring stacking fault energy for high ductility and high strength in ultrafine grained Cu and its alloy
,”
Appl. Phys. Lett.
89
,
121906
(
2006
).
3.
M.
Chen
,
E.
Ma
,
K. J.
Hemker
,
H.
Sheng
,
Y.
Wang
, and
X.
Cheng
, “
Deformation twinning in nanocrystalline aluminum
,”
Science
300
,
1275
1277
(
2003
).
4.
X.
Wu
,
Y.
Zhu
,
M.
Chen
, and
E.
Ma
, “
Twinning and stacking fault formation during tensile deformation of nanocrystalline Ni
,”
Scr. Mater.
54
,
1685
1690
(
2006
).
5.
X.
Wu
,
X.
Liao
,
S.
Srinivasan
,
F.
Zhou
,
E.
Lavernia
,
R.
Valiev
, and
Y.
Zhu
, “
New deformation twinning mechanism generates zero macroscopic strain in nanocrystalline metals
,”
Phys. Rev. Lett.
100
,
095701
(
2008
).
6.
X.
Wu
and
Y.
Zhu
, “
Inverse grain-size effect on twinning in nanocrystalline Ni
,”
Phys. Rev. Lett.
101
,
025503
(
2008
).
7.
Y.
Zhu
,
X.
Liao
, and
X.
Wu
, “
Deformation twinning in nanocrystalline materials
,”
Prog. Mater. Sci.
57
,
1
62
(
2012
).
8.
Y.
Wang
,
M.
Sui
, and
E.
Ma
, “
In situ observation of twin boundary migration in copper with nanoscale twins during tensile deformation
,”
Philos. Mag. Lett.
87
,
935
942
(
2007
).
9.
C.
Huang
,
K.
Wang
,
S.
Wu
,
Z.
Zhang
,
G.
Li
, and
S.
Li
, “
Deformation twinning in polycrystalline copper at room temperature and low strain rate
,”
Acta Mater.
54
,
655
665
(
2006
).
10.
Y.
Zhu
,
X.
Wu
,
X.
Liao
,
J.
Narayan
,
L.
Kecskes
, and
S.
Mathaudhu
, “
Dislocation–twin interactions in nanocrystalline fcc metals
,”
Acta Mater.
59
,
812
821
(
2011
).
11.
V.
Yamakov
,
D.
Wolf
,
S.
Phillpot
, and
H.
Gleiter
, “
Deformation twinning in nanocrystalline Al by molecular-dynamics simulation
,”
Acta Mater.
50
,
5005
5020
(
2002
).
12.
H.
Van Swygenhoven
,
P. M.
Derlet
, and
A.
Frøseth
, “
Stacking fault energies and slip in nanocrystalline metals
,”
Nat. Mater.
3
,
399
(
2004
).
13.
A. G.
Frøseth
,
P. M.
Derlet
, and
H.
Van Swygenhoven
, “
Twinning in nanocrystalline fcc metals
,”
Adv. Eng. Mater.
7
,
16
20
(
2005
).
14.
X.
Li
,
Y.
Wei
,
L.
Lu
,
K.
Lu
, and
H.
Gao
, “
Dislocation nucleation governed softening and maximum strength in nano-twinned metals
,”
Nature
464
,
877
(
2010
).
15.
A.
Frøseth
,
H.
Van Swygenhoven
, and
P.
Derlet
, “
The influence of twins on the mechanical properties of nc-Al
,”
Acta Mater.
52
,
2259
2268
(
2004
).
16.
J.
Wang
,
N.
Li
,
O.
Anderoglu
,
X.
Zhang
,
A.
Misra
,
J.
Huang
, and
J.
Hirth
, “
Detwinning mechanisms for growth twins in face-centered cubic metals
,”
Acta Mater.
58
,
2262
2270
(
2010
).
17.
I.
Shabib
and
R. E.
Miller
, “
A molecular dynamics study of twin width, grain size and temperature effects on the toughness of 2D-columnar nanotwinned copper
,”
Model. Simul. Mater. Sci. Eng.
17
,
055009
(
2009
).
18.
I.
Shabib
and
R. E.
Miller
, “
Deformation characteristics and stress–strain response of nanotwinned copper via molecular dynamics simulation
,”
Acta Mater.
57
,
4364
4373
(
2009
).
19.
C.
Deng
and
F.
Sansoz
, “
Enabling ultrahigh plastic flow and work hardening in twinned gold nanowires
,”
Nano Lett.
9
,
1517
1522
(
2009
).
20.
Q.
Fang
and
F.
Sansoz
, “
Influence of intrinsic kink-like defects on screw dislocation–coherent twin boundary interactions in copper
,”
Acta Mater.
123
,
383
393
(
2017
).
21.
Z.-H.
Jin
,
P.
Gumbsch
,
K.
Albe
,
E.
Ma
,
K.
Lu
,
H.
Gleiter
, and
H.
Hahn
, “
Interactions between non-screw lattice dislocations and coherent twin boundaries in face-centered cubic metals
,”
Acta Mater.
56
,
1126
1135
(
2008
).
22.
L.
Li
and
N. M.
Ghoniem
, “
Twin-size effects on the deformation of nanotwinned copper
,”
Phys. Rev. B.
79
,
075444
(
2009
).
23.
A.
Stukowski
,
K.
Albe
, and
D.
Farkas
, “
Nanotwinned fcc metals: Strengthening versus softening mechanisms
,”
Phys. Rev. B.
82
,
224103
(
2010
).
24.
X.
Liao
,
F.
Zhou
,
E.
Lavernia
,
D.
He
, and
Y.
Zhu
, “
Deformation twins in nanocrystalline Al
,”
Appl. Phys. Lett.
83
,
5062
5064
(
2003
).
25.
X.
An
,
Q.
Lin
,
S.
Wu
,
Z.
Zhang
,
R.
Figueiredo
,
N.
Gao
, and
T.
Langdon
, “
Formation of fivefold deformation twins in an ultrafine-grained copper alloy processed by high-pressure torsion
,”
Scr. Mater.
64
,
249
252
(
2011
).
26.
Y.
Sun
,
Y.
Ren
,
Y.
Liu
,
J.
Wen
,
J.
Okasinski
, and
D.
Miller
, “
Ambient-stable tetragonal phase in silver nanostructures
,”
Nat. Commun.
3
,
971
971
(
2012
).
27.
F.
Niekiel
,
E.
Bitzek
, and
E.
Spiecker
, “
Combining atomistic simulation and x-ray diffraction for the characterization of nanostructures: A case study on fivefold twinned nanowires
,”
ACS Nano
8
,
1629
1638
(
2014
).
28.
D.
Kim
,
S.-H.
Kim
,
J. H.
Kim
,
J.-C.
Lee
,
J.-P.
Ahn
, and
S. W.
Kim
, “
Failure criterion of silver nanowire electrodes on a polymer substrate for highly flexible devices
,”
Sci. Rep.
7
,
45903
(
2017
).
29.
H.
Hofmeister
, “Fivefold twinned nanoparticles,” in Encyclopedia of Nanoscience and Nanotechnology (American Scientific Publishers, Stevenson Ranch, CA, 2004), Vol. 3, pp. 431–452.
30.
Y.
Zhu
,
X.
Liao
, and
R.
Valiev
, “
Formation mechanism of fivefold deformation twins in nanocrystalline face-centered-cubic metals
,”
Appl. Phys. Lett.
86
,
103112
(
2005
).
31.
J.
Huang
,
Y.
Wu
, and
H.
Ye
, “
Deformation structures in ball milled copper
,”
Acta Mater.
44
,
1211
1221
(
1996
).
32.
P.
Huang
,
G.
Dai
,
F.
Wang
,
K.
Xu
, and
Y.
Li
, “
Fivefold annealing twin in nanocrystalline Cu
,”
Appl. Phys. Lett.
95
,
203101
(
2009
).
33.
A.
Cao
and
Y.
Wei
, “
Formation of fivefold deformation twins in nanocrystalline face-centered-cubic copper based on molecular dynamics simulations
,”
Appl. Phys. Lett.
89
,
041919
(
2006
).
34.
Z.
Zhang
,
S.
Huang
,
L.
Chen
,
Z.
Zhu
, and
D.
Guo
, “
Formation mechanism of fivefold deformation twins in a face-centered cubic alloy
,”
Sci. Rep.
7
,
45405
(
2017
).
35.
E.
Bringa
,
D.
Farkas
,
A.
Caro
,
Y.
Wang
,
J.
McNaney
, and
R.
Smith
, “
Fivefold twin formation during annealing of nanocrystalline Cu
,”
Scr. Mater.
59
,
1267
1270
(
2008
).
36.
S. L.
Thomas
,
A. H.
King
, and
D. J.
Srolovitz
, “
When twins collide: Twin junctions in nanocrystalline nickel
,”
Acta Mater.
113
,
301
310
(
2016
).
37.
T.
Shen
,
Y.
Wu
, and
X.
Lu
, “
Structural evolution of five-fold twins during the solidification of Fe 5601 nanoparticle: A molecular dynamics simulation
,”
J. Mol. Model.
19
,
751
755
(
2013
).
38.
A.
Mahata
,
M. A.
Zaeem
, and
M. I.
Baskes
, “
Understanding homogeneous nucleation in solidification of aluminum by molecular dynamics simulations
,”
Model. Simul. Mater. Sci. Eng.
26
,
025007
(
2018
).
39.
Z.
Hou
,
K.
Dong
,
Z.
Tian
,
R.
Liu
,
Z.
Wang
, and
J.
Wang
, “
Cooling rate dependence of solidification for liquid aluminium: A large-scale molecular dynamics simulation study
,”
Phys. Chem. Chem. Phys.
18
,
17461
17469
(
2016
).
40.
A.
Cao
and
Y.
Wei
, “
Atomistic simulations of the mechanical behavior of fivefold twinned nanowires
,”
Phys. Rev. B.
74
,
214108
(
2006
).
41.
M.
Sun
,
R.
Cao
,
F.
Xiao
, and
C.
Deng
, “
Surface and interface controlled yielding and plasticity in fivefold twinned Ag nanowires
,”
Comput. Mater. Sci.
79
,
289
295
(
2013
).
42.
Y.
Gao
,
Y.
Fu
,
W.
Sun
,
Y.
Sun
,
H.
Wang
,
F.
Wang
, and
J.
Zhao
, “
Investigation on the mechanical behavior of fivefold twinned silver nanowires
,”
Comput. Mater. Sci.
55
,
322
328
(
2012
).
43.
T.
Filleter
,
S.
Ryu
,
K.
Kang
,
J.
Yin
,
R. A.
Bernal
,
K.
Sohn
,
S.
Li
,
J.
Huang
,
W.
Cai
, and
H. D.
Espinosa
, “
Nucleation-controlled distributed plasticity in penta-twinned silver nanowires
,”
Small
8
,
2986
2993
(
2012
).
44.
S.
Narayanan
,
G.
Cheng
,
Z.
Zeng
,
Y.
Zhu
, and
T.
Zhu
, “
Strain hardening and size effect in five-fold twinned Ag nanowires
,”
Nano Lett.
15
,
4037
4044
(
2015
).
45.
J.
Wu
,
S.
Nagao
,
J.
He
, and
Z.
Zhang
, “
Role of five-fold twin boundary on the enhanced mechanical properties of fcc Fe nanowires
,”
Nano Lett.
11
,
5264
5273
(
2011
).
46.
F.
Niekiel
,
E.
Spiecker
, and
E.
Bitzek
, “
Influence of anisotropic elasticity on the mechanical properties of fivefold twinned nanowires
,”
J. Mech. Phys. Solids.
84
,
358
379
(
2015
).
47.
A.
Singh
and
S.
Ranganathan
, “
A transmission electron microscopic study of icosahedral twins—I. Rapidly solidified Al-Mn-Fe alloys
,”
Acta Metall. Mater.
43
,
3539
3551
(
1995
).
48.
A.
Singh
and
S.
Ranganathan
, “
A transmission electron microscopic study of icosahedral twins—II. A rapidly solidified Al-Cu-Fe alloy
,”
Acta Metall. Mater.
43
,
3553
3562
(
1995
).
49.
S.
Plimpton
,
P.
Crozier
, and
A.
Thompson
, “
LAMMPS: Large-scale atomic/molecular massively parallel simulator
,”
Sandia Natl. Lab.
18
,
43
(
2007
).
50.
Y.
Mishin
,
M.
Mehl
,
D.
Papaconstantopoulos
,
A.
Voter
, and
J.
Kress
, “
Structural stability and lattice defects in copper: Ab initio, tight-binding, and embedded-atom calculations
,”
Phys. Rev. B
63
,
224106
(
2001
).
51.
D. J.
Evans
and
B. L.
Holian
, “
The Nose–Hoover thermostat
,”
J. Chem. Phys.
83
,
4069
4074
(
1985
).
52.
A.
Stukowski
, “
Visualization and analysis of atomistic simulation data with OVITO—The open visualization tool
,”
Model. Simul. Mater. Sci. Eng.
18
,
015012
(
2009
).
53.
J.
Schiøtz
,
F. D.
DiTolla
, and
K. W.
Jacobsen
, “
Softening of nanocrystalline metals at very small grain sizes
,”
Nature
391
,
561
(
1998
).
54.
J.
Schiøtz
,
T.
Vegge
,
F.
Di Tolla
, and
K. W.
Jacobsen
, “
Atomic-scale simulations of the mechanical deformation of nanocrystalline metals
,”
Phys. Rev. B.
60
,
11971
(
1999
).
55.
V.
Yamakov
,
D.
Wolf
,
S. R.
Phillpot
,
A. K.
Mukherjee
, and
H.
Gleiter
, “
Dislocation processes in the deformation of nanocrystalline aluminium by molecular-dynamics simulation
,”
Nat. Mater.
1
,
45
(
2002
).
56.
V.
Yamakov
,
D.
Wolf
,
S.
Phillpot
,
A.
Mukherjee
, and
H.
Gleiter
, “
Deformation mechanism crossover and mechanical behaviour in nanocrystalline materials
,”
Philos. Mag. Lett.
83
,
385
393
(
2003
).
57.
V.
Yamakov
,
D.
Wolf
,
S.
Phillpot
,
A.
Mukherjee
, and
H.
Gleiter
, “
Deformation-mechanism map for nanocrystalline metals by molecular-dynamics simulation
,”
Nat. Mater.
3
,
43
(
2004
).
58.
H.
Van Swygenhoven
,
P.
Derlet
, and
A.
Frøseth
, “
Nucleation and propagation of dislocations in nanocrystalline fcc metals
,”
Acta Mater.
54
,
1975
1983
(
2006
).
59.
G.
Voronoi
, “
Nouvelles applications des paramètres continus à la théorie des formes quadratiques. premier mémoire. sur quelques propriétés des formes quadratiques positives parfaites
,”
J. reine angew. Math.
133
,
97
178
(
1908
).
60.
U.
Kocks
and
H.
Mecking
, “
Physics and phenomenology of strain hardening: The fcc case
,”
Prog. Mater. Sci.
48
,
171
273
(
2003
).
61.
J. H.
Hollomon
, “
Tensile deformation
,”
AIME Trans.
12
,
1
22
(
1945
).
62.
L.
Cao
,
A.
Hunter
,
I. J.
Beyerlein
, and
M.
Koslowski
, “
The role of partial mediated slip during quasi-static deformation of 3D nanocrystalline metals
,”
J. Mech. Phys. Solids
78
,
415
426
(
2015
).
63.
L.
Cao
and
M.
Koslowski
, “
Rate-limited plastic deformation in nanocrystalline Ni
,”
J. Appl. Phys.
117
,
244301
(
2015
).
64.
P.
Hirel
, “
Atomsk: A tool for manipulating and converting atomic data files
,”
Comput. Phys. Commun.
197
,
212
219
(
2015
).
65.
L.
Cao
and
M.
Koslowski
, “
Effect of microstructural uncertainty on the yield stress of nanocrystalline nickel
,”
Acta Mater.
61
,
1413
1420
(
2013
).
66.
E.
Hall
, “
The deformation and ageing of mild steel: III Discussion of results
,”
Proc. Phys. Soc. Sec. B
64
,
747
(
1951
).
67.
N.
Petch
, “
The cleavage strength of polycrystals
,”
J. Iron Steel Inst.
174
,
25
28
(
1953
).
68.
J. P.
Hirth
and
J.
Lothe
,
Theory of Dislocations
(
John Wiley & Sons
,
1982
).
69.
L.
Cao
,
A.
Sengupta
,
D.
Pantuso
, and
M.
Koslowski
, “
Effect of texture and grain size on the residual stress of nanocrystalline thin films
,”
Mod. Simul. Mater. Sci. Eng.
25
,
075004
(
2017
).