Strain hardening in one-dimensional nanotwinned metals

Metallic NWs usually exhibit ultrahigh strength but low tensile ductility owing to their limited strain-hardening capability.^{Reference Zhu, Li, Ogata and Yip3–Reference Greer and De Hosson5} Single-crystalline NWs of fcc metals (Figure 1a) deform via dislocation-mediated plasticity^{Reference Park, Gall and Zimmerman6–Reference Wang, Narayanan, Huang, Zhang, Zhu and Mao9} or via deformation twinning and lattice reorientation,^{Reference Seo, Yoo, Park, Yoon, Lee, Han, Lee, Seong, Lee, Lee, Cha, Park, Kim and Ahn10–Reference Wang, Liu, Guan, Yang, Sun, Cheng, Hirata, Zhang, Ma, Chen and Han12} without exhibiting pronounced hardening. To promote strain hardening, one can engineer TBs into NWs to act as barriers to dislocation motion. Figure 1b–d shows schematics of different-ordered arrangements of TBs in NWs, including horizontal, inclined, and vertical (fivefold twinned) TBs.

Figure 1. Strain hardening in nanotwinned nanowires (NWs).^{Reference Narayanan, Cheng, Zeng, Zhu and Zhu22} (a–d) Schematics of NWs with different-ordered arrangements of twin boundaries (TBs) (colored in brown): single crystal without TBs, with horizontal, inclined, or vertical TBs. (e–f) Scanning electron microscope images of a fivefold twinned Ag NW. (g) Measured stress–strain data (symbols) for fivefold twinned Ag NWs of various diameters, d, with the power-law fitting curves (solid lines). (h–i) Molecular dynamics snapshots showing (h) surface nucleation of dislocations and (i) obstruction of surface-nucleated dislocations by vertical TBs in a fivefold twinned Ag NW.

Several groups have studied NWs with horizontal TBs (Figure 1b).^{Reference Jang, Li, Gao and Greer13–Reference Wang, Sansoz, Huang, Liu, Sun, Zhang and Mao16} In periodically twinned NWs, strain-hardening behavior was only evidenced in low stacking-fault energy (SFE) metals such as NT Au and Ag.^{Reference Deng and Sansoz17} In contrast, no strain hardening was observed in high SFE metals like NT Cu pillars.^{Reference Jang, Li, Gao and Greer13} This fundamental difference is attributable to the relative change as a function of the unstable SFE between the stress required to nucleate new dislocations from free surfaces and that to overcome the TB resistance on the glide of partial dislocations.^{Reference Deng and Sansoz17} Furthermore, past studies^{Reference Deng and Sansoz18,Reference Wang, Sansoz, Deng, Xu, Han and Mao19} have shown a strong inverse square root dependence of the elastic strain limit and tensile yield stress on twin thickness in ultrathin twinned NWs, resulting in surface dislocations always being emitted from the NW region with the largest twin size. Effective hardening due to these horizontal TBs requires uniformly small twin spacing across the entire length of the NWs, thus imposing a challenge to NW synthesis.

Inclined TBs (Figure 1c) in NWs are subjected to nonzero-resolved shear stresses during axial tension/compression of NWs and are prone to migrate, causing twin coarsening.^{Reference Zhu, Li, Ogata and Yip3} In contrast, vertical TBs (i.e., the fivefold twinned structure in Figure 1d) in axially loaded NWs are subjected to zero-resolved shear stresses and are more stable than the inclined TBs. Interestingly, NWs containing vertical TBs have shown promising results for strain hardening. Zhu et al.^{Reference Zhu, Qin, Xu, Fan, Ding, Zhang, Wiley and Wang20} reported pronounced strain-hardening behavior in Ag NWs with a well-defined fivefold vertical twin structure (Figure 1e–f). Filleter et al.^{Reference Filleter, Ryu, Kang, Yin, Bernal, Sohn, Li, Huang, Cai and Espinosa21} further studied this type of Ag NWs of various diameters and found that the Ag NWs with smaller diameters exhibited stronger strain hardening than those with larger diameters.

Recently, Narayanan et al.^{Reference Narayanan, Cheng, Zeng, Zhu and Zhu22} reported an in-depth study of the work-hardening response and size effects in fivefold twinned Ag NWs by combining in situ tensile testing inside a scanning electron microscope and molecular dynamics (MD) simulations. Figure 1g shows that Ag NWs of smaller diameters harden more than those with larger diameters. MD simulations further showed that the hardening response and size effect were dominantly controlled by surface nucleation of dislocations as well as effective obstruction of dislocations by TBs (Figure 1h–i). They highlighted the important role of statistical variation of source strengths of surface-nucleated dislocations in macroscopic hardening of the fivefold twinned Ag NWs.^{Reference Argon23}

Microscopic plasticity mechanisms in bulk nanotwinned metals

Compression of NT Cu pillars without GBs^{Reference Jang, Li, Gao and Greer13} revealed that TBs alone are not sufficient to mediate the plasticity of NT metals, and that a reasonable mix of TBs and GBs acting as a continuous source for dislocations is helpful to achieve high ductility. Significant experimental progress was made by controlling GB growth in {111}-textured NT Cu films fabricated using either physical vapor deposition^{Reference Hodge, Wang and Barbee24} or direct electrodeposition.^{Reference You, Lu and Lu25} These films exhibited long columnar grains grown in the same upward direction with TBs perfectly parallel to the film, see Figure 2a. In contrast to NT metals with randomly oriented grains,^{Reference Lu, Shen, Chen, Qian and Lu1,Reference Lu, Chen, Huang and Lu26} columnar-grained microstructures present strong anisotropy in plastic behavior when the loading direction changes with respect to the TB orientation.^{Reference Ye, Wang, Barbee and Hamza27–Reference You, Li, Gui, Lu, Zhu, Gao and Lu29} Ye at al.^{Reference Ye, Wang, Barbee and Hamza27} have experimentally observed a twin-orientation-dependent hardness and strain-rate sensitivity in NT Cu, and argued that hard-deformation modes, such as slip-transfer mechanisms, were apparently more strain-rate sensitive than soft deformation modes (e.g., threading dislocations gliding between TBs).

Figure 2. Plasticity of bulk columnar-grained nanotwinned metals with perfect or defective twin boundaries (TBs). (a) Schematic of grain boundary (GB) and TB morphology. Adapted with permission from Reference Reference Ye, Wang, Barbee and Hamza27. © 2012 AIP Publishing, LLC. (b) Uniaxial loading perpendicular to the TB planes resulting in strengthening by blockage of GB-nucleated dislocations by coherent twin boundaries (CTBs), or (c) parallel to the TB planes leading to the propagation of threading dislocations cutting the CTBs with little resistance. (d) Pure shear loading (θ = 45°) causing softening by detwinning. Atomistic simulations of (e) pinning of a threading partial dislocation by a kink-step defect leading to strengthening, and (f) dislocation emission at a kink-line–GB intersection leading to softening.^{Reference Wang, Sansoz, LaGrange, Ott, Barbee and Hamza34} Note: White arrows in (e–f) indicate the direction of propagation of the partial dislocation in each image.

You et al.^{Reference You, Li, Gui, Lu, Zhu, Gao and Lu29} used experiments and atomistic simulations to study isolated dislocation processes under either pure tension, compression, or shear loadings and identified three distinct processes of plastic deformation in columnar-grained Cu with TBs (Figure 2). First, uniaxial loading perpendicular to TBs produces partial dislocations emitted from high-energy GBs that are blocked by TBs if their slip plane crosses the interface (hard slip mode, Figure 2b), contributing to strengthening.^{Reference Jin, Gumbsch, Albe, Ma, Lu, Gleiter and Hahn30,Reference Zhu, Li, Samanta, Kim and Suresh31} Second, shearing parallel to the TB planes (or tension of inclined TBs) forms twinning partial dislocations propagating along TBs (soft slip mode, Figure 2c), leading to softening by detwinning.^{Reference Li, Wei, Lu, Lu and Gao32} However, MD simulations also predicted detwinning in NT Cu, but not in NT Pd, proving that SFE plays a critical role in this behavior.^{Reference Stukowski, Albe and Farkas33} Third, tension parallel to TBs (e.g., films deformed in pure tension) gives rise to threading dislocations confined inside the twin lamellae and propagating in a direction parallel to TBs (Figure 2d). If the twin spacing is small, dislocation loops can extend over several twins to form necklace-like jogged dislocations that can move freely from one GB to the opposite GB.^{Reference Wang, Sansoz, LaGrange, Ott, Barbee and Hamza34,Reference Zhou, Li, Qu, Yang and Gao35}

However, in situ synchrotron x-ray diffraction scattering tensile tests^{Reference Wang, Sansoz, LaGrange, Ott, Barbee and Hamza34} have shown significant nonreversible peak broadening after failure of columnar-grained NT Cu, corresponding to a buildup of dislocations, unlike the behavior of nanocrystalline metals.^{Reference Budrovic, Van Swygenhoven, Derlet, Van Petegem and Schmitt36} This contradicts the assumption that threading dislocations confined between two TBs glide freely without creating new dislocations. Furthermore, significant detwinning occurred at low temperatures in grains not favorably oriented to activate twinning partial dislocations due to low resolved shear stress. High-resolution transmission electron microscope (TEM) inverse-pole-figure-orientation mapping^{Reference Wang, Sansoz, LaGrange, Ott, Barbee and Hamza34} revealed that TBs originally thought to be perfect contain many kink-like steps along the interfaces and are imperfect. These steps were found to be incoherent segments, 1–5 nm in height, substantially larger than the height of a single Shockley twinning partial previously reported on CTBs. MD simulations^{Reference Wang, Sansoz, LaGrange, Ott, Barbee and Hamza34} and experiments^{Reference Lu, Du, Lu and Ye37} have found several new kink-dependent deformation mechanisms in NT Cu with defective TBs that could elucidate the observed abnormal phenomena: (1) Pinning of threading dislocations intersecting kink lines (Figure 2e); (2) dislocation nucleation from kink-line–GB intersection (Figure 2f); (3) detwinning from kink motion; and (4) twinning partial dislocations emitted from kink steps.

Microstructure evolution of nanotwins during severe rolling deformation

Another important aspect in the deformability of high-strength NT materials^{Reference Beyerlein, Zhang and Misra38} is the plastic flow stability (i.e., changes in the morphology and texture during plastic deformation). In the case of columnar-grained NT Cu composed of 5-nm-thick twins, the plastic flow stability was evaluated by room-temperature rolling of NT foils stacked between stainless-steel sheets.^{Reference Anderoglu, Wang, Hirth, Hoagland, Misra and Zhang39} Despite the very fine structure and high strength, NT Cu films exhibited stable plastic flow in room-temperature rolling without localized shear bands that are known to limit deformability in high-strength nanocrystalline metals. Examination of the rolled microstructures revealed the following key characteristics of the deformation behavior of NT Cu after rolling to 50% reduction: (1) the average twin thickness did not change significantly; (2) the {111} fiber texture was retained; and (3) significant work hardening occurred.^{Reference Anderoglu, Wang, Hirth, Hoagland, Misra and Zhang39}

Figure 3 shows cross-sectional TEM images and corresponding measured twin thickness statistics for NT Cu foils. The retention of average lamellae thickness after 50% reduction in sample thickness implies elimination of some twin interfaces during rolling. This is confirmed by the measured statistics of twin-lamellae thickness before and after rolling. Figure 3b shows that the fraction of twins with a thickness less than approximately 2 nm are missing in the histogram from the rolled sample. Indentation of NT Cu in situ in a TEM^{Reference Wang, Li, Anderoglu, Zhang, Misra, Huang and Hirth40,Reference Li, Wang, Huang, Misra and Zhang41} revealed detwinning of very thin twins that was interpreted via atomistic modeling^{Reference Wang, Li, Anderoglu, Zhang, Misra, Huang and Hirth40,Reference Wang, Misra and Hirth42} and finite element analysis^{Reference Mirkhani and Joshi43} as the migration of short incoherent TB segments connecting two parallel TBs.

Figure 3. Plastic flow stability of rolled nanotwinned (NT) Cu foils. (a–b) Histograms showing transmission electron microscope (TEM)-measured statistics of twin-lamellae thickness before and after rolling, respectively. Note: the disappearance of the twins with thickness <2 nm after rolling. (c) TEM image and corresponding selected-area electron diffraction pattern showing the rolled NT microstructure and (d) higher magnification TEM image showing strain contrast along twin boundaries consistent with dislocation storage.^{Reference Anderoglu, Wang, Hirth, Hoagland, Misra and Zhang39}

For the twins that are retained after rolling, the measured {111} pole figures indicated preservation of the twin-plane orientation parallel to the rolling direction. The limited out-of-plane rotation of the twins can be interpreted in terms of symmetric slip, consistent with nanolayered composites where the interfaces act as effective barriers to slip transmission, thereby confining slip to the nanolayered channels. For compression normal to the TB, the resolved shear stress is constant for all active {111}〈110〉 slip systems, and plastic deformation can take place in a symmetrical mode on either side of TB, thereby suppressing net rotation of the (111) twin plane.^{Reference Anderoglu, Wang, Hirth, Hoagland, Misra and Zhang39,Reference Li, Wang, Misra, Zhang, Huang and Hirth44}

Strengthening from deformation of nanotwins in bulk metals

High strain rates or low temperatures may effectively suppress dislocation slip and facilitate deformation twinning in fcc metals. Copious deformation twins with nanoscale thickness were induced by DPD (with rates typically 10^1–3 s^–1) at low temperatures in a number of bulk metals and alloys with low or medium SFEs, including pure Cu,^{Reference Li, Tao and Lu45,Reference Li, Zhang, Tao and Lu46} Cu-Zn,^{Reference Xiao, Tao and Lu47} and Cu-Al alloys,^{Reference Zhang, Tao and Lu48} as well as austenitic steels.^{Reference Yan, Liu, Tao and Lu49–Reference Bouaziz, Barbier, Cugy and Petitgand51} The deformation twin thickness in Cu-Al alloys decreases (i.e., density of TBs increases) with a reduction in SFE induced by higher Al concentrations. For the same alloy, twin thickness becomes smaller when the sample is deformed at higher strain rates and lower temperatures. The twin thickness can be as small as 12 nm for Cu-Al alloys^{Reference Zhang, Tao and Lu48} and are on average 5 nm in Fe-25Mn steels^{Reference Wang, Tao and Lu50} under the current DPD conditions.

Strength and ductility of the deformation-induced NT austenitic grains in a 316L stainless steel have been characterized by means of tensile tests and nanoindentation, respectively.^{Reference Yan, Liu, Tao and Lu49,Reference Wang, Tao and Lu50,Reference Yan, Zhang, Wang, Tao and Lu52} Ductility of deformation-induced NT austenitic grains is considerable, especially for those after recovery annealing. A uniform elongation of about 5% with considerable work hardening has been observed in a DPD 316L sample after recovery annealing in which 55% in volume are NT grains.^{Reference Yan, Tao and Lu53} TEM observations^{Reference Yan, Tao, Archie, Gutierrez-Urrutia, Raabe and Lu54} showed that at small tensile strains (<5%), the NT grains deform homogeneously in conjunction with the surrounding statically recrystallized (SRX) grains without generating notable strain localization near their interfaces, distinct from the conventional dual-phase structures.

NT austenitic steels with a single-phase duplex NT/SRX structure (NT grain outlined by yellow dotted line, Figure 4a), exhibit enhanced strength-ductility synergy and higher work-hardening rates than conventional austenitic and dual-phase steels (Figure 4b). Tensile ductility increases almost linearly with the volume fraction of SRX grains, thereby offering a promising approach to strengthening austenitic steels and other alloys.^{Reference Lu, Yan, Wang and Tao55,Reference Lu, Lu and Suresh57} A combination of 1.0 GPa tensile strength with elongation-to-failure of 27% is achieved in the NT 316L stainless steel.

Figure 4. Strengthening by deformation nanotwins. (a) Bright-field transmission electron microscope (TEM) image of a nanotwinned (NT) austenitic grain (NT-γ; outlined by the yellow dotted line) embedded in the statically recrystallized grains in a dynamic plastic deformation 316L stainless-steel sample annealed at 750°C for 20 min.^{Reference Yan, Liu, Tao and Lu49} Inset shows a selected-area diffraction pattern of the nanotwin grain (circled). (b) Variations of uniform elongation with tensile strength for three austenite steels strengthened by NT grains (Fe-25Mn,^{Reference Wang, Tao and Lu50} 316L,^{Reference Yan, Liu, Tao and Lu49} Fe-22Mn-0.6C),^{Reference Lu, Yan, Wang and Tao55} in comparison with that of dual-phase (DP) steels and high-strength low-alloy (HSLA) steels. Reprinted with permission from Reference Reference Davies56. © 1978 Springer.

Outlook for future research

Several questions remain for the underlying physics of strengthening and softening mechanisms in NT metals. TB imperfections play an important role in nanoscale plasticity of NT metals, yet their role has been largely ignored in past studies. Future computational and theoretical studies should focus on modeling the intrinsic contribution of TB defects in dislocation–CTB interactions.

Also, we note that the strain hardening in NT NWs other than fcc type has not been studied extensively. Recent in situ experiments inside a TEM have shown that twinning is the dominant deformation mechanism in body-centered-cubic tungsten NWs.^{Reference Wang, Zeng, Weinberger, Zhang, Zhu and Mao58} In the future, it would be interesting to explore the strain-hardening behavior and mechanism in non-fcc nanostructures that contain internal TBs, introduced by either growth or predeformation.

GBs are one primary source of dislocations in NT polycrystals. Dramatic changes in mechanical behavior of bulk NT metals are expected as a function of composition, structure, and morphology of the GB network. Past evidence has proved that microalloying can significantly enhance grain refinement in nanocrystalline Cu alloys,^{Reference Vo, Schäfer, Averback, Albe, Ashkenazy and Bellon59} where atom segregation to GBs not only prevents grain growth, but also plays an important role as a strengthening precursor. This strategy could hold great promise for the fabrication of nanocrystalline NT alloys with enhanced strength and ductility.