Fracture of nanotwinned metals

Fracture is a common failure mode in nanostructured materials with ultrahigh strength. However, to date, there have been few reports on the fracture of NT metals. Here, we first present unique fracture behaviors related to coherent TBs (CTBs). Next, we review recent studies of the fracture of various NT specimens in bulk, thin-film, and nanopillar/nanowire forms or with hierarchically twinned structures. Finally, we introduce recent reports of the interaction between cracks and TBs.

In contrast to general GBs, CTBs exhibit remarkably unusual fracture behaviors due to their low energy and high symmetry. When an atomistically sharp crack lies on a {111} CTB, it cleaves in one of the 〈112〉 directions along the TB, indicating the intrinsic brittleness of TBs. However, the crack emits dislocations when propagating in the opposite direction. This directional anisotropy in brittle-ductile responses (Figure 2a) of CTBs has been demonstrated by atomistic simulations and theoretical analyses.^{Reference Cheng, Jin, Zhang and Gao36} A recent experimental study^{Reference Seita, Hanson, Gradecak and Demkowicz37} on the hydrogen-assisted fracture of a Ni-based superalloy showed that a CTB is more susceptible to crack initiation than general GBs in a hydrogen environment. This is thought to originate from enhanced dislocation activity along the CTB.

Figure 2.

Fracture of nanotwinned (NT) metals. (a) Directional anisotropy in brittle-ductile responses of a coherent twin boundary (CTB). Dark blue atoms have face-centered-cubic symmetry, light blue atoms have hexagonal close-packed symmetry, and atoms with other colors are disordered. Reprinted with permission from Reference Reference Cheng, Jin, Zhang and Gao36. © 2010 Elsevier. (b) Scanning electron microscope image of the fracture surface of NT Cu prepared by dynamic plastic deformation. Coarse/deep dimples are indicated by the solid circles, while fine/shallow dimples are highlighted by the dashed circle. Reprinted with permission from Reference Reference Qin, Lu, Tao and Lu11. © 2009 Elsevier. (c) Transmission electron microscope (TEM) image of crack bridging by nanoscale twins. Main crack is indicated by an arrow, and interfacial cracks (ICs) are marked. (d) TEM image showing the region ahead of a growing crack tip and TBs that appear highly dislocated. Dislocation walls are highlighted by the circle. (c–d) Reprinted with permission from Reference Reference Kim, Li, Gao and Kumar38. © 2012 Elsevier.

Qin et al.^{Reference Qin, Lu, Tao, Tan and Lu10,Reference Qin, Lu, Tao and Lu11} measured the fracture toughness of NT bulk Cu (with TB spacing λ = 40∼50 nm) prepared by DPD using three-point bending tests, and found that the fracture toughness increases with an increase in the volume fraction of nanoscale twins. They also observed three types of dimples on the fracture surface: (1) fine/shallow dimples with an average size of 4–6 μm (dashed circle in Figure 2b), (2) equiaxed dimples with a size of tens of micrometers, and (3) coarse/deep dimples with an elongated core at the bottom (solid circles in Figure 2b). The size of fine/shallow dimples is several times larger than the mean grain size of the specimen, similar to what is observed for nanocrystalline metals. However, the coarse/deep dimple is an unusual fracture characteristic in NT metals, and it is not observed in the fracture of nanocrystalline metals. Its formation is due to the presence of highly anisotropic NT bundles. The enhanced fracture toughness is primarily attributed to the formation of coarse/deep dimples. Singh et al.^{Reference Singh, Tang, Dao, Lu and Suresh12} observed increased fracture toughness with decreasing average TB spacing using two electrodeposited NT Cu specimens with equiaxed grains (with the same mean grain size d = 400–500 nm, but λ = 32–85 nm), which is a different size dependence as observed in nanocrystalline metals.^{Reference Lu, Lu and Suresh3} They also pointed out the important influence of the plastic anisotropy of nanoscale twins.

Kim et al.^{Reference Kim, Li, Gao and Kumar38} performed in situ TEM tensile testing on ultrafine-grained (UFG) Cu thin films with nanoscale twins and a thickness of ∼100 nm. They observed a nanoscale toughening mechanism whereby the crack is arrested by TBs and nanoscale twins serve as crack-bridging ligaments (Figure 2c).^{Reference Kim, Li, Gao and Kumar38} Kim et al.^{Reference Kim, Li, Gao and Kumar38} also performed relevant atomistic simulations that showed a large number of dislocations emitted from a crack interacted with TBs ahead of the crack tip, transforming clean CTBs into impenetrable dislocation walls. These dislocation walls can strongly resist crack propagation, leading to crack arrest and bridging. The transformation from TBs to dislocation walls is evidenced by the TEM image shown in Figure 2d.

Although this experimental study^{Reference Kim, Li, Gao and Kumar38} was conducted on thin-film samples, it reveals two important toughening mechanisms that might be operative in NT bulk samples. Specifically, crack bridging due to nanoscale twins might provide an explanation of the formation of coarse/deep dimples in NT bulk samples. Shan et al.^{Reference Shan, Lu, Minor, Stach and Mao39} conducted in situ TEM tensile experiments that showed the crack was deflected by TBs, resulting in a zigzag crack path when the thickness of the NT metal thin film was reduced to tens of nanometers. Recent molecular dynamics (MD) simulations^{Reference Zeng, Li, Lu and Zhu40} indicated that such zigzag cracking is due to screw dislocation-mediated local thinning ahead of the crack. Kobler et al.^{Reference Kobler, Hodge, Hahn and Kübel41} recently conducted in situ TEM tensile testing on a columnar-grained NT Cu thin film (with λ = ∼9 nm). They observed orientation-dependent fracture/deformation behaviors whereby when the tensile direction was parallel to the TBs, fracture occurred along the original CTBs and incoherent TBs (ITBs) formed during deformation; when the tensile direction was perpendicular to the TBs, plastic deformation was accommodated by detwinning and the formation of new grains.

Jang et al.^{Reference Jang, Li, Gao and Greer9} synthesized NT Cu nanopillars with diameters of 50–250 nm and λ = 0.6–4.3 nm and they performed in situ TEM tension tests on these specimens. They found that when the tensile direction was perpendicular to the TBs, the specimen failed due to cleavage fracture (a brittle fracture mode in which the cross section of the specimen remains unchanged at fracture) if λ > 3–4 nm; otherwise, the specimen failed due to necking, showing a significant reduction of the cross-section area prior to final fracture. They also performed MD simulations for Mode I crack propagation in quasi-3D samples (i.e., samples with a periodic boundary imposed in the thickness direction, and the thicknesses is usually much smaller than the other two dimensions) to reveal the mechanism behind this brittle-to-ductile transition.^{Reference Jang, Li, Gao and Greer9} The simulation results showed that when TB spacing was larger than a critical value, cleavage occurred along a TB due to the intrinsic brittleness of the TBs;^{Reference Cheng, Jin, Zhang and Gao36} otherwise, the stress field around the crack-tip induced dislocation nucleation on a neighboring TB, eventually giving rise to ductile fracture of the sample. Jang et al.^{Reference Jang, Li, Gao and Greer9} developed a theoretical model, based on the important insights from experiments and simulations, to predict the critical TB spacing for the brittle-to-ductile transition, with predictions consistent with experimental and simulation results.

Wang et al.^{Reference Wang, Sansoz, Huang, Liu, Sun, Zhang and Mao42} conducted in situ TEM tension tests on NT Au nanowires with diameters of 8–20 nm and λ = 0.7–5.6 nm, and they observed that as TB spacing decreased, the fracture strain of nanowires decreased. When the TB spacing was smaller than 2.8 nm, dislocations nucleated inside nanowires (but near TB-surface intersections) interacted with the adjacent TBs, leading to detwinning of neighboring regions. At high stress levels, strain localization occurred in the detwinned region, which induced nanowire failure with a relatively small fracture strain (7–10%). However, when TB spacing was much larger, dislocations nucleated from the free surface and then slipped on activated slip planes within the wide twin or matrix domains. Such dislocation plasticity contributes to sample failure with large fracture strain (∼30%). These behaviors are different from those observed in NT Cu nanopillars.^{Reference Jang, Li, Gao and Greer9} The difference may be attributed to three factors:^{Reference Wang, Sansoz, Huang, Liu, Sun, Zhang and Mao42} (1) Cu and Au have different stacking-fault energy curves and critical stress for dislocation nucleation; (2) the diameters of the investigated Cu nanopillars are approximately 2 to 12 times larger than those of the studied Au nanowires; and (3) these Au nanowires have special surface facets, different from the relatively smooth circular surfaces of the investigated Cu nanopillars.

Recently, Yuan and Wu^{Reference Yuan and Wu43} investigated the fracture behavior of NT Cu with hierarchically twinned structures using MD simulations on quasi-3D samples. For the simulated samples, TB spacing in the first-order twin varied from 10.44–20.87 nm, whereas the TB spacing in the second-order twin was in the range of 2.09–10.44 nm. The simulation results showed that due to the presence of second-order twins, the cracks on TBs in the first-order twins became blunt due to dislocation emission, or due to coalescence with nanovoids nucleated ahead of the crack tip, even if the cracks originally propagated via cleavage along a single TB. The results also indicated that for fixed first-order TB spacing, the fracture toughness could be improved by decreasing second-order TB spacing. A theoretical model^{Reference Li, Ni, Soh and Wu44} was proposed to further explain the enhancement of fracture toughness in metals with hierarchically twinned structures. The results revealed that the detwinning in the second-order twins to some extent facilitates strong crack blunting,^{Reference Li, Ni, Soh and Wu44} and there exists an optimized second-order TB spacing corresponding to maximum fracture toughness.^{Reference Li, Ni, Soh and Wu44}

To date, a clear and comprehensive understanding of the interaction between cracks and TBs is still lacking. Recent high-resolution TEM observations in NT Ag thin films^{Reference Liu, Wang, Gong and Mao45} revealed the detailed process of crack penetration across a twin with λ = ∼4 nm. This process involves alternating crack-tip blunting, crack deflection, and TB migration. These deformation mechanisms are associated with the types of dislocations emitted from crack tips and the distance between crack tips and TBs. Zhou and Gao^{Reference Zhou and Gao46} performed full 3D MD simulations of dislocation interactions with TBs in front of a crack tip in NT Cu (with λ = 10 nm). They found that the dislocation-TB interaction leads to the formation of necklace-like dislocations with unit jogs (i.e., a dislocation segment produced by interaction between two dislocation lines) on TBs. This jogged dislocation motion requires overcoming the lattice friction on unit jogs.^{Reference Zhou and Gao46} This new type of TB-related dislocation mechanism may play an important role in deformation near crack tips in NT metals.

Fatigue of nanotwinned metals

Fatigue reflects the mechanical response of materials under cyclic loading. Fatigue properties of materials are central to the design and application of materials in engineering. Limited information is available on the fatigue properties of NT metals.

Singh et al.^{Reference Singh, Tang, Dao, Lu and Suresh12} conducted the earliest study on low-cycle fatigue of a NT metal. They studied tension–tension cyclic loading of two electrodeposited NT Cu specimens with equiaxed grains (with the same mean grain size d = 400–500 nm, but λ = 32–85 nm) and one UFG twin-free counterpart. Figure 3a shows the variation of the fatigue crack growth rate da/dN, where a is the crack length and N is the number of load cycles, as a function of stress intensity amplitude ΔK from the experimental measurements.^{Reference Singh, Tang, Dao, Lu and Suresh12} This result indicates that for a fixed grain size, the fatigue resistance of NT metals can be enhanced by increasing the twin density (i.e., decreasing TB spacing). An estimation of the crack-tip opening displacement (CTOD) versus TB spacing suggested that significantly reduced CTOD with smaller TB spacing contributes to the enhanced fatigue resistance.^{Reference Singh, Tang, Dao, Lu and Suresh12}

Figure 3.

Fatigue of nanotwinned (NT) metals. (a) Variation of log₁₀da/dN versus log₁₀ΔK of fatigue testing on ultrafine-grained (UFG), LDNT, and HDNT Cu. Note: LD, low-density; HD, high-density. Reprinted with permission from Reference Reference Singh, Tang, Dao, Lu and Suresh12. © 2011 Elsevier. (b) S–N curves (i.e., stress versus number of cycles) for NT, UFG, and coarse-grained Cu. Reprinted with permission from Reference Reference Shute, Myer, Xie, Li, Barbee, Hodge and Weertman13. © 2011 Elsevier. (c) Transmission electron microscope image of detwinned region with the formation of dislocations. New dislocation structures are bounded by straight walls at an angle to the original twin boundaries (TBs), as indicated by the arrows. Reprinted with permission from Reference Reference Shute, Myer, Xie, Li, Barbee, Hodge and Weertman13. © 2011 Elsevier. (d) Fatigue cracking mechanism of twinned bicrystals of Cu with different TB orientations. S1, S2, and S3 represent three slip modes. Note: SB = slip band. Reprinted with permission from Reference Reference Li, Zhang, Zhang, Wang and Zhang52. © 2014 Macmillan Publishers Ltd.

Shute et al.^{Reference Shute, Myer, Xie, Li, Barbee, Hodge and Weertman13} also performed tension–tension fatigue tests on magnetron sputtered NT Cu with columnar grains (with λ = 35 nm), but found that the S–N curve (i.e., stress versus number of cycles) of the NT specimen was remarkably similar to that of UFG specimens^{Reference Shute, Myer, Xie, Li, Barbee, Hodge and Weertman13} (as shown in Figure 3b). The TEM image in Figure 3c shows that some original columnar NT structures were destroyed due to detwinning during fatigue, with the formation of dislocation structures. As a result, the detwinned regions became softer compared to the neighboring twinned regions. The similarity of the S–N curves between the NT and UFG specimens is thought to arise from the crack nucleation/initiation from the boundary of the two columns and the intersection between detwinned soft regions and the free surface.

Yoo et al.^{Reference Yoo, Bolesb, Liu, Zhang, Schwaiger, Eberl and Kraft47} recently performed high-cycle fatigue experiments on magnetron sputtered 20-µm-thick columnar-grained NT Cu foils (with λ = 25 nm), where CTBs were oriented parallel to the surface. Quantitative characterization of the final twin density after fatigue-induced detwinning showed a strong coupling to the applied strain amplitude.^{Reference Yoo, Bolesb, Liu, Zhang, Schwaiger, Eberl and Kraft47} Due to the experimental setup, detwinning started near the cantilever fixture from the surface, allowing for extrusion formation and crack initiation at the surface.^{Reference Yoo, Bolesb, Liu, Zhang, Schwaiger, Eberl and Kraft47} The cracks started to extend perpendicular to the surface in a Mode I orientation, until the interaction with a CTB led to crack branching as well as diversion into a Mode II orientation,^{Reference Yoo, Bolesb, Liu, Zhang, Schwaiger, Eberl and Kraft47} disabling the cracks altogether. This is in contrast to the tension–tension experiments conducted by Shute et al.,^{Reference Singh, Tang, Dao, Lu and Suresh12} as local softening would not lead to uncontrolled detwinning followed by plastic localization and failure. Such “disabled” cracks could be found at various locations while detwinning continued below and around the cracks.^{Reference Yoo, Bolesb, Liu, Zhang, Schwaiger, Eberl and Kraft47} This hints at the possibility of disabling cracks by using CTBs to divert a Mode I crack into a Mode II configuration.

Zhou et al.^{Reference Zhou, Li and Chen48} most recently performed a series of atomistic simulations for the cyclic deformation of NT Cu (with d = 10–20 nm and λ = 0.83–5.01 nm). They observed from the atomistic simulations that the fatigue cracks in NT samples advanced by alternating crack-tip blunting and resharpening due to dislocation emission and slip. This is distinct from the fatigue mechanism in the twin-free counterparts, where the fatigue crack grows by linking the nanovoids ahead of the crack tip. The simulations also revealed that detwinning dominates plastic deformation during fatigue of NT samples with a high density of twins, which is consistent with observations from the fatigue experiments.^{Reference Shute, Myer, Xie, Li, Barbee, Hodge and Weertman13}

A combination of the experimental^{Reference Singh, Tang, Dao, Lu and Suresh12} and simulation results^{Reference Zhou, Li and Chen48} indicates that as the twin density (quantified by d/λ) increases, the fatigue resistance of NT metals is substantially enhanced. Zhou et al.^{Reference Zhou, Li and Chen48} showed that stable fatigue crack growth conforms to Paris’s Law (i.e., a power law ${{da} \over {dN}} = C{\left( {{\rm{\Delta }}K} \right)^m}$, where C and m are material constants) with an exponent m∼4 by analyzing the relationship between fatigue crack growth rate da/dN and the amplitude of applied stress intensity factor ΔK from experiments and simulations. Based on the damage accumulation model, they also derived the following equation^{Reference Zhou, Li and Chen48} in the form of Paris’s Law:

(1)$${{da} \over {dN}} = {{5{\rm{\pi }}} \over {96{\rm{\alpha }}\sigma _{\rm{y}}^2K_{{\rm{IC}}}^2}}{\left( {{\rm{\Delta }}K} \right)^4}$$ ,

where σ_y is the yield strength, K _IC is the fracture toughness under quasistatic loading, and α is a material constant (approximately 3000 for Cu). The prediction of the constant coefficient in Paris’s Law from Equation 1 is in agreement with experimental measurements.^{Reference Singh, Tang, Dao, Lu and Suresh12}Equation 1 implies that NT metals have stronger fatigue resistance because of their higher strength and fracture toughness than their twin-free counterparts.

Chowdhury et al.^{Reference Chowdhury, Sehitoglu and Rateick49,Reference Chowdhury, Sehitoglu and Rateick50} recently developed a combined atomistic and mesoscopic model to highlight the role of cyclic dislocation–TB interactions and the irreversibility of cyclic dislocation slip during fatigue crack propagation in NT metals. Based on the irreversibility of dislocation slip from crack tips during the cyclic flow, they also predicted an effective threshold of stress intensity factor range for fatigue and noted that the threshold level of short cracks was significantly affected by nanoscale twins.^{Reference Chowdhury, Sehitoglu and Rateick50}

A high density of TBs can enhance fatigue resistance, but a TB is not always strong enough to resist fatigue cracking. Some experimental observations^{Reference Qu, Zhang, Wu, Zang and Zhang51–Reference Stein, Cerrone, Ozturka, Lee, Kenesei, Tucker, Pokharel, Lind, Hefferan, Suter, Ingraffea and Rollett53} showed that fatigue cracks can initiate from CTBs. Li et al.^{Reference Li, Zhang, Zhang, Wang and Zhang52} systematically investigated the cyclic deformation of Cu bicrystals with a single TB, and revealed the fatigue cracking behavior of TBs strongly depended on TB orientation with respect to the loading direction. As illustrated in Figure 3d, when the loading direction is parallel or perpendicular to the TB (Regimes I or V in Figure 3d), the fracture crack always prefers to nucleate along the slip band (SB); when the loading direction is inclined to the TB (Regimes II, III, or IV in Figure 3d), the fatigue crack first initiates from the TB. Essentially, this fatigue crack behavior is associated with the activation of different slip modes. This work provides important implications for designing engineering materials with optimized interfacial fatigue properties. It is to be noted that in the above studies,^{Reference Qu, Zhang, Wu, Zang and Zhang51–Reference Stein, Cerrone, Ozturka, Lee, Kenesei, Tucker, Pokharel, Lind, Hefferan, Suter, Ingraffea and Rollett53} the TB spacing is around several microns, and sometimes even larger. If the TB spacing is reduced below 100 nm, whether the crack can still initiate from TBs during fatigue remains unknown. The fatigue properties of nanoscale twins clearly require further detailed studies, where in situ observations of fatigue crack initiation around nanoscale twins are key.

Creep of nanotwinned metals

In contrast to fracture and fatigue, there is much less research on the creep properties of NT metals. Bezares et al.^{Reference Bezares, Jiao, Liu, Bufford, Lu, Zhang, Kulkarni and Asaro14} performed cyclic nano- and microindentation creep measurements on NT Cu and Ag. Figure 4a shows the indentation creep of electrodeposited NT Cu under a peak load of 1700 μN.^{Reference Bezares, Jiao, Liu, Bufford, Lu, Zhang, Kulkarni and Asaro14} The creep strains became saturated after tens of seconds, which is 2–3 orders of magnitude shorter than the typical creep time for nanocrystalline Cu.^{Reference Bezares, Jiao, Liu, Bufford, Lu, Zhang, Kulkarni and Asaro14} It was also found that during creep, the hardness of NT Cu (with λ = 40 nm) initially decreased and then tended to saturate after hundreds of seconds.

Figure 4.

Indentation creep of nanotwinned (NT) metals. (a) Displacement versus time during indentation of electrodeposited NT Cu under a fixed load of 1700 μN. (b) Microindentation creep performed on NT Cu, Ag, and nanocrystalline Cu. Note: ED, electrodeposited; MS, magnetron sputtered. Reprinted with permission from Reference Reference Bezares, Jiao, Liu, Bufford, Lu, Zhang, Kulkarni and Asaro14. © 2012 Elsevier.

Figure 4b summarizes the microindentation creep results for four samples: electrodeposited NT Cu (λ = 30 nm), nanocrystalline Cu (d = 45 nm), magnetron sputtered NT Cu (λ = 7 nm), and Ag (λ = 9 nm). The hardness reduced over a considerable indenter dwell-time period with an approximately linear relationship between hardness and the logarithm of time. NT Cu exhibits a lower reduction rate of hardness than nanocrystalline Cu, indicating that NT metals have enhanced creep and structural stability compared to their twin-free counterparts. For nanocrystalline metals, the reduction in hardness is attributed to the rapid growth of nanosized grains.^{Reference Zhang, Weertman and Eastman54} However, for NT metals, the mechanisms responsible for the reduction in hardness during creep remain unknown. It should be noted in Figure 4b that the magnetron sputtered NT Cu exhibited better stability than the electrodeposited NT Cu, due to the much thinner twin lamellae of magnetron sputtered NT Cu.

Jiao and Kulkarni^{Reference Jiao and Kulkarni55} recently conducted a series of MD simulations for high-temperature creep in polycrystalline NT Cu (with d = 10.3 nm and λ = 0.6–5.0 nm). The simulation results showed that the creep stability significantly depended on TB spacing, and the creep strain rate had a power–law relationship with the applied stress, where the stress exponent increased from 1 to ∼5 as the applied stress increased. It was observed that in NT samples with smaller TB spacing, TB migration due to dislocation nucleation from TB–GB intersections was a controlling mechanism during creep at high stress levels. This mechanism is distinct from the observed GB diffusion and sliding during the creep of nanocrystalline metals.

It is well known that for metals with low stacking-fault energy, continuous radiation exposure can induce noticeable void growth and swelling in materials.^{Reference Chen, Yu, Liu, Shao, Wang, Kirk, Wang and Zhang56} Chen et al.^{Reference Chen, Yu, Liu, Shao, Wang, Kirk, Wang and Zhang56} conducted a recent experimental study and reported that NT Cu with preexisting nanovoids could efficiently absorb radiation-induced defects (such as point defects and dislocation loops), leading to the elimination of nanovoids. This self-healing capability arises from the underlying behavior whereby networks consisting of a high density of CTBs/ITBs are able to rapidly transport the radiation-induced defects to nanovoids. This study suggests that NT metals with initial nanovoids might have good creep stability in extreme irradiation environments.

Summary

This article presented a brief survey of recent studies on the fracture, fatigue, and creep of NT metals. Experimental and computational studies have shown that NT metals exhibit remarkable fracture toughness, strong fatigue resistance, and good creep stability in comparison to their twin-free nanocrystalline or UFG counterparts. We discussed some underlying deformation mechanisms responsible for these unusual mechanical properties of NT metals, placing emphasis on the complex interactions among dislocations, cracks, and TBs.

Despite the rapid progress made in recent years, a fundamental understanding of the damage/failure process in the fracture, fatigue, and creep of NT metals is still in its infancy. There are unsolved problems that are crucial for understanding the failure of NT metals, such as (a) How do coarse/deep dimples form during fracture of NT metals?; (b) How do cracks interact with TBs during fracture or fatigue in NT metals?; (c) How do crack-TB interactions depend on TB spacing and TB orientation?; and (d) What is the mechanism behind the hardness reduction of NT metals during indentation creep? In order to improve our understanding of, and to enhance the mechanical properties of NT materials, there is an urgent need to carry out further experimental and computational investigations on fracture, fatigue, and creep of NT metals.