Dimples on Nanocrystalline Fracture Surfaces As Evidence for Shear Plane Formation

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Science  06 Jun 2003:
Vol. 300, Issue 5625, pp. 1550-1552
DOI: 10.1126/science.1084284


Tensile experiments of fully dense nanocrystalline structures with a mean grain size of less than 100 nanometers demonstrate a considerable increase in hardness but a remarkable drop in elongation-to-failure, indicating brittle behavior. However, dimple structures are often observed at the fracture surface, indicating some type of ductile fracture mechanism. Guided by large-scale atomistic simulations, we propose that these dimple structures result from local shear planes formed around clustered grains that, because of their particular misorientation, cannot participate in the grain boundary accommodation processes necessary to sustain plastic deformation. This raises the expectation that general high-angle grain boundaries are necessary for good ductility.

In nanocrystalline metals with mean grain sizes of less than 100 nm, the tensile stress-strain curves at room temperature show very limited uniform deformation and an early onset of necking, a manifestation of local deformation instabilities (1, 2). It is generally accepted that the limited uniform deformation can be ascribed to the limited dislocation activity in the nanosized grains. In coarse-grained polycrystals, plastic deformation is carried by dislocations, which are continuously nucleated at sources within the grains. In the nanocrystalline regime, the spatial confinement of the grains smaller than several tens of nanometers inhibits the operation of dislocation sources inside grains, limiting the dislocation activity and therefore the plastic deformation. In contrast, it is expected that in nanocrystalline metals, plastic deformation can be accommodated by the grain boundaries (GBs). For instance, the GB sliding process could be enhanced by increased atomic activity in GBs (3).

The onset of early necking, related to catastrophic failure, has often been attributed to flaws such as porosity, impurities, and high internal stresses (4, 5). However, large homogeneous strains are also not observed in fully dense nanocrystalline or near-nanocrystalline metals that do not contain considerably more impurities than their coarser grained counter-parts, such as nanocrystalline materials prepared by severe plastic deformation (6). Measurements of sample free volumes, using positron annihilation lifetime spectroscopy, show the presence of nanopores (10 to 20 vacancies) in all samples, independent of their synthesis technique (7). The location of these voids is not known with certainty because defects of this size cannot be directly observed by transmission electron microscopy (TEM). It has been suggested that they are located in GBs or triple junctions, and that they may eventually be filled with residual gases. Atomistic simulations of crack propagation in nanocrystalline materials demonstrate intergranular fracture, preceded by coalescence of microvoids ahead of the crack and very limited dislocation activity (8). Preexisting nanovoids along the crack path would certainly influence crack propagation and therefore the failure properties of the nanocrystalline material.

A dimple structure is often observed in the experimental fracture surface in a nanocrystalline metal and is typical of polycrystalline metals during ductile fracture. Figure 1 shows a scanning electron micrograph of the fracture surface after failure in a sample of nanocrystalline Ni made by high-pressure torsion (9). The figure shows a dimple structure at a minimum scale of about 300 nm. The mean grain size is 70 nm for this material, which resulted from a TEM distribution analysis. Similar dimple-like features with an average dimple size of several grain sizes have also been observed in electrodeposited nanocrystalline metals (5, 10). In polycrystals, a dimple fracture surface results from the formation and coalescence of microvoids along the fracture path, a process that involves a considerable level of localized plastic deformation as witnessed by sample necking. The dimple size and shape depend on the type of loading and the extent of microvoid coalescence but are not particularly related to the grain size. When a polycrystal fractures in a brittle way, the fracture path runs intergranularly and the three-dimensional (3D) nature of the grains can be observed in the fracture surface. The sizes of the dimple-like features observed on the fracture surface in nanocrystalline metals are, however, considerably larger than the grain sizes. This observation suggests that fracture mechanisms operate at a larger scale than the grain size and eventually involve collective grain activity. This is not in contradiction with the intergranular fracture observed in the atomistic simulations of Farkas et al. (8), because by virtue of sample geometry and size, general homogeneous plasticity does not occur before crack propagation. Therefore, eventual changes in the interfacial structure during deformation involving collective grain activity and the formation of shear planes extending over a number of grains will not be observed.

Fig. 1.

A scanning electron microscope picture of a high-pressure torsion nanocrystalline Ni fracture surface showing a dimple structure with dimples typically the size of several grains. This sample has an average grain diameter of 70 nm, as derived from TEM analysis.

The existence of local shear planes in nanocrystalline metals is experimentally very difficult to verify, except when shear planes extend over the whole sample size, in which case shear bands are observed on the surface and in the electron microscope (4, 11). The importance of local shear planes in the deformation mechanism of nanocrystalline metals has also been proposed in the model of Hahn and Padmanabhan (12). Shearing that involves groups of grains has been observed by means of specific deformation relief on the surface of Al samples with a mean grain size of 10 μm (13). A similar process was observed in submicrometer-sized Cu samples (14). However, the determination of the surface relief of grain structures in nanocrystalline samples has not been successful, which is probably due to the unavoidable surface oxidation that obscures the grain morphology. With its inherently atomic-scale resolution, atomistic simulation can provide additional insight into the nature of local shear planes that span several grain sizes within the nanocrystalline environment.

Massive parallel molecular dynamics (MD) computer simulations of nanocrystalline face-centered cubic (fcc) metals have been helpful in the understanding of GB-related phenomena. They (1517) have shown that at these small grain sizes, GBs can play an active role in the deformation process by operating as dislocation sources (18, 19) or promoting GB sliding triggered by atomic activity (3). To observe collective grain motion in a simulation, we had to reduce the constraints imposed by the 3D periodicity used in the simulation technique by simulating samples that contained many grains. Our present simulation contains 125 grains with randomly selected misorientations, representing a sample with a narrow grain-size distribution and a mean grain size of 6 nm (9) (Fig. 2). In Fig. 2, the symmetry classification (9) of the atoms has been color coded, allowing for the identification of the atoms inside the grain (gray fcc atoms) and defect atoms such as those in GBs. To enhance atomic activity in the GBs, we performed the MD simulation at a temperature of 800 K, which is 0.45 of the melting temperature (Tm). Because of the short simulation times inherent in the MD technique, GB migration by way of long-range diffusion is limited at 0.45 of Tm. A uniaxial tensile stress of 1.5 GPa is applied for 350 ps to obtain a strain-versus-time curve, with typical strain rates of 107 s–1. Such a high strain rate regime is several orders of magnitude greater than that seen in a typical experimental tensile test and is an accepted caveat of the simulation technique to reduce the time-scale problem inherent in the MD method (15, 17).

Fig. 2.

Computer-generated nanocrystalline Ni sample containing 1.25 million atoms, corresponding to 125 grains with an average grain diameter equal to6 nm. The GB structure is identified by the non-gray (non-fcc) atoms. Gray represents fcc atoms, red represents hcp atoms, green represents other 12-coordinated atoms, and blue represents non–12-coordinated atoms.

Cooperative grain activity was observed in this sample (20), and it has been shown that this leads to the formation of local shear planes that extend over several grain sizes. It was shown that three mechanisms contribute to the formation of local shear planes: (i) GB sliding–induced migration to form a single shear plane consisting of a number of collinear GBs, (ii) the coalescence via reorientation of neighboring grains that have an initially low-angle GB, and (iii) continuity of the shear plane by intragranular slip. Up to this point, we did not investigate the influence of special GBs on the collective processes. Because the simulated sample had random grain orientations, it contained all kinds of general high-angle GBs but also a few special GBs that are known to be resistant to sliding, such as GBs close to a perfect twin structure. Here, we demonstrate that during deformation, a number of neighboring grains can be collectively immobilized around such sliding-resistant GBs, creating several interfaces between grains that contribute and grains that offer resistance to plastic deformation.

Figure 3 shows a section of the simulated nanocrystalline sample. The tensile direction is along the red coordinate axis, and thus the viewing is approximately along the [011] simulation cell direction. The atoms are colored according to their local crystallinity, allowing for identification of the GB structure. Grains 110 and 7 form a grain boundary close to a perfect twin boundary (sigma = 3), as evidenced by the red [hexagonal close-packed (hcp)-coordinated] 111 planes forming structural units separated by regions of disorder. Atomic details of this type of GB are given in (21). It is known that twin GBs form an obstacle to GB sliding. The arrows in the surrounding grains indicate the direction (but not the magnitude) of the sliding, relative to the GB formed by grains 110 and 7. The relative sliding vector for a particular GB is determined by transforming the sample to the center of mass of one of the grains and then calculating the average atomic displacement vector between two stages of deformation. Thus grains 110 and 7 form a central structure around which several grains move cooperatively within the nanocrystalline structure. We observed other sections around the same central grains 110 and 7 that involve cooperative GB sliding. To elucidate the 3D character of this cooperative movement, Fig. 4 shows another section of the same sample that again involves parts of grains 110 and 7. The normal to the plane of this section of atoms is along the tensile direction and intersects Fig. 3 along the line indicated by the two black arrows in Fig. 3. For this figure, the displacement vectors are given, indicating atomic displacement between configurations before loading and at 2.2% plastic strain (3.7% total strain). Abrupt changes in color across GB regions indicate relative sliding between the concerned grains, and continuous changes in color within the grains represent internal strain. It is clear that the grains marked 110 and 7, together with at least five surrounding grains, form an entity inside the simulation cell that resists plastic deformation.

Fig. 3.

A section of atoms in which each atom is colored according to its local symmetry. This cut of atoms intersects those of Fig. 4 along the line indicated by the twoblack arrows. Grains 110 and 7 move collectively, as indicated by the white GB sliding vectors (white arrows). Together Figs. 3 and 4 demonstrate the 3D nature of the collective grain activity. The simulation bounding box and Cartesian coordinate axes are shown.

Fig. 4.

Section of the computer nanocrystalline Ni sample, where only the GB atoms (colored blue) are shown. For clarity, the fcc atoms are omitted. The atomic displacement vectors of all atoms in the cut are shown, where the color represents the magnitude of displacement (red represents displacements of 2.5 Å and higher). Grains 110 and 7 form a low-angle GB that is resistant tosliding, underpinning a nucleus of grains that move collectively under applied stress.

The central discovery of the present MD simulations of nanocrystalline structures is that because of the presence of GBs that are resistant to sliding, local shear planes are concentrated around their neighboring planes, creating a cluster of grains embedded in a sliding environment (Figs. 3 and 4). Thus, a plasticity length scale emerges on the order of several grain sizes corresponding to, and therefore providing an explanation of, the dimensions of the dimple structures seen in the experimental fracture surface. Fracture is not observed in simulations. This is partly a result of the subnano-second time-scale restriction and thus a limited amount of GB sliding, and also because the 3D periodic boundary used to simulate bulk conditions is expected to suppress such a global fracture event. Experimentally, the formation of such a local network of shear planes would lead to the formation of nanocavities by way of unaccommodated GB sliding, and eventually macroscopic fracture that would be additionally enhanced in the presence of preexisting voids. This result indicates that if nanocrystalline structures can be designed without the incorporation of many special GBs that are resistant to sliding, such as low-angle GBs and twin boundaries, GB sliding can be expected to take place more homogeneously, contributing to a larger uniform strain before fracture and thus to enhanced ductility. In such a microstructure, the dimple size would be on the scale of the grain size because fracture is expected to be intergranular (8). First indications for the beneficial effect of an increased content of high-angle GBs have been given in a recent work of Valiev et al. (22), where an increase in ductility was obtained when the fraction of high-angle GBs was increased by extensive equal-channel angular pressing processing beyond the saturation grain size.

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