**3.1. Grain growth under monotonic deformation**

Although NC materials show superior mechanical properties as compared to the coarsegrained counterpart, their application has been severely limited by their microstructural instability under the monotonic mechanical deformation [20–33]. For pure NC metallic materials, the grain coarsening process often occurs even at ambient temperatures [34–36]. Ames et al. reported on the observation of the room temperature grain growth in high-purity NC Pd with an initial grain size of about 10 nm [35]. They found a transition from an initially self-similar slow growth to abnormal grain growth. However, they argued that abnormal grain growth is a transient state since a monomodal grain size distribution was observed in the late stage of coarsening. Discontinuous grain growth in NC materials during the deformation processes seems to be a common phenomenon. Zhang et al. examined the effect of the temperature and sample purity on the grain coarsening behavior and found that many of the grains under the indenter have grown to several hundred nanometers while the unindented microstructure remains unchanged [20, 28], as shown in **Figure 4**. Due to the complex and large stress/strain field of the Vickers indenter is not yet known, the detailed mechanism of the grain growth is not known. However, the increased rate of growth at cryogenic than at the room temperature indicates that the growth is primarily mechanical, not diffusion-driven. In order to elucidate the effect of stress and strain on mechanically induced grain growth, Rupert et al. fabricated specimens with specially designed stress and strain concentrators to reveal the relative importance of these parameters on grain growth [24]. Statistical results of grain size in horizontal-hole specimens showed that grain growth occurred at both high strain region and high stress region. However, grain size was greater in the high stress region, indicating that the grain growth is driven by stress. Statistics results of grain size of angled-hole specimens demonstrated that grain growth was scaled with shear stress. Gianola et al. have investigated the tensile mechanical properties of 180-nm-thick NC Al films with grain size about 40 nm [22]. The specimens that exhibit high strength maintain their NC microstructure, the limited elongation, and the dramatic strain softening. By contrast, specimens that undergo discontinuous grain growth show intermediate strengths and the unexpected development of a region of extended plasticity. Statistical results of grain size outside of the deformed region of specimens that exhibited the grain growth are similar to the initial state indicating that the grain growth is directly tied to the applied stress or deformation in the sample [37].

**Figure 4.** TEM images of Cu sample after indentation tests (a) in a region away from the indents, and (b) inside an indent made at room temperature with a dwell-time of 30 min [20].

## **3.2. Grain growth under fatigue test**

**Figure 4.** TEM images of Cu sample after indentation tests (a) in a region away from the indents, and (b) inside an indent

made at room temperature with a dwell-time of 30 min [20].

148 Study of Grain Boundary Character

Grain growth is also observed during the cyclic deformation of NC materials [38–50]. Early fatigue experiments by Witney et al. on the NC Cu reported modest grain growth due to pullpull cyclic loading [38]. They found that the protrusions stick out on the order of a micrometer which is far greater than the initial grain size, and extend several microns parallel to the surface, similar to extrusions formed during the fatigue test of a coarse-grained Cu. Detailed TEM studies of NC Ni-Fe alloy under cyclic deformation demonstrates that the grain coarsening is accompanied by the fatigue crack growth. Stress concentration at the crack tip causes the lattice reorientation under the cyclic deformation [41]. GB dislocations play a critical role in grain rotation and in the formation of subgrain in larger grains. Boyce and Padilla have reported the fatigue crack initiation and growth behavior in NC Ni, Ni-Mn, and Ni-Fe alloy [42]. They found localized regions of grain growth during fatigue loading. Coarsened Ni grains did not favor any particular orientation, while Ni-0.5Mn coarse grains showed a <1 1 0> preferred orientation. Their observations also suggest that grain stability is an important factor affecting the crack initiation and propagation process in these NC alloys. Meirom et al. reported fatigueinduced grain coarsening during crack propagation in NC Pt films with a strong <1 1 1> texture [43, 44]. They found a clear evidence of increased grain size in the crack wake and ahead of the crack tip. Coarsened grains underwent a nearly one order of magnitude increase in size compared with the as-received one. They also found that many of the grain boundaries in the Pt films are "low-angle" in character and the grain coarsening by the annihilation of low-angle GB through the dislocation slip near the crack tip [43, 44]. Recently, Zhang et al. investigated the fatigue behavior of 100-nm-thick NC Cu film on a polymer substrate [49]. They found that

**Figure 5.** Microstructure of Cu films (a) as-deposited (AD) and (b) annealed (AN). (c and d) Statistical results of the grain size of the AD and the AN Cu films before and after fatigue test. Microstructure of Cu films after fatigue test (e) AD and (f) AN [49].

the mean grain size of both the as-deposited and annealed Cu samples increase after the fatigue test, as shown in **Figure 5**. However, the grain growth is greatly suppressed in the annealed NC Cu film, which leads to the enhanced resistance to the fatigue cracking as compared with that of the as-deposited one. The enhanced fatigue strength of Cu film after annealing may be related to the GB structure readjustment during the annealing process.
