Blocking effect of twin boundaries on partial dislocation emission from void surfaces
© Zhang et al; licensee Springer. 2012
Received: 3 November 2011
Accepted: 2 March 2012
Published: 2 March 2012
Recent discovery that nanoscale twin boundaries can be introduced in ultrafine-grained metals to improve strength and ductility has renewed interest in the mechanical behavior and deformation mechanisms of these nanostructured materials. By controlling twin boundary spacing, the effect of twin boundaries on void growth is investigated by using atomistic simulation method. The strength is significantly enhanced due to the discontinuous slip system associated with these coherent interfaces. Atomic-scale mechanisms underlying void growth, as well as the interaction between twin boundaries and the void, are revealed in details.
Keywordstwin boundaries void dislocations strength molecular dynamics simulations
Ultrahigh strength and large elongation to failure can be concurrently achieved in nano-twinned (NT) polycrystals [1–3]. The rate-controlling process governing the plastic deformation in these materials is mediated by coherent twin boundaries (TBs). It is known that TBs not only provide barriers to dislocation motion but also sustain the strain hardening capability of the specimens without early shear localization [4, 5].
Voids are crucial point defects that are inevitable during fabrication and deformation of materials. Nanocrystals with voids have many unique properties, including lattice orientation sensitivity [6–8], size-dependent yielding stresses [6, 9, 10], void volume fraction-dependent elastic modulus , and void shape effect on stress concentration . Considerable efforts have been devoted to investigate the nucleation, growth, and coalescence of voids. Specifically, void growth has been proven to be governed by a dislocation-emission-based mechanism . It is found that dislocation loops carrying outward flux of matters are nucleated at void surfaces [9, 13]. Simulations performed by Seppala et al. are focused on void coalescence, involving both single and double voids cases . It is revealed that the onset of void coalescence occurs when the intervoid ligament distance reaches approximately one void radius. However, the deformation mechanisms associated with voids in nanostructured crystals with internal boundaries, especially coherent TBs, are yet to be understood.
In the present work, molecular dynamics simulations are performed to investigate the process of void growth in NT crystals. It is shown that the motion of surface dislocations emitted from void defects is strongly confined by surrounding TBs, resulting in higher strengths. Atomistic analysis is performed to illustrate the interaction between TBs and voids.
The embedded atom method potential  for Cu was applied. Periodic boundary conditions were imposed on all three dimensions. The time step was chosen as 1 fs. For the precise control of temperature and pressure, Nose-Hoover thermostat and barostat were adopted [16, 17]. The crystal was first annealed at 300 K and 0 pressure for 100 ps to reach equilibrium. After relaxation, uniaxial tension along the Y  direction (indicated by the blue arrows in Figure 1) with a constant strain rate of 1 × 108 s-1 is performed on the crystal during which the stress components, σxx and σzz, are kept as zero.
Common neighbor analysis [18, 19] was used to clarify defects. The coloring scheme for various local structures is as follows: gray for face centered cubic (fcc) atoms, red for hexagonal close packed atoms, and green for atoms with other local crystal structures.
Results and discussion
Dependence of yielding stress on void size
TB strengthening behavior
To demonstrate the blocking effect of twin planes, another set of tension simulations were performed on Cu samples with various void sizes but this time, two parallel twin planes with a spacing of λ = 25 nm were added into each sample. As shown in Figure 2b, the samples deform elastically at small strains. Sudden strain excursions associated with surface dislocation nucleation are observed, indicating the onset of yielding, at stresses about the same level as those corresponding to the yielding peaks in Figure 2a. Upon further loading, the stresses continue to rise with the increasing strain, in contrast to the stress drops observed in Figure 2a after the emergence of the first stress peaks, implying that the dislocation propagation may be hindered by the twin planes nearby.
Mechanisms of yielding and TB strengthening
A lot of efforts have been devoted to understand the mechanisms of TB interactions with different types of dislocations [2, 5, 20, 21]. A detailed discussion on this topic is not within the scope of this paper. We emphasize here that the strength of the NT material, which is reflected by the first peaks on the stress-strain curves in Figure 2b, is actually determined by the strength of the twin planes against dislocation penetration. This is demonstrated by Figure 5f, which is captured on the occasion of the first peak of the stress-strain curve. At that time, there is an obvious sign of dislocation nucleation around the TB segments intersected by the deformed twin nucleus, leading to slipping either in the crystal or along the twin planes (indicated by arrows in Figure 5f). These dislocation activities clearly indicate that the twin planes have reached their limitation of strengthening. In other words, dislocation barriers have become dislocation sources since then. The sudden stress drops in Figure 2b is another evidence of this transition.
Dependence of void yielding and sample strength on TB spacing
The above results make it clear that the yielding stress of a crystalline metal embedded with nanoscale voids depends mainly on the size of these voids but much less on the surrounding coherent TBs. The strength of a Cu sample, on the other hand, can be significantly enhanced by introducing coherent TBs into the crystal. It is also shown that the intrinsic strength of an individual twin plane imposes limitation on the blocking effects of the embedded TBs. The influence of the spacing between two twin planes, however, seems to be less significant, as demonstrated in Figure 7. It is worth noting that although the change in TB spacing leads to unnoticeable fluctuations in materials strength, further investigation is still required to understand the underlying atomistic mechanisms especially in samples with larger dimensions and higher densities of nanoscale voids.
This work is supported by the National Natural Science Foundation of China (no. 50890174, 11172264), the Program for New Century Excellent Talents in University (NCET-08-0480), Zhejiang Provincial Natural Science Foundation of China (no. R6100325), the Fundamental Research Funds for the Central Universities, and the Science and Technology Innovative Research Team of Zhejiang Province (no. 2009R50010). HFZ acknowledges the financial support from the Scholarship Award for Excellent Doctoral Student granted by the Ministry of Education. Large scale simulations were performed on Dawning 5000A, Shanghai Supercomputer Center.
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