Plastic deformation mechanisms in nanocrystalline columnar 2007. 9. 20.¢  Plastic...

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  • Plastic deformation mechanisms in nanocrystalline columnar grain structures

    Diana Farkasa and William A. Curtinb a Department of Materials Science and Engineering, Virginia Tech, Blacksburg, VA 24061, USA

    b Division of Engineering, Brown University, Providence, RI 02912, USA

    Elsevier use only: Received date here; revised date here; accepted date here

    Abstract

    We present an atomistic study of the plastic deformation mechanisms occurring in columnar structures of nanocrystalline Ni. The samples are constructed with grain boundaries characterized by random tilt misorientations around a common type axis. All samples contain the same 36 grain polycrystalline microstructure, with grain sizes ranging from 4 to 20 nm in order to isolate size effects on the deformation mechanisms. Tensile deformations up to 8% were simulated and the strain stress curves observed for these samples show grain size effects in both the elastic and plastic portions. An inverse Hall-Petch effect is observed for the nominal stress at a fixed strain, but disappears when the grain-size-dependent elastic modulus is used to construct an 0.5% offset yield stress. Both dislocation emission from the grain boundaries and grain boundary accommodation of plasticity are observed. Dislocation emission comes largely from pre-existing dislocation-like structures in the grain boundaries, and increases rapidly for grain sizes > 4 nm. However, the number of dislocations per unit length of grain boundary saturates to a constant value at large grain sizes, indicating a fixed density pre-existing sources in the grain boundaries. A simple model wherein dislocation emission is prohibited within a small distance from grain triple junctions accounts for the overall density versus grain size. Grain boundary sliding was observed in the same regions of the microstructure in all grain sizes, and to approximately the same degree. A simple model accounting for both dislocations and sliding is consistent with the observed trends in plastic strain versus grain size. The implications of these observations for more realistic three dimensional samples are briefly discussed. © 2001 Elsevier Science. All rights reserved

    Kewords: Dislocations, grain boundaries, deformation. PACS: Type your PACS codes here, separated by semicolons ;

  • Submitted to Elsevier Science 2

    1. Introduction The mechanical behavior of nanocrystalline materials has been the subject of extensive research in recent years. The main observation prompting these studies is the dramatically increased yield strength due to the Hall–Petch relation [1]. However, below a critical grain size, the conventional dislocation slip mechanism does not operate and the yield stresses decrease with decreasing grain size, as shown by several simulation studies [2-4]. Computer simulation in general provides a level of detail regarding the deformation mechanisms operating in metallic materials that is not attainable using experimental techniques [5]. In previous work by several investigators fully three dimensional finite temperature molecular dynamics calculations have been performed for grain sizes up to 40 nm. Generally, these data show a crossover in deformation mechanism from dislocation mechanisms at larger grain sizes to grain boundary deformation mechanisms at smaller grain sizes [2,4]. There are several rationalizations of this crossover that take into account various ways in which the grain size can influence the relative importance of these two mechanisms, ranging from assumptions that dislocation emission is easier from grain boundaries in the case of larger grain sizes [6] to the fact that grain boundary sliding can be easier at smaller grain sizes, with a grain size dependence of 1/d [7]. The crossover has also been linked to the length scale of dislocation splitting [3]. The details of the processes of grain boundary sliding are not well understood and there is no quantitative measure of the ease of dislocation emission from grain boundaries or the sliding process. Van Swygenhoven et al [8] have proposed that the grain boundary re-accommodates after the emission of dislocations and that the process occurs through the migration of free volume. The details of the dislocation emission process are very difficult to grasp in 3D samples, as is the process of grain boundary sliding. Detailed simulations can be performed in the columnar grain geometry in reasonable computing times for relatively large grain sizes. In addition, the columnar grain structure makes visualization much easier and analysis of the various mechanisms of plastic deformation is possible without the complications of the fully 3D configuration. Although the columnar grain structure introduces specific constraints to the overall deformation behavior of the sample, it does yield information on how grain size can affect the various deformation mechanisms. In particular, in order to understand the behavior of nanocrystalline materials in general it is important to understand how very small grain sizes affect the plastic deformation processes of dislocation emission/ propagation and grain boundary sliding. The purpose of the present work is to use the simple geometry of columnar crystals in order to study aspects of the dislocation emission process and the grain boundary sliding process, and their corresponding effects on the stress strain curves. We apply molecular statics [9] to study samples with many (36) grains in a columnar structure with common axis and a constant microstructure to investigate a reasonable statistical distribution of grains and boundaries and a systematic analysis of changes with grain size with no other changes in the simulations. We find increasing dislocation activity with increasing grain size, but with the dislocations per unit grain boundary length saturating at large grain sizes. We also observe grain boundary sliding at all grain sizes, largely independent of the grain size. We relate these observations to features of the measured stress-strain curves through a simple model that qualitatively accounts for the observed plastic strains and predicts an inverse-Hall-Petch regime at small grain sizes.

    2. Methodology

    The initial atomic configurations are generated using a Voronoi construction, as described in detail in previous simulations [2]. The columnar grains in the sample are generating by using a common [110] axis for all grains and a random rotation angle around this axis for the various grains. The samples contained 36 grains with average grain sizes of 4 to 20 nm. Periodicity is maintained in all directions. The periodicity

  • Submitted to Elsevier Science 3

    along the [110] axis common to all grains is kept at the lattice periodicity along that direction. The resulting samples contain up to about one quarter million atoms, for grain sizes of 20 nm. The present simulations utilize an EAM potential for Ni that is based on first principle calculations [9]. The potential was developed to reproduce not only many equilibrium lattice and defect properties of fcc Ni, but also the predictions of ab-initio LAPW calculations for metastable phases for Ni. The latter calculations span a wide range of configurations far from equilibrium and the transferability of this potential to situations very far from equilibrium is therefore very good. This is an important consideration for large plastic deformation simulations, since regions such as dislocation cores can be in configurations that are very different from equilibrium lattice situations. After their initial creation, the samples were fully relaxed using a conjugate gradient technique, including simultaneous energy minimization with respect to the total sample volume. The grain boundaries present in samples generated in this manner have been fully characterized in previous work [11]. A large degree of structural coherence is observed across most of the grain boundaries present, in spite of the fact that the orientations of each grain and grain boundary location are the result of random selection. The samples of different grain sizes and the same number of grains were constructed with the same misorientations and grain boundary planes to facilitate comparison and isolate particular effect of the grain size. The grain boundary structures themselves are independent of grain size and it is only the extent of grain boundary material that is different in the samples with different grain sizes. As shown in our previous work there is no tendency for amorphization in the boundary region. The relaxed configuration is used as a starting configuration in the molecular statics technique to study the response to an applied strain that mimics uniaxial loading. For the visualization of dislocations we primarily use the local stress tensor (multiplied by the atomic volume) calculated at each atom, which also provides information on the overall state of stress of the sample corresponding to the imposed strain. We use contour plots of the hydrostatic stress to show the location of the grain boundaries and the dislocations that are emitted in the plastic regime, with dark areas representing compression and light areas representing tension. Figure 1a shows the overall structure of the sample containing 36 grains of 10 nm average diameter. Figures 1b and 1c show detail of a low angle and a high angle grain boundary respectively, with atomic symbols corresponding to the positions of the atoms projected onto the {110} plane also shown. Note that this visualization technique allows for the clear identification of the individual dislocations that compose the low angle grain boundary. The