A model to explain extensive superplasticity in polycrystalline materials

Abstract

Superplastic behavior has been observed in a variety of metallic systems during high temperature deformation. The possibility of superplastic flow in nanocrystalline materials at low temperatures is reported in molecular-dynamics simulations [1, 2] and in experimental evidences [3–6]. Karch et al. [3] observed that conventional brittle ceramics became ductile at low temperature if a polycrystalline ceramics was generated with a crystal size of a few nm. Lu et al. [4] showed recently that bulk, highly pure nanocrystalline copper could be strained at room temperature by up to 5,000% without strain hardening and changing grain size. These experimental results indicate that conventional dislocation mechanisms are not responsible for the large strain and that the extensive superplasticity seems to originate from grain boundary (GB) diffusion (Coble creep). This novel behavior, however, could not be explained by present models and theories. Lee [7] proposed a model to show grain rearrangement process by Coble creep and GB migration, which is shown in Fig. 1 from a to e. The model consists of hexagonal single-phase grains of uniform size and shape loaded in tension (Fig. 1a). On first loading, the GB diffusion fluxes flow (see Fig. 2a) causing the grains to elongate along the stress axis (Fig. 1b). At a strain e = 0.55, the grains become diamond-shaped (Fig. 1c). At this point the four-grain junctions become unstable. GB migration (with no additional strain) will return the diamond-shaped grain to initial one, and switch grain neighbors with a rotation of 30 (Fig. 1e). The Lee model shows a plausible way to switch grain neighbors, resulting in a strain e = 0.55 while retaining the equiaxed grain structure. However, Lee model fails to give a reasonable physical path for a continuous elongation beyond the 55% strain, and therefore can not be used to explain extensive superplasticity. To go beyond the first grain switching event and account for the existence of a sequence of such switching events we look at the microstructure tilted by 30 (or –30 ) as shown in a¢. Although the grain structure after first grain switching (Fig. 1e) is a ‘‘dead end’’ for the model operating along the vertical direction, the grain structure in the tilted direction is equivalent to a. Therefore, the Lee model can operate in the slant loading direction as described by several representative steps a¢, b¢ and e¢, corresponding to steps a, b and e, respectively. At step e¢, the arrangement of grains returns to initial one as shown in Fig. 1a, but switches their neighbors with a resulting strain e = 1.0. Evidently, after step e¢ the deformation process shown in Fig. 1 from steps a to e¢ can always repeat during loading. If the model operates n-cycles in observation time, obvious superplasticity of n · 100% occurs. Thus, the extended Lee model gives a reasonable physical path for explaining the extensive superplasticity observed in polycrystalline materials. However, whether there is an obvious superplasticity for the materials depends on how fast the model operates one cycle (from a to e¢ in Fig. 1). Lee made no attempt to develop a solution for his model. Spingarn and Nix [8] made a solution for Lee model having not yet deformed (the model shown in Fig. 1a). This Y. Dong Z. Li (&) Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200240, P.R. China e-mail: zhli@sjtu.edu.cn