PSI - Issue 31

V. Romanova et al. / Procedia Structural Integrity 31 (2021) 64–69 V. Romanova et al. / Structural Integrity Procedia 00 (2019) 000–000

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respect to a local Cartesian frame with the axes coinciding with the [210], [010] and [001] crystallographic directions (Fig. 1a). The boundary conditions simulate uniaxial tension along the RD-axis as shown in Fig. 1d and 2a. The top and lateral surfaces are free from external loading, and the bottom one is a symmetry plane. In order to minimize wave effects inevitable in the dynamic problems, the loading velocity is gradually increased up to a stationary value and then kept constant. 3. Results Figure 3 shows plastic strain fields and roughness patterns calculated for the smallest and largest polycrystals, with the conclusions being drawn for all models listed in Table 1. The plastic strain fields at the developed deformation stage demonstrate a set of mesoscale bands going through the grains irrespective of their orientations (Fig. 3a, c). The bands lie at an angle of about 45 degrees to the load axis on the rolled surface and perpendicular to the load direction on the lateral side, which is the evidence of the texture effect. The hcp grains have a low ability to deform plastically along the prismatic axes, resulting in anisotropic contractions in the two directions perpendicular to the tensile axis. As a result, the specimen acquires a bow shape in necking, much like in the experiment (cf. Fig. 2b and 3d). Prismatic slip in its turn gives rise to in-plane shear banding on the top surface, which also agrees with the experimental observations by Panin et al. (2018), Romanova et al. (2020). Accordingly, the roughness pattern is much smoother on the top surface while strong mesoscale undulations develop on the lateral sides; the latter are especially pronounced in the large polycrystalline model where the mesoscale roughening is followed by macroscopic necking in the final deformation stage (Fig. 3d). This conclusion is additionally illustrated by the surface profiles evolving on the top and lateral surfaces along the axis of tension (Fig. 4a, b).

Fig. 3 Plastic strain (a, c) and roughness patterns (b, d) in the reference (a-b) and translated polycrystals (c-d) at 26 and 46% strains, respectively.

The roughness patterns for all models directly correlate with the local plastic strains and with the engineering tensile strain. The calculations reveal that the scales of strain localization are getting larger as deformation develops and so do the surface undulations. These results are consistent with the experimental observations of Romanova et al. (2019a) suggesting roughness intensification on larger scales when lower-scale deformation mechanisms are exhausted. The mesoscale undulations initially formed by 3-5 grains progressively involve 15-20 grain clusters in the necking stage. Apparently, the more grains are arranged along the axis of tension, the larger plastic strain the model is able to accommodate. When the scale of plastic strain localization becomes comparable with the model size, the model can no longer describe the mesoscale deformation properly. It is worth noting that in the initial deformation stage (up to 10%) the plastic strain and roughness patterns develop in all models in a rather similar way and the homogenized stress-strain curves also nearly coincide (Fig. 4c). Further discrepancy occurs due to early necking in small models, which is an unphysical effect. Nevertheless, in the limited