PSI - Issue 35

E. Emelianova et al. / Procedia Structural Integrity 35 (2022) 203–209 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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(c) (d) Fig. 3. (0001) and (101̅ 0) pole figures for four polycrystalline models of α -titanium.

In the present study, a set of calculations was performed for four polycrystalline models with the same grain geometry (Fig. 1b) but a basal texture of different severity. The grain orientations in the four models were described by four sets of Euler angles to determine the deviation of the grain prismatic axes about the ND in the ranges of ±10˚, ±20˚, ±40˚ and ±60˚, respectively. Hereinafter, these models are abbreviated by two capital letters denoting basal texture (BT) and numbers standing for the scattering angle. Figure 3 shows the (0001) and (101̅ 0) pole figures for the four models under study. The generated models were implemented into Abaqus/Explicit. A user-defined subroutine VUMAT was adapted to implement the anisotropic elasticity and crystal plasticity equations with respect to the local coordinate system (Fig. 1a). The kinematic boundary conditions simulated uniaxial tension along the RD-axis, with the top and lateral surfaces being free from external loading and the bottom one being a symmetry plane. To minimize wave effects inevitable in dynamic problems, we set the loading velocity to gradually increase up to a stationary value and then keep it constant. For further details of numerical implementation, a reader is referred to (Romanova et al., 2019b). 3. Results Figures 4 and 5 present the roughness patterns calculated for the polycrystals under study at a strain of 15% and the evolution of corresponding roughness profiles considered along the model centerlines in the course of tension. Common for all models, irregularly-shaped hills and valleys appear on the surface under deformation. Their size covers 2-3 grain diameters, as seen from the comparison of the roughness patterns with the grain structure (cf. Figs. 1b and 4). Along with the surface irregularities formed by the grain clusters (hereinafter, they are referred to as mesoscale), the displacements of individual grains relative to each other take place in the weakly textured polycrystals (Fig. 4c, d). However, their contribution to overall roughening is insignificant in comparison to the mesoscale out-of-plane displacements. The mesoscale surface patterns are certainly affected by the severity of a basal texture. The sharp texture effectively suppresses the displacements of individual grains perpendicular to the free surface (the orange peel pattern) and significantly reduces the peak-to-valley distance of the mesoscale surface irregularities. This finding is in line with previous conclusions made for titanium polycrystals with hardened and unhardened surface layers characterized by different grain orientations (Emelianova et al., 2020; Romanova et al., 2020). For quantitative estimations of the roughness patterns and their evolution under plastic deformation, the dimensionless roughness parameter R d was calculated by Eq. (3) for the whole set of numerical profiles. The strain-