Dataset for Random marked nested tessellations applied to the modeling of deformation twinning in polycrystalline materials.

Figure 1.: Inverse pole figures with respect to the direction z = (0, 0, 1)T with simulated orientations from the density (2.2) for u = (0, 0, 1)T , v = (1, 1, 1)T and different parameters κ. The centres of four clusters in (b) correspond to preferred orientations ⟨111⟩ (in the notation of Miller indexes [8, Section 2.9]). Figure 2.: Cubic lattice projected onto (¯110) plane in the configuration before (red) and after (blue) twinning described the twinning elements K1 = (-1-14), K0 = (-1-10), η1 = [-2-2-1], η1 = [001]. Figure 3.: Planar projection of a 3D cell with Ferret segment [α, β] along the direction n and simulated lamellae (grey) of centers di and some semi-widths wi. Figure 4.: Histogram of the cell volumes (a), histogram of the number of neighbors of inner cells (b). Sample size: n = 423. Figure 5.: Histograms of the propensity to twinning are displayed for different values of κ with IM and for the moving average model (MA). Figure 6.: Histograms of the volume fraction Vt of lamellae in cells are displayed for different values of κ with IM and for the moving average model (MA). Figure 7.: Relative frequencies of lamellae counts in cells for lmax = 3 with varying macroscopic strain levels εm under different sampling conditions. Each subplot showsthe evolution of the estimated probabilities with increasing εm, for either the moving average or for independent marking with κ = 0, 10, 30. Figure 8.: 2D kernel density estimates (KDEs) of normalized lamella center position and semi-width in cells with exactly two lamellae under different combinations of κand εm. The first, second lamellae are plotted on the left, right subfigure, respectively. KDEs are computed over lamella geometries normalized by the Feret diameter. Figure 9.: Visualization of the marked nested tessellation TN in Q for lmax = 3 with cells colored according to the propensity to twinning. The subcells corresponding tolamellae are gray. The parameters are a) κ = 0, εm = 0.05, b) κ = 0, εm = 0.2, c) κ = 30, εm = 0.05, a) κ = 30, εm = 0.2 . Figure 10.: (a) Inverse pole figure of (0, 0, 1)T direction for mother cells before twinning for the case of ⟨111⟩ preferential orientation with κ = 30. (b) Corresponding inversepole figure of (0, 0, 1)T direction for all subcells after twinning (blue poles) for the case of macroscopic strain of 0.2. In addition, the reorientation due to {114} twinningis illustrated by four ⟨111⟩ poles (yellow dots) that may reorient under tension into twelve orientations represented by magenta poles. The reorientation of four ⟨111⟩ polestake place in {110} planes denoted by thin black solid lines. Figure 11.: The fitted regression surface from model (5.4), showing the joint effect of macroscopic strain εm and texture κ on TSED. Increasing κ leads to a reductionin the strain energy response, indicating enhanced energy dissipation in more aligned systems. Figure 12.: Residual diagnostics for the regression model (5.4) analyzing total strain energy density (TSED) under independent marking. (a) Normal Q-Q plot of residuals,(b) residuals vs. fitted values. Figure 13.: Fitted regression surfaces as a function of macroscopic strain and texture parameter. (a) Model (5.5) for the lamellar phase, (b) model (5.6) for the matrix phase. Figure 14.: Visualization of the effect of macroscopic strain εm on TSED for the two marking models. Data points are indicated by dots (IM model) and triangles (MAmodel), respectively, with their corresponding fitted regression curves shown as dashed (IM) and solid (MA) lines.