This is the 2D counterpart of the 3D mechanical-alloying simulator. It integrates the exact same Kocks-Mecking dislocation-density equation strike by strike:
dρ/dε = k₁√ρ − k₂ρ
steady state: ρ_sat = (k₁/k₂)²
d = K/√ρ (similitude spacing)
But instead of redrawing an isotropic cubic voxel grid, this view models how subgrain boundaries actually appear during severe plastic deformation: dislocations first organise into long, roughly parallel geometrically-necessary boundaries aligned with the material's active slip trace, spaced at the similitude distance d. At low strain very few transverse boundaries have formed yet, so the cross-section looks like elongated lamellae. As ρ climbs toward saturation, transverse (incidental) boundaries fill in at the same spacing, and the lamellae close up into small, roughly equiaxed nanograins — the lamellar-to-equiaxed transition reported in cold-worked and ball-milled metals (Hughes & Hansen cell-block subdivision).
n_primary = round(300 nm / d)
frac = ρ / ρ_sat
n_secondary = round(frac · n_primary)
aspect = (300 nm / n_secondary) / (300 nm / n_primary) → 1 at saturation
- Material — sets k₁, k₂, K, G, b and an indicative slip-trace angle (BCC iron ≈45°, FCC copper/aluminium ≈32–35°), so each metal saturates at its own grain size, strength, and lamella orientation.
- Milling energy — equivalent strain injected per impact; harder swings drive faster subdivision.
- Impact / Auto-mill — apply strain increments one at a time or continuously; the square is a fixed 300 nm × 300 nm cross-section of the powder particle.
- Boundary aspect ratio — spacing of transverse boundaries divided by spacing of primary boundaries; 1.0 means fully equiaxed nanograins, higher numbers mean elongated lamellar bands.
Real-world relevance: the lamellar-to-equiaxed subdivision path shown here is the actual microscopic route by which ball milling, cold rolling, and equal-channel angular pressing convert a coarse grain into a nanocrystalline one — grain refinement does not happen by shrinking an isotropic cube, it happens by boundaries cutting across the grain in stages.