Nanocrystalline Superplasticity 2D — Grain-Boundary Sliding Map

A 2D cross-section of a fine, equiaxed-grain block is pulled in uniaxial tension. Instead of dislocations gliding through the crystal lattice, whole grains slide past each other along their boundaries while grain-boundary diffusion relocates material at the triple junctions to keep the microstructure coherent — the mechanism behind nanocrystalline superplasticity, where strains of 100–1000% are reached without necking. Grain size, temperature and applied stress drive a real Mukherjee–Bird–Dorn grain-boundary-sliding creep equation with live strain-rate and elongation readouts, while a cavitation-risk score — the ratio of the sliding rate to the diffusional accommodation rate at triple junctions — tracks when coarse grains or excessive stress let sliding outrun diffusion, nucleating voids and ending the superplastic regime early. A second panel plots the live operating point on a grain-size/strain-rate deformation-mechanism map against the GBS-creep field boundary.