Nanocrystalline Superplasticity — Grain-Boundary Sliding

Deformation Conditions

Grain size d 1.0 µm

Temperature T 800 K

Applied stress σ 20 MPa

Sim time ×200×

Live Readouts

Strain rate ε̇

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Elongation

Cavitation risk0%

Diffusion-accommodated (superplastic)

How it works

Below about 15 µm grain size and above ~0.5 T_melt, fine-grained metals can stretch hundreds of percent without necking. The mechanism isn't dislocation glide — it's whole grains sliding past each other along their boundaries, with grain-boundary diffusion relocating atoms at triple junctions to keep everything fitting together (Ashby–Verrall / Mukherjee–Bird–Dorn grain-boundary-sliding creep):

ε̇ = A · (D_gb·G·b)/(kT) · (b/d)² · (σ/G)²
D_gb = D₀ · exp(−Q/RT)

where d is grain size, σ applied stress, G shear modulus, b the Burgers vector, and D_gb the temperature-activated grain-boundary diffusivity. Because grains slide rather than internally stretch, they stay roughly equiaxed at any strain — that's the visual signature of superplasticity, unlike ordinary dislocation creep where grains elongate and neck.

Sliding only stays smooth while diffusion can keep up. This sim scores a cavitation risk as the ratio of the sliding rate to a diffusional accommodation rate at the triple junctions:

accommodation rate ≈ D_gb·b / d³
risk = ε̇ / (ε̇ + accommodation rate)

Coarser grains and higher stress push sliding faster than diffusion can accommodate it — cavities nucleate at triple junctions (shown as dark voids), strain localizes, and the specimen fails early instead of stretching uniformly. This is exactly why superplastic forming alloys are deliberately processed to keep grains sub-micron: it buys ductility by keeping the accommodation rate high.

Grain size, temperature and applied stress sliders drive the live constitutive equation; Sim time × compresses the (very slow, real-world minutes-to-hours) process into a watchable animation.

Grains (equiaxed) Cavities (triple junctions)

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