Nanocrystalline Superplasticity 2D — Grain-Boundary Sliding Map

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

–

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 2D view shows a cross-section grain cell in the main panel — drag to pan, scroll/pinch to zoom — plus a live deformation-mechanism map (grain size vs. strain rate) below it, with the operating point plotted against the GBS-creep field boundary and the current risk-driven regime it falls in.

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)

drag to pan · scroll to zoom

Deformation-mechanism map — grain size vs. strain rate