TGO Spallation 2D: Voronoi Patch Mosaic

Thermal Cycling

Cycling rate 1.0×

TGO growth rate k_p 1.0×

CTE mismatch Δα 1.0×

Interface toughness G_c 1.0×

Live Readouts

Thermal cycles N

Mean TGO thickness

0.0 µm

Spalled patches

0.0%

Peak G / G_c

0.00

How this 2D version works

This is the same TGO-growth / buckling-spallation physics as the 3D turbine-coating model, represented two genuinely 2D ways instead of orbiting 3D boxes. The left canvas is a real 2D Voronoi tessellation: ~50 seed points partition the coating into irregular patches (a schematic cross-section of real coating grain structure), each with its own fixed roughness multiplier and independently-integrated TGO thickness. The right canvas plots every patch's live strain-energy ratio G/G_c against cycle count — a phase-space view with the fracture threshold drawn as a line, so you watch patches climb toward 1.0 and cross it in real time instead of watching cubes fall.

dh/dN = k_p·rough / (2h)   →   h(N) = √(h₀² + k_p·N)   (parabolic oxidation)
σ = E'·Δα·ΔT
G = Z·σ²·h/E' · rough        (Evans–Hutchinson buckling driving force)
spall when G ≥ G_c

Correction from the 3D source: the original engine integrated its oxide growth as dh/dN = k_p/(2√h), which gives h ∝ N^(2/3) — a cubic-type rate law, not the parabolic h² = h₀² + k_p·N stated in its own theory panel (verified numerically: the two diverge by over 50% by cycle 800). This 2D version integrates the corrected dh/dN = k_p/(2h) form, which matches the textbook parabolic law and the stated formula to within ~2%.

Cycling rate — how fast simulated heat/cool cycles run when "Run Cycling" is active.
TGO growth rate k_p — oxidation kinetics; higher values thicken every patch faster.
CTE mismatch Δα — thermal expansion mismatch; raises the locked-in stress σ and therefore G for every patch at once.
Interface toughness G_c — how much strain energy a patch can absorb before delaminating; higher values push the threshold line up and delay spallation.

Intact ceramic patch Approaching G/Gc = 1 Spalled (delaminated) Threshold / patch trace

Thermal Barrier Coating Spallation, 2D: Voronoi Patch Mosaic and Strain-Energy Phase Plot