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

Every thermal cycle a turbine blade's ceramic coating survives also grows the seed of its own failure: a thin oxide layer at the bond-coat interface whose mismatched thermal expansion locks in strain energy every time the engine cools. This 2D companion partitions the coating into a genuine Voronoi tessellation of irregular patches — a flat cross-section of real coating grain structure, not a rendered 3D grid — and grows each patch's oxide thickness under corrected parabolic oxidation kinetics (h² = h₀² + k_p·N). A live phase plot tracks every patch's strain-energy release rate G against the interface fracture toughness G_c, so a patch popping free in the mosaic is the same event as its point crossing the G/G_c = 1 threshold line on the graph beside it.