An arc weld is modeled as a point heat source of net power Q moving at travel speed v across a thick steel plate (Rosenthal, 1941). In the quasi-steady frame moving with the arc, the temperature rise at a point a radial distance r from the arc — directly beneath it — behaves as:
T(r) − T₀ ≈ Q / (2π k r) · exp(−v·r / (2α))
k = thermal conductivity
α = thermal diffusivity (α = k/ρc)
T₀ = plate / preheat temperature
r = √(y² + z²), offset from the weld centerline
Because the source is quasi-steady, this value at r is essentially the peak temperature every point at that offset ever reaches as the arc sweeps past — which is what fixes the final microstructure there, independent of position along the weld. Each voxel in the plate is colored by which zone its peak temperature falls into:
- Fusion zone — melted and resolidified as a cast dendritic structure.
- Coarse-grained HAZ — held near the solidus long enough for rapid grain growth; the most crack-sensitive band.
- Fine-grained HAZ — fully re-austenitized and refined on cooling; usually the toughest region of the joint.
- Intercritical HAZ — only partially transformed (between A₁ and A₃), giving a mixed microstructure.
- Subcritical HAZ — below A₁, no phase change, just tempering of the existing structure.
Stainless steel stays austenitic throughout (no A₁/A₃ transformation) but instead risks sensitization: chromium-carbide precipitation at grain boundaries between roughly 450–850 °C that depletes chromium and can trigger intergranular corrosion.
The cooling severity that governs hardness and hydrogen-cracking risk is the t₈/₅ time — how long the weld metal spends between 800 °C and 500 °C. For a thick plate:
t₈/₅ = (Q/v) / (2πλ) · [ 1/(500−T₀) − 1/(800−T₀) ]
Higher heat input or preheat slows cooling (coarser, softer microstructure); higher travel speed or a lower-conductivity material speeds it up (harder, more crack-prone). Drag the sliders and watch both the zone widths and t₈/₅ respond.