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Weld Cooling Rate (t8/5)

Estimate the 800→500 °C cooling time of a weld from heat input, preheat, and plate thickness — the number that sets HAZ hardness.

Input3-D: t₈₅ = ηUI/(2πλ·vs)·[1/(500−T₀) − 1/(800−T₀)] , 2-D: t₈₅ = (ηUI/vs·d)²/(4πλρc)·[1/(500−T₀)² − 1/(800−T₀)²]

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The engineering

t8/5 is the time a weld spends cooling from 800 °C to 500 °C — the range where austenite decomposes and HAZ microstructure is decided. Fast cooling (short t8/5) drives martensite and hydrogen-crack risk in hardenable steels; slow cooling (long t8/5) coarsens grain and can drop toughness. Heat input, preheat, and plate mass are the three knobs you actually control on the bench.

Which Rosenthal branch applies depends on whether heat escapes in two dimensions (thin plate, through-thickness flow saturates) or three (thick plate). The card computes the transition thickness and picks automatically. Rule of thumb: raising preheat is a far more powerful way to lengthen t8/5 than raising heat input, because the (T−T₀) terms are squared in the thin-plate case.

Feed net heat input, not gross: multiply arc power by process efficiency (η ≈ 0.8 for SMAW/FCAW, ~0.9 for SAW, ~0.7 for GMAW spray). Property values ρc and λ are for carbon steel near the transformation range; adjust for stainless or aluminum.

Where this math comes from

The physics comes from Daniel Rosenthal, a Belgian-born engineer at MIT who in 1941 solved the moving-point-heat-source problem for welding — treating the arc as a point (3-D) or line (2-D) source gliding across a semi-infinite plate. His closed-form temperature fields let welding engineers predict cooling for the first time instead of guessing from experience.

The 800→500 °C window was singled out by German and Scandinavian researchers in the 1960s–70s because it brackets the pearlite/bainite/martensite decision for structural steels. It became the workhorse parameter in the European welding codes and the SINTEF/IIW cooling-time charts, and it underpins the preheat and heat-input controls in AWS D1.1 and EN 1011-2.

  1. 1941Daniel RosenthalPublishes the moving-heat-source solution giving weld temperature fields.
  2. 1946Rosenthal (ASME)Refines 2-D thin-plate and 3-D thick-plate forms used for cooling estimates.
  3. 1973IIW / SINTEFStandardizes t8/5 as the HAZ cooling parameter with transition-thickness rules.
  4. 2001EN 1011-2Codifies t8/5 heat-input and preheat guidance for steel welding.
  5. 2020AWS D1.1/D1.1MStructural Welding Code ties preheat and heat-input limits to HAZ cooling control.

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