Welding math
Preheat and Interpass Temperature
Preheat slows the rate at which a weld cools through the transformation range, giving hydrogen time to diffuse out and giving the heat affected zone a chance to form something tougher than untempered martensite.
The formula
T_preheat rises with thickness, carbon equivalent, hydrogen, and restraint
The preheat a joint needs rises with section thickness, with the hardenability of the steel, with the diffusible hydrogen the process introduces, and with how heavily the joint is restrained; interpass temperature is the same idea applied between passes.
What each symbol means
| Symbol | Meaning | Units |
|---|---|---|
| T_p | Preheat temperature, measured just before the arc is struck | deg F |
| T_i | Interpass temperature, measured just before each subsequent pass | deg F |
| t_c | Combined thickness, the sum of the member thicknesses meeting at the joint | in |
| CE | Carbon equivalent of the base metal, a hardenability index | weight percent |
Why it works
Three things have to line up before hydrogen cracking happens: a susceptible hard microstructure, dissolved hydrogen, and tensile stress. Preheat attacks the first two at once. By raising the starting temperature of the plate, it slows the cooling curve so the heat affected zone transforms into a softer product, and it keeps the joint warm long enough for hydrogen to diffuse out instead of collecting at the fusion line.
Combined thickness is the usual first cut at how much heat a joint will drain. A quarter-inch plate welded to a two-inch base plate acts like a heavy section, not a thin one, because the heavy member pulls heat away in three dimensions. Adding the thicknesses of all members meeting at the joint captures that behaviour crudely but usefully, and it is why a small fillet on a heavy base often needs more preheat than a butt weld twice its size.
Interpass temperature is preheat applied continuously. A maximum exists as well as a minimum: let the joint get too hot between passes and the weld metal and heat affected zone cool slowly enough to coarsen, which costs toughness, and on quenched and tempered steels it can undo the heat treatment the plate arrived with. Limits for a given job come from that job's engineering and its qualified procedures, not from a rule of thumb.
Worked examples
Sizing up a joint by combined thickness
- Web member
- 0.5 in thick
- Flange member
- 0.75 in thick
- Base plate
- 1.0 in thick
- Add the thicknesses of every member meeting at the joint: 0.5 + 0.75 + 1.0.
- Compare the 2.25 in combined thickness against the 0.5 in web a welder might otherwise size the job by.
- Recognise that the joint drains heat like a heavy section, so the preheat reasoning should follow the combined figure, not the thinnest member.
Result: Combined thickness 2.25 in, so the joint behaves as a heavy section
Sizing preheat from the half-inch web would badly underestimate the quench this joint delivers. The engineering that sets the actual temperature for the job has to work from the combined figure.
Holding interpass temperature between passes
- Example procedure minimum
- 225 deg F
- Example procedure maximum
- 450 deg F
- Measured after the third pass
- 480 deg F
- Compare the measured 480 deg F against this example procedure's 450 deg F ceiling; the joint is 30 deg F too hot to restart.
- Wait for the joint to fall back inside the window, then check again about an inch from the groove edge rather than on the hot bead itself.
- Confirm the reading is still above the 225 deg F minimum before striking the next pass, so the joint has not overshot downward while cooling.
Result: Wait until the joint falls back within the 225 to 450 deg F window before restarting
Both bounds matter. Restarting hot risks coarsening and lost toughness; letting the joint fall below the minimum reintroduces the fast cooling the preheat was there to prevent. The numbers used here are an illustration only.
In practice
- Measure preheat on the side opposite the heating source, or wait after removing the torch, so the reading reflects a soaked section rather than a hot skin.
- Preheat is measured over an area around the joint, not at a single point on the groove. A torch played on the groove face alone leaves the surrounding plate cold and still drawing heat away.
- Low hydrogen consumables reduce, but do not remove, the need for preheat. Rods that have picked up moisture in storage behave like high hydrogen consumables no matter what the classification says.
- Every preheat and interpass value used on a real job comes from that job's engineering and qualified procedures. Numbers in worked examples here are illustrations for the arithmetic, nothing more.
Related topics
Practise the arithmetic under pressure
The welding-math domain in the question bank is where these formulas get tested the way they get tested on paper — with distractors built from the mistakes people actually make.