Cooling Time t8/5 (Thick Plate)

Austenite decides what it is going to become on the way down through roughly 800 to 500 °C. Cool it slowly and it transforms to ferrite and pearlite: soft, tough, forgiving. Cool it fast and it has no time to do that, and what comes out is martensite — hard, strong, brittle, and with a lattice that will hold onto diffusible hydrogen and crack days later. $t_{8/5}$, the number of seconds spent between those two temperatures, is therefore the single quantity that governs the microstructure of the heat-affected zone, and it is what heat input, preheat and plate thickness are all really arguing about.

The expression on this page is the three-dimensional Rosenthal solution — heat flowing away from a moving line source in all directions through thick plate. Daniel Rosenthal published the moving-source solutions in the early 1940s, and although the assumptions are severe (constant properties, a point or line source, no latent heat, no convection or radiation) the results match measurement well enough that EN 1011-2 and its equivalents build their guidance on them.

Now look at what is missing from the equation: plate thickness. That is not an oversight, and it is the most important thing on this page. Once a plate is thick enough for heat to run away in all three directions, adding more thickness changes nothing — the heat never reaches the far surface during the time that matters, so the far surface may as well not exist. Below that transition thickness the heat is trapped between two surfaces, flow becomes two-dimensional, and a completely different expression applies — one in which $t_{8/5}$ goes as the SQUARE of the heat input and inversely as the square of the thickness. The two forms cross over at a thickness that itself depends on heat input and preheat, and that transition is tabulated in the standards. Using the thick-plate form on thin plate underestimates the cooling time, sometimes by a lot. If your plate is thin, or you are not sure, find the transition thickness before you trust the answer.

This is also the precise reason a heat input alone tells you nothing. Two welds at identical heat input on 6 mm and 40 mm plate are not similar welds; they are not even governed by the same equation. Anyone who quotes a heat input as though it settled the cracking question has skipped the only step that matters.

Preheat is the other large lever, and it works differently from heat input. Both slow the cooling, but heat input also coarsens the grain in the coarse-grained heat-affected zone and adds distortion, while preheat does neither. Preheat also holds the joint warm long enough for diffusible hydrogen to escape, which is a benefit this equation — being about heat flow alone — knows nothing about. Where you have the choice, buy the cooling time with preheat. And preheat means the whole joint region heated through, both sides, checked with a crayon or a contact pyrometer at a distance from the joint the code specifies; a flame waved at the surface leaves a plate hot on the face and cold at the back, which cools nearly as fast as a cold one. On a multi-pass weld the interpass temperature matters as much as the initial preheat, and it usually carries a maximum as well as a minimum.

What this page will not do is tell you what preheat to use. That comes from AWS D1.1, CSA W59, EN 1011-2 or whatever governs your work, through a table keyed to the carbon equivalent, the thickness, the restraint and the hydrogen level of the consumable. The table is the authority. What the equation is good for is understanding: it shows you how much preheat is worth in seconds, it shows you why thickness matters so much, and it lets you see in advance when a code requirement is going to be easy and when it is going to mean blankets, a torch and somebody standing there with a crayon.

Two final honesty notes. The shape factor smuggles joint geometry into a solution derived for a bead run on a flat plate; about 1 for bead on plate, lower where the joint gathers heat into a corner as a fillet on a T-joint does, and it is a table entry in the standard. And thermal conductivity is taken as a constant, which it plainly is not over an 800-degree range — carbon steel sits near 40 W/(m·K) at room temperature and falls as it heats, austenitic stainless is roughly a third of that (which is why the same procedure on stainless cools far more slowly and distorts far more), and aluminium is five times steel. The whole family of these expressions is an engineering approximation calibrated against measurement, not a first-principles prediction, and the number it gives you is worth about two significant figures.