P_cm Cracking Parameter (Ito–Bessyo)

Ito and Bessyo published this parameter in 1968 out of a different kind of experiment. Rather than fitting hardenability, they ran restraint cracking tests — the y-groove test and its relatives, where a joint is deliberately made rigid so that any tendency to crack shows itself — on the low-carbon steels that were then arriving, and asked which composition variable actually predicted the cracking they saw. The answer was carbon, far more strongly than the older hardenability-weighted expressions implied.

Compare the coefficients side by side and the whole argument is visible. In the IIW carbon equivalent, manganese is divided by six. Here it is divided by twenty. Carbon carries a coefficient of 1 in both, so relative to carbon, manganese has been discounted by more than a factor of three. Silicon appears here and does not appear in the IIW expression at all. Nickel is divided by sixty. The practical effect on a modern plate at 0.08 % C and 1.50 % Mn: the IIW expression charges a quarter of a point for the manganese alone and returns about 0.39, while $P_{cm}$ charges 0.075 for it and returns about 0.19. That divergence is the entire point of the parameter existing. One of those numbers will send you looking for preheat that the steel does not need.

Boron is the outlier and deserves its own paragraph. Its coefficient is 5 — the only coefficient greater than 1 anywhere in either expression, and about a hundred and fifty times the weighting silicon gets. Twenty parts per million of boron, which is 0.0020 % and looks like a rounding error on a certificate, adds a full hundredth to $P_{cm}$, as much as a fifth of a per cent of manganese. Boron is added deliberately to some quenched-and-tempered plate because it buys hardenability more cheaply per unit weight than anything else known. It also turns up as an unwanted residual in scrap-based electric-arc steel, where nobody asked for it and nobody mentions it — and that is the case that catches people out. If a certificate reports boron at all, read it.

This is still a screening number, and it has limits of its own. It was fitted below roughly 0.17 % carbon and becomes less trustworthy above that — which is precisely the range where the IIW expression is at its most reliable. The two are complements, not rivals, and knowing which one your code and your steel supplier are using matters more than having an opinion about which is better. Some standards specify $P_{cm}$ for higher-strength steels and CE for ordinary structural grades, and some hand you both.

Neither parameter knows anything about plate thickness, restraint, cooling rate, or the diffusible hydrogen in your consumables — and hydrogen-assisted cold cracking needs all of those together with a susceptible microstructure. $P_{cm}$ is the input to the Japanese-derived preheat methods, which pair it with a hydrogen content and a restraint intensity to produce a temperature. The temperature comes out of that method, or out of the code you are working to; it does not come out of this page. And the procedure comes out of a qualification test, which is the only place where your steel, your consumable, your joint, your position and your welder are tested together.