Welding math
Pcm Cracking Parameter
Pcm is a carbon equivalent tuned for modern low-carbon steels, where the older expression penalises manganese so heavily that a perfectly weldable plate can be flagged as difficult.
The formula
Pcm = C + Si/30 + (Mn + Cu + Cr)/20 + Ni/60 + Mo/15 + V/10 + 5B
The Pcm parameter is carbon, plus silicon over thirty, plus the sum of manganese, copper, and chromium over twenty, plus nickel over sixty, plus molybdenum over fifteen, plus vanadium over ten, plus five times boron.
What each symbol means
| Symbol | Meaning | Units |
|---|---|---|
| Pcm | Cracking parameter weighted for low-carbon modern steels | weight percent |
| C | Carbon content, weighted far more heavily here than in the IIW expression | weight percent |
| Mn, Cu, Cr | Manganese, copper, and chromium, grouped under a divisor of twenty | weight percent |
| B | Boron, multiplied by five because trace amounts transform hardenability | weight percent |
Why it works
The IIW carbon equivalent was developed against the steels of its era, which carried more carbon and less deliberate micro-alloying. Applied to a modern low-carbon, high-strength, thermomechanically processed plate, it tends to overstate the difficulty, because such a steel gets its strength from grain refinement and precipitation rather than from carbon, while still carrying substantial manganese.
Pcm rebalances the weighting. Carbon stands alone at full value, while manganese, copper, and chromium share a divisor of twenty rather than six or five, and nickel falls all the way to sixty. The practical effect is that carbon dominates the result. A steel at 0.08 percent carbon with a full point of manganese lands low on Pcm even though the same chemistry looks worse under the older formula.
Boron is the striking term. It appears multiplied by five rather than divided, because a few parts per million of boron segregating to austenite grain boundaries suppresses transformation out of all proportion to its concentration. A boron-treated steel with a nominally clean analysis can behave far more hardenable than its carbon and manganese would ever suggest, and this term is where that shows up.
Worked examples
A modern low-carbon micro-alloyed plate
- Carbon and silicon
- 0.08 and 0.25 percent
- Manganese, copper, chromium
- 1.20, 0.20, 0.10 percent
- Nickel and molybdenum
- 0.30 and 0.05 percent
- Vanadium and boron
- 0.02 and 0.0005 percent
- Silicon term: 0.25 / 30 = 0.008333.
- Manganese plus copper plus chromium: 1.50 / 20 = 0.075.
- Nickel 0.30 / 60 = 0.005, molybdenum 0.05 / 15 = 0.003333, vanadium 0.02 / 10 = 0.002.
- Boron term: 5 x 0.0005 = 0.0025. Add everything to the 0.08 carbon.
Result: 0.176
A low figure, which is the point of the parameter. The same chemistry run through the older carbon equivalent would look considerably worse purely because of the manganese, and would suggest precautions this steel does not need.
A mid-carbon pressure vessel chemistry
- Carbon and silicon
- 0.15 and 0.30 percent
- Manganese, copper, chromium
- 1.00, 0.10, 0.20 percent
- Nickel and molybdenum
- 0.10 and 0.10 percent
- Vanadium and boron
- none reported
- Silicon term: 0.30 / 30 = 0.01.
- Manganese plus copper plus chromium: 1.30 / 20 = 0.065.
- Nickel 0.10 / 60 = 0.001667 and molybdenum 0.10 / 15 = 0.006667; vanadium and boron contribute nothing.
- Sum with carbon: 0.15 + 0.01 + 0.065 + 0.001667 + 0.006667.
Result: 0.233
Noticeably higher than the micro-alloyed plate, and almost all of the increase is the carbon term. Pcm makes that dependence obvious in a way the older expression obscures.
In practice
- Pcm and the IIW carbon equivalent are not interchangeable and their numbers are not comparable. Quoting one where the other is expected is a common and consequential mix-up.
- Pcm suits low-carbon steels, roughly below the middle of the range covered by ordinary structural grades. Above that the older expression generally tracks behaviour better.
- Watch for boron on the mill certificate even at a few parts per million. It is easy to skim past and it moves the answer more than any other trace element.
- As with any composition index, this is a screening tool. The preheat and procedure a job actually uses come from its own engineering and qualification, not from a threshold read off a chart.
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.