What the Folias bulging factor actually does

Take a flat plate with a thin patch in it, pull on it, and the calculation is simple: less section, more stress, in proportion.

Now put that same thin patch in the wall of a pressurised cylinder. Something extra happens. The thinned area is less stiff than the wall around it, so internal pressure pushes it outward relative to its neighbours. That local bulge introduces bending on top of the membrane stress, and the stress at the flaw goes up by more than the loss of section alone accounts for.

The Folias factor is the multiplier that captures this. It is named after L. F. Folias, whose work in the 1960s on cracks in pressurised shells produced the original solution, and it appears throughout API 579, ASME B31G and the pipeline assessment methods that came from the same lineage.

What it depends on

Not on depth. This surprises people. The bulging factor depends on the length of the flaw, the diameter and the wall thickness — combined into one dimensionless group:

The quantity √(D·t) is a characteristic length for a shell — roughly, the distance over which the shell can redistribute a local disturbance. A flaw much shorter than √(D·t) is carried by the surrounding wall and barely bulges. A flaw much longer has no help available and bulges freely.

The bulging factor then follows, in the form API 579 uses for a Level 1 assessment:

Real numbers

For a vessel of 576 mm inside diameter and 12 mm wall, so √(D·t) = 83.1 mm:

Three things are visible in that table and all three are useful.

Short flaws are nearly free

At 25 mm the bulging factor is 1.035 — a 3.5% penalty. Half the wall is gone and the component still has 97% of its capacity. A short flaw, however deep, is largely carried by the metal around it.

The damage arrives fast between 50 and 200 mm

RSF falls from 0.894 to 0.634 across that range at constant depth. Nothing about the depth changed. That entire loss is the flaw getting longer.

Then it flattens out

From 200 to 400 mm, RSF only moves from 0.634 to 0.564. Once a flaw is long compared with √(D·t) there is no more help to lose — the shell has already stopped supporting it, and further length adds little.

Why this changes how you read an inspection report

A report that says "minimum remaining thickness 6 mm" is half an answer. The other half is how far the thinning extends, and the table above shows it can matter more.

Which is a direct argument for corrosion mapping over spot readings wherever the damage is localised: a grid gives you a minimum and no extent, and the assessment cannot be done without the extent.

Variants you will meet

Several bulging factor expressions exist and they do not all agree.

• API 579 uses the form above for Level 1 local metal loss, and a different, more detailed treatment at Level 2.
• Original B31G uses a two-part expression with a parabolic area assumption, and caps the flaw length it will treat.
• Modified B31G uses a three-term polynomial below a threshold and a linear form above it, with a 0.85-depth area assumption. It is less conservative than original B31G and is the common choice for pipelines.

They give different answers on the same flaw. Which is correct depends on which code you are working to — and mixing the bulging factor from one method with the acceptance criterion from another is a real and surprisingly common error.

Where it appears beyond metal loss

The same physics applies to crack-like flaws in shells, so a bulging correction appears in Part 9 fracture assessments too — there it raises the stress intensity for a flaw in a curved pressurised shell above the flat-plate value. Same reason, same behaviour: the shell bulges locally and the flaw feels more stress than the membrane calculation suggests.