Autofrettage of pressure vessels

Why does deliberately overloading a thick tube once make it safer at every load afterwards?

A thick steel tube is destined to hold high pressure for thousands of cycles. Before it goes into service, the maker deliberately pressurises it far beyond anything it will ever see in use — hard enough that part of the metal permanently deforms. Then the pressure is released, and the tube is fitted.

Every instinct about materials says this should be damage. We spend our lives avoiding overload, and here overload is the manufacturing step. Yet the treated tube outlives an untreated one by a wide margin under the same service pressure. Something about that one excursion has left the tube in a better condition than it started in, and it is worth working out what a piece of steel could possibly be keeping from an event that is over.

Begin with how stress sits in a thick-walled tube under internal pressure. It is not uniform. The hoop stress — the tension trying to split the tube lengthwise — is highest at the bore and falls off toward the outside. The inner surface is always the most heavily loaded material in the wall, which is also why cracks start there.

Now raise the pressure past the point where the bore reaches its yield strength. What happens? The inner layer starts to deform plastically — permanently. But the outer layer, still below yield, does not: it is stretched elastically, like a spring being extended. So the wall is now in two conditions at once, an inner sleeve that has permanently grown and an outer sleeve that is merely stretched.

Here is the step worth pausing on. Ask yourself what happens when the pressure comes off. The outer sleeve wants to return to exactly its original size — elastic strain is fully recoverable, that is what elastic means. The inner sleeve does not want to return, because part of its stretch was permanent. But they are one piece of metal. They cannot go to different sizes.

So the outer sleeve wins the argument, partly. It contracts and, in doing so, squeezes the inner sleeve back down — putting the bore into compression while the outer wall is left in mild tension. The tube is now sitting, unloaded, with a locked-in internal stress field that sums to zero across the wall but is emphatically not zero at any given radius.

And now the payoff. When service pressure is applied, the stresses simply add. The applied hoop tension at the bore has to first cancel the residual compression before the bore sees any net tension at all. The most vulnerable point in the wall has been given a head start. Since fatigue crack initiation and growth are driven by tensile stress — a crack cannot open under compression — lowering the tensile peak at the bore is precisely the intervention that matters most.

That is the whole mechanism: the tube adapted. Not by getting stronger in any material sense — the yield strength and toughness of the steel are essentially what they were — but by permanently rearranging where its internal load sits, in response to the one event that was severe enough to make the rearrangement stick.

Two honest limits belong in the picture. Real steels show the Bauschinger effect: material that has yielded in tension yields more easily in the opposite direction afterwards, so the compression that arrives on unloading can itself cause a little reverse yielding, and the residual field is measurably weaker than a simple calculation predicts. Designers account for this explicitly. And the benefit is specific: autofrettage improves fatigue life and delays crack initiation at the bore. It does not meaningfully raise the pressure at which the tube bursts, because burst is governed by the whole wall going plastic, and a redistribution that sums to zero does not add material.

Three refinements.

First, the misconception: nothing was strengthened. If you cut a coupon from the tube and pulled it, you would find much the same steel, slightly work-hardened. The improvement lives in the residual stress field, which is a property of the assembled geometry, not of the material.

Second, this is one member of a family, and seeing the family makes the idea stick. Shot peening hammers a surface into compression for the same reason. Prestressed concrete is tensioned steel holding concrete in compression so that service loads must first cancel it. Toughened glass is chilled so its skin ends up compressed. All four do the same thing: pay once to lock in a stress opposite to the one that will do the damage.

Third, more is not simply better. Push the overload too far and the plastic zone reaches the outer wall, at which point there is no elastic sleeve left to do the squeezing, and reverse yielding on unload begins to eat the benefit. There is an optimum depth of plastic penetration, and it is a design calculation rather than a case of pressing harder.

• Shot peening and case hardening, the surface-level members of the same family.
• The Bauschinger effect, and how much of the theoretical benefit it actually removes.
• Why residual stresses relax under heat or long-term creep, and what that means for service temperature limits.

Every term the collection defines is gathered in the glossary.