The amount of energy absorbed when a pressure vessel ruptures? 2

[leopardforest]

Hi all,

I have an analysis that I am having trouble on how I should approach.

I have a spherical pressure vessel with a known internal pressure and therefore a known potential energy. I am trying to figure out the amount of energy that is absorbed (from the potential energy) when the pressure vessel fails. What is the best way to approach this? I have been looking at Charpy V-Notch test results and trying to make a correlation between the energy absorbed in the v-notch cross section area to the cross sections of the sphere. I am looking a two failure modes: the sphere shears/tears at the hemisphere into two equal halves (and turned into a potential projectile), and a plug of varying sizes shears/tares out of the sphere and is turned into a projectile.

For example: If we assume a hollow sphere with cross sectional area of 33.56 in (thick walled pressure vessel) made from 316 Stainless Steel with a potential stored energy of 100,000 Joules (J). The Charpy Impact test results of the same material is 105 J. Can I assume the cross sectional area of a standard v-notch Charpy test specimen (10mm x 10mm x 55 mm, with a notch depth of 2mm) of 80mm[sup]2[/sup] or 0.1240 in[sup]2[/sup] can be applied to the cross section of my sphere? So 33.56/0.1240= 270., then 270 * 105 J = 28417 J. Would it then be correct to say that the sphere cross section absorbs 28417 J in the fracture/tear/shear?

Thank you in advance!

-Leo

 

[racookpe1978]

Let me re-phrase your question, I think you will see that you've not addresses the right part of the problem:

If I open a 1" hole in the wall by opening a valve, and let all of the gas escape through that hole, how much energy is "lost" from the system?

If I drill a 1" hole in the wall, and let all of the gas escape through that hole, how much energy is "lost" from the system?

If a 1" hole in the wall bursts loose, and that "plug" gets thrown out of the tank 150 meters away, and that hole lets all of the gas escape through that hole, how much energy is "lost" from the system?

Your problem is only partially defined by the tear resistance of the tank wall, it is more defined by HOW the tank wall tears apart and what happens to the wall as it is destroyed.

 

[israelkk]

Pressure vessel is considered a being a bomb with a stored energy = Pressure x Volume.
See MIL-STD-1522 STANDARD GENERAL REQUIREMENTS FOR SAFE DESIGN AND OPERATION OF PRESSURIZED MISSILE AND SPACE SYSTEMS.

No one can guaranty that the vessel can stay as one piece when ruptured. Even though there are test such as gun fire etc. There is never a 100% assurance that some of the vessels from a manufactured batch will not rupture just as a bomb. We had a lab destroyed by a vessel ruptured over the weekend (luckily everyone was at home) even though it passed all tests.

 

[leopardforest]

racookpe,

I agree that in all those situations, all of the energy is lost from the system.

Right now we are making a very conservative estimate that when the vessel fails that all the energy is transferred into the projectile, which is a huge over estimate. We are trying to see how much energy is going into cold work of "tearing" the vessel so we can make an estimate how much energy is left to propel a projectile. I would be looking at hemispheres in two failures: that it fails in pure shear (unlikely) and in pure tensile.

 

[leopardforest]

israelkk,

I completely understand that there is never a 100% assurance as we have had similar failures both in our lab and in vessel testing. We have seen vessels fail at both our designed parameters and below.

I guess I should have made it a little more clear why I am trying to see how much energy is being lost in a material deformation, so we can ensure that our safety shielding could withstand a projectile.

Does that help make it a little more clear what I am trying to do?

 

[TGS4]

Assume that the energy consumed by the ductile tearing is negligible/zero and that all energy is transferred into the projectile.

 

[leopardforest]

TGS4,

That is what we have done, but I have been assigned to look into evaluating how much is consumed by ductile tearing.

 

[rb1957]

is the charpy test a measure of material toughness, or "just" a bencjmark for hardness ?

i mean, doesn't the energy reading "only" reflect the energy absorbed in the test.

i'd've thought you'd be looking more at strain energy ?

Quando Omni Flunkus Moritati

 

[israelkk]

Those who assigned you to look into evaluating how much is consumed by ductile tearing are trying to be "smart". However, there are legal safety issues here. Ask them if they are willing to risk their necks and take responsibility in case of a disaster. I suggest they should call their lawyers and consult with them.

 

[SNORGY]

I think racookpe1978 is saying something that aligns with my thoughts on this, but I look at it from a different angle maybe.

A "rupture" or "explosion" of a vessel implies a catastrophic failure, with lethal pieces of steel and debris being launched for considerable distances away from the blast zone. For that to happen, the common perception is that most or all of the stored energy is available for instantaneous conversion to kinetic energy in the form of lethal, flying fragments of steel. My thought is - and I once tried to view things in the same way that you are now being asked to view things, in a sense - that some of that potential energy is lost in the form of what I would describe as "tear-away" energy that you might be able to correlate to the material's fracture toughness. My approach was obviously wrong, because in many cases, I ended up calculating that the net effect was that if the vessel ruptured the pieces of it wouldn't go anywhere (very loosely speaking). The topic of instantaneous release of stored energy arising from the failure of a pressure vessel full of gas has been a continuing source of debate in the various fora here, particularly as it relates to pneumatic testing, and there is merit to the suggestion that not all of that energy is available all at once to give rise to such completely catastrophic events. To put it very simplistically, that's because it takes some time for all of that gas to either "get to" or "become aware of" the failure site, and as you postulate, some energy needs to be expended towards initiating the fragmentation.

So, when you compare the energy released from the vessel under a controlled blowdown to flare, for example, versus that released when you just blow it up, it becomes clear that it is the rate of energy release that is important, not the amount of energy released. Thus, the fracture mechanics phenomena behind what I believe you are trying to quantify have to be rate-dependent, and I don't think that Charpy fracture toughness by itself is going to be of much benefit in assessing the net effect.

I believe that there is complete merit in what you are being asked to investigate, but to me, apart from academia, no matter how visionary, it's a difficult pursuit - what the Legislators and Regulators want boils down to:

[total stored energy at t=0] = [total kinetic energy at t=0+dt] where dt -->0

That said, israelkk and TGS4 have kind of nailed it. No matter what you come up with, the guys who write and enforce the laws will take a red pen to it and refer you to the above.

 

[racookpe1978]

TGS4 (Mechanical)
29 Oct 13 16:11

Assume that the energy consumed by the ductile tearing is negligible/zero and that all energy is transferred into the projectile.

israelkk (Aerospace)
30 Oct 13 1:49

Those who assigned you to look into evaluating how much is consumed by ductile tearing are trying to be "smart". However, there are legal safety issues here. Ask them if they are willing to risk their necks and take responsibility in case of a disaster. I suggest they should call their lawyers and consult with themcompletely separated..

True: Worst case scenario "could" have a pressure vessel suddenly rupture across the midpoint seam (or PV-Head weld seam) and transfer all of that potential internal energy into a single moving head across the landscape. But that doesn't happen in real life accidents. Look at the PV failures. There IS ripping and trearing as the vecssel is opened up, and the internal gasses obviously leak out (often burning or contributing to an already-existing fire outside the PV) but the vessel "parts" are very, very rarely separated from each other. Rather, what happens physically each time is that as soon as the first through-crack appears, the rushing gasses through that hole (or tear) concentrate the forces in two ways: The first is as escaping energy through the hole (thus, less energy is available to tear the rest of the vessel wall) and secondly, as a tearing force across the crystal perpendicular the crack edge at both edges of the first crack. The further the crack goes around the PV circumference, the more area is opened up for gasses to escape and the less energy there is to promulgate the crack into "good weld" (or un-broken steel.) Even MythBusters needs to cut off the PV heads suddenly with a guillotine-type slice to get their TV-show images of PV's going through walls.)

If there is still concern about parts ripping off and traveling, then wrapping the PV with several layers of fiberglass or Kevlar tape and epoxy will absorb the moving parts' kinetic energy and minimize the number of thrown parts. (An outside fire could damage that fiberglass though.)

 

[Jughandle]

As a rough approximation, why not calculate the change in PV? Let
P1 = 0.
P2 = that needed to make the stress in the walls of the container = UTS of the material.
V1 = V2, assuming a negligible change.
What you get is the elastic and plastic and work done on the metal, no? (Is that what you meant by, “I am trying to figure out the amount of energy that is absorbed when the pressure vessel fails.”)
Generally, CVN values are not useful in design. Much better, but harder to measure, is plane strain fracture toughness, or J-integral. See several ASTMs. I would expect 316 SS to be pretty tough.

Sorry to make this more complicated, but for closer approximations you would also need to know fracture toughness and flaw size presence (there are always flaws and microscopic cracks). Get a copy of Dieter, Mechanical Metallurgy or Hertzberg, Deformation...
Also might want to search out Leak-Before-Break phenomenon, Gurney Model, an N.F. Mott for background.

Lastly, have some fun. Tell your the experiment to verify things.

 

[TGS4]

The best case scenario is that the flaw that initiates the failure behaves in a ductile manner, and you get the classic fish-mouth failure with no fragments/ projectiles. However, as racookepe1978 said, a leak might occur first. This could lead to Joule-Thompson cooling, which could bring the material below a ductile-to-brittle transition temperature. Then it behaves in a brittle manner, and brittle fracture absorbs MUCH less energy than a ductile failure.

Selection of the projectile size is the critical aspect. And for the failure of an entire vessel, it is likely to be a WAG.

 

[LittleInch]

All this is highly interesting in an abstract sort of way and also seems to assume a wholly gas filled vessel.

The problems occur when you get volatile liquids which continue to release gas even after some of it has escaped. Thus the driving force doesn't die down anywhere near as much. Just look at some BLEVE images - really scary. You might not get the same issues in pressure vessels, but ductile failure of pipelines has a velocity component to it whereby the speed of the crack opening is an important factor to see if it develops or not. Most PVs and pipelines are now designed with enough metal and the right grade of metal not to fail in ductile fracture, but if it does fail that way then it will truly unzip....

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way