# Maximum Pressure of Stainless Steel Pipe

Hello,

I'm looking to experiment with an Electrothermal-Chemical (ETC) system of accelerating a projectile. Basically, it will involve using energetic materials and large amounts of electrical power to create very high pressures inside of a tube in a very short amount of time, behind the projectile.

Browsing the McMaster.com website, I see that the strongest pipe I can buy, given the 0.5-inch inside diameter I'm interested in, has a 0.5-inch wall-thickness.

So, my question is, how do I calculate the maximum pressure, for both plastic deformation and rupture, of a stainless steel (304) with an inside diameter of 0.5 inches, outside diameter of 1.5 inches, wall thickness of 0.5 inches, and yield strength of 42,000 PSI (according to McMaster's description).

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Would this be correct?

P = 2st/((d-2t)SF)

where,

P = max. working pressure (psig)
s = material strength (psi)
t = wall thickness (in)
d = outside diameter (in)
SF = safety factor (in general 1.5 to 10)

So, with a safety factor of 2,

P = 2(42,000)(0.5)/((1.5-1.0)2.0)

P = 42,000 PSI

Anyone know if this is correct? The equation is from (http://www.engineeringtoolbox.com/barlow-d_1003.html)

Q_Goest
Homework Helper
Gold Member
Hi axi0m. The equation you're pointing to is for thin wall pressure vessels and some assumptions are invalid for the thickness of tube you're suggesting. From Wikipedia:
When the cylinder to be studied has a d/t ratio of less than 10 the thin-walled cylinder equations no longer hold since stresses vary significantly between inside and outside surfaces and shear stress through the cross section can no longer be neglected.
Ref: http://en.wikipedia.org/wiki/Cylinder_stresses
You might want to http://www.google.com/search?hl=en&...=9&aqi=g5g-s1g4&aql=&oq=thick+wall+&gs_rfai=" thick wall pressure vessel or something like that.

There's a few interesting links there. Here are two:
http://www.mechengcalculations.com/jmm/beam34_process.jsp
http://courses.washington.edu/me354a/Thick Walled Cylinders.pdf

Note also that the tubing provided by McMaster Carr is not pressure grade material. I don't know that makes a lot of difference, but I can tell you that industry does not allow that particular grade of material to be used in pressure applications. What pressure do you need to go to? There are other materials that may be better suited to your need.

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Q_Goest, you've been an incredible help here, as you were to me in the past in another thread.

One of the links you provided to me was apparently a calculator that provides the additional stresses involved with a thick walled tube. I'm now looking at stainless steel type 440C, which has a yield strength of nearly 300,000 PSI when hardened. I'm also now looking at different dimensions as indicated in the calculation below.

***** Calculator *****
Input:
Inside radius = 0.0127 meters (1 inch)
Outside radius = 0.0381 meters (3 inches)
Modulus of elasticity (for 440C SS) = 204 GPa
Poisson's ratio = 0.283
Internal pressure = 689 MPa (~100,000 PSI)
External pressure = 0.1 MPa (atmospheric pressure)

Output:
Max hoop stress = 861 MPa (124,877 PSI)
Max radial stress = -689 MPa
Axial stress = 86 MPa
Increase in inner radius = 65.74 *10^-6 meters (0.002588 inches)
Increase in outer radius = 32.15 *10^-6 meters (0.001265 inches)
********************

So, being that the hoop stress peaks at 861 MPa (124,877 PSI) and the yield strength is at least 250,000 PSI for hardened 440C stainless steel, under ideal circumstances, there shouldn't be any plastic deformation (permanent) or ruptures with an internal pressure of roughly 100,000 PSI.

minger
You need to be real sure when dealing with pressures of that magnitude. Doing a quick Google doesn't turn up much more than knives for 440C stainless. Is this really a tool steel? If so, how does it do at high temperatures? What are your temperatures, and how does the material handle that.

Also, those calculators typically assume an infinitely long tube. You will have edge effects which will increase the stress locally.

Lastly, make sure that you account for any fatigue effects. Your pipe may be good for the first firing and not so on the 10th.

Here is where I collected some of the data for the 440C stainless steel: http://www.matweb.com/search/DataSheet.aspx?MatGUID=850c5024f8d844af8ef95afab1a08792&ckck=1

There is also the following information via a description at McMaster.com:

"Ideal for use in bearings, valve parts, and knife blades. This high-carbon stainless steel offers good wear resistance and is one of the hardest stainless steels when heat treated. Maintains corrosion resistance up to 800° deg F. Magnetic."

Though there are many metals available with higher corrosion resistance temperatures, the reaction will take place within an insulating sleeve that should shield the metal's surface from the majority of the corrosive takings-place. Regardless, the temperature of the reaction will be well beyond the melting point of practically any metal, and beyond the boiling point of many metals. Fortunately, it will only take the projectile less than one millisecond to escape from the tube and release the heat and pressure.

Concerning the edge effects to which you referred, are those not represented by axial stress in the output?

Concerning the fatigue effects, I truly have no idea how to calculate anything to that regard. Perhaps I will have to gather empirical data for fatigue effects via safe experimentation.

Thanks again, everyone.

Q_Goest
Homework Helper
Gold Member
Hi axi0m. 440 can be hardened to a very high strength but of course it isn't ductile at all at higher strength levels. If it breaks, it will break catastrophically. Material for pressure systems is best if it yields significantly before breaking. Not to say you shouldn't use it, but you might consider other materials.

First, a better understanding of the stress the material is under would help. I've attached a graph for your particular application that looks at the hoop stress level in the material as a function of radius. Note that it starts at r=1" where stress is 125 ksi and quickly drops off to 40 ksi at r=2" and 25 ksi at r=3". That's because there is a tremendous compressive load on the ID that translates to a hoop stress. For a ductile material with a yield below 125 ksi, you might get a bit of yielding on the ID but not much. The OD material won't yield. Generally, the safety factor isn't applied to this 'artificially' high hoop stress on the ID. For thick walled vessels and piping, it isn't unusual to find the pressure exceed the yield. For example, there are numerous manufacturers of "cone and thread" type high pressure tube and fittings. This is a very thick wall 300 series stainless steel tube that's been work harded. The end of the tube is cut into a cone shape and threaded, with a nut that holds it into a fitting. The tube can withstand pressure up to 100,000 psi or even higher but I don't think the yield stress of the material is that high. Doing a calculation on the 1/4" tube you find a hoop stress on the ID of 113 ksi, and this is just work hardened 316. A couple of manufacturers include http://www.newport-scientific.com/" [Broken]. The point here is that the kind of pressure you're looking at achieving isn't all that unusual, and 440C or other high tensile strength materials is typically not used. Generally a work hardened 316 or 304 is the most common. You might also consider Nitronic which is a very high strength austenitic stainless steel that can be work hardened, but will still retain considerable ductility. The austenitic stainless steels will also have better corrosion resistance, though I don't understand what you need that for quite honestly. I'll take your word for it.

Regarding the ends, having generous radiuses is always a plus to minimize stress concentrations. You might consider posting a drawing to show what it is.

Regarding fatigue, (http://mmd.sdsmt.edu/fatigue_text/Image289.jpg" [Broken]) is a typical curve, but is valid for most iron based metals like the 300 or 400 series stainless steels and all carbon steels. We see this graph starts at 10^3 cycles with a limit of S/Su = .9 which means the stress it takes to break the material under completely reversed stress is 90% of the ultimate tensile strength after being exposed to 1000 cycles. I wouldn't put too much thought into this, the point is that if your material isn't exposed to more than 1000 cycles (or even 10,000 cycles), and as long as you're looking at "normal" factors of safety to yield of at least 1.5, you really don't have to consider fatigue. If your material is under much higher levels of stress or the number of cycles exceeds at least 1000 cycles, you should consider how fatigue may affect your material. Do you expect more than 1000 cycles on the material?

I wonder why you need stainless though. Are you concerned about corrosive attack? If so, you may need to retest the unit after a few uses just to assure yourself the material isn't being degraded by some kind of corrosive affect. I'd be surprised if it were, but I don't know what your situation is. Perhaps you could better describe what your concerns are.

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Q_Goest, thanks for the graph. I gather from what you are saying that it is often acceptable for the hoop stress to exceed the yield strength of the material for a thick-walled tube, given that the central and outer regions of the tube wall experience far less stress. My ignorance of the subject would lead me to ask, to what extent can that be accepted? Would a pipe generally be safe as long as the outer region is experiencing stress below its yield strength? It seems to me that at some point, the inner region would fracture because of the elasticity of the material, regardless of how little stress the outer region is experiencing. As such, it would seem to me that there is some guideline as to how much hoop stress can be allowed to exceed a given yield strength with a given thickness. Perhaps the safest thing to do would be allow the hoop stress of the inside diameter to simply equal the yield strength of the material. Given your description, that would seem logical and safe.

Another facet of the project is the electrothermal (possibly electrothermal-chemical) event that will generate as high of a pressure as is possible and will take place at one end of this tube, which will be closed. Though I am still researching that facet, I am researching what level of pressure can realistically be contained on a generous but finite budget -- thanks to your help and I am succeeding in that area. This ET-C event will probably involve a very high current being passed through a resistive load, such that it generates a large amount of heat and pressure. An example would be a mixture of aluminum powder with water. Though I am still unsure of the exact processes, a relatively general consensus seems to be that the aluminum powder is turned into plasma via ohmic heating and the water is superheated and turned into steam. The vaporization of aluminum within the oxidized watery environment seems to be corrosive. Additionally, various energetic substances could be introduced that would add to the pressures created along with adding to the corrosive nature of the event.

I'm not exactly sure how the closed end will be constructed.

Also, it's great to hear that the fatigue stresses won't be an issue, as I don't expect the material, for the time being, to be subjected to nearly 1000 cycles.

Q_Goest
Homework Helper
Gold Member
Just to clarify, the maximum hoop stress is on the inner surface of the wall and hoop stress decays exponentially as you move out to the outer most surface of the wall.

Regarding yield, it's a good question. I don't deal with it enough to know what is commonly done. But if you do a force balance on the entire cylinder, you find the nominal stress (assuming the hoop stress were constant throughout) is relatively low. If you had a SF of 2 overall, as opposed to a SF of 2 on the inner fibers of the vessel, I'd say you're ok.

This situation is not unlike the relatively high stress levels in parts where there are stress concentrations or the ASME code for pipe that allows ductile yielding for thermal contraction/expansion cases. ASME B31.3 allows the yield stress to be exceeded when going from ambient temp to maximum temp. That's because the pipe will yield the first time but on cooling will be put into a stressed condition that 'springs' the pipe the opposite way. When it goes back up to the higher temperature, the pipe doesn't yield again. Instead, it goes from one stressed state at ambient to an opposite stressed state at high temperature.

You might consider having a proper analysis done on the vessel and even getting it ASME coded. Not sure how the BPV does the stress at high pressure like this. I have to believe it's covered by the code but I'm not familiar enough to pinpoint it for you.

Checkout these two producers of ultra high pressure tubing. Harwood has the highest rated tubes. I've used both sources and the technical help was excellant

[noparse]http://www.barton.com/inventory.asp?catid={E2AE6636-25B1-4909-9A11-912DFCE9B994} [Broken]

http://harwoodeng.com/products/tubing/seamless-high-pressre/[/noparse] [Broken]

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Forgot to add I would not use 440C SS. or 1095 carbon steel. To hard to work with peroid.

In our work in developing a reactor for the direct oxidation of chemical with 100% Oxygen we had difficulty in calculation the MAWP of the tubes we used. We took the easy route and worked from the proof pressure of the tubing.
Another route to get an idea of the stress involved we used a modification of the shrink-fit calculations. Unfortunately I can't run the program any moire.
Our pressures were transient, up to around 60,000 psig, temperatures unknown, but high.

AlephZero