Thin vs Thick Cylinder Pressure Vessel

[Zeke04]

I am in the midst of designing a titanium pressure vessel to be deployed at a 6km (8800 psi) depth and needs to have a FOS of 1.25 minimum. The design as it now exists has an ID of 4.375" and a wall thickness of .302" and an unsupported length of 16.7". Most of the critical design equations for buckling of cylinders focus on "thin" cylinder defined as R/t>10, where this design incorporates a ratio of 7.73. I have read most of the available research on buckling of cylinders and how less than predicted pressures buckling occurs, but again these were all thin cylinders and not titanium. My question is can the predictions made on the basis of the thin cylinder analysis and testing be considered conservative for a design which is just outside the strict definition of a thin cylinder?

 

[JStephen]

I would think that to actually have a FS of 1.25, you'd either have to do testing or some fairly-involved finite element analysis. The buckling equations and ASME charts all assume a SF of 2-3 will be used, and there seems to be a good bit of variation when people do go testing things like this.

 

[TGS4]

You're going to need to do an elastic-plastic analysis with non-linear geometry that considers initial imperfections. Your failure mode will be a hybrid of buckling and plastic collapse - something that only an elastic-plastic analysis will provide.

This FOS you state, 1.25, is against which failure mode and which loading condition(s)?

 

[Zeke04]

The loading is from uniform external hydrostatic pressure found at the 6km depth of about 8800psi. The end caps are sealed with double O-rings and are .70" thick. At this facility we do not have access to finite element analysis other than basic static, which indicates that the pressure vessel as designed will withstand this environment with a 1.25 FOS, i.e. will not yield to a plastic condition. Some manual calculations indicate that elastic instability (buckling) will occur at a pressure less than that required to cause yielding, actually the analysis is not clear. The one report I could find that included testing of similar pressure vessels (Inelastic Buckling of Geometrically Imperfect Tubes under External Hydrostatic Pressure, Little, Ross, Short and Graham, Journal of Ocean Technology, 2008) indicates that buckling occurs at a pressure far lower than any manual calculation would indicate, including Eigen buckling in ANSYS (which admittedly is linear). They propose a "Plastic Knockdown Factor" (PKD) to account for the difference between test results and predicted results which in their paper varies from .86 to 2.6. All these cylinders fit the requirements of a thin walled cylinder. In the design chart that summarizes this paper our design falls in the "safe side", but is made from an entirely different material.

 

[SnTMan]

Zeke04, ASME Sec VIII, Div 1 contains rules for external pressure design of both thin and thick wall cylinders in several titanium alloys. FOS will likely be 3 1/2 to 4 to 1, if this is acceptable to you.

Regards,

Mike

 

[Zeke04]

The engineering team here (I am contract) does not want to design to those standards as it would create a bulkier and more expensive pressure vessel. I have not been able to find a copy of the ASME spec, this firm does not have a copy in house.

 

[TGS4]

If you want to design something to a hybrid plastic-buckling failure mode with a design margin of only slightly greater than unity (1.25), you are going to need to perform some sort of analysis. You are also going to need to have VERY tight tolerances on out-of-roundness and other geometric and material defects.

Whether or not you have the in-house capability to perform such work doesn't relieve you of the necessity to perform such analysis.

 

[Zeke04]

We will have parts to test soon, they do have a tank capable of these pressures, but not much more. Not sure the 1.25 FOS can be demonstrated. These guys don't even have a mechanical incoming QC department, they are living on the edge. Quite a difference from the Lockheed Martin engineering practices I worked to in the past. I have performed all the calculations I could think of and this design is marginal at best.

 

[TGS4]

Even when you do tests, remember that your production vessels will need to meet the tolerances of the test vessels. In buckling, the limiting factor will be the tolerances.

 

[Zeke04]

These are very small quantities, all pressure vessels will be tested. Do you have experience that nonlinear FEA analysis will produce accurate results?

 

[TGS4]

Yes, provided that the initial imperfections are included.

 

[Zeke04]

That is hard to predict without having the machined part in hand.

 

[TGS4]

In your testing, make sure that you are testing to at least the design external pressure multiplied by the design margin.

Yes, it is quite the condundrum. What are your fabrication tolerances on things like out-of-roundness?

 

[Zeke04]

Not sure the tank here can get beyond the 8800psi that is approximately the pressure at 6km. There has been no control on the out-of-roundness, drawings went out without my review.

 

[racookpe1978]

Sounds like the design practices and management care that led to the oil leak/blowout in the Gulf.

ASME PV standards not in the office. No control of critical features. Poor testing protocols.