Collapse and deformation of a circle (tube)

[jeff davis]

TL;DR Summary

I am looking for a formula to calculate the collapse and deformation of a piece of plastic tubing.

Hello:
I am looking for a formula that can help me determine the collapse and deformation strengths of plastic tubing. I have been scouring the internet for this information and i have yet to find a satsifactory formula.

I have found a formula that seems pretty wide spread ~ however it gives me a result that does not seem correct.

Can anyone point me in the right direction?

Thanks

Jeff

 

[jrmichler]

Collapse how? Lengthwise like this:

This is Castigliano buckling. There are other types of longitudinal buckling, for which I don't remember the names. Step on an empty beverage can for an example. The type of buckling depends on tube diameter, wall thickness, material properties, and end conditions. Each type needs a different equation.

Or, are you talking about the buckling of an externally pressurized tube? If so, look carefully at the origin of the formula. Does it assume that the tubing is perfectly round? Real tubing is at least a little out of round, and that has a large effect on buckling under external pressure.

 

[jeff davis]

Thank you very much for your reply!

I am talking about an externally pressurized tube. The equation provided most likely does expect perfectly round specimen. My search is for a more reasonable equation;
Maybe there is some decay rate that must be applied in order to more accurately depict the real world scenario? The formula will probably contain a related rate of deformation vs strength. Maybe i could have a variable that presumes an initial tube deformation?

My goal is to have a rough idea of the deformation on medical catheters before we commit to a certain wall thickness. Testing would obviously be the second step but a mathematical approach would ease my mind for the initial designing.

 

[jrmichler]

Here is an equation from Formulas for Stress and Strain, by Roark and Young, 5th Edition:

You want #19a. That equation also assumes a perfectly round tube with thin wall thickness.

Buckling of thin wall tubes is normally an all or nothing situation. When one buckles, it buckles all the way instantly. Thick wall tubes can collapse more slowly. Sometimes.

You should consider a test. Medical catheters are subject to low pressures. You could take a piece of tube, plug the ends, coil it up inside a one or two liter clear plastic pop bottle, then add pressure. I remember measuring the pressure of a room temperature carbonated beverage at about 50 PSI, so there should be no problems if you stay under that pressure. Drill a hole in the cap, add a bulkhead fitting (ask the person behind the counter at your local auto parts store), connect to a water line, pump it up, and watch for collapse. Don't forget to plumb in a pressure gauge. If the pressure is low enough, you could use a water manometer to measure pressure.

 

[anorlunda]

Wouldn't collapse be most likely where the tube makes a sharp bend, or a kink?

 

[Baluncore]

Wouldn't collapse be most likely where the tube makes a sharp bend, or a kink?

Yes. A catheter must be modeled as an asymmetric elastic tube. A kink is a collapse.

Where there is a bend, the outside of the bend will be thinner and less curved than the inside of the bend. Tension in the outside of the bend will also tend to pull that wall in. Being thinner walled, with flatter curvature and longitudinal tension outside the bend, all subject the outer tube wall to increased collapse under external pressure.

A minimum radius of curvature must be specified for the tube before collapse pressure can be calculated.

 

[jeff davis]

You should consider a test. Medical catheters are subject to low pressures. You could take a piece of tube, plug the ends, coil it up inside a one or two liter clear plastic pop bottle, then add pressure. I remember measuring the pressure of a room temperature carbonated beverage at about 50 PSI, so there should be no problems if you stay under that pressure. Drill a hole in the cap, add a bulkhead fitting (ask the person behind the counter at your local auto parts store), connect to a water line, pump it up, and watch for collapse. Don't forget to plumb in a pressure gauge. If the pressure is low enough, you could use a water manometer to measure pressure.

Thank you very Much!
I can't say enough how i appreciate genuine answers and technical help.
The test procedure you outlined is very intelligent. This setup would be easy to create in the lab and i think that it would be an invaluable resource for our applications.

I am also going to apply this formula. Thank you for your help.

 

[jeff davis]

Yes. A catheter must be modeled as an asymmetric elastic tube. A kink is a collapse.

Where there is a bend, the outside of the bend will be thinner and less curved than the inside of the bend. Tension in the outside of the bend will also tend to pull that wall in. Being thinner walled, with flatter curvature and longitudinal tension outside the bend, all subject the outer tube wall to increased collapse under external pressure.

A minimum radius of curvature must be specified for the tube before collapse pressure can be calculated.

Very true! We often try to compose the catheter in such a way in which we can minimize the bend radius before collapse. If one could imagine wrapping the flexible catheter around a finger. How small we can get that finger before collapse is one parameter in the design. Dialysis catheters are what i am working with. They actually have a unique feature in the form of a center septum which throws a wrench in some calculations. This gives two passages (arterial and venous).

The tubing for which this question arose is for an introducer however and not a "flexible" catheter. The tubing will not be bent at all during the procedure but will have to withstand the compression forces from the tissue around it. If the tube deforms too much then the item it is introducing will no longer be easily inserted into the body.

Often times i have noticed that it is common practice to just accept what is already on the market because it is working. This seems to apply especially for those aspects that are more difficult to calculate. That policy gets projects fairly far in the game; but when we start to question the methods in search of better ones the calculations are invaluable.

Thank everybody for all of your comments and help! it is not so easy to find such information.