Radial deflection from an axial load 3

[random_guy]

I've got a polyethylene disk with a short width compared to the diameter. The disk will have an axial pressure placed upon it, and I wish to find the radial displacement as a result of this axial pressure. It will form a bulge in the center of the disk around the circumference, and the height of that bulge is what I'm looking to find.

Looking through my books, the only similar case is delta = PL/E (from PL/AE); however, the displacement is only axial displacement.

Any ideas? Thanks in advance!

 

[dhengr]

Look up Poisson’s ratio.

 

[random_guy]

Thank you!

It can be easy to forget where our everyday values come from.

 

[zekeman]

If you are after the height of the bulge, isn't that an axial displacement.

If you are asking for that motion due to a pressure on the disk, then you can find it in Rourke's book on stresses and strains for various edge conditions.

 

[random_guy]

I don't have Roark's book, but I will attempt to get a copy of it.

The disk is within a cylinder, and I am trying to find the pressure at which that disk contacts the wall of the cylinder. Using Poisson's ratio:

nu = -lateral strain / axial strain

nu = (gap/ID)/(deltaX/L)

I can solve for deltaX, then use

deltaX = PL/E

to find the pressure at which I will make contact.

However, the results I get from this do not agree with the results I am getting from Pro/E Mechanica. I trust these hand calcs more than I trust Pro/E, but it would be nice if they lined up.

 

[dhengr]

We do have a fair handle on Poisson’s ratio, as relates to a 1" x 1" x 8" steel bar in tension or compression. You get a uniform nominal stress. With my quick glance at your calcs. that’s what you are analyzing. I’ll bet if you look at a Theory of Elasticity text, instead of a Strength of Materials text, that you’ll find that Poisson’s ratio is somewhat sensitive to object volume vs. load application area size; stress uniformity and constraint by non-loaded material in the volume. What happens when you have a softer disc .25" thick x 8" dia., with Modulus of Elasticity and Poisson’s ratio much different than steel? And, are you applying the load with a 7.99" dia. ram? If so, and with a soft enough disc, it almost becomes just a redistribution of volume of material, by shear flow. If you have a stiffer disc and are applying the load with a 4" ram you have a different problem, again. I don’t know anything about Pro/E Mehcanica, but take a look at how it is treating the above variations.

 

[random_guy]

I do have a softer material, a "plastic" disc that I am using; however, it is a hard form of plastic (MDPE). It is loaded uniformly across the entire surface area.

Perhaps this is the incorrect method to use when analyzing the deformation of a plastic? I have been using my Strength of Materials textbook to determine the proper method of calculation; I have never studied elasticity theory.

Thank you for your advice.

 

[MintJulep]

Is it loaded uniformly across the surface on both sides?

 

[dhengr]

Now, you have added another dimension or variable, creep and plastic flow, although those are kinda hidden ‘shear flow’ phrase.

 

[prex]

nsgoldberg, in your formula, if gap is the radial gap, then the lateral strain is (2*gap/ID). Does this correction, if applicable, result in a better agreement with Pro/E?

prex

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[CoryPad]

Are you plastically deforming the disk? Poisson's ratio is only accurate for elastic deformation.

 

[random_guy]

Sorry for the delay in getting back, I was off Friday. I appreciate all the suggestions here, and I've got answers to your questions.

-Is it loaded uniformly across the surface on both sides?

Yes

-If gap is the radial gap, then the lateral strain is (2*gap/ID). Does this correction, if applicable, result in a better agreement with Pro/E?

The gap I am using in my calculations is diametrical gap, not radial.

-Are you plastically deforming the disk? Poisson's ratio is only accurate for elastic deformation.

I can't say for sure here, but since the disc is a polyethylene and the gap is only a few thousandths of an inch, I would think that the disk is deforming elastically, although I would like to check the numbers against plastic deformation. However, I do not believe there are equations for finding the deformation in the plastic region. Any ideas?

Thanks for your input.

 

[random_guy]

Just found out the tensile strength is higher than I am running it at - it is fully elastic deformation.

 

[prex]

A consideration that comes to mind.
In your first post you refer of a bulge in the middle of the lateral surface. This is not exact for the ideal case of your hand calc and you should check what Pro/E gives. In fact, if the pressure is really uniform on both faces and there are no tangential forces, such as those that would be applied by a piston and due to friction, the disk will be uniformly compressed in the axial direction and also uniformly extended in the radial direction (see Timoshenko & Goodier 3rd ed., page 226).
However those ideal conditions are very difficult to be implemented in practice, I wonder what you can realistically obtain for a relatively hard material and a correspondingly small gap.

prex

http://www.xcalcs.com

: Online engineering calculations

http://www.megamag.it

: Magnetic brakes and launchers for fun rides

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