Minimum coil diameter prior to yield

[SPND]

I've got a situation where I need to determine the minimum bend radius a tube can take prior to material yield and I am having a heck of a time getting reasonable results. Something tells me this should be a relatively simple exercise but I am not getting any results that make sense.

My situation is this:

347 stainless tube, 1/4" OD, 3/16" ID being inserted into a slightly larger guide tube. Tube enters verically into a radiused section of the guide path and exists 135 degrees relative to vertical. What is the minimum diameter of curvature the tube can take prior to yield? I've tried reducing the curved section to a situation where I can use a case from Roark's on beams but I am not getting believable results. Roark's states that depth of beam curvature must be less than 1/10th radius of curvature, I think this may have something to do with bad results form this method. Any takers?

Thanks.

 

[BigInch]

If it doesn't yield, how are you going to bend it permanently? If you don't reach the yield stress, it will only be in the elastic range and it will straighten when released.

Stress = M d/2/I M /E/I = 1/R

Stress = E / R * d/2


Set stress = yield stress - .01 and
solve for R = Radius (to the centerline)

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[desertfox]

SPND

What is length of pipe your pushing in, the deflection of the pipe be dependant on its length and whether it stays elastic or not.

regards

desertfox

 

[hydtools]

How about looking at the problem from the point of strain. If the strain exceeds the yield strain then the tube is permanently bent.

The outer fiber length for the bent tube is the elongated length. The length of the neutral axis is the reference length before bending. The difference between the stretched outer fiber length and the neutral axis length through the same bend angle divided by the neutral axis length equals the strain of the outer fiber. I ran through the equation and rearrange to solve for the bend radius at the neutral axis and got r = OD/(2*strain).

Yield stress for annealed 347 is 30,000 psi.
E = 28 x 10^6 lb/in^2
Yield strain is 0.0011 in/in
OD is .25 in
r = 116.7 in bend radius at yield. That seems large, but it doesn't take much to bend small tube to yield.

What do you think?

Ted

 

[BigInch]

If the material obeys Hooks law, stress is directly proportional to strain, so if you exceed the "yield strain" you've also exceeded yield stress.

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[BillBirch]

Isn't is usual when discussing stainless steel to refer to the 0.2 percent elongation (stress) rather than yield stress, which may not be easily or definately established?

 

[hydtools]

billbirch, that leads to an interesting conclusion. For round tube or rod of any material whose yield is determined by .2% elongation offset, the yield bend radius is only a function of the tube or rod OD.
In this case, r = OD/.004 = 62.5 in.

Ted

 

[israelkk]

hydtools

It should be r=OD/.004 or even more accurate r = 250.5 x OD. The rest of the formula is an error.

 

[BigInch]

If it retains the bend, its yielded.

The rule of thumb for pipe bending any diameter of any wall thickness is 1º bend over a length equal to the diameter, which works since c = d/2 is independent of wall thickness and c and I are the same in all directions.

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[SPND]

Hey guys,

Thanks for the speedy input. Ted, I particularly like the idea of looking at it from a strain perspective. As far as the 116" bend redius, yes, that seems quite large and in-field practical experience would indicate we can get away with a radius much smaller than that. Could it be possible that as the tube elastically collapses that some additional leeway is possible for a smaller than calculated radius?

To give you an idea of what we can get away with: we routinely get tubing in that's got OD's at or less than .450", .030" wall and less and it comes in 10' coils. It's usually a wee bit set but a little tug with a hydraulic ram (in reverse) at 200lbs and she's as straight as when it came of the draw machine. Most of the tubing we use is Inconel 600/690 and 316L. In fact, one particular I690 tube we use is less than .100" OD x .015 wall and it comes in 18" coils and a small tug gets it nice and straight as well.

This particular application I am posting about is an in-core instrument, a customer is asking us to give them an instrument that can handle under 2' radius bends and desires that without working the material. Experience tells me that's way too small but I know that we can do much better than 116" without issues. This is one of those cases where theory will give us a comfortable margin but doesn't allow us to get an exact practical value.

 

[hydtools]

From your description of the 10' coil having a little set, the tube has yielded with a 60" bend radius. It may be easily straightened. But it has yielded at the coil radius. If the tube had not yielded it would spring out of the coil and be straight.

Using the .2% offset definition for yield, the resulting bend radius limit is 62.5" for the .25 tube. That seems to compare well with your experience. Minimum bend radius to just before yield for the .100 diameter tube would be 25". It must be wound in 18" coils so it stays coiled for handling.

You were asking for bend radius with no yield.

Ted