Metal Tube Radial Dent/Crush equation?

[jmblur]

I'm working with structural metal tubing (of an elongated octagonal cross section (height is about 17% taller than width) that's subject to high enough radial impacts (generally with another tube of similar size and strength) to cause both denting (generally on the edges), usually only small dents but occasionally enough to cause actual bending of the tubing. The tubes are basically cantilevered, with negligible axial load and usually low bending loads (which can be neglected in most cases).

We're looking at a good way to compare these materials for dent resistance under these high-dynamic loads (generally high speed/low mass impacts).

Is there an equation (even for cylindrical tubing) that approximates resistance to this kind of dynamic denting? I've found plenty on panel denting, and axial crushing, but nothing so far on radial denting. I'm aware that it has relations to hardness, yield strength, and wall thickness, but can't find the relation and don't have the equipment to do the testing to derive it.

Cheers!

 

[jmblur]

In addition, if you could point me to any books that might have this kind of information covered well, it would be most helpful!

to clarify the above (been talking too much to marketing lately...), I'm looking for an equation to approximate the local plastic deformation due to high strain rate radial loading on a tube.

Cheers!

 

[MSUKeith]

There is probably not a simple formula for this solution. It will be greatly dependent on not just the material property variables - modulus, yield strength, thickness - but also the shape of the impacting piece. Example: a sharp, pointed piece will concentrate stress, a large ball shaped piece will distribute stress and have a different force value to cause a permanent dent.

For stress calculations (and just generally good reference materials):
'Roark's Formulas for Stress and Strain'
'Peterson's Stress Concentration Factors'

 

[jmblur]

Thanks MSU, I realize it gets real complex real fast, was hoping there was a kind of simplified "higher this = better impact resistance" type equation, even if it was just comparative for one type of impact with one profile and one impactor - obviously it wont' be perfect, but it will at least be good guidance.

Guess this just gives me more fodder for setting up a physical test rig - will certainly be cheaper (and easier) than buying and learning abaqus explicit!

Any ideas on material properties that would help with toughness? Obviously Hardness, Yield Strength, some contribution of Young's Mod, thickness (based on equal weight, thicker is obviously going to be better all else being equal)... any others? Ignoring profile and impactor differences, since those will be the same.

 

[Hansmeister]

One option you might consider is to convert the impact loading into an equivalent static load, and then use the Biijlard equations to evaluate radial stresses on a cylindrical shell.

If the equivalent load causes yielding of the shell, then you will get a dent.

 

[MSUKeith]

Blur,

I consider toughness and impact loading a fracture phenomenon - to simplify: way over on the right of the stress strain curve. Where 'denting' and 'bending' are yield phenomenon defined by the transition from elastic to plastic deformation - the left side of the stress strain curve. Obviously strain rate plays a role - you have not defined rate in this case. I don't believe toughness or hardness will come into play.

Deformation amount will be effected by R value and n value once you exceed yield - particularly for thin wall cylinders. There are lots of dent test rigs available at material companies that service automotive - as this is a big focus of attention with lighter gauge, lighter weight and higher strength materials put into service on door outers/hoods/etc. Check with your material supplier to see if the can help with testing.

Note: Explicit code always comes handy if you've got the time and money.

 

[jmblur]

Rate is approximately 10m/s, although there's quite a bit of variation. I haven't yet done a thorough study of the loads and speeds behind the denting phenomenon (been too busy getting next year's product out, once I get some breathing room it's going to the top of the list). The angles and force behind the impact can vary quite a bit as well - it's a sporting goods product in a very dynamic environment, so it makes simulation... lets just say difficult

The actual loading is caused by the impact of one tube against another tube - usually edge-on-edge loading, although the edges are approximately 5mm radiused.

We see bending in low speed, "Cross check" type situations, and denting (and occasional fracture, cracking, or full on soda-can like crushing and breakage depending on the material used). The actual impulse is extremely short due to the metal-on-metal collision. I've assumed in this case that, similar to a baseball swing, the speed and mass of the shaft determine the force, rather than any input force from the user in the stick-on-stick contact situation due to the shortness of the impulse and the non-rigid connection to the hands. (Obviously in the lower speed cross-check situation this is exactly opposite.)

This really does seem like an abaqus explicit type problem, was just hoping there might be a shortcut to get ballpark comparisons. Since abaqus is out of the question (they already sunk money into solidworks simulation, which is certainly easier to use but definitely not good for impact), so it looks like I'll simply have to build or buy a test rig and get my answers the old fashioned way.

Thanks again folks

 

[jmblur]

One more thing I forgot to mention -

We also do 4 point bend tests on these shafts for ultimate strength (why 4 and not 3 you'd have to ask the last engineer, but for sake of continuity I use the same test). Generally these deform ~2.5 inches before failure, where they generally collapse and fracture at one or both moving points. This is more similar to the "cross check" situation.

The denting issues we see are from the high speed shaft-on-shaft impacts, in which plastic deformation is extremely localized to the point of impact and generally does not result in any plastic deflection of the shaft, just surface damage. Of course, this damage often leads to catastrophic failure later.

 

[Bribyk]

Sounds similar to the failure mode of composite hockey sticks. Localized damage that causes catastrophic failure in bending (slap shot, crosscheck or leaning on it).

I am curious about your application though, lacrosse?

 

[CoryPad]

Four-point bending loads the material between the narrow span in uniform tension, while three-point bending creates a single-point stress maximum at the center of the part. Four-point bending is a worse-case scenario since the flaw does not have to be co-located with the point of maximum stress.

 

[jmblur]

Good guess Bribyk, that's the one.

Four point doesn't really make sense for the types of loading we see where bending or breakage-through-bending occurs - generally it's either a point load or a non-uniform distributed load (human body contact), either while cantilevered or when supported from either side.

I don't believe that for metal extrusions the 4 point bending is necessarily a bad comparative test, albeit worst case, but when we test composites it seems like an unnecessarily harsh loading condition as the 2 center points cause extreme line loads that cause matrix and fiber damage. In use, composite shafts show very similar failure modes to hockey sticks, although the impact loads are often more severe and more common leading to more fiber/matrix damage.