Strain gage errors: bending cancellation in thin metal? 3

[dmalicky]

We are trying to measure tensile/compressive strains in 0.020" thick steel, using strain gages. With material this thin, the surface strains are dominated by local bending effects (e.g., oil canning). As usual, I average the top and bottom strains to get the neutral axis strain. I setup some cantilever bending pilot studies (method below) to verify that the bending effects cancel.

But in these pilot studies, my measured tensile (T) strains are consistently 5% to 10% lower than the compressive (C) strains when using the .020" material. (Pilots on 0.125" or 0.187" thickness steel show T and C match <1%.) Compressive strains match theory <1%, so the tensile strains are the error. Usually, the %error grows with the applied strain: at 200 applied microstrain (ue), T<C by 2-3%; %error increases to 5-10% at 500ue. All gages show some creep (typical for the CA adhesive): zero-return shifts 5-10 microstrain (1-2%) after applying 500 microstrain. We would like to avoid the epoxies if possible bc of the pot life or heat-cure requirements.

Here are some ideas, mine and Vishay’s, on why the tensile %error only shows up with the thin material:
1) Curved beam theory: Nope -- we aren’t near that territory.
2) The gages locally reinforce the material, and the polymer backing is stiffer in T than C. Vishay’s CEA gages are .003" thick; the EA gages are .001" thick. But my tests show EA gages are only slightly better than CEA gages for the %error.
3) The CA slips more when it is in convex curvature than in concave curvature. ?
4) The CA is slipping much more when under load, and more in T than C, than the zero-return values would suggest (visco-_elastic_). But shear is shear, right? Why would T be different than C, and error only show up with thin material?
5) ?


Details on the method:
1) I make a 1" x 8" x .020" steel strip "beam" (we have tried both stress relieved and as-rolled steel).
2) Mount a uniaxial gage on one side (or both), in the middle of the beam, using standard Vishay techniques, gages, instruments (MBond 200). I have tried various ways of clamping and other CAs but none solve it.
3) Precondition the gage by bending back and forth +/- 500ue and then lower strains.
4) Zero the meter by carefully holding the beam vertically (produces <1ue tension).
5) Secure one end of the beam and record the initial strain due to beam weight. Turn beam over and record strain due to opposite loading.
6) Apply a cantilever bending load to the end of the beam and record strain. I angle the mounted end of the beam up slightly so that the gage is roughly horizontal as the beam curves over.
7) Turn the beam over, mount identically as possible, and apply identical end load. (Results are not sensitive to these variations).
8) Repeat 5 and 6 with greater and greater loads, to about 600ue. I order it as T-C, C-T, T-C, C-T... to cancel order effects.


Thanks for any leads you might have!
David Malicky

 

[JStephen]

Two ideas:

First, in the analysis of beams, you normally assume that the tension and compression flanges are not restrained in the lateral direction, and therefore there is no lateral stress in them. (There is some lateral strain, due to Poisson's effect.) However, in the case of a thin bar bent the easy way, the tension and compression surfaces are fixed to each other so that lateral expansion and contraction are not possible. This in turn introduces lateral stresses that one might not expect. It also makes the bar stiffer than you would think. If I remember right, the difference is a 1-nu^2 or about 10%. Maybe this effect is cropping up.

Secondly, strain in a bent object is proportional to the distance from the neutral axis. Normally, you'd assume a strain gage was very thin relative to the object, and so the strain in strain gauge is the same as the strain on the surface. But if the strain gauge thickness is significant relative to the material thickness, then there would actually be a variation in strain through the thickness of the gauge, with the indicated strain corresponding to the strain at the mid-thickness, more ore less. Maybe this effect is cropping up.

 

[MintJulep]

dmalicky,

I'm puzzled by your test method step 7. How are you mounting the test coupon, and you are you applying the load?

How much variation exists when you flip the coupon over?

You state that the results are not sensitive to whatever variations exist. How do you know this?

Consider a mounting that allows you to flip the coupon and fixture together without disturbing the interface between test coupon and fixture.

I would not consider 0.125 and 0.187 test coupons of this size as "thin". Also, these are a full order of magnitude thicker than the 0.020 material that you are interested in. Have you tested other thin coupons?

 

[dmalicky]

Thanks for the helpful replies.

Jstephen, I had forgotten about thin beam theory--yes, we are certainly in that territory. You are correct--that boosts the effective modulus by 1/(1-nu^2). That would imply that our gages are reading a little high when in compression, and a little low (but less than I thought) when in tension. Yes, I have been accounting for gage thickness offset w.r.t. the neutral axis. Vishay says it is about 0.0015" to the foil, including CA, though will vary since CA cures so fast.

MintJulep, I am fixing the end by sandwiching the beam between a steel bar (top) and a wedge shaped piece of aluminum (bottom). The wedge angle is about 10 degrees to aim the beam slightly up, to minimize any moment-arm losses/variations as the beam bends, and also to keep the gage ~horizontal when loaded. Loads are applied via tape and small weights, at the very end of the beam. I’ve checked the effects of mounting and loading by repeatability: measure, disassemble, remount, repeat. And purposely making errors, e.g., hanging the weight off-center (puts the beam in a little torsion). But yes, it is a good idea to make a flipable integral mount, as there may be unknown confounds.

Flipping the beam over causes the 5-10% differences, depending on strain magnitude, gage application skill, and unknown factors. I.e., the %diff can vary *between* specimens ~+/-3% (at same strain mag) for no known reason. %diff can be up to 15% with sloppy technique. %diff is very consistent for the same specimen, though. Here is the data from 1 typical beam at increasing end loads (in microstrain):
T C %Diff
24 -24 0.0%
91 -9 1.1%
159 -164 3.0%
251 -262 4.2%
387 -411 5.8%
449 -481 6.7%
511 -555 7.9%

The .125" and .187" beams were done to verify the problem wasn’t my general gage application technique (e.g., contamination), and to narrow the problem down to the (complex) variable of beam thickness. Early on I did a few 0.025" and 0.017" beams; problem seemed similar but not enough n to test differences. That would be an interesting variation study.

From conversations w/ Vishay, current theory is that the CA creep, CA & polyimide non-linearities, and the relatively thick gages w.r.t. the beam combine (in an unknown way) such that 5-10% may be as good as can be done. I'd still like to know why though. Between gages, 5-10% seems plausible given the variations in gluelines, but reversing the strain on the same gage--that is still a puzzle.

If we aren't able to solve the %diff problem, we could calibrate individual opposing gage pairs by, at the end of the test, cutting them out of the panel and checking their %diffs. Then correct the data by the %diffs. Time consuming, but it may be our best solution.

Thanks again for the help. David Malicky

 

[ccw]

Hi Dmalicky,

As soon as the metal leaves the elastic limit region, which in some metals is very early from the quiescent point, the bending neutral axis begins to move around. Someone on here (Locock?)did a time history narrative of near yield / post yield behavior of metal in reverse bending a while back. It was very revealing about non-intuitive behavior in the bend. All that to say, I am not surprised at your results.

Here is another idea. The material testing business uses small knife edge precision extensiometers, designed much the same way as your test article, (deflection vs. strain) to measure strains in the throat, or necked-down section, of pull specimens. The use of the extensiometers avoids influencing the test results of the specimen with gage cement, etc. Perhaps you could independently verify your strain data by using one of those.