Finding Stress-Strain Curve from Load-Deflection Data

[davidmandis]

Hi,
I have the load-deflection data for a composite tube and would like to find the stress-strain curve. I know the dimensions of the tube.
Is it just calculating stress=force/area & strain = change in length/original length at each point from the load-deflection curve or do I have to take anything else into consideration?

Thanks,
David

 

[CoryPad]

You equations are correct. The only complicating factor is what to use for original length. For tension testing, it is the length between grips. For compression testing, it is the part's overall length. For bending, you have non-uniform stress and strain, and you would need to modify your equations.

Regards,

Cory

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[vc66]

I am assuming this is load-deflection data for a cantilevered beam. If so:

Stress = ( Force * distance to force * distance from neutral axis to force ) / area moment of inertia

Therefore, if you have the force (load data), the cross-sectional measurements, and the distance to the force, then you should be able to retrieve the stress.

From there you know that strain = stress / Young's Modulus.

Assuming you know the modulus for this material, you can find the strain.

Keep in mind, that this is probably only good for the linear elastic region of the material. Afterwards, all bets are off, and the data may take an odd turn.

V

Mechanical Engineer
"When I am working on a problem, I do not think of beauty, but when I've finished, if the solution is not beautiful, I know it is wrong."

- R. Buckminster Fuller

 

[davidmandis]

Thanks for the reply & sorry for not providing details. This is a composite tube with a quasi-static compressive force applied to it, so I guess it would be the parts overall length that is used for calculating strain. The load-deflection curve is highly non-linear so no constant Young's modulus.

Thanks,
David

 

[vc66]

Then yes, I agree with CoryPad regarding using the part's overall length. Good luck with you calculation!

V

Mechanical Engineer
"When I am working on a problem, I do not think of beauty, but when I've finished, if the solution is not beautiful, I know it is wrong."

- R. Buckminster Fuller

 

[rb1957]

be careful interpreting your results ... i don't think your results will give you the compressive stress/strain for the material, but rather for the piece (the geometry tested), particularly if your results are highly non-linear (i'd've expected composite to show almost a brittle result).

i don't think it's relevant for your case, but rememebr poisson's effect (affecting the area).

did you measure the change in diameter of the test piece ? i suspect that the sides of your tube might have bowed outwards, affecting your results (if you were trying to charactise the material).

 

[davidmandis]

Yes you are right but I want the stress strain curve for the geometry only and don't want to characterize the material.
The load-deflection curve was obtained from a reference standard handbook so even though there must have been some bowing, I do not know the values of the out of plane deformations (poisson's effect).

 

[rb1957]

a couple of things ...

poisson accounts to the thickness change (like the necking of a tension test specimen) ... i don't think it a pplies in this particular case, i mentioned it just in case you were going onto other things.

but if you've got a load/deflection curve from a standard reference, then i'd divide the loa by the area, and the deflection by the original length of the specimen. (like your OP!)