Question regarding to load-deflection and stress-strain data

[Sirm]

Hi, I hope this is the right place to ask this question.

I have done a 3 point bending test to my rectangular sandwich sample and I only have the load-deflection data obtained from the test. However I wish to obtain the toughness of my sample. The following steps are what I did and I hope someone can shed some light on me whether doing this way is correct or not.

Firstly I converted the load to stress using the following formula (obtained from wikipedia):
sigma = (3FL)/(2bd^2)
where sigma = flexural stress
F = load
L = support span
b = width of the sample
d = depth of the sample

As for the flexural strain, I used:
epsilon = (6Dd)/L^2
where epsilon = flexural strain
D = deflection
d = depth of the specimen
L = support span

So now I have data in term of flexural stress and flexural strain and I can plot the stress-strain curve. After that, I can obtain overall toughness of the sample by measuring the area under this curve.
I have learnt this in my uni but I forgot a lot of the stuff already. Haha. Also sorry for my English if it is hard to understand.

Thank you

 

[rb1957]

your section is not truly rectangular, as understood by the bending stress equation. Wiki is a reasonable first reference, but you should dig into "strength of materials" textbooks for this.

bending stress = My/I
M = FL/4 for a three point bend
y = d/2
I = bd^3/12 for a rectangle, but I = 2bt*(d/2)^2 ... more exact is d/2-t/2 but the difference should be small
so you can see wiki's solution ... FL/4*(d/2)/(bd^3/12) = 12FL/(8bd^2)
but for your panel it should be FL/4*(d/2)/(2bt*(d/2)^2) = FL/(4bdt)

i'm not sure i understand "toughness" the way you're explaining it (the integral of stress/strain is strain energy) ?
"toughness" to me is a fracture mechanics term

another day in paradise, or is paradise one day closer ?

 

[Sirm]

Hi, rb1957

I will definitely look deeper into that, thanks for the heads up . Just want to confirm it again, is that "t" in equation the thickness of the face sheet?

Sorry I have not clearly introduced my project yet. Here is what I have done. The core material and face sheets are made of pine and balsa wood respectively. Half of samples are bonded together using epoxy and the rest uses polyvinyl acetate. They all subjected to bending test until it fractured. So I want to see which one gives better result, based on their toughness.

Here's what I've got from Wikipedia again, toughness is the ability of a material to absorb energy and plastically deform without fracturing. It can be determined by integrating the stress-strain curve. In my case, to find toughness I just find the area under curve just before the point of fracture. However the Instron machine only gives data in term of load and deflection. So that's why I wish to convert those data to stress and strain in the first place.

Again, thank you very much for your time for helping me! I really appreciate it.