I am trying to determine the modulus of elasticity (Young's Modulus) for a rigid paper sheet. The issue I am having is that my results for the Young's Modulus change depending on what orientation (length extending out or width extending out) I use to measure it.
The material of the paper is not trivial, and as a result I am not able to find a datasheet on the material itself. Instead, I did some simple tests to calculate the Young's Modulus, especially since it is a thick sheet that behaves more like a sheet of metal than floppy paper.
I took the sheet, fixed one end, and measured the deflection at the other end (and other relevant parameters). I did this with both the length and the width extending freely over the fixed end. I accounted for curvature in the sheet when measuring the deflection in order to make the measurement as representative of an ideal beam as possible (there were some assumptions I made about the curvature, but I will not go into details about how I eliminated the effect of curvature in my deflection measurement unless I have to, as I believe the problem lies elsewhere). I then used the Euler-Bernoulli beam equations for distributed load, $q$, (in this case, the distributed load was due to gravity) to arrive at the Young's Modulus, $E$. $$E = \frac{qL^4}{8I\delta_{gravity}}$$ $q=$ distributed load, $L=$ the length of the paper extending over the fixed end, $I=$ second moment of area, which changed depending on orientation, and $\delta_{gravity}=$ deflection after removing effects of curvature.
The results I achieved were consistent ( within 0.3 GPa of each other), but changed drastically, by almost an order of magnitude or more, when changing whether it was the width of the paper that was modeled as the "length" of my beam, or the length of the paper.
I am wondering what caused this big change in the Young's Modulus, since I don´t know if it is typical for Young's Modulus to vary by such a large amount between orientations (10-90 times difference). Paper is an anisotropic material (thank you, alephzero), so it could be related to this fact. I believe I am missing some factor in the equation that is depenedent on orientation, such as a correction factor for structural stiffness due to sheet curvature, or something with the Poisson ratio, but of course, this belief can be misleading me.
Things to note:
The material is foamboard, only the outside of the material is made of paper in the strictest sense. The inside is made of foam.
I changed the distributed load, $q$, depending on the orientation, since the weight/length changes depending on whether the width or the length. I did the same thing for the second moment of area, $I$.
For the second moment of area, $I$, I modified the equation to more precisely model the shape of the curvature, but it did not change the value of $I$ significantly.