Convert Load Deformation (Extension) Data to Stress-Strain Curve

Question

I am trying to manipulate some data that were obtained from a three point load experiment on a porcine tibia.

I would like to obtain a stress-strain curve for the various specimens; however, the only data that was given from the Instron three-point loading set up was Load (N) vs Deformation/Extension (mm).

My question is: how do you convert the Load vs Deformation curve to a Stress-Strain curve?

Answer 1

It's fairly complicated. I found an article in The Bone Journal Comparison of three-point bending test and peripheral quantitative computed tomography analysis in the evaluation of the strength of mouse femur and tibia where they used tomogrphy to calculate inertia. However if you don't have CT you can try the hard way.

1. You'll have to calculate bending moment M. It should be simple.
2. Locate Neutral Axis. You can assume it as a simple shape but probably you have a complicated shape and have to calculate it.
3. Calculate Area Moment of Inertia. Again if you assume simple shape it's easy else complicated.
4. Formula for bending stress is $\sigma = -\frac{M\cdot y }{I}$ which is called flexure formula M is moment, y is distance from neutral axis and I is area moment of inertia.
5. Strain is $\varepsilon = \frac{y}{\rho }$ where $\rho$ is radius of curvature. A simple presantation is here (PDF)

This presentation (PDF) and this course notes are also informative.