I've recently done 3-point bending on mice femurs. Unfortunately, the software did not produce any graph. To my knowledge the graph is needed to calculate the Young's modulus and yield strength. What can be done with these results that I have?
Attached are the results that I have obtained.
In my opinion, if you could not obtain a stress-strain curve from the 3-point bending test on mice femurs, you may still be able to calculate Young's modulus and yield strength by using other methods. Here are some options:
*Use the data from the test to calculate the load and displacement at the yield point, and use these values to calculate the yield strength.
*You can estimate Young's modulus by assuming that the material is linearly elastic and using the equation E = (4L^3)/(3πbh^3), where L is the distance between the supports, b is the width of the femur, h is the height of the femur, and E is Young's modulus. However, this method assumes that the material is homogeneous and isotropic, which may not be true for biological materials like bone.
*You can also use empirical equations to estimate Young's modulus based on the bone density or other properties that can be measured.
It's important to note that these methods may not be as accurate as obtaining a stress-strain curve from the test, but they can still provide some helpful information about the mechanical properties of the bone.
M. Janane Allah thank you so much for the insight. I'll try it out.
Michelle:
Janane's answer is a good one to use the maximum bending stress at the center of the tension surface to estimate parameters such as the elastic modulus and the stress at yielding or fracture, but in general measuring the elastic modulus by such mechanical techniques can be severely inaccurate as you're not measuring the strain accuarately enough (or even at all) and there is the situation mentioned by Janane with respect to the inhomogeneous nature of the structure of bone. The elastic modulus of bone is roughly 15 to 20 GPa but if you perform bend tests on mouse bone, you are like to get numbers as low as 3 GPa for these (and a few other) reasons.
The best way to measure the elastic modulus is any material is by measuring the propagation rate of a compression wave (or equivalent) but again even this is a problem in bone due to its inhomogeneous structure and geometry. If you are studying the cortical bone, the best way in my opinion is to use nanoindentation but to take many readings on a sinlge bone to compensate for the fact that each nanoindentation measure is examning only a very small volume.
I hope that this helps.
ROR
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