Question

How can I calculate elastic modulus from 3 point bend data?

I have acquired load vs deflection data from a 3 point bend test, as per the following setup:

Three-point Loading 厂12

Fro this data, I have attempted to calculate the Youngs modulus of the bone specimen at a load of 2002 N with a deflection of 1.18 N. the specimen is also 80mm long, with a hollow circular cross-section, being 25mm outer diameter and inner diameter of 16mm.

To do so, I have utilised the deflection formula, re-arranging to calculate E, as shown below:

from this calculation, I find that the elastic modulus is equal to approximately 1.5 Gpa. relevant literature suggests that cortical bone has an approximate youngs modulus of 11-20 Gpa, so my calculations are off by a factor of approximately 10. Any help is very much appreciated.

Answer 1

Yes, your are write. Your answer for young's modulus is off by a factor of approx 10. The following could be the reasons for this.,

1. First and foremost check the unit consistancy. This deflection you have given is 1.18, but you have given the unit as N (newton). The unit should be in mm/cm/m (unit of deflection).

2. According to me, the elastic modulus of cortical bone is very less (11-20 GPa), i.e has got very less stiffness against deflection. So what I am coming to say is, the defleciton 'd' which you have given could be in centimeters (1.18 cm). So if you use this one, you will get the right answer. So kindly check for unit consistancy.

3. Also check wheather you work within the elastic limit. After the elastic limit, the youngs modulus will be non-linear and the value comes down very drastically.

4. Check wheather the cortical bone is isotropic or anisotropic or orthotropic. The youngs modulus will change with respect to direciton in anisotropic and orthotropic materials. However for isotropic materials the youngs modulus will remain constant in all the directions within the elastic limit.

Kindly check for the above point..