Well I think we have a different view on this rod Gordy, the linear part of the stiffness is about 1N/m (some 10 grams for 9.9 cm deflection).
Merlin,
As we have found this rod may be better suited to doing a 5th order fit rather than the third order fit that we have used in the past. However, with a 5th order term I don't know if the Duffing-type non-linear spring analysis can still be used, and the k3/k1 characterization of the spring non-linearity no longer applies.
I have looked at doing a "hybrid" cubic fit to that data that gives results more in line with your values. This essentially calculates the best linear fit for deflections that are less than 12% of the clamped length, and then finds a cubic term to go along with that forced linear term that minimizes the square of the fitting errors. Matlab has a fmins function that makes such a fit easy to do. That gives a larger least squares error than a true cubic fit, but provides a much better fit to the force vs deflection points for small deflections. Essentially it reduces the fitting error for small deflection values at the expense of larger errors for the bigger deflections.
That approach tends to increase the linear term and reduces the cubic term coefficient, so it gave a k3/k1 ratio of around .96 for Bernd's data as noted below. That is a value we have seen before for other tip flex rods.
Gordy