I'm not exactly sure what modulus you used but ASTM A228 is music wire so E≈207GPa. With that value the spring constant I found was:
\kappa = \frac{Ed^4}{10.8DN} = \frac{(207GPa)(2mm)^4}{10.8(6mm)(20)}=2.556Nm/rev
As for your question, to calculate the force the spring will apply you...