difference of 1st, 2nd ,3rd principal stretch

Studiot

You need the axis of rotation to answer that question.

Let us say that the test specimen is a cylindrical bar with the test tension applied along the cylinder axis.

The principal axes will be

e₁ will be along the cylinder axis

e₂ & e₃ will be any pair of orthogonal lines in a disk through the cylinder at right angles to the axis.
If the spin axis is e₁ then the centrifugal effects will be along these axes (e₂ & e₃) and will therefore subtract from the stresses and strains on these axes since they are of opposite sign.
That is the poisson strains represent a contraction, the centrifugal strain represents an expansion.

http://www.roymech.co.uk/Useful_Tabl...cylinders.html

edit : Of course since the rotation imposes real external loads and stresses there will be a poisson effect in the e₁ direction ie against the applied tension.