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

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.

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