Your title is 2D Plane Stress. That assumes the thickness of the rings in the Z direction is small compared to the diameter and stress in the Z direction is zero.
Or did you mean 2D Plane Strain which implies the thickness of the rings in the Z direction is large and the strain in the Z direction is zero. Probably not or you would have called the rings pipes or tubes.
In either case, you can use a Remote Displacement on the inner circle and set all three DOF to 0. Notice that I have made a Cylindrical Coordinate system to plot the Normal Stress in the X direction. For this model, the stress at the interface is -9.26 MPa.
You could build an Axisymmetric model which does not assume zero stress in the Z direction, it calculates stress in 3 directions: Radial (X), Axial (Y) and Hoop (Z).
Create new geometry in the XY plane for an Axisymmetric model. The 2 rings are represented as 2 rectangles on the +X side of the Y axis, which is the axis of rotation. In SpaceClaim, create a New Component called Inner and draw one rectangle. Create a New Component called Outer and draw the other rectangle.
In Workbench, make sure to set the Geometry cell property to Analysis Type 2D.
In Mechanical, make sure to set the Geometry 2D Behavoir to Axisymmetric.
Add a Y=0 Displacement boundary condition to one vertex. That properly supports the rings with no restriction on thermal expansion.
If you want the rings bonded at the interface, add a Bonded Contact.
If you want the rings to slip at the interface, add a Frictional Contact and assign a non-zero coefficient of friction.
Create a Normal Stress for the X axis, which is the radial direction. Now you see the variation in stress along the Y axis, which is the Axial direction. There are end effects but in the center, there is a region that behaves similar to the Plane Stress solution.