The difference between your model and my model is that I have used a changing force (between 0 and maximum force) as a load and you used a changing displacement.

I think I had/have a misunderstanding with the physics. You said ANSYS calculates the true stress/strain. Is it right that the material behaves like the following picture when using isotropic hardening and a constant maximum force in every cycle? So in the first cycle the cross-sectional area decreases and a balance between stress, cross-sectional area and strain is reached (Point 1)? In the next cycles the material is changing between Point 1 and Point 2 in the stress-strain curve? In this case ANSYS did the right job in the simulation I did.

I would like to know the total displacement/plastic strain of my part after 10 cycles. There has to be an increasing elastic strain in every cycle (ratcheting?). So do I need to model it with Chaboche? How do I have to do it?