The force you calculated is to get an Engineering Stress of 650 MPa. Ansys calculates True Stress, which is why you got a value of 750 MPa. For small values of strain, Engineering Stress and True Stress are almost equal. Perhaps the curved sides of this geometry is creating a stress concentration that cuases the engineering stress to rise slightly.

The warning is very useful because fatigue calculations using an S-N curve are valid when equivalent stress is less than yield strength. This is also called high-cycle fatigue. When stress is greater than yield strength, different fatigue calculations use strain-life equations. This is also called low-cycle fatigue. Please show the material properties. What is the UTS?

Do you have a textbook that has a good chapter on Fatigue? I recommend *Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue *by Norman E. Dowling. This will show you how to do Fatigue hand calculations using equations and S-N data. I suggest you first complete case (a) using the textbook equations.

Have you read the Ansys Help on the Fatigue Tool? Here is the URL:

https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/corp/v231/en/wb_sim/ds_Fatigue_Overview.html

Click the Help menu in Workbench to open Ansys Workbench Help, then copy/paste the above URL into the browser address bar. This will help you to understand what the Fatigue Tool is doing. Then you can complete case (a) using the Fatigue Tool and see if you get the same answer.