does anybody knows how can i get the change in the distance between the notch nodes (two points showing in the figure ) vs the applied force in every step as a table out put or curve in Abaqus.?
You can create History Outputs Requests for the two marked nodes, and write the displacement for each increment to the .odb file.
When the simulation is finished, you can combine the obtained displacement data with the applied force using Tools > XY-Data > Create ... and selecting the option Operate on XY data. Here you can apply mathematical operators to the data.
You can go to query and see the distance between two nodes, but do not forget to change step. Otherwise you can ask it in history OP either manually or by writing a Python code.