But the surface and crack are always independent when I do the calculations.
How can I generate a case with a crack cutting of the surface?
Thanks a lot for anyone’s help.

Welcome to the forum. If you are given a finite width for the crack as shown in this problem, I might create the mesh model as shown in the following commands.

reset
create surf rect width 1 height 1
create surf rect width .01 height .1
subtract body 2 from 1
compress # This is just so that I can work on surface with id 1
surf 1 scheme trimesh
Curve 5 7 interval 4
mesh surf 1