Effects of notch's position along a rod that is in tension

[yonese]

Say I have a rod with a notch at the very centre and another ro with a notch at the very end. Both rods are identical in length radius materials etc. Who would be impacted by the notch more? And if then both were to support a load at the end of the rod (both in tension), what effects would the load have on the stress concentration caused by the noth? Obviously any cracks under fatigue loads will significantly reduce the rod strength, but how does the effect positioning of a notch vary?

I understand a notch causes a stress concentration that typically leads to local plastic strain which eventually leads to cracking. I'm certain that the positioning of a notch will affect the stress concentration, I just don't know how. I am also guessing that a notch at the middle of the rod will have more significant effect than a notch at the end.

 

[Baluncore]

I'm certain that the positioning of a notch will affect the stress concentration, I just don't know how.

For a static analysis, the position of the notch will only become important when there is a side force or a misalignment of the end attachments.
The dynamic analysis of a spinning shaft with a notch, will be more complex.

 

[Frodo]

See diagram.

Simplistically (because it is a very non-linear problem):

The average stress at B is P/Area B
The average stress at A is P/Area A, which is higher

The stress will therefore fall as you move away from the notch. The rate and shape of fall will be dependent on the bar cross section shape, the notch shape and notch depth and is difficult to analyse simply.

As long the bar is longer than the area where the stress is varying (and assuming you are loading the entire end faces uniformly) the length of the bar is irrelevant. If it isn't, it isn't.

There is a stress concentration at the tip of the notch.

Google for lots of information - eg NOTCHES AND THEIR EFFECTS from the University of Toledo.