I have a case here where i would like to know what the stress concentration factor conservatively (see below). I have heard that if you set 3 then you are safe?
Yes it depends on a lot of factors.
You have to make a bunch of assumptions; ductile materials, properties largely unchanged by welding, weld filler modestly stronger than base metal, loads a small fraction of ultimate, no high cycle fatigue, and so on.
Of course a lot of this goes away if they just use a full pen weld
Slightly different perspective. IMO the weld, in practical, is full pen weld since root of 1mm will get melt. Then the stress concentration will not be of big concern since the weld is/going to become full pen.