You have two things floating around:
- (a) the yield stress as a material property listed as force per
- (b) the yield strength at which the part itself yields listed as
However, you have four different names that can be assigned to these two things:
- yield stress of a material
- yield strength of a material
- yield strength of a part
- yield stress of a part
So when you think about a material or part withstanding "stress" are you really thinking about stress? Or are you actually thinking about strength?
In normal language, when you "stress" a part, are you stressing the material? Or are you stressing the part? Or are you "forcing" the material? Or are you "forcing" the part? Or are you doing all of them so it doesn't really matter what word you use? Of course, that doesn't mean stress and strength are the same thing so don't fall into the trap of thinking that they are or taking the terms at face value when you hear other people use them without accounting for context.
Technically, (1) and (2) are both equivalent to (a) because nothing else makes sense. Materials don't inherently have geometry so you cannot use units of force alone to specify the yield strength of a material. You must refer to yield stress.
However, parts do have inherent geometry and in this case part strength and part stress mean different things. (3) means (b) since strength is units of force, whereas (4) means (a) since stress is force per unit area distributed in the part which is the same as force per unit area distributed in the material that makes up the part.
In any case regardless of the name of things, force/area is geometry independent but when translated to force it must be geometry dependent.