K should change because it inversely related to the length of a spring. So cutting a uniform spring in half with yield a doubled k value
Edit:
If you cut the spring in half you now are moving the spring half the distance of the original size so it will require 2x the same force. Where k is equal to force over delta length.
I'll have to look into what you are saying closer. We are missing something in our communications here. I think it has to do with the free length of the spring after it is cut. Again coming back to the amount of material and bar length. Because I am pretty sure I can't just go cut my LJ coil and magically have a stiffer spring to carry a load better. So I maintain that cutting in half will not change the rate. Only the free standing length gets shorter. Cutting the amount of material in half is a different story.
EDIT: Which I guess we are doing as well if we cut the spring in half. The question that remains then is free height. (Assuming all else is equal)
I'm going on pause now. I'll have to re-read and think through everything. I don't know this stuff as much as I am just able to think through it, but that takes time if I haven't considered it before.
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