BOLT CLAMP FORCE / THREAD STRETCH 3

[Matt206]

Background:
A simple relatively accurate formula to relate Torque to Clamp Force is: T = (F)(D)(K).
Where D --= Diameter of bolt, T = Torque, Lets ignore K for this.
I am encountering a situation where a screw designed like #1 has an appropriate clamp force with the hand toque that we are able to generate. While a screw designed like #2 does not achieve the appropriate clamp force.
Thread type, thread engagement, material, is all exactly the same. As the above formula suggests, the diameter difference is the reason for the difference in holding force. I can actually feel the stretch that I am looking for when turning the smaller screw.

Question:My question is WHY does Diameter have an impact on this? I would think it would be cross sectional-area of the screw, But after drilling a through-hole in the larger diameter screw to decrease the cross sectional area (with the intention of making it function as a thinner spring to generate more stretch) this did not impact the clamp force.
If unable to change thread type, engagement, and diameter – I am unable to achieve the required clamping force with a given torque.

Picture 1:

Picture 2:

 

[SwinnyGG]

If you can use no other means of positive fastener locking, your best alternative is probably to neck the bolt down to the smallest possible diameter that will handle the service load (thus maximizing bolt stretch at your installed bolt preload). You want this neck to be as long as possible.

I'll ask again- is this threaded into organic material (bone?)

Your restrictions sound more and more like this is a screw for an internal medical device.

If so, you then have to be very careful about necking the screws unless you can guarantee that your fasteners see no load other than preload (I.e. the clamped part is sufficiently fixed that no bending loads are applied to the fasteners).