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Suppose I have two parts with holes aligned and I have to install a solid rivet into the "combined" hole.

Clearly the rivet diameter must be slightly smaller than the hole diameter, otherwise it simply won't fit. So I heat this slightly smaller rivet, insert it into the hole and then deform its tail so that the rivet now has two heads and sit properly in place.

Assume I follow all the procedures and best practices.

Does the deformation only affect the tail or does it also make the middle of the rivet expand and fill the gap between the hole walls and the rivet?

In other words, if I wait till the rivet cools down and then grind the rivet head off - will it leave its place easily or will I have to force it out?

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The short answer is: Yes, as the rivet head is formed, the shank of the rivet is also deformed to fill the hole.

Just like structural bolts, rivets are installed in holes that are 1/16 inch larger in diameter than the rivet. This clearance allows for manufacturing imperfections and clearance for easily placing the rivet in the hole.

A US military specification for riveting (MIL-R-47196A) states in 3.3.3.3:

The driven rivet shall completely fill the hole...

The figures in that MIL Spec show that rivets that do not completely fill the hole are one of the ways that a rivet can be unacceptable.

An image of this from a web page on riveting shows this as well:

Rivet diagram

Video of Hydraulic Riveting

You can also see video of a hydraulic rivet on YouTube that shows just how much deformation is involved with riveting.

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