Steel expanding in a tight space

Question

Hypothetical question: What would happen if I were to cool down a steel cylinder to make it contract, and then slide it all the way into a cylindrical hole in a room-temperature solid steel box? The hole's diameter is very slightly bigger that's the diameter of the cylinder when cold, but meaningfully smaller than the diameter of the cylinder when in room temperature.

Answer 1

The cylinder would expand until constrained by the cylindrical hole. After that it depends on the relative strengths. If the block has thin walls it may be stretched by the expanding cylinder and might even crack. If not the combination would behave like a solid block.

What you have described is a standard industrial technique for interference fit. See Liquid Nitrogen Shrinking of a Shaft for a YouTube example.

Answer 2

Assuming your hypotethical question as what it would be for a difference of 200 degrees celsius and assuming the hole as rigid.

The volumetric expansion index of steel is

$$ \text{ $9*10^{-6}$ - per 1°C – for regular steels; $16*10^{− 6} $ per 1°C – for low-alloyed steels.}$$ Let the length and radius of the steel rod be

• $L$ = length
• $R$ = radius

The volume of the rod will try to increase by the amount of $$\Delta V=9*10^{-6}*200=0.0002$$ Because the rod can expand only axially the length $L$ has to increase.

$$L_\text{final}=L_\text{initial}*1.0002$$ And it will undergo compressive lateral stress proportional to strain it would experience if free to expand radially!

In reality the rod will expand the cylinder proprtional to their bulk modulus of elasticty. The bar will elongate a bit less and will expand laterally a bit.

If we close the top of the hole immediately after inserting the rod, and assuming a rigid confined hole, the rod will undergo complex 3d stresses related to its bulk modulus of elasticity, which for steel is 156-165 GPa.

Answer 3

Every material can stretch or compress, even steel. The equations used to predict how tightly the rod would be squeezed in the hole are the same equations that would apply if the hulk stuck his fingers in the hole, stretched it out like a rubber band and placed it around the rod. Or, more realistically, if there was a taper and you hammered the rod in.

All of these scenarios are called interference fits, since if the steel were to relax into it's natrual shape, the parts would interfere with each other.