No, no, no! That's a bad idea. Without even going into the issues of putting metal on the ground, putting rusty metal above a plant isn't likely to help iron availability in the soil. Most machine shop metal filings come with cutting oil residues, and this is a tree hugger you are advising. Putting industrial oil spills on the base of a tree just isn't a good plan. Yeah, I know. Brake drum filings are not generated by using any cutting oil. But where are you going to find anybody that turns brakes these days? All the shops I know have quit doing it.
Instead, just get some iron sulfate from any decent farm or garden supplier. Broadcast, or better yet, drill a lot of holes around the tree in the soil and fill them with the iron sulfate mixed with the dirt you dug up. An 1 1/2 drill bit works great for that. This does two things: it adds soluble iron to the soil (usually not needed), and more importantly, it acidifies the soil, thereby making the iron in the soil more available to the plant. This is the old fashioned gold standard treatment for iron chlorosis in trees. And iron sulfate is really not expensive, as soil amendments go.
Now if you aren't observing any iron chlorosis, then you probably don't need such treatments, anyway. Iron is one of the most common elements on the planet, and not many soils are truly iron deficient. What happens is that a lot of soils get too basic (high pH), and the available iron in the soil is reduced. Acidify the soil (by any means; not just iron sulfate), and your iron chlorosis problem goes away.