Do you want to hold it using  the large area surfaces or the 'thin' way?.

And relative to this what is the direction of the axis of the 40nm torque ? (are you making a thing  on a stick like a lollipop on a shaft. or more like a mushroom ?)

I have for example in the  past. super-glued things onto a a chuck plate. machined them and then dissolved the glue away in hot acetone.  This is probably no good for you, but With a better understanding of hte direction of the forces and which surface can be touched, better methods may become apparent.
mike.

Thanks for the reply.

The way I'd describe it is that the torque is applied in the axis perpendicular to the flat surface of the part.

I'm not sure if that makes any sense so I attached a picture for reference. 

Which way it is held doesn't matter provided that the top surface remains clear.

So the "sides" can be used and the bottom can be used.

But I can't make any physical changes to the part like drilling holes etc. 

OK, 'mushroom' then ;-)  the 'obvious' is to lay the flat area and clamp onto the circumference, but I presume this is what you are doing, and the jaws are damaging the outer edge ?
If the diameter is very fixed then a collet chuck and a spacer column a mm or so less in diameter  beneath to set the height may be an answer.
(example images  taken from    www.rdgtools.co.uk/.../14-15mm-ER32-Collet-2622.html)

plus

This is both cheaper and  less damaging than a traditional 3 jaw chuck

But maybe you could avoid all this and just use the glue trick if precision you need is not great. ?
Mike.

There are others on here of a more mechanical inclination, it may be worth waiting to see what other folk suggest. !

Depending on the circumstances another approach might be like fitting a steel "tyre" to a wheel - i.e. made a "holder" with a round hole somewhat smaller than the part you're trying to grip - then heat it up to expand it and drop your part in - as it cools it'll then grip the circumference very evenly. Heat again to release. I gather induction heaters are often used for this sort of thing in industry. Obviously no good if your part isn't tolerant of rather severe heating, but might work for a few cases.

   - Andy.

How about a magnetic chuck? www.ebay.co.uk/.../i.html

I've been using a 5C collet in a pneumatic fixture to clamp it. It had a step machined so no need for a spacer column. We even got diamond coating put on it to improve the grip but the part is still twisting which results in damage.

I thought about using a chuck too but the part is quite small and it's a production issue because I imagine the operators might struggle and the process wouldn't be very controlled if different operators over or under-tighten the grip on the jaws.

I don't think the glue trick is an option for me unfortunately because I need a process that's quick and repeatable.

Either way, thanks for your input.

This definitely seems worth looking into.

I'll need to check whether the size of the part will be a hinderance since I assume you probably require a somewhat large surface area.

Thanks for the suggestion! 

A pot chuck may be the best solution here. This is a fixture bored out to fit the part, split, and then held in a conventional chuck. The force is transmitted over almost the full circumfrence  and there work piece is kept flat and concentric.

And a few details:

Workholding with Pot-Chucks (modelenginenews.org)

Dagmara Sajdak said:

I've been using a 5C collet in a pneumatic fixture to clamp it

Aah. Now the 5c collet is only single ended  split I think, which means it grips very well at the front, but less well further back. This may not matter on a thin sample but the accepted wisdom is that double split collets like ER and TG give a more parallel gripping action  for cutters shanks etc. I am not sure how much this would matter for holding a disk. 

How good is the finish of the circumference of the disk?  - I can imagine diamond only working well  on a smooth surface.
I can imagine an all-round paralell grip is best
Mike

(https://mellowpine.com/blog/collet-types/)

I did come across that information at some point, but given that I'm interested in gripping 3 mm of the part I didn't think it would make enough difference to warrant buying a new collet since from my understanding the ER collet clamps down in its entire length which I don't think would solve my problem.

The finish on the part is good, probably no more than a couple microns. Some of them are also plated up to 4 microns thick.

I might look into the TG collets if I don't find an overall better solution.