I'm using hard drive platters to create a Tesla Turbine. I'd like to get as much efficiency out of it as possible. That being said, for safety concerns, I'd need to know a generic range at which they'd shatter.
If there's no range that anyone has found, then how could I (safely) test what speed they shatter at?
I think it's going to depend upon the individual platters and what type of drive you sourced them from.
The technology for hard disk drives (HDD) that can easily handle 5,400 rpm is comparatively old and very easily sourced. Slightly newer technology allows for drives that can handle 7,200 rpm. Keep in mind that those are the internal speeds of the drives themselves during regular operations, and not necessarily their upper rotational speed limit. And there are newer drives that can handle up to 15,000 rpm with claims of some companies researching 20,000 rpm drives.
That said, you'd be wise to take a conservative value. YouTube has a number of videos of CD's shattering when running at excessive rpm, and there's a particularly awesome one captured at an extremely high fps rate of a CD shattering when the disc was spun at 23,000 rpm.
But it may be possible to run older 5,400 rpm style platters at much higher speeds, as demonstrated in this video that claims to run the platters at 15,000 rpm.
The prudent approach would be to test some platters at your preferred target rate along with a very substantial safety margin. This instructable tutorial shows how to build a Tesla Turbine and run the platters at 15,000 rpm. It would also seem prudent to build some form of protective barrier around the turbine should any of the parts shatter.
The other answers give some information as far as how fast hard drives can run during normal use, but your application doesn't involve normal use, so you might be able to crank some higher speeds out of them. If you want to take a rough theoretical approach to this problem, you can look at the stresses in a spinning disk and compare them to the strength of the hard drive platter material (aluminum in your case, but some platters are made from glass and other materials).
Assuming the aluminum part of the platter is bearing most of the load, and it can be approximated as a solid disk (any hole in the middle is very small), and ignoring stresses generated by the fluid flow in your Tesla Turbine (possibly not a safe assumption, but very complicated otherwise) then the stress in the disk can be calculated as follows (from Engineering Toolbox):
$$ \sigma = \frac{\omega^2 r^2 \rho}{3} $$ where $\sigma$ is the stress (N/m^2), $\omega$ is the angular velocity (rad/s), $r$ is the radius of the disk (m), and $\rho$ is the density of the disk material (kg/m^3).
Rearrange for $\omega$ and you have: $$ \omega_{max} = \sqrt{\frac{3\sigma_{yield}}{r^2 \rho}} $$ where $\omega_{max}$ is the maximum theoretical velocity at which the disk would start to break apart and $\sigma_{yield}$ is the yield stress of the disk material.
If you have a 3.5'' (0.0889 m) disk, made of some aluminum alloy with yield stress $\sigma_{yield} = 24.1 \times 10^6$ Pa (I wasn't sure which alloy is used in HD construction, so I picked the lowest yield strength I could find from Aluminum Alloys), and density $\rho = 2700$ kg/m^3, then you would have a maximum rotation speed of: $$ \omega_{max} = \sqrt{\frac{3(24.1 \times 10^6)}{(0.0889/2)^2 (2700)}} \approx 3680 \text{ rad/s} \approx 35200 \text{ rpm} $$
Obviously this is very fast, you wouldn't actually want to run your drives that fast due to many factors. Consider that even below the yield stress materials can stretch due to creep and, as other answers have mentioned, higher speeds will cause increased wear in the bearings and other parts. However, this would be a good way to estimate a hard upper limit on your drive speed.
Given the number of assumptions and approximations I made in this analysis, I would feel comfortable with a safety factor of 4 (i.e. $\sigma_{max} = \sigma_{yield}/4$) which would suggest that my example drive could run with low risk of the platters shattering at a speed of approximately 17,600 rpm, albeit with increased wear.
I suggest you look further into your application to figure out what parameters are relevant for you.
For a very long time, the rate-limiting factor for HDDs is the speed at which they spin. With modern drives with cacheing, etc, this is less true, but essentially manufacturers push every drive to what they deem safe maximum operating speeds. Any higher and the bearings would wear out much quicker, seals would get too hot and rupture, etc.
So the speed of the drive you have is likely the speed you should be spinning it at even if you dont care about reading/writing data.
