Is there a formula to determine the frequency at which...

[454Casull]

... a diaphragm enters breakup?

http://www.linkwitzlab.com/x-mid_dist.htm

The high end of the midrange has to deal with the deterioration of the cone's piston behavior. As a rule of thumb, this occurs when its effective diameter becomes larger than 1/2 wavelength, i.e. at frequencies above 500 Hz for a 21 cm driver, and above 650 Hz for a 18 cm driver.

Is this correct? I thought the stiffness of the material was a factor.

[Mr Evil]

The quote is correct, but it's a different mechanism to breakup. What the quote describes is that the limited speed of sound in air means that, off-axis, sound radiating from opposite sides of the cone will no longer be in phase as the wavelength approaches the size of the cone. This means that a driver will start to become directional at higher frequencies, instead of radiating spherically.

On the other hand, breakup of a cone occurs near various resonant modes of the cone. The result is a very peaky frequency response at those frequencies. It depends on the geometry and material of the cone, and is not something that a DIYer would be able to calculate.

[wunhuanglo]

Going back to GA Briggs in the 50's, it does seem that in general you can expect a first severe break-up from an 8" paper cone driver at around 3.5 to 4 KHz.

There's no doubt whatsoever that geometry and material properties play a huge role, but driving a cone from the center with a compliant edge mount does tend to limit the range of possibilities.

[CeramicMan]

I think many people could be quite surprised at how low the break-up frequencies can be. In the picture of Vifa's measurement of their TC14WG49-08 speaker which is only 5.5 inches, I'd estimate the first severe break-up mode to be at about 1.1kHz-1.3kHz. The glitch may be next-to invisible considering the flatness of the frequency response, and there are only 2 small clues that suggest cone break-up:
1) A very small change in frequency causes a relatively large ripple in the amplitude response - ie: a high-Q notch or bandpass filter.
2) There is a small peak in the impedance plot caused by a sudden change in the effective mass of the cone.