# Effect of resonance on Fatigue Life

In summary, the researcher is considering using a cantilever beam design for a test specimen and is considering using glass as the material to be tested. They expect resonance to produce a fatigue life different from the same deformation and frequency without resonance. They also expect operation at resonance to precipitate a fatigue failure.f

I'm doing a research project which aims to develop a mathematical correlation for fatigue life prediction at resonance frequency. An experimental setup is also to be created which would be used to carry out the experiment, cyclic loading cycles until failure. For this a Cussons linear vibrator apparatus will be used, which also knows as mechanical shaker, and a suitable test specimen and clamping arrangement has to be designed.

I'm considering using a cantilever beam design for test specimen, since it's a continuous system and it's easy to achieve the natural frequency that way. The material is yet to be finalized, but I'm considering glass, since it is brittle.

Suggest me which material would be ideal to carry out this experiment, like which one would realize fatigue failure in a reasonable amount of time? And which parameters are to be investigated in order to successfully carry out the experiment?

To test fatigue break, I would NOT use a brittle material! It's my understanding that tiny creeping is essential in fatigue break. And results on engineering alloys would be more useful.

As a shape, you should consider one that balances all torques, since torque at fastening points is the main source of damping - followed by sound radiation.

The experiments may take long, and an actuator that vibrates less than the tested element would have some chances to survive it... A good reason to use rotations in such tests, for instance with a radially loaded shaft.

Do you expect resonance to produce a fatigue life different from the same deformation and frequency without resonance?

The electro-mechanical shaker (vibrator) I've with me has peak sine force of 8.9 N, total stroke of 2.54mm and frequency range of 3-50 Hz. So, the strength of material being tested has to be low enough to fatigue break in sufficient amount of time. Considering the capabilities of available shaker, it's unlikely that any engineering alloy would break with that input. Hence, I'm in favour of a thing rectangular strip of glass, like soda lime glass. We can select the dimensions such that it's natural frequency falls inside the frequency range of mechanical shaker.

The proposed specimen is a cantilever beam, so the moment has to be balanced only along with the vertical reaction force. Yeah I know that friction in the clamp is the main source of damping.

I expect operation at resonance to precipitate a fatigue failure, and that's what I'm investigating.

What's your take on this now?

With a thin sheet, acoustic loss will be very important. Can you operate in vacuum?

In case you want to stay with a thin material, metals are available as well as sheet. I used austenitic stainless 17-7 steel cold-rolled to 50µm, and thinner exists, hot-rolled as well, just like carbon steel, copper alloys and more.

Wires can be thin as well, and will radiate less. Very common of extra-hard carbon steel of any diameter, also available in hard-drawn austenitic stainless steel.

Cantilever beam: it must be symmetrical left and right of the shaker's axis. If you add separate parts to symmetrize the torque, fastening the added parts will absorb the vibration. Less so if you can weld through the whole thickness.

Do you really want to use the shaker? An (elastic) bent shaft requires little torque to rotate, hence a small motor. No worry with impedance matching, acoustic losses, bench durability. But more difficult to resonate, sure.

This seems to be a tiny shaker. If you have a peak-to-peak displacement of 2.54mm, a force of 8.9N, and a frequency of 50Hz, an estimate of the power output assuming a square wave force-displacement graph would be 2 x 50 x 0.00254 x 8.9 = about 2 watts.

That isn't going to do much fatigue damage to anything except a very small test piece, and then its resonant frequency would probably be much higher than 50Hz.

At 50 Hz, you are only accumulating 180,000 load cycles in a 1 hour test. (I'm assuming that if this is a research project, you don't want to do tests where the time to failure will be months or years.) For a material like aluminum you would need a stress of the order of 100MPa to get a life as short as that. For a force of only 10N, that would mean a specimen with a cross section area of 0.1 sq mm...

If you had a 2-watt shaker or ultrasonic transducer that would run at 50kHz, or a 50Hz shaker that would deliver 8kN (and with a bigger displacement amplitude) you would have a lot more chance of designing a successful test.

@ AlephZero : Yeah that's a pretty tiny shaker that I've got with me and I've to perform the experiment with this only due to budget limitations. So, keeping in view the specifications of this shaker, which material you'd suggest to be tested, which would require a lot less stress than usual engineering metals? How about soda lime glass? Since we're only investigating the effect of resonance at fatigue life , and the research is not supposed to have practical repercussions immediately.

@ Enthalpy : No can't operate in vacuum. Symmetry issue can be taken care of. Any suggestions for material selection keeping in view the shaker specifications ?

If you have a shaker with a frequency response of 3Hz to 50Hz, and you want to test something at resonance, the obvious first step is design a test specimen that resonates in that frequency range. If you keep the size fiixed and change the material, the material property that determines the resonant frequency is sqrt(Youngs modulus / density). Find material properties for as may types of materials as you can e.g. from http://www.kayelaby.npl.co.uk/ and look for the "outliers". (You will find that most structural materials have very similar values).

To be honest, I don't really see a direct connection between fatigue life and resonance so I'm not sure what you are trying to test here.

Sure, there is an indirect connection: resonance -> increased amplitude or motion -> higher stress -> lower fatigue life. But there is nothing very new in modelling that chain of cause and effect...