Fatigue failure of yielded material

[brashear]

We are planning to preload a spring past its yield strength, but before its ultimate tensile strength. The spring will then be used in service for 10^7 cycles, but with a small amplitude. The amplitude stress is about 30% of its endurance strength. Even though the spring has a permanent deformation, it will not break statically, because the stress has not reached its UTS. My question is, how do we analyze if it will fail in fatigue? Thanks

 

[salmon2]

After you preload beyond its yield strength, you basically has a new stress/strain curve, with higher yield strength. And then you are still working in a elastic range, a new elastic range though. I feel you then need a S/N curve and your new yield strength to evaluate your fatigue life. I personally never did this, just some random idea.

 

[TVP]

Is this a cold-wound helical compression spring using a common material (music wire, oil-tempered Cr-Si steel, etc.)? If so, it is common for springs to be preloaded to the point that they plastically deform (usually called "taking a set"), which causes a redistribution of the stresses, and has a fundamental impact on their behavior under cyclic loading. Analysis of springs with respect to fatigue require attention to all of the details, including residual stresses. There is a lot of empirical data on this subject, and some companies have invested in FEM simulation. Have you discussed this with any spring manufacturers?

 

[brashear]

I haven't discussed it with any spring manufacturers because it's not a helical spring. It's just a diaphragm made of full hard temper stainless steel, which acts as a spring.

I think I got it though. Let me know if this makes sense. See the attached drawing. So after I preload the spring, it will be at its new yield strength Sy preload. Then after the first cycle, the spring is deformed to a higher stress inelastically to Sy new (along blue line). Then when it is relaxed, it travels down a new elastic line (along green line). The stress will be alternating between the stress at C and B. In reality, the strain difference between A and B would be slightly different than between C and B, because of redistribution of stress due to plastic deformation.

So since the new mean stress is less than its new yield strength, the material could still be safe against fatigue failure provided the stress amplitude is small enough.

It's always reassuring to know when something is already done in industry.

 

[brashear]

Attachment didn't work:

http://i.imgur.com/qWXz6.png

 

[sreid]

If you will be operating the spring near a yield point, the fatigue life will be short You haven't been clear what the cyclic stresses will be. To get to 10 million cycles [reliably], the stress shoulld be below half of the yield stress.

 

[brashear]

Well, not really.

According to Goodman and Soderberg, when calculating fatigue life, one should take into consideration mean stress and stress amplitude. For example, in the extreme case where the mean stress is almost equal to yield and the amplitude is zero, you just have static loading and it will not fail.

You are probably thinking of a cyclic load with zero mean stress (a rotating shaft), in which case the stress amplitude must be below half of the UTS multiplied by Marin factors (an estimate for endurance strength).

 

[sreid]

Brashear, You are, of course, absolutely correct. My intent was to point out to the orginal poster that he had not been clear about what stress levels he planed to operate at after the "Original Set" had been done.