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# Fatigue - Multiaxiality and other pitfalls

## Fatigue - Multiaxiality and other pitfalls

(OP)
Hi forum,

I am currently trying to decide how to classify what I am up against, and how to rectify it..

Imagine a plate that has weights bolted to it, that is spun up to several hundred rpms (this is accomplished in ANSYS via rotational velocity BC), but also has cyclical torsional acceleration (rotational acceleration BC) as well.. to be clear, the load steps are as follows:

L1 = bolt plate to shaft, bolt weights to plate
L2 = rotational velocity effects
L3 = rotational velocity effects + positive torsional vibration
L4 = rotational velocity effects + negative torsional vibration

As you can imagine, between the bolts included in the FEA and the semi-complicated loading scheme that the stresses (particularly the peak stresses) are far from uniaxial... and the loading is non-proportional really.

So, the typical fatigue life assessment for me is to
1) find alternating maximum principal stress using a 'solution combination' (all this does is take L4's stress tensors and subtract L3's from them, then find the principal stresses of the resulting stress tensor)
2) align a coordinate system with said max alternating stress
3) use aligned csys to get actual stress values for the two time steps
4) use such values for strain life evaluations WITH mean stress effects (correcting for plasticity when necessary using Neuber's).

So, the caveat(and pitfall) to my process though is that, WITH mean stress effects, the orientation of the max alternating stress is NOT necessarily the worst case overall with respect to fatigue. For example, my usual process gave me a -12 to -19 ksi stress cycle... this is arguably much better off than the orthogonal orientation (middle alternating principal stress orientation) in which I found the stress stat to be +24 - 29 ksi, which is pretty rough by the time a person accounts for mean stress effects. So...

I don't really know what to do to find the worst case stresses for fatigue evaluation now. Sure, I can probably try ANSYS fatigue tool for stress life, but its quite frankly a bit cheesy IMO. All it is doing is finding the difference of stress tensors between the two steps (similar to what I am doing)... but for the equivalent alternating stress, it is just taking the max of alternating components... and the mean stress correction value is simply the maximum mean stress of the components between the two steps. So, if you have something super multiaxial... it seems kind of silly.

Thoughts? Buzz words of stuff to study on? Am I crazy?

### RE: Fatigue - Multiaxiality and other pitfalls

I work in industrial agitators with vertical shafts, which present many of the same stress-analysis complexities. Stresses are variable in direction and magnitude but they are rarely purely alternating. We use proprietary design methods that are relatively simple buy highly effective. Long story short, we study the shafting as a static stress analysis and use stress limits that have been proven to endure 25+ years. The failures, when overload is encountered, are fatigue failures. While we're not actually performing any fatigue analysis, our design limits have proven to track with real-world design limits.

I've seen others apply general fatigue approaches to the same agitator shafting problem and they are lost in the weeds of numerous layered assumptions and interpreting noisy real-world data into alternating and mean loads. Adding complexity doesn't make that situation better. Is this analysis going down a rabbit hole when a simpler analytical model could do the job with clearer uncertainties?

### RE: Fatigue - Multiaxiality and other pitfalls

(OP)
Thanks geesaman.d.

I am not exactly sure how I would reduce the complexity of my analysis, but I'll think on it.

### RE: Fatigue - Multiaxiality and other pitfalls

would a canned fatigue analysis, like ncode, help ?

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

### RE: Fatigue - Multiaxiality and other pitfalls

an approach to simplify would be a max/min envelope of principal stress covering the 4 cases (and any others) and use that as your cyclic stress,
0 to max principal (or min principal to max principal).

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

### RE: Fatigue - Multiaxiality and other pitfalls

(OP)
@rb1957:

Gonna try it out! Also going to look at critical plane theory/method so I can understand somewhat how nCode might be pulling off the 'stress state' sorting I am alluding to above.

Thanks!

### RE: Fatigue - Multiaxiality and other pitfalls

If you are dealing with multiaxial fatigue there are several methods depending on weather the fluctuating load is simple, and whether the mean stress fluctuation is in sync or out of sync with the alternating stress fluctuation.

This is not a new problem, virtually any book on fatigue will address this. I would recommend:
Schijve, Fatigue of Structures,
Machine Design by Robert Norton
Mechanics of Materials by Norman Dowling

For Buzz words, try searching von Mises method, Sine's method, or SEQA methods for multiaxial fatigue.

Keep em' Flying
//Fight Corrosion!

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