How are notch or stress concentration factors in FEA of shaft strength considered?

[namelessudhay]

Hi,
I want to understand how stress concentration factor or notch factor is considered in FEA method.
Lets assume a case of stepped shaft which has got the left end of the shaft fixed with rigid wall and the other end being pulled by an axial load.(pic. attached)

In the case of conventional calculation method, stress is given by load over area. At the location of the step, the stress found is multiplied by a stress concentration or a notch factor based on some guideline.

If it is done using any 3D FEA package, the software, by its own, shows the highest stress at the step.

How does FEA find out a suitable stress concentration factor? Can someone help? Thanks.

 

[csk62]

If you have a step, there will be an "infinite" stress concentration, although this is impossible to achieve in reality since there will be finite machining radius albeit very small.
FEA is used when your data is out of the typical range used for Peterson's handbook etc. However, without modelling any transition radius, whatever your program spits out is useless at the 90deg step.
If you use a small radius I recommend using strain criteria, because you will most likely have local yielding. Obviously try to incorporate as large of a radius as possible if you are concerned about life of the part. Unless you have a fit, and then you probably need to use FEA to design an undercut with a suitable radius.

 

[rb1957]

as above, you have to consider a real part.

you can mesh the crap out of the concentration, and run non-linear (as the peak stress is probably plastic).

if a purely static problem, you can say that the highly localised yielding has a negligible reduction on gross section allowable load.

you can run you FEA and extract gross section stresses, then use a Kt solution to determine the peak stress 9though this is likely plastic).

another day in paradise, or is paradise one day closer ?

 

[namelessudhay]

Hi. Thanks for your answers. I am more interested in knowing how FEA finds out the high stress in that area than the best method to model it. Pl. help. Thanks.

 

[rb1957]

"interested in knowing how FEA finds out the high stress in that area" ... exactly the same way that FE calculates stress anywhere. why would a stress concentration be any different ??

it sounds like you need to review a text on FEA method ...

another day in paradise, or is paradise one day closer ?

 

[kan123]

You won't be able to use the finite element method to determine the stress concentration factor for this geometry because the sharp corner is a singularity. If you were to keep refining the mesh and look for the highest stress each time, you would see it keep rising without bound. This phenomena is discussed in "Reliability of the Finite Element Method for Calculating Free Edge Stresses in Composite Laminates" by Whitcomb, et al in Computers & Structures Vol 15, No 1, pp 23-37, 1982. If you need to make an estimate of the stress at that corner, try plotting the stress along the surface while ignoring the 2 or 3 elements closest to the singularity, then extraplote to the location.

If you had a plate with a hole in it, you could use FEM to find the stress concentration factor. That geometry doesn't have a discontinuity, so repeatedly refining the mesh would give results that asymptotically approach the true stress. In general, a brute force way to determine if you are getting good results from any finite element model is to keep refining the mesh until the critcal stresses don't change very much.

People forget that FEM was originally developed to determine load distribution between multiple load paths. Engineers then plugged those load results into closed-form equations for various joints to do sizing, life prediction, etc. Nowadays people (especially managers) expect FEM to do everything and overlook its limitations.

 

[rb1957]

"you would see it keep rising without bound" ... only if you're running linear FEA. Non-linear FEA would appreciate the local yielding and limit the local stress. as for the detail geometry, even the sharpest corner rad is not zero.

another day in paradise, or is paradise one day closer ?