Corner Radii vs Notch Factor

[ICanBreakIt]

We have been working on a part that is shaped like a horse shoe with machined bosses on the ends. Where the bosses connect to the horse shoe we have a generous 3/16 radius. When we run the fea we are getting very high stress concentrations on the corner radii. When we modify the model and reduce them the stress levels drop significantly. Obviously there is a trade off between too small a radius and too large. Although I would not have expected too large to make that much difference. I would have thought a 3/16 radius would be better for fatigue and notch factor than a 1/16 radius but it sure doesn't look that way on the results. Any thoughts?

 

[GregLocock]

I agree with your intuition. However, are you applying forces or displacements as a load case?

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[corus]

I'd check that you are getting sufficient mesh density with the smaller radius fillet. The problem with FEA is that it underestimates the stiffness the coarser the mesh. If you've used a coarser mesh for the smaller radius then you may get lower stresses.

corus

 

[vonlueke]

Generally, stresses will be higher for a smaller radius fillet, not lower. I agree with the first and last sentence by corus. And, see if you have stress averaging across elements turned on or off, to see if that's making your results seem unintuitive.

Just one comment on the second sentence by corus. I thought a coarser mesh overestimates stiffness, since it has fewer dofs (assuming typical shell or solid elements).

 

[ICanBreakIt]

We are appling forces to our model. I will check and see if we have refined the mesh in the higher stress areas.

Thanks

 

[mtnengr]

The problem of the re-entrant corner was examined by M. L. Williams (ASME JAM Vol 74, pp 526, 1957). This work is based upon the assumption of a symmetric stress tensor. If the FEM program is also based upon this assumption, then a stress singularity will be encountered, no matter the density of the mesh. As radius of curvature is increased, some relief can be attained. You can use Peterson's Stress Concentration book for estimates associated with radius curvature.

There have been some investigations as to determining the stress level when considering a mixed-boundary condition. A group of Italians examined this problem and published their work : "Mathematical Theory of Elastic Equilibrium", by G. Grioli, 1962, Academic Press. Finite stress levels have been predicted when the non-symmetry of the stress tensor is assumed. Also, one should examine: "An Application of the Lagrangian Multiplier method to a Mixed Boundary Value Problem", by R. L. Citerley, J. Franklin Institute, Vol. 281, No. 4, April 1966 and the documentation associated with MSC Nastran's crack element.