Where is the stress?

[melomania]

Hi,

I'm getting some strange results from my FEA.

I reduced the issue to a very simple case:

A block metal of 100x100x50 mm. A 10000N force is applied in the middle of the block on a area of 10x10mm.

A would expect a stress inside that 10x10 area of 10000N/100mm2 = 100MPa.

But I see a low stress in the middle (about 20Mpa) increasing towards the corners.

But the peak stress is still only 49MPa.

I used a 1mm mesh on the whole top of the block to get a accurate analysis.

When changing the mesh to 2 mm I get a 50MPa peak. So it seems to converg.

How is this possible? Why I do not see the 100MPa on the whole area.

Or is the stress in the corners in praktice very very high so that the mean stress is 100MPa?

In which case the analysis does not show this to me.

[henderh · Accepted solution]

Hi melomania,

  If you'd like to verify that the compressive stress is equal to 100 MPa in this scenario, don't look at the Equivalent (Von Mises) stress.  Instead look at the 3rd principal (or the Stress ZZ component).

  You'll see that it is a uniform 100 MPa:

The reason you see the "hot spots" at the corners of the small face are primarily from to the shear stress effects of the load discontinuity. You can view these more clearly with the "Stress XZ" or "Stress YZ" components.

If the load is applied to the entire top face (not just to the smaller face) the Von Mises stress would more closely match the 3rd Principal stress.

The "split face method" is a good way to apply a localized load, but care must be taken interpreting the results near that area.

Hope this helps.  Please let us know if you have any additional questions, comments or suggestions.

Best regards, -Hugh

[melomania]

Thanks for explaining Hugh,

Do you know if there is some literature explaining the differences between Von Misess and 1st or 3rd principal stresses?

[henderh]

Hi melomania,

  I was able to find some decent descriptions on the web.

  Von Mises stress is related to distortion energy theory here: http://en.wikipedia.org/wiki/Yield_(engineering)

  2-D principal stresses are described here: http://www.mesubjects.com/strength-of-materials-principal-stresses-and-strains.htm

  In three dimensions, we get a 3rd principal stress: http://www.engapplets.vt.edu/Mohr/java/nsfapplets/MohrCircles2-3D/Theory/theory.htm

  The last link contains reference to a really good textbook: James M. Gere and Stephen P. Timoshenko, "Mechanics of Materials", Third Edition, PWS-KENT Publishing Company, Boston, 1990

Thanks, -Hugh