Out of plane stresses

[zmat]

I am trying to model thermal stresses in a rectangular ceramic bar and have used a 2-D model. Is the out-of plane stresses that were calculated valid, or do I need a 3-D model fo see what the stresses in the Z-axis are?

 

[GBor]

What software are you using and what material model?

Garland E. Borowski, PE
Borowski Engineering & Analytical Services, Inc.
Lower Alabama SolidWorks Users Group

 

[zmat]

I am using Abaqus, and am using heat loss from the surface into a heat sink (-h(T-T*)) (film condition) and then heat flow condition through the body

 

[GBor]

I'm not familiar with the specifics of Abaqus' calculation engine, but I suspect that the calculation is a volumetric expansion calculation. If it is a pure heat transfer, then I would suspect that this calculation of stresses is probably as accurate as anything else so long as you are not dealing with volumetric expansion constraints that can't be applied in the 2-D model.

 

[corus]

The 3D stresses will be different from the 2D stresses depending on the length of the bar. If you've used generalised plane strain then you'll get a good approximation at the centre of a long bar. At the free ends of the bar, however, plane stress will occur and the stresses will be different.

corus

 

[EdR]

I guess I must be confused....You indicated you had a rectangular bar....unless otherwise constrained a bar will be in plane stress in two directions and subject to an axial load in the 3-rd direction...The only thermal effects for a bar in this condition are (alpha*dt) strains (plus and strains due to load); the stresses in the normal directions are zero....whether stresses are generated in the 3-rd direction depends on the axial constraints....

Ed.R.

 

[zmat]

Thank you for the responses. The sample has no mechanical loading and the thermal stresses are simply caused by the thermal gradient within (i.e. thermal shock). We chose to run a 3-D model with large elements to see if the stresses in the middle of the bar are roughly the same as the 2-D out of plane stresses. I will post the results tomorrow.

 

[corus]

EdR,
Thermal stresses in the 3rd direction arn't necessarily generated by constraints, they can be generated by differential thermal expansion if there is a non-uniform temperature distribution. As such if there are no loads, no constraints, there can be a longitudianl stress within a long bar, but zero at the ends.

corus

 

[EdR]

Corus:

Thanks.....I missed the point in the original post that there was a non-uniform temperature distribution......

Ed.R.

 

[zmat]

We have run the numbers and the out of plane stresses were significantly greater (680 MPa versus 400 MPa) than the max principal stresses when run in 3D. The 3-D model does allow heat to escape from the ends of the bars, however the length of the bar is greater than 10x the thickness.

I am new to FEA and my understanding of the inputs and outputs are limited. Does anyone have any suggestions of how to set up these types (thermal shock) problems?

 

[corus]

You're probably using plane strain in your 2D model rather than generalised plane strain to account for such a significant difference. Plane strain will give you zero out of plane strains, ie. no out of plane thermal expansion. Generalised plane strain will give a uniform out of plane strain (non zero) and will thus allow thermal expansion and thus represent a section through the bar away from the ends. Abaqus can model generalised plane strain but if your code doesn't you can calculate the mean axial stress of the 2D section and subtract that from your results, if you don't want to use a 3D model.

corus

 

[rb1957]

"We have run the numbers ..." ... accountants "run numbers", and hopefully none of them have the sense to be listening in on us !!