von Mises vs Tsai Wu

[whitebalance]

Hi,
I'm trying to find out for what assumptions the von Mises yield criterion equals the Tsai Wu failure criterion.
Is it so that if you assume plane stress and input isotropic material properties into the Tsai-Wu criteria the result will be the same as von Mises yield criteria?

WB

 

[RPstress]

You can arrange Tsai-Wu and von Mises to predict failure at the four points where the X and Y stresses are at yield but the curves between these points are different shapes.

It would be more apposite to use the modified (so that the top left and bottom right corners are cut off) max stress criterion and compare it with Tresca but probably of similarly little point.

Failure criteria for composites often appear more like a curve-fitting exercise than an exercise in theoretical elasticity. It is the more complicated behaviour of composites that makes their more complicated failure criteria occasionally vaguely useful.

Check out the World Wide Failure Exercise (WWFE) work that's been done.

http://www.sciencedirect.com/science/book/9780080444758

to buy plus numerous hits on Google. The WWFE work has a lot of work on glass fibres where the lower modulus makes the failure behavour even more complicated than it is for carbon.

When mixing metals and composites it's usually sensible to stick to max stress criteria. This can allow comparison of metal layers with composite ones. I don't know of any of the current failure criteria that will go further for both metals and composites. Can someone correct me? Is there a failure criteria useful for both isotropic and orthotropic?

As long ago as 1988 Benson Black of McDonnell Douglas wrote a paper aptly titled 'Failure Criterion No. 1 975 372'. The true number was probably higher even then...

 

[whitebalance]

Thank you for the answer, RPstress!

Another question came to mind here:
If you have a structure made out of composites and you assume that the laminate is considered in-plane isotropic (i.e. CSM).
When considering plane stress, wouldn't a von Mises stress color plot and a Tsai-Wu failure criteria color plot, be the same?

WB

 

[RPstress]

Humble pie time: I may have misinformed you! If shear is zero and all the Tsai-Wu allowables are the same as yield then (von Mises/yield)^2 and Tsai-Wu failure index are the same. They seem to differ slightly only in their treatment of shear. Tsai-Wu is more mathematically rigorous and more closely related to von Mises than I thought. Not quite sure in my own mind why they differ in their treatment of shear. Apologies. For CSM Tsai-Wu should differ from (von_Mises/yield_stress)^2 only if there's a significant amount of shear and not much direct stress. It depends on how the shear allowable is handled. I think if the allowable shear on the tsai-Wu equation is direct_yield_stress/√3 then Tsai-Wu and (von_Mises/yield_stress)^2 match.