## Tsai-Wu - continuous analytic function?

## Tsai-Wu - continuous analytic function?

(OP)

Hello,

I was reading an article recently about composite failure criteria, and it stated that the Tsai-Wu criterion is often preferred, since it is a “continuous analytic function that adequately represents all modes of ply failure while including stress interaction effects.”

I understand what continuous means, and I understand what analytic means mathematically (infinitely differentiable), but I’m not sure I understand why this makes the Tsai-Wu criterion preferable.

Can anyone help me out?

Thanks!

I was reading an article recently about composite failure criteria, and it stated that the Tsai-Wu criterion is often preferred, since it is a “continuous analytic function that adequately represents all modes of ply failure while including stress interaction effects.”

I understand what continuous means, and I understand what analytic means mathematically (infinitely differentiable), but I’m not sure I understand why this makes the Tsai-Wu criterion preferable.

Can anyone help me out?

Thanks!

## RE: Tsai-Wu - continuous analytic function?

Moving beyond simple unnotched failure prediction, ANY ply level failure criterion, especially the interactive ones, lose physical meaning. For example, laminates with holes, fastened joints, strength after impact, are what structures are usually designed to. Because of the notch sensitively, hole filling effects, installation torque, etc., strength prediction using ply level criteria has little meaning. Instead, one can use analytical and test methods (semi-empirical) to account for the practical effects. The Tsai-Wu criterion is probably best used for academic study and comparison to other ply level failure criterion. Beyond that, it has limited value.

From a historical perspective, it was hoped that a ply level criterion could ultimately lead to accurate laminate level failure predictions. This would be a best case scenario because the required test data would be minimal. Eventually it became clear that this was insufficient for practical laminates and practical considerations. However, failure criteria such as Tsai-Wu remain popular in academia. This is because academic approaches do not go beyond the unnotched strength prediction level. Unfortunately, structures are almost never designed to the unnotched strength.

Brian

www.espcomposites.com

## RE: Tsai-Wu - continuous analytic function?

However, and speaking as a (sort of) academic, I disagree with Brian's view that Tsai-Wu or Tsai-Wu like criteria are, or should be, used for academic work... . In the academic sphere, criteria like Tsai-Wu are basically used for teaching, not research. Students learning about composites will learn about Tsai-Wu along with max stress, strain ,etc..., so their eyes can then be opened to the world of damage based models, traction-separation laws, multi-scale approaches, etc...(at least this is what we do at Imperial College).

For example; The most well known, recent failure 'criteria' (they're more like methodologies than discrete criteria) to come out of Imperial College are probably the LaRC04 and LaRC05. Both of these have multiple, competing failure criteria to account for various failure/damage modes and some of them are 'interactive' (e.g. matrix compression failure) so factors like the relative proportion of hydrostatic and deviatoric stress components can be accounted for. This is very much in contrast to Tsai-Hill or -Wu type approaches and I'd be surprised if any researchers here would seriously suggest that criteria for composites that can't discriminate between various observed failure modes would be a worthwhile matter to research.

## RE: Tsai-Wu - continuous analytic function?

Moving beyond that to something like Puck, Larc04, Larc05 gives a more physically consistent result. But even these improved criterion tend to be academic unless you are strictly interested in unnotched strength. For most practical structures, you usually consider open hole strength, filled hole strength (function of installation torque and clearance, etc), the hole size effect, BVID, bearing-bypass interaction, in-situ vs ex-situ effects, scatter, processing effects, stacking sequence effects, etc. Once you consider the practical effects, the failure mechanisms (especially at the local and microscopic level) become too much for the criterion that attempt to physically capture all of these mechanisms. Instead, you think about an approach that works with OHT, OHC, FHT, FHC, CAI, etc. coupon data.

Brian

www.espcomposites.com

## RE: Tsai-Wu - continuous analytic function?

Brian

www.espcomposites.com

## RE: Tsai-Wu - continuous analytic function?

mightuse Tsai-Wu with open hole data for an initial rough sizing situation where there's limited data and a combination of applied 1, 2 and 12-directions present, but we'd always use max stress/strain as well.As to why it might be preferred in some situations by some people it may boil down to the fact that it's easy to implement without a huge amount of testing and gives a nice simple single number. However, that also makes it fairly inaccurate and uninformative—you can separate out the different terms that get added up for a clue as to what loading is contributing most to the final number, but that's not much different from checking with max stress/strain. Use at your peril (as adfergusson and Brian Esp have observed, generating any margin on composite is fairly perilous and keeping it simple with max stress/strain is often best for preliminary work).

## RE: Tsai-Wu - continuous analytic function?

Andrew