Tsai-Wu and Tsai-Hill failure criteria [Abaqus]

[StructuralCivilFEA]

How is Tsai-Wu and Tsai-Hill failure criteria related to cross-product term coefficient and stress limit? And is cross-product term coefficient and stress limit somehow related to max stress and max strain failure criteria?

 

[SWComposites]

No, the interaction failure criteria cross terms are not at all related to max strain or stress criteria.

And despite what is in a lot of text books, the interactive failure criteria DO NOT correlate to laminate test data. See past posts on the Composite engineering forum under Materials Engineers.

 

[FEA way]

Take a look at the Abaqus documentation chapter "Plane stress orthotropic failure measures" (Analysis User's Guide). It features formulas that should help you understand the relationship between these parameters for each criterion. For example Tsai-Hill criterion is:

(σ_11^2/X^2)-((σ_11*σ_22)/X^2)+(σ_22^2/Y^2)+(σ_12^2/S^2) < 1

X = X_t for σ_11 > 0, otherwise X = X_c
Y = Y_t for σ_22 > 0, otherwise Y = Y_c

where: X_t and X_c - tensile and compressive stress limit in 1 direction, Y_t and Y_c - tensile and compressive stress limit in 2 direction, S - maximum shear stress in X-Y plane

The term σ_11*σ_22 is a cross-product that you've mentioned.

Similar relationships are described in the documentation for remaining criteria. There's no point to rewrite them here (especially that Tsai-Wu formulas are quite long).