# Tsai-Wu Failure Criterion

The Tsai-Wu criterion is applied to determine the factor of safety for composite orthotropic shells.

This criterion considers the total strain energy (both distortion energy and dilatation energy) for predicting failure. It is more general than the Tsai-Hill failure criterion because it distinguishes between compressive and tensile failure strengths.

For a 2D state plane stress (σ3 = 0, τ13 =0, τ23 =0), the Tsai-Wu failure criterion is expressed as:

The coefficients Fij of the orthotropic Tsai-Wu failure criterion are related to the material strength parameters of the lamina and are determined by experiments. They are calculated from these formulas:

XT1
tensile material strength of laminate along fiber direction
XC1
compressive material strength of laminate along fiber direction
XT2
tensile material strength of laminate transverse to fiber direction
XC2
compressive material strength of laminate transverse to fiber direction
XT12
positive shear strength of laminate
XC12
negative shear strength of laminate (the solver considers it equal to the positive shear strength)
The stress state of the lamina calculated by the program is described by the components: σ1, σ2, and τ12
σ1
laminate stress along fiber direction
σ2
laminate stress transverse to fiber direction
τ12
laminate shear stress

See how the Composite principal ply material directions are defined.

The program reports the factor of safety (FOS), which is the coefficient by which all laminate stress components should be multiplied to reach laminate failure according to the Tsai-Wu criterion stated above. The FOS for laminate failure is calculated from:

, where the coefficients are given by:

A factor of safety larger than 1.0 indicates that the laminate is safe from failure.

Attention: The Tsai-Wu failure criterion cannot predict different failure modes including fiber failure, matrix failure, and fiber-matrix interface failure.

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