Tsai-Wu failure analysis (2D)

Failure Index

The expression of the Tsai-Wu failure criterion is:

Where F is the failure index and:

In the absence of test data, the following is recommended for defining the Tsai-Wu interaction coefficient, F12 [1, 2]:

The software performs the following stability check:

If the stability check passes, the software uses the user-defined value for F12. If the stability check fails, the software uses F12 = 0.0.

For other variable definitions see Laminate failure analysis nomenclature.

Margin of Safety

To calculate the margin of safety for the Tsai-Wu failure criterion, we must first determine the value of the proportionality factor α such that the state of stress given by ασ1, ασ2, and ατ12 gives a failure index F of 1. To calculate the value of α, we rewrite the first equation in this section:

Which is a quadratic equation in α that can be rewritten:

Where:

The solutions to this quadratic equation are:

The software takes α to be the smallest positive value between α1 and α2. If both α1 and α2 are negative, α is set to zero. It calculates the margin of safety, MS, as follows:

MS = (α/FS – 1) X 100

Strength Ratio

The strength ratio, SR, is the proportionality factor α:

SR = α

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