Chemistry:Tsai-Hill failure criterion

From HandWiki

The Tsai–Hill failure criterion is one of the phenomenological material failure theories, which is widely used for anisotropic composite materials which have different strengths in tension and compression. The Tsai-Hill criterion predicts failure when the failure index in a laminate reaches 1.

Tsai–Hill failure criterion in plane stress

The Tsai-Hill criterion is based on an energy theory with interactions between stresses. Ply rupture appears when:[1]

[math]\displaystyle{ \begin{align} \left(\cfrac{\sigma_{11}}{X_{11}}\right)^2 - \left(\cfrac{\sigma_{11} \sigma_{22}}{X_{11}^2}\right) + \left(\cfrac{\sigma_{22}}{X_{22}}\right)^2 + \left(\cfrac{\sigma_{12}}{X_{12}}\right)^2 \le 1 \end{align} }[/math]


[math]\displaystyle{ \begin{align} X_{11} \end{align} }[/math] is the allowable strength of the ply in the longitudinal direction (0° direction)
[math]\displaystyle{ \begin{align} X_{22} \end{align} }[/math] is the allowable strength of the ply in the transversal direction (90° direction)
[math]\displaystyle{ \begin{align} X_{12} \end{align} }[/math] is the in-plane shear allowable strength of the ply between the longitudinal and the transversal directions[math]\displaystyle{ }[/math]


  1. Niu, Michael C. Composite Airframe Structures, Hong Kong Conmilit Press LTD. 2010. ISBN:9789627128069.