The Tsai–Hill failure criterion is one of the phenomenological material failure theories, which is widely used for

anisotropic Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...

composite materials A composite material (also called a composition material or shortened to composite, which is the common name) is a material which is produced from two or more constituent materials. These constituent materials have notably dissimilar chemical or ...

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: :

\begin
    \left(\cfrac\right)^2 - \left(\cfrac\right) + \left(\cfrac\right)^2 + \left(\cfrac\right)^2 \geq 1
  \end

Where: :

\begin
    X_ \end

is the allowable strength of the ply in the longitudinal direction (0° direction) :

\begin
    X_ \end

is the allowable strength of the ply in the transversal direction (90° direction) :

\begin
    S_ \end

is the allowable in-plane shear strength of the ply between the longitudinal and the transversal directions

The Tsai hill criterion is ''interactive'', i.e. the stresses in different directions are not decoupled and do affect the failure simultaneously. Furthermore, it is a

failure mode Failure causes are defects in design, process, quality, or part application, which are the underlying cause of a failure or which initiate a process which leads to failure. Where failure depends on the user of the product or process, then human er ...

independent criterion, as it does not predict the way in which the material will fail, as opposed to mode-dependent criteria such as the Hashin criterion, or the Puck failure criterion. This can be important as some types of failure can be more critical than others.

References

{{reflist, refs= Niu, Michael C. ''Composite Airframe Structures,'' Hong Kong Conmilit Press LTD. 2010. {{ISBN, 9789627128069. {{Cite web, url=https://help.solidworks.com/2012/english/SolidWorks/cworks/Tsai-Hill_Failure_Criterion.htm, title = Tsai-Hill Failure Criterion - 2012 - SOLIDWORKS Help Composite materials Mechanical failure