The Tsai–Wu failure criterion is a phenomenological material failure theory which is widely used for anisotropic composite materials which have different strengths in tension and compression. The Tsai-Wu criterion predicts failure when the failure index in a laminate reaches 1. This failure criterion is a specialization of the general quadratic failure criterion proposed by Gol'denblat and Kopnov and can be expressed in the form
Contents
- TsaiWu failure criterion for orthotropic materials
- Tsai Wu failure criterion for transversely isotropic materials
- TsaiWu failure criterion in plane stress
- TsaiWu criterion for foams
- TsaiWu criterion for bone
- References
where
which implies that all the
Tsai–Wu failure criterion for orthotropic materials
For orthotropic materials with three planes of symmetry oriented with the coordinate directions, if we assume that
Let the failure strength in uniaxial tension and compression in the three directions of anisotropy be
The coefficients
The near impossibility of performing these equibiaxial tests has led to there being a severe lack of experimental data on the parameters
It can be shown that the Tsai-Wu criterion is a particular case of the generalized Hill yield criterion.
Tsai-Wu failure criterion for transversely isotropic materials
For a transversely isotropic material, if the plane of isotropy is 1–2, then
Then the Tsai–Wu failure criterion reduces to
where
In order to maintain closed and ellipsoidal failure surfaces for all stress states, Tsai and Wu also proposed stability conditions which take the following form for transversely isotropic materials
Tsai–Wu failure criterion in plane stress
For the case of plane stress with
The strengths in the expressions for
Tsai–Wu criterion for foams
The Tsai–Wu criterion for closed cell PVC foams under plane strain conditions may be expressed as
where
For DIAB Divinycell H250 PVC foam (density 250 kg/cu.m.), the values of the strengths are
For aluminum foams in plane stress, a simplified form of the Tsai–Wu criterion may be used if we assume that the tensile and compressive failure strengths are the same and that there are no shear effects on the failure strength. This criterion may be written as
where
Tsai–Wu criterion for bone
The Tsai–Wu failure criterion has also been applied to trabecular bone/cancellous bone with varying degrees of success. The quantity