Tsai–Wu failure criterion

The Tsai -Wu criterion belongs to the non - differentiating failure criteria or blanket criteria for fiber -plastic composite. It goes back to Stephen W. Tsai and Edward M. Wu, who published it in 1971 for plane stress states.

Characteristic of these materials is their structural anisotropy compared to homogeneous materials, which have largely isotropic material behavior. Fully therefore can only describe a fiber composite material that not only the elasticities and the material strengths, so the material failure, are direction-dependent writable.

Mathematical derivation

Are shown. The Tsai -Wu criterion is now finally a special case, in which only the first two terms of the series expansion are taken into account. Is further assumed for the exponent, the Tsai -Wu criterion results in the form

Determination of strength

The Festigkeitstensoren and must be adapted to the anisotropic strength properties of fiber composites. If only the two-dimensional, planar material properties, ie only the indexes and as well as for the strength coefficient and a transversely isotropic material symmetry is considered, the equation simplifies to

The strength coefficient will now be determined from standard tests ( train, pressure, thrust), plus the strength of uniaxial stress along () and transverse ( ) can be determined to the fiber direction. The compressive and tensile strength in the fiber direction and the compressive and tensile strength transverse to the fiber direction and the shear strengths of the coefficients of the tensor strength values ​​calculated as follows:

The coefficient of Tsai called the interaction coefficient, may consist of a combined biaxial normal stress can be determined with. A variety of different criteria differ in just only this coefficient. Tsai specifies a valid range of this coefficient.

Tsai -Wu criterion

Written out, the strength criterion yields according to Tsai- Wu to:

With

Conclusion, discussion

The Tsai -Wu criterion is a manageable approach to account for direction-dependent material strengths. Wins appeal of this criterion by the ease of implementation and clarity. In contrast to other criteria, the Tsai -Wu criterion has no information for different fracture modes. Thus, inter-fiber fracture is ( ZFB ) determined fiber breakage (Fb ) and failure under compressive and tensile stresses in a criterion. This property of the criterion is considered to be a disadvantage, since the designer does not receive any information about the break mode. Accordingly, no information such as the design of a component is to be changed in order to avoid failure is obtained.