Tsai-Wu failure criterion

Thus, the Tsai-Wu tensor failure criterion is obviously of more general character than the Tsai-Hill or Hoffman failure criteria. Specific advantages of the Tsai-Wu failure criterion include (1) invariance under rotation or redefinition of coordinates (2) transformation via known tensor-transformation laws (so data interpretation is eased) and (3) symmetry properties similar to those of the stiffnesses and compliances. Accordingly, the mathematical operations with this tensor failure criterion are well-known and relatively straightforward. 

An essential step in developing an interactive reliability model requires formulating a deterministic failure criterion that reflects the limit state behavior of the material. Miki et al.,21 and de Roo and Paluch22 have adopted this approach in computing the reliability of unidirectional composites. In both articles, the Tsai-Wu failure criterion is adopted, where different failure behavior is allowed in tension and compression, both in the fiber direction and... 

The three-dimensional Tsai-Wu failure criterion can be expressed as follows [22] ... 

Equation (1) must be less than 1 failure is predicted when F/ is > 1. Based on the three-dimensional Tsai-Wu failure criterion, tensile load bearing capacities of the co-cured single and double lap joints were calculated. 

Tsai-Wu failure criterion —O— Ve-delaminatian criterion ExpeTimenial results... 

Tsai-Wu failure criterion -O—Ye-delaminatlon criterion Experimental results... 

Figure 15 compares the tensile load bearing capacity of the co-cured double lap joint calculated from the two failure criteria with experimental results. The tensile load bearing capacity of the co-cured double lap joint evaluated through the three dimensional Tsai-Wu failure criterion was in good agreement with the experimental results because of its failure mechanism, interlaminar delamination failure at the 1 ply of the composite adherend. 

Despite the improvement in differentiating between tension and compression strength values, the Tsai—Wu failure criterion remains a curve fit and does not capture well the mechanism of failure, nor the failure load itself, especially in cases of combined loading with biaxial compression being one of the major problem areas [7]. However, it has been shown to work well in many cases especially when substantiated, and, if necessary, modihed, by experimental results. 

In the absence of experimental or manufacturers data the Tsai-Wu failure criterion may be used. 

P(l) The Tsai Wu failure criterion should be used for design in the absence of experimental or manufacturers data. The design strengths, which shall be divided by the appropriate partial safety factors, may be estimated iisiino the rhararteristir sfrenaths of the fibres and the matrix The... 

When using the Tsai-Wu failure criterion, the laminate strains, obtained by global analysis of the structural system, are used to obtain the respective lamina stresses. The laminate is deemed to have failed at fust ply failure, i.e. when the failure criterion is no longer satisfied for any one of its constitutive laminae. 

The theory considers multiple failure modes by superposition, in contrast to the Tsai-Wu failure criterion where there is assumed to be interaction between the various stress components. 

The Tsai-Wu failure criterion considers interaction between the various stress components. The Tsai-Wu failure criterion for plane stress loading conditions is given here in terms of a calculated stress ratio. 

The Tsai-Wu failure criterion requires prior knowledge of the lamina longitudinal tension and compression strengths, the transverse tension and compression strengths and the shear strength in the 1-2 (longitudinaltranverse) plane of the lamina. 

For a multi ply laminate the Tsai-Wu failure criterion should be evaluated for stress components parallel to and perpendicular to the fibre directions, for each lamina of the laminate. The laminate is deemed to have failed if Equation 4.51 is not satisfied for any of its constitutive laminae, i.e. for first ply failure. 

Note that these calculations are conservative and are included to allow the designer to use the Tsai-Wu failure criterion in the absence of measured data. However, for an economic design it is recommended that the lamina strengths be determined experimentally and that the HartSmith failure criterion be employed. 

The Tsai-Wu failure criterion was used to prediet the failure of the glass fibre reinforced polypropylene plies. As can be seen in Figures 10 and 11, for a internal pressure of 3 MPa the thermoplastic layers are not damaged (R>1). 

Modified Tsai-Wu Failure Criterion for Fiber-Reinforced Composite Laminates , Polym. Comp. 13 (1992), 273-277... 

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