Tsai/Wu criterion

According the Tsai-Wu criterion (6), the non-failure is ensured as far as the constraint... 

Criteria such as the Tsai-Wu criterion have only a limited ability to describe multiaxial failure of trabecular bone for arbitrary stress states. Coupling between normal strengths in different directions (longitudinal versus transverse, for example) appears to be minimal. 

In the absence of strength data for the laminae and the laminate, failure of the laminate should be examined using the Tsai-Wu criterion, see... 

The strength of laminates is usually predicted from a combination of laminated plate theory and a failure criterion for the individual larnina. A general treatment of composite failure criteria is beyond the scope of the present discussion. Broadly, however, composite failure criteria are of two types noninteractive, such as maximum stress or maximum strain, in which the lamina is taken to fail when a critical value of stress or strain is reached parallel or transverse to the fibers in tension, compression, or shear or interactive, such as the Tsai-Hill or Tsai-Wu (1,7) type, in which failure is taken to be when some combination of stresses occurs. Generally, the ply materials do not have the same strengths in tension and compression, so that five-ply strengths must be deterrnined ... 

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. 

Figure 2-45 Tsai-Wu Tensor Failure Criterion (After Pipes and Cole [2-25])...

The Tsai-Wu faiiure criterion has several important characteristics (1)... 

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... 

Based on the failure mechanisms and stress distributions at the interface between steel and composite adherends of the co-cured single and double lap joints, tensile load bearing capacities of the two joints were evaluated. Since failure started at the edge of the interface between steel and composite adherends, it is important to consider the failure criterion using interfacial out-of-plane stress distributions at the interface. Three-dimensional Tsai-Wu and Ye-delamination failure criteria were used to predict partial cohesive failure or interlaminar delamination failure in the co-cured single and double lap joints. 

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. 

Tsai—Wu In a further refinement of the Tsai—Hill failure criterion, Tsai and Wu [6] proposed a criterion that accounts for the differences in magnitude of tension and compression strengths in the form ... 

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 material will have a given strength expressed as stress or strain, beyond which it fails. In order to postulate the failure, it is necessary to have a failure criterion with an associate theory to be able to effect a satisfactory design. Such theories include maximum stress, maximum strain, Tsai-Hill (based on deviatoric strain energy theory) and Tsai-Wu (based on interactive polynomial theory). The Tsai-Wu theory is the most commonly used. 

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... 

The preceding biaxial failure criteria suffer from various inadequacies in their representation of experimental data. One obvious way to improve the correlation between a criterion and experiment is to increase the number of terms in the prediction equation. This increase in curvefitting ability plus the added feature of representing the various strengths in tensor form was used by Tsai and Wu [2-26]. In the process, a new strength definition is required to represent the interaction between stresses in two directions. 

Another form of a combined stress theory of failure is given by Tsai and Wu, and by Goldenblat and Kopnov. This failure criterion is expressed by... 

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