Reduction in the Number of Independent Parameters for the Tsai—Wu Tensor Polynomial Theory of Strength for Composite Materials

Abstract

It is shown that the number of required parameters for the Tsai-Wu tensor polynomial strength criterion for fiber composites can be reduced from seven to five for composite materials that do not fail under practical levels of either hydrostatic or transverse pressure. For these materials, the interactive strength parameters can be defined in terms of their commonly measured uniaxial or noninteracting strength parameters, thereby eliminating the need to conduct combined stress tests. The derived parameters are given by F ₁₂ = − F ₁₁/4 F ₂₃ = − F ₂₂ These parameters fall within the stability limits of the theory, yet they lead to open failure surfaces in the compressive stress quadrant. The assumptions used to derive the interactive parameters were supported by measurements that showed typical carbon fiber composites did not fail under significant levels of hydrostatic pressure or unequal transverse compression. Comparison with previous work where the interactive parameters had been determined from combined stress experiments showed that predictions based on the derived parameters were generally in good agreement with test results. In evaluating the tensor polynomial failure theory, the behaviors under hydrostatic and transverse pressure were shown to be more discerning than other multiaxial stress states. It is therefore proposed that these two stress states be used in assessing other proposed three-dimensional failure models for fiber composites.