Failure criteria for fiber composite materials, the astonishing sixty year search, definitive usable results

A materials failure postulate is established giving upper and lower bounds on the numbers of failure parameters involved with any associated failure criterion. The failure postulate is based upon the symmetry properties for the material, any macroscopically homogeneous material form. It is of significant and decisive help in deriving failure criteria. A wide variety of examples of its usage are given but most of them are aimed at the standard forms for fiber composite materials. Specific failure criteria are the end result for everything from unidirectional, highly anisotropic composites at one extreme to the quasi-isotropic laminate form at the other extreme. Almost all of the work is for fiber composites with any degree of anisotropy. Section 7 and part of Section 4 have highly anisotropic conditions taken as appropriate to carbon fiber/polymeric matrix composites. The results are summarized in Section 8 and they are responsive to the fields many years of searching for the failure criteria of composite materials.