VARIANCES IN FAILURE TENSOR POLYNOMIALS FOR ANISOTROPIC BODIES

Failure criteria based on tenser polynomials present an advantage over the old classical criteria in that the coefficients of their terms ar e no longer scalar quantities defined by either some simple assumption , defining the shape of their loci, or evaluated by a curve-fitting pr ocess, but they belong to the terms of a fourth-order tenser expressin g the mode of failure of the respective material. While the first gene ration of these criteria defined the coefficients of the terms of the respective tenser polynomial experimentally, by testing the material i n different modes of loading, associated by a curve-fitting process, r ecent forms of this type of criteria have rejected the arbitrariness o f definition of the coefficients of the tenser terms and accepted in a dvance the validity of some phenomenological conjecture, associated wi th and derived from the validity of some physical law. In this paper, failure criteria, expressed in the form of tenser polynomials, are for mulated appropriately according to justified postulates. Two different variations of the failure tenser polynomial criterion will be present ed in this paper, the one being based on the assumption that the mater ial does not fail by a predominant type of hydrostatic stress, whereas the other being established by conjecturing that a safe loading for t he material is expressed by a stress tenser, whose associated strain t enser in the context of Hookean elasticity is a spherical one. The var iances between these two extreme cases of definition of failure criter ia are studied in the paper and suggestions for the superiority of a s afe criterion are proposed, although the final decision depends exclus ively on a comparison of experimental results derived from compound te sts appropriately selected, which, up to now, are almost totally missi ng in the literature.