Yield Loci of Reinforced Plates Made from Rigid-Plastic Unequiresistant Materials Considering the Two-Dimensional Stress State in Fibers I. Unidirectional Reinforcement

Abstract

Models for unidirectional fiber-reinforced hybrid composites of a regular periodic structure that allow one to determine the yield loci for fibrous composites are constructed. The plane stress state in all components of compositions having different tensile and compressive strengths is considered. Components of the compositions are homogeneous and isotropic, and their mechanical behavior is described by the associated flow rule for rigidplastic bodies with piecewise linear yield states of Johansen, Hu, and Tresca-Hu types. Analytical expressions for the equations of yield loci convenient for a further analysis and application are obtained. It is proved that the plastic flow in the reinforced medium is associated with the yield loci constructed. It is shown that, in contrast to the structural model with a one-dimensional stress state in fibers (Nemirovsky and Mruz-Shamiev models), considering the complex stress state in the reinforcement in the case of different yield stresses of composite components, in the general case, leads to yield loci with more than six regimes of plastic flow.