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

Abstract

Structural models of hybrid fiber composites orthogonally reinforced in the plane are constructed. They allow one to calculate the yield loci taking into account the plane stress state in all composition components with different tensile and compressive yield stresses. Materials of the components are homogeneous and isotropic, and their mechanical behavior is described by the associated flow rule for a rigid-plastic body with the piecewise linear yield criteria of Johansen, Hu, and Tresca–Hu types. The fibers are located along the directions of principal stresses in the reinforced body. Analytical expressions for the equations of regimes on the yield loci of the composition are obtained, which can be used further in practical calculations. Different limit processes, from orthogonally reinforced composites to unidirectional reinforced ones and from fibrous media to homogeneous ones, are analyzed. It is proved that the plastic flow in a reinforced medium is associated with the yield loci constructed for it. The yield loci obtained for the composition are compared with those determined on the basis of the structural model with a one-dimensional stress state in fibers.