An endochronic theory of plastic deformation of fibrous composite materials

Abstract

An endochronic theory of plasticity is used to describe plastic (irreversible, rate-independent) deformation of fibrous composite. Depending on the conditions of the problem to be solved, the unidirectional fibrous composite is considered to be either a transversely isotropic or an orthotropic solid. Constitutive equations are represented as relations of hereditary type with an exponential kernel. The equations are solved for the stress tensor. The paper considers an incremental form of the constitutive equations. The intrinsic-time parameter is the function of the arc length of the trajectory of deformation in the space of total strains. Constitutive equations for unidirectional and laminated composites are given in the matrix form. The capabilities of a computer program are outlined. The program helps to analyze the plastic behavior of fibrous composites. The plastic properties of the unidirectional boron/aluminum composite are investigated under uniaxial tension, pure shear and hydrostatic pressure. Theoretical results are compared with experimental data taken from the literature. Adequate agreement is obtained between theoretical and experimental results. It is shown that constitutive equations and a quadratic failure criterion adequately describe the plastic and strength properties of glass fiber reinforced plastics (GFRP's) under plane stress state. Failure envelopes of GFRP's are determined with consideration for the plastic behavior of unidirectional layers. Predicted failure envelopes fit the experimental data well. Deformation features of laminated composites containing isotropic plastic layer are illustrated by the example of a composite pressure tanks with a metal liner. Simplified relations are given for the analysis and design of the pressure tank with the metal liner.