"Elasticity" Variables Parameters of Nonlinear Deformable Transversely-Isotropic Medium

Abstract

A method for predicting nonlinear behavior of unidirectional reinforced composite is developed. It is based on nonlinear strain of matrix material described modified relations flow theory to account for the technological defects.  The developed approach allows to build  stress-strain curves of unidirectional-reinforced composite at tensile along the fibers, at tensile and shear in the reinforcement plane and explore resistance reinforced unidirectional composite complex loading.Composite materials based on metal and ceramic matrices appear in the design of parts and structures. The mechanical properties of the constituents of these com-posite materials are comparable. The design of parts made of polymer composite materials is usually based on the assumption of elastic deformations of constituents of the composite material, including the polymer matrix. This assumption does not always work for metal and ceramic composite materials, which makes it difficult to optimize products made of such materials. In addition, the assumption of the elas-ticity of the composites makes it impossible to estimate the ultimate deformation of the parts. In this connection, nonlinear properties of inhomogeneous, transversally anisotropic composite materials based on metallic or intermetallic matrices are dis-cussed here. It is assumed that the nonlinear properties of composite materials are formed by the nonlinear behavior of the matrix. Earlier, on the basis of the modi-fied theory of plastic flow, nonlinear dependences of the deformation of an anisot-ropic matrix were obtained. The modified theory of plastic flow makes it possible to take into account the nonlinear dependence not only between deviators of stresses and deformations, but also between the first invariants of stresses and de-formations. The nonlinearity in the dependence of the first invariants can be caused by particular manufacturing technology. Five independent strain curves for unidi-rectionally reinforced composite materials were obtained using the Maxwell and Feucht models. The obtained relations are used to find the stress-strain curves of an aluminum alloy unidirectionally reinforced with boron fibers.

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