On the exact solution of elastoplastic response of an infinitely long composite cylinder during cyclic radial loading

摘要

The exact solution is determined for the elastoplastic response of an infinitely long composite cylinder subjected to cyclic, radial loading on the transverse plane. A circular cylinder (the fiber phase) is concentrically embedded in an annular cylinder (the matrix phase) with circular cross-section. Both cylinders are infinitely extended along their axis, and always remain perfectly bonded at their interface. Both phases are taken as elastical1y isotropic, with the fiber being taken as softer than the matrix. The latter is also taken as elastically incompressible. While the fiber is assumed to always remain elastic, a isotropically hardening bilinear matrix is considered. Yielding in the matrix is assumed to occur by the vonMises' criterion. Based on these aforementioned conditions, and the restriction that the matrix is in a fully plastic state during a 1oad reversal, an inductive approach is used to determine the exact radial stress-strain relations for any number of loading cycles. The inductive approach is validated by comparing the predictions of the developed solution with finite element computations. Finally, the exact solution is used to study the evolution of the composite Bauschinger effect during a stress-controlled process. It is seen that irrespective of the relative stiffness of the two phases, the strength coefficient of the matrix and the fiber volume fraction. the initial composite response is primarily governed by isotropic hardening whereas the asymptotic composite response is such that both isotropic and kinematic hardening play equally important roles.