Abstract
An analytical solution is obtained for the elastic response of a three coax ial cylinder model of a composite to thermal and mechanical loading. Calculations of the thermal stresses for various fiber coatings reveal certain relationships between the coating stresses that make it possible to solve for the plastic flow of the coating. In the case of a high expansivity coating, the elastic solution indicates that the radial and hoop stresses are the extreme stresses which satisfy the conditions for Tresca flow in the r-θ plane. However, as the temperature changes, plastic flow is shown to relax the hoop stress to the extent that it becomes less than the axial stress which violates the condition for Tresca flow. In order to obtain solutions for plastic flow in the coating it is then necessary to consider plastic flow in more than a single plane. The Prandtl-Reuss flow rule can be used to solve for flow in three planes but because of the mathematical complexity it is necessary to use numeri cal techniques for the calculations. As an alternative, analytical solutions are developed for flow in two planes using an approximation for the Prandtl-Reuss flow. Three different solutions are obtained to include flow in the r-θ r-z, z-r z-θ, and θ-r θ-z planes. Each of these is applied for a different expansivity value of the fiber coating with various linear work hardening coefficients of the coating.
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