Elastoplastic response of a long functionally graded tube subjected to internal pressure

Abstract

Plane strain analytical solutions to functionally graded elastic and elastic-plastic pressurized tube problems are obtained in the framework of small deformation theory. The modulus of elasticity of the tube material is assumed to vary radially according to a 2 parametric model in a general parabolic form. The analytical plastic model is based on Tresca's yield criterion, its associated flow rule and ideally plastic material behavior. Exact solutions of field equations for elastic and plastic deformations are obtained. It is shown that the elastoplastic response of the functionally graded pressurized tube is affected notably by the radial variation of modulus of elasticity. It is also shown mathematically that the nonhomogeneous solution presented here reduces to that of a homogeneous one by the appropriate choice of the material parameters.