The elastic-plastic response of the functionally graded thick-walled tube
subjected to internal pressure is investigated by using the relation of the volume average
stresses of constituents and the macroscopic stress of composite material in micromechanics.
The tube consists of two idealized isotropic elastic-plastic materials
whose volume fractions are power functions of the radius. As the internal pressure
increases, the deformations of one phase and two phases from elastic to plastic are analyzed.
In order to simplify the calculations we assume both materials with the same
Poisson’s ratio. By using the assumption of a uniform strain field within the representative
volume element and the Tresca yield criterion, the theoretical solutions are
obtained for the case of two elastic phases and the case of two plastic phases, and the
function of the radial displacement is presented for the case with both elastic and plastic
phases. The yield criterion of functionally graded material is given in terms of the
yield stresses and volume fractions of constituents rather than Young’s modulus and
yield stress with different unknown parameters of the whole material in the existing
papers. Finally we also discuss the position where the plastic deformation first occurs
and the conditions for which material first yields in the tube.