Abstract:

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 Voigt constant strain approximation 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 dispalcement is presented for the case with elastic phase and plastic phase together. The yield criterion of functionally graded material is given in terms of the yield stresses and volume fractions of constituents rather than the 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 in the tube and the conditions for which material first yields.