Hydrogen elasticity solution of functionally-graded spheres, cylinders and disks

Abstract

Hydrogen induced stresses in functionally-graded axisymmetric spheres, cylinders and disks are investigated by the combine use of infinitesimal theory of plane elasticity and Complementary Functions Method for the first time. Computations of the stresses in circular members under hydrogenation and dehydrogenation have been carried out. The material properties of circular members are assumed to be varied through the radial coordinate. The plane analysis of hydrogenated inhomogeneous materials leads to two-point boundary value problem with a governing differential equation of variable coefficients. The implementation of Complementary Functions Method into the analysis results in a powerful solution scheme to the hydrogen elasticity problems of functionally graded circular members. Three different grading rules are considered and effects of mixing ratios investigated. The variation on the grading rules affects the radial stress more than hoop stress which may be the crucial finding in the design of hydrogenated inhomogeneous materials. Validation of the results is done using benchmark solutions available in the literature for isotropic sphere.