A Semi-analytical Approach to Elastic-plastic Stress Analysis of FGM Pressure Vessels

An analytical method for predicting elastic–plastic stress distribution in a cylindrical pressure vessel has been presented. The vessel material was a ceramic/metal functionally graded material, i.e. a particle–reinforcement composite. It was assumed that the material’s plastic deformation follows an isotropic strain-hardening rule based on the von-Mises yield criterion, and that the vessel was under plane-stress conditions. The mechanical properties of the graded layer were modelled by the modified rule of mixtures. By assuming small strains, Hencky’s stress–strain relation was used to obtain the governing differential equations for the plastic region. A numerical method for solving those differential equations was then proposed that enabled the prediction of stress state within the structure. Selected finite element results were also presented to establish supporting evidence for the validation of the proposed analytical modelling approach. Similar analyses were performed and solutions for spherical pressure made of FGMs were also provided.