Analytical Solutions and Multiscale Creep Analysis of Functionally Graded Cylindrical Pressure Vessels

Abstract

This study deals with the time-dependent creep analysis of functionally graded thick-cylinders under various thermal and mechanical boundary conditions. Firstly, exact thermoelastic stress, and iterative creep solutions for a heat generating and rotating cylindrical vessel made of functionally graded thermal and mechanical properties are proposed. Equations of equilibrium, compatibility, stress-strain, and strain-displacement relations are solved to obtain closed-form initial stress and strain solutions. It is found that material gradient indices have significant influences on thermoelastic stress profiles. For creep analysis, Norton’s model is incorporated into rate forms of the above-mentioned equations to obtain time-dependent stress and strain results using an iterative method. Validity of our solutions are at first verified using finite element analysis, and numerical results found in the recent literature have been enhanced. Investigation of effects of material gradients reveals that radial variation of density and creep coefficient have significant effects on strains histories, while Young’s modulus and thermal property distributions only influence stress redistribution at an early stage of creep deformation. Next, a more realistic model of introducing microscale creep effects into a macroscopic modeling is employed to investigate the creep behavior of functionally graded hollow cylinders. Finite element (FE) simulations are employed to evaluate the position-dependent parameters associated with creep constitutive law at the microscale. A macroscopic FE model solves the non-linear boundary value problem to determine the time-varying creep stresses and strains. The framework proposed is capable of predicting the creep response of functionally graded pressure vessels based on the constitutive behavior of the creeping matrix, and volume fraction profile. Effective creep properties have been computed using three different micromechanical models and the homogenized creep response and its effect on the macroscopic behavior are compared. Considering the computational expenses associated with the large 3D finite element models, the simple 2D axisymmetric model is able to closely capture the creep behavior in such multiscale methods. Finally, a multi-objective particle swarm optimization algorithm is implemented to minimize the initial stress and final creep strain of functionally graded cylinder subjected to mechanical and thermal loads.