Effect of Heat Flux on Creep Stresses of Thick-Walled Cylindrical Pressure Vessels

Assuming that the thermo-creep response of the material is governed by Norton’s law, an analytical solution is presented for the calculation of time-dependent creep stresses and displacements of homogeneous thick-walled cylindrical pressure vessels. For the stress analysis in a homogeneous pressure vessel, having material creep behavior, the solutions of the stresses at a time equal to zero (i.e. the initial stress state) are needed. This corresponds to the solution of materials with linear elastic behavior. Therefore, using equations of equilibrium, stress-strain and strain-displacement, a differential equation for displacement is obtained and then the stresses at a time equal to zero are calculated. Using Norton’s law in the multi-axial form in conjunction with the above-mentioned equations in the rate form, the radial displacement rate is obtained and then the radial, circumferential and axial creep stress rates are calculated. When the stress rates are known, the stresses at any time are calculated iteratively. The analytical solution is obtained for the conditions of plane strain and plane stress. The thermal loading is as follows: inner surface is exposed to a uniform heat flux, and the outer surface is exposed to an airstream. The heat conduction equation for the one-dimensional problem in polar coordinates is used to obtain temperature distribution in the cylinder. The pressure, inner radius and outer radius are considered constant. Material properties are considered as constant. Following this, profiles are plotted for the radial displacements, radial stress, circumferential stress and axial stress as a function of radial direction and time.