Edge fixing effect on the life of a vacuum chamber thin spherical cover subjected to creep damage

Abstract

Within framework of the numerical studies of creep resource of a thin spherical cover of a vacuum chamber, we present mathematical formulation and the calculation method for the solution of the initial boundary value problems of the creep theory of thin shells with account of the damage accumulation process of the material. The effect of edge fixing along the normal and tangential lines to the median surface, as well as angular edge fixings, on the cover life in creep are studied under atmospheric pressure creep conditions. The calculation data obtained made it possible to determine the dependence between the cover life in creep and its edge fixing conditions: this effect is strong by the latent fracture time and weak by the allowable deflection values.Keywords: life, creep, damageability, fracture time, cover of a vacuum chamber, spherical shell, the BubnovGalerkin method.Introduction. Vacuum systems are used for a variety of processes and scientific development purposes. Due to a specific nature of the latter applications, system components can operate under creep conditions. The life prediction for structural elements in-service is governed by ensuring their safe operation and therefore presents an urgent scientific and technical problem.The required life of vacuum system elements at the given levels of temperatures and intensities of mechanical loads is traditionally achieved by selecting materials, geometry and certain sizes. The limited nature of the choice in materials and sizes of structures is due to the known objective reasons. The fixing of structural elements influences their life and is an additional factor in its ensuring.The goal of the present work is to perform a computational study of the effect of edge fastening of a spherical cover of the vacuum chamber on its life in creep. The investigation technique is the mathematical simulation of the processes of deformation and damaging due to creep and the generalization of the accumulated results of numerical experiments.Mathematical Formulation of the Problem. We consider the spherical cover of vacuum chamber that separates the vacuum enclosure from the atmosphere as a thin shell, namely, a spherical dome of constant thickness h, radius R, and with the apex angle 2q (see Fig. 1) loaded by the pressure p. To model the high-temperature creep and damage of the cover material, we adopt the creep law, such as the Bailey-Norton creep law, and a continuum version of the damage theory proposed by Rabotnov [1,2]. Under the axisymmetric deformation of thin shells [2, 3], the Lame parameters of the median surface of a spherical shell are dependent only on the coordinate x 1 , whereas the parameters of the stress-strain state and damaging due to creep vary with the time t and are dependent on the coordinates x 1 and x 3 .The resolving differential equations in the mixed form with respect to the unknown internal forces, moments, displacements, and rotation angle of the spherical shell median surface normal are of the following form [2, 3]: