Study of the Influence of the Kinetics of Hydrogen Saturation on the Stress-deformed State of a Spherical Shell Made from Titanium Alloy

In this paper, a mathematical model is considered that allows one to determine the stress-strain state of a spherical shell made of titanium alloy VT1-0, the external load is assumed to be transverse uniformly distributed, acting on the outer surface, the medium is assumed to act on the inner surface of the shell. For this, a nonlinear model was used, presented in normalized stress spaces. Fastening along the contour of the shell is rigid. Nonlinear resolving equations for calculating a spherical shell are obtained. An algorithm for solving the problem of hydrogenation of titanium alloy shells has been developed. A practical solution was made by a two-step method of sequential perturbations of parameters using the MatLab and Maple software packages. To solve the system of the obtained differential equations, the method of finite differences is applied. The calculation of the stress-strain state of the shell is obtained taking into account the diffusion process of an aggressive hydrogen-containing medium, and the obtained solution is compared with the results of the classical nonlinear theory without taking into account the aggressive medium. The results of comparing these solutions demonstrate quantitative differences in the parameters of the shell deformation process, which are explained by a more accurate account of the influence of the type of stress state. This approach has a rather flexible mechanism for considering the initial and induced differential resistance, demonstrates a high accuracy of matching the obtained theoretical results with empirical data on loading a wide range of materials under complex types of stress state.