On the Application of a Linear Fractional Model in the Problem of Long-Term Destruction of a Cylindrical Shell Under Creep Conditions in an Active Medium

The long-term destruction of a long thin-walled cylindrical shell during creep under conditions of a non-stationary complex stress state is studied, taking into account the influence of the active medium. The influence of the active medium on the creep and long-term strength of the shell is determined by the diffusion penetration of medium elements into the shell material. Using the kinetic theory of Yu.N. Rabotnov determined the times to fracture of such a shell under unsteady loading. A singular linear fractional model of creep and long-term strength is used, in which the ultimate strength of the material at the appropriate temperature plays the role of the ultimate stress. To take into account the accumulation of damage during creep and determine the criterion before failure, scalar and vector damage parameters are used, while the components of the vector damage parameter are related to the space of principal stresses. To estimate the rate of the diffusion process, an approximate method for solving the diffusion equation is used, based on the introduction of a diffusion front. Taking into account the influence of the medium on the time to fracture is carried out by introducing a function of the integral average concentration into the constitutive and kinetic linear fractional relations. A comparison of times to fracture using scalar and vector damage parameters was carried out. The features of using a linear fractional model to describe processes of long-term destruction are determined.