Creep and long-term fracture of a narrow rectangular membrane inside a rigid low matrix with proportional dependence on the transverse pressure on time

In this work, we studied the creep and long-term fracture of a narrow rectangular membrane in confined conditions (inside a rigid low matrix) with a proportional dependence on the magnitude of transverse pressure on time.
Deformation of the membrane is considered as a sequence of three stages. At first stage, the membrane is deformed under free conditions until it touches the transverse side of the rigid matrix. At second stage, the membrane is deformed when it touches the transverse wall of the matrix until it touches its longitudinal walls. At third stage, the membrane is already deformed while simultaneously touching the longitudinal and transverse walls of matrix.
The study is carried out under two types of contact conditions: 1) ideal sliding of the membrane along the walls of the matrix; 2) sticking of the membrane to the walls of the matrix.
The analysis of the gradual long-term fracture of the membrane is carried out using the kinetic theory of creep by Yu. N. Rabotnov, while the parameter of material damage in this problem has a scalar character.
The obtained equations are used to analyze the creep and long-term fracture of a membrane made of 2.15Cr-1Mo steel, which is deformed under variable transverse pressure at a temperature of $600\,^\circ$C until its destruction.
As a result of solving the system of constitutive and kinetic equations, the values of the damage parameter accumulated during each stage of deformation, as well as the time to fracture of the membrane, are obtained. In the case of membrane fracture at the first stage of deformation, the time to fracture at the first stage does not depend on the type of contact conditions, and in the case of membrane fracture at the second and third stages of deformation, the time to fracture in the case of ideal slip is not less than in the case of sticking.