Creep and long-term fracture of a narrow rectangular membrane inside a high rigid 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 high rigid 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 longitudinal sides of the rigid matrix. At second stage, the membrane is deformed when it touches the longitudinal walls of matrix until it touches its transverse wall. At third stage, the membrane is already deformed while simultaneously touching the longitudinal and transverse walls of matrix. Membrane deformation occurs under creep conditions under two types of contact conditions: sliding of the membrane along the walls of matrix and adhesion of membrane to the walls of matrix. The dependence of the time until the fracture of membrane at different rates of increase in the magnitude of the transverse pressure is obtained.
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 solution of the system consisting of constitutive and kinetic equations showed that during the membrane deformation at the first stage regardless of the type of contact conditions, the level of damage accumulates in the membrane, which is close to its limiting value. In this regard, the creep processes of the membrane at second and third stages of deformation under both considered types of contact conditions practically coincide.
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.