Method for nonlinear stochastic problem of creep solving for a plane taking into account damage of the material

Abstract

The analytical method for nonlinear stochastic problem of creep solving for a plane taking into account the damage of the material and the third stage of creep is developed. Determinative creep equations are taken in accordance with the energy version of the nonlinear theory of a viscous flow in a stochastic form. Stochasticity of the material is determined by two random functions of coordinates $x_1$ and $x_2$. Linearization of the problem relative to the nominal stress on the basis of small parameter method is produced. The variance of the random stress fields is found on the hypothesis that processes of creep and damage accumulation are independent. The case when the plane is stretched in two orthogonal directions in proportion to some parameter is given as an example. The provided analysis showed that at the third stage of creep magnitude stress fluctuation is increased relative to the value at the stage in steady-state creep.

Keywords

• small parameter method
• third stage of creep
• damage
• stochastic problem
• stress fluctuation
• random function