We present a method for solving problems of high-temperature cyclic creep and damage accumulation in structural elements. The asymptotic expansion and averaging techniques both over the period of forced vibrations of a body and that of slowly varying loads are used for the set of equations describing the creep and damage processes in thin-walled structural elements.Introduction. Structural elements of up-to-date equipment operating at elevated temperatures and under the combined action of both static and slowly or rapidly varying cyclic stresses are characterized by the processes of evolution of irreversible creep deformations and accumulation of concealed damage. Many of such elements correspond to calculation schemes for thin shells of revolution. Due to a wide use of thin-walled shells of revolution in aerospace, aircraft and power engineering, the questions arise as to simulation of their stress-strain states (SSS) under cyclic loading conditions [1].Most of the computational studies on the creep and fracture of shell structures were carried out only for the case of static loads. A number of works dealing with the evaluation of the influence of cyclic loading on the creep and long-term strength characteristics of plates and shells were published recently [2,3]. Under actual operating conditions of structural elements, their loading is a complex process -a combination of temperature and load cycles with greatly different periods. In this connection, the development of the method for solving problems of cyclic creep and damage accumulation is of importance. This paper presents the developed method as applied to thin-walled structures consisting of shells of revolution.Problem Statement and Solution Method. The formulated problems are solved using the finite element method (FEM). A finite element is used as a conical shell. According to the FEM approach, we write down the basic variational equality [2, 3] − − + =

Creep of cyclically loaded thin shells of revolution and their fracture due to creep and fatigue mechanisms are studied. Creep-damage equations for steels and nickel-based alloys are built by the use of scalar damage parameter. Constitutive equations were derived using the method of asymptotic expansions and averaging over a period of cyclic loading. The cases of fast and slow varying of temperature and loading are regarded. General problem statement and method for solution of creep problems at cyclic loading are presented. Strain-stress state in shell structures is determined by the use of homemade FEM creep-damage code, where the finite element of conical shell is used. Results of creep-damage problem for conical panel are discussed.

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Creep-damage processes in notched specimens subjected to static and periodic loading are studied experimentally. Subsequent simulations were carried out using Rabotnov evolution equation. In case of dynamic creep (fast periodic loading) the constitutive equations derived by use of asymptotic and averaging methods were used. Numerical results were obtained by the combination of FEM and predictor-corrector time integration scheme. Fracture process was studied using designed numerical procedure based on the elimination of the finite elements with critical values of damage parameter. The fracture times and directions of the crack propagation were determined. The qualitative difference between processes of crack propagation in cases of static and periodic loading were observed.

Deformation and damage of nuclear power station fuel element shells under irradiation and cyclic loading due vibrations are studied. Constitutive equations include dependencies for a creep-damage equation with a scalar damage parameter, as well as terms for thermal and irradiation creep strains, elastic, thermal, and swelling strains. The acceleration of the creep-damage process due to cyclic variation of internal pressure is considered with a dynamic creep model, for which constitutive equations are derived using the method of asymptotic expansions and averaging over a period of cyclic loading. Stress and strain states in the fuel element shell are determined by use of an in-house finite element method creep-damage code for shells of revolution. Results show the essential variation in the initially symmetric fuel element shell form, as well as the acceleration of creep-damage processes due to the cyclic pressure.