High-temperature creep and long-term strength of structural elements under cyclic loading

Abstract

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] − − + =

Cyclic thermal creep model for the bodies of revolution

“…The new equations of state are put forward to describe the creep of materials at constant temperature, high-and low-rate stress variations [11,12]. However, for the practically significant case of cyclic temperature variations, with creep developing in structural materials, the equations of state suitable for calculations in the multiaxial stress state heretofore have not been derived.…”

“…Substitute expansions (12) and (13) into system of equations (2) and solve the relations using period averaging (9). Then for the equilibrium equations and for the stress-strain relations we accordingly have …”

“…Subsystems (16) and (17) that describe slow-and fast-drift motions are not independent. They are related by the equation of state [12]. In the examined case, it is the equation of cyclic thermal creep.…”

“…The equations of state for cyclic creep of structural materials were used to calculate creep and damage accumulation in the multiaxial stress state [10][11][12].…”

“…Using asymptotic expansions and (21) and (22) for equations (20), after T-period averaging under cyclic stress, we have[12] g n and g r are the functions of cyclic loading amplitude factors. specimen temperature is time-variable, then similarly to the above procedure, we derive the equations of state for the case of cyclic temperature variations and g r T are the functions of cyclic heating-cooling amplitude factors.Examine the more complicated case of joint cyclic temperature and mechanical loading effects.…”