Cyclic thermal creep model for the bodies of revolution

Abstract

The new method of solving thermal creep problems, accounting for cyclic variations of external force and thermal fields was put forward. Asymptotic expansions and period averagings were used to derive the systems of basic and auxiliary equations. The equation of state for cyclic thermal creep was proposed and validated. Numerical simulation of the creep of cylinders under cyclic temperature variations was carried out.Introduction. One of the most widespread classes of engineering structural elements is the bodies of revolution, viz pressure vessels and valves, pipe lines, internal combustion engine cylinders, steam and gas turbine rotors, etc. Since such structural elements operate under the joint action of force and thermal fields, evaluation of their deformation behavior is one of the important problems for ensuring necessary service life. As is known, the level and frequency of load and temperature variations can greatly influence creep and time to fracture [1][2][3][4][5][6][7].Increasing requirements to materials consumption, life, and reliability gave rise to significant results obtained in creep and creep rupture strength calculations for materials and structures [1,[5][6][7]. Polymer structural elements are usually subjected to analysis for studying the interaction between cyclic force and thermal fields [8]. Most calculations of service life and creep rupture strength of structural elements manufactured from metals and their alloys are performed only for the case of time-invariant thermal fields. The exception is represented by the studies under the direction of Academician G. S. Pisarenko [6,7,9,10], in which equations of state for materials on cyclic high-temperature heating were suggested and verified as well as by experimental investigations of the models of high-temperature structural elements (blades, internal combustion engine pistons, etc.).Thus, the development of a method for calculating cyclic thermal creep and damage accumulation in structural elements remains the topical problem of modern mechanics. 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.In this study, the statement of the problem is presented and the new equations of state are proposed to describe the cyclic thermal creep of metallic materials and their alloys. The calculations are based on the methods of two time scales and asymptotic expansions. Calculated and experimental cyclic creep data obtained for different temperatures and thermal cycles were compared and verified. The problem was solved by the finite element method and by multistep time integration. The method of solving cyclic thermal creep problems was applied to the two-dimensional ones. As an example, the solutions of cyclic thermal c...

Numerical simulation of two-dimensional problems of creep crack growth with material damage consideration

“…The system of equations for determining the stress-strain state of a body under creep is as follows [18]:…”

Creep and damage in shells of revolution under cyclic loading and heating

“…Finally let us note that although constructed constitutive model (19) and damage kinetic Eq. (20) look complicated, the practical use of them is simple.…”

“…Validation of the particular parts of Eqs. (19)-(21) for complex stress state had been done [16,18,19,24,[26][27][28]31]. In addition, the thermodynamic justification of those equations was performed.…”

“…It is necessary to calculate the current values of influence functions in constitutive Eqs. (19) and (20). Here [M] is the mass matrix of the system; Ω k , Ω are the frequencies of external loading; Δ ak , Δ a are the vectors of amplitude values at poly-harmonic loading through a cycle and at forced vibrations, correspondingly.…”

“…Further interaction between damage accumulation from dynamic creep process and high cycle high temperature fatigue has been analyzed for thin shells of revolution in [17]. The situations of slow variation of stresses and temperatures were studied in [18,19].…”