Nonlinear creep problems of bodies under the action of fast field oscillations

Морачковский, О. К.

doi:10.1007/bf00847065

Cited by 4 publications

(11 citation statements)

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“…13 Dynamic creep can also be described by power law creep constitutive equation modified by a function of the stress cycle asymmetry parameter. 28,29 Figure 7 illustrates the evolution of backstress for different values of the stress amplitude. An increase of the stress amplitude leads to an increase of the hardening rate and to an increase of the backstress saturation value.…”

Section: Analysis Of Cyclic Creepmentioning

confidence: 99%

“…Asymptotic time-scale methods were originally developed to solve differential equations for non-linear dynamical systems. [25][26][27] With regard to inelastic material response, the asymptotic approach was firstly applied in the literature 28,29 to analyze dynamic creep, i.e. the increase of inelastic strain under combined static and rapidly varying cyclic loading with a small amplitude.…”

Section: Introductionmentioning

confidence: 99%

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Two-time-scales and time-averaging approaches for the analysis of cyclic creep based on Armstrong–Frederick type constitutive model

Altenbach

Breslavsky

Naumenko

et al. 2018

Proceedings of the Institution of Mechanical Engineers, Part C:

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The aim of this paper is the analysis of inelastic behavior under periodic cyclic loading regimes for materials showing recovery effects. Starting with the Armstrong–Frederick type model and applying the two-time-scale asymptotic technique, the constitutive equation for the mean inelastic strain rate and the evolution equation for the mean backstress variable are derived. The advantage of the presented technique is the closed analytical form of the solutions such that the influence of the loading profiles on the resulting slow cycle-by-cycle strain accumulation can be analyzed explicitly. To validate the derived equations, the original constitutive model is integrated numerically by applying the time-step procedure for various cyclic loading profiles. Numerical examples are presented to illustrate cyclic creep behavior of X20CrMoV12-1 heat resistant steel.

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Section: Analysis Of Cyclic Creepmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two-time-scales and time-averaging approaches for the analysis of cyclic creep based on Armstrong–Frederick type constitutive model

Altenbach

Breslavsky

Naumenko

et al. 2018

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…Incommensurability of the static and cyclic periods allows asymptotic expansions in terms of the small parameter m to be written for the unknowns of system (2) [13] z z x t z x t…”

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confidence: 99%

“…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 …”

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confidence: 99%

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Cyclic thermal creep model for the bodies of revolution

2011

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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...

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Initial-Boundary Value Problems and Solution Procedures

Naumenko

Altenbach

2019

Advanced Structured Materials

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Nonlinear creep problems of bodies under the action of fast field oscillations

Cited by 4 publications

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Two-time-scales and time-averaging approaches for the analysis of cyclic creep based on Armstrong–Frederick type constitutive model

Two-time-scales and time-averaging approaches for the analysis of cyclic creep based on Armstrong–Frederick type constitutive model

Cyclic thermal creep model for the bodies of revolution

Initial-Boundary Value Problems and Solution Procedures

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