Mechanics Of Damaged Media Research Articles

ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ УСТАЛОСТНОЙ ДОЛГОВЕЧНОСТИ ДЕТАЛЕЙ АВИАЦИОННЫХ ГТД ПРИ ЦИКЛИЧЕСКОМ ДВУХЧАСТОТНОМ НАГРУЖЕНИИ

The problem of assessing the resource characteristics of responsible engineering facilities, taking into account the peculiarities of operational loading modes, is discussed. The processes of fatigue durability of polycrystalline structural alloys under cyclic two-frequency loading (with the combined action of mechanisms of low and multi-cycle fatigue) are considered. A mathematical model describing the processes of cyclic elastoplastic deformation and accumulation of fatigue damage in structural alloys under multiaxial disproportionate modes of combined thermomechanical loading has been developed from the modern positions of damaged medium mechanics and fracture mechanics. The model consists of three interrelated parts: relations determining the cyclic elastic-plastic behavior of the material, taking into account the dependence on the destruction process; evolutionary equations describing the kinetics of fatigue damage accumulation; criteria for the strength of the damaged material. The variant of the defining elastic-plasticity relations is based on the idea of the yield surface and the principle of gradiency of the velocity vector of plastic deformations to the yield surface at the loading point. This version of the equations of state reflects the main effects of cyclic elastic-plastic deformation of the material for arbitrary folded loading trajectories. The variant of kinetic equations of fatigue damage accumulation is based on the introduction of a scalar damage parameter, is based on energy principles and takes into account the main effects of formation, growth and fusion of microdefects under arbitrary complex cyclic loading regimes. A joint form of the evolutionary equation of fatigue damage accumulation in the areas of low- and multi-cycle fatigue is proposed. As a criterion of the strength of the damaged material, the condition of reaching the critical value of the damage value is used. The results of numerical simulation of fatigue durability of a compact sample (model of the disk deflector of the high pressure turbine of an aviation gas turbine engine) are presented with cyclic two-frequency loading. The results of the comparison of the calculated and experimental data showed that the proposed model qualitatively and with the accuracy necessary for practical calculations quantitatively describes the fatigue life of structural elements under cyclic two-frequency loading.

МОДЕЛИРОВАНИЕ УСТАЛОСТНОЙ ДОЛГОВЕЧНОСТИ КОНСТРУКЦИОННЫХ СПЛАВОВ ПРИ ДВУХЧАСТОТНОМ НАГРУЖЕНИИ

The processes of fatigue life of polycrystalline structural alloys under the combined action of low- and high-cycle fatigue mechanisms are considered. From the standpoint of damaged medium mechanics (DMM), a mathematical model has been developed that describes the processes of plastic deformation and the accumulation of fatigue damage. The DMM model consists of three interrelated parts: relations that determine the cyclic elastoplastic behavior of the material, taking into account the dependence on the fracture process; equations describing the kinetics of fatigue damage accumulation; criterion for the strength of the damaged material. Variant of the constitutive relations for elastoplasticity is based on the concept of a microplastic loading surface in the von Mises form and the principle of the gradient of the plastic strain rate vector to the surface at the loading point. This version of the equations of state reflects the main effects of the process of cyclic plastic deformation of the material for arbitrary complex loading trajectories. A variant of the kinetic equations for the accumulation of fatigue damage is based on the introduction of a scalar damage parameter, is based on energy principles and takes into account the main effects of the formation, growth and fusion of microdefects under arbitrary complex loading conditions. A unified form of the evolutionary equation for the accumulation of fatigue damages for low-cycle and high-cycle fatigue is proposed. As a criterion for the strength of the damaged material, the condition for reaching the critical value of the damage is used. To assess the reliability and determine the limits of applicability of the constitutive relations of the DMM, numerical studies of the processes of accumulation of fatigue damage by cyclic inelastic deformation and fatigue failure of steel 20 and 08Х18Н12Т were carried out under single-frequency loading of the upper frequency and two-frequency loading with different amplitude ratios. And the comparison of the obtained numerical results with the data of field experiments is carried out. The results of comparing the calculated and experimental data showed that the developed model of the damaged environment reliably describes the durability of structures under the action of low- and high-cycle fatigue mechanisms.

Defining relations of mechanics of damaged media effected by fatigue and creep

A possible version of a model describing degradation of initial strength properties of structural alloys affected by fatigue and creep is introduced, based on the modern viewpoint of mechanics of damaged media (MDM). Processes of viscoplastic deformation and damager accumulation in structural alloys are analyzed using numerical modeling. Special attention is paid to the issues of modeling the processes of viscoplastic deformation and damage accumulation for complex deformation processes accompanied by the rotation of main sites of stress and strain tensors. New qualitative and quantitative features of the failure process are noted, which are connected with stressed-strained state history, damage degree, stress relaxation and other factors.

МОДЕЛИРОВАНИЕ УСТАЛОСТНОЙ ДОЛГОВЕЧНОСТИ ПОЛИКРИСТАЛЛИЧЕСКИХ КОНСТРУКЦИОННЫХ СПЛАВОВ ПРИ СОВМЕСТНОМ ДЕЙСТВИИ МЕХАНИЗМОВ МАЛО- И МНОГОЦИКЛОВОЙ УСТАЛОСТИ

Processes of fatigue life of polycrystalline structural alloys under a combined effect of low- and high-cycle fatigue are considered. In the framework of mechanics of damaged media (MDM), a mathematical model is developed, which describes processes of plastic deformation and fatigue damage accumulation. The MDM model consists of three interrelated parts: relations defining cyclic elastoplastic behavior of the material, accounting for its dependence on the failure process; equations describing fatigue damage accumulation kinetics; a strength criterion of the damaged material. The version of defining relations of elastoplasticity is based on the notion of yield surface and the principle of orthogonality of the plastic strain rate vector to the yield surface at the loading point. This version of equations of state reflects the main effects of the cyclic plastic deformation process of the material for arbitrarily complex loading trajectories. The version of kinetic equations of damage accumulation is based on introducing a scalar parameter of damage degree. The construction uses energy-based principles and accounts for the main effects of the process of nucleation, growth and merging of microdefects under arbitrarily complex multiaxial loading regimes. A combined form of the evolutionary equation of fatigue damage accumulation in the regions of low-cycle (LCF) and high-cycle (HCF) fatigue is proposed. It is shown that, under regular cyclic loading of the material, the stress amplitude of the cycle decreases by degrees during the transition from LCF to HCF and depends on the physical interaction of these mechanisms in the transition zone. The condition when the damage degree attains its critical value is taken as the strength criterion of the damaged material. A methodology of numerically determining parameters of the evolutionary equation of fatigue damage accumulation in the conditions of HCF is presented. To assess the reliability and the limits of applicability of the defining relations of MDM, processes of plastic deformation and fatigue damage accumulation in a number of structural alloys in cyclic tests have been numerically studied, and the obtained numerical results have been compared with the data of full-scale experiments. The results of comparison of the numerical and experimental data reveal that the developed model of mechanics of damaged media adequately describes durability of structures subjected to a combined effect of low- and high-cycle fatigue mechanisms. It is shown that the introduced MDM model qualitatively and, accurately enough for practical engineering purposes, quantitatively describes the main effects of the processes of plastic deformation and fatigue damage accumulation in structural alloys under cyclic loading.

A model of damaged media for describing a creep-induced damage accumulation process

In the framework of mechanics of damaged media (MDM), a mathematical model describing creep-induced processes of inelastic deformation and damage accumulation is developed. The MDM model consists of three interrelated parts: relations defining inelastic behavior of the material, accounting for its dependence on the failure process; equations describing damage accumulation kinetics; a strength criterion of the damaged material.The results of experimentally studying short-term creep of the VZh-159 heat-resistant alloy at constant temperature values and different values of applied stresses in the specimens are given.Comparison of the numerical and experimental results makes it possible to conclude that the proposed defining relations of MDM are reliable in describing degrading initial strength properties of structural materials according to the long strength mechanism.

Modeling fatigue life of structural materials under block-type nonsymmetrical loading

In the framework of mechanics of damaged media (MDM), a mathematical model describing processes of thermo-plastic deformation and fatigue damage accumulation under low-cycle loading is developed. The MDM model consists of three interconnected parts: relations defining cyclic thermoplastic behavior of the material included for its dependence on the failure process; equations describing damage accumulation kinetics; a strength criterion of the damaged material.To assess the reliability and the scope of applicability of the defining relations of MDM, processes of plastic deformation and damage accumulation in a number of structural steels in low-cycle tests have been numerically analyzed, and the obtained results have been compared with the data from full-scale experiments. It is shown that the proposed MDM model qualitatively and, accurately enough for engineering purposes, quantitatively describes the main effects of the processes of plastic deformation and fatigue damage accumulation in structural alloys under block-type nonstationary nonsymmetrical low-cycle loading.

Evaluation of fatigue life of polycrystalline structural alloys

A mathematical model describing the processes of elastoplastic deformation and damage accumulation under low-cycle loading has been developed, based on the viewpoint of mechanics of damaged media (MDM). The MDM model consists of three interrelated parts: defining relations describing elastoplastic behavior of the materials, taking into account its dependence on the failure process; evolutionary equations describing the kinetics of damage accumulation; strength criteria of the damaged material. In order to assess the reliability and scope of applicability of the defining relations of mechanics of damaged media, the processes of plastic deformation and damage accumulation in variety of structural steels in low-cycle tests have been numerically analyzed, and numerical results obtained have been compared with the data of full-scale experiments. It is shown that the presented model of mechanics of damaged media adequately describes, both qualitatively and quantitatively, with accuracy, necessary for practical calculations, the main effects of the processes of plastic deformation and damage accumulation in structural alloys under block-type non-stationary non-symmetrical low-cycle loading.

Modeling dynamic deformation and failure of thin-walled structures under explosive loading

In the framework of mechanics of damaged media, behavior of thin-walled structures under pulsed loading is described. Account is taken of the interaction of the processes of dynamic deformation and damage accumulation, as well as of the main characteristic features of the dynamic failure process: the multi-staged character, nonlinear summation of damage, stressed state history and accumulated damage level. The chosen system of equations of thermo-plasticity describes the main effects of dynamic deformation of the material for random deformation trajectories. The equations of state are based on the notions of yield surface and the principle of gradientality of the plastic strain rate vector. Evolutionary equations of damage accumulation are written for a scalar parameter of damage level and are based on energy principles. The effect of the stressed state type and the accumulated damage level on the processes of nucleation, growth and merging of microdefects is accounted for. Results of numerically modelling processes of dynamic deformation and failure of spherical and closed cylindrical shells with plane and hemispherical bottoms under single pulsed explosive loading are presented. The computational results are compared with experimental data.

Evaluating fatigue life of materials and structures under low-cycle loading

The problem of evaluating strength and fatigue life of critical engineering objects, the operational properties of which are characterized by multi-parametric nonstationary thermal-mechanical effects, is discussed. The main degradation mechanisms of structural materials (metals and their alloys) characteristic of such objects are considered. The main requirements for mathematical models of fatigue damage accumulation are formulated. To evaluate the stress-strained state (SSS) and fatigue life of critical engineering facilities (CEF) in the framework of modern achievements of mechanics of damaged media (MDM), a mathematical model is developed which describes the processes of cyclic thermal-plastic deformation and fatigue damage accumulation in structural alloys subject to multiaxial non-proportional paths of combined thermal-mechanical loading. The MDM model consists of three interconnected parts: thermal plasticity constitutive equations, accounting for their dependence on the failure process; an evolution equation of damage accumulation and a strength criterion of a damaged material. To qualitatively and quantitatively assess the constitutive relations of MDM for low-cycle modes of thermal-cyclic loading, the numerical and experimental results for the fatigue life of a notched compact sample in a non-uniaxial stress state under block modes of thermal-cyclic loading were compared, which supported the validity of the constitutive relations of the MDM model for thermal fatigue. An approach based on the Palmgren-Miner rule of linear summation of damage, when used for evaluating the fatigue life of structural elements, may result in both conservative and non-conservative estimates. This conclusion is confirmed by the experimental and theoretical studies of foreign and domestic authors. The results of numerical modeling of the fatigue durability of a compact specimen with an obtuse notch are presented for two loading histories. It is shown that several cycles of more intensive loading at the beginning of the strain history are the reason why the rule of linear summation of damage can overestimate or underestimate the value.

МОДЕЛЬ ПОВРЕЖДЕННОЙ СРЕДЫ ДЛЯ ОПИСАНИЯ ДЛИТЕЛЬНОЙ ПРОЧНОСТИ КОНСТРУКЦИОННЫХ МАТЕРИАЛОВ (МЕТАЛЛОВ И ИХ СПЛАВОВ)

The main laws of processes of deformation and degradation of the initial strength properties of structural materials (metals and their alloys) according to the long-term strength mechanism are considered. In the framework of damaged medium mechanics, a mathematical model describing processes of inelastic deformation and damage accumulation in the presence of creep is developed. The model consists of three interconnected parts: relations defining inelastic behavior of the material, accounting for the effect of the failure process; equations describing kinetics of damage accumulation; a strength criterion of the damaged material. Results of experimentally studying short-term creep of VZh-159 heat-resistant alloy under constant temperatures and different values of stress applied to the specimens are given. The deformation and damage accumulation process is numerically analyzed; the obtained numerical results are compared with the data of full-scale experiments. The comparison of the numerical and experimental data makes it possible to conclude that the present defining relations of damaged medium mechanics in the presence of degradation of the initial strength properties of structural materials according to the long-term strength mechanism are adequate. Keywords: transient creep, long-term strength, modeling, defining relations, damaged medium mechanics, temperature, damage degree, material parameters, numerical and full-scale experiments.

ЧИСЛЕННЫЙ АНАЛИЗ ТЕРМОЦИКЛИЧЕСКОЙ ДОЛГОВЕЧНОСТИ МОДЕЛЕЙ ЖАРОВЫХ ТРУБ С РАЗЛИЧНЫМИ УГЛАМИ НАКЛОНА ОХЛАЖДАЮЩИХ КАНАЛОВ

The issue of evaluating strength and service life of critical engineering objects, whose exploitation properties are characterized by multi-parametric nonstationary thermal-mechanical effects, is discussed. Basic degradation mechanisms of structural materials (metals and alloys) characteristic of such objects are considered. The main criteria for mathematical models of fatigue damage accumulation are formulated. Based on the developed version of defining equations of damaged medium mechanics, the effect of the angle of inclination of the cooling channels on thermal-cyclic life of the models of flue tubes of combustion chambers gas turbine engines is numerically analyzed. Special attention is paid to studying the processes of complex thermal-cyclic deformation and fatigue damage accumulation, accompanied by rotation of the main sites of stress tensors, complete and plastic deformations, as well as the processes of fatigue damage accumulation. Comparison of the obtained numerical results with experimental data shows that the developed model of damaged medium mechanics adequately and accurately enough for engineering calculations quantitatively describes experimental data and can be effectively used for evaluating thermal-cyclic life of materials and structures under multiaxial non-proportional modes of thermal-cyclic loading. Keywords: thermal-cyclic life, damaged medium mechanics, complex deformation, models of flue tubes, cooling channel, inclination, macroscopic crack, strength, fracture.

КОНЕЧНО-ЭЛЕМЕНТНОЕ МОДЕЛИРОВАНИЕ РАЗВИТИЯ ТРЕЩИНЫ В ОБРАЗЦЕ С КОНЦЕНТРАТОРОМ В УСЛОВИЯХ ВЫСОКОТЕМПЕРАТУРНОЙ ПОЛЗУЧЕСТИ

A numerical methodology for analyzing failure processes in structures in the framework of relations of damaged medium mechanics is considered; the methodology makes it possible to analyze the behavior of structures, accounting for characteristic failure processes at both the initial stage of nucleation and the final stage of crack propagation. The results of numerically studying laws of nucleation and propagation of cracks in a cylindrical specimen with a concentrator, loaded in axial tension under high-temperature creep in the assumption of a viscous character of failure of the specimen, are given, as obtained using the present methodology. The results of the analyses are shown to depend on the parameters of the FE-discretization of the specimen in the region of the crack propagation trajectory. Nucleation time, stable propagation time and crack propagation rate are correlated with the value of the stress concentration coefficient in the notch and the intensity of tensile stresses. Keywords: creep, stress concentrator, damage accumulation, fracture, crack, finite element method.

A Damaged Medium Model for Describing Dynamic Spallation Fracture

The main physical laws of the failure process in structural materials under dynamic loading modes and mathematical models of such processes are considered. To describe dynamic spallation fracture, a version of governing equations of damaged medium mechanics is developed, consisting of three interrelated parts: governing equations describing plastic behavior of the material as a function of the failure process, evolution equations of damage accumulation, and a strength criterion of the damaged material. A methodology for determining material parameters of kinetic equations of damage accumulation, based on minimizing the quadratic deviation between theoretical and experimental data is used. Comparison of the obtained computational results with the experimental data on dynamic spallation fracture in plates during plane impact shows that the present model of damaged medium mechanics adequately describes experimental data and can be effectively used in analyzing dynamic spallation fracture.

Assessment of the service life of structural steels by using degradation models with allowance for fatigue and creep of the material

A mathematical model is developed within the framework of equations of damaged medium mechanics to describe the processes of viscoplastic straining and damage accumulation in structural steels with allowance for fatigue and creep of the material. A model of damage summation due to interaction of low-cycle fatigue and creep of the material is proposed. Material parameters and scalar functions of equations of mechanics of damaged media are determined. Viscoplastic straining and fatigue-induced damage accumulation in 08Kh18N10T and 12Kh18N9 are studied numerically, and the data obtained are compared with available results of physical experiments.

Verification of Mathematical Models of Damaged Medium Mechanics in the System for the in-Service Monitoring of the Life of Reactor Plants*

The paper presents the main statements of a mathematical model of fatigue damage accumulation in structural materials of reactor plant equipment and systems, which was developed on the basis of methods of damaged medium mechanics, and the results of its verification.

ЭКСПЕРИМЕНТАЛЬНО-ТЕОРЕТИЧЕСКОЕ ИССЛЕДОВАНИЕ УСТАЛОСТНОЙ ДОЛГОВЕЧНОСТИ СТАЛИ 08Х18Н10Т ПРИ РЕГУЛЯРНОМ И БЛОЧНЫХ ЦИКЛИЧЕСКИХ НАГРУЖЕНИЯХ

The results of the experimentally and theoretically studying the fatigue life of the 08Х18Н10Т austenitic steel under regular and block cyclic modes of low-cycle loading are presented. In the frame of damaged medium mechanics, processes of fatigue damage accumulation for low-cycle fatigue are modeled. The presented model of the methodology for evaluating fatigue life of structural steels has been verified by comparing the results of numerically modeling deformation and failure processes in laboratory specimens with experimental data. The comparison of computational and experimental data makes it possible to corroborate the adequacy of the determining relations of damaged medium mechanics and the methodology for determining material parameters under the effect of the low-cycle fatigue mechanism. A number of characteristic features accompanying the fatigue failure process under block modes of low-cycle loading are noted. Keywords: stressed-strained state, plasticity, fatigue, failure, damage accumulation, number of cycles to failure, fatigue life, resource.

Numerical modeling of elastoplastic deformation and damage accumulation in metals under low-cycle fatigue conditions

A mathematical model that describes the processes of fatigue damage accumulation in structural materials (metals and alloys) under multiaxial disproportionate combined thermomechanical loading is advanced from the standpoint of the damaged medium mechanics. Based on the results of basic experiments performed in a special way, an experimental-theoretical procedure for finding material parameters of the advanced constitutive relations of the damaged medium mechanics is put forward. The advanced version of the constitutive relations of the damaged medium mechanics is shown to adequately (qualitatively and quantitatively) reflect the main effects of elastoplastic deformation and damage accumulation in metals under low-cycle fatigue.