Components Of Stress Tensor Research Articles

Asymptotic Analysis of the Crack Tip Stress Field (Consideration of Higher Order Terms)

This paper presents multi-parameter asymptotic description of the stress field near the tip of a central crack in a linear-elastic plate under: (1) normal tensile stress; (2) transverse shear; (3) mixed mode deformation in the full range of mixed modes of loading, from the opening mode fracture to antiplane shear. A multi-parameter expansion of the stress tensor components including higher order terms has been constructed. All the scale (amplitude) factors—coefficients of the complete Williams asymptotic expansion—have been determined as functions of the crack length and parameters of loading. The expansion constructed and formulas obtained for the expansion coefficients can be used for keeping any preassigned number of terms in asymptotic representations of mechanical fields at a crack tip in a plate. The number of components to keep at different distances from the tip of defect was subjected to analysis. The angles of crack propagation under conditions of mixed-mode loading were calculated using a multi-parameter expansion of stress field by means of (1) the maximum tangential stress criterion and (2) the criterion of minimum elastic strain energy density.

A new algorithm for fatigue life assessment of automotive safety components based on the probabilistic approach: The case of the steering knuckle

In the present paper, the author has attempted to examine fatigue life of automotive safety components under axial variable amplitude loading conditions. To this end, the time components of stress tensor in the critical area of the knuckle and Liu-Zenner criterion were used to calculate the time history of equivalent stress. Then, the probability distribution function (PDF) of stress was extracted by applying the stress level counting technique. The Fourier curve fitting method was employed in order to formulate the PDF. Subsequently, the fatigue life of the component was estimated using the probabilistic approach. Finally, the results of the higher order of Fourier curve fitting and different counting ranges were compared with the experimental results. Thus, the best algorithm for precisely determining fatigue life of automotive components was obtained.

Three-Component Turbulence Measurements and Analysis of a Supersonic, Axisymmetric Base Flow

The wake formed behind an axisymmetric body aligned with a Mach 2.49 freestream is studied experimentally using non-time-correlated stereoscopic particle image velocimetry (S-PIV), which simultaneously measures all three components of velocity in a two-dimensional plane. To obtain high-resolution data of the entire near-wake flow field, two overlapping measurement fields of view were simultaneously obtained and merged together. The quality of these data is validated using an extensive global experimental uncertainty analysis, and comparisons are drawn and discussed with previous reference laser Doppler velocimetry data of the same flow field. Turbulence statistics were derived from the S-PIV measurements, including all six independent components of the kinematic Reynolds stress tensor, as well as their isotropic and anisotropic tendencies, and fluctuating velocity triple products. These statistics revealed clear spatial trends of dominant turbulence mechanisms, including a well-defined region of fluid entrainment from the recirculation region into the shear layer near the rear stagnation point. A modified turbulent quadrant analysis method was also used, which revealed a clear organization and consistency to the turbulence structure throughout a large portion of the measured flow field.

Computational Elucidation of Elastic Percolation Threshold in Isotropic and Anisotropic Microstructures with Voronoi Tessellation

In this paper, the mechanical properties of randomly shaped microstructures containing two different elastic materials are investigated. Representative volume elements (RVE) containing random tessellations were created using a random generating procedure. The procedure divides the RVE surface by Voronoi tessellations and the elastic behavior of the surface is analyzed under tensile and shear deformations using the finite element method (FEM). Components of stress tensor for each element obtained from FE analysis were used to compute the overall elastic properties of the microstructure. Percolation threshold was defined based on the instantaneous gradient of the tensile and shear modulus diagrams. Numerical results reveal that the percolation thresholds in tensile and shear modes for isotropic RVE are almost the same while there is a remarkable difference between percolation thresholds for an anisotropic case. Furthermore, in the procedure performed in this study, a distinct inconsistency in elastic properties of anisotropic microstructure in longitudinal and transverse directions is observed. The mentioned method presents a paradigmatic overview for generating random isotropic and anisotropic tessellations with different aspect ratios on microstructures and evaluating their overall properties and percolation limit for them.

Crack propagation in a brittle DCB specimen assessed by means of the Williams’ power expansion

A double cantilever beam geometry has been chosen in order to investigate the importance of the higher-order terms of the Williams’ power expansion for the crack path estimation. The crack propagation has been tested experimentally on a brittle polymethylmethacrylate (PMMA) specimen and although the mode I loading conditions were applied, the crack kinked from its original plane immediately and propagated towards the bottom side of the specimen. It has been shown that this phenomenon is connected to the magnitude and sign of the T-stress and to the level of the constraint generally. In this work, the influence of the third and higher terms of the Williams’ series on the crack propagation is investigated. The generalized form of the well-known maximum tangential stress fracture criterion for determination of the crack propagation angle has been tested and discussed. The observed differences in the crack trajectory of different specimens have been found to be related to the magnitude of the higher-order terms of the stress tensor components at the crack tip.

Shape of the power spectral density matrix components: Influence on fatigue damage

AbstractThe damage estimation for a structure under random loading is a challenge in fatigue assessment, especially when the loading is multiaxial. The comparison of the effect of different spectra on fatigue damage is essential when the structure can be subjected to different types of loadings. Therefore, in the present paper, the expected fatigue damage produced on metallic structures by combined bending and torsion stationary proportional and nonproportional loading is evaluated varying the shape of spectra of the normal and shear stress tensor components.

Direct integration of three-dimensional thermoelasticity equations for a transversely isotropic layer

An application of the direct integration method is presented for analytical solution of a three-dimensional thermoelasticity problem for a transversely isotropic layer subjected to general thermal loadings on the limiting planes and internal heat sources. By making use of relations between the stress-tensor components, derived from the equilibrium equations, the original thermoelasticity problem was reduced to a set of governing equations for individual stresses with corresponding boundary conditions. In the mapping domain of the Fourier double-integral transform, the explicit analytical solutions for the stresses and temperature are obtained and then reproduced in physical domain.

Про один метод визначення параметрів ядер спадковості нелінійно в’язкопржних матеріалів за умов складного напруженого стану

The deformation of viscoelastic medium given by means of constitutive equations of the hereditary type. These equations establish the relationship between the components of strain tensor, the components of stress tensor and the integral time operator, and contain the set of function and coefficients that are determined from the basic experiments. А method of the heredity kernel parameters determination of nonlinear viscoelastic materials is developed. As the visco-elastic model, the constitutive equations of the hereditary type are chosen in which the relationship between the components of the strain tensor and the stress tensor is given based on the hypothesis of the deviators proportionality. The nonlinearity of the viscoelastic properties is given by the equations of Ratotnov’s type. The method is based on the relations between the creep kernels under complex stress state and the creep kernels under one-dimensional stress state. The method verified experimentally for the problems of determination of creep deformations under combined loading applied to the thin-walled tubular elements made of polyethylene of high density.

ПРИМЕНЕНИЕ СТРУКТУРНОЙ МОДЕЛИ ДЛЯ РАСЧЕТА УСТАЛОСТНОЙ ДОЛГОВЕЧНОСТИ ПО КОРРЕКТИРОВАННОЙ ЛИНЕЙНОЙ ГИПОТЕЗЕ СУММИРОВАНИЯ ПОВРЕЖДЕНИЙ

The paper proposes a method for calculating the fatigue life under multi-cycle loading. The method is based on the use of a structural rheological model. The paper considers multiparameter random loading when random changes in stress tensor components are independent. The structural model is characterized by a set of yield surfaces (spheres) in the space of the strain deviator. To develop it, we decribed the material deformation diagram with the Ramberg – Osgood equation. The error of the material deformation diagram approximated by this dependence usually does not exceed 5%. The structural model was used to calculate microplastic deformations that cause an accumulation of damages under high-cycle loading. The paper presents the basic relations of the method and the technique for identifying the damage accumulation model. The identification of the model is based on the usual fatigue characteristics of the material. To improve the accuracy of the estimated durability, it was proposed to use a corrected linear hypothesis of damage accumulation. The paper presents an algorithm for plotting a loading block and determining a correction coefficient based on the calculation results according to the structural model. The results of test calculations are given. It was shown that for the case of one-parameter random loading, the results of the proposed method are consistent with those of traditional approaches. For the case of multi-parametric loading, we compared the calculation results with experimental data for a plane stressed state. The difference in the resource evaluation does not exceed 15-20%. Given the large natural characteristic spread of materials, such a difference is quite acceptable. The paper proposes an algorithm for determining the number of cycles of different amplitudes in a random process. The algorithm is based on counting the number of reverses during the displacement of yield surfaces of the structural model. This algorithm may be of interest as one of the ways of schematizing random processes.

Contribution to the modeling and the mechanical characterization of the subsoil in the LSBB environment

The present research work aims at better characterizing the specific underground environment of the LSBB (Low Noise Inter-Disciplinary Underground Science and Technology, Rustrel, France) using mechanical wave propagation information. The LSBB experimental environment is characterized by a system of cylindrical galleries, some of them presenting a concrete layer. In the global project, three steps are considered : firstly the construction of an efficient forward mechanical wave propagation model to calculate the displacement vector and stress tensor components; secondly a sensitivity analysis to extract the pertinent parameters in the configurations and models under study (viscoelastic or poroviscoelastic media with potential anisotropy); and lastly an inversion strategy to recover some of the pertinent parameters. In this proposal, the first step, under progress, is described. The work carried out is in the continuity of the work presented by Yi et al. (2016) [1] who studied the harmonic response of a cylindrical elastic tunnel, impacted by a plane compressional wave, embedded in an infinite elastic ground. The interface between the rock mass and the linen is an imperfect contact modeled with two spring parameters, Achenbach and Zhu (1989) [2]. We choose a semi-analytical approach to calculate the two-dimensional displacement and stress fields in order to get a fast tool, from the numerical point of view. The main steps of the theoretical approach are : use of the Helmholtz decomposition, solving the wave equation based on the separation method and the expansion in Bessel function series in the harmonic domain. The harmonic results are validated by comparison with Yi et al. (2016) [1] and new ones are presented. Moreover, the transient regime case obtained with the use of a Fourier transform on the time variable, is under progress.

К РАСЧЕТУ ВНУТРЕННИХ НАПРЯЖЕНИЙ ОТ МЕЗОДЕФЕКТОВ, НАКАПЛИВАЮЩИХСЯ НА ГРАНИЦАХ РАЗДЕЛА ПРИ ПЛАСТИЧЕСКОЙ ДЕФОРМАЦИИ ТВЕРДЫХ ТЕЛ

A new method of calculation of elastic stress fields from internal interfaces (intergranular and interphase boundaries) of plastically deformed polycrystals is proposed. As elementary sources of stress fields, rectangular boundary segments containing uniformly distributed segments of dislocation families accumulating on these segments during plastic deformation are considered. It is shown that the elastic stresses field from a segment with arbitrary geometry of plastic flow and segment orientation can be represented as a superposition of fields from four families of continually distributed dislocation segments with tangential and normal components of the Burgers vector. Analytical expressions for the elastic stress tensor components from each of the four families are obtained. In the limiting case, when the length of dislocation segments tends to infinity, the resulting expressions for the components of the elastic stress field transform known expressions for rotational and shear mesodefects. If dislocation segments have a normal burgers vector, then the stress field is equivalent to the stress field from the biaxial dipole of wedge disclinations. In the case of tangential components of the burgers vector, the field is equivalent to the stress field of the planar mesodefect. As an example of the method application, the calculation of internal stress fields in the plastically deformed crystal containing uniformly distributed cubic particles of the second phase is given. It is shown that the intensity of internal stresses at a given value of strain increases with increasing volume fraction of particles. It is found that for a given volume fraction of the second phase, the internal stresses does not depend on their size.

Fluid Flow and Convective Heat Transfer Analysis on a Rotor of Wind Turbine Alternator with an Impinging Jet.

This work presents a numerical and experimental study of convection heat transfer in the unconfined air gap of a discoidal technology rotor-stator system. In particular, the rotor is cooled here by an eccentric air jet impingement. The cavity is characterized by a dimensionless spacing G = 0.02 and a low aspect ratio for the jet H/D= 0.25. the rotational Reynolds numbers from 2.38*10^5 to 5.44*10^5 and the jet Reynolds number between 16.5*10^3 and 49.5*10^3 are used. The experimental technique is based on using infrared thermography to access the rotor surface temperature measurement, and on the numerical resolution of the energy equation at steady state to evaluate the local convective coefficient. The numerical study is based on the turbulence model RSM (Reynolds Stress Model). The results of this study are described in terms of radial distributions of the mean velocity components, Reynolds stress tensor components and corresponding local and mean Nusselt numbers. Three flow regions have been identified: a region dominated by the air jet, a mixed zone at low radii and a zone dominated by outward rotation. A good agreement between the two approaches has been obtained, which confirms our choice of numerical turbulence model.

Recent progress in the application of multiaxial fatigue criteria to lifetime calculations

This paper presents the concept of life-dependent material parameters applied to multiaxial fatigue damage models. Every multiaxial fatigue limit criterion based on the history of the stress tensor components is defined by a scalar parameter that is compared with the fatigue limit. The defined damage parameter is usually also a function of some characteristic material parameters. These material parameters are usually derived from fatigue limits obtained under uniaxial and torsion loading. Attempts to extend this classic form of the damage parameter beyond the fatigue limit domain, i.e. to lifetime calculations, fail even within the high cycle fatigue domain. The aim of this paper is to demonstrate that the material parameters derived from fatigue limits should not be applied in multiaxial fatigue criteria for lifetime calculations. A definition of these material parameters based on applying fatigue uniaxial and torsion characteristics instead of fatigue limits implies that the resulting parameters are functions of the fatigue life. Applying a life-dependent material parameter to the Matake multiaxial fatigue criterion leads to a remarkable improvement in the fatigue life prediction for 2124-T851 aluminium alloy.

Analysis of residual stress in circular cross-section wires after drawing process

Residual stresses arising in the drawing process have a significant impact on the quality of the cold-drawn wire. Knowledge of residual stresses and their distribution makes it possible to predict the behavior of metal products under operating loads and to prevent their possible destruction. In this regard, it is necessary to adjust the main parameters of the drawing process, including the geometry of the die channel. The work is devoted to the study of residual stresses arising from inhomogeneity of plastic deformation depending on the reduction value and the die angle. Computer simulation of wire drawing process by finite element method is performed. The distributions of residual stress tensor components along the wire radius are calculated for different values of reduction and die angle. The analysis of the obtained relations is carried out. The influence of the die angle on the distribution of residual stresses is most noticeable at small reductions. After the maximum values of residual stresses are reached at the reduction values of 35-40%, they noticeable decrease occurs.

The Metal Surface Layer Mechanical Condition Transformation in Machining Processes

The metal surface layer mechanical condition transformation at the product life cycle stages key provisions are presented. The described approach feature is the hardened body effect consideration: the metal mechanical properties changing during it displacement through the deformation zone space. On the basis of the developed for surface plastic deformation process hardened elastic-plastic body model, the cumulative shear strain level, plasticity reserve exhaustion level and residual stress tensor components calculations are performed. It is established that the greatest residual compressive stresses are characteristic for the axial component, and the extremum can be located both on the workpiece surface and at some distance from it. The metal hardening influence on the residual stresses distribution is revealed. On the axial (largest) component example shown that the difference between the maximum values is almost 30%. The obtained result corresponds to the idea that the hardened metal having an increased yield strength allows a larger residual stresses presence.

Метод безпосереднього інтегрування у тривимірних задачах теорії пружності та термопружності для неоднорідних трансверсально ізотропних тіл: ключові рівняння в напруженнях

An efficient technique for thermoelastic analysis of inhomogeneous anisotropic solids is suggested within the framework of three-dimensional formulation. By making use of the direct integration method, a system of governing equations is derived in order to solve three-dimensional problems of elasticity and thermoelasticity for transversely isotropic inhomogeneous solids with elastic and thermo-physical properties represented by differentiable functions of the variable in the direction that is transversal to the plane of isotropy. By implementing the relevant separation of variables, the obtained equations can be uncoupled and reduced to second-kind integral equations for individual stress-tensor components and the total stress, which represents the trace of the stress tensor. The latter equations can be attempted by any of the numerical, analyticalnumerical, or analytical means available for the solution of the second-kind integral equations. In order to construct the solutions in an explicit form, an advanced solution technique can be developed on the basis of the resolvent-kernel method implying the series representation by the recurring kernels, computed iteratively by the original kernel of an integral equation.

Theory of the multilayer thin anisotropic shells, based on the asymptotic analysis of the general equations for the elasticity theory

A new theory of thin multilayer anisotropic elastic shells is proposed, based on the application of the asymptotic analysis over small geometric parameter to the general 3-dimensional equations of the elasticity theory for curvilinear coordinates. In deriving the equations of the shell theory no assumptions are made concerning to the distribution of displacements, deformations, or displacements trough thickness. Recurrent consequences of local problems of the elasticity theory for shells are formulated and an analytical solutions are obtained. The averaged equations of the asymptotic theory of shells that are of the same type as the classical equations of the Kirchhoff-Love theory of shells are derived. It is shown that the asymptotic theory makes it possible to obtain in explicit form the distributions of all 6 components of the stress tensor over the thickness of the shell. An example of the calculation of a cylindrical shell under axisymmetric bending is considered. The case of monoclinic shell layers, which have no more than 13 independent elastic constants, is considered. An algorithm is proposed for obtaining explicit analytical equations for calculating the distribution of components of the total stress tensor over the cylindrical shell. The effect of the geometric d imensions of the shell on the character of the distribution of displacements and stresses in the shell is analyzed.

Моделирование ползучести и релаксации остаточных напряжений в поверхностно упрочненных элементах статически не определимых стержневых систем

Предложен метод моделирования напряженно-деформированного состояния в поверхностно упрочненных элементах статически не определимых стержневых систем в условиях ползучести на примере трехэлементной несимметричной стержневой системы. Решение задачи состоит из двух этапов: реконструкции напряженно-деформированного состояния после процедуры поверхностного пластического упрочнения цилиндрических элементов системы (пневмодробеструйная обработка микрошариками) и методики расчета релаксации остаточных напряжений в упрочненных элементах на фоне ползучести всей стержневой конструкции как целого. В качестве определяющих реологических соотношений использовалась модель, описывающая первую и вторую стадии ползучести. Результаты решений на обоих этапах проиллюстрированы на модельном примере ползучести систем с упрочненными элементами из сплава ЖС6У при температуре 650 °C. Для упрочнения стержней из этого сплава использовались реальные экспериментальные данные для осевых и окружных остаточных напряжений, детально проиллюстрирована методика реконструкции напряженно-деформированного состояния после пневмодробеструйной обработки. Для построения реологической модели использовались опытные данные для кривых одноосной ползучести сплава ЖС6У при различных постоянных напряжениях при температуре 650 °C, приведены численные значения параметров модели. Выполнено обобщение одноосной модели на сложное напряженное состояние. Решение основной задачи выполнено численно с использованием дискретизации по пространственной и временной координатам. Исследовано стационарное асимптотическое напряженно-деформированное состояние стержневой системы, соответствующее стадии установившейся ползучести, которое использовалось для оценки сходимости численного метода. Получены зависимости кинетики всех компонент тензора остаточных напряжений во всех трех упрочненных элементах системы вследствие ползучести при заданной внешней нагрузке. Выполнен сравнительный анализ скорости релаксации остаточных напряжений в различных стержнях. Разработано алгоритмическое и программное обеспечение для решения поставленной задачи. Основные результаты работы иллюстрируются эпюрами распределения остаточных напряжений по глубине упрочненного слоя. Обсуждаются вопросы применения полученных в работе результатов в прикладных задачах оценки надежности упрочненных стержневых систем.

Investigations of data-driven closure for subgrid-scale stress in large-eddy simulation

Data-driven machine learning algorithms, random forests and artificial neural network (ANN), are used to establish the subgrid-scale (SGS) model for large-eddy simulation. A total of 30 flow variables are examined as the potential input features. A priori tests indicate that the ANN algorithm provides a better solution for this regression problem. The relative importance of the input variables is evaluated by the two algorithms. It reveals that the gradient of filtered velocity and the second derivative of filtered velocity account for a vast majority of the importance. Besides, a pattern is found for the dependence of each component of the SGS stress tensor on the input features. Accordingly, a new uniform ANN model is proposed to provide closure for all the components of the SGS stress, and a correlation coefficient over 0.7 is reached. The proposed new model is tested by large-eddy simulation of isotropic turbulence. By examining the energy budget and the dissipative properties, the ANN model shows good agreement with direct numerical simulation and it provides better predictions than the Smagorinsky model and the dynamic Smagorinsky model. The current research suggests that data-driven algorithms are effective approaches to help us discover knowledge from large amounts of data.

Criteria of Strength and Plasticity of Asphalt Concrete with the Account of Effect of Accumulation of the Damage while Influence of Re-Load

The paper presents a method for modifying the strength criteria and plasticity conditions, based on the fundamental properties of the algebra of matrices. The essence of the method is that applying the basic property of the algebra of matrices, the stress tensor in the solid body is multiplied by the damage function. As a result of this mathematical operation, a stress tensor is obtained in the damaged body. Then, from the component of stress tensor of the damaged body, its invariant characteristics are determined and formed, which are substituted into the known criteria of strength and plasticity. Thus, the new criteria contain damage. The modification of both simple two or three invariant criteria and modern multi-surface criteria capable of changing the shape of the limit surface depending on the value of one of the material parameters is considered.